Subgroups — C₃×#62985 #10681592

Order 768.

7694 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#3522	C₂	1	4	yes	maximal, complemented
2	C₃×#3520	C₂	1	6	yes	maximal, complemented
3	C₃×#3517	C₂	1	2	yes	maximal, complemented
4	C₃×#3513	C₂	1	12	yes	maximal, complemented
5	C₃×#3511	C₂	1	3	yes	maximal, complemented
6	C₃×#3506	C₂	1	3	yes	maximal, complemented
7	C₃×#3503	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#3494	C₂	1	6	yes	maximal, complemented
9	C₃×#3492	C₂	1	6	yes	maximal, complemented
10	C₃×#3488	C₂	1	2	yes	maximal, complemented
11	C₃×#3482	C₂	1	2	yes	maximal, complemented
12	C₃×#3475	C₂	1	3	yes	maximal, complemented
13	C₃×D₄×#41	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×D₄×#41	C₂	1	6	yes	maximal, complemented
15	C₂×C₃×#547	C₂	1	3	yes	maximal, complemented
16	C₃×C₄×H(5,𝔽₂)	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₃×#520	C₂	1	2	yes	maximal, complemented
18	#62985	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₂×C₃×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
20	C₂²×C₃×#41	C₂²	1	2	yes	—
21	C₂²×C₃×#41	C₂²	1	6	yes	complemented
22	C₃×#559	C₂²	1	12	yes	complemented
23	C₃×Q₈²	C₂²	1	2	yes	complemented
24	C₃×#557	C₂²	1	2	yes	complemented
25	C₃×#556	C₂²	1	3	yes	complemented
26	C₃×#556	C₂²	1	6	yes	complemented
27	C₃×#555	C₂²	1	3	yes	complemented
28	C₃×#555	C₂²	1	6	yes	complemented
29	C₃×#554	C₂²	1	1	yes	characteristic, complemented
30	C₃×#554	C₂²	1	6	yes	complemented
31	C₃×#554	C₂²	1	12	yes	complemented
32	C₃×#554	C₂²	1	6	yes	complemented
33	C₃×#553	C₂²	1	6	yes	complemented
34	C₃×#553	C₂²	1	12	yes	complemented
35	C₃×#553	C₂²	1	12	yes	complemented
36	C₃×#553	C₂²	1	12	yes	complemented
37	C₃×#552	C₂²	1	6	yes	complemented
38	C₃×#552	C₂²	1	6	yes	complemented
39	C₃×#552	C₂²	1	12	yes	complemented
40	C₃×#551	C₂²	1	12	yes	complemented
41	C₃×#551	C₂²	1	24	yes	complemented
42	C₃×#550	C₂²	1	6	yes	complemented
43	C₃×#550	C₂²	1	1	yes	characteristic, complemented
44	C₃×#550	C₂²	1	4	yes	complemented
45	C₃×D₄×Q₈	C₂²	1	1	yes	characteristic, complemented
46	C₃×D₄×Q₈	C₂²	1	6	yes	complemented
47	C₃×#548	C₂²	1	12	yes	complemented
48	C₃×#548	C₂²	1	2	yes	complemented
49	C₃×#548	C₂²	1	4	yes	complemented
50	C₃×#547	C₂²	1	3	yes	complemented
51	C₃×#547	C₂²	1	6	yes	complemented
52	C₃×#547	C₂²	1	12	yes	complemented
53	C₃×#547	C₂²	1	6	yes	complemented
54	C₃×#547	C₂²	1	12	yes	complemented
55	C₃×#547	C₂²	1	6	yes	complemented
56	C₃×#547	C₂²	1	12	yes	complemented
57	C₃×#547	C₂²	1	3	yes	complemented
58	C₃×#546	C₂²	1	6	yes	complemented
59	C₃×#546	C₂²	1	24	yes	complemented
60	C₃×#546	C₂²	1	6	yes	complemented
61	C₃×#546	C₂²	1	12	yes	complemented
62	C₃×D₄²	C₂²	1	3	yes	complemented
63	C₃×D₄²	C₂²	1	12	yes	complemented
64	C₃×#544	C₂²	1	6	yes	complemented
65	C₃×#542	C₂²	1	12	yes	complemented
66	C₃×#542	C₂²	1	12	yes	complemented
67	C₃×#540	C₂²	1	12	yes	complemented
68	C₃×#539	C₂²	1	24	yes	complemented
69	C₃×#538	C₂²	1	12	yes	complemented
70	C₃×#537	C₂²	1	6	yes	complemented
71	C₃×#535	C₂²	1	6	yes	complemented
72	C₃×#533	C₂²	1	3	yes	complemented
73	C₃×#533	C₂²	1	6	yes	complemented
74	C₃×#532	C₂²	1	12	yes	complemented
75	C₃×#532	C₂²	1	3	yes	complemented
76	C₃×#532	C₂²	1	6	yes	complemented
77	C₂×C₃×C₄⋊Q₈	C₂²	1	3	yes	complemented
78	C₃×#529	C₂²	1	12	yes	complemented
79	C₃×#529	C₂²	1	6	yes	complemented
80	C₃×#529	C₂²	1	12	yes	complemented
81	C₃×#525	C₂²	1	6	yes	complemented
82	C₃×#525	C₂²	1	24	yes	complemented
83	C₃×#525	C₂²	1	12	yes	complemented
84	C₃×#525	C₂²	1	6	yes	complemented
85	C₂×C₃×#123	C₂²	1	12	yes	complemented
86	C₂×C₃×C₂²⋊Q₈	C₂²	1	6	yes	complemented
87	C₂×C₃×#121	C₂²	1	6	yes	complemented
88	C₃×#520	C₂²	1	1	yes	characteristic
89	C₃×#520	C₂²	1	2	yes	—
90	C₃×#520	C₂²	1	6	yes	complemented
91	C₃×#520	C₂²	1	6	yes	complemented
92	C₃×#520	C₂²	1	12	yes	complemented
93	C₃×#520	C₂²	1	4	yes	complemented
94	C₃×#520	C₂²	1	3	yes	complemented
95	C₃×#520	C₂²	1	2	yes	complemented
96	C₃×#518	C₂²	1	3	yes	complemented
97	C₃×#518	C₂²	1	6	yes	complemented
98	C₃×C₄×#41	C₂²	1	1	yes	characteristic
99	C₃×C₄×#41	C₂²	1	3	yes	complemented
100	C₃×C₄×#41	C₂²	1	2	yes	complemented
101	C₃×C₄×#41	C₂²	1	6	yes	complemented
102	C₂×C₃×C₄×Q₈	C₂²	1	4	yes	complemented
103	C₂×C₃×C₄×D₄	C₂²	1	12	yes	complemented
104	C₂×C₃×C₄×D₄	C₂²	1	3	yes	complemented
105	C₂×C₃×C₄×D₄	C₂²	1	6	yes	complemented
106	C₂×C₃×C₄×D₄	C₂²	1	3	yes	complemented
107	C₂×C₃×#117	C₂²	1	6	yes	complemented
108	C₂²×C₃×C₄⋊C₄	C₂²	1	6	yes	complemented
109	#3522	C₂×C₃	1	4	yes	complemented
110	#3520	C₂×C₃	1	6	yes	complemented
