Subgroups — C₃×#34472 #10653079

Order 768.

2480 conjugacy classes of subgroups.

The subgroup lattice has 1072 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#548	C₂	1	1	yes	maximal, characteristic
2	C₃×#2379	C₂	1	2	yes	maximal, complemented
3	C₃×#2378	C₂	1	2	yes	maximal, complemented
4	C₃×#2367	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#2364	C₂	1	2	yes	maximal, complemented
6	C₃×#2361	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#2360	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#2355	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#2349	C₂	1	2	yes	maximal, complemented
10	C₃×D₄×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×Q₈×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#2339	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#2337	C₂	1	2	yes	maximal, complemented
14	C₃×#2329	C₂	1	2	yes	maximal, complemented
15	C₃×#2326	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#2325	C₂	1	2	yes	maximal, complemented
17	C₃×#2323	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃×#2320	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃×#2318	C₂	1	2	yes	maximal, complemented
20	C₃×#2311	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃×C₄×#121	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₃×#391	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃×#2290	C₂	1	1	yes	maximal, characteristic, complemented
24	#34472	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂²×C₃×#41	C₂²	1	1	yes	characteristic
26	C₂³×C₃×Q₈	C₂²	1	1	yes	characteristic
27	C₃×#548	C₄	1	16	yes	complemented
28	C₂×C₃×#124	C₂²	1	1	yes	characteristic
29	C₂×C₃×#124	C₂²	1	2	yes	—
30	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
31	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
32	C₂×C₃×#121	C₂²	1	1	yes	characteristic
33	C₂×C₃×#121	C₂²	1	2	yes	—
34	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
35	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
36	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
37	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
38	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
39	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
40	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
41	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
42	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
43	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
44	C₂×C₃×#117	C₂²	1	1	yes	characteristic
45	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
46	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
47	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
48	C₃×#391	C₂²	1	1	yes	characteristic
49	C₃×#391	C₂²	1	2	yes	—
50	C₃×#391	C₂²	1	2	yes	—
51	C₃×#391	C₂²	1	2	yes	—
52	C₃×#391	C₂²	1	1	yes	characteristic
53	C₃×#391	C₂²	1	1	yes	characteristic
54	C₃×#391	C₂²	1	2	yes	—
55	C₃×#391	C₂²	1	1	yes	characteristic
56	C₃×#391	C₂²	1	1	yes	characteristic
57	C₃×#391	C₂²	1	1	yes	characteristic
58	C₃×#390	C₂²	1	1	yes	characteristic
59	C₃×#390	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	2	yes	—
63	C₃×#389	C₂²	1	2	yes	—
64	C₃×#389	C₂²	1	1	yes	characteristic
65	C₃×#388	C₂²	1	2	yes	—
66	C₃×#388	C₂²	1	2	yes	—
67	C₃×#388	C₂²	1	2	yes	—
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	1	yes	characteristic
72	C₃×#388	C₂²	1	1	yes	characteristic
73	C₃×#388	C₂²	1	2	yes	—
74	C₃×#388	C₂²	1	2	yes	—
75	C₃×#387	C₂²	1	2	yes	—
76	C₃×#387	C₂²	1	2	yes	—
77	C₃×#387	C₂²	1	2	yes	—
78	C₃×#387	C₂²	1	1	yes	characteristic
79	C₃×#387	C₂²	1	2	yes	—
80	C₃×#387	C₂²	1	1	yes	characteristic
81	C₃×#387	C₂²	1	2	yes	—
82	C₃×#387	C₂²	1	2	yes	—
83	C₃×#386	C₂²	1	2	yes	—
84	C₃×#386	C₂²	1	1	yes	characteristic
85	C₃×#386	C₂²	1	2	yes	—
86	C₃×#386	C₂²	1	2	yes	—
87	C₃×#386	C₂²	1	2	yes	—
88	C₃×#386	C₂²	1	1	yes	characteristic
89	C₃×#386	C₂²	1	2	yes	—
90	C₃×#386	C₂²	1	2	yes	—
91	C₃×#385	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×#385	C₂²	1	2	yes	—
