Subgroups — C₃×#62991 #10681598

Order 768.

7050 conjugacy classes of subgroups.

The subgroup lattice has 1032 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#3521	C₂	1	8	yes	maximal, complemented
2	C₃×#3520	C₂	1	4	yes	maximal, complemented
3	C₃×#3515	C₂	1	8	yes	maximal, complemented
4	C₃×#3515	C₂	1	4	yes	maximal, complemented
5	C₃×#3509	C₂	1	2	yes	maximal, complemented
6	C₃×#3505	C₂	1	4	yes	maximal, complemented
7	C₃×#3501	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#3495	C₂	1	4	yes	maximal, complemented
9	C₃×#3491	C₂	1	8	yes	maximal, complemented
10	C₃×#3485	C₂	1	2	yes	maximal, complemented
11	C₃×#3482	C₂	1	4	yes	maximal, complemented
12	C₃×#3475	C₂	1	2	yes	maximal, complemented
13	C₃×#3475	C₂	1	4	yes	maximal, complemented
14	C₂×C₃×#552	C₂	1	4	yes	maximal, complemented
15	C₂×C₃×#547	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×C₄×H(5,𝔽₂)	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×#3428	C₂	1	2	yes	maximal, complemented
18	#62991	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	C₃×#557	C₂²	1	4	yes	complemented
22	C₃×#557	C₂²	1	4	yes	complemented
23	C₃×#556	C₂²	1	2	yes	complemented
24	C₃×#556	C₂²	1	4	yes	complemented
25	C₃×#556	C₂²	1	8	yes	complemented
26	C₃×#556	C₂²	1	4	yes	complemented
27	C₃×#555	C₂²	1	2	yes	complemented
28	C₃×#554	C₂²	1	4	yes	complemented
29	C₃×#554	C₂²	1	2	yes	complemented
30	C₃×#554	C₂²	1	8	yes	complemented
31	C₃×#554	C₂²	1	8	yes	complemented
32	C₃×#553	C₂²	1	8	yes	complemented
33	C₃×#553	C₂²	1	4	yes	complemented
34	C₃×#553	C₂²	1	16	yes	complemented
35	C₃×#552	C₂²	1	4	yes	complemented
36	C₃×#552	C₂²	1	8	yes	complemented
37	C₃×#552	C₂²	1	16	yes	complemented
38	C₃×#552	C₂²	1	8	yes	complemented
39	C₃×#552	C₂²	1	8	yes	complemented
40	C₃×#552	C₂²	1	16	yes	complemented
41	C₃×#552	C₂²	1	8	yes	complemented
42	C₃×#552	C₂²	1	4	yes	complemented
43	C₃×#552	C₂²	1	16	yes	complemented
44	C₃×#552	C₂²	1	8	yes	complemented
45	C₃×#552	C₂²	1	16	yes	complemented
46	C₃×#552	C₂²	1	8	yes	complemented
47	C₃×#551	C₂²	1	8	yes	complemented
48	C₃×#551	C₂²	1	16	yes	complemented
49	C₃×#551	C₂²	1	16	yes	complemented
50	C₃×#551	C₂²	1	16	yes	complemented
51	C₃×D₄×Q₈	C₂²	1	4	yes	complemented
52	C₃×#548	C₂²	1	8	yes	complemented
53	C₃×#547	C₂²	1	4	yes	complemented
54	C₃×#547	C₂²	1	4	yes	complemented
55	C₃×#547	C₂²	1	8	yes	complemented
56	C₃×#547	C₂²	1	2	yes	complemented
57	C₃×#547	C₂²	1	8	yes	complemented
58	C₃×#547	C₂²	1	8	yes	complemented
59	C₃×#546	C₂²	1	8	yes	complemented
60	C₃×#546	C₂²	1	4	yes	complemented
61	C₃×#546	C₂²	1	8	yes	complemented
62	C₃×#544	C₂²	1	2	yes	complemented
63	C₃×#543	C₂²	1	4	yes	complemented
64	C₃×#542	C₂²	1	8	yes	complemented
65	C₃×#541	C₂²	1	8	yes	complemented
66	C₃×#541	C₂²	1	8	yes	complemented
67	C₃×#539	C₂²	1	16	yes	complemented
68	C₃×#539	C₂²	1	16	yes	complemented
69	C₃×#539	C₂²	1	8	yes	complemented
70	C₃×#538	C₂²	1	8	yes	complemented
71	C₃×#536	C₂²	1	4	yes	—
72	C₃×#534	C₂²	1	8	yes	—
73	C₃×#533	C₂²	1	2	yes	complemented
74	C₃×#533	C₂²	1	4	yes	complemented
75	C₃×#533	C₂²	1	8	yes	complemented
76	C₃×#533	C₂²	1	4	yes	complemented
77	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
78	C₃×#529	C₂²	1	16	yes	complemented
79	C₃×#529	C₂²	1	8	yes	complemented
80	C₃×#529	C₂²	1	4	yes	complemented
81	C₃×#529	C₂²	1	8	yes	complemented
82	C₃×#529	C₂²	1	16	yes	complemented
83	C₃×#529	C₂²	1	8	yes	complemented
84	C₂×C₃×#126	C₂²	1	8	yes	complemented
85	C₂×C₃×#125	C₂²	1	8	yes	complemented
86	C₂×C₃×#125	C₂²	1	4	yes	complemented
87	C₃×#525	C₂²	1	4	yes	—
88	C₃×#525	C₂²	1	8	yes	complemented
89	C₂×C₃×#123	C₂²	1	8	yes	—
90	C₂×C₃×#123	C₂²	1	4	yes	complemented
91	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
92	C₂×C₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
93	C₂×C₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
94	C₂×C₃×#121	C₂²	1	2	yes	complemented
95	C₃×#520	C₂²	1	2	yes	—
96	C₃×#520	C₂²	1	8	yes	complemented
97	C₃×#520	C₂²	1	8	yes	complemented
98	C₃×#520	C₂²	1	4	yes	complemented
99	C₃×#519	C₂²	1	4	yes	complemented
100	C₃×#518	C₂²	1	1	yes	characteristic
101	C₃×#518	C₂²	1	2	yes	—
102	C₃×#518	C₂²	1	4	yes	—
103	C₃×#518	C₂²	1	8	yes	complemented
104	C₃×#518	C₂²	1	4	yes	complemented
105	C₃×C₄×#41	C₂²	1	2	yes	—
106	C₃×C₄×#41	C₂²	1	8	yes	complemented
107	C₃×C₄×#41	C₂²	1	8	yes	complemented
108	C₃×C₄×#41	C₂²	1	4	yes	complemented
109	C₃×C₄×#41	C₂²	1	4	yes	complemented
110	C₂×C₃×C₄×Q₈	C₂²	1	4	yes	complemented
111	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
112	C₂×C₃×C₄×D₄	C₂²	1	4	yes	—
113	C₂×C₃×C₄×D₄	C₂²	1	4	yes	complemented
114	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
115	C₂×C₃×#117	C₂²	1	8	yes	complemented
116	C₂×C₃×#117	C₂²	1	4	yes	complemented
117	C₂×C₃×#117	C₂²	1	4	yes	complemented
118	C₂²×C₃×C₄⋊C₄	C₂²	1	2	yes	complemented
119	#3521	C₂×C₃	1	8	yes	complemented
120	#3520	C₂×C₃	1	4	yes	complemented
121	#3515	C₂×C₃	1	8	yes	complemented
122	#3515	C₂×C₃	1	4	yes	complemented
123	#3509	C₂×C₃	1	2	yes	complemented
124	#3505	C₂×C₃	1	4	yes	complemented
