Subgroups — C₃×#62818 #10681425

Order 768.

8042 conjugacy classes of subgroups.

The subgroup lattice has 1110 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#3542	C₂	1	8	yes	maximal, complemented
2	C₃×#3537	C₂	1	4	yes	maximal, complemented
3	C₃×#3536	C₂	1	4	yes	maximal, complemented
4	C₃×#3534	C₂	1	8	yes	maximal, complemented
5	C₃×#3519	C₂	1	8	yes	maximal, complemented
6	C₃×#3505	C₂	1	4	yes	maximal, complemented
7	C₃×#3496	C₂	1	4	yes	maximal, complemented
8	C₃×#3494	C₂	1	4	yes	maximal, complemented
9	C₃×#3492	C₂	1	2	yes	maximal, complemented
10	C₃×#3490	C₂	1	4	yes	maximal, complemented
11	C₃×#3488	C₂	1	4	yes	maximal, complemented
12	C₃×#3484	C₂	1	2	yes	maximal, complemented
13	C₃×#3484	C₂	1	4	yes	maximal, complemented
14	C₂×C₃×#525	C₂	1	2	yes	maximal, complemented
15	C₂²×C₃×#121	C₂	1	1	yes	maximal, characteristic, complemented
16	#62818	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	C₂×C₃×H(5,𝔽₂)	C₂²	1	2	yes	complemented
18	C₂×C₃×H(5,𝔽₂)	C₂²	1	4	yes	complemented
19	C₂²×C₃×#41	C₂²	1	2	yes	complemented
20	C₂³×C₃×D₄	C₂²	1	2	yes	complemented
21	C₂³×C₃×D₄	C₂²	1	1	yes	characteristic, complemented
22	C₂⁴×C₃×C₄	C₂²	1	1	yes	characteristic, complemented
23	C₃×#562	C₂²	1	16	yes	complemented
24	C₃×#560	C₂²	1	16	yes	complemented
25	C₃×#555	C₂²	1	8	yes	complemented
26	C₃×#554	C₂²	1	8	yes	complemented
27	C₃×#553	C₂²	1	8	yes	complemented
28	C₃×#553	C₂²	1	8	yes	complemented
29	C₃×#553	C₂²	1	8	yes	complemented
30	C₃×#553	C₂²	1	16	yes	complemented
31	C₃×#552	C₂²	1	8	yes	complemented
32	C₃×#551	C₂²	1	16	yes	complemented
33	C₃×#551	C₂²	1	16	yes	complemented
34	C₃×#550	C₂²	1	8	yes	complemented
35	C₃×#548	C₂²	1	8	yes	complemented
36	C₃×#547	C₂²	1	8	yes	complemented
37	C₃×#547	C₂²	1	8	yes	complemented
38	C₃×#546	C₂²	1	16	yes	complemented
39	C₃×#546	C₂²	1	8	yes	complemented
40	C₃×#546	C₂²	1	16	yes	complemented
41	C₃×#546	C₂²	1	8	yes	complemented
42	C₃×#546	C₂²	1	16	yes	complemented
43	C₃×#546	C₂²	1	16	yes	complemented
44	C₃×#546	C₂²	1	8	yes	complemented
45	C₃×#546	C₂²	1	16	yes	complemented
46	C₃×D₄²	C₂²	1	16	yes	complemented
47	C₃×D₄²	C₂²	1	8	yes	complemented
48	C₃×D₄²	C₂²	1	8	yes	complemented
49	C₃×D₄²	C₂²	1	16	yes	complemented
50	C₃×D₄²	C₂²	1	8	yes	complemented
51	C₃×#544	C₂²	1	2	yes	complemented
52	C₃×#543	C₂²	1	4	yes	complemented
53	C₃×#542	C₂²	1	8	yes	complemented
54	C₃×#540	C₂²	1	8	yes	complemented
55	C₃×#540	C₂²	1	16	yes	complemented
56	C₃×#539	C₂²	1	8	yes	complemented
57	C₃×#539	C₂²	1	8	yes	complemented
58	C₃×#538	C₂²	1	8	yes	complemented
59	C₃×#538	C₂²	1	8	yes	complemented
60	C₃×#538	C₂²	1	8	yes	complemented
61	C₃×#538	C₂²	1	16	yes	complemented
62	C₃×#537	C₂²	1	2	yes	complemented
63	C₃×#537	C₂²	1	8	yes	complemented
64	C₃×#537	C₂²	1	8	yes	complemented
65	C₃×#535	C₂²	1	4	yes	complemented
66	C₃×#535	C₂²	1	8	yes	complemented
67	C₃×#535	C₂²	1	8	yes	complemented
68	C₃×#534	C₂²	1	8	yes	complemented
69	C₃×#534	C₂²	1	8	yes	complemented
70	C₃×#534	C₂²	1	8	yes	complemented
71	C₃×#534	C₂²	1	4	yes	complemented
72	C₃×#534	C₂²	1	8	yes	complemented
73	C₃×#532	C₂²	1	8	yes	complemented
74	C₃×#529	C₂²	1	8	yes	complemented
75	C₃×#525	C₂²	1	4	yes	complemented
76	C₃×#525	C₂²	1	4	yes	complemented
77	C₃×#525	C₂²	1	8	yes	complemented
78	C₃×#525	C₂²	1	4	yes	complemented
79	C₃×#525	C₂²	1	4	yes	complemented
80	C₃×#525	C₂²	1	4	yes	complemented
81	C₃×#525	C₂²	1	4	yes	complemented
82	C₃×#525	C₂²	1	4	yes	complemented
83	C₃×#525	C₂²	1	4	yes	complemented
84	C₃×#525	C₂²	1	8	yes	complemented
85	C₂×C₃×#123	C₂²	1	4	yes	complemented
86	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
87	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
88	C₂×C₃×#121	C₂²	1	4	yes	complemented
89	C₂×C₃×#121	C₂²	1	4	yes	complemented
90	C₂×C₃×#121	C₂²	1	4	yes	complemented
91	C₂×C₃×#121	C₂²	1	4	yes	complemented
92	C₂×C₃×#121	C₂²	1	4	yes	complemented
93	C₂×C₃×#121	C₂²	1	4	yes	complemented
94	C₂×C₃×#121	C₂²	1	2	yes	complemented
95	C₂×C₃×#121	C₂²	1	2	yes	complemented
96	C₂×C₃×#121	C₂²	1	8	yes	complemented
97	C₂×C₃×#120	C₂²	1	4	yes	complemented
98	C₂×C₃×#120	C₂²	1	8	yes	complemented
99	C₃×#520	C₂²	1	4	yes	complemented
100	C₃×#518	C₂²	1	2	yes	complemented
101	C₃×#518	C₂²	1	4	yes	complemented
102	C₃×#518	C₂²	1	8	yes	complemented
103	C₂×C₃×C₄×D₄	C₂²	1	4	yes	complemented
104	C₂×C₃×C₄×D₄	C₂²	1	4	yes	complemented
105	C₂×C₃×#117	C₂²	1	2	yes	complemented
106	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
107	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
108	#3542	C₂×C₃	1	8	yes	complemented
109	#3537	C₂×C₃	1	4	yes	complemented
110	#3536	C₂×C₃	1	4	yes	complemented
111	#3534	C₂×C₃	1	8	yes	complemented
112	#3519	C₂×C₃	1	8	yes	complemented
113	#3505	C₂×C₃	1	4	yes	complemented
114	#3496	C₂×C₃	1	4	yes	complemented
115	#3494	C₂×C₃	1	4	yes	complemented
116	#3492	C₂×C₃	1	2	yes	complemented
117	#3490	C₂×C₃	1	4	yes	complemented
118	#3488	C₂×C₃	1	4	yes	complemented
119	#3484	C₂×C₃	1	2	yes	complemented
120	#3484	C₂×C₃	1	4	yes	complemented
121	C₂×#525	C₂×C₃	1	2	yes	complemented
122	C₂²×#121	C₂×C₃	1	1	yes	characteristic, complemented
123	C₂⁵×C₃	C₂³	1	1	yes	characteristic
124	C₂⁵×C₃	C₂³	1	2	yes	—
125	C₃×H(5,𝔽₂)	—	4	16	no	—
126	C₃×H(5,𝔽₂)	—	4	8	no	—
127	C₂×C₃×#41	—	4	8	no	—
128	C₂×C₃×#41	C₂³	1	4	yes	—
129	C₂×C₃×#41	C₂³	1	4	yes	—
130	C₂×C₃×#41	C₂³	1	8	yes	—
131	C₂×C₃×#41	C₂³	1	4	yes	complemented
132	C₂×C₃×#41	C₂³	1	4	yes	complemented
133	C₂×C₃×#41	C₂³	1	8	yes	complemented
134	C₂×C₃×#41	C₂³	1	16	yes	complemented
135	C₂²×C₃×Q₈	C₂³	1	2	yes	complemented
136	C₂²×C₃×D₄	—	4	4	no	—
137	C₂²×C₃×D₄	—	4	8	no	—
138	C₂²×C₃×D₄	C₂³	1	4	yes	—
139	C₂²×C₃×D₄	C₂³	1	2	yes	—
140	C₂²×C₃×D₄	C₂³	1	4	yes	—
141	C₂²×C₃×D₄	C₂³	1	2	yes	—
142	C₂²×C₃×D₄	C₂³	1	4	yes	—
143	C₂²×C₃×D₄	C₂³	1	4	yes	—
144	C₂²×C₃×D₄	C₂³	1	4	yes	—
145	C₂²×C₃×D₄	C₂³	1	8	yes	—
146	C₂²×C₃×D₄	C₂³	1	8	yes	—
147	C₂²×C₃×D₄	C₂³	1	4	yes	—
148	C₂²×C₃×D₄	C₂³	1	8	yes	—
149	C₂²×C₃×D₄	C₂³	1	8	yes	—
150	C₂²×C₃×D₄	C₂³	1	4	yes	—
151	C₂²×C₃×D₄	C₂³	1	8	yes	—
152	C₂²×C₃×D₄	C₂³	1	2	yes	complemented
153	C₂²×C₃×D₄	C₂³	1	16	yes	complemented
154	C₂²×C₃×D₄	C₂³	1	8	yes	complemented
155	C₂³×C₃×C₄	—	4	4	no	—
156	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