96	C₃×#385	C₂²	1	1	yes	characteristic
97	C₃×#385	C₂²	1	1	yes	characteristic
98	C₃×#385	C₂²	1	2	yes	—
99	C₃×#385	C₂²	1	2	yes	—
100	C₃×#384	C₂²	1	1	yes	characteristic
101	C₃×#383	C₂²	1	2	yes	—
102	C₃×#382	C₂²	1	2	yes	—
103	C₃×#382	C₂²	1	2	yes	—
104	C₃×#381	C₂²	1	2	yes	—
105	C₃×#380	C₂²	1	2	yes	—
106	C₃×#380	C₂²	1	1	yes	characteristic
107	C₃×#380	C₂²	1	2	yes	—
108	C₃×#380	C₂²	1	1	yes	characteristic
109	C₃×#380	C₂²	1	2	yes	—
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	1	yes	characteristic
113	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
114	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
115	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
116	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
117	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
118	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
119	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
120	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
121	C₃×#376	C₂²	1	1	yes	characteristic
122	C₂×C₃×#95	C₂²	1	2	yes	—
123	C₂×C₃×#95	C₂²	1	2	yes	—
124	C₂×C₃×#95	C₂²	1	2	yes	—
125	C₂×#548	C₂×C₃	1	1	yes	characteristic
126	#2379	C₂×C₃	1	2	yes	complemented
127	#2378	C₂×C₃	1	2	yes	complemented
128	#2367	C₂×C₃	1	1	yes	characteristic, complemented
129	#2364	C₂×C₃	1	2	yes	complemented
130	#2361	C₂×C₃	1	1	yes	characteristic, complemented
131	#2360	C₂×C₃	1	1	yes	characteristic, complemented
132	#2355	C₂×C₃	1	1	yes	characteristic, complemented
133	#2349	C₂×C₃	1	2	yes	complemented
134	D₄×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
135	Q₈×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
136	#2339	C₂×C₃	1	1	yes	characteristic, complemented
137	#2337	C₂×C₃	1	2	yes	complemented
138	#2329	C₂×C₃	1	2	yes	complemented
139	#2326	C₂×C₃	1	1	yes	characteristic, complemented
140	#2325	C₂×C₃	1	2	yes	complemented
141	#2323	C₂×C₃	1	1	yes	characteristic, complemented
142	#2320	C₂×C₃	1	1	yes	characteristic, complemented
143	#2318	C₂×C₃	1	2	yes	complemented
144	#2311	C₂×C₃	1	1	yes	characteristic, complemented
145	C₄×#121	C₂×C₃	1	1	yes	characteristic, complemented
146	C₂×#391	C₂×C₃	1	1	yes	characteristic, complemented
147	#2290	C₂×C₃	1	1	yes	characteristic, complemented
148	C₂×C₃×#41	—	4	2	no	—
149	C₂×C₃×#41	—	4	2	no	—
150	C₂×C₃×#41	C₂×C₄	1	8	yes	complemented
151	C₂²×C₃×Q₈	—	4	2	no	—
152	C₂²×C₃×Q₈	—	4	2	no	—
153	C₂²×C₃×Q₈	C₂×C₄	1	8	yes	complemented
154	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
155	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
156	C₂²×C₃×Q₈	C₂³	1	2	yes	—
157	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
158	C₂²×C₃×D₄	C₂³	1	2	yes	—
159	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
160	C₂²×C₃×D₄	C₂³	1	2	yes	—
161	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
162	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
163	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
164	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
165	C₂³×C₃×C₄	C₂³	1	2	yes	—
166	C₂³×C₃×C₄	C₂³	1	2	yes	—
167	C₂³×C₃×C₄	C₂³	1	2	yes	—
168	C₂³×C₃×C₄	C₂³	1	2	yes	—
169	C₂³×C₃×C₄	C₂³	1	2	yes	—
170	C₂³×C₃×C₄	C₂³	1	2	yes	—
171	C₃×#124	C₂×C₄	1	8	yes	complemented
172	C₃×#124	C₂×C₄	1	16	yes	complemented
173	C₃×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
174	C₃×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
175	C₃×#121	C₂×C₄	1	8	yes	complemented
176	C₃×#121	C₂×C₄	1	16	yes	complemented
177	C₃×C₄×Q₈	—	4	2	no	—
178	C₃×C₄×Q₈	—	4	2	no	—
179	C₃×C₄×Q₈	C₂×C₄	1	8	yes	complemented
180	C₃×C₄×D₄	—	4	2	no	—
181	C₃×C₄×D₄	—	4	2	no	—
182	C₃×C₄×D₄	—	4	4	no	—
183	C₃×C₄×D₄	—	4	4	no	—
184	C₃×C₄×D₄	—	4	4	no	—
185	C₃×C₄×D₄	C₂×C₄	1	8	yes	complemented
186	C₃×C₄×D₄	C₂×C₄	1	16	yes	complemented
187	C₃×#117	—	4	2	no	—
188	C₂×C₃×C₄⋊C₄	—	4	2	no	—
189	C₂×C₃×C₄⋊C₄	—	4	2	no	—
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	1	yes	characteristic
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	1	yes	characteristic
