Subgroups — C₃×#34482 #10653089

Order 768.

2024 conjugacy classes of subgroups.

The subgroup lattice has 966 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#552	C₂	1	1	yes	maximal, characteristic
2	C₃×#2382	C₂	1	2	yes	maximal, complemented
3	C₃×#2376	C₂	1	2	yes	maximal
4	C₃×#2373	C₂	1	2	yes	maximal, complemented
5	C₃×#2370	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#2362	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#2360	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#2352	C₂	1	1	yes	maximal, characteristic
9	C₃×#2351	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#2346	C₂	1	2	yes	maximal, complemented
11	C₃×#2346	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#2345	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#2335	C₂	1	2	yes	maximal
14	C₃×#2334	C₂	1	2	yes	maximal, complemented
15	C₃×#2330	C₂	1	2	yes	maximal, complemented
16	C₃×#2323	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×#2323	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃×#2317	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃×#2316	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃×#2314	C₂	1	2	yes	maximal, complemented
21	C₃×C₄×#125	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃×#2295	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃×#2293	C₂	1	1	yes	maximal, characteristic
24	#34482	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₃×#552	C₄	1	16	yes	complemented
26	C₂×C₃×#126	C₂²	1	2	yes	—
27	C₂×C₃×#125	C₂²	1	1	yes	characteristic
28	C₂×C₃×#125	C₂²	1	2	yes	—
29	C₂×C₃×#123	C₂²	1	2	yes	—
30	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
31	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
32	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
33	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
34	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
35	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
36	C₂×C₃×#117	C₂²	1	1	yes	characteristic
37	C₂×C₃×#117	C₂²	1	1	yes	characteristic
38	C₂×C₃×#117	C₂²	1	1	yes	characteristic
39	C₂×C₃×#117	C₂²	1	1	yes	characteristic
40	C₂×C₃×#117	C₂²	1	2	yes	—
41	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
42	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
43	C₃×#391	C₂²	1	1	yes	characteristic
44	C₃×#391	C₂²	1	1	yes	characteristic
45	C₃×#390	C₂²	1	1	yes	characteristic
46	C₃×#390	C₂²	1	1	yes	characteristic
47	C₃×#389	C₂²	1	1	yes	characteristic
48	C₃×#389	C₂²	1	2	yes	—
49	C₃×#389	C₂²	1	1	yes	characteristic
50	C₃×#389	C₂²	1	2	yes	—
51	C₃×#389	C₂²	1	2	yes	—
52	C₃×#389	C₂²	1	2	yes	—
53	C₃×#389	C₂²	1	1	yes	characteristic
54	C₃×#389	C₂²	1	2	yes	—
55	C₃×#389	C₂²	1	2	yes	—
56	C₃×#389	C₂²	1	1	yes	characteristic
57	C₃×#389	C₂²	1	1	yes	characteristic
58	C₃×#389	C₂²	1	1	yes	characteristic
59	C₃×#389	C₂²	1	1	yes	characteristic
60	C₃×#389	C₂²	1	1	yes	characteristic
61	C₃×#389	C₂²	1	2	yes	—
62	C₃×#389	C₂²	1	1	yes	characteristic
63	C₃×#389	C₂²	1	1	yes	characteristic
64	C₃×#389	C₂²	1	2	yes	—
65	C₃×#388	C₂²	1	2	yes	—
66	C₃×#388	C₂²	1	2	yes	—
67	C₃×#388	C₂²	1	1	yes	characteristic
68	C₃×#388	C₂²	1	2	yes	—
69	C₃×#388	C₂²	1	2	yes	—
70	C₃×#388	C₂²	1	2	yes	—
71	C₃×#388	C₂²	1	2	yes	—
72	C₃×#388	C₂²	1	1	yes	characteristic
73	C₃×#388	C₂²	1	1	yes	characteristic
74	C₃×#388	C₂²	1	1	yes	characteristic
75	C₃×#388	C₂²	1	2	yes	—
76	C₃×#388	C₂²	1	2	yes	—
77	C₃×#388	C₂²	1	2	yes	—
78	C₃×#387	C₂²	1	2	yes	—
79	C₃×#387	C₂²	1	2	yes	—
80	C₃×#387	C₂²	1	2	yes	—
81	C₃×#387	C₂²	1	2	yes	—
82	C₃×#387	C₂²	1	2	yes	—
83	C₃×#387	C₂²	1	2	yes	—
84	C₃×#387	C₂²	1	2	yes	—
85	C₃×#387	C₂²	1	2	yes	—
86	C₃×#387	C₂²	1	2	yes	—
87	C₃×#387	C₂²	1	2	yes	—
88	C₃×#387	C₂²	1	2	yes	—
89	C₃×#387	C₂²	1	2	yes	—
90	C₃×#387	C₂²	1	2	yes	—
91	C₃×#386	C₂²	1	2	yes	—
92	C₃×#385	C₂²	1	2	yes	—
93	C₃×#385	C₂²	1	2	yes	—
94	C₃×#385	C₂²	1	2	yes	—
95	C₃×#384	C₂²	1	2	yes	—
96	C₃×#382	C₂²	1	2	yes	—
97	C₃×#382	C₂²	1	2	yes	—
98	C₃×#382	C₂²	1	1	yes	characteristic
99	C₃×#382	C₂²	1	2	yes	—
100	C₃×#380	C₂²	1	2	yes	—
101	C₃×#380	C₂²	1	2	yes	—
102	C₃×#380	C₂²	1	2	yes	—
103	C₃×#380	C₂²	1	1	yes	characteristic
104	C₃×#380	C₂²	1	1	yes	characteristic
105	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
106	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
107	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
108	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
109	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
110	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
111	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
112	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
113	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