125	#3501	C₂×C₃	1	1	yes	characteristic, complemented
126	#3495	C₂×C₃	1	4	yes	complemented
127	#3491	C₂×C₃	1	8	yes	complemented
128	#3485	C₂×C₃	1	2	yes	complemented
129	#3482	C₂×C₃	1	4	yes	complemented
130	#3475	C₂×C₃	1	2	yes	complemented
131	#3475	C₂×C₃	1	4	yes	complemented
132	C₂×#552	C₂×C₃	1	4	yes	complemented
133	C₂×#547	C₂×C₃	1	1	yes	characteristic, complemented
134	C₄×H(5,𝔽₂)	C₂×C₃	1	1	yes	characteristic, complemented
135	#3428	C₂×C₃	1	2	yes	complemented
136	C₃×H(5,𝔽₂)	—	2	8	no	—
137	C₂×C₃×#41	—	2	16	no	—
138	C₂×C₃×#41	C₂³	1	8	yes	—
139	C₂×C₃×#41	C₂³	1	8	yes	—
140	C₂×C₃×#41	C₂³	1	2	yes	—
141	C₂×C₃×#41	C₂³	1	4	yes	—
142	C₂×C₃×#41	C₂³	1	4	yes	—
143	C₂²×C₃×Q₈	C₂³	1	2	yes	—
144	C₂²×C₃×Q₈	C₂³	1	4	yes	—
145	C₂²×C₃×D₄	C₂³	1	4	yes	—
146	C₂²×C₃×D₄	C₂³	1	4	yes	—
147	C₂²×C₃×D₄	C₂³	1	4	yes	—
148	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
149	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
150	C₂³×C₃×C₄	C₂³	1	4	yes	—
151	C₂³×C₃×C₄	C₂³	1	2	yes	—
152	C₂³×C₃×C₄	C₂³	1	2	yes	—
153	C₂³×C₃×C₄	C₂³	1	4	yes	—
154	C₃×C₄⋊Q₈	C₂³	1	4	yes	—
155	C₃×C₄⋊Q₈	C₂³	1	4	yes	—
156	C₃×C₄⋊Q₈	C₂³	1	2	yes	—
157	C₃×C₄⋊Q₈	C₂³	1	2	yes	—
158	C₃×C₄⋊Q₈	C₂³	1	8	yes	—
159	C₃×C₄⋊Q₈	C₂³	1	8	yes	—
160	C₃×#126	C₂³	1	8	yes	—
161	C₃×#126	C₂³	1	16	yes	—
162	C₃×#126	C₂³	1	16	yes	—
163	C₃×#126	C₂³	1	16	yes	—
164	C₃×#126	C₂³	1	8	yes	—
165	C₃×#126	C₂³	1	8	yes	—
166	C₃×#126	C₂³	1	16	yes	—
167	C₃×#126	C₂³	1	16	yes	—
168	C₃×#126	C₂³	1	16	yes	—
169	C₃×#125	C₂³	1	8	yes	—
170	C₃×#125	C₂³	1	4	yes	—
171	C₃×#125	C₂³	1	16	yes	—
172	C₃×#125	C₂³	1	8	yes	—
173	C₃×#125	C₂³	1	16	yes	—
174	C₃×#125	C₂³	1	16	yes	—
175	C₃×#125	C₂³	1	16	yes	—
176	C₃×#125	C₂³	1	16	yes	—
177	C₃×#125	C₂³	1	8	yes	—
178	C₃×#125	C₂³	1	8	yes	—
179	C₃×#125	C₂³	1	4	yes	—
180	C₃×#124	C₂³	1	4	yes	—
181	C₃×#124	C₂³	1	8	yes	—
182	C₃×#124	C₂³	1	8	yes	—
183	C₃×#124	C₂³	1	16	yes	—
184	C₃×#123	C₂³	1	8	yes	—
185	C₃×#123	C₂³	1	16	yes	—
186	C₃×#123	C₂³	1	16	yes	—
187	C₃×#123	C₂³	1	16	yes	—
188	C₃×#123	C₂³	1	16	yes	—
189	C₃×#123	C₂³	1	16	yes	—
190	C₃×#123	C₂³	1	16	yes	—
191	C₃×#123	C₂³	1	16	yes	—
192	C₃×#123	C₂³	1	16	yes	—
193	C₃×#123	C₂³	1	8	yes	—
194	C₃×#123	C₂³	1	8	yes	—
195	C₃×#123	C₂³	1	8	yes	—
196	C₃×C₂²⋊Q₈	C₂³	1	4	yes	—
197	C₃×C₂²⋊Q₈	C₂³	1	4	yes	—
198	C₃×C₂²⋊Q₈	C₂³	1	8	yes	—
199	C₃×C₂²⋊Q₈	C₂³	1	8	yes	—
200	C₃×C₂²⋊Q₈	C₂³	1	8	yes	—
201	C₃×C₂²⋊Q₈	C₂³	1	8	yes	—
202	C₃×C₂²⋊Q₈	C₂³	1	16	yes	—
203	C₃×C₂²⋊Q₈	C₂³	1	8	yes	—
204	C₃×C₂²⋊Q₈	C₂³	1	8	yes	—
205	C₃×C₂²⋊Q₈	C₂³	1	4	yes	—
206	C₃×C₂²⋊Q₈	C₂³	1	4	yes	—
207	C₃×C₂²⋊Q₈	C₂³	1	8	yes	—
208	C₃×C₂²⋊Q₈	C₂³	1	16	yes	—
209	C₃×C₂²⋊Q₈	C₂³	1	16	yes	—
210	C₃×C₂²⋊Q₈	C₂³	1	8	yes	—
211	C₃×C₂²⋊Q₈	C₂³	1	8	yes	—
212	C₃×C₂²⋊Q₈	C₂³	1	16	yes	—
213	C₃×C₂²⋊Q₈	C₂³	1	8	yes	—
214	C₃×C₂²⋊Q₈	C₂³	1	4	yes	—
215	C₃×#121	C₂³	1	8	yes	—
216	C₃×#121	C₂³	1	8	yes	—
217	C₃×#121	C₂³	1	4	yes	—
218	C₃×#121	C₂³	1	4	yes	—
219	C₃×#121	C₂³	1	4	yes	—
220	C₃×#121	C₂³	1	16	yes	—
221	C₃×#121	C₂³	1	16	yes	—
222	C₃×#121	C₂³	1	8	yes	—
223	C₃×#120	C₂³	1	8	yes	—
224	C₃×#120	C₂³	1	16	yes	—
225	C₃×C₄×Q₈	C₂³	1	4	yes	—
226	C₃×C₄×Q₈	C₂³	1	8	yes	—
227	C₃×C₄×Q₈	C₂³	1	16	yes	—
228	C₃×C₄×Q₈	C₂³	1	2	yes	—
229	C₃×C₄×Q₈	C₂³	1	2	yes	—
230	C₃×C₄×Q₈	C₂³	1	8	yes	—
231	C₃×C₄×Q₈	C₂³	1	8	yes	—
232	C₃×C₄×Q₈	C₂³	1	8	yes	—
233	C₃×C₄×Q₈	C₂³	1	8	yes	—
234	C₃×C₄×Q₈	C₂³	1	4	yes	—
235	C₃×C₄×Q₈	C₂³	1	4	yes	—
236	C₃×C₄×Q₈	C₂³	1	8	yes	—
237	C₃×C₄×Q₈	C₂³	1	4	yes	—
238	C₃×C₄×D₄	C₂³	1	4	yes	—
239	C₃×C₄×D₄	C₂³	1	4	yes	—
240	C₃×C₄×D₄	C₂³	1	8	yes	—
241	C₃×C₄×D₄	C₂³	1	8	yes	—
242	C₃×C₄×D₄	C₂³	1	4	yes	—
243	C₃×C₄×D₄	C₂³	1	8	yes	—
244	C₃×C₄×D₄	C₂³	1	2	yes	—
245	C₃×C₄×D₄	C₂³	1	4	yes	—
246	C₃×C₄×D₄	C₂³	1	2	yes	—
247	C₃×C₄×D₄	C₂³	1	8	yes	—
248	C₃×C₄×D₄	C₂³	1	4	yes	—
249	C₃×C₄×D₄	C₂³	1	2	yes	—
250	C₃×C₄×D₄	C₂³	1	4	yes	—
251	C₃×C₄×D₄	C₂³	1	4	yes	—
252	C₃×C₄×D₄	C₂³	1	2	yes	—
253	C₃×C₄×D₄	C₂³	1	4	yes	—
254	C₃×C₄×D₄	C₂³	1	8	yes	—
255	C₃×C₄×D₄	C₂³	1	8	yes	—
256	C₃×C₄×D₄	C₂³	1	8	yes	—
257	C₃×C₄×D₄	C₂³	1	16	yes	—
258	C₃×C₄×D₄	C₂³	1	16	yes	—
259	C₃×C₄×D₄	C₂³	1	16	yes	—
260	C₃×C₄×D₄	C₂³	1	16	yes	—
261	C₃×C₄×D₄	C₂³	1	8	yes	—
262	C₃×C₄×D₄	C₂³	1	4	yes	—
263	C₃×C₄×D₄	C₂³	1	8	yes	—
264	C₃×C₄×D₄	C₂³	1	8	yes	—
265	C₃×C₄×D₄	C₂³	1	16	yes	—
266	C₃×#117	C₂³	1	8	yes	—
267	C₃×#117	C₂³	1	2	yes	—
268	C₃×#117	C₂³	1	4	yes	—
269	C₃×#117	C₂³	1	16	yes	—
270	C₃×#117	C₂³	1	4	yes	—
271	C₃×#117	C₂³	1	4	yes	—
272	C₃×#117	C₂³	1	4	yes	—
273	C₃×#117	C₂³	1	16	yes	—
274	C₃×#117	C₂³	1	8	yes	—
275	C₃×#117	C₂³	1	16	yes	—
276	C₃×#117	C₂³	1	8	yes	—
277	C₃×#117	C₂³	1	16	yes	—
278	C₃×#117	C₂³	1	4	yes	—
279	C₃×#117	C₂³	1	8	yes	—
280	C₃×#117	C₂³	1	4	yes	—
281	C₃×#117	C₂³	1	8	yes	—
282	C₃×#117	C₂³	1	8	yes	—
283	C₃×#117	C₂³	1	16	yes	—
284	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
285	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
286	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
287	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
288	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
289	C₂×C₃×C₄⋊C₄	C₂³	1	8	yes	—
290	C₂×C₃×C₄⋊C₄	C₂³	1	8	yes	—
291	C₂×C₃×C₄⋊C₄	C₂³	1	8	yes	—