157	C₂³×C₃×C₄	C₂³	1	2	yes	—
158	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
159	C₂³×C₃×C₄	C₂³	1	2	yes	—
160	C₂³×C₃×C₄	C₂³	1	2	yes	—
161	C₂³×C₃×C₄	C₂³	1	2	yes	—
162	C₂³×C₃×C₄	C₂³	1	2	yes	—
163	C₂³×C₃×C₄	C₂³	1	2	yes	—
164	C₂³×C₃×C₄	C₂³	1	2	yes	—
165	C₂³×C₃×C₄	C₂³	1	4	yes	complemented
166	C₃×C₄⋊Q₈	C₂³	1	8	yes	complemented
167	C₃×#127	C₂³	1	16	yes	complemented
168	C₃×#127	C₂³	1	8	yes	complemented
169	C₃×#126	C₂³	1	16	yes	complemented
170	C₃×#126	C₂³	1	16	yes	complemented
171	C₃×#126	C₂³	1	16	yes	complemented
172	C₃×#125	C₂³	1	16	yes	complemented
173	C₃×#125	C₂³	1	8	yes	complemented
174	C₃×#124	C₂³	1	16	yes	complemented
175	C₃×#124	C₂³	1	16	yes	complemented
176	C₃×#124	C₂³	1	8	yes	complemented
177	C₃×#124	C₂³	1	16	yes	complemented
178	C₃×#123	C₂³	1	8	yes	—
179	C₃×#123	C₂³	1	8	yes	—
180	C₃×#123	C₂³	1	16	yes	—
181	C₃×#123	C₂³	1	8	yes	complemented
182	C₃×#123	C₂³	1	16	yes	complemented
183	C₃×#123	C₂³	1	16	yes	complemented
184	C₃×#123	C₂³	1	16	yes	complemented
185	C₃×#123	C₂³	1	16	yes	complemented
186	C₃×#123	C₂³	1	16	yes	complemented
187	C₃×#123	C₂³	1	8	yes	complemented
188	C₃×#123	C₂³	1	16	yes	complemented
189	C₃×#123	C₂³	1	16	yes	complemented
190	C₃×C₂²⋊Q₈	C₂³	1	4	yes	—
191	C₃×C₂²⋊Q₈	C₂³	1	4	yes	—
192	C₃×C₂²⋊Q₈	C₂³	1	4	yes	—
193	C₃×C₂²⋊Q₈	C₂³	1	4	yes	—
194	C₃×C₂²⋊Q₈	C₂³	1	8	yes	—
195	C₃×C₂²⋊Q₈	C₂³	1	8	yes	—
196	C₃×C₂²⋊Q₈	C₂³	1	4	yes	complemented
197	C₃×C₂²⋊Q₈	C₂³	1	16	yes	complemented
198	C₃×C₂²⋊Q₈	C₂³	1	16	yes	complemented
199	C₃×C₂²⋊Q₈	C₂³	1	16	yes	complemented
200	C₃×C₂²⋊Q₈	C₂³	1	4	yes	complemented
201	C₃×C₂²⋊Q₈	C₂³	1	4	yes	complemented
202	C₃×C₂²⋊Q₈	C₂³	1	4	yes	complemented
203	C₃×C₂²⋊Q₈	C₂³	1	8	yes	complemented
204	C₃×#121	C₂³	1	8	yes	—
205	C₃×#121	C₂³	1	8	yes	—
206	C₃×#121	C₂³	1	8	yes	—
207	C₃×#121	C₂³	1	8	yes	—
208	C₃×#121	C₂³	1	8	yes	—
209	C₃×#121	C₂³	1	8	yes	—
210	C₃×#121	C₂³	1	8	yes	—
211	C₃×#121	C₂³	1	8	yes	—
212	C₃×#121	C₂³	1	4	yes	—
213	C₃×#121	C₂³	1	4	yes	—
214	C₃×#121	C₂³	1	4	yes	—
215	C₃×#121	C₂³	1	4	yes	—
216	C₃×#121	C₂³	1	8	yes	—
217	C₃×#121	C₂³	1	8	yes	—
218	C₃×#121	C₂³	1	4	yes	complemented
219	C₃×#121	C₂³	1	16	yes	complemented
220	C₃×#121	C₂³	1	16	yes	complemented
221	C₃×#121	C₂³	1	16	yes	complemented
222	C₃×#121	C₂³	1	16	yes	complemented
223	C₃×#121	C₂³	1	16	yes	complemented
224	C₃×#121	C₂³	1	16	yes	complemented
225	C₃×#121	C₂³	1	16	yes	complemented
226	C₃×#121	C₂³	1	4	yes	complemented
227	C₃×#121	C₂³	1	4	yes	complemented
228	C₃×#121	C₂³	1	4	yes	complemented
229	C₃×#121	C₂³	1	16	yes	complemented
230	C₃×#121	C₂³	1	8	yes	complemented
231	C₃×#121	C₂³	1	8	yes	complemented
232	C₃×#121	C₂³	1	16	yes	complemented
233	C₃×#121	C₂³	1	8	yes	complemented
234	C₃×#121	C₂³	1	16	yes	complemented
235	C₃×#120	C₂³	1	8	yes	—
236	C₃×#120	C₂³	1	8	yes	—
237	C₃×#120	C₂³	1	8	yes	—
238	C₃×#120	C₂³	1	8	yes	—
239	C₃×#120	C₂³	1	16	yes	—
240	C₃×#120	C₂³	1	16	yes	—
241	C₃×#120	C₂³	1	16	yes	—
242	C₃×#120	C₂³	1	16	yes	complemented
243	C₃×#120	C₂³	1	16	yes	complemented
244	C₃×#120	C₂³	1	16	yes	complemented
245	C₃×#120	C₂³	1	16	yes	complemented
246	C₃×C₄×Q₈	C₂³	1	8	yes	complemented
247	C₃×C₄×D₄	C₂³	1	8	yes	—
248	C₃×C₄×D₄	C₂³	1	8	yes	—
249	C₃×C₄×D₄	C₂³	1	8	yes	—
250	C₃×C₄×D₄	C₂³	1	8	yes	—
251	C₃×C₄×D₄	C₂³	1	16	yes	—
252	C₃×C₄×D₄	C₂³	1	16	yes	—
253	C₃×C₄×D₄	C₂³	1	8	yes	complemented
254	C₃×C₄×D₄	C₂³	1	8	yes	complemented
255	C₃×C₄×D₄	C₂³	1	8	yes	complemented
256	C₃×C₄×D₄	C₂³	1	8	yes	complemented
257	C₃×C₄×D₄	C₂³	1	16	yes	complemented
258	C₃×C₄×D₄	C₂³	1	16	yes	complemented
259	C₃×C₄×D₄	C₂³	1	16	yes	complemented
260	C₃×C₄×D₄	C₂³	1	8	yes	complemented
261	C₃×C₄×D₄	C₂³	1	16	yes	complemented
262	C₃×C₄×D₄	C₂³	1	8	yes	complemented
263	C₃×C₄×D₄	C₂³	1	8	yes	complemented
264	C₃×#117	C₂³	1	4	yes	—
265	C₃×#117	C₂³	1	4	yes	—
266	C₃×#117	C₂³	1	8	yes	—
267	C₃×#117	C₂³	1	4	yes	complemented
268	C₃×#117	C₂³	1	4	yes	complemented
269	C₃×#117	C₂³	1	16	yes	complemented
270	C₃×#117	C₂³	1	8	yes	complemented
271	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
272	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
273	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
274	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
275	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	complemented
276	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	complemented
277	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	complemented
278	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	complemented
279	C₂×C₃×C₄⋊C₄	C₂³	1	8	yes	complemented
280	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
281	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
282	C₂×C₃×C₂²⋊C₄	C₂³	1	8	yes	—
283	C₂×C₃×C₂²⋊C₄	C₂³	1	8	yes	—
284	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
285	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
286	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
287	C₂×C₃×C₂²⋊C₄	C₂³	1	8	yes	—
288	C₂×C₃×C₂²⋊C₄	C₂³	1	8	yes	—
289	C₂×C₃×C₂²⋊C₄	C₂³	1	8	yes	—
290	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	complemented
291	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	complemented
292	C₂×C₃×C₂²⋊C₄	C₂³	1	16	yes	complemented
293	C₂×C₃×C₄²	C₂³	1	4	yes	complemented
294	C₂×H(5,𝔽₂)	C₂²×C₃	1	2	yes	complemented
295	C₂×H(5,𝔽₂)	C₂²×C₃	1	4	yes	complemented
296	C₂²×#41	C₂²×C₃	1	2	yes	complemented
297	C₂³×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
298	C₂³×D₄	C₂²×C₃	1	2	yes	complemented
299	C₂⁴×C₄	C₂²×C₃	1	1	yes	characteristic, complemented
300	#562	C₂²×C₃	1	16	yes	complemented
301	#560	C₂²×C₃	1	16	yes	complemented
302	#555	C₂²×C₃	1	8	yes	complemented
303	#554	C₂²×C₃	1	8	yes	complemented
304	#553	C₂²×C₃	1	8	yes	complemented
305	#553	C₂²×C₃	1	8	yes	complemented
306	#553	C₂²×C₃	1	8	yes	complemented
307	#553	C₂²×C₃	1	16	yes	complemented
308	#552	C₂²×C₃	1	8	yes	complemented
309	#551	C₂²×C₃	1	16	yes	complemented
310	#551	C₂²×C₃	1	16	yes	complemented
311	#550	C₂²×C₃	1	8	yes	complemented
312	#548	C₂²×C₃	1	8	yes	complemented
313	#547	C₂²×C₃	1	8	yes	complemented
314	#547	C₂²×C₃	1	8	yes	complemented
315	#546	C₂²×C₃	1	16	yes	complemented
316	#546	C₂²×C₃	1	8	yes	complemented
317	#546	C₂²×C₃	1	16	yes	complemented
318	#546	C₂²×C₃	1	8	yes	complemented