114	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
115	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
116	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
117	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
118	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
119	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
120	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
121	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
122	C₃×#376	C₂²	1	2	yes	—
123	C₃×#376	C₂²	1	2	yes	—
124	C₃×C₄³	C₂²	1	1	yes	characteristic
125	C₂×#552	C₂×C₃	1	1	yes	characteristic
126	#2382	C₂×C₃	1	2	yes	complemented
127	#2376	C₂×C₃	1	2	yes	—
128	#2373	C₂×C₃	1	2	yes	complemented
129	#2370	C₂×C₃	1	1	yes	characteristic, complemented
130	#2362	C₂×C₃	1	1	yes	characteristic, complemented
131	#2360	C₂×C₃	1	1	yes	characteristic, complemented
132	#2352	C₂×C₃	1	1	yes	characteristic
133	#2351	C₂×C₃	1	1	yes	characteristic, complemented
134	#2346	C₂×C₃	1	1	yes	characteristic, complemented
135	#2346	C₂×C₃	1	2	yes	complemented
136	#2345	C₂×C₃	1	1	yes	characteristic, complemented
137	#2335	C₂×C₃	1	2	yes	—
138	#2334	C₂×C₃	1	2	yes	complemented
139	#2330	C₂×C₃	1	2	yes	complemented
140	#2323	C₂×C₃	1	1	yes	characteristic, complemented
141	#2323	C₂×C₃	1	1	yes	characteristic, complemented
142	#2317	C₂×C₃	1	1	yes	characteristic, complemented
143	#2316	C₂×C₃	1	1	yes	characteristic, complemented
144	#2314	C₂×C₃	1	2	yes	complemented
145	C₄×#125	C₂×C₃	1	1	yes	characteristic, complemented
146	#2295	C₂×C₃	1	1	yes	characteristic, complemented
147	#2293	C₂×C₃	1	1	yes	characteristic
148	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
149	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
150	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
151	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
152	C₂³×C₃×C₄	C₂³	1	2	yes	—
153	C₂³×C₃×C₄	C₂³	1	2	yes	—
154	C₃×#126	C₂×C₄	1	16	yes	—
155	C₃×#125	C₂×C₄	1	16	yes	complemented
156	C₃×#125	C₂×C₄	1	8	yes	complemented
157	C₃×#123	C₂×C₄	1	16	yes	—
158	C₃×C₂²⋊Q₈	C₂×C₄	1	8	yes	—
159	C₃×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
160	C₃×C₄×Q₈	—	4	2	no	—
161	C₃×C₄×Q₈	—	4	2	no	—
162	C₃×C₄×Q₈	C₂×C₄	1	8	yes	complemented
163	C₃×C₄×D₄	C₂×C₄	1	8	yes	—
164	C₃×#117	—	4	2	no	—
165	C₃×#117	—	4	2	no	—
166	C₃×#117	—	4	2	no	—
167	C₃×#117	C₂×C₄	1	8	yes	—
168	C₃×#117	C₂×C₄	1	16	yes	complemented
169	C₂×C₃×C₄⋊C₄	—	4	2	no	—
170	C₂×C₃×C₄⋊C₄	C₂×C₄	1	8	yes	complemented
171	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
172	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
173	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
174	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
175	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
176	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
177	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
178	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
179	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
180	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
181	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
182	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
183	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
184	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
185	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
186	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
187	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
188	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
189	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
190	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
191	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
192	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
193	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
194	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
195	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
196	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
197	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
198	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
199	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
200	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
201	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
202	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
203	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
204	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
205	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
206	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
207	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