292	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
293	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
294	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
295	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
296	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
297	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
298	C₂×C₃×C₄⋊C₄	C₂³	1	8	yes	—
299	C₂×C₃×C₄⋊C₄	C₂³	1	8	yes	—
300	C₂×C₃×C₄⋊C₄	C₂³	1	8	yes	—
301	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
302	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
303	C₂×C₃×C₂²⋊C₄	C₂³	1	8	yes	—
304	C₂×C₃×C₂²⋊C₄	C₂³	1	8	yes	—
305	C₂×C₃×C₂²⋊C₄	C₂³	1	8	yes	—
306	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
307	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
308	C₂×C₃×C₂²⋊C₄	C₂³	1	8	yes	—
309	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
310	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
311	C₂×C₃×C₂²⋊C₄	C₂³	1	8	yes	—
312	C₂×C₃×C₄²	C₂³	1	8	yes	—
313	C₂×C₃×C₄²	C₂³	1	8	yes	—
314	C₂×C₃×C₄²	C₂³	1	8	yes	—
315	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
316	C₂×C₃×C₄²	C₂³	1	4	yes	—
317	C₂×C₃×C₄²	C₂³	1	4	yes	—
318	C₂×H(5,𝔽₂)	C₂²×C₃	1	1	yes	characteristic
319	C₂²×#41	C₂²×C₃	1	2	yes	—
320	#557	C₂²×C₃	1	4	yes	complemented
321	#557	C₂²×C₃	1	4	yes	complemented
322	#556	C₂²×C₃	1	2	yes	complemented
323	#556	C₂²×C₃	1	4	yes	complemented
324	#556	C₂²×C₃	1	8	yes	complemented
325	#556	C₂²×C₃	1	4	yes	complemented
326	#555	C₂²×C₃	1	2	yes	complemented
327	#554	C₂²×C₃	1	4	yes	complemented
328	#554	C₂²×C₃	1	2	yes	complemented
329	#554	C₂²×C₃	1	8	yes	complemented
330	#554	C₂²×C₃	1	8	yes	complemented
331	#553	C₂²×C₃	1	8	yes	complemented
332	#553	C₂²×C₃	1	4	yes	complemented
333	#553	C₂²×C₃	1	16	yes	complemented
334	#552	C₂²×C₃	1	4	yes	complemented
335	#552	C₂²×C₃	1	8	yes	complemented
336	#552	C₂²×C₃	1	16	yes	complemented
337	#552	C₂²×C₃	1	8	yes	complemented
338	#552	C₂²×C₃	1	8	yes	complemented
339	#552	C₂²×C₃	1	16	yes	complemented
340	#552	C₂²×C₃	1	8	yes	complemented
341	#552	C₂²×C₃	1	4	yes	complemented
342	#552	C₂²×C₃	1	16	yes	complemented
343	#552	C₂²×C₃	1	8	yes	complemented
344	#552	C₂²×C₃	1	16	yes	complemented
345	#552	C₂²×C₃	1	8	yes	complemented
346	#551	C₂²×C₃	1	8	yes	complemented
347	#551	C₂²×C₃	1	16	yes	complemented
348	#551	C₂²×C₃	1	16	yes	complemented
349	#551	C₂²×C₃	1	16	yes	complemented
350	D₄×Q₈	C₂²×C₃	1	4	yes	complemented
351	#548	C₂²×C₃	1	8	yes	complemented
352	#547	C₂²×C₃	1	4	yes	complemented
353	#547	C₂²×C₃	1	4	yes	complemented
354	#547	C₂²×C₃	1	8	yes	complemented
355	#547	C₂²×C₃	1	2	yes	complemented
356	#547	C₂²×C₃	1	8	yes	complemented
357	#547	C₂²×C₃	1	8	yes	complemented
358	#546	C₂²×C₃	1	8	yes	complemented
359	#546	C₂²×C₃	1	4	yes	complemented
360	#546	C₂²×C₃	1	8	yes	complemented
361	#544	C₂²×C₃	1	2	yes	complemented
362	#543	C₂²×C₃	1	4	yes	complemented
363	#542	C₂²×C₃	1	8	yes	complemented
364	#541	C₂²×C₃	1	8	yes	complemented
365	#541	C₂²×C₃	1	8	yes	complemented
366	#539	C₂²×C₃	1	16	yes	complemented
367	#539	C₂²×C₃	1	16	yes	complemented
368	#539	C₂²×C₃	1	8	yes	complemented
369	#538	C₂²×C₃	1	8	yes	complemented
370	#536	C₂²×C₃	1	4	yes	—
371	#534	C₂²×C₃	1	8	yes	—
372	#533	C₂²×C₃	1	2	yes	complemented
373	#533	C₂²×C₃	1	4	yes	complemented
374	#533	C₂²×C₃	1	8	yes	complemented
375	#533	C₂²×C₃	1	4	yes	complemented
376	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
377	#529	C₂²×C₃	1	16	yes	complemented
378	#529	C₂²×C₃	1	8	yes	complemented
379	#529	C₂²×C₃	1	4	yes	complemented
380	#529	C₂²×C₃	1	8	yes	complemented
381	#529	C₂²×C₃	1	16	yes	complemented
382	#529	C₂²×C₃	1	8	yes	complemented
383	C₂×#126	C₂²×C₃	1	8	yes	complemented
384	C₂×#125	C₂²×C₃	1	8	yes	complemented
385	C₂×#125	C₂²×C₃	1	4	yes	complemented
386	#525	C₂²×C₃	1	4	yes	—
387	#525	C₂²×C₃	1	8	yes	complemented
388	C₂×#123	C₂²×C₃	1	8	yes	—
389	C₂×#123	C₂²×C₃	1	4	yes	complemented
390	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
391	C₂×C₂²⋊Q₈	C₂²×C₃	1	4	yes	complemented
392	C₂×C₂²⋊Q₈	C₂²×C₃	1	4	yes	complemented
393	C₂×#121	C₂²×C₃	1	2	yes	complemented
394	#520	C₂²×C₃	1	2	yes	—
395	#520	C₂²×C₃	1	8	yes	complemented
396	#520	C₂²×C₃	1	8	yes	complemented
397	#520	C₂²×C₃	1	4	yes	complemented
398	#519	C₂²×C₃	1	4	yes	complemented
399	#518	C₂²×C₃	1	1	yes	characteristic
400	#518	C₂²×C₃	1	2	yes	—
401	#518	C₂²×C₃	1	4	yes	—
402	#518	C₂²×C₃	1	8	yes	complemented
403	#518	C₂²×C₃	1	4	yes	complemented
404	C₄×#41	C₂²×C₃	1	2	yes	—
405	C₄×#41	C₂²×C₃	1	8	yes	complemented
406	C₄×#41	C₂²×C₃	1	8	yes	complemented
407	C₄×#41	C₂²×C₃	1	4	yes	complemented
408	C₄×#41	C₂²×C₃	1	4	yes	complemented
409	C₂×C₄×Q₈	C₂²×C₃	1	4	yes	complemented
410	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
411	C₂×C₄×D₄	C₂²×C₃	1	4	yes	—
412	C₂×C₄×D₄	C₂²×C₃	1	4	yes	complemented
413	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
414	C₂×#117	C₂²×C₃	1	8	yes	complemented
415	C₂×#117	C₂²×C₃	1	4	yes	complemented
416	C₂×#117	C₂²×C₃	1	4	yes	complemented
417	C₂²×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
418	C₂⁴×C₃	C₂⁴	1	2	yes	—