111	#3517	C₂×C₃	1	2	yes	complemented
112	#3513	C₂×C₃	1	12	yes	complemented
113	#3511	C₂×C₃	1	3	yes	complemented
114	#3506	C₂×C₃	1	3	yes	complemented
115	#3503	C₂×C₃	1	1	yes	characteristic, complemented
116	#3494	C₂×C₃	1	6	yes	complemented
117	#3492	C₂×C₃	1	6	yes	complemented
118	#3488	C₂×C₃	1	2	yes	complemented
119	#3482	C₂×C₃	1	2	yes	complemented
120	#3475	C₂×C₃	1	3	yes	complemented
121	D₄×#41	C₂×C₃	1	1	yes	characteristic, complemented
122	D₄×#41	C₂×C₃	1	6	yes	complemented
123	C₂×#547	C₂×C₃	1	3	yes	complemented
124	C₄×H(5,𝔽₂)	C₂×C₃	1	1	yes	characteristic, complemented
125	C₂×#520	C₂×C₃	1	2	yes	complemented
126	C₃×H(5,𝔽₂)	—	2	8	no	—
127	C₂×C₃×#41	—	2	16	no	—
128	C₂×C₃×#41	—	4	24	no	—
129	C₂×C₃×#41	C₂³	1	6	yes	—
130	C₂×C₃×#41	C₂³	1	6	yes	—
131	C₂×C₃×#41	C₂³	1	2	yes	—
132	C₂×C₃×#41	C₂³	1	6	yes	—
133	C₂×C₃×#41	C₂³	1	3	yes	—
134	C₂×C₃×#41	C₂³	1	2	yes	—
135	C₂×C₃×#41	C₂³	1	24	yes	—
136	C₂×C₃×#41	C₂³	1	12	yes	—
137	C₂×C₃×#41	C₂³	1	1	yes	characteristic
138	C₂²×C₃×Q₈	C₂³	1	2	yes	—
139	C₂²×C₃×Q₈	C₂³	1	6	yes	—
140	C₂²×C₃×D₄	C₂³	1	6	yes	—
141	C₂²×C₃×D₄	C₂³	1	3	yes	—
142	C₂²×C₃×D₄	C₂³	1	3	yes	—
143	C₂²×C₃×D₄	C₂³	1	6	yes	—
144	C₂²×C₃×D₄	C₂³	1	12	yes	—
145	C₂³×C₃×C₄	C₂³	1	6	yes	—
146	C₂³×C₃×C₄	C₂³	1	12	yes	—
147	C₂³×C₃×C₄	C₂³	1	6	yes	—
148	C₃×C₄⋊Q₈	C₂³	1	6	yes	—
149	C₃×C₄⋊Q₈	C₂³	1	12	yes	—
150	C₃×C₄⋊Q₈	C₂³	1	3	yes	—
151	C₃×C₄⋊Q₈	C₂³	1	6	yes	—
152	C₃×C₄⋊Q₈	C₂³	1	6	yes	—
153	C₃×C₄⋊Q₈	C₂³	1	3	yes	—
154	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
155	C₃×#127	C₂³	1	12	yes	—
156	C₃×#127	C₂³	1	3	yes	—
157	C₃×#126	C₂³	1	24	yes	—
158	C₃×#126	C₂³	1	12	yes	—
159	C₃×#126	C₂³	1	12	yes	—
160	C₃×#126	C₂³	1	12	yes	—
161	C₃×#125	C₂³	1	2	yes	—
162	C₃×#125	C₂³	1	12	yes	—
163	C₃×#125	C₂³	1	12	yes	—
164	C₃×#125	C₂³	1	12	yes	—
165	C₃×#125	C₂³	1	6	yes	—
166	C₃×#124	C₂³	1	12	yes	—
167	C₃×#124	C₂³	1	6	yes	—
168	C₃×#124	C₂³	1	12	yes	—
169	C₃×#124	C₂³	1	6	yes	—
170	C₃×#124	C₂³	1	24	yes	—
171	C₃×#123	C₂³	1	24	yes	—
172	C₃×#123	C₂³	1	24	yes	—
173	C₃×#123	C₂³	1	12	yes	—
174	C₃×#123	C₂³	1	24	yes	—
175	C₃×#123	C₂³	1	24	yes	—
176	C₃×#123	C₂³	1	12	yes	—
177	C₃×#123	C₂³	1	12	yes	—
178	C₃×#123	C₂³	1	12	yes	—
179	C₃×#123	C₂³	1	12	yes	—
180	C₃×C₂²⋊Q₈	C₂³	1	6	yes	—
181	C₃×C₂²⋊Q₈	C₂³	1	12	yes	—
182	C₃×C₂²⋊Q₈	C₂³	1	24	yes	—
183	C₃×C₂²⋊Q₈	C₂³	1	2	yes	—
184	C₃×C₂²⋊Q₈	C₂³	1	6	yes	—
185	C₃×C₂²⋊Q₈	C₂³	1	6	yes	—
186	C₃×C₂²⋊Q₈	C₂³	1	6	yes	—
187	C₃×C₂²⋊Q₈	C₂³	1	24	yes	—
188	C₃×C₂²⋊Q₈	C₂³	1	24	yes	—
189	C₃×C₂²⋊Q₈	C₂³	1	6	yes	—
190	C₃×C₂²⋊Q₈	C₂³	1	4	yes	—
191	C₃×C₂²⋊Q₈	C₂³	1	12	yes	—
192	C₃×C₂²⋊Q₈	C₂³	1	6	yes	—
193	C₃×#121	C₂³	1	6	yes	—
194	C₃×#121	C₂³	1	12	yes	—
195	C₃×#121	C₂³	1	12	yes	—
196	C₃×#121	C₂³	1	12	yes	—
197	C₃×#121	C₂³	1	6	yes	—
198	C₃×#121	C₂³	1	6	yes	—
199	C₃×#121	C₂³	1	6	yes	—
200	C₃×#121	C₂³	1	6	yes	—
201	C₃×#121	C₂³	1	24	yes	—
202	C₃×#121	C₂³	1	24	yes	—
203	C₃×#121	C₂³	1	6	yes	—
204	C₃×#121	C₂³	1	12	yes	—
205	C₃×#121	C₂³	1	12	yes	—
206	C₃×#121	C₂³	1	6	yes	—
207	C₃×#121	C₂³	1	12	yes	—
208	C₃×#120	C₂³	1	12	yes	—
209	C₃×#120	C₂³	1	12	yes	—
210	C₃×#120	C₂³	1	24	yes	—
211	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
212	C₃×C₄×Q₈	C₂³	1	6	yes	—
213	C₃×C₄×Q₈	C₂³	1	4	yes	—
214	C₃×C₄×Q₈	C₂³	1	12	yes	—
215	C₃×C₄×Q₈	C₂³	1	2	yes	—
216	C₃×C₄×Q₈	C₂³	1	12	yes	—
217	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
218	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
219	C₃×C₄×Q₈	C₂³	1	3	yes	—
220	C₃×C₄×Q₈	C₂³	1	6	yes	—
221	C₃×C₄×Q₈	C₂³	1	6	yes	—
222	C₃×C₄×D₄	C₂³	1	6	yes	—
223	C₃×C₄×D₄	C₂³	1	12	yes	—
224	C₃×C₄×D₄	C₂³	1	24	yes	—
225	C₃×C₄×D₄	C₂³	1	6	yes	—
226	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
227	C₃×C₄×D₄	C₂³	1	3	yes	—
228	C₃×C₄×D₄	C₂³	1	6	yes	—
229	C₃×C₄×D₄	C₂³	1	3	yes	—
230	C₃×C₄×D₄	C₂³	1	6	yes	—
231	C₃×C₄×D₄	C₂³	1	3	yes	—
232	C₃×C₄×D₄	C₂³	1	12	yes	—
233	C₃×C₄×D₄	C₂³	1	6	yes	—
234	C₃×C₄×D₄	C₂³	1	6	yes	—
235	C₃×C₄×D₄	C₂³	1	12	yes	—
236	C₃×C₄×D₄	C₂³	1	24	yes	—
237	C₃×C₄×D₄	C₂³	1	12	yes	—
238	C₃×C₄×D₄	C₂³	1	24	yes	—
239	C₃×C₄×D₄	C₂³	1	6	yes	—
240	C₃×C₄×D₄	C₂³	1	6	yes	—
241	C₃×C₄×D₄	C₂³	1	3	yes	—
242	C₃×C₄×D₄	C₂³	1	3	yes	—
243	C₃×C₄×D₄	C₂³	1	3	yes	—
244	C₃×C₄×D₄	C₂³	1	2	yes	—
245	C₃×C₄×D₄	C₂³	1	6	yes	—
246	C₃×C₄×D₄	C₂³	1	6	yes	—
247	C₃×C₄×D₄	C₂³	1	3	yes	—
248	C₃×C₄×D₄	C₂³	1	12	yes	—
249	C₃×C₄×D₄	C₂³	1	12	yes	—
250	C₃×C₄×D₄	C₂³	1	12	yes	—
251	C₃×C₄×D₄	C₂³	1	6	yes	—
252	C₃×C₄×D₄	C₂³	1	12	yes	—
253	C₃×#117	C₂³	1	3	yes	—
254	C₃×#117	C₂³	1	6	yes	—
255	C₃×#117	C₂³	1	12	yes	—
256	C₃×#117	C₂³	1	12	yes	—
257	C₃×#117	C₂³	1	6	yes	—
258	C₃×#117	C₂³	1	6	yes	—