208	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
209	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
210	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
211	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
212	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
213	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
214	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
215	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
216	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
217	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
218	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
219	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
220	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
221	C₂×C₃×C₄²	C₂³	1	2	yes	—
222	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
223	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
224	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
225	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
226	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
227	C₂×C₃×C₄²	C₂³	1	2	yes	—
228	C₂×C₃×C₄²	C₂³	1	2	yes	—
229	C₂×C₃×C₄²	C₂³	1	2	yes	—
230	C₂×C₃×C₄²	C₂³	1	2	yes	—
231	C₂×C₃×C₄²	C₂³	1	2	yes	—
232	C₂×C₃×C₄²	C₂³	1	2	yes	—
233	C₂×C₃×C₄²	C₂³	1	2	yes	—
234	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
235	C₂×C₃×C₄²	C₂³	1	2	yes	—
236	C₂×C₃×C₄²	C₂³	1	2	yes	—
237	C₃×#95	C₂³	1	2	yes	—
238	C₃×#95	C₂³	1	1	yes	characteristic
239	C₃×#95	C₂³	1	2	yes	—
240	C₃×#95	C₂³	1	2	yes	—
241	C₃×#95	C₂³	1	2	yes	—
242	C₃×#95	C₂³	1	2	yes	—
243	C₃×#95	C₂³	1	2	yes	—
244	C₃×#95	C₂³	1	2	yes	—
245	C₃×#95	C₂³	1	1	yes	characteristic
246	C₃×#95	C₂³	1	2	yes	—
247	C₃×#95	C₂³	1	2	yes	—
248	C₃×#95	C₂³	1	2	yes	—
249	C₃×#95	C₂³	1	1	yes	characteristic
250	C₃×#95	C₂³	1	1	yes	characteristic
251	C₃×#95	C₂³	1	1	yes	characteristic
252	C₃×#95	C₂³	1	1	yes	characteristic
253	C₃×#95	C₂³	1	2	yes	—
254	C₃×#95	C₂³	1	2	yes	—
255	C₃×#95	C₂³	1	2	yes	—
256	C₃×#95	C₂³	1	2	yes	—
257	C₃×#95	C₂³	1	2	yes	—
258	C₃×#95	C₂³	1	2	yes	—
259	C₃×#95	C₂³	1	2	yes	—
260	C₃×#95	C₂³	1	2	yes	—
261	C₃×#95	C₂³	1	2	yes	—
262	C₃×#95	C₂³	1	2	yes	—
263	C₃×#95	C₂³	1	2	yes	—
264	#552	C₃×C₄	1	16	yes	complemented
265	C₂×#126	C₂²×C₃	1	2	yes	—
266	C₂×#125	C₂²×C₃	1	1	yes	characteristic
267	C₂×#125	C₂²×C₃	1	2	yes	—
268	C₂×#123	C₂²×C₃	1	2	yes	—
269	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
270	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
271	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
272	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
273	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
274	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
275	C₂×#117	C₂²×C₃	1	1	yes	characteristic
276	C₂×#117	C₂²×C₃	1	1	yes	characteristic
277	C₂×#117	C₂²×C₃	1	1	yes	characteristic
278	C₂×#117	C₂²×C₃	1	1	yes	characteristic
279	C₂×#117	C₂²×C₃	1	2	yes	—
280	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
281	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
282	#391	C₂²×C₃	1	1	yes	characteristic
283	#391	C₂²×C₃	1	1	yes	characteristic
284	#390	C₂²×C₃	1	1	yes	characteristic
285	#390	C₂²×C₃	1	1	yes	characteristic
286	#389	C₂²×C₃	1	1	yes	characteristic
287	#389	C₂²×C₃	1	1	yes	characteristic
288	#389	C₂²×C₃	1	1	yes	characteristic
289	#389	C₂²×C₃	1	2	yes	—
290	#389	C₂²×C₃	1	1	yes	characteristic
291	#389	C₂²×C₃	1	1	yes	characteristic
292	#389	C₂²×C₃	1	2	yes	—
293	#389	C₂²×C₃	1	1	yes	characteristic
294	#389	C₂²×C₃	1	1	yes	characteristic
295	#389	C₂²×C₃	1	2	yes	—
296	#389	C₂²×C₃	1	2	yes	—
297	#389	C₂²×C₃	1	1	yes	characteristic
298	#389	C₂²×C₃	1	2	yes	—
299	#389	C₂²×C₃	1	2	yes	—
300	#389	C₂²×C₃	1	2	yes	—
301	#389	C₂²×C₃	1	2	yes	—
302	#389	C₂²×C₃	1	1	yes	characteristic
303	#389	C₂²×C₃	1	1	yes	characteristic
304	#388	C₂²×C₃	1	1	yes	characteristic
305	#388	C₂²×C₃	1	2	yes	—
306	#388	C₂²×C₃	1	2	yes	—
307	#388	C₂²×C₃	1	2	yes	—
308	#388	C₂²×C₃	1	2	yes	—
309	#388	C₂²×C₃	1	2	yes	—
310	#388	C₂²×C₃	1	2	yes	—
311	#388	C₂²×C₃	1	1	yes	characteristic
312	#388	C₂²×C₃	1	2	yes	—
313	#388	C₂²×C₃	1	2	yes	—
314	#388	C₂²×C₃	1	2	yes	—
315	#388	C₂²×C₃	1	1	yes	characteristic
316	#388	C₂²×C₃	1	1	yes	characteristic
317	#387	C₂²×C₃	1	2	yes	—
318	#387	C₂²×C₃	1	2	yes	—
319	#387	C₂²×C₃	1	2	yes	—
320	#387	C₂²×C₃	1	2	yes	—
321	#387	C₂²×C₃	1	2	yes	—
322	#387	C₂²×C₃	1	2	yes	—
323	#387	C₂²×C₃	1	2	yes	—
324	#387	C₂²×C₃	1	2	yes	—
325	#387	C₂²×C₃	1	2	yes	—
326	#387	C₂²×C₃	1	2	yes	—
327	#387	C₂²×C₃	1	2	yes	—
328	#387	C₂²×C₃	1	2	yes	—
329	#387	C₂²×C₃	1	2	yes	—
330	#386	C₂²×C₃	1	2	yes	—
331	#385	C₂²×C₃	1	2	yes	—
332	#385	C₂²×C₃	1	2	yes	—
333	#385	C₂²×C₃	1	2	yes	—