196	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
197	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
202	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
203	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
204	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
205	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
206	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
207	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
208	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
209	C₂×C₃×C₄⋊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	2	yes	—
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×C₂²⋊C₄	C₂³	1	2	yes	—
219	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
220	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
221	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
222	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
223	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
224	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
225	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
226	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
227	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
228	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
229	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
230	C₂×C₃×C₄²	—	4	2	no	—
231	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
232	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
233	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
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	C₂×C₃×C₄²	C₂³	1	2	yes	—
238	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
239	C₂×C₃×C₄²	C₂³	1	2	yes	—
240	C₂×C₃×C₄²	C₂³	1	2	yes	—
241	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
242	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
243	C₂×C₃×C₄²	C₂³	1	2	yes	—
244	C₃×#95	C₂³	1	1	yes	characteristic
245	C₃×#95	C₂³	1	2	yes	—
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	2	yes	—
250	C₃×#95	C₂³	1	2	yes	—
251	C₃×#95	C₂³	1	2	yes	—
252	C₃×#95	C₂³	1	2	yes	—
253	C₃×#95	C₂³	1	2	yes	—
254	C₃×#95	C₂³	1	2	yes	—
255	C₃×#95	C₂³	1	1	yes	characteristic
256	C₃×#95	C₂³	1	1	yes	characteristic
257	C₃×#95	C₂³	1	1	yes	characteristic
258	C₃×#95	C₂³	1	1	yes	characteristic
259	C₃×#95	C₂³	1	1	yes	characteristic
260	C₃×#95	C₂³	1	2	yes	—
261	C₃×#95	C₂³	1	2	yes	—
262	C₃×#95	C₂³	1	1	yes	characteristic
263	C₃×#95	C₂³	1	2	yes	—
264	C₃×#95	C₂³	1	2	yes	—
265	C₃×#95	C₂³	1	2	yes	—
266	C₃×#95	C₂³	1	1	yes	characteristic
267	C₃×#95	C₂³	1	1	yes	characteristic
268	C₃×#95	C₂³	1	2	yes	—
269	C₃×#95	C₂³	1	2	yes	—
270	C₃×#95	C₂³	1	2	yes	—
271	C₃×#95	C₂³	1	2	yes	—
272	C₃×#95	C₂³	1	1	yes	characteristic
273	C₂²×#41	C₂²×C₃	1	1	yes	characteristic
274	C₂³×Q₈	C₂²×C₃	1	1	yes	characteristic
275	#548	C₃×C₄	1	16	yes	complemented
276	C₂×#124	C₂²×C₃	1	1	yes	characteristic
277	C₂×#124	C₂²×C₃	1	2	yes	—
278	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
279	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
280	C₂×#121	C₂²×C₃	1	2	yes	—
281	C₂×#121	C₂²×C₃	1	1	yes	characteristic
282	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
283	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
284	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
285	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
286	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
287	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
288	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
289	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
290	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
291	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
292	C₂×#117	C₂²×C₃	1	1	yes	characteristic
293	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
294	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
295	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