319	#546	C₂²×C₃	1	16	yes	complemented
320	#546	C₂²×C₃	1	16	yes	complemented
321	#546	C₂²×C₃	1	8	yes	complemented
322	#546	C₂²×C₃	1	16	yes	complemented
323	D₄²	C₂²×C₃	1	16	yes	complemented
324	D₄²	C₂²×C₃	1	8	yes	complemented
325	D₄²	C₂²×C₃	1	8	yes	complemented
326	D₄²	C₂²×C₃	1	16	yes	complemented
327	D₄²	C₂²×C₃	1	8	yes	complemented
328	#544	C₂²×C₃	1	2	yes	complemented
329	#543	C₂²×C₃	1	4	yes	complemented
330	#542	C₂²×C₃	1	8	yes	complemented
331	#540	C₂²×C₃	1	8	yes	complemented
332	#540	C₂²×C₃	1	16	yes	complemented
333	#539	C₂²×C₃	1	8	yes	complemented
334	#539	C₂²×C₃	1	8	yes	complemented
335	#538	C₂²×C₃	1	8	yes	complemented
336	#538	C₂²×C₃	1	8	yes	complemented
337	#538	C₂²×C₃	1	8	yes	complemented
338	#538	C₂²×C₃	1	16	yes	complemented
339	#537	C₂²×C₃	1	2	yes	complemented
340	#537	C₂²×C₃	1	8	yes	complemented
341	#537	C₂²×C₃	1	8	yes	complemented
342	#535	C₂²×C₃	1	4	yes	complemented
343	#535	C₂²×C₃	1	8	yes	complemented
344	#535	C₂²×C₃	1	8	yes	complemented
345	#534	C₂²×C₃	1	8	yes	complemented
346	#534	C₂²×C₃	1	8	yes	complemented
347	#534	C₂²×C₃	1	8	yes	complemented
348	#534	C₂²×C₃	1	4	yes	complemented
349	#534	C₂²×C₃	1	8	yes	complemented
350	#532	C₂²×C₃	1	8	yes	complemented
351	#529	C₂²×C₃	1	8	yes	complemented
352	#525	C₂²×C₃	1	4	yes	complemented
353	#525	C₂²×C₃	1	4	yes	complemented
354	#525	C₂²×C₃	1	8	yes	complemented
355	#525	C₂²×C₃	1	4	yes	complemented
356	#525	C₂²×C₃	1	4	yes	complemented
357	#525	C₂²×C₃	1	4	yes	complemented
358	#525	C₂²×C₃	1	4	yes	complemented
359	#525	C₂²×C₃	1	4	yes	complemented
360	#525	C₂²×C₃	1	4	yes	complemented
361	#525	C₂²×C₃	1	8	yes	complemented
362	C₂×#123	C₂²×C₃	1	4	yes	complemented
363	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
364	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
365	C₂×#121	C₂²×C₃	1	4	yes	complemented
366	C₂×#121	C₂²×C₃	1	4	yes	complemented
367	C₂×#121	C₂²×C₃	1	4	yes	complemented
368	C₂×#121	C₂²×C₃	1	4	yes	complemented
369	C₂×#121	C₂²×C₃	1	4	yes	complemented
370	C₂×#121	C₂²×C₃	1	4	yes	complemented
371	C₂×#121	C₂²×C₃	1	2	yes	complemented
372	C₂×#121	C₂²×C₃	1	2	yes	complemented
373	C₂×#121	C₂²×C₃	1	8	yes	complemented
374	C₂×#120	C₂²×C₃	1	4	yes	complemented
375	C₂×#120	C₂²×C₃	1	8	yes	complemented
376	#520	C₂²×C₃	1	4	yes	complemented
377	#518	C₂²×C₃	1	2	yes	complemented
378	#518	C₂²×C₃	1	4	yes	complemented
379	#518	C₂²×C₃	1	8	yes	complemented
380	C₂×C₄×D₄	C₂²×C₃	1	4	yes	complemented
381	C₂×C₄×D₄	C₂²×C₃	1	4	yes	complemented
382	C₂×#117	C₂²×C₃	1	2	yes	complemented
383	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
384	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
385	C₂⁴×C₃	—	2	4	no	—
386	C₂⁴×C₃	—	4	2	no	—
387	C₂⁴×C₃	—	4	2	no	—
388	C₂⁴×C₃	—	4	4	no	—
389	C₂⁴×C₃	—	4	4	no	—
390	C₂⁴×C₃	—	4	4	no	—
391	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
392	C₂⁴×C₃	C₂⁴	1	2	yes	—
393	C₂⁴×C₃	C₂⁴	1	2	yes	—
394	C₂⁴×C₃	C₂⁴	1	4	yes	—
395	C₂⁴×C₃	C₂⁴	1	4	yes	—
396	C₂⁴×C₃	C₂⁴	1	4	yes	—
397	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
398	C₂⁴×C₃	C₂⁴	1	4	yes	—
399	C₂⁴×C₃	C₂⁴	1	8	yes	—
400	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
401	C₃×#41	—	2	16	no	—
402	C₃×#41	—	4	8	no	—
403	C₃×#41	—	4	8	no	—
404	C₃×#41	—	4	16	no	—
405	C₃×#41	—	4	32	no	—
406	C₃×#41	—	4	8	no	—
407	C₃×#41	—	4	16	no	—
408	C₂×C₃×Q₈	—	4	4	no	—
409	C₂×C₃×Q₈	C₂⁴	1	4	yes	—
410	C₂×C₃×Q₈	C₂⁴	1	4	yes	—
411	C₂×C₃×Q₈	C₂⁴	1	8	yes	—
412	C₂×C₃×D₄	—	2	16	no	—
413	C₂×C₃×D₄	—	2	16	no	—
414	C₂×C₃×D₄	—	2	8	no	—
415	C₂×C₃×D₄	—	4	8	no	—
416	C₂×C₃×D₄	—	4	8	no	—
417	C₂×C₃×D₄	—	4	4	no	—
418	C₂×C₃×D₄	—	4	16	no	—
419	C₂×C₃×D₄	—	4	4	no	—
420	C₂×C₃×D₄	—	4	8	no	—
421	C₂×C₃×D₄	—	4	16	no	—
422	C₂×C₃×D₄	—	4	16	no	—
423	C₂×C₃×D₄	—	4	8	no	—
424	C₂×C₃×D₄	—	4	16	no	—
425	C₂×C₃×D₄	—	4	8	no	—
426	C₂×C₃×D₄	—	4	16	no	—
427	C₂×C₃×D₄	—	4	16	no	—
428	C₂×C₃×D₄	—	4	32	no	—
429	C₂×C₃×D₄	C₂⁴	1	8	yes	—
430	C₂×C₃×D₄	C₂⁴	1	8	yes	—
431	C₂×C₃×D₄	C₂⁴	1	8	yes	—
432	C₂×C₃×D₄	C₂⁴	1	8	yes	—
433	C₂×C₃×D₄	C₂⁴	1	16	yes	—
434	C₂×C₃×D₄	C₂⁴	1	8	yes	—
435	C₂×C₃×D₄	C₂⁴	1	4	yes	—
436	C₂×C₃×D₄	C₂⁴	1	16	yes	—
437	C₂×C₃×D₄	C₂⁴	1	8	yes	—
438	C₂×C₃×D₄	C₂⁴	1	8	yes	—
439	C₂×C₃×D₄	C₂⁴	1	16	yes	—
440	C₂×C₃×D₄	C₂⁴	1	16	yes	—
441	C₂×C₃×D₄	C₂⁴	1	4	yes	—
442	C₂×C₃×D₄	C₂⁴	1	8	yes	—
443	C₂×C₃×D₄	C₂⁴	1	8	yes	—
444	C₂×C₃×D₄	C₂⁴	1	16	yes	—
445	C₂²×C₃×C₄	—	2	4	no	—
446	C₂²×C₃×C₄	—	2	8	no	—
447	C₂²×C₃×C₄	—	4	4	no	—
448	C₂²×C₃×C₄	—	4	4	no	—
449	C₂²×C₃×C₄	—	4	4	no	—
450	C₂²×C₃×C₄	—	4	4	no	—
451	C₂²×C₃×C₄	—	4	8	no	—
452	C₂²×C₃×C₄	—	4	4	no	—
453	C₂²×C₃×C₄	—	4	2	no	—
454	C₂²×C₃×C₄	—	4	4	no	—
455	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
456	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
457	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
458	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
459	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
460	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
461	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
462	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
463	C₂²×C₃×C₄	C₂⁴	1	8	yes	—
464	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
465	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
466	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
467	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
468	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
469	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
470	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
471	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
472	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
473	C₂²×C₃×C₄	C₂⁴	1	8	yes	—
474	C₂²×C₃×C₄	C₂⁴	1	8	yes	—
475	C₂²×C₃×C₄	C₂⁴	1	8	yes	—
476	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
477	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
478	C₂²×C₃×C₄	C₂⁴	1	8	yes	—
479	C₂²×C₃×C₄	C₂⁴	1	16	yes	—
480	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
481	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
482	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
483	C₃×C₄⋊C₄	C₂⁴	1	8	yes	—
484	C₃×C₄⋊C₄	C₂⁴	1	8	yes	—
485	C₃×C₄⋊C₄	C₂⁴	1	4	yes	—
486	C₃×C₄⋊C₄	C₂⁴	1	4	yes	—
487	C₃×C₄⋊C₄	C₂⁴	1	4	yes	—
488	C₃×C₄⋊C₄	C₂⁴	1	4	yes	—