334	#384	C₂²×C₃	1	2	yes	—
335	#382	C₂²×C₃	1	1	yes	characteristic
336	#382	C₂²×C₃	1	2	yes	—
337	#382	C₂²×C₃	1	2	yes	—
338	#382	C₂²×C₃	1	2	yes	—
339	#380	C₂²×C₃	1	2	yes	—
340	#380	C₂²×C₃	1	2	yes	—
341	#380	C₂²×C₃	1	2	yes	—
342	#380	C₂²×C₃	1	1	yes	characteristic
343	#380	C₂²×C₃	1	1	yes	characteristic
344	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
345	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
346	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
347	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
348	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
349	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
350	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
351	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
352	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
353	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
354	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
355	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
356	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
357	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
358	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
359	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
360	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
361	#376	C₂²×C₃	1	2	yes	—
362	#376	C₂²×C₃	1	2	yes	—
363	C₄³	C₂²×C₃	1	1	yes	characteristic
364	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
365	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
366	C₂×C₃×Q₈	—	2	2	no	—
367	C₂×C₃×Q₈	—	2	2	no	—
368	C₂×C₃×Q₈	C₂²×C₄	1	4	yes	—
369	C₂×C₃×D₄	—	4	1	no	—
370	C₂×C₃×D₄	—	4	1	no	—
371	C₂×C₃×D₄	C₂²×C₄	1	4	yes	—
372	C₂²×C₃×C₄	—	2	2	no	—
373	C₂²×C₃×C₄	—	2	2	no	—
374	C₂²×C₃×C₄	—	2	2	no	—
375	C₂²×C₃×C₄	—	2	2	no	—
376	C₂²×C₃×C₄	—	4	2	no	—
377	C₂²×C₃×C₄	—	4	2	no	—
378	C₂²×C₃×C₄	—	4	2	no	—
379	C₂²×C₃×C₄	—	4	2	no	—
380	C₂²×C₃×C₄	—	4	2	no	—
381	C₂²×C₃×C₄	C₂²×C₄	1	4	yes	—
382	C₂²×C₃×C₄	C₂²×C₄	1	4	yes	—
383	C₂²×C₃×C₄	C₂²×C₄	1	8	yes	—
384	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
385	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
386	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
387	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
388	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
389	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
390	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
391	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
392	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
393	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
394	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
395	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
396	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
397	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
398	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
399	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
400	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
401	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
402	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
403	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
404	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
405	C₃×C₄⋊C₄	—	2	2	no	—
406	C₃×C₄⋊C₄	—	2	2	no	—
407	C₃×C₄⋊C₄	—	2	2	no	—
408	C₃×C₄⋊C₄	—	2	2	no	—
409	C₃×C₄⋊C₄	—	4	2	no	—
410	C₃×C₄⋊C₄	—	4	2	no	—
411	C₃×C₄⋊C₄	—	4	2	no	—
412	C₃×C₄⋊C₄	—	4	2	no	—
413	C₃×C₄⋊C₄	—	4	2	no	—
414	C₃×C₄⋊C₄	—	4	1	no	—
415	C₃×C₄⋊C₄	—	4	1	no	—
416	C₃×C₄⋊C₄	—	4	2	no	—
417	C₃×C₄⋊C₄	—	4	2	no	—
418	C₃×C₄⋊C₄	—	4	2	no	—
419	C₃×C₄⋊C₄	—	4	2	no	—
420	C₃×C₄⋊C₄	—	4	1	no	—
421	C₃×C₄⋊C₄	—	4	1	no	—
422	C₃×C₄⋊C₄	—	4	1	no	—
423	C₃×C₄⋊C₄	—	4	1	no	—
424	C₃×C₄⋊C₄	—	4	2	no	—
425	C₃×C₄⋊C₄	—	4	2	no	—
426	C₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
427	C₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
428	C₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
429	C₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
430	C₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
431	C₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
432	C₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
433	C₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
434	C₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
435	C₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
436	C₃×C₂²⋊C₄	—	2	2	no	—
437	C₃×C₂²⋊C₄	—	2	2	no	—
438	C₃×C₂²⋊C₄	—	4	1	no	—
439	C₃×C₂²⋊C₄	—	4	2	no	—
440	C₃×C₂²⋊C₄	—	4	1	no	—
441	C₃×C₂²⋊C₄	—	4	2	no	—
442	C₃×C₂²⋊C₄	—	4	1	no	—
443	C₃×C₂²⋊C₄	—	4	1	no	—
444	C₃×C₂²⋊C₄	—	4	1	no	—
445	C₃×C₂²⋊C₄	—	4	1	no	—
446	C₃×C₂²⋊C₄	—	4	2	no	—