419	C₂⁴×C₃	C₂⁴	1	4	yes	—
420	C₂⁴×C₃	C₂⁴	1	2	yes	—
421	C₃×#41	—	2	32	no	—
422	C₃×#41	—	2	32	no	—
423	C₃×#41	—	2	16	no	—
424	C₃×#41	—	2	8	no	—
425	C₃×#41	—	4	8	no	—
426	C₂×C₃×Q₈	—	2	8	no	—
427	C₂×C₃×Q₈	—	4	8	no	—
428	C₂×C₃×Q₈	C₂⁴	1	4	yes	—
429	C₂×C₃×Q₈	C₂⁴	1	8	yes	—
430	C₂×C₃×Q₈	C₂⁴	1	2	yes	—
431	C₂×C₃×Q₈	C₂⁴	1	4	yes	—
432	C₂×C₃×Q₈	C₂⁴	1	8	yes	—
433	C₂×C₃×D₄	—	2	16	no	—
434	C₂×C₃×D₄	—	2	16	no	—
435	C₂×C₃×D₄	—	2	16	no	—
436	C₂×C₃×D₄	—	4	2	no	—
437	C₂×C₃×D₄	#41	1	8	yes	complemented
438	C₂×C₃×D₄	C₂⁴	1	4	yes	—
439	C₂×C₃×D₄	C₂⁴	1	16	yes	—
440	C₂×C₃×D₄	C₂⁴	1	2	yes	—
441	C₂×C₃×D₄	C₂⁴	1	8	yes	—
442	C₂×C₃×D₄	C₂⁴	1	2	yes	—
443	C₂×C₃×D₄	C₂⁴	1	8	yes	—
444	C₂×C₃×D₄	C₂⁴	1	8	yes	—
445	C₂×C₃×D₄	C₂⁴	1	2	yes	—
446	C₂×C₃×D₄	C₂⁴	1	4	yes	—
447	C₂²×C₃×C₄	—	2	16	no	—
448	C₂²×C₃×C₄	—	2	8	no	—
449	C₂²×C₃×C₄	—	4	4	no	—
450	C₂²×C₃×C₄	—	4	8	no	—
451	C₂²×C₃×C₄	C₂⁴	1	8	yes	—
452	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
453	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
454	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
455	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
456	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
457	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
458	C₂²×C₃×C₄	C₂⁴	1	8	yes	—
459	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
460	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
461	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
462	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
463	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
464	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
465	C₂²×C₃×C₄	C₂⁴	1	8	yes	—
466	C₂²×C₃×C₄	C₂⁴	1	8	yes	—
467	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
468	C₂²×C₃×C₄	C₂⁴	1	8	yes	—
469	C₂²×C₃×C₄	C₂⁴	1	8	yes	—
470	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
471	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
472	C₂²×C₃×C₄	C₂⁴	1	8	yes	—
473	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
474	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
475	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
476	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
477	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
478	C₃×C₄⋊C₄	C₂⁴	1	8	yes	—
479	C₃×C₄⋊C₄	C₂⁴	1	8	yes	—
480	C₃×C₄⋊C₄	C₂⁴	1	4	yes	—
481	C₃×C₄⋊C₄	C₂⁴	1	8	yes	—
482	C₃×C₄⋊C₄	C₂⁴	1	4	yes	—
483	C₃×C₄⋊C₄	C₂⁴	1	8	yes	—
484	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
485	C₃×C₄⋊C₄	C₂⁴	1	4	yes	—
486	C₃×C₄⋊C₄	C₂⁴	1	4	yes	—
487	C₃×C₄⋊C₄	C₂⁴	1	8	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	4	yes	—
493	C₃×C₄⋊C₄	C₂⁴	1	4	yes	—
494	C₃×C₄⋊C₄	C₂⁴	1	16	yes	—
495	C₃×C₄⋊C₄	C₂⁴	1	16	yes	—
496	C₃×C₄⋊C₄	C₂⁴	1	8	yes	—
497	C₃×C₄⋊C₄	C₂⁴	1	16	yes	—
498	C₃×C₄⋊C₄	C₂⁴	1	16	yes	—
499	C₃×C₄⋊C₄	C₂⁴	1	8	yes	—
500	C₃×C₄⋊C₄	C₂⁴	1	16	yes	—
501	C₃×C₄⋊C₄	C₂⁴	1	4	yes	—
502	C₃×C₄⋊C₄	C₂⁴	1	4	yes	—
503	C₃×C₄⋊C₄	C₂⁴	1	8	yes	—
504	C₃×C₂²⋊C₄	C₂⁴	1	4	yes	—
505	C₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
506	C₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
507	C₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
508	C₃×C₂²⋊C₄	C₂⁴	1	4	yes	—
509	C₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
510	C₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
511	C₃×C₂²⋊C₄	C₂⁴	1	4	yes	—
512	C₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
513	C₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
514	C₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
515	C₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
516	C₃×C₂²⋊C₄	C₂⁴	1	4	yes	—
517	C₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
518	C₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
519	C₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
520	C₃×C₂²⋊C₄	C₂⁴	1	4	yes	—
521	C₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
522	C₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
523	C₃×C₄²	C₂⁴	1	8	yes	—
524	C₃×C₄²	C₂⁴	1	4	yes	—
525	C₃×C₄²	C₂⁴	1	8	yes	—
526	C₃×C₄²	C₂⁴	1	2	yes	—
527	C₃×C₄²	C₂⁴	1	4	yes	—
528	C₃×C₄²	C₂⁴	1	8	yes	—
529	C₃×C₄²	C₂⁴	1	4	yes	—
530	C₃×C₄²	C₂⁴	1	16	yes	—
531	C₃×C₄²	C₂⁴	1	16	yes	—
532	C₃×C₄²	C₂⁴	1	2	yes	—
533	C₃×C₄²	C₂⁴	1	8	yes	—
534	H(5,𝔽₂)	—	2	8	no	—
535	C₂×#41	—	2	16	no	—
536	C₂×#41	C₂³×C₃	1	2	yes	—
537	C₂×#41	C₂³×C₃	1	8	yes	—
538	C₂×#41	C₂³×C₃	1	4	yes	—
539	C₂×#41	C₂³×C₃	1	8	yes	—
540	C₂×#41	C₂³×C₃	1	4	yes	—
541	C₂²×Q₈	C₂³×C₃	1	2	yes	—
542	C₂²×Q₈	C₂³×C₃	1	4	yes	—
543	C₂²×D₄	C₂³×C₃	1	4	yes	—
544	C₂²×D₄	C₂³×C₃	1	4	yes	—
545	C₂²×D₄	C₂³×C₃	1	4	yes	—
546	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
547	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
548	C₂³×C₄	C₂³×C₃	1	4	yes	—
549	C₂³×C₄	C₂³×C₃	1	2	yes	—
550	C₂³×C₄	C₂³×C₃	1	2	yes	—
551	C₂³×C₄	C₂³×C₃	1	4	yes	—
552	C₄⋊Q₈	C₂³×C₃	1	4	yes	—
553	C₄⋊Q₈	C₂³×C₃	1	4	yes	—
554	C₄⋊Q₈	C₂³×C₃	1	2	yes	—
555	C₄⋊Q₈	C₂³×C₃	1	2	yes	—
556	C₄⋊Q₈	C₂³×C₃	1	8	yes	—
557	C₄⋊Q₈	C₂³×C₃	1	8	yes	—
558	#126	C₂³×C₃	1	8	yes	—
559	#126	C₂³×C₃	1	16	yes	—
560	#126	C₂³×C₃	1	16	yes	—
561	#126	C₂³×C₃	1	16	yes	—