489	C₃×C₄⋊C₄	C₂⁴	1	8	yes	—
490	C₃×C₄⋊C₄	C₂⁴	1	8	yes	—
491	C₃×C₄⋊C₄	C₂⁴	1	8	yes	—
492	C₃×C₄⋊C₄	C₂⁴	1	8	yes	—
493	C₃×C₄⋊C₄	C₂⁴	1	16	yes	—
494	C₃×C₄⋊C₄	C₂⁴	1	8	yes	—
495	C₃×C₄⋊C₄	C₂⁴	1	8	yes	—
496	C₃×C₄⋊C₄	C₂⁴	1	16	yes	—
497	C₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
498	C₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
499	C₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
500	C₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
501	C₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
502	C₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
503	C₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
504	C₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
505	C₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
506	C₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
507	C₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
508	C₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
509	C₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
510	C₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
511	C₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
512	C₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
513	C₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
514	C₃×C₄²	C₂⁴	1	8	yes	—
515	C₃×C₄²	C₂⁴	1	8	yes	—
516	C₃×C₄²	C₂⁴	1	16	yes	—
517	C₂⁵	C₂³×C₃	1	1	yes	characteristic
518	C₂⁵	C₂³×C₃	1	2	yes	—
519	H(5,𝔽₂)	—	4	16	no	—
520	H(5,𝔽₂)	—	4	8	no	—
521	C₂×#41	—	4	8	no	—
522	C₂×#41	C₂³×C₃	1	4	yes	—
523	C₂×#41	C₂³×C₃	1	4	yes	—
524	C₂×#41	C₂³×C₃	1	8	yes	—
525	C₂×#41	C₂³×C₃	1	4	yes	complemented
526	C₂×#41	C₂³×C₃	1	4	yes	complemented
527	C₂×#41	C₂³×C₃	1	8	yes	complemented
528	C₂×#41	C₂³×C₃	1	16	yes	complemented
529	C₂²×Q₈	C₂³×C₃	1	2	yes	complemented
530	C₂²×D₄	—	4	4	no	—
531	C₂²×D₄	—	4	8	no	—
532	C₂²×D₄	C₂³×C₃	1	4	yes	—
533	C₂²×D₄	C₂³×C₃	1	4	yes	—
534	C₂²×D₄	C₂³×C₃	1	2	yes	—
535	C₂²×D₄	C₂³×C₃	1	4	yes	—
536	C₂²×D₄	C₂³×C₃	1	8	yes	—
537	C₂²×D₄	C₂³×C₃	1	4	yes	—
538	C₂²×D₄	C₂³×C₃	1	8	yes	—
539	C₂²×D₄	C₂³×C₃	1	8	yes	—
540	C₂²×D₄	C₂³×C₃	1	2	yes	—
541	C₂²×D₄	C₂³×C₃	1	4	yes	—
542	C₂²×D₄	C₂³×C₃	1	4	yes	—
543	C₂²×D₄	C₂³×C₃	1	4	yes	—
544	C₂²×D₄	C₂³×C₃	1	8	yes	—
545	C₂²×D₄	C₂³×C₃	1	8	yes	—
546	C₂²×D₄	C₂³×C₃	1	2	yes	complemented
547	C₂²×D₄	C₂³×C₃	1	16	yes	complemented
548	C₂²×D₄	C₂³×C₃	1	8	yes	complemented
549	C₂³×C₄	—	4	4	no	—
550	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
551	C₂³×C₄	C₂³×C₃	1	2	yes	—
552	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
553	C₂³×C₄	C₂³×C₃	1	2	yes	—
554	C₂³×C₄	C₂³×C₃	1	2	yes	—
555	C₂³×C₄	C₂³×C₃	1	2	yes	—
556	C₂³×C₄	C₂³×C₃	1	2	yes	—
557	C₂³×C₄	C₂³×C₃	1	2	yes	—
558	C₂³×C₄	C₂³×C₃	1	2	yes	—
559	C₂³×C₄	C₂³×C₃	1	4	yes	complemented
560	C₄⋊Q₈	C₂³×C₃	1	8	yes	complemented
561	#127	C₂³×C₃	1	8	yes	complemented
562	#127	C₂³×C₃	1	16	yes	complemented
563	#126	C₂³×C₃	1	16	yes	complemented
564	#126	C₂³×C₃	1	16	yes	complemented
565	#126	C₂³×C₃	1	16	yes	complemented
566	#125	C₂³×C₃	1	8	yes	complemented
567	#125	C₂³×C₃	1	16	yes	complemented
568	#124	C₂³×C₃	1	8	yes	complemented
569	#124	C₂³×C₃	1	16	yes	complemented
570	#124	C₂³×C₃	1	16	yes	complemented
571	#124	C₂³×C₃	1	16	yes	complemented
572	#123	C₂³×C₃	1	8	yes	—
573	#123	C₂³×C₃	1	8	yes	—
574	#123	C₂³×C₃	1	16	yes	—
575	#123	C₂³×C₃	1	8	yes	complemented
576	#123	C₂³×C₃	1	8	yes	complemented
577	#123	C₂³×C₃	1	16	yes	complemented
578	#123	C₂³×C₃	1	16	yes	complemented
579	#123	C₂³×C₃	1	16	yes	complemented
580	#123	C₂³×C₃	1	16	yes	complemented
581	#123	C₂³×C₃	1	16	yes	complemented
582	#123	C₂³×C₃	1	16	yes	complemented
583	#123	C₂³×C₃	1	16	yes	complemented
584	C₂²⋊Q₈	C₂³×C₃	1	4	yes	—
585	C₂²⋊Q₈	C₂³×C₃	1	4	yes	—
586	C₂²⋊Q₈	C₂³×C₃	1	4	yes	—
587	C₂²⋊Q₈	C₂³×C₃	1	4	yes	—
588	C₂²⋊Q₈	C₂³×C₃	1	8	yes	—
589	C₂²⋊Q₈	C₂³×C₃	1	8	yes	—
590	C₂²⋊Q₈	C₂³×C₃	1	4	yes	complemented
591	C₂²⋊Q₈	C₂³×C₃	1	4	yes	complemented
592	C₂²⋊Q₈	C₂³×C₃	1	4	yes	complemented
593	C₂²⋊Q₈	C₂³×C₃	1	4	yes	complemented
594	C₂²⋊Q₈	C₂³×C₃	1	8	yes	complemented
595	C₂²⋊Q₈	C₂³×C₃	1	16	yes	complemented
596	C₂²⋊Q₈	C₂³×C₃	1	16	yes	complemented
597	C₂²⋊Q₈	C₂³×C₃	1	16	yes	complemented
598	#121	C₂³×C₃	1	8	yes	—
599	#121	C₂³×C₃	1	8	yes	—
600	#121	C₂³×C₃	1	8	yes	—
601	#121	C₂³×C₃	1	8	yes	—
602	#121	C₂³×C₃	1	8	yes	—
603	#121	C₂³×C₃	1	8	yes	—
604	#121	C₂³×C₃	1	8	yes	—
605	#121	C₂³×C₃	1	8	yes	—
606	#121	C₂³×C₃	1	4	yes	—
607	#121	C₂³×C₃	1	4	yes	—
608	#121	C₂³×C₃	1	4	yes	—
609	#121	C₂³×C₃	1	4	yes	—
610	#121	C₂³×C₃	1	8	yes	—
611	#121	C₂³×C₃	1	8	yes	—
612	#121	C₂³×C₃	1	4	yes	complemented
613	#121	C₂³×C₃	1	4	yes	complemented
614	#121	C₂³×C₃	1	4	yes	complemented
615	#121	C₂³×C₃	1	4	yes	complemented
616	#121	C₂³×C₃	1	16	yes	complemented
617	#121	C₂³×C₃	1	8	yes	complemented
618	#121	C₂³×C₃	1	8	yes	complemented
619	#121	C₂³×C₃	1	16	yes	complemented
620	#121	C₂³×C₃	1	8	yes	complemented
621	#121	C₂³×C₃	1	16	yes	complemented
622	#121	C₂³×C₃	1	16	yes	complemented
623	#121	C₂³×C₃	1	16	yes	complemented
624	#121	C₂³×C₃	1	16	yes	complemented
625	#121	C₂³×C₃	1	16	yes	complemented
626	#121	C₂³×C₃	1	16	yes	complemented
627	#121	C₂³×C₃	1	16	yes	complemented
628	#121	C₂³×C₃	1	16	yes	complemented
629	#120	C₂³×C₃	1	8	yes	—
630	#120	C₂³×C₃	1	8	yes	—
631	#120	C₂³×C₃	1	8	yes	—
632	#120	C₂³×C₃	1	8	yes	—
633	#120	C₂³×C₃	1	16	yes	—
634	#120	C₂³×C₃	1	16	yes	—
635	#120	C₂³×C₃	1	16	yes	—
636	#120	C₂³×C₃	1	16	yes	complemented
637	#120	C₂³×C₃	1	16	yes	complemented
638	#120	C₂³×C₃	1	16	yes	complemented
639	#120	C₂³×C₃	1	16	yes	complemented
640	C₄×Q₈	C₂³×C₃	1	8	yes	complemented
641	C₄×D₄	C₂³×C₃	1	8	yes	—
642	C₄×D₄	C₂³×C₃	1	8	yes	—
643	C₄×D₄	C₂³×C₃	1	8	yes	—
644	C₄×D₄	C₂³×C₃	1	8	yes	—
645	C₄×D₄	C₂³×C₃	1	16	yes	—
646	C₄×D₄	C₂³×C₃	1	16	yes	—
647	C₄×D₄	C₂³×C₃	1	8	yes	complemented
648	C₄×D₄	C₂³×C₃	1	8	yes	complemented
649	C₄×D₄	C₂³×C₃	1	8	yes	complemented
650	C₄×D₄	C₂³×C₃	1	8	yes	complemented
651	C₄×D₄	C₂³×C₃	1	16	yes	complemented
652	C₄×D₄	C₂³×C₃	1	16	yes	complemented
653	C₄×D₄	C₂³×C₃	1	16	yes	complemented
654	C₄×D₄	C₂³×C₃	1	8	yes	complemented
655	C₄×D₄	C₂³×C₃	1	16	yes	complemented
656	C₄×D₄	C₂³×C₃	1	8	yes	complemented
657	C₄×D₄	C₂³×C₃	1	8	yes	complemented
658	#117	C₂³×C₃	1	4	yes	—
659	#117	C₂³×C₃	1	4	yes	—