447	C₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
448	C₃×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
449	C₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
450	C₃×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
451	C₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
452	C₃×C₄²	—	2	2	no	—
453	C₃×C₄²	—	2	2	no	—
454	C₃×C₄²	—	2	2	no	—
455	C₃×C₄²	—	2	2	no	—
456	C₃×C₄²	—	2	4	no	—
457	C₃×C₄²	—	2	2	no	—
458	C₃×C₄²	—	4	2	no	—
459	C₃×C₄²	—	4	1	no	—
460	C₃×C₄²	—	4	2	no	—
461	C₃×C₄²	—	4	1	no	—
462	C₃×C₄²	—	4	2	no	—
463	C₃×C₄²	—	4	2	no	—
464	C₃×C₄²	—	4	1	no	—
465	C₃×C₄²	—	4	2	no	—
466	C₃×C₄²	—	4	2	no	—
467	C₃×C₄²	—	4	2	no	—
468	C₃×C₄²	C₂²×C₄	1	8	yes	—
469	C₃×C₄²	C₂²×C₄	1	8	yes	—
470	C₃×C₄²	C₂²×C₄	1	4	yes	—
471	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
472	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
473	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
474	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
475	C₂³×C₄	C₂³×C₃	1	2	yes	—
476	C₂³×C₄	C₂³×C₃	1	2	yes	—
477	#126	C₂×C₃×C₄	1	16	yes	—
478	#125	C₂×C₃×C₄	1	16	yes	complemented
479	#125	C₂×C₃×C₄	1	8	yes	complemented
480	#123	C₂×C₃×C₄	1	16	yes	—
481	C₂²⋊Q₈	C₂×C₃×C₄	1	8	yes	—
482	C₂²⋊Q₈	C₂×C₃×C₄	1	8	yes	complemented
483	C₄×Q₈	—	4	2	no	—
484	C₄×Q₈	—	4	2	no	—
485	C₄×Q₈	C₂×C₃×C₄	1	8	yes	complemented
486	C₄×D₄	C₂×C₃×C₄	1	8	yes	—
487	#117	—	4	2	no	—
488	#117	—	4	2	no	—
489	#117	—	4	2	no	—
490	#117	C₂×C₃×C₄	1	8	yes	—
491	#117	C₂×C₃×C₄	1	16	yes	complemented
492	C₂×C₄⋊C₄	—	4	2	no	—
493	C₂×C₄⋊C₄	C₂×C₃×C₄	1	8	yes	complemented
494	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
495	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
496	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
497	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
498	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
499	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
500	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
501	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
502	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
503	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
504	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
505	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
506	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
507	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
508	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
509	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
510	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
511	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
512	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
513	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
514	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
515	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
516	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
517	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
518	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
519	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
520	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
521	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
522	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
523	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
524	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
525	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
526	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
527	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
528	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
529	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
530	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
531	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
532	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
533	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
534	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
535	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
536	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
537	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
538	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
539	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
540	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
541	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
542	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
543	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
544	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
545	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
546	C₂×C₄²	C₂³×C₃	1	2	yes	—