259	C₃×#117	C₂³	1	3	yes	—
260	C₃×#117	C₂³	1	6	yes	—
261	C₃×#117	C₂³	1	6	yes	—
262	C₃×#117	C₂³	1	12	yes	—
263	C₃×#117	C₂³	1	6	yes	—
264	C₃×#117	C₂³	1	12	yes	—
265	C₂×C₃×C₄⋊C₄	C₂³	1	6	yes	—
266	C₂×C₃×C₄⋊C₄	C₂³	1	3	yes	—
267	C₂×C₃×C₄⋊C₄	C₂³	1	12	yes	—
268	C₂×C₃×C₄⋊C₄	C₂³	1	6	yes	—
269	C₂×C₃×C₄⋊C₄	C₂³	1	12	yes	—
270	C₂×C₃×C₄⋊C₄	C₂³	1	12	yes	—
271	C₂×C₃×C₄⋊C₄	C₂³	1	12	yes	—
272	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
273	C₂×C₃×C₄⋊C₄	C₂³	1	6	yes	—
274	C₂×C₃×C₄⋊C₄	C₂³	1	3	yes	—
275	C₂×C₃×C₄⋊C₄	C₂³	1	6	yes	—
276	C₂×C₃×C₂²⋊C₄	C₂³	1	12	yes	—
277	C₂×C₃×C₂²⋊C₄	C₂³	1	6	yes	—
278	C₂×C₃×C₂²⋊C₄	C₂³	1	12	yes	—
279	C₂×C₃×C₂²⋊C₄	C₂³	1	6	yes	—
280	C₂×C₃×C₂²⋊C₄	C₂³	1	12	yes	—
281	C₂×C₃×C₄²	C₂³	1	12	yes	—
282	C₂×C₃×C₄²	C₂³	1	3	yes	—
283	C₂×C₃×C₄²	C₂³	1	6	yes	—
284	C₂×H(5,𝔽₂)	C₂²×C₃	1	1	yes	characteristic
285	C₂²×#41	C₂²×C₃	1	2	yes	—
286	C₂²×#41	C₂²×C₃	1	6	yes	complemented
287	#559	C₂²×C₃	1	12	yes	complemented
288	Q₈²	C₂²×C₃	1	2	yes	complemented
289	#557	C₂²×C₃	1	2	yes	complemented
290	#556	C₂²×C₃	1	3	yes	complemented
291	#556	C₂²×C₃	1	6	yes	complemented
292	#555	C₂²×C₃	1	3	yes	complemented
293	#555	C₂²×C₃	1	6	yes	complemented
294	#554	C₂²×C₃	1	1	yes	characteristic, complemented
295	#554	C₂²×C₃	1	6	yes	complemented
296	#554	C₂²×C₃	1	12	yes	complemented
297	#554	C₂²×C₃	1	6	yes	complemented
298	#553	C₂²×C₃	1	6	yes	complemented
299	#553	C₂²×C₃	1	12	yes	complemented
300	#553	C₂²×C₃	1	12	yes	complemented
301	#553	C₂²×C₃	1	12	yes	complemented
302	#552	C₂²×C₃	1	6	yes	complemented
303	#552	C₂²×C₃	1	6	yes	complemented
304	#552	C₂²×C₃	1	12	yes	complemented
305	#551	C₂²×C₃	1	12	yes	complemented
306	#551	C₂²×C₃	1	24	yes	complemented
307	#550	C₂²×C₃	1	6	yes	complemented
308	#550	C₂²×C₃	1	1	yes	characteristic, complemented
309	#550	C₂²×C₃	1	4	yes	complemented
310	D₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
311	D₄×Q₈	C₂²×C₃	1	6	yes	complemented
312	#548	C₂²×C₃	1	12	yes	complemented
313	#548	C₂²×C₃	1	2	yes	complemented
314	#548	C₂²×C₃	1	4	yes	complemented
315	#547	C₂²×C₃	1	3	yes	complemented
316	#547	C₂²×C₃	1	6	yes	complemented
317	#547	C₂²×C₃	1	12	yes	complemented
318	#547	C₂²×C₃	1	6	yes	complemented
319	#547	C₂²×C₃	1	12	yes	complemented
320	#547	C₂²×C₃	1	6	yes	complemented
321	#547	C₂²×C₃	1	12	yes	complemented
322	#547	C₂²×C₃	1	3	yes	complemented
323	#546	C₂²×C₃	1	6	yes	complemented
324	#546	C₂²×C₃	1	24	yes	complemented
325	#546	C₂²×C₃	1	6	yes	complemented
326	#546	C₂²×C₃	1	12	yes	complemented
327	D₄²	C₂²×C₃	1	3	yes	complemented
328	D₄²	C₂²×C₃	1	12	yes	complemented
329	#544	C₂²×C₃	1	6	yes	complemented
330	#542	C₂²×C₃	1	12	yes	complemented
331	#542	C₂²×C₃	1	12	yes	complemented
332	#540	C₂²×C₃	1	12	yes	complemented
333	#539	C₂²×C₃	1	24	yes	complemented
334	#538	C₂²×C₃	1	12	yes	complemented
335	#537	C₂²×C₃	1	6	yes	complemented
336	#535	C₂²×C₃	1	6	yes	complemented
337	#533	C₂²×C₃	1	3	yes	complemented
338	#533	C₂²×C₃	1	6	yes	complemented
339	#532	C₂²×C₃	1	12	yes	complemented
340	#532	C₂²×C₃	1	3	yes	complemented
341	#532	C₂²×C₃	1	6	yes	complemented
342	C₂×C₄⋊Q₈	C₂²×C₃	1	3	yes	complemented
343	#529	C₂²×C₃	1	12	yes	complemented
344	#529	C₂²×C₃	1	6	yes	complemented
345	#529	C₂²×C₃	1	12	yes	complemented
346	#525	C₂²×C₃	1	6	yes	complemented
347	#525	C₂²×C₃	1	24	yes	complemented
348	#525	C₂²×C₃	1	12	yes	complemented
349	#525	C₂²×C₃	1	6	yes	complemented
350	C₂×#123	C₂²×C₃	1	12	yes	complemented
351	C₂×C₂²⋊Q₈	C₂²×C₃	1	6	yes	complemented
352	C₂×#121	C₂²×C₃	1	6	yes	complemented
353	#520	C₂²×C₃	1	1	yes	characteristic
354	#520	C₂²×C₃	1	2	yes	—
355	#520	C₂²×C₃	1	6	yes	complemented
356	#520	C₂²×C₃	1	6	yes	complemented
357	#520	C₂²×C₃	1	12	yes	complemented
358	#520	C₂²×C₃	1	4	yes	complemented
359	#520	C₂²×C₃	1	3	yes	complemented
360	#520	C₂²×C₃	1	2	yes	complemented
361	#518	C₂²×C₃	1	3	yes	complemented
362	#518	C₂²×C₃	1	6	yes	complemented
363	C₄×#41	C₂²×C₃	1	1	yes	characteristic
364	C₄×#41	C₂²×C₃	1	3	yes	complemented
365	C₄×#41	C₂²×C₃	1	2	yes	complemented
366	C₄×#41	C₂²×C₃	1	6	yes	complemented
367	C₂×C₄×Q₈	C₂²×C₃	1	4	yes	complemented
368	C₂×C₄×D₄	C₂²×C₃	1	12	yes	complemented
369	C₂×C₄×D₄	C₂²×C₃	1	3	yes	complemented
370	C₂×C₄×D₄	C₂²×C₃	1	6	yes	complemented
371	C₂×C₄×D₄	C₂²×C₃	1	3	yes	complemented
372	C₂×#117	C₂²×C₃	1	6	yes	complemented
373	C₂²×C₄⋊C₄	C₂²×C₃	1	6	yes	complemented
374	C₂⁴×C₃	C₂⁴	1	6	yes	—
375	C₂⁴×C₃	C₂⁴	1	6	yes	—
376	C₃×#41	—	2	8	no	—
377	C₃×#41	—	2	8	no	—
378	C₃×#41	—	2	24	no	—
379	C₃×#41	—	2	24	no	—
380	C₃×#41	—	2	24	no	—
381	C₃×#41	—	2	12	no	—
382	C₃×#41	—	4	48	no	—