562	#126	C₂³×C₃	1	8	yes	—
563	#126	C₂³×C₃	1	8	yes	—
564	#126	C₂³×C₃	1	16	yes	—
565	#126	C₂³×C₃	1	16	yes	—
566	#126	C₂³×C₃	1	16	yes	—
567	#125	C₂³×C₃	1	8	yes	—
568	#125	C₂³×C₃	1	4	yes	—
569	#125	C₂³×C₃	1	16	yes	—
570	#125	C₂³×C₃	1	8	yes	—
571	#125	C₂³×C₃	1	16	yes	—
572	#125	C₂³×C₃	1	16	yes	—
573	#125	C₂³×C₃	1	16	yes	—
574	#125	C₂³×C₃	1	16	yes	—
575	#125	C₂³×C₃	1	8	yes	—
576	#125	C₂³×C₃	1	8	yes	—
577	#125	C₂³×C₃	1	4	yes	—
578	#124	C₂³×C₃	1	4	yes	—
579	#124	C₂³×C₃	1	8	yes	—
580	#124	C₂³×C₃	1	8	yes	—
581	#124	C₂³×C₃	1	16	yes	—
582	#123	C₂³×C₃	1	8	yes	—
583	#123	C₂³×C₃	1	16	yes	—
584	#123	C₂³×C₃	1	16	yes	—
585	#123	C₂³×C₃	1	16	yes	—
586	#123	C₂³×C₃	1	16	yes	—
587	#123	C₂³×C₃	1	16	yes	—
588	#123	C₂³×C₃	1	16	yes	—
589	#123	C₂³×C₃	1	16	yes	—
590	#123	C₂³×C₃	1	16	yes	—
591	#123	C₂³×C₃	1	8	yes	—
592	#123	C₂³×C₃	1	8	yes	—
593	#123	C₂³×C₃	1	8	yes	—
594	C₂²⋊Q₈	C₂³×C₃	1	4	yes	—
595	C₂²⋊Q₈	C₂³×C₃	1	4	yes	—
596	C₂²⋊Q₈	C₂³×C₃	1	8	yes	—
597	C₂²⋊Q₈	C₂³×C₃	1	8	yes	—
598	C₂²⋊Q₈	C₂³×C₃	1	8	yes	—
599	C₂²⋊Q₈	C₂³×C₃	1	8	yes	—
600	C₂²⋊Q₈	C₂³×C₃	1	16	yes	—
601	C₂²⋊Q₈	C₂³×C₃	1	8	yes	—
602	C₂²⋊Q₈	C₂³×C₃	1	8	yes	—
603	C₂²⋊Q₈	C₂³×C₃	1	4	yes	—
604	C₂²⋊Q₈	C₂³×C₃	1	4	yes	—
605	C₂²⋊Q₈	C₂³×C₃	1	8	yes	—
606	C₂²⋊Q₈	C₂³×C₃	1	16	yes	—
607	C₂²⋊Q₈	C₂³×C₃	1	16	yes	—
608	C₂²⋊Q₈	C₂³×C₃	1	8	yes	—
609	C₂²⋊Q₈	C₂³×C₃	1	8	yes	—
610	C₂²⋊Q₈	C₂³×C₃	1	16	yes	—
611	C₂²⋊Q₈	C₂³×C₃	1	8	yes	—
612	C₂²⋊Q₈	C₂³×C₃	1	4	yes	—
613	#121	C₂³×C₃	1	8	yes	—
614	#121	C₂³×C₃	1	8	yes	—
615	#121	C₂³×C₃	1	4	yes	—
616	#121	C₂³×C₃	1	4	yes	—
617	#121	C₂³×C₃	1	4	yes	—
618	#121	C₂³×C₃	1	16	yes	—
619	#121	C₂³×C₃	1	16	yes	—
620	#121	C₂³×C₃	1	8	yes	—
621	#120	C₂³×C₃	1	8	yes	—
622	#120	C₂³×C₃	1	16	yes	—
623	C₄×Q₈	C₂³×C₃	1	4	yes	—
624	C₄×Q₈	C₂³×C₃	1	8	yes	—
625	C₄×Q₈	C₂³×C₃	1	16	yes	—
626	C₄×Q₈	C₂³×C₃	1	2	yes	—
627	C₄×Q₈	C₂³×C₃	1	2	yes	—
628	C₄×Q₈	C₂³×C₃	1	8	yes	—
629	C₄×Q₈	C₂³×C₃	1	8	yes	—
630	C₄×Q₈	C₂³×C₃	1	8	yes	—
631	C₄×Q₈	C₂³×C₃	1	8	yes	—
632	C₄×Q₈	C₂³×C₃	1	4	yes	—
633	C₄×Q₈	C₂³×C₃	1	4	yes	—
634	C₄×Q₈	C₂³×C₃	1	8	yes	—
635	C₄×Q₈	C₂³×C₃	1	4	yes	—
636	C₄×D₄	C₂³×C₃	1	4	yes	—
637	C₄×D₄	C₂³×C₃	1	4	yes	—
638	C₄×D₄	C₂³×C₃	1	8	yes	—
639	C₄×D₄	C₂³×C₃	1	8	yes	—
640	C₄×D₄	C₂³×C₃	1	4	yes	—
641	C₄×D₄	C₂³×C₃	1	8	yes	—
642	C₄×D₄	C₂³×C₃	1	2	yes	—
643	C₄×D₄	C₂³×C₃	1	4	yes	—
644	C₄×D₄	C₂³×C₃	1	2	yes	—
645	C₄×D₄	C₂³×C₃	1	8	yes	—
646	C₄×D₄	C₂³×C₃	1	4	yes	—
647	C₄×D₄	C₂³×C₃	1	2	yes	—
648	C₄×D₄	C₂³×C₃	1	4	yes	—
649	C₄×D₄	C₂³×C₃	1	4	yes	—
650	C₄×D₄	C₂³×C₃	1	2	yes	—
651	C₄×D₄	C₂³×C₃	1	4	yes	—
652	C₄×D₄	C₂³×C₃	1	8	yes	—
653	C₄×D₄	C₂³×C₃	1	8	yes	—
654	C₄×D₄	C₂³×C₃	1	8	yes	—
655	C₄×D₄	C₂³×C₃	1	16	yes	—
656	C₄×D₄	C₂³×C₃	1	16	yes	—
657	C₄×D₄	C₂³×C₃	1	16	yes	—
658	C₄×D₄	C₂³×C₃	1	16	yes	—
659	C₄×D₄	C₂³×C₃	1	8	yes	—
660	C₄×D₄	C₂³×C₃	1	4	yes	—
661	C₄×D₄	C₂³×C₃	1	8	yes	—
662	C₄×D₄	C₂³×C₃	1	8	yes	—
663	C₄×D₄	C₂³×C₃	1	16	yes	—
664	#117	C₂³×C₃	1	8	yes	—
665	#117	C₂³×C₃	1	2	yes	—
666	#117	C₂³×C₃	1	4	yes	—
667	#117	C₂³×C₃	1	16	yes	—
668	#117	C₂³×C₃	1	4	yes	—
669	#117	C₂³×C₃	1	4	yes	—
670	#117	C₂³×C₃	1	4	yes	—
671	#117	C₂³×C₃	1	16	yes	—
672	#117	C₂³×C₃	1	8	yes	—
673	#117	C₂³×C₃	1	16	yes	—
674	#117	C₂³×C₃	1	8	yes	—
675	#117	C₂³×C₃	1	16	yes	—
676	#117	C₂³×C₃	1	4	yes	—
677	#117	C₂³×C₃	1	8	yes	—
678	#117	C₂³×C₃	1	4	yes	—
679	#117	C₂³×C₃	1	8	yes	—
680	#117	C₂³×C₃	1	8	yes	—
681	#117	C₂³×C₃	1	16	yes	—
682	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
683	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
684	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
685	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
686	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
687	C₂×C₄⋊C₄	C₂³×C₃	1	8	yes	—
688	C₂×C₄⋊C₄	C₂³×C₃	1	8	yes	—
689	C₂×C₄⋊C₄	C₂³×C₃	1	8	yes	—
690	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
691	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
692	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
693	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
694	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
695	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
696	C₂×C₄⋊C₄	C₂³×C₃	1	8	yes	—
697	C₂×C₄⋊C₄	C₂³×C₃	1	8	yes	—
698	C₂×C₄⋊C₄	C₂³×C₃	1	8	yes	—
699	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
700	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
701	C₂×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
702	C₂×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
703	C₂×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
704	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
705	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
706	C₂×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
707	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
708	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
709	C₂×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
710	C₂×C₄²	C₂³×C₃	1	8	yes	—
711	C₂×C₄²	C₂³×C₃	1	8	yes	—
712	C₂×C₄²	C₂³×C₃	1	8	yes	—
713	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
714	C₂×C₄²	C₂³×C₃	1	4	yes	—
715	C₂×C₄²	C₂³×C₃	1	4	yes	—
716	C₂³×C₃	—	2	4	no	—