660	#117	C₂³×C₃	1	8	yes	—
661	#117	C₂³×C₃	1	4	yes	complemented
662	#117	C₂³×C₃	1	4	yes	complemented
663	#117	C₂³×C₃	1	16	yes	complemented
664	#117	C₂³×C₃	1	8	yes	complemented
665	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
666	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
667	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
668	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
669	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	complemented
670	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	complemented
671	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	complemented
672	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	complemented
673	C₂×C₄⋊C₄	C₂³×C₃	1	8	yes	complemented
674	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
675	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
676	C₂×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
677	C₂×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
678	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
679	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
680	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
681	C₂×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
682	C₂×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
683	C₂×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
684	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	complemented
685	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	complemented
686	C₂×C₂²⋊C₄	C₂³×C₃	1	16	yes	complemented
687	C₂×C₄²	C₂³×C₃	1	4	yes	complemented
688	C₂³×C₃	—	2	2	no	—
689	C₂³×C₃	—	2	2	no	—
690	C₂³×C₃	—	2	2	no	—
691	C₂³×C₃	—	2	4	no	—
692	C₂³×C₃	—	2	4	no	—
693	C₂³×C₃	—	2	4	no	—
694	C₂³×C₃	—	2	2	no	—
695	C₂³×C₃	—	2	4	no	—
696	C₂³×C₃	—	2	8	no	—
697	C₂³×C₃	—	2	8	no	—
698	C₂³×C₃	—	2	8	no	—
699	C₂³×C₃	—	2	8	no	—
700	C₂³×C₃	—	4	1	no	—
701	C₂³×C₃	—	4	2	no	—
702	C₂³×C₃	—	4	1	no	—
703	C₂³×C₃	—	4	1	no	—
704	C₂³×C₃	—	4	2	no	—
705	C₂³×C₃	—	4	1	no	—
706	C₂³×C₃	—	4	4	no	—
707	C₂³×C₃	—	4	4	no	—
708	C₂³×C₃	—	4	4	no	—
709	C₂³×C₃	—	4	4	no	—
710	C₂³×C₃	—	4	4	no	—
711	C₂³×C₃	—	4	4	no	—
712	C₂³×C₃	—	4	4	no	—
713	C₂³×C₃	—	4	4	no	—
714	C₂³×C₃	—	4	8	no	—
715	C₂³×C₃	—	4	8	no	—
716	C₂³×C₃	—	4	8	no	—
717	C₂³×C₃	—	4	16	no	—
718	C₂³×C₃	—	8	16	no	—
719	C₂³×C₃	H(5,𝔽₂)	1	4	yes	complemented
720	C₂³×C₃	C₂⁵	1	8	yes	—
721	C₂³×C₃	C₂⁵	1	2	yes	—
722	C₂³×C₃	C₂⁵	1	8	yes	—
723	C₂³×C₃	C₂⁵	1	1	yes	characteristic
724	C₂³×C₃	C₂⁵	1	1	yes	characteristic
725	C₂³×C₃	C₂⁵	1	2	yes	—
726	C₂³×C₃	C₂⁵	1	1	yes	characteristic
727	C₃×Q₈	—	2	8	no	—
728	C₃×Q₈	—	4	4	no	—
729	C₃×Q₈	—	4	8	no	—
730	C₃×D₄	—	2	32	no	—
731	C₃×D₄	—	2	16	no	—
732	C₃×D₄	—	2	16	no	—
733	C₃×D₄	—	2	16	no	—
734	C₃×D₄	—	2	16	no	—
735	C₃×D₄	—	2	16	no	—
736	C₃×D₄	—	2	8	no	—
737	C₃×D₄	—	4	8	no	—
738	C₃×D₄	—	4	16	no	—
739	C₃×D₄	—	4	8	no	—
740	C₃×D₄	—	4	16	no	—
741	C₃×D₄	—	4	16	no	—
742	C₃×D₄	—	4	16	no	—
743	C₃×D₄	—	4	8	no	—
744	C₃×D₄	—	4	4	no	—
745	C₃×D₄	—	4	8	no	—
746	C₂×C₃×C₄	—	2	2	no	—
747	C₂×C₃×C₄	—	2	4	no	—
748	C₂×C₃×C₄	—	2	8	no	—
749	C₂×C₃×C₄	—	2	8	no	—
750	C₂×C₃×C₄	—	2	4	no	—
751	C₂×C₃×C₄	—	2	4	no	—
752	C₂×C₃×C₄	—	2	4	no	—
753	C₂×C₃×C₄	—	2	4	no	—
754	C₂×C₃×C₄	—	2	4	no	—
755	C₂×C₃×C₄	—	2	4	no	—
756	C₂×C₃×C₄	—	2	16	no	—
757	C₂×C₃×C₄	—	4	1	no	—
758	C₂×C₃×C₄	—	4	2	no	—
759	C₂×C₃×C₄	—	4	2	no	—
760	C₂×C₃×C₄	—	4	2	no	—
761	C₂×C₃×C₄	—	4	2	no	—
762	C₂×C₃×C₄	—	4	2	no	—
763	C₂×C₃×C₄	—	4	1	no	—
764	C₂×C₃×C₄	—	4	4	no	—
765	C₂×C₃×C₄	—	4	4	no	—
766	C₂×C₃×C₄	—	4	4	no	—
767	C₂×C₃×C₄	—	4	8	no	—
768	C₂×C₃×C₄	—	4	4	no	—
769	C₂×C₃×C₄	—	4	8	no	—
770	C₂×C₃×C₄	—	4	16	no	—
771	C₂×C₃×C₄	—	4	8	no	—
772	C₂×C₃×C₄	—	4	8	no	—
773	C₂×C₃×C₄	H(5,𝔽₂)	1	4	yes	complemented
774	C₂×C₃×C₄	C₂⁵	1	8	yes	—
775	C₂×C₃×C₄	C₂⁵	1	2	yes	—
776	C₂×C₃×C₄	C₂⁵	1	8	yes	—
777	C₂×C₃×C₄	C₂⁵	1	8	yes	—
778	C₂×C₃×C₄	C₂⁵	1	8	yes	—
779	C₂×C₃×C₄	C₂⁵	1	2	yes	—
780	C₂×C₃×C₄	C₂⁵	1	2	yes	—
781	C₂×C₃×C₄	C₂⁵	1	2	yes	—
782	C₂⁴	—	2	4	no	—
783	C₂⁴	—	4	2	no	—
784	C₂⁴	—	4	2	no	—
785	C₂⁴	—	4	4	no	—
786	C₂⁴	—	4	4	no	—
787	C₂⁴	—	4	4	no	—
788	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
789	C₂⁴	C₂⁴×C₃	1	2	yes	—
790	C₂⁴	C₂⁴×C₃	1	2	yes	—
791	C₂⁴	C₂⁴×C₃	1	4	yes	—
792	C₂⁴	C₂⁴×C₃	1	4	yes	—
793	C₂⁴	C₂⁴×C₃	1	4	yes	—
794	C₂⁴	C₂⁴×C₃	1	4	yes	—
795	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
796	C₂⁴	C₂⁴×C₃	1	8	yes	—
797	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
798	#41	—	2	16	no	—
799	#41	—	4	8	no	—
800	#41	—	4	8	no	—
801	#41	—	4	16	no	—
802	#41	—	4	32	no	—
803	#41	—	4	8	no	—
804	#41	—	4	16	no	—
805	C₂×Q₈	—	4	4	no	—
806	C₂×Q₈	C₂⁴×C₃	1	4	yes	—
807	C₂×Q₈	C₂⁴×C₃	1	4	yes	—
808	C₂×Q₈	C₂⁴×C₃	1	8	yes	—
809	C₂×D₄	—	2	16	no	—
810	C₂×D₄	—	2	16	no	—
811	C₂×D₄	—	2	8	no	—
812	C₂×D₄	—	4	8	no	—
813	C₂×D₄	—	4	8	no	—
814	C₂×D₄	—	4	4	no	—
815	C₂×D₄	—	4	16	no	—
816	C₂×D₄	—	4	4	no	—
817	C₂×D₄	—	4	8	no	—
818	C₂×D₄	—	4	16	no	—
819	C₂×D₄	—	4	16	no	—
820	C₂×D₄	—	4	8	no	—
821	C₂×D₄	—	4	16	no	—
822	C₂×D₄	—	4	16	no	—
823	C₂×D₄	—	4	8	no	—
824	C₂×D₄	—	4	16	no	—
825	C₂×D₄	—	4	32	no	—
826	C₂×D₄	C₂⁴×C₃	1	8	yes	—
827	C₂×D₄	C₂⁴×C₃	1	8	yes	—
828	C₂×D₄	C₂⁴×C₃	1	8	yes	—
829	C₂×D₄	C₂⁴×C₃	1	8	yes	—
830	C₂×D₄	C₂⁴×C₃	1	16	yes	—
831	C₂×D₄	C₂⁴×C₃	1	8	yes	—
832	C₂×D₄	C₂⁴×C₃	1	4	yes	—
833	C₂×D₄	C₂⁴×C₃	1	16	yes	—
834	C₂×D₄	C₂⁴×C₃	1	8	yes	—
835	C₂×D₄	C₂⁴×C₃	1	8	yes	—
836	C₂×D₄	C₂⁴×C₃	1	16	yes	—
837	C₂×D₄	C₂⁴×C₃	1	16	yes	—
838	C₂×D₄	C₂⁴×C₃	1	4	yes	—
839	C₂×D₄	C₂⁴×C₃	1	8	yes	—
840	C₂×D₄	C₂⁴×C₃	1	8	yes	—
841	C₂×D₄	C₂⁴×C₃	1	16	yes	—
842	C₂²×C₄	—	2	4	no	—
843	C₂²×C₄	—	2	8	no	—
844	C₂²×C₄	—	4	4	no	—
845	C₂²×C₄	—	4	4	no	—
846	C₂²×C₄	—	4	4	no	—
847	C₂²×C₄	—	4	4	no	—
848	C₂²×C₄	—	4	8	no	—
849	C₂²×C₄	—	4	4	no	—
850	C₂²×C₄	—	4	2	no	—
851	C₂²×C₄	—	4	4	no	—
852	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
853	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
854	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
855	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
856	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
857	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
858	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
859	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
860	C₂²×C₄	C₂⁴×C₃	1	8	yes	—