383	C₃×#41	—	4	24	no	—
384	C₃×#41	#41	1	8	yes	complemented
385	C₂×C₃×Q₈	—	2	8	no	—
386	C₂×C₃×Q₈	—	4	12	no	—
387	C₂×C₃×Q₈	C₂⁴	1	1	yes	characteristic
388	C₂×C₃×Q₈	C₂⁴	1	6	yes	—
389	C₂×C₃×Q₈	C₂⁴	1	6	yes	—
390	C₂×C₃×Q₈	C₂⁴	1	2	yes	—
391	C₂×C₃×Q₈	C₂⁴	1	12	yes	—
392	C₂×C₃×Q₈	C₂⁴	1	1	yes	characteristic
393	C₂×C₃×D₄	—	2	24	no	—
394	C₂×C₃×D₄	—	2	24	no	—
395	C₂×C₃×D₄	—	2	12	no	—
396	C₂×C₃×D₄	—	2	12	no	—
397	C₂×C₃×D₄	—	4	24	no	—
398	C₂×C₃×D₄	C₂⁴	1	12	yes	—
399	C₂×C₃×D₄	C₂⁴	1	6	yes	—
400	C₂×C₃×D₄	C₂⁴	1	3	yes	—
401	C₂×C₃×D₄	C₂⁴	1	6	yes	—
402	C₂×C₃×D₄	C₂⁴	1	6	yes	—
403	C₂×C₃×D₄	C₂⁴	1	6	yes	—
404	C₂×C₃×D₄	C₂⁴	1	12	yes	—
405	C₂×C₃×D₄	C₂⁴	1	3	yes	—
406	C₂×C₃×D₄	C₂⁴	1	12	yes	—
407	C₂×C₃×D₄	C₂⁴	1	6	yes	—
408	C₂×C₃×D₄	C₂⁴	1	24	yes	—
409	C₂×C₃×D₄	C₂⁴	1	3	yes	—
410	C₂×C₃×D₄	C₂⁴	1	1	yes	characteristic
411	C₂²×C₃×C₄	—	2	24	no	—
412	C₂²×C₃×C₄	—	4	12	no	—
413	C₂²×C₃×C₄	—	4	24	no	—
414	C₂²×C₃×C₄	C₂⁴	1	6	yes	—
415	C₂²×C₃×C₄	C₂⁴	1	12	yes	—
416	C₂²×C₃×C₄	C₂⁴	1	6	yes	—
417	C₂²×C₃×C₄	C₂⁴	1	3	yes	—
418	C₂²×C₃×C₄	C₂⁴	1	6	yes	—
419	C₂²×C₃×C₄	C₂⁴	1	6	yes	—
420	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
421	C₂²×C₃×C₄	C₂⁴	1	6	yes	—
422	C₂²×C₃×C₄	C₂⁴	1	6	yes	—
423	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
424	C₂²×C₃×C₄	C₂⁴	1	3	yes	—
425	C₂²×C₃×C₄	C₂⁴	1	6	yes	—
426	C₂²×C₃×C₄	C₂⁴	1	6	yes	—
427	C₂²×C₃×C₄	C₂⁴	1	12	yes	—
428	C₂²×C₃×C₄	C₂⁴	1	12	yes	—
429	C₂²×C₃×C₄	C₂⁴	1	24	yes	—
430	C₂²×C₃×C₄	C₂⁴	1	3	yes	—
431	C₃×C₄⋊C₄	C₂⁴	1	3	yes	—
432	C₃×C₄⋊C₄	C₂⁴	1	6	yes	—
433	C₃×C₄⋊C₄	C₂⁴	1	6	yes	—
434	C₃×C₄⋊C₄	C₂⁴	1	12	yes	—
435	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
436	C₃×C₄⋊C₄	C₂⁴	1	12	yes	—
437	C₃×C₄⋊C₄	C₂⁴	1	24	yes	—
438	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
439	C₃×C₄⋊C₄	C₂⁴	1	3	yes	—
440	C₃×C₄⋊C₄	C₂⁴	1	6	yes	—
441	C₃×C₄⋊C₄	C₂⁴	1	6	yes	—
442	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
443	C₃×C₄⋊C₄	C₂⁴	1	4	yes	—
444	C₃×C₄⋊C₄	C₂⁴	1	3	yes	—
445	C₃×C₄⋊C₄	C₂⁴	1	12	yes	—
446	C₃×C₄⋊C₄	C₂⁴	1	6	yes	—
447	C₃×C₄⋊C₄	C₂⁴	1	3	yes	—
448	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
449	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
450	C₃×C₄⋊C₄	C₂⁴	1	6	yes	—
451	C₃×C₄⋊C₄	C₂⁴	1	12	yes	—
452	C₃×C₄⋊C₄	C₂⁴	1	12	yes	—
453	C₃×C₄⋊C₄	C₂⁴	1	4	yes	—
454	C₃×C₄⋊C₄	C₂⁴	1	12	yes	—
455	C₃×C₂²⋊C₄	C₂⁴	1	6	yes	—
456	C₃×C₂²⋊C₄	C₂⁴	1	2	yes	—
457	C₃×C₂²⋊C₄	C₂⁴	1	6	yes	—
458	C₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
459	C₃×C₂²⋊C₄	C₂⁴	1	6	yes	—
460	C₃×C₂²⋊C₄	C₂⁴	1	6	yes	—
461	C₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
462	C₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
463	C₃×C₂²⋊C₄	C₂⁴	1	6	yes	—
464	C₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
465	C₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
466	C₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
467	C₃×C₂²⋊C₄	C₂⁴	1	6	yes	—
468	C₃×C₂²⋊C₄	C₂⁴	1	6	yes	—
469	C₃×C₂²⋊C₄	C₂⁴	1	4	yes	—
470	C₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
471	C₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
472	C₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
473	C₃×C₄²	C₂⁴	1	6	yes	—
474	C₃×C₄²	C₂⁴	1	1	yes	characteristic
475	C₃×C₄²	C₂⁴	1	3	yes	—
476	C₃×C₄²	C₂⁴	1	2	yes	—
477	C₃×C₄²	C₂⁴	1	6	yes	—
478	C₃×C₄²	C₂⁴	1	12	yes	—
479	C₃×C₄²	C₂⁴	1	12	yes	—
480	C₃×C₄²	C₂⁴	1	3	yes	—
481	C₃×C₄²	C₂⁴	1	3	yes	—
482	C₃×C₄²	C₂⁴	1	12	yes	—
483	H(5,𝔽₂)	—	2	8	no	—
484	C₂×#41	—	2	16	no	—
485	C₂×#41	—	4	24	no	—
486	C₂×#41	C₂³×C₃	1	3	yes	—
487	C₂×#41	C₂³×C₃	1	2	yes	—
488	C₂×#41	C₂³×C₃	1	6	yes	—
489	C₂×#41	C₂³×C₃	1	6	yes	—
490	C₂×#41	C₂³×C₃	1	6	yes	—
491	C₂×#41	C₂³×C₃	1	2	yes	—
492	C₂×#41	C₂³×C₃	1	24	yes	—
493	C₂×#41	C₂³×C₃	1	12	yes	—
494	C₂×#41	C₂³×C₃	1	1	yes	characteristic
495	C₂²×Q₈	C₂³×C₃	1	2	yes	—
496	C₂²×Q₈	C₂³×C₃	1	6	yes	—
497	C₂²×D₄	C₂³×C₃	1	6	yes	—
498	C₂²×D₄	C₂³×C₃	1	3	yes	—
499	C₂²×D₄	C₂³×C₃	1	6	yes	—
500	C₂²×D₄	C₂³×C₃	1	3	yes	—
501	C₂²×D₄	C₂³×C₃	1	12	yes	—
502	C₂³×C₄	C₂³×C₃	1	6	yes	—
503	C₂³×C₄	C₂³×C₃	1	12	yes	—
504	C₂³×C₄	C₂³×C₃	1	6	yes	—
505	C₄⋊Q₈	C₂³×C₃	1	3	yes	—
506	C₄⋊Q₈	C₂³×C₃	1	6	yes	—
507	C₄⋊Q₈	C₂³×C₃	1	6	yes	—
508	C₄⋊Q₈	C₂³×C₃	1	6	yes	—
509	C₄⋊Q₈	C₂³×C₃	1	3	yes	—
510	C₄⋊Q₈	C₂³×C₃	1	12	yes	—
511	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
512	#127	C₂³×C₃	1	3	yes	—
513	#127	C₂³×C₃	1	12	yes	—
514	#126	C₂³×C₃	1	24	yes	—
515	#126	C₂³×C₃	1	12	yes	—
516	#126	C₂³×C₃	1	12	yes	—
517	#126	C₂³×C₃	1	12	yes	—
518	#125	C₂³×C₃	1	2	yes	—
519	#125	C₂³×C₃	1	12	yes	—
520	#125	C₂³×C₃	1	12	yes	—
521	#125	C₂³×C₃	1	12	yes	—
522	#125	C₂³×C₃	1	6	yes	—
523	#124	C₂³×C₃	1	6	yes	—