547	C₂×C₄²	C₂³×C₃	1	2	yes	—
548	C₂×C₄²	C₂³×C₃	1	2	yes	—
549	C₂×C₄²	C₂³×C₃	1	2	yes	—
550	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
551	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
552	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
553	C₂×C₄²	C₂³×C₃	1	2	yes	—
554	C₂×C₄²	C₂³×C₃	1	2	yes	—
555	C₂×C₄²	C₂³×C₃	1	2	yes	—
556	C₂×C₄²	C₂³×C₃	1	2	yes	—
557	C₂×C₄²	C₂³×C₃	1	2	yes	—
558	C₂×C₄²	C₂³×C₃	1	2	yes	—
559	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
560	#95	C₂³×C₃	1	2	yes	—
561	#95	C₂³×C₃	1	1	yes	characteristic
562	#95	C₂³×C₃	1	2	yes	—
563	#95	C₂³×C₃	1	2	yes	—
564	#95	C₂³×C₃	1	2	yes	—
565	#95	C₂³×C₃	1	2	yes	—
566	#95	C₂³×C₃	1	2	yes	—
567	#95	C₂³×C₃	1	2	yes	—
568	#95	C₂³×C₃	1	1	yes	characteristic
569	#95	C₂³×C₃	1	2	yes	—
570	#95	C₂³×C₃	1	2	yes	—
571	#95	C₂³×C₃	1	2	yes	—
572	#95	C₂³×C₃	1	1	yes	characteristic
573	#95	C₂³×C₃	1	1	yes	characteristic
574	#95	C₂³×C₃	1	1	yes	characteristic
575	#95	C₂³×C₃	1	1	yes	characteristic
576	#95	C₂³×C₃	1	2	yes	—
577	#95	C₂³×C₃	1	2	yes	—
578	#95	C₂³×C₃	1	2	yes	—
579	#95	C₂³×C₃	1	2	yes	—
580	#95	C₂³×C₃	1	2	yes	—
581	#95	C₂³×C₃	1	2	yes	—
582	#95	C₂³×C₃	1	2	yes	—
583	#95	C₂³×C₃	1	2	yes	—
584	#95	C₂³×C₃	1	2	yes	—
585	#95	C₂³×C₃	1	2	yes	—
586	#95	C₂³×C₃	1	2	yes	—
587	C₂³×C₃	—	2	1	no	—
588	C₂³×C₃	—	2	1	no	—
589	C₂³×C₃	—	2	1	no	—
590	C₂³×C₃	—	2	1	no	—
591	C₂³×C₃	—	2	1	no	—
592	C₂³×C₃	—	2	1	no	—
593	C₂³×C₃	—	2	1	no	—
594	C₂³×C₃	—	2	1	no	—
595	C₂³×C₃	—	2	1	no	—
596	C₂³×C₃	—	2	1	no	—
597	C₂³×C₃	—	2	1	no	—
598	C₂³×C₃	—	2	1	no	—
599	C₂³×C₃	C₂³×C₄	1	2	yes	—
600	C₂³×C₃	C₂³×C₄	1	2	yes	—
601	C₂³×C₃	C₂⁵	1	1	yes	characteristic
602	C₃×Q₈	—	2	8	no	—
603	C₃×D₄	—	4	4	no	—
604	C₂×C₃×C₄	—	2	1	no	—
605	C₂×C₃×C₄	—	2	2	no	—
606	C₂×C₃×C₄	—	2	1	no	—
607	C₂×C₃×C₄	—	2	1	no	—
608	C₂×C₃×C₄	—	2	2	no	—
609	C₂×C₃×C₄	—	2	1	no	—
610	C₂×C₃×C₄	—	2	1	no	—
611	C₂×C₃×C₄	—	2	1	no	—
612	C₂×C₃×C₄	—	2	2	no	—
613	C₂×C₃×C₄	—	2	1	no	—
614	C₂×C₃×C₄	—	2	1	no	—
615	C₂×C₃×C₄	—	2	2	no	—
616	C₂×C₃×C₄	—	2	2	no	—
617	C₂×C₃×C₄	—	2	2	no	—
618	C₂×C₃×C₄	—	2	1	no	—
619	C₂×C₃×C₄	—	2	1	no	—
620	C₂×C₃×C₄	—	2	2	no	—
621	C₂×C₃×C₄	—	2	2	no	—
622	C₂×C₃×C₄	—	2	8	no	—
623	C₂×C₃×C₄	—	2	8	no	—
624	C₂×C₃×C₄	—	2	1	no	—
625	C₂×C₃×C₄	—	2	1	no	—
626	C₂×C₃×C₄	—	2	1	no	—
627	C₂×C₃×C₄	—	2	1	no	—
628	C₂×C₃×C₄	—	2	1	no	—
629	C₂×C₃×C₄	—	2	1	no	—
630	C₂×C₃×C₄	—	2	2	no	—
631	C₂×C₃×C₄	—	2	2	no	—
632	C₂×C₃×C₄	—	2	2	no	—
633	C₂×C₃×C₄	—	2	1	no	—
634	C₂×C₃×C₄	—	2	2	no	—
635	C₂×C₃×C₄	—	2	1	no	—
636	C₂×C₃×C₄	—	2	1	no	—
637	C₂×C₃×C₄	—	2	1	no	—
638	C₂×C₃×C₄	—	2	2	no	—
639	C₂×C₃×C₄	—	2	1	no	—
640	C₂×C₃×C₄	—	2	2	no	—
641	C₂×C₃×C₄	—	2	1	no	—
642	C₂×C₃×C₄	—	2	1	no	—
643	C₂×C₃×C₄	—	2	2	no	—
644	C₂×C₃×C₄	—	2	1	no	—
645	C₂×C₃×C₄	—	2	1	no	—
646	C₂×C₃×C₄	—	2	1	no	—
647	C₂×C₃×C₄	—	2	1	no	—
648	C₂×C₃×C₄	—	2	2	no	—
649	C₂×C₃×C₄	—	2	2	no	—
650	C₂×C₃×C₄	—	2	2	no	—
651	C₂×C₃×C₄	—	2	1	no	—
652	C₂×C₃×C₄	—	2	2	no	—
653	C₂×C₃×C₄	—	2	1	no	—
654	C₂×C₃×C₄	—	2	1	no	—
655	C₂×C₃×C₄	—	2	1	no	—
656	C₂×C₃×C₄	—	2	2	no	—
657	C₂×C₃×C₄	—	4	8	no	—
658	C₂×C₃×C₄	—	8	4	no	—
659	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
660	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
661	C₂×C₃×C₄	C₂³×C₄	1	4	yes	—
662	C₂×C₃×C₄	C₂³×C₄	1	4	yes	—
663	C₂×C₃×C₄	C₂³×C₄	1	4	yes	—
664	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
665	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
666	C₂×C₃×C₄	C₂³×C₄	1	4	yes	—
667	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
668	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
669	C₂×C₃×C₄	2₋¹⁺⁴	1	2	yes	—
670	C₂×C₃×C₄	2₋¹⁺⁴	1	2	yes	—
671	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
672	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
673	C₂×Q₈	—	2	2	no	—
674	C₂×Q₈	—	2	2	no	—
675	C₂×Q₈	C₂²×C₃×C₄	1	4	yes	—
676	C₂×D₄	—	4	1	no	—
677	C₂×D₄	—	4	1	no	—
678	C₂×D₄	C₂²×C₃×C₄	1	4	yes	—
679	C₂²×C₄	—	2	2	no	—
680	C₂²×C₄	—	2	2	no	—
681	C₂²×C₄	—	2	2	no	—
682	C₂²×C₄	—	2	2	no	—
683	C₂²×C₄	—	4	2	no	—
684	C₂²×C₄	—	4	2	no	—
685	C₂²×C₄	—	4	2	no	—
686	C₂²×C₄	—	4	2	no	—
687	C₂²×C₄	—	4	2	no	—
688	C₂²×C₄	C₂²×C₃×C₄	1	4	yes	—
689	C₂²×C₄	C₂²×C₃×C₄	1	4	yes	—
690	C₂²×C₄	C₂²×C₃×C₄	1	8	yes	—
691	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
692	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
693	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
694	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
695	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
696	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
697	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
698	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
699	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