717	C₂³×C₃	—	2	8	no	—
718	C₂³×C₃	—	4	2	no	—
719	C₂³×C₃	—	4	2	no	—
720	C₂³×C₃	—	4	4	no	—
721	C₂³×C₃	—	4	2	no	—
722	C₂³×C₃	—	4	4	no	—
723	C₂³×C₃	—	4	2	no	—
724	C₂³×C₃	C₂×#41	1	8	yes	—
725	C₂³×C₃	C₂⁵	1	4	yes	—
726	C₂³×C₃	C₂⁵	1	4	yes	—
727	C₂³×C₃	C₂⁵	1	1	yes	characteristic
728	C₂³×C₃	C₂⁵	1	4	yes	—
729	C₃×Q₈	—	2	16	no	—
730	C₃×Q₈	—	2	4	no	—
731	C₃×Q₈	—	2	8	no	—
732	C₃×Q₈	—	4	8	no	—
733	C₃×Q₈	—	4	4	no	—
734	C₃×D₄	—	2	8	no	—
735	C₃×D₄	—	2	16	no	—
736	C₃×D₄	—	2	32	no	—
737	C₃×D₄	—	2	4	no	—
738	C₃×D₄	—	2	4	no	—
739	C₃×D₄	—	4	2	no	—
740	C₃×D₄	—	4	8	no	—
741	C₃×D₄	—	4	8	no	—
742	C₃×D₄	C₂×#41	1	16	yes	—
743	C₂×C₃×C₄	—	2	4	no	—
744	C₂×C₃×C₄	—	2	8	no	—
745	C₂×C₃×C₄	—	2	16	no	—
746	C₂×C₃×C₄	—	2	16	no	—
747	C₂×C₃×C₄	—	2	8	no	—
748	C₂×C₃×C₄	—	2	8	no	—
749	C₂×C₃×C₄	—	2	8	no	—
750	C₂×C₃×C₄	—	2	8	no	—
751	C₂×C₃×C₄	—	2	2	no	—
752	C₂×C₃×C₄	—	2	8	no	—
753	C₂×C₃×C₄	—	2	8	no	—
754	C₂×C₃×C₄	—	4	4	no	—
755	C₂×C₃×C₄	—	4	8	no	—
756	C₂×C₃×C₄	—	4	4	no	—
757	C₂×C₃×C₄	—	4	2	no	—
758	C₂×C₃×C₄	—	4	4	no	—
759	C₂×C₃×C₄	—	4	8	no	—
760	C₂×C₃×C₄	—	4	4	no	—
761	C₂×C₃×C₄	—	4	8	no	—
762	C₂×C₃×C₄	—	4	1	no	—
763	C₂×C₃×C₄	—	4	8	no	—
764	C₂×C₃×C₄	—	4	8	no	—
765	C₂×C₃×C₄	C₂×#41	1	4	yes	—
766	C₂×C₃×C₄	C₂⁵	1	4	yes	—
767	C₂×C₃×C₄	C₂⁵	1	2	yes	—
768	C₂×C₃×C₄	C₂⁵	1	4	yes	—
769	C₂×C₃×C₄	C₂⁵	1	2	yes	—
770	C₂×C₃×C₄	C₂⁵	1	8	yes	—
771	C₂×C₃×C₄	C₂⁵	1	8	yes	—
772	C₂×C₃×C₄	C₂⁵	1	8	yes	—
773	C₂×C₃×C₄	C₂⁵	1	4	yes	—
774	C₂×C₃×C₄	C₂⁵	1	4	yes	—
775	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
776	C₂×C₃×C₄	C₂⁵	1	2	yes	—
777	C₂×C₃×C₄	C₂⁵	1	2	yes	—
778	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
779	C₂⁴	C₂⁴×C₃	1	2	yes	—
780	C₂⁴	C₂⁴×C₃	1	4	yes	—
781	C₂⁴	C₂⁴×C₃	1	2	yes	—
782	#41	—	2	32	no	—
783	#41	—	2	32	no	—
784	#41	—	2	16	no	—
785	#41	—	2	8	no	—
786	#41	—	4	8	no	—
787	C₂×Q₈	—	2	8	no	—
788	C₂×Q₈	—	4	8	no	—
789	C₂×Q₈	C₂⁴×C₃	1	4	yes	—
790	C₂×Q₈	C₂⁴×C₃	1	8	yes	—
791	C₂×Q₈	C₂⁴×C₃	1	2	yes	—
792	C₂×Q₈	C₂⁴×C₃	1	4	yes	—
793	C₂×Q₈	C₂⁴×C₃	1	8	yes	—
794	C₂×D₄	—	2	16	no	—
795	C₂×D₄	—	2	16	no	—
796	C₂×D₄	—	2	16	no	—
797	C₂×D₄	—	4	2	no	—
798	C₂×D₄	C₃×#41	1	8	yes	complemented
799	C₂×D₄	C₂⁴×C₃	1	4	yes	—
800	C₂×D₄	C₂⁴×C₃	1	16	yes	—
801	C₂×D₄	C₂⁴×C₃	1	2	yes	—
802	C₂×D₄	C₂⁴×C₃	1	8	yes	—
803	C₂×D₄	C₂⁴×C₃	1	2	yes	—
804	C₂×D₄	C₂⁴×C₃	1	8	yes	—
805	C₂×D₄	C₂⁴×C₃	1	8	yes	—
806	C₂×D₄	C₂⁴×C₃	1	2	yes	—
807	C₂×D₄	C₂⁴×C₃	1	4	yes	—
808	C₂²×C₄	—	2	16	no	—
809	C₂²×C₄	—	2	8	no	—
810	C₂²×C₄	—	4	4	no	—
811	C₂²×C₄	—	4	8	no	—
812	C₂²×C₄	C₂⁴×C₃	1	8	yes	—
813	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
814	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
815	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
816	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
817	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
818	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
819	C₂²×C₄	C₂⁴×C₃	1	8	yes	—
820	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
821	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
822	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
823	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
824	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
825	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
826	C₂²×C₄	C₂⁴×C₃	1	8	yes	—
827	C₂²×C₄	C₂⁴×C₃	1	8	yes	—
828	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
829	C₂²×C₄	C₂⁴×C₃	1	8	yes	—
830	C₂²×C₄	C₂⁴×C₃	1	8	yes	—
831	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
832	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
833	C₂²×C₄	C₂⁴×C₃	1	8	yes	—
834	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
835	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
836	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
837	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
838	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
839	C₄⋊C₄	C₂⁴×C₃	1	8	yes	—
840	C₄⋊C₄	C₂⁴×C₃	1	8	yes	—
841	C₄⋊C₄	C₂⁴×C₃	1	4	yes	—
842	C₄⋊C₄	C₂⁴×C₃	1	8	yes	—
843	C₄⋊C₄	C₂⁴×C₃	1	4	yes	—
844	C₄⋊C₄	C₂⁴×C₃	1	8	yes	—
845	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
846	C₄⋊C₄	C₂⁴×C₃	1	4	yes	—
847	C₄⋊C₄	C₂⁴×C₃	1	4	yes	—
848	C₄⋊C₄	C₂⁴×C₃	1	8	yes	—
849	C₄⋊C₄	C₂⁴×C₃	1	4	yes	—
850	C₄⋊C₄	C₂⁴×C₃	1	8	yes	—
851	C₄⋊C₄	C₂⁴×C₃	1	8	yes	—
852	C₄⋊C₄	C₂⁴×C₃	1	8	yes	—
853	C₄⋊C₄	C₂⁴×C₃	1	4	yes	—
854	C₄⋊C₄	C₂⁴×C₃	1	4	yes	—
855	C₄⋊C₄	C₂⁴×C₃	1	16	yes	—
856	C₄⋊C₄	C₂⁴×C₃	1	16	yes	—
857	C₄⋊C₄	C₂⁴×C₃	1	8	yes	—
858	C₄⋊C₄	C₂⁴×C₃	1	16	yes	—
859	C₄⋊C₄	C₂⁴×C₃	1	16	yes	—
860	C₄⋊C₄	C₂⁴×C₃	1	8	yes	—
861	C₄⋊C₄	C₂⁴×C₃	1	16	yes	—
862	C₄⋊C₄	C₂⁴×C₃	1	4	yes	—
863	C₄⋊C₄	C₂⁴×C₃	1	4	yes	—
864	C₄⋊C₄	C₂⁴×C₃	1	8	yes	—
865	C₂²⋊C₄	C₂⁴×C₃	1	4	yes	—
866	C₂²⋊C₄	C₂⁴×C₃	1	8	yes	—
867	C₂²⋊C₄	C₂⁴×C₃	1	8	yes	—
868	C₂²⋊C₄	C₂⁴×C₃	1	8	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	4	yes	—
873	C₂²⋊C₄	C₂⁴×C₃	1	8	yes	—
874	C₂²⋊C₄	C₂⁴×C₃	1	16	yes	—
875	C₂²⋊C₄	C₂⁴×C₃	1	8	yes	—
876	C₂²⋊C₄	C₂⁴×C₃	1	8	yes	—
877	C₂²⋊C₄	C₂⁴×C₃	1	4	yes	—
878	C₂²⋊C₄	C₂⁴×C₃	1	16	yes	—
879	C₂²⋊C₄	C₂⁴×C₃	1	16	yes	—
880	C₂²⋊C₄	C₂⁴×C₃	1	16	yes	—
881	C₂²⋊C₄	C₂⁴×C₃	1	4	yes	—