524	#124	C₂³×C₃	1	12	yes	—
525	#124	C₂³×C₃	1	12	yes	—
526	#124	C₂³×C₃	1	24	yes	—
527	#124	C₂³×C₃	1	6	yes	—
528	#123	C₂³×C₃	1	12	yes	—
529	#123	C₂³×C₃	1	24	yes	—
530	#123	C₂³×C₃	1	24	yes	—
531	#123	C₂³×C₃	1	24	yes	—
532	#123	C₂³×C₃	1	12	yes	—
533	#123	C₂³×C₃	1	12	yes	—
534	#123	C₂³×C₃	1	12	yes	—
535	#123	C₂³×C₃	1	24	yes	—
536	#123	C₂³×C₃	1	12	yes	—
537	C₂²⋊Q₈	C₂³×C₃	1	6	yes	—
538	C₂²⋊Q₈	C₂³×C₃	1	12	yes	—
539	C₂²⋊Q₈	C₂³×C₃	1	24	yes	—
540	C₂²⋊Q₈	C₂³×C₃	1	2	yes	—
541	C₂²⋊Q₈	C₂³×C₃	1	6	yes	—
542	C₂²⋊Q₈	C₂³×C₃	1	6	yes	—
543	C₂²⋊Q₈	C₂³×C₃	1	6	yes	—
544	C₂²⋊Q₈	C₂³×C₃	1	24	yes	—
545	C₂²⋊Q₈	C₂³×C₃	1	24	yes	—
546	C₂²⋊Q₈	C₂³×C₃	1	6	yes	—
547	C₂²⋊Q₈	C₂³×C₃	1	4	yes	—
548	C₂²⋊Q₈	C₂³×C₃	1	12	yes	—
549	C₂²⋊Q₈	C₂³×C₃	1	6	yes	—
550	#121	C₂³×C₃	1	6	yes	—
551	#121	C₂³×C₃	1	12	yes	—
552	#121	C₂³×C₃	1	12	yes	—
553	#121	C₂³×C₃	1	12	yes	—
554	#121	C₂³×C₃	1	6	yes	—
555	#121	C₂³×C₃	1	6	yes	—
556	#121	C₂³×C₃	1	6	yes	—
557	#121	C₂³×C₃	1	6	yes	—
558	#121	C₂³×C₃	1	24	yes	—
559	#121	C₂³×C₃	1	24	yes	—
560	#121	C₂³×C₃	1	6	yes	—
561	#121	C₂³×C₃	1	12	yes	—
562	#121	C₂³×C₃	1	12	yes	—
563	#121	C₂³×C₃	1	6	yes	—
564	#121	C₂³×C₃	1	12	yes	—
565	#120	C₂³×C₃	1	12	yes	—
566	#120	C₂³×C₃	1	12	yes	—
567	#120	C₂³×C₃	1	24	yes	—
568	C₄×Q₈	C₂³×C₃	1	2	yes	—
569	C₄×Q₈	C₂³×C₃	1	4	yes	—
570	C₄×Q₈	C₂³×C₃	1	12	yes	—
571	C₄×Q₈	C₂³×C₃	1	12	yes	—
572	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
573	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
574	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
575	C₄×Q₈	C₂³×C₃	1	3	yes	—
576	C₄×Q₈	C₂³×C₃	1	6	yes	—
577	C₄×Q₈	C₂³×C₃	1	6	yes	—
578	C₄×Q₈	C₂³×C₃	1	6	yes	—
579	C₄×D₄	C₂³×C₃	1	6	yes	—
580	C₄×D₄	C₂³×C₃	1	1	yes	characteristic
581	C₄×D₄	C₂³×C₃	1	3	yes	—
582	C₄×D₄	C₂³×C₃	1	6	yes	—
583	C₄×D₄	C₂³×C₃	1	3	yes	—
584	C₄×D₄	C₂³×C₃	1	6	yes	—
585	C₄×D₄	C₂³×C₃	1	3	yes	—
586	C₄×D₄	C₂³×C₃	1	12	yes	—
587	C₄×D₄	C₂³×C₃	1	6	yes	—
588	C₄×D₄	C₂³×C₃	1	6	yes	—
589	C₄×D₄	C₂³×C₃	1	6	yes	—
590	C₄×D₄	C₂³×C₃	1	12	yes	—
591	C₄×D₄	C₂³×C₃	1	24	yes	—
592	C₄×D₄	C₂³×C₃	1	12	yes	—
593	C₄×D₄	C₂³×C₃	1	24	yes	—
594	C₄×D₄	C₂³×C₃	1	12	yes	—
595	C₄×D₄	C₂³×C₃	1	6	yes	—
596	C₄×D₄	C₂³×C₃	1	6	yes	—
597	C₄×D₄	C₂³×C₃	1	3	yes	—
598	C₄×D₄	C₂³×C₃	1	3	yes	—
599	C₄×D₄	C₂³×C₃	1	3	yes	—
600	C₄×D₄	C₂³×C₃	1	2	yes	—
601	C₄×D₄	C₂³×C₃	1	6	yes	—
602	C₄×D₄	C₂³×C₃	1	6	yes	—
603	C₄×D₄	C₂³×C₃	1	3	yes	—
604	C₄×D₄	C₂³×C₃	1	12	yes	—
605	C₄×D₄	C₂³×C₃	1	12	yes	—
606	C₄×D₄	C₂³×C₃	1	24	yes	—
607	C₄×D₄	C₂³×C₃	1	12	yes	—
608	C₄×D₄	C₂³×C₃	1	6	yes	—
609	C₄×D₄	C₂³×C₃	1	12	yes	—
610	#117	C₂³×C₃	1	3	yes	—
611	#117	C₂³×C₃	1	6	yes	—
612	#117	C₂³×C₃	1	12	yes	—
613	#117	C₂³×C₃	1	12	yes	—
614	#117	C₂³×C₃	1	6	yes	—
615	#117	C₂³×C₃	1	6	yes	—
616	#117	C₂³×C₃	1	3	yes	—
617	#117	C₂³×C₃	1	6	yes	—
618	#117	C₂³×C₃	1	6	yes	—
619	#117	C₂³×C₃	1	12	yes	—
620	#117	C₂³×C₃	1	6	yes	—
621	#117	C₂³×C₃	1	12	yes	—
622	C₂×C₄⋊C₄	C₂³×C₃	1	6	yes	—
623	C₂×C₄⋊C₄	C₂³×C₃	1	3	yes	—
624	C₂×C₄⋊C₄	C₂³×C₃	1	12	yes	—
625	C₂×C₄⋊C₄	C₂³×C₃	1	6	yes	—
626	C₂×C₄⋊C₄	C₂³×C₃	1	12	yes	—
627	C₂×C₄⋊C₄	C₂³×C₃	1	12	yes	—
628	C₂×C₄⋊C₄	C₂³×C₃	1	12	yes	—
629	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
630	C₂×C₄⋊C₄	C₂³×C₃	1	6	yes	—
631	C₂×C₄⋊C₄	C₂³×C₃	1	3	yes	—
632	C₂×C₄⋊C₄	C₂³×C₃	1	6	yes	—
633	C₂×C₂²⋊C₄	C₂³×C₃	1	12	yes	—
634	C₂×C₂²⋊C₄	C₂³×C₃	1	6	yes	—
635	C₂×C₂²⋊C₄	C₂³×C₃	1	12	yes	—
636	C₂×C₂²⋊C₄	C₂³×C₃	1	6	yes	—
637	C₂×C₂²⋊C₄	C₂³×C₃	1	12	yes	—
638	C₂×C₄²	C₂³×C₃	1	12	yes	—
639	C₂×C₄²	C₂³×C₃	1	3	yes	—
640	C₂×C₄²	C₂³×C₃	1	6	yes	—
641	C₂³×C₃	—	2	12	no	—
642	C₂³×C₃	—	2	12	no	—
643	C₂³×C₃	—	2	12	no	—
644	C₂³×C₃	—	4	6	no	—
645	C₂³×C₃	—	4	6	no	—
646	C₂³×C₃	—	4	6	no	—
647	C₂³×C₃	C₂⁵	1	6	yes	—
648	C₂³×C₃	C₂⁵	1	6	yes	—
649	C₂³×C₃	C₂⁵	1	3	yes	—
650	C₂³×C₃	C₂⁵	1	2	yes	—
651	C₃×Q₈	—	2	12	no	—
652	C₃×Q₈	—	2	2	no	—
653	C₃×Q₈	—	2	12	no	—
654	C₃×Q₈	—	4	12	no	—
655	C₃×Q₈	—	4	2	no	—
656	C₃×Q₈	C₂×#41	1	4	yes	complemented
657	C₃×D₄	—	2	12	no	—
658	C₃×D₄	—	2	24	no	—
659	C₃×D₄	—	2	12	no	—
660	C₃×D₄	—	2	24	no	—
661	C₃×D₄	—	2	6	no	—
662	C₃×D₄	—	2	12	no	—
663	C₃×D₄	—	2	12	no	—
664	C₃×D₄	—	2	6	no	—
665	C₃×D₄	—	4	24	no	—
666	C₃×D₄	—	4	6	no	—
667	C₃×D₄	—	4	12	no	—
668	C₃×D₄	C₂×#41	1	12	yes	complemented
669	C₃×D₄	H(5,𝔽₂)	1	4	yes	complemented
670	C₂×C₃×C₄	—	2	12	no	—
671	C₂×C₃×C₄	—	2	24	no	—
672	C₂×C₃×C₄	—	2	4	no	—
673	C₂×C₃×C₄	—	2	12	no	—
674	C₂×C₃×C₄	—	2	12	no	—
675	C₂×C₃×C₄	—	2	12	no	—
676	C₂×C₃×C₄	—	2	12	no	—
677	C₂×C₃×C₄	—	2	6	no	—
678	C₂×C₃×C₄	—	2	12	no	—
679	C₂×C₃×C₄	—	4	6	no	—
680	C₂×C₃×C₄	—	4	12	no	—
681	C₂×C₃×C₄	—	4	12	no	—
682	C₂×C₃×C₄	—	4	24	no	—
683	C₂×C₃×C₄	—	4	6	no	—