700	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
701	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
702	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
703	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
704	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
705	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
706	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
707	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
708	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
709	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
710	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
711	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
712	C₄⋊C₄	—	2	2	no	—
713	C₄⋊C₄	—	2	2	no	—
714	C₄⋊C₄	—	2	2	no	—
715	C₄⋊C₄	—	2	2	no	—
716	C₄⋊C₄	—	4	2	no	—
717	C₄⋊C₄	—	4	1	no	—
718	C₄⋊C₄	—	4	1	no	—
719	C₄⋊C₄	—	4	1	no	—
720	C₄⋊C₄	—	4	1	no	—
721	C₄⋊C₄	—	4	2	no	—
722	C₄⋊C₄	—	4	2	no	—
723	C₄⋊C₄	—	4	2	no	—
724	C₄⋊C₄	—	4	2	no	—
725	C₄⋊C₄	—	4	2	no	—
726	C₄⋊C₄	—	4	2	no	—
727	C₄⋊C₄	—	4	1	no	—
728	C₄⋊C₄	—	4	1	no	—
729	C₄⋊C₄	—	4	2	no	—
730	C₄⋊C₄	—	4	2	no	—
731	C₄⋊C₄	—	4	2	no	—
732	C₄⋊C₄	—	4	2	no	—
733	C₄⋊C₄	C₂²×C₃×C₄	1	4	yes	—
734	C₄⋊C₄	C₂²×C₃×C₄	1	4	yes	—
735	C₄⋊C₄	C₂²×C₃×C₄	1	8	yes	—
736	C₄⋊C₄	C₂²×C₃×C₄	1	4	yes	—
737	C₄⋊C₄	C₂²×C₃×C₄	1	8	yes	—
738	C₄⋊C₄	C₂²×C₃×C₄	1	8	yes	—
739	C₄⋊C₄	C₂²×C₃×C₄	1	4	yes	—
740	C₄⋊C₄	C₂²×C₃×C₄	1	8	yes	—
741	C₄⋊C₄	C₂²×C₃×C₄	1	8	yes	—
742	C₄⋊C₄	C₂²×C₃×C₄	1	8	yes	—
743	C₂²⋊C₄	—	2	2	no	—
744	C₂²⋊C₄	—	2	2	no	—
745	C₂²⋊C₄	—	4	1	no	—
746	C₂²⋊C₄	—	4	1	no	—
747	C₂²⋊C₄	—	4	1	no	—
748	C₂²⋊C₄	—	4	1	no	—
749	C₂²⋊C₄	—	4	2	no	—
750	C₂²⋊C₄	—	4	1	no	—
751	C₂²⋊C₄	—	4	2	no	—
752	C₂²⋊C₄	—	4	1	no	—
753	C₂²⋊C₄	—	4	2	no	—
754	C₂²⋊C₄	C₂²×C₃×C₄	1	8	yes	—
755	C₂²⋊C₄	C₂²×C₃×C₄	1	4	yes	—
756	C₂²⋊C₄	C₂²×C₃×C₄	1	8	yes	—
757	C₂²⋊C₄	C₂²×C₃×C₄	1	4	yes	—
758	C₂²⋊C₄	C₂²×C₃×C₄	1	8	yes	—
759	C₄²	—	2	2	no	—
760	C₄²	—	2	2	no	—
761	C₄²	—	2	2	no	—
762	C₄²	—	2	2	no	—
763	C₄²	—	2	4	no	—
764	C₄²	—	2	2	no	—
765	C₄²	—	4	2	no	—
766	C₄²	—	4	2	no	—
767	C₄²	—	4	2	no	—
768	C₄²	—	4	2	no	—
769	C₄²	—	4	1	no	—
770	C₄²	—	4	2	no	—
771	C₄²	—	4	1	no	—
772	C₄²	—	4	2	no	—
773	C₄²	—	4	2	no	—
774	C₄²	—	4	1	no	—
775	C₄²	C₂²×C₃×C₄	1	8	yes	—
776	C₄²	C₂²×C₃×C₄	1	8	yes	—
777	C₄²	C₂²×C₃×C₄	1	4	yes	—
778	C₂²×C₃	—	2	2	no	—
779	C₂²×C₃	—	2	2	no	—
780	C₂²×C₃	—	2	2	no	—
781	C₂²×C₃	—	2	2	no	—
782	C₂²×C₃	—	2	2	no	—
783	C₂²×C₃	—	2	2	no	—
784	C₂²×C₃	—	4	1	no	—
785	C₂²×C₃	—	4	1	no	—
786	C₂²×C₃	—	4	1	no	—
787	C₂²×C₃	—	4	1	no	—
788	C₂²×C₃	—	4	1	no	—
789	C₂²×C₃	—	4	1	no	—
790	C₂²×C₃	—	4	1	no	—
791	C₂²×C₃	—	4	1	no	—
792	C₂²×C₃	C₂⁴×C₄	1	1	yes	characteristic
793	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
794	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
795	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
796	C₂²×C₃	#585	1	1	yes	characteristic
797	C₂²×C₃	#585	1	1	yes	characteristic
798	C₂²×C₃	#585	1	1	yes	characteristic
799	C₃×C₄	—	2	2	no	—
800	C₃×C₄	—	2	2	no	—
801	C₃×C₄	—	2	4	no	—
802	C₃×C₄	—	2	4	no	—
803	C₃×C₄	—	2	4	no	—
804	C₃×C₄	—	2	2	no	—
805	C₃×C₄	—	2	2	no	—
806	C₃×C₄	—	2	4	no	—
807	C₃×C₄	—	2	2	no	—
808	C₃×C₄	—	4	1	no	—
809	C₃×C₄	—	4	1	no	—
810	C₃×C₄	—	4	1	no	—
811	C₃×C₄	—	4	2	no	—
812	C₃×C₄	—	4	1	no	—
813	C₃×C₄	—	4	1	no	—
814	C₃×C₄	—	4	1	no	—
815	C₃×C₄	—	4	2	no	—
816	C₃×C₄	—	4	2	no	—
817	C₃×C₄	—	4	1	no	—
818	C₃×C₄	—	4	2	no	—
819	C₃×C₄	#520	1	4	yes	—
820	C₂³	—	2	1	no	—
821	C₂³	—	2	1	no	—
822	C₂³	—	2	1	no	—
823	C₂³	—	2	1	no	—
824	C₂³	—	2	1	no	—
825	C₂³	—	2	1	no	—
826	C₂³	—	2	1	no	—
827	C₂³	—	2	1	no	—
828	C₂³	—	2	1	no	—
829	C₂³	—	2	1	no	—
830	C₂³	—	2	1	no	—
831	C₂³	—	2	1	no	—
832	C₂³	C₂³×C₃×C₄	1	2	yes	—
833	C₂³	C₂³×C₃×C₄	1	2	yes	—
834	C₂³	C₂⁵×C₃	1	1	yes	characteristic
835	Q₈	—	2	8	no	—
836	D₄	—	4	4	no	—
837	C₂×C₄	—	2	1	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	1	no	—
840	C₂×C₄	—	2	1	no	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	1	no	—
843	C₂×C₄	—	2	1	no	—
844	C₂×C₄	—	2	1	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	2	1	no	—
847	C₂×C₄	—	2	1	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	1	no	—
852	C₂×C₄	—	2	1	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	8	no	—
856	C₂×C₄	—	2	8	no	—
857	C₂×C₄	—	2	1	no	—
858	C₂×C₄	—	2	1	no	—
859	C₂×C₄	—	2	1	no	—
860	C₂×C₄	—	2	1	no	—
861	C₂×C₄	—	2	1	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	2	2	no	—
864	C₂×C₄	—	2	2	no	—
865	C₂×C₄	—	2	2	no	—
866	C₂×C₄	—	2	1	no	—
867	C₂×C₄	—	2	2	no	—
868	C₂×C₄	—	2	1	no	—
869	C₂×C₄	—	2	1	no	—
870	C₂×C₄	—	2	1	no	—
871	C₂×C₄	—	2	2	no	—
872	C₂×C₄	—	2	1	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	1	no	—
875	C₂×C₄	—	2	1	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	1	no	—