861	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
862	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
863	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
864	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
865	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
866	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
867	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
868	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
869	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
870	C₂²×C₄	C₂⁴×C₃	1	8	yes	—
871	C₂²×C₄	C₂⁴×C₃	1	8	yes	—
872	C₂²×C₄	C₂⁴×C₃	1	8	yes	—
873	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
874	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
875	C₂²×C₄	C₂⁴×C₃	1	8	yes	—
876	C₂²×C₄	C₂⁴×C₃	1	16	yes	—
877	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
878	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
879	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
880	C₄⋊C₄	C₂⁴×C₃	1	8	yes	—
881	C₄⋊C₄	C₂⁴×C₃	1	8	yes	—
882	C₄⋊C₄	C₂⁴×C₃	1	4	yes	—
883	C₄⋊C₄	C₂⁴×C₃	1	4	yes	—
884	C₄⋊C₄	C₂⁴×C₃	1	4	yes	—
885	C₄⋊C₄	C₂⁴×C₃	1	4	yes	—
886	C₄⋊C₄	C₂⁴×C₃	1	8	yes	—
887	C₄⋊C₄	C₂⁴×C₃	1	8	yes	—
888	C₄⋊C₄	C₂⁴×C₃	1	8	yes	—
889	C₄⋊C₄	C₂⁴×C₃	1	8	yes	—
890	C₄⋊C₄	C₂⁴×C₃	1	16	yes	—
891	C₄⋊C₄	C₂⁴×C₃	1	8	yes	—
892	C₄⋊C₄	C₂⁴×C₃	1	8	yes	—
893	C₄⋊C₄	C₂⁴×C₃	1	16	yes	—
894	C₂²⋊C₄	C₂⁴×C₃	1	16	yes	—
895	C₂²⋊C₄	C₂⁴×C₃	1	8	yes	—
896	C₂²⋊C₄	C₂⁴×C₃	1	8	yes	—
897	C₂²⋊C₄	C₂⁴×C₃	1	8	yes	—
898	C₂²⋊C₄	C₂⁴×C₃	1	16	yes	—
899	C₂²⋊C₄	C₂⁴×C₃	1	16	yes	—
900	C₂²⋊C₄	C₂⁴×C₃	1	8	yes	—
901	C₂²⋊C₄	C₂⁴×C₃	1	8	yes	—
902	C₂²⋊C₄	C₂⁴×C₃	1	16	yes	—
903	C₂²⋊C₄	C₂⁴×C₃	1	16	yes	—
904	C₂²⋊C₄	C₂⁴×C₃	1	8	yes	—
905	C₂²⋊C₄	C₂⁴×C₃	1	8	yes	—
906	C₂²⋊C₄	C₂⁴×C₃	1	16	yes	—
907	C₂²⋊C₄	C₂⁴×C₃	1	8	yes	—
908	C₂²⋊C₄	C₂⁴×C₃	1	8	yes	—
909	C₂²⋊C₄	C₂⁴×C₃	1	8	yes	—
910	C₂²⋊C₄	C₂⁴×C₃	1	16	yes	—
911	C₄²	C₂⁴×C₃	1	8	yes	—
912	C₄²	C₂⁴×C₃	1	8	yes	—
913	C₄²	C₂⁴×C₃	1	16	yes	—
914	C₂²×C₃	—	2	8	no	—
915	C₂²×C₃	—	2	2	no	—
916	C₂²×C₃	—	2	1	no	—
917	C₂²×C₃	—	2	1	no	—
918	C₂²×C₃	—	2	1	no	—
919	C₂²×C₃	—	2	1	no	—
920	C₂²×C₃	—	2	2	no	—
921	C₂²×C₃	—	2	1	no	—
922	C₂²×C₃	—	2	1	no	—
923	C₂²×C₃	—	2	2	no	—
924	C₂²×C₃	—	2	8	no	—
925	C₂²×C₃	—	2	8	no	—
926	C₂²×C₃	—	2	8	no	—
927	C₂²×C₃	—	2	8	no	—
928	C₂²×C₃	—	2	2	no	—
929	C₂²×C₃	—	2	8	no	—
930	C₂²×C₃	—	2	8	no	—
931	C₂²×C₃	—	2	2	no	—
932	C₂²×C₃	—	4	4	no	—
933	C₂²×C₃	—	4	8	no	—
934	C₂²×C₃	—	4	8	no	—
935	C₂²×C₃	—	4	4	no	—
936	C₂²×C₃	—	8	8	no	—
937	C₂²×C₃	—	8	8	no	—
938	C₂²×C₃	—	8	8	no	—
939	C₂²×C₃	—	8	8	no	—
940	C₂²×C₃	—	16	8	no	—
941	C₂²×C₃	C₂×H(5,𝔽₂)	1	2	yes	—
942	C₂²×C₃	C₂×H(5,𝔽₂)	1	2	yes	—
943	C₂²×C₃	C₂×H(5,𝔽₂)	1	4	yes	—
944	C₂²×C₃	#585	1	2	yes	—
945	C₂²×C₃	C₂⁶	1	1	yes	characteristic
946	C₃×C₄	—	2	2	no	—
947	C₃×C₄	—	2	2	no	—
948	C₃×C₄	—	2	2	no	—
949	C₃×C₄	—	2	8	no	—
950	C₃×C₄	—	2	8	no	—
951	C₃×C₄	—	2	8	no	—
952	C₃×C₄	—	2	8	no	—
953	C₃×C₄	C₂×H(5,𝔽₂)	1	4	yes	—
954	C₂³	—	2	2	no	—
955	C₂³	—	2	2	no	—
956	C₂³	—	2	2	no	—
957	C₂³	—	2	4	no	—
958	C₂³	—	2	4	no	—
959	C₂³	—	2	4	no	—
960	C₂³	—	2	2	no	—
961	C₂³	—	2	4	no	—
962	C₂³	—	2	8	no	—
963	C₂³	—	2	8	no	—
964	C₂³	—	2	8	no	—
965	C₂³	—	2	8	no	—
966	C₂³	—	4	1	no	—
967	C₂³	—	4	2	no	—
968	C₂³	—	4	1	no	—
969	C₂³	—	4	1	no	—
970	C₂³	—	4	2	no	—
971	C₂³	—	4	1	no	—
972	C₂³	—	4	4	no	—
973	C₂³	—	4	4	no	—
974	C₂³	—	4	4	no	—
975	C₂³	—	4	4	no	—
976	C₂³	—	4	4	no	—
977	C₂³	—	4	4	no	—
978	C₂³	—	4	4	no	—
979	C₂³	—	4	4	no	—
980	C₂³	—	4	8	no	—
981	C₂³	—	4	8	no	—
982	C₂³	—	4	8	no	—
983	C₂³	—	4	16	no	—
984	C₂³	—	8	16	no	—
985	C₂³	C₃×H(5,𝔽₂)	1	4	yes	complemented
986	C₂³	C₂⁵×C₃	1	8	yes	—
987	C₂³	C₂⁵×C₃	1	2	yes	—
988	C₂³	C₂⁵×C₃	1	8	yes	—
989	C₂³	C₂⁵×C₃	1	1	yes	characteristic
990	C₂³	C₂⁵×C₃	1	1	yes	characteristic
991	C₂³	C₂⁵×C₃	1	2	yes	—
992	C₂³	C₂⁵×C₃	1	1	yes	characteristic
993	Q₈	—	2	8	no	—
994	Q₈	—	4	4	no	—
995	Q₈	—	4	8	no	—
996	D₄	—	2	32	no	—
997	D₄	—	2	16	no	—
998	D₄	—	2	16	no	—
999	D₄	—	2	16	no	—
1000	D₄	—	2	16	no	—
1001	D₄	—	2	16	no	—
1002	D₄	—	2	8	no	—
1003	D₄	—	4	8	no	—
1004	D₄	—	4	16	no	—
1005	D₄	—	4	8	no	—
1006	D₄	—	4	16	no	—
1007	D₄	—	4	16	no	—
1008	D₄	—	4	4	no	—
1009	D₄	—	4	8	no	—
1010	D₄	—	4	16	no	—
1011	D₄	—	4	8	no	—
1012	C₂×C₄	—	2	2	no	—
1013	C₂×C₄	—	2	4	no	—
1014	C₂×C₄	—	2	8	no	—
1015	C₂×C₄	—	2	8	no	—
1016	C₂×C₄	—	2	4	no	—
1017	C₂×C₄	—	2	4	no	—
1018	C₂×C₄	—	2	4	no	—
1019	C₂×C₄	—	2	4	no	—
1020	C₂×C₄	—	2	4	no	—
1021	C₂×C₄	—	2	4	no	—
1022	C₂×C₄	—	2	16	no	—
1023	C₂×C₄	—	4	1	no	—
1024	C₂×C₄	—	4	2	no	—
1025	C₂×C₄	—	4	2	no	—
1026	C₂×C₄	—	4	2	no	—
1027	C₂×C₄	—	4	2	no	—
1028	C₂×C₄	—	4	2	no	—
1029	C₂×C₄	—	4	1	no	—
1030	C₂×C₄	—	4	4	no	—
1031	C₂×C₄	—	4	4	no	—
1032	C₂×C₄	—	4	4	no	—
1033	C₂×C₄	—	4	8	no	—
1034	C₂×C₄	—	4	16	no	—
1035	C₂×C₄	—	4	8	no	—
1036	C₂×C₄	—	4	8	no	—
1037	C₂×C₄	—	4	4	no	—
1038	C₂×C₄	—	4	8	no	—
1039	C₂×C₄	C₃×H(5,𝔽₂)	1	4	yes	complemented
1040	C₂×C₄	C₂⁵×C₃	1	8	yes	—
1041	C₂×C₄	C₂⁵×C₃	1	2	yes	—
1042	C₂×C₄	C₂⁵×C₃	1	8	yes	—
1043	C₂×C₄	C₂⁵×C₃	1	8	yes	—
1044	C₂×C₄	C₂⁵×C₃	1	8	yes	—
1045	C₂×C₄	C₂⁵×C₃	1	2	yes	—
1046	C₂×C₄	C₂⁵×C₃	1	2	yes	—
1047	C₂×C₄	C₂⁵×C₃	1	2	yes	—
1048	C₂×C₃	—	2	2	no	—
1049	C₂×C₃	—	2	2	no	—
1050	C₂×C₃	—	2	2	no	—
1051	C₂×C₃	—	2	4	no	—
1052	C₂×C₃	—	4	2	no	—
1053	C₂×C₃	—	4	8	no	—
1054	C₂×C₃	—	4	8	no	—
1055	C₂×C₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
1056	C₂×C₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
1057	C₂×C₃	C₂×#585	1	1	yes	characteristic
1058	C₂²	—	2	8	no	—
1059	C₂²	—	2	2	no	—
1060	C₂²	—	2	1	no	—
1061	C₂²	—	2	1	no	—
1062	C₂²	—	2	1	no	—
1063	C₂²	—	2	1	no	—
1064	C₂²	—	2	2	no	—
1065	C₂²	—	2	1	no	—
1066	C₂²	—	2	1	no	—
1067	C₂²	—	2	2	no	—
1068	C₂²	—	2	8	no	—
1069	C₂²	—	2	8	no	—
1070	C₂²	—	2	8	no	—
1071	C₂²	—	2	8	no	—
1072	C₂²	—	2	2	no	—
1073	C₂²	—	2	8	no	—
1074	C₂²	—	2	8	no	—
1075	C₂²	—	2	2	no	—
1076	C₂²	—	4	4	no	—
1077	C₂²	—	4	8	no	—
1078	C₂²	—	4	8	no	—
1079	C₂²	—	4	4	no	—
1080	C₂²	—	8	8	no	—
1081	C₂²	—	8	8	no	—
1082	C₂²	—	8	8	no	—
1083	C₂²	—	8	8	no	—
1084	C₂²	—	16	8	no	—
1085	C₂²	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
1086	C₂²	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
1087	C₂²	C₂×C₃×H(5,𝔽₂)	1	4	yes	—
1088	C₂²	C₃×#585	1	2	yes	—
1089	C₂²	C₂⁶×C₃	1	1	yes	characteristic
1090	C₄	—	2	2	no	—
1091	C₄	—	2	2	no	—
1092	C₄	—	2	2	no	—