684	C₂×C₃×C₄	—	4	4	no	—
685	C₂×C₃×C₄	—	4	3	no	—
686	C₂×C₃×C₄	C₂×#41	1	12	yes	complemented
687	C₂×C₃×C₄	C₂⁵	1	2	yes	—
688	C₂×C₃×C₄	C₂⁵	1	4	yes	—
689	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
690	C₂×C₃×C₄	C₂⁵	1	3	yes	—
691	C₂×C₃×C₄	C₂⁵	1	6	yes	—
692	C₂×C₃×C₄	C₂⁵	1	2	yes	—
693	C₂×C₃×C₄	C₂⁵	1	6	yes	—
694	C₂×C₃×C₄	C₂⁵	1	3	yes	—
695	C₂×C₃×C₄	C₂⁵	1	12	yes	—
696	C₂×C₃×C₄	C₂⁵	1	2	yes	—
697	C₂×C₃×C₄	C₂⁵	1	3	yes	—
698	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
699	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
700	C₂⁴	C₂⁴×C₃	1	6	yes	—
701	C₂⁴	C₂⁴×C₃	1	6	yes	—
702	#41	—	2	8	no	—
703	#41	—	2	8	no	—
704	#41	—	2	24	no	—
705	#41	—	2	24	no	—
706	#41	—	2	24	no	—
707	#41	—	2	12	no	—
708	#41	—	4	48	no	—
709	#41	—	4	24	no	—
710	#41	C₃×#41	1	8	yes	complemented
711	C₂×Q₈	—	2	8	no	—
712	C₂×Q₈	—	4	12	no	—
713	C₂×Q₈	C₂⁴×C₃	1	1	yes	characteristic
714	C₂×Q₈	C₂⁴×C₃	1	6	yes	—
715	C₂×Q₈	C₂⁴×C₃	1	6	yes	—
716	C₂×Q₈	C₂⁴×C₃	1	2	yes	—
717	C₂×Q₈	C₂⁴×C₃	1	12	yes	—
718	C₂×Q₈	C₂⁴×C₃	1	1	yes	characteristic
719	C₂×D₄	—	2	24	no	—
720	C₂×D₄	—	2	24	no	—
721	C₂×D₄	—	2	12	no	—
722	C₂×D₄	—	2	12	no	—
723	C₂×D₄	—	4	24	no	—
724	C₂×D₄	C₂⁴×C₃	1	12	yes	—
725	C₂×D₄	C₂⁴×C₃	1	6	yes	—
726	C₂×D₄	C₂⁴×C₃	1	3	yes	—
727	C₂×D₄	C₂⁴×C₃	1	6	yes	—
728	C₂×D₄	C₂⁴×C₃	1	6	yes	—
729	C₂×D₄	C₂⁴×C₃	1	6	yes	—
730	C₂×D₄	C₂⁴×C₃	1	12	yes	—
731	C₂×D₄	C₂⁴×C₃	1	3	yes	—
732	C₂×D₄	C₂⁴×C₃	1	12	yes	—
733	C₂×D₄	C₂⁴×C₃	1	6	yes	—
734	C₂×D₄	C₂⁴×C₃	1	24	yes	—
735	C₂×D₄	C₂⁴×C₃	1	3	yes	—
736	C₂×D₄	C₂⁴×C₃	1	1	yes	characteristic
737	C₂²×C₄	—	2	24	no	—
738	C₂²×C₄	—	4	12	no	—
739	C₂²×C₄	—	4	24	no	—
740	C₂²×C₄	C₂⁴×C₃	1	6	yes	—
741	C₂²×C₄	C₂⁴×C₃	1	12	yes	—
742	C₂²×C₄	C₂⁴×C₃	1	6	yes	—
743	C₂²×C₄	C₂⁴×C₃	1	3	yes	—
744	C₂²×C₄	C₂⁴×C₃	1	6	yes	—
745	C₂²×C₄	C₂⁴×C₃	1	6	yes	—
746	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
747	C₂²×C₄	C₂⁴×C₃	1	6	yes	—
748	C₂²×C₄	C₂⁴×C₃	1	6	yes	—
749	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
750	C₂²×C₄	C₂⁴×C₃	1	3	yes	—
751	C₂²×C₄	C₂⁴×C₃	1	6	yes	—
752	C₂²×C₄	C₂⁴×C₃	1	6	yes	—
753	C₂²×C₄	C₂⁴×C₃	1	12	yes	—
754	C₂²×C₄	C₂⁴×C₃	1	12	yes	—
755	C₂²×C₄	C₂⁴×C₃	1	24	yes	—
756	C₂²×C₄	C₂⁴×C₃	1	3	yes	—
757	C₄⋊C₄	C₂⁴×C₃	1	3	yes	—
758	C₄⋊C₄	C₂⁴×C₃	1	6	yes	—
759	C₄⋊C₄	C₂⁴×C₃	1	6	yes	—
760	C₄⋊C₄	C₂⁴×C₃	1	12	yes	—
761	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
762	C₄⋊C₄	C₂⁴×C₃	1	12	yes	—
763	C₄⋊C₄	C₂⁴×C₃	1	24	yes	—
764	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
765	C₄⋊C₄	C₂⁴×C₃	1	3	yes	—
766	C₄⋊C₄	C₂⁴×C₃	1	6	yes	—
767	C₄⋊C₄	C₂⁴×C₃	1	6	yes	—
768	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
769	C₄⋊C₄	C₂⁴×C₃	1	4	yes	—
770	C₄⋊C₄	C₂⁴×C₃	1	3	yes	—
771	C₄⋊C₄	C₂⁴×C₃	1	12	yes	—
772	C₄⋊C₄	C₂⁴×C₃	1	6	yes	—
773	C₄⋊C₄	C₂⁴×C₃	1	3	yes	—
774	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
775	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
776	C₄⋊C₄	C₂⁴×C₃	1	6	yes	—
777	C₄⋊C₄	C₂⁴×C₃	1	12	yes	—
778	C₄⋊C₄	C₂⁴×C₃	1	12	yes	—
779	C₄⋊C₄	C₂⁴×C₃	1	4	yes	—
780	C₄⋊C₄	C₂⁴×C₃	1	12	yes	—
781	C₂²⋊C₄	C₂⁴×C₃	1	6	yes	—
782	C₂²⋊C₄	C₂⁴×C₃	1	2	yes	—
783	C₂²⋊C₄	C₂⁴×C₃	1	6	yes	—
784	C₂²⋊C₄	C₂⁴×C₃	1	12	yes	—
785	C₂²⋊C₄	C₂⁴×C₃	1	6	yes	—
786	C₂²⋊C₄	C₂⁴×C₃	1	6	yes	—
787	C₂²⋊C₄	C₂⁴×C₃	1	12	yes	—
788	C₂²⋊C₄	C₂⁴×C₃	1	12	yes	—
789	C₂²⋊C₄	C₂⁴×C₃	1	6	yes	—
790	C₂²⋊C₄	C₂⁴×C₃	1	12	yes	—
791	C₂²⋊C₄	C₂⁴×C₃	1	12	yes	—
792	C₂²⋊C₄	C₂⁴×C₃	1	24	yes	—
793	C₂²⋊C₄	C₂⁴×C₃	1	6	yes	—
794	C₂²⋊C₄	C₂⁴×C₃	1	6	yes	—
795	C₂²⋊C₄	C₂⁴×C₃	1	4	yes	—
796	C₂²⋊C₄	C₂⁴×C₃	1	12	yes	—
797	C₂²⋊C₄	C₂⁴×C₃	1	12	yes	—
798	C₂²⋊C₄	C₂⁴×C₃	1	12	yes	—
799	C₄²	C₂⁴×C₃	1	6	yes	—
800	C₄²	C₂⁴×C₃	1	1	yes	characteristic
801	C₄²	C₂⁴×C₃	1	3	yes	—
802	C₄²	C₂⁴×C₃	1	2	yes	—
803	C₄²	C₂⁴×C₃	1	6	yes	—
804	C₄²	C₂⁴×C₃	1	12	yes	—
805	C₄²	C₂⁴×C₃	1	12	yes	—
806	C₄²	C₂⁴×C₃	1	3	yes	—
807	C₄²	C₂⁴×C₃	1	3	yes	—
808	C₄²	C₂⁴×C₃	1	12	yes	—
809	C₂²×C₃	—	2	2	no	—
810	C₂²×C₃	—	2	3	no	—
811	C₂²×C₃	—	2	2	no	—
812	C₂²×C₃	—	2	3	no	—
813	C₂²×C₃	—	2	6	no	—
814	C₂²×C₃	—	2	6	no	—
815	C₂²×C₃	—	2	6	no	—
816	C₂²×C₃	—	2	6	no	—
817	C₂²×C₃	—	2	6	no	—
818	C₂²×C₃	—	2	6	no	—
819	C₂²×C₃	—	4	24	no	—
820	C₂²×C₃	—	8	12	no	—
821	C₂²×C₃	C₂²×#41	1	6	yes	—
822	C₂²×C₃	C₂×H(5,𝔽₂)	1	4	yes	—
823	C₂²×C₃	C₂⁶	1	1	yes	characteristic
824	C₃×C₄	—	2	2	no	—
825	C₃×C₄	—	2	2	no	—
826	C₃×C₄	—	2	6	no	—
827	C₃×C₄	—	2	6	no	—
828	C₃×C₄	—	2	3	no	—
829	C₃×C₄	—	2	12	no	—
830	C₃×C₄	—	2	2	no	—
831	C₃×C₄	—	2	3	no	—
832	C₃×C₄	—	2	1	no	—
833	C₃×C₄	—	2	4	no	—
834	C₃×C₄	C₂²×#41	1	2	yes	—
835	C₃×C₄	C₂²×#41	1	6	yes	—
836	C₃×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
837	C₂³	—	2	12	no	—
838	C₂³	—	2	12	no	—
839	C₂³	—	2	12	no	—