882	C₂²⋊C₄	C₂⁴×C₃	1	8	yes	—
883	C₂²⋊C₄	C₂⁴×C₃	1	8	yes	—
884	C₄²	C₂⁴×C₃	1	8	yes	—
885	C₄²	C₂⁴×C₃	1	4	yes	—
886	C₄²	C₂⁴×C₃	1	8	yes	—
887	C₄²	C₂⁴×C₃	1	2	yes	—
888	C₄²	C₂⁴×C₃	1	4	yes	—
889	C₄²	C₂⁴×C₃	1	8	yes	—
890	C₄²	C₂⁴×C₃	1	4	yes	—
891	C₄²	C₂⁴×C₃	1	16	yes	—
892	C₄²	C₂⁴×C₃	1	16	yes	—
893	C₄²	C₂⁴×C₃	1	2	yes	—
894	C₄²	C₂⁴×C₃	1	8	yes	—
895	C₂²×C₃	—	2	4	no	—
896	C₂²×C₃	—	2	1	no	—
897	C₂²×C₃	—	2	4	no	—
898	C₂²×C₃	—	2	1	no	—
899	C₂²×C₃	—	2	4	no	—
900	C₂²×C₃	—	2	4	no	—
901	C₂²×C₃	—	2	4	no	—
902	C₂²×C₃	—	2	4	no	—
903	C₂²×C₃	—	2	4	no	—
904	C₂²×C₃	—	2	4	no	—
905	C₂²×C₃	—	4	8	no	—
906	C₂²×C₃	—	8	4	no	—
907	C₂²×C₃	—	8	8	no	—
908	C₂²×C₃	C₂²×#41	1	2	yes	—
909	C₂²×C₃	C₂²×#41	1	8	yes	—
910	C₂²×C₃	C₂⁶	1	1	yes	characteristic
911	C₃×C₄	—	2	2	no	—
912	C₃×C₄	—	2	2	no	—
913	C₃×C₄	—	2	4	no	—
914	C₃×C₄	—	2	8	no	—
915	C₃×C₄	—	2	4	no	—
916	C₃×C₄	—	2	1	no	—
917	C₃×C₄	—	2	4	no	—
918	C₃×C₄	—	2	8	no	—
919	C₃×C₄	—	2	4	no	—
920	C₃×C₄	—	2	8	no	—
921	C₃×C₄	—	2	2	no	—
922	C₃×C₄	C₂²×#41	1	4	yes	—
923	C₃×C₄	#585	1	2	yes	—
924	C₂³	—	2	4	no	—
925	C₂³	—	2	8	no	—
926	C₂³	—	4	2	no	—
927	C₂³	—	4	2	no	—
928	C₂³	—	4	4	no	—
929	C₂³	—	4	2	no	—
930	C₂³	—	4	4	no	—
931	C₂³	—	4	2	no	—
932	C₂³	C₂×C₃×#41	1	8	yes	—
933	C₂³	C₂⁵×C₃	1	4	yes	—
934	C₂³	C₂⁵×C₃	1	4	yes	—
935	C₂³	C₂⁵×C₃	1	1	yes	characteristic
936	C₂³	C₂⁵×C₃	1	4	yes	—
937	Q₈	—	2	16	no	—
938	Q₈	—	2	4	no	—
939	Q₈	—	2	8	no	—
940	Q₈	—	4	8	no	—
941	Q₈	—	4	4	no	—
942	D₄	—	2	8	no	—
943	D₄	—	2	16	no	—
944	D₄	—	2	32	no	—
945	D₄	—	2	4	no	—
946	D₄	—	2	4	no	—
947	D₄	—	4	2	no	—
948	D₄	—	4	8	no	—
949	D₄	—	4	8	no	—
950	D₄	C₂×C₃×#41	1	16	yes	—
951	C₂×C₄	—	2	4	no	—
952	C₂×C₄	—	2	8	no	—
953	C₂×C₄	—	2	16	no	—
954	C₂×C₄	—	2	16	no	—
955	C₂×C₄	—	2	8	no	—
956	C₂×C₄	—	2	8	no	—
957	C₂×C₄	—	2	8	no	—
958	C₂×C₄	—	2	8	no	—
959	C₂×C₄	—	2	2	no	—
960	C₂×C₄	—	2	8	no	—
961	C₂×C₄	—	2	8	no	—
962	C₂×C₄	—	4	4	no	—
963	C₂×C₄	—	4	8	no	—
964	C₂×C₄	—	4	4	no	—
965	C₂×C₄	—	4	2	no	—
966	C₂×C₄	—	4	8	no	—
967	C₂×C₄	—	4	8	no	—
968	C₂×C₄	—	4	4	no	—
969	C₂×C₄	—	4	8	no	—
970	C₂×C₄	—	4	4	no	—
971	C₂×C₄	—	4	8	no	—
972	C₂×C₄	—	4	1	no	—
973	C₂×C₄	C₂×C₃×#41	1	4	yes	—
974	C₂×C₄	C₂⁵×C₃	1	4	yes	—
975	C₂×C₄	C₂⁵×C₃	1	2	yes	—
976	C₂×C₄	C₂⁵×C₃	1	4	yes	—
977	C₂×C₄	C₂⁵×C₃	1	2	yes	—
978	C₂×C₄	C₂⁵×C₃	1	8	yes	—
979	C₂×C₄	C₂⁵×C₃	1	8	yes	—
980	C₂×C₄	C₂⁵×C₃	1	8	yes	—
981	C₂×C₄	C₂⁵×C₃	1	4	yes	—
982	C₂×C₄	C₂⁵×C₃	1	4	yes	—
983	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
984	C₂×C₄	C₂⁵×C₃	1	2	yes	—
985	C₂×C₄	C₂⁵×C₃	1	2	yes	—
986	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
987	C₂×C₃	—	2	2	no	—
988	C₂×C₃	—	2	8	no	—
989	C₂×C₃	—	4	4	no	—
990	C₂×C₃	—	4	4	no	—
991	C₂×C₃	C₂³×#41	1	1	yes	characteristic
992	C₂×C₃	C₂×#585	1	1	yes	characteristic
993	C₂×C₃	2₋¹⁺⁶	1	1	yes	characteristic
994	C₂²	—	2	4	no	—
995	C₂²	—	2	1	no	—
996	C₂²	—	2	4	no	—
997	C₂²	—	2	1	no	—
998	C₂²	—	2	4	no	—
999	C₂²	—	2	4	no	—
1000	C₂²	—	2	4	no	—
1001	C₂²	—	2	4	no	—
1002	C₂²	—	2	4	no	—
1003	C₂²	—	2	4	no	—
1004	C₂²	—	4	8	no	—
1005	C₂²	—	8	4	no	—
1006	C₂²	—	8	8	no	—
1007	C₂²	C₂²×C₃×#41	1	2	yes	—
1008	C₂²	C₂²×C₃×#41	1	8	yes	—
1009	C₂²	C₂⁶×C₃	1	1	yes	characteristic
1010	C₄	—	2	2	no	—
1011	C₄	—	2	2	no	—
1012	C₄	—	2	4	no	—
1013	C₄	—	2	8	no	—
1014	C₄	—	2	4	no	—
1015	C₄	—	2	1	no	—
1016	C₄	—	2	4	no	—
1017	C₄	—	2	8	no	—
1018	C₄	—	2	4	no	—
1019	C₄	—	2	8	no	—
1020	C₄	—	2	2	no	—
1021	C₄	C₂²×C₃×#41	1	4	yes	—
1022	C₄	C₃×#585	1	2	yes	—
1023	C₃	#62991	1	1	yes	characteristic, direct product factor, Sylow
1024	C₂	—	2	2	no	—
1025	C₂	—	2	8	no	—
1026	C₂	—	4	4	no	—
1027	C₂	—	4	4	no	—
1028	C₂	C₂³×C₃×#41	1	1	yes	characteristic
1029	C₂	C₂×C₃×#585	1	1	yes	characteristic
1030	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×#3521	C₂	semidirect
2. C₃×#3520	C₂	semidirect
3. C₃×#3515	C₂	semidirect
4. C₃×#3515	C₂	semidirect
5. C₃×#3509	C₂	semidirect
6. C₃×#3505	C₂	semidirect
7. C₃×#3501	C₂	semidirect
8. C₃×#3495	C₂	semidirect
9. C₃×#3491	C₂	semidirect
10. C₃×#3485	C₂	semidirect
11. C₃×#3482	C₂	semidirect
12. C₃×#3475	C₂	semidirect
13. C₃×#3475	C₂	semidirect
14. C₂×C₃×#552	C₂	semidirect
15. C₂×C₃×#547	C₂	semidirect
16. C₃×C₄×H(5,𝔽₂)	C₂	semidirect
17. C₃×#3428	C₂	semidirect
18. #62991	C₃	direct (N × H)
21. C₃×#557	C₂²	semidirect
22. C₃×#557	C₂²	semidirect
23. C₃×#556	C₂²	semidirect
24. C₃×#556	C₂²	semidirect
25. C₃×#556	C₂²	semidirect
26. C₃×#556	C₂²	semidirect
27. C₃×#555	C₂²	semidirect
28. C₃×#554	C₂²	semidirect
29. C₃×#554	C₂²	semidirect
30. C₃×#554	C₂²	semidirect
31. C₃×#554	C₂²	semidirect
32. C₃×#553	C₂²	semidirect
33. C₃×#553	C₂²	semidirect
34. C₃×#553	C₂²	semidirect
35. C₃×#552	C₂²	semidirect
36. C₃×#552	C₂²	semidirect
37. C₃×#552	C₂²	semidirect
38. C₃×#552	C₂²	semidirect
39. C₃×#552	C₂²	semidirect
40. C₃×#552	C₂²	semidirect
41. C₃×#552	C₂²	semidirect
42. C₃×#552	C₂²	semidirect
43. C₃×#552	C₂²	semidirect
44. C₃×#552	C₂²	semidirect
45. C₃×#552	C₂²	semidirect
46. C₃×#552	C₂²	semidirect
47. C₃×#551	C₂²	semidirect
48. C₃×#551	C₂²	semidirect
49. C₃×#551	C₂²	semidirect
50. C₃×#551	C₂²	semidirect
51. C₃×D₄×Q₈	C₂²	semidirect