1093	C₄	—	2	8	no	—
1094	C₄	—	2	8	no	—
1095	C₄	—	2	8	no	—
1096	C₄	—	2	8	no	—
1097	C₄	C₂×C₃×H(5,𝔽₂)	1	4	yes	—
1098	C₃	#62818	1	1	yes	characteristic, direct product factor, Sylow
1099	C₂	—	2	2	no	—
1100	C₂	—	2	2	no	—
1101	C₂	—	2	2	no	—
1102	C₂	—	2	4	no	—
1103	C₂	—	4	2	no	—
1104	C₂	—	4	8	no	—
1105	C₂	—	4	8	no	—
1106	C₂	C₂²×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1107	C₂	C₂²×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1108	C₂	C₂×C₃×#585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃	C₂⁶
commutator, Frattini, cosocle	C₂²	C₂⁶×C₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₃×#3542	C₂	semidirect
2. C₃×#3537	C₂	semidirect
3. C₃×#3536	C₂	semidirect
4. C₃×#3534	C₂	semidirect
5. C₃×#3519	C₂	semidirect
6. C₃×#3505	C₂	semidirect
7. C₃×#3496	C₂	semidirect
8. C₃×#3494	C₂	semidirect
9. C₃×#3492	C₂	semidirect
10. C₃×#3490	C₂	semidirect
11. C₃×#3488	C₂	semidirect
12. C₃×#3484	C₂	semidirect
13. C₃×#3484	C₂	semidirect
14. C₂×C₃×#525	C₂	semidirect
15. C₂²×C₃×#121	C₂	semidirect
16. #62818	C₃	direct (N × H)
17. C₂×C₃×H(5,𝔽₂)	C₂²	semidirect
18. C₂×C₃×H(5,𝔽₂)	C₂²	semidirect
19. C₂²×C₃×#41	C₂²	semidirect
20. C₂³×C₃×D₄	C₂²	semidirect
21. C₂³×C₃×D₄	C₂²	semidirect
22. C₂⁴×C₃×C₄	C₂²	semidirect
23. C₃×#562	C₂²	semidirect
24. C₃×#560	C₂²	semidirect
25. C₃×#555	C₂²	semidirect
26. C₃×#554	C₂²	semidirect
27. C₃×#553	C₂²	semidirect
28. C₃×#553	C₂²	semidirect
29. C₃×#553	C₂²	semidirect
30. C₃×#553	C₂²	semidirect
31. C₃×#552	C₂²	semidirect
32. C₃×#551	C₂²	semidirect
33. C₃×#551	C₂²	semidirect
34. C₃×#550	C₂²	semidirect
35. C₃×#548	C₂²	semidirect
36. C₃×#547	C₂²	semidirect
37. C₃×#547	C₂²	semidirect
38. C₃×#546	C₂²	semidirect
39. C₃×#546	C₂²	semidirect
40. C₃×#546	C₂²	semidirect
41. C₃×#546	C₂²	semidirect
42. C₃×#546	C₂²	semidirect
43. C₃×#546	C₂²	semidirect
44. C₃×#546	C₂²	semidirect
45. C₃×#546	C₂²	semidirect
46. C₃×D₄²	C₂²	semidirect
47. C₃×D₄²	C₂²	semidirect
48. C₃×D₄²	C₂²	semidirect
49. C₃×D₄²	C₂²	semidirect
50. C₃×D₄²	C₂²	semidirect
51. C₃×#544	C₂²	semidirect
52. C₃×#543	C₂²	semidirect
53. C₃×#542	C₂²	semidirect
54. C₃×#540	C₂²	semidirect
55. C₃×#540	C₂²	semidirect
56. C₃×#539	C₂²	semidirect
57. C₃×#539	C₂²	semidirect
58. C₃×#538	C₂²	semidirect
59. C₃×#538	C₂²	semidirect
60. C₃×#538	C₂²	semidirect
61. C₃×#538	C₂²	semidirect
62. C₃×#537	C₂²	semidirect
63. C₃×#537	C₂²	semidirect
64. C₃×#537	C₂²	semidirect
65. C₃×#535	C₂²	semidirect
66. C₃×#535	C₂²	semidirect
67. C₃×#535	C₂²	semidirect
68. C₃×#534	C₂²	semidirect
69. C₃×#534	C₂²	semidirect
70. C₃×#534	C₂²	semidirect
71. C₃×#534	C₂²	semidirect
72. C₃×#534	C₂²	semidirect
73. C₃×#532	C₂²	semidirect
74. C₃×#529	C₂²	semidirect
75. C₃×#525	C₂²	semidirect
76. C₃×#525	C₂²	semidirect
77. C₃×#525	C₂²	semidirect
78. C₃×#525	C₂²	semidirect
79. C₃×#525	C₂²	semidirect
80. C₃×#525	C₂²	semidirect
81. C₃×#525	C₂²	semidirect
82. C₃×#525	C₂²	semidirect
83. C₃×#525	C₂²	semidirect
84. C₃×#525	C₂²	semidirect
85. C₂×C₃×#123	C₂²	semidirect
86. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
87. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
88. C₂×C₃×#121	C₂²	semidirect
89. C₂×C₃×#121	C₂²	semidirect
90. C₂×C₃×#121	C₂²	semidirect
91. C₂×C₃×#121	C₂²	semidirect
92. C₂×C₃×#121	C₂²	semidirect
93. C₂×C₃×#121	C₂²	semidirect
94. C₂×C₃×#121	C₂²	semidirect
95. C₂×C₃×#121	C₂²	semidirect
96. C₂×C₃×#121	C₂²	semidirect
97. C₂×C₃×#120	C₂²	semidirect
98. C₂×C₃×#120	C₂²	semidirect
99. C₃×#520	C₂²	semidirect
100. C₃×#518	C₂²	semidirect
101. C₃×#518	C₂²	semidirect
102. C₃×#518	C₂²	semidirect
103. C₂×C₃×C₄×D₄	C₂²	semidirect
104. C₂×C₃×C₄×D₄	C₂²	semidirect
105. C₂×C₃×#117	C₂²	semidirect
106. C₂²×C₃×C₄⋊C₄	C₂²	semidirect
107. C₂²×C₃×C₂²⋊C₄	C₂²	semidirect
108. #3542	C₂×C₃	semidirect
109. #3537	C₂×C₃	semidirect
110. #3536	C₂×C₃	semidirect
111. #3534	C₂×C₃	semidirect
112. #3519	C₂×C₃	semidirect
113. #3505	C₂×C₃	semidirect
114. #3496	C₂×C₃	semidirect
115. #3494	C₂×C₃	semidirect
116. #3492	C₂×C₃	semidirect
117. #3490	C₂×C₃	semidirect
118. #3488	C₂×C₃	semidirect
119. #3484	C₂×C₃	semidirect
120. #3484	C₂×C₃	semidirect
121. C₂×#525	C₂×C₃	semidirect
122. C₂²×#121	C₂×C₃	semidirect
131. C₂×C₃×#41	C₂³	semidirect
132. C₂×C₃×#41	C₂³	semidirect
133. C₂×C₃×#41	C₂³	semidirect
134. C₂×C₃×#41	C₂³	semidirect
135. C₂²×C₃×Q₈	C₂³	semidirect
152. C₂²×C₃×D₄	C₂³	semidirect
153. C₂²×C₃×D₄	C₂³	semidirect
154. C₂²×C₃×D₄	C₂³	semidirect
165. C₂³×C₃×C₄	C₂³	semidirect
166. C₃×C₄⋊Q₈	C₂³	semidirect
167. C₃×#127	C₂³	semidirect
168. C₃×#127	C₂³	semidirect
169. C₃×#126	C₂³	semidirect
170. C₃×#126	C₂³	semidirect
171. C₃×#126	C₂³	semidirect
172. C₃×#125	C₂³	semidirect
173. C₃×#125	C₂³	semidirect
174. C₃×#124	C₂³	semidirect
175. C₃×#124	C₂³	semidirect
176. C₃×#124	C₂³	semidirect
177. C₃×#124	C₂³	semidirect
181. C₃×#123	C₂³	semidirect
182. C₃×#123	C₂³	semidirect
183. C₃×#123	C₂³	semidirect
184. C₃×#123	C₂³	semidirect
185. C₃×#123	C₂³	semidirect
186. C₃×#123	C₂³	semidirect
187. C₃×#123	C₂³	semidirect
188. C₃×#123	C₂³	semidirect
189. C₃×#123	C₂³	semidirect
196. C₃×C₂²⋊Q₈	C₂³	semidirect
197. C₃×C₂²⋊Q₈	C₂³	semidirect
198. C₃×C₂²⋊Q₈	C₂³	semidirect
199. C₃×C₂²⋊Q₈	C₂³	semidirect
200. C₃×C₂²⋊Q₈	C₂³	semidirect
201. C₃×C₂²⋊Q₈	C₂³	semidirect
202. C₃×C₂²⋊Q₈	C₂³	semidirect
203. C₃×C₂²⋊Q₈	C₂³	semidirect
218. C₃×#121	C₂³	semidirect
219. C₃×#121	C₂³	semidirect
220. C₃×#121	C₂³	semidirect
221. C₃×#121	C₂³	semidirect
222. C₃×#121	C₂³	semidirect
223. C₃×#121	C₂³	semidirect
224. C₃×#121	C₂³	semidirect
225. C₃×#121	C₂³	semidirect
226. C₃×#121	C₂³	semidirect
227. C₃×#121	C₂³	semidirect
228. C₃×#121	C₂³	semidirect
229. C₃×#121	C₂³	semidirect
230. C₃×#121	C₂³	semidirect
231. C₃×#121	C₂³	semidirect
232. C₃×#121	C₂³	semidirect
233. C₃×#121	C₂³	semidirect
234. C₃×#121	C₂³	semidirect
242. C₃×#120	C₂³	semidirect
243. C₃×#120	C₂³	semidirect
244. C₃×#120	C₂³	semidirect
245. C₃×#120	C₂³	semidirect
246. C₃×C₄×Q₈	C₂³	semidirect
253. C₃×C₄×D₄	C₂³	semidirect
254. C₃×C₄×D₄	C₂³	semidirect
255. C₃×C₄×D₄	C₂³	semidirect
256. C₃×C₄×D₄	C₂³	semidirect
257. C₃×C₄×D₄	C₂³	semidirect
258. C₃×C₄×D₄	C₂³	semidirect
259. C₃×C₄×D₄	C₂³	semidirect
260. C₃×C₄×D₄	C₂³	semidirect
261. C₃×C₄×D₄	C₂³	semidirect