840	C₂³	—	4	6	no	—
841	C₂³	—	4	6	no	—
842	C₂³	—	4	6	no	—
843	C₂³	C₂⁵×C₃	1	6	yes	—
844	C₂³	C₂⁵×C₃	1	6	yes	—
845	C₂³	C₂⁵×C₃	1	3	yes	—
846	C₂³	C₂⁵×C₃	1	2	yes	—
847	Q₈	—	2	12	no	—
848	Q₈	—	2	2	no	—
849	Q₈	—	2	12	no	—
850	Q₈	—	4	12	no	—
851	Q₈	—	4	2	no	—
852	Q₈	C₂×C₃×#41	1	4	yes	complemented
853	D₄	—	2	12	no	—
854	D₄	—	2	24	no	—
855	D₄	—	2	12	no	—
856	D₄	—	2	24	no	—
857	D₄	—	2	6	no	—
858	D₄	—	2	12	no	—
859	D₄	—	2	12	no	—
860	D₄	—	2	6	no	—
861	D₄	—	4	24	no	—
862	D₄	—	4	6	no	—
863	D₄	—	4	12	no	—
864	D₄	C₂×C₃×#41	1	12	yes	complemented
865	D₄	C₃×H(5,𝔽₂)	1	4	yes	complemented
866	C₂×C₄	—	2	12	no	—
867	C₂×C₄	—	2	24	no	—
868	C₂×C₄	—	2	4	no	—
869	C₂×C₄	—	2	12	no	—
870	C₂×C₄	—	2	12	no	—
871	C₂×C₄	—	2	12	no	—
872	C₂×C₄	—	2	12	no	—
873	C₂×C₄	—	2	6	no	—
874	C₂×C₄	—	2	12	no	—
875	C₂×C₄	—	4	6	no	—
876	C₂×C₄	—	4	12	no	—
877	C₂×C₄	—	4	12	no	—
878	C₂×C₄	—	4	24	no	—
879	C₂×C₄	—	4	6	no	—
880	C₂×C₄	—	4	4	no	—
881	C₂×C₄	—	4	3	no	—
882	C₂×C₄	C₂×C₃×#41	1	12	yes	complemented
883	C₂×C₄	C₂⁵×C₃	1	2	yes	—
884	C₂×C₄	C₂⁵×C₃	1	4	yes	—
885	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
886	C₂×C₄	C₂⁵×C₃	1	3	yes	—
887	C₂×C₄	C₂⁵×C₃	1	6	yes	—
888	C₂×C₄	C₂⁵×C₃	1	2	yes	—
889	C₂×C₄	C₂⁵×C₃	1	6	yes	—
890	C₂×C₄	C₂⁵×C₃	1	3	yes	—
891	C₂×C₄	C₂⁵×C₃	1	12	yes	—
892	C₂×C₄	C₂⁵×C₃	1	2	yes	—
893	C₂×C₄	C₂⁵×C₃	1	3	yes	—
894	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
895	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
896	C₂×C₃	—	2	4	no	—
897	C₂×C₃	—	2	6	no	—
898	C₂×C₃	—	4	6	no	—
899	C₂×C₃	—	4	6	no	—
900	C₂×C₃	C₂³×#41	1	1	yes	characteristic
901	C₂×C₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
902	C₂×C₃	2₋¹⁺⁶	1	1	yes	characteristic
903	C₂²	—	2	2	no	—
904	C₂²	—	2	3	no	—
905	C₂²	—	2	2	no	—
906	C₂²	—	2	3	no	—
907	C₂²	—	2	6	no	—
908	C₂²	—	2	6	no	—
909	C₂²	—	2	6	no	—
910	C₂²	—	2	6	no	—
911	C₂²	—	2	6	no	—
912	C₂²	—	2	6	no	—
913	C₂²	—	4	24	no	—
914	C₂²	—	8	12	no	—
915	C₂²	C₂²×C₃×#41	1	6	yes	—
916	C₂²	C₂×C₃×H(5,𝔽₂)	1	4	yes	—
917	C₂²	C₂⁶×C₃	1	1	yes	characteristic
918	C₄	—	2	2	no	—
919	C₄	—	2	2	no	—
920	C₄	—	2	6	no	—
921	C₄	—	2	6	no	—
922	C₄	—	2	3	no	—
923	C₄	—	2	12	no	—
924	C₄	—	2	2	no	—
925	C₄	—	2	3	no	—
926	C₄	—	2	1	no	—
927	C₄	—	2	4	no	—
928	C₄	C₂²×C₃×#41	1	2	yes	—
929	C₄	C₂²×C₃×#41	1	6	yes	—
930	C₄	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
931	C₃	#62985	1	1	yes	characteristic, direct product factor, Sylow
932	C₂	—	2	4	no	—
933	C₂	—	2	6	no	—
934	C₂	—	4	6	no	—
935	C₂	—	4	6	no	—
936	C₂	C₂³×C₃×#41	1	1	yes	characteristic
937	C₂	C₂²×C₃×H(5,𝔽₂)	1	1	yes	characteristic
938	C₂	C₃×2₋¹⁺⁶	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×#3522	C₂	semidirect
2. C₃×#3520	C₂	semidirect
3. C₃×#3517	C₂	semidirect
4. C₃×#3513	C₂	semidirect
5. C₃×#3511	C₂	semidirect
6. C₃×#3506	C₂	semidirect
7. C₃×#3503	C₂	semidirect
8. C₃×#3494	C₂	semidirect
9. C₃×#3492	C₂	semidirect
10. C₃×#3488	C₂	semidirect
11. C₃×#3482	C₂	semidirect
12. C₃×#3475	C₂	semidirect
13. C₃×D₄×#41	C₂	semidirect
14. C₃×D₄×#41	C₂	semidirect
15. C₂×C₃×#547	C₂	semidirect
16. C₃×C₄×H(5,𝔽₂)	C₂	semidirect
17. C₂×C₃×#520	C₂	semidirect
18. #62985	C₃	direct (N × H)
21. C₂²×C₃×#41	C₂²	semidirect
22. C₃×#559	C₂²	semidirect
23. C₃×Q₈²	C₂²	semidirect
24. C₃×#557	C₂²	semidirect
25. C₃×#556	C₂²	semidirect
26. C₃×#556	C₂²	semidirect
27. C₃×#555	C₂²	semidirect
28. C₃×#555	C₂²	semidirect
29. C₃×#554	C₂²	semidirect
30. C₃×#554	C₂²	semidirect
31. C₃×#554	C₂²	semidirect
32. C₃×#554	C₂²	semidirect
33. C₃×#553	C₂²	semidirect
34. C₃×#553	C₂²	semidirect
35. C₃×#553	C₂²	semidirect
36. C₃×#553	C₂²	semidirect
37. C₃×#552	C₂²	semidirect
38. C₃×#552	C₂²	semidirect
39. C₃×#552	C₂²	semidirect
40. C₃×#551	C₂²	semidirect
41. C₃×#551	C₂²	semidirect
42. C₃×#550	C₂²	semidirect
43. C₃×#550	C₂²	semidirect
44. C₃×#550	C₂²	semidirect
45. C₃×D₄×Q₈	C₂²	semidirect
46. C₃×D₄×Q₈	C₂²	semidirect
47. C₃×#548	C₂²	semidirect
48. C₃×#548	C₂²	semidirect
49. C₃×#548	C₂²	semidirect
50. C₃×#547	C₂²	semidirect
51. C₃×#547	C₂²	semidirect
52. C₃×#547	C₂²	semidirect
53. C₃×#547	C₂²	semidirect
54. C₃×#547	C₂²	semidirect
55. C₃×#547	C₂²	semidirect
56. C₃×#547	C₂²	semidirect
57. C₃×#547	C₂²	semidirect
58. C₃×#546	C₂²	semidirect
59. C₃×#546	C₂²	semidirect
60. C₃×#546	C₂²	semidirect
61. C₃×#546	C₂²	semidirect
62. C₃×D₄²	C₂²	semidirect
63. C₃×D₄²	C₂²	semidirect
64. C₃×#544	C₂²	semidirect
65. C₃×#542	C₂²	semidirect
66. C₃×#542	C₂²	semidirect
67. C₃×#540	C₂²	semidirect
68. C₃×#539	C₂²	semidirect
69. C₃×#538	C₂²	semidirect
70. C₃×#537	C₂²	semidirect
71. C₃×#535	C₂²	semidirect