52. C₃×#548	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×#547	C₂²	semidirect
59. C₃×#546	C₂²	semidirect
60. C₃×#546	C₂²	semidirect
61. C₃×#546	C₂²	semidirect
62. C₃×#544	C₂²	semidirect
63. C₃×#543	C₂²	semidirect
64. C₃×#542	C₂²	semidirect
65. C₃×#541	C₂²	semidirect
66. C₃×#541	C₂²	semidirect
67. C₃×#539	C₂²	semidirect
68. C₃×#539	C₂²	semidirect
69. C₃×#539	C₂²	semidirect
70. C₃×#538	C₂²	semidirect
73. C₃×#533	C₂²	semidirect
74. C₃×#533	C₂²	semidirect
75. C₃×#533	C₂²	semidirect
76. C₃×#533	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×#529	C₂²	semidirect
82. C₃×#529	C₂²	semidirect
83. C₃×#529	C₂²	semidirect
84. C₂×C₃×#126	C₂²	semidirect
85. C₂×C₃×#125	C₂²	semidirect
86. C₂×C₃×#125	C₂²	semidirect
88. C₃×#525	C₂²	semidirect
90. C₂×C₃×#123	C₂²	semidirect
91. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
92. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
93. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
94. C₂×C₃×#121	C₂²	semidirect
96. C₃×#520	C₂²	semidirect
97. C₃×#520	C₂²	semidirect
98. C₃×#520	C₂²	semidirect
99. C₃×#519	C₂²	semidirect
103. C₃×#518	C₂²	semidirect
104. C₃×#518	C₂²	semidirect
106. C₃×C₄×#41	C₂²	semidirect
107. C₃×C₄×#41	C₂²	semidirect
108. C₃×C₄×#41	C₂²	semidirect
109. C₃×C₄×#41	C₂²	semidirect
110. C₂×C₃×C₄×Q₈	C₂²	semidirect
113. C₂×C₃×C₄×D₄	C₂²	semidirect
114. C₂×C₃×C₄×D₄	C₂²	semidirect
115. C₂×C₃×#117	C₂²	semidirect
116. C₂×C₃×#117	C₂²	semidirect
117. C₂×C₃×#117	C₂²	semidirect
118. C₂²×C₃×C₄⋊C₄	C₂²	semidirect
119. #3521	C₂×C₃	semidirect
120. #3520	C₂×C₃	semidirect
121. #3515	C₂×C₃	semidirect
122. #3515	C₂×C₃	semidirect
123. #3509	C₂×C₃	semidirect
124. #3505	C₂×C₃	semidirect
125. #3501	C₂×C₃	semidirect
126. #3495	C₂×C₃	semidirect
127. #3491	C₂×C₃	semidirect
128. #3485	C₂×C₃	semidirect
129. #3482	C₂×C₃	semidirect
130. #3475	C₂×C₃	semidirect
131. #3475	C₂×C₃	semidirect
132. C₂×#552	C₂×C₃	semidirect
133. C₂×#547	C₂×C₃	semidirect
134. C₄×H(5,𝔽₂)	C₂×C₃	semidirect
135. #3428	C₂×C₃	semidirect
320. #557	C₂²×C₃	semidirect
321. #557	C₂²×C₃	semidirect
322. #556	C₂²×C₃	semidirect
323. #556	C₂²×C₃	semidirect
324. #556	C₂²×C₃	semidirect
325. #556	C₂²×C₃	semidirect
326. #555	C₂²×C₃	semidirect
327. #554	C₂²×C₃	semidirect
328. #554	C₂²×C₃	semidirect
329. #554	C₂²×C₃	semidirect
330. #554	C₂²×C₃	semidirect
331. #553	C₂²×C₃	semidirect
332. #553	C₂²×C₃	semidirect
333. #553	C₂²×C₃	semidirect
334. #552	C₂²×C₃	semidirect
335. #552	C₂²×C₃	semidirect
336. #552	C₂²×C₃	semidirect
337. #552	C₂²×C₃	semidirect
338. #552	C₂²×C₃	semidirect
339. #552	C₂²×C₃	semidirect
340. #552	C₂²×C₃	semidirect
341. #552	C₂²×C₃	semidirect
342. #552	C₂²×C₃	semidirect
343. #552	C₂²×C₃	semidirect
344. #552	C₂²×C₃	semidirect
345. #552	C₂²×C₃	semidirect
346. #551	C₂²×C₃	semidirect
347. #551	C₂²×C₃	semidirect
348. #551	C₂²×C₃	semidirect
349. #551	C₂²×C₃	semidirect
350. D₄×Q₈	C₂²×C₃	semidirect
351. #548	C₂²×C₃	semidirect
352. #547	C₂²×C₃	semidirect
353. #547	C₂²×C₃	semidirect
354. #547	C₂²×C₃	semidirect
355. #547	C₂²×C₃	semidirect
356. #547	C₂²×C₃	semidirect
357. #547	C₂²×C₃	semidirect
358. #546	C₂²×C₃	semidirect
359. #546	C₂²×C₃	semidirect
360. #546	C₂²×C₃	semidirect
361. #544	C₂²×C₃	semidirect
362. #543	C₂²×C₃	semidirect
363. #542	C₂²×C₃	semidirect
364. #541	C₂²×C₃	semidirect
365. #541	C₂²×C₃	semidirect
366. #539	C₂²×C₃	semidirect
367. #539	C₂²×C₃	semidirect
368. #539	C₂²×C₃	semidirect
369. #538	C₂²×C₃	semidirect
372. #533	C₂²×C₃	semidirect
373. #533	C₂²×C₃	semidirect
374. #533	C₂²×C₃	semidirect
375. #533	C₂²×C₃	semidirect
376. C₂×C₄⋊Q₈	C₂²×C₃	semidirect
377. #529	C₂²×C₃	semidirect
378. #529	C₂²×C₃	semidirect
379. #529	C₂²×C₃	semidirect
380. #529	C₂²×C₃	semidirect
381. #529	C₂²×C₃	semidirect
382. #529	C₂²×C₃	semidirect
383. C₂×#126	C₂²×C₃	semidirect
384. C₂×#125	C₂²×C₃	semidirect
385. C₂×#125	C₂²×C₃	semidirect
387. #525	C₂²×C₃	semidirect
389. C₂×#123	C₂²×C₃	semidirect
390. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
391. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
392. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
393. C₂×#121	C₂²×C₃	semidirect
395. #520	C₂²×C₃	semidirect
396. #520	C₂²×C₃	semidirect
397. #520	C₂²×C₃	semidirect
398. #519	C₂²×C₃	semidirect
402. #518	C₂²×C₃	semidirect
403. #518	C₂²×C₃	semidirect
405. C₄×#41	C₂²×C₃	semidirect
406. C₄×#41	C₂²×C₃	semidirect
407. C₄×#41	C₂²×C₃	semidirect
408. C₄×#41	C₂²×C₃	semidirect
409. C₂×C₄×Q₈	C₂²×C₃	semidirect
412. C₂×C₄×D₄	C₂²×C₃	semidirect
413. C₂×C₄×D₄	C₂²×C₃	semidirect
414. C₂×#117	C₂²×C₃	semidirect
415. C₂×#117	C₂²×C₃	semidirect
416. C₂×#117	C₂²×C₃	semidirect
417. C₂²×C₄⋊C₄	C₂²×C₃	semidirect
437. C₂×C₃×D₄	#41	semidirect
798. C₂×D₄	C₃×#41	semidirect
1023. C₃	#62991	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×#3521	2
C₃×#3520	2
C₃×#3515	2
C₃×#3509	2
C₃×#3505	2
C₃×#3501	2
C₃×#3495	2
C₃×#3491	2
C₃×#3485	2
C₃×#3482	2
C₃×#3475	2
C₂×C₃×#552	2
C₂×C₃×#547	2
C₃×C₄×H(5,𝔽₂)	2
C₃×#3428	2
#62991	3

Subgroups — C3×#62991 #10681598

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#62991 #10681598