878	C₂×C₄	—	2	1	no	—
879	C₂×C₄	—	2	1	no	—
880	C₂×C₄	—	2	1	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	2	2	no	—
883	C₂×C₄	—	2	2	no	—
884	C₂×C₄	—	2	1	no	—
885	C₂×C₄	—	2	2	no	—
886	C₂×C₄	—	2	1	no	—
887	C₂×C₄	—	2	1	no	—
888	C₂×C₄	—	2	1	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	4	8	no	—
891	C₂×C₄	—	8	4	no	—
892	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
893	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
894	C₂×C₄	C₂³×C₃×C₄	1	4	yes	—
895	C₂×C₄	C₂³×C₃×C₄	1	4	yes	—
896	C₂×C₄	C₂³×C₃×C₄	1	4	yes	—
897	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
898	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
899	C₂×C₄	C₂³×C₃×C₄	1	4	yes	—
900	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
901	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
902	C₂×C₄	C₃×2₋¹⁺⁴	1	2	yes	—
903	C₂×C₄	C₃×2₋¹⁺⁴	1	2	yes	—
904	C₂×C₃	—	4	2	no	—
905	C₂×C₃	—	4	2	no	—
906	C₂×C₃	C₂×#520	1	1	yes	characteristic
907	C₂×C₃	#3428	1	1	yes	characteristic
908	C₂×C₃	C₄×2₋¹⁺⁴	1	1	yes	characteristic
909	C₂×C₃	#3547	1	1	yes	characteristic
910	C₂×C₃	#3551	1	1	yes	characteristic
911	C₂×C₃	#3563	1	1	yes	characteristic
912	C₂×C₃	#3565	1	1	yes	characteristic
913	C₂²	—	2	2	no	—
914	C₂²	—	2	2	no	—
915	C₂²	—	2	2	no	—
916	C₂²	—	2	2	no	—
917	C₂²	—	2	2	no	—
918	C₂²	—	2	2	no	—
919	C₂²	—	4	1	no	—
920	C₂²	—	4	1	no	—
921	C₂²	—	4	1	no	—
922	C₂²	—	4	1	no	—
923	C₂²	—	4	1	no	—
924	C₂²	—	4	1	no	—
925	C₂²	—	4	1	no	—
926	C₂²	—	4	1	no	—
927	C₂²	C₂⁴×C₃×C₄	1	1	yes	characteristic
928	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
929	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
930	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
931	C₂²	C₃×#585	1	1	yes	characteristic
932	C₂²	C₃×#585	1	1	yes	characteristic
933	C₂²	C₃×#585	1	1	yes	characteristic
934	C₄	—	2	2	no	—
935	C₄	—	2	2	no	—
936	C₄	—	2	4	no	—
937	C₄	—	2	4	no	—
938	C₄	—	2	4	no	—
939	C₄	—	2	2	no	—
940	C₄	—	2	2	no	—
941	C₄	—	2	4	no	—
942	C₄	—	2	2	no	—
943	C₄	—	4	1	no	—
944	C₄	—	4	1	no	—
945	C₄	—	4	1	no	—
946	C₄	—	4	2	no	—
947	C₄	—	4	2	no	—
948	C₄	—	4	2	no	—
949	C₄	—	4	1	no	—
950	C₄	—	4	1	no	—
951	C₄	—	4	1	no	—
952	C₄	—	4	1	no	—
953	C₄	—	4	2	no	—
954	C₄	C₃×#520	1	4	yes	—
955	C₃	#34482	1	1	yes	characteristic, direct product factor, Sylow
956	C₂	—	4	2	no	—
957	C₂	—	4	2	no	—
958	C₂	C₂×C₃×#520	1	1	yes	characteristic
959	C₂	C₃×#3428	1	1	yes	characteristic
960	C₂	C₃×C₄×2₋¹⁺⁴	1	1	yes	characteristic
961	C₂	C₃×#3547	1	1	yes	characteristic
962	C₂	C₃×#3551	1	1	yes	characteristic
963	C₂	C₃×#3563	1	1	yes	characteristic
964	C₂	C₃×#3565	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator	C₂²	C₂⁴×C₃×C₄
Frattini, cosocle	C₂³	C₂⁵×C₃
prime radical	C₂²×C₃×D₄	C₂³
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×#2382	C₂	semidirect
4. C₃×#2373	C₂	semidirect
5. C₃×#2370	C₂	semidirect
6. C₃×#2362	C₂	semidirect
7. C₃×#2360	C₂	semidirect
9. C₃×#2351	C₂	semidirect
10. C₃×#2346	C₂	semidirect
11. C₃×#2346	C₂	semidirect
12. C₃×#2345	C₂	semidirect
14. C₃×#2334	C₂	semidirect
15. C₃×#2330	C₂	semidirect
16. C₃×#2323	C₂	semidirect
17. C₃×#2323	C₂	semidirect
18. C₃×#2317	C₂	semidirect
19. C₃×#2316	C₂	semidirect
20. C₃×#2314	C₂	semidirect
21. C₃×C₄×#125	C₂	semidirect
22. C₃×#2295	C₂	semidirect
24. #34482	C₃	direct (N × H)
25. C₃×#552	C₄	semidirect
126. #2382	C₂×C₃	semidirect
128. #2373	C₂×C₃	semidirect
129. #2370	C₂×C₃	semidirect
130. #2362	C₂×C₃	semidirect
131. #2360	C₂×C₃	semidirect
133. #2351	C₂×C₃	semidirect
134. #2346	C₂×C₃	semidirect
135. #2346	C₂×C₃	semidirect
136. #2345	C₂×C₃	semidirect
138. #2334	C₂×C₃	semidirect
139. #2330	C₂×C₃	semidirect
140. #2323	C₂×C₃	semidirect
141. #2323	C₂×C₃	semidirect
142. #2317	C₂×C₃	semidirect
143. #2316	C₂×C₃	semidirect
144. #2314	C₂×C₃	semidirect
145. C₄×#125	C₂×C₃	semidirect
146. #2295	C₂×C₃	semidirect
155. C₃×#125	C₂×C₄	semidirect
156. C₃×#125	C₂×C₄	semidirect
159. C₃×C₂²⋊Q₈	C₂×C₄	semidirect
162. C₃×C₄×Q₈	C₂×C₄	semidirect
168. C₃×#117	C₂×C₄	semidirect
170. C₂×C₃×C₄⋊C₄	C₂×C₄	semidirect
264. #552	C₃×C₄	semidirect
478. #125	C₂×C₃×C₄	semidirect
479. #125	C₂×C₃×C₄	semidirect
482. C₂²⋊Q₈	C₂×C₃×C₄	semidirect
485. C₄×Q₈	C₂×C₃×C₄	semidirect
491. #117	C₂×C₃×C₄	semidirect
493. C₂×C₄⋊C₄	C₂×C₃×C₄	semidirect
955. C₃	#34482	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×#552	2
C₃×#2382	2
C₃×#2376	2
C₃×#2373	2
C₃×#2370	2
C₃×#2362	2
C₃×#2360	2
C₃×#2352	2
C₃×#2351	2
C₃×#2346	2
C₃×#2345	2
C₃×#2335	2
C₃×#2334	2
C₃×#2330	2
C₃×#2323	2
C₃×#2317	2
C₃×#2316	2
C₃×#2314	2
C₃×C₄×#125	2
C₃×#2295	2
C₃×#2293	2
#34482	3

Subgroups — C3×#34482 #10653089

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#34482 #10653089