72. C₃×#533	C₂²	semidirect
73. C₃×#533	C₂²	semidirect
74. C₃×#532	C₂²	semidirect
75. C₃×#532	C₂²	semidirect
76. C₃×#532	C₂²	semidirect
77. C₂×C₃×C₄⋊Q₈	C₂²	semidirect
78. C₃×#529	C₂²	semidirect
79. C₃×#529	C₂²	semidirect
80. C₃×#529	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×#121	C₂²	semidirect
90. C₃×#520	C₂²	semidirect
91. C₃×#520	C₂²	semidirect
92. C₃×#520	C₂²	semidirect
93. C₃×#520	C₂²	semidirect
94. C₃×#520	C₂²	semidirect
95. C₃×#520	C₂²	semidirect
96. C₃×#518	C₂²	semidirect
97. C₃×#518	C₂²	semidirect
99. C₃×C₄×#41	C₂²	semidirect
100. C₃×C₄×#41	C₂²	semidirect
101. C₃×C₄×#41	C₂²	semidirect
102. C₂×C₃×C₄×Q₈	C₂²	semidirect
103. C₂×C₃×C₄×D₄	C₂²	semidirect
104. C₂×C₃×C₄×D₄	C₂²	semidirect
105. C₂×C₃×C₄×D₄	C₂²	semidirect
106. C₂×C₃×C₄×D₄	C₂²	semidirect
107. C₂×C₃×#117	C₂²	semidirect
108. C₂²×C₃×C₄⋊C₄	C₂²	semidirect
109. #3522	C₂×C₃	semidirect
110. #3520	C₂×C₃	semidirect
111. #3517	C₂×C₃	semidirect
112. #3513	C₂×C₃	semidirect
113. #3511	C₂×C₃	semidirect
114. #3506	C₂×C₃	semidirect
115. #3503	C₂×C₃	semidirect
116. #3494	C₂×C₃	semidirect
117. #3492	C₂×C₃	semidirect
118. #3488	C₂×C₃	semidirect
119. #3482	C₂×C₃	semidirect
120. #3475	C₂×C₃	semidirect
121. D₄×#41	C₂×C₃	semidirect
122. D₄×#41	C₂×C₃	semidirect
123. C₂×#547	C₂×C₃	semidirect
124. C₄×H(5,𝔽₂)	C₂×C₃	semidirect
125. C₂×#520	C₂×C₃	semidirect
286. C₂²×#41	C₂²×C₃	semidirect
287. #559	C₂²×C₃	semidirect
288. Q₈²	C₂²×C₃	semidirect
289. #557	C₂²×C₃	semidirect
290. #556	C₂²×C₃	semidirect
291. #556	C₂²×C₃	semidirect
292. #555	C₂²×C₃	semidirect
293. #555	C₂²×C₃	semidirect
294. #554	C₂²×C₃	semidirect
295. #554	C₂²×C₃	semidirect
296. #554	C₂²×C₃	semidirect
297. #554	C₂²×C₃	semidirect
298. #553	C₂²×C₃	semidirect
299. #553	C₂²×C₃	semidirect
300. #553	C₂²×C₃	semidirect
301. #553	C₂²×C₃	semidirect
302. #552	C₂²×C₃	semidirect
303. #552	C₂²×C₃	semidirect
304. #552	C₂²×C₃	semidirect
305. #551	C₂²×C₃	semidirect
306. #551	C₂²×C₃	semidirect
307. #550	C₂²×C₃	semidirect
308. #550	C₂²×C₃	semidirect
309. #550	C₂²×C₃	semidirect
310. D₄×Q₈	C₂²×C₃	semidirect
311. D₄×Q₈	C₂²×C₃	semidirect
312. #548	C₂²×C₃	semidirect
313. #548	C₂²×C₃	semidirect
314. #548	C₂²×C₃	semidirect
315. #547	C₂²×C₃	semidirect
316. #547	C₂²×C₃	semidirect
317. #547	C₂²×C₃	semidirect
318. #547	C₂²×C₃	semidirect
319. #547	C₂²×C₃	semidirect
320. #547	C₂²×C₃	semidirect
321. #547	C₂²×C₃	semidirect
322. #547	C₂²×C₃	semidirect
323. #546	C₂²×C₃	semidirect
324. #546	C₂²×C₃	semidirect
325. #546	C₂²×C₃	semidirect
326. #546	C₂²×C₃	semidirect
327. D₄²	C₂²×C₃	semidirect
328. D₄²	C₂²×C₃	semidirect
329. #544	C₂²×C₃	semidirect
330. #542	C₂²×C₃	semidirect
331. #542	C₂²×C₃	semidirect
332. #540	C₂²×C₃	semidirect
333. #539	C₂²×C₃	semidirect
334. #538	C₂²×C₃	semidirect
335. #537	C₂²×C₃	semidirect
336. #535	C₂²×C₃	semidirect
337. #533	C₂²×C₃	semidirect
338. #533	C₂²×C₃	semidirect
339. #532	C₂²×C₃	semidirect
340. #532	C₂²×C₃	semidirect
341. #532	C₂²×C₃	semidirect
342. C₂×C₄⋊Q₈	C₂²×C₃	semidirect
343. #529	C₂²×C₃	semidirect
344. #529	C₂²×C₃	semidirect
345. #529	C₂²×C₃	semidirect
346. #525	C₂²×C₃	semidirect
347. #525	C₂²×C₃	semidirect
348. #525	C₂²×C₃	semidirect
349. #525	C₂²×C₃	semidirect
350. C₂×#123	C₂²×C₃	semidirect
351. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
352. C₂×#121	C₂²×C₃	semidirect
355. #520	C₂²×C₃	semidirect
356. #520	C₂²×C₃	semidirect
357. #520	C₂²×C₃	semidirect
358. #520	C₂²×C₃	semidirect
359. #520	C₂²×C₃	semidirect
360. #520	C₂²×C₃	semidirect
361. #518	C₂²×C₃	semidirect
362. #518	C₂²×C₃	semidirect
364. C₄×#41	C₂²×C₃	semidirect
365. C₄×#41	C₂²×C₃	semidirect
366. C₄×#41	C₂²×C₃	semidirect
367. C₂×C₄×Q₈	C₂²×C₃	semidirect
368. C₂×C₄×D₄	C₂²×C₃	semidirect
369. C₂×C₄×D₄	C₂²×C₃	semidirect
370. C₂×C₄×D₄	C₂²×C₃	semidirect
371. C₂×C₄×D₄	C₂²×C₃	semidirect
372. C₂×#117	C₂²×C₃	semidirect
373. C₂²×C₄⋊C₄	C₂²×C₃	semidirect
384. C₃×#41	#41	semidirect
656. C₃×Q₈	C₂×#41	semidirect
668. C₃×D₄	C₂×#41	semidirect
669. C₃×D₄	H(5,𝔽₂)	semidirect
686. C₂×C₃×C₄	C₂×#41	semidirect
710. #41	C₃×#41	semidirect
852. Q₈	C₂×C₃×#41	semidirect
864. D₄	C₂×C₃×#41	semidirect
865. D₄	C₃×H(5,𝔽₂)	semidirect
882. C₂×C₄	C₂×C₃×#41	semidirect
931. C₃	#62985	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×#3522	2
C₃×#3520	2
C₃×#3517	2
C₃×#3513	2
C₃×#3511	2
C₃×#3506	2
C₃×#3503	2
C₃×#3494	2
C₃×#3492	2
C₃×#3488	2
C₃×#3482	2
C₃×#3475	2
C₃×D₄×#41	2
C₂×C₃×#547	2
C₃×C₄×H(5,𝔽₂)	2
C₂×C₃×#520	2
#62985	3

Subgroups — C3×#62985 #10681592

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#62985 #10681592