262. C₃×C₄×D₄	C₂³	semidirect
263. C₃×C₄×D₄	C₂³	semidirect
267. C₃×#117	C₂³	semidirect
268. C₃×#117	C₂³	semidirect
269. C₃×#117	C₂³	semidirect
270. C₃×#117	C₂³	semidirect
275. C₂×C₃×C₄⋊C₄	C₂³	semidirect
276. C₂×C₃×C₄⋊C₄	C₂³	semidirect
277. C₂×C₃×C₄⋊C₄	C₂³	semidirect
278. C₂×C₃×C₄⋊C₄	C₂³	semidirect
279. C₂×C₃×C₄⋊C₄	C₂³	semidirect
290. C₂×C₃×C₂²⋊C₄	C₂³	semidirect
291. C₂×C₃×C₂²⋊C₄	C₂³	semidirect
292. C₂×C₃×C₂²⋊C₄	C₂³	semidirect
293. C₂×C₃×C₄²	C₂³	semidirect
294. C₂×H(5,𝔽₂)	C₂²×C₃	semidirect
295. C₂×H(5,𝔽₂)	C₂²×C₃	semidirect
296. C₂²×#41	C₂²×C₃	semidirect
297. C₂³×D₄	C₂²×C₃	semidirect
298. C₂³×D₄	C₂²×C₃	semidirect
299. C₂⁴×C₄	C₂²×C₃	semidirect
300. #562	C₂²×C₃	semidirect
301. #560	C₂²×C₃	semidirect
302. #555	C₂²×C₃	semidirect
303. #554	C₂²×C₃	semidirect
304. #553	C₂²×C₃	semidirect
305. #553	C₂²×C₃	semidirect
306. #553	C₂²×C₃	semidirect
307. #553	C₂²×C₃	semidirect
308. #552	C₂²×C₃	semidirect
309. #551	C₂²×C₃	semidirect
310. #551	C₂²×C₃	semidirect
311. #550	C₂²×C₃	semidirect
312. #548	C₂²×C₃	semidirect
313. #547	C₂²×C₃	semidirect
314. #547	C₂²×C₃	semidirect
315. #546	C₂²×C₃	semidirect
316. #546	C₂²×C₃	semidirect
317. #546	C₂²×C₃	semidirect
318. #546	C₂²×C₃	semidirect
319. #546	C₂²×C₃	semidirect
320. #546	C₂²×C₃	semidirect
321. #546	C₂²×C₃	semidirect
322. #546	C₂²×C₃	semidirect
323. D₄²	C₂²×C₃	semidirect
324. D₄²	C₂²×C₃	semidirect
325. D₄²	C₂²×C₃	semidirect
326. D₄²	C₂²×C₃	semidirect
327. D₄²	C₂²×C₃	semidirect
328. #544	C₂²×C₃	semidirect
329. #543	C₂²×C₃	semidirect
330. #542	C₂²×C₃	semidirect
331. #540	C₂²×C₃	semidirect
332. #540	C₂²×C₃	semidirect
333. #539	C₂²×C₃	semidirect
334. #539	C₂²×C₃	semidirect
335. #538	C₂²×C₃	semidirect
336. #538	C₂²×C₃	semidirect
337. #538	C₂²×C₃	semidirect
338. #538	C₂²×C₃	semidirect
339. #537	C₂²×C₃	semidirect
340. #537	C₂²×C₃	semidirect
341. #537	C₂²×C₃	semidirect
342. #535	C₂²×C₃	semidirect
343. #535	C₂²×C₃	semidirect
344. #535	C₂²×C₃	semidirect
345. #534	C₂²×C₃	semidirect
346. #534	C₂²×C₃	semidirect
347. #534	C₂²×C₃	semidirect
348. #534	C₂²×C₃	semidirect
349. #534	C₂²×C₃	semidirect
350. #532	C₂²×C₃	semidirect
351. #529	C₂²×C₃	semidirect
352. #525	C₂²×C₃	semidirect
353. #525	C₂²×C₃	semidirect
354. #525	C₂²×C₃	semidirect
355. #525	C₂²×C₃	semidirect
356. #525	C₂²×C₃	semidirect
357. #525	C₂²×C₃	semidirect
358. #525	C₂²×C₃	semidirect
359. #525	C₂²×C₃	semidirect
360. #525	C₂²×C₃	semidirect
361. #525	C₂²×C₃	semidirect
362. C₂×#123	C₂²×C₃	semidirect
363. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
364. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
365. C₂×#121	C₂²×C₃	semidirect
366. C₂×#121	C₂²×C₃	semidirect
367. C₂×#121	C₂²×C₃	semidirect
368. C₂×#121	C₂²×C₃	semidirect
369. C₂×#121	C₂²×C₃	semidirect
370. C₂×#121	C₂²×C₃	semidirect
371. C₂×#121	C₂²×C₃	semidirect
372. C₂×#121	C₂²×C₃	semidirect
373. C₂×#121	C₂²×C₃	semidirect
374. C₂×#120	C₂²×C₃	semidirect
375. C₂×#120	C₂²×C₃	semidirect
376. #520	C₂²×C₃	semidirect
377. #518	C₂²×C₃	semidirect
378. #518	C₂²×C₃	semidirect
379. #518	C₂²×C₃	semidirect
380. C₂×C₄×D₄	C₂²×C₃	semidirect
381. C₂×C₄×D₄	C₂²×C₃	semidirect
382. C₂×#117	C₂²×C₃	semidirect
383. C₂²×C₄⋊C₄	C₂²×C₃	semidirect
384. C₂²×C₂²⋊C₄	C₂²×C₃	semidirect
525. C₂×#41	C₂³×C₃	semidirect
526. C₂×#41	C₂³×C₃	semidirect
527. C₂×#41	C₂³×C₃	semidirect
528. C₂×#41	C₂³×C₃	semidirect
529. C₂²×Q₈	C₂³×C₃	semidirect
546. C₂²×D₄	C₂³×C₃	semidirect
547. C₂²×D₄	C₂³×C₃	semidirect
548. C₂²×D₄	C₂³×C₃	semidirect
559. C₂³×C₄	C₂³×C₃	semidirect
560. C₄⋊Q₈	C₂³×C₃	semidirect
561. #127	C₂³×C₃	semidirect
562. #127	C₂³×C₃	semidirect
563. #126	C₂³×C₃	semidirect
564. #126	C₂³×C₃	semidirect
565. #126	C₂³×C₃	semidirect
566. #125	C₂³×C₃	semidirect
567. #125	C₂³×C₃	semidirect
568. #124	C₂³×C₃	semidirect
569. #124	C₂³×C₃	semidirect
570. #124	C₂³×C₃	semidirect
571. #124	C₂³×C₃	semidirect
575. #123	C₂³×C₃	semidirect
576. #123	C₂³×C₃	semidirect
577. #123	C₂³×C₃	semidirect
578. #123	C₂³×C₃	semidirect
579. #123	C₂³×C₃	semidirect
580. #123	C₂³×C₃	semidirect
581. #123	C₂³×C₃	semidirect
582. #123	C₂³×C₃	semidirect
583. #123	C₂³×C₃	semidirect
590. C₂²⋊Q₈	C₂³×C₃	semidirect
591. C₂²⋊Q₈	C₂³×C₃	semidirect
592. C₂²⋊Q₈	C₂³×C₃	semidirect
593. C₂²⋊Q₈	C₂³×C₃	semidirect
594. C₂²⋊Q₈	C₂³×C₃	semidirect
595. C₂²⋊Q₈	C₂³×C₃	semidirect
596. C₂²⋊Q₈	C₂³×C₃	semidirect
597. C₂²⋊Q₈	C₂³×C₃	semidirect
612. #121	C₂³×C₃	semidirect
613. #121	C₂³×C₃	semidirect
614. #121	C₂³×C₃	semidirect
615. #121	C₂³×C₃	semidirect
616. #121	C₂³×C₃	semidirect
617. #121	C₂³×C₃	semidirect
618. #121	C₂³×C₃	semidirect
619. #121	C₂³×C₃	semidirect
620. #121	C₂³×C₃	semidirect
621. #121	C₂³×C₃	semidirect
622. #121	C₂³×C₃	semidirect
623. #121	C₂³×C₃	semidirect
624. #121	C₂³×C₃	semidirect
625. #121	C₂³×C₃	semidirect
626. #121	C₂³×C₃	semidirect
627. #121	C₂³×C₃	semidirect
628. #121	C₂³×C₃	semidirect
636. #120	C₂³×C₃	semidirect
637. #120	C₂³×C₃	semidirect
638. #120	C₂³×C₃	semidirect
639. #120	C₂³×C₃	semidirect
640. C₄×Q₈	C₂³×C₃	semidirect
647. C₄×D₄	C₂³×C₃	semidirect
648. C₄×D₄	C₂³×C₃	semidirect
649. C₄×D₄	C₂³×C₃	semidirect
650. C₄×D₄	C₂³×C₃	semidirect
651. C₄×D₄	C₂³×C₃	semidirect
652. C₄×D₄	C₂³×C₃	semidirect
653. C₄×D₄	C₂³×C₃	semidirect
654. C₄×D₄	C₂³×C₃	semidirect
655. C₄×D₄	C₂³×C₃	semidirect
656. C₄×D₄	C₂³×C₃	semidirect
657. C₄×D₄	C₂³×C₃	semidirect
661. #117	C₂³×C₃	semidirect
662. #117	C₂³×C₃	semidirect
663. #117	C₂³×C₃	semidirect
664. #117	C₂³×C₃	semidirect
669. C₂×C₄⋊C₄	C₂³×C₃	semidirect
670. C₂×C₄⋊C₄	C₂³×C₃	semidirect
671. C₂×C₄⋊C₄	C₂³×C₃	semidirect
672. C₂×C₄⋊C₄	C₂³×C₃	semidirect
673. C₂×C₄⋊C₄	C₂³×C₃	semidirect
684. C₂×C₂²⋊C₄	C₂³×C₃	semidirect
685. C₂×C₂²⋊C₄	C₂³×C₃	semidirect
686. C₂×C₂²⋊C₄	C₂³×C₃	semidirect
687. C₂×C₄²	C₂³×C₃	semidirect
719. C₂³×C₃	H(5,𝔽₂)	semidirect
773. C₂×C₃×C₄	H(5,𝔽₂)	semidirect
985. C₂³	C₃×H(5,𝔽₂)	semidirect
1039. C₂×C₄	C₃×H(5,𝔽₂)	semidirect
1098. C₃	#62818	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×#3542	2
C₃×#3537	2
C₃×#3536	2
C₃×#3534	2
C₃×#3519	2
C₃×#3505	2
C₃×#3496	2
C₃×#3494	2
C₃×#3492	2
C₃×#3490	2
C₃×#3488	2
C₃×#3484	2
C₂×C₃×#525	2
C₂²×C₃×#121	2
#62818	3

Subgroups — C3×#62818 #10681425

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#62818 #10681425