296	#391	C₂²×C₃	1	1	yes	characteristic
297	#391	C₂²×C₃	1	1	yes	characteristic
298	#391	C₂²×C₃	1	1	yes	characteristic
299	#391	C₂²×C₃	1	1	yes	characteristic
300	#391	C₂²×C₃	1	2	yes	—
301	#391	C₂²×C₃	1	2	yes	—
302	#391	C₂²×C₃	1	2	yes	—
303	#391	C₂²×C₃	1	1	yes	characteristic
304	#391	C₂²×C₃	1	1	yes	characteristic
305	#391	C₂²×C₃	1	2	yes	—
306	#390	C₂²×C₃	1	1	yes	characteristic
307	#390	C₂²×C₃	1	1	yes	characteristic
308	#389	C₂²×C₃	1	1	yes	characteristic
309	#389	C₂²×C₃	1	1	yes	characteristic
310	#389	C₂²×C₃	1	2	yes	—
311	#389	C₂²×C₃	1	2	yes	—
312	#389	C₂²×C₃	1	2	yes	—
313	#388	C₂²×C₃	1	2	yes	—
314	#388	C₂²×C₃	1	2	yes	—
315	#388	C₂²×C₃	1	2	yes	—
316	#388	C₂²×C₃	1	2	yes	—
317	#388	C₂²×C₃	1	2	yes	—
318	#388	C₂²×C₃	1	2	yes	—
319	#388	C₂²×C₃	1	1	yes	characteristic
320	#388	C₂²×C₃	1	2	yes	—
321	#388	C₂²×C₃	1	2	yes	—
322	#388	C₂²×C₃	1	1	yes	characteristic
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	1	yes	characteristic
329	#387	C₂²×C₃	1	2	yes	—
330	#387	C₂²×C₃	1	1	yes	characteristic
331	#386	C₂²×C₃	1	2	yes	—
332	#386	C₂²×C₃	1	2	yes	—
333	#386	C₂²×C₃	1	2	yes	—
334	#386	C₂²×C₃	1	2	yes	—
335	#386	C₂²×C₃	1	1	yes	characteristic
336	#386	C₂²×C₃	1	2	yes	—
337	#386	C₂²×C₃	1	2	yes	—
338	#386	C₂²×C₃	1	1	yes	characteristic
339	#385	C₂²×C₃	1	1	yes	characteristic
340	#385	C₂²×C₃	1	2	yes	—
341	#385	C₂²×C₃	1	2	yes	—
342	#385	C₂²×C₃	1	2	yes	—
343	#385	C₂²×C₃	1	2	yes	—
344	#385	C₂²×C₃	1	2	yes	—
345	#385	C₂²×C₃	1	2	yes	—
346	#385	C₂²×C₃	1	2	yes	—
347	#385	C₂²×C₃	1	1	yes	characteristic
348	#384	C₂²×C₃	1	1	yes	characteristic
349	#383	C₂²×C₃	1	2	yes	—
350	#382	C₂²×C₃	1	2	yes	—
351	#382	C₂²×C₃	1	2	yes	—
352	#381	C₂²×C₃	1	2	yes	—
353	#380	C₂²×C₃	1	2	yes	—
354	#380	C₂²×C₃	1	2	yes	—
355	#380	C₂²×C₃	1	1	yes	characteristic
356	#380	C₂²×C₃	1	2	yes	—
357	#380	C₂²×C₃	1	1	yes	characteristic
358	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
359	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
360	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
361	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
362	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
363	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
364	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
365	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
366	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
367	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
368	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
369	#376	C₂²×C₃	1	1	yes	characteristic
370	C₂×#95	C₂²×C₃	1	2	yes	—
371	C₂×#95	C₂²×C₃	1	2	yes	—
372	C₂×#95	C₂²×C₃	1	2	yes	—
373	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
374	C₂⁴×C₃	C₂⁴	1	2	yes	—
375	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
376	C₃×#41	—	4	16	no	—
377	C₂×C₃×Q₈	—	2	2	no	—
378	C₂×C₃×Q₈	—	2	2	no	—
379	C₂×C₃×Q₈	—	2	2	no	—
380	C₂×C₃×Q₈	—	2	2	no	—
381	C₂×C₃×Q₈	—	4	2	no	—
382	C₂×C₃×Q₈	—	4	2	no	—
383	C₂×C₃×Q₈	—	4	16	no	—
384	C₂×C₃×Q₈	C₂²×C₄	1	4	yes	—
385	C₂×C₃×Q₈	C₂²×C₄	1	4	yes	—
386	C₂×C₃×Q₈	C₂²×C₄	1	8	yes	—
387	C₂×C₃×D₄	—	2	4	no	—
388	C₂×C₃×D₄	—	2	2	no	—
389	C₂×C₃×D₄	—	2	4	no	—
390	C₂×C₃×D₄	—	2	2	no	—
391	C₂×C₃×D₄	—	2	2	no	—
392	C₂×C₃×D₄	—	2	2	no	—
393	C₂×C₃×D₄	—	4	2	no	—
394	C₂×C₃×D₄	—	4	2	no	—
395	C₂×C₃×D₄	C₂²×C₄	1	4	yes	—
396	C₂×C₃×D₄	C₂²×C₄	1	8	yes	—
397	C₂×C₃×D₄	C₂²×C₄	1	4	yes	—
398	C₂×C₃×D₄	C₂²×C₄	1	8	yes	—
399	C₂²×C₃×C₄	—	2	2	no	—
400	C₂²×C₃×C₄	—	2	2	no	—
401	C₂²×C₃×C₄	—	2	2	no	—
402	C₂²×C₃×C₄	—	2	2	no	—
403	C₂²×C₃×C₄	—	2	2	no	—
404	C₂²×C₃×C₄	—	2	2	no	—
405	C₂²×C₃×C₄	—	2	4	no	—
406	C₂²×C₃×C₄	—	2	2	no	—
407	C₂²×C₃×C₄	—	2	4	no	—
408	C₂²×C₃×C₄	—	4	1	no	—
409	C₂²×C₃×C₄	—	4	1	no	—
410	C₂²×C₃×C₄	—	4	1	no	—
411	C₂²×C₃×C₄	—	4	2	no	—
412	C₂²×C₃×C₄	—	4	2	no	—
413	C₂²×C₃×C₄	—	4	2	no	—
414	C₂²×C₃×C₄	—	4	2	no	—
415	C₂²×C₃×C₄	—	4	2	no	—
416	C₂²×C₃×C₄	—	4	2	no	—
417	C₂²×C₃×C₄	—	4	2	no	—
418	C₂²×C₃×C₄	—	4	2	no	—
419	C₂²×C₃×C₄	—	4	2	no	—
420	C₂²×C₃×C₄	—	4	2	no	—
421	C₂²×C₃×C₄	—	4	2	no	—
422	C₂²×C₃×C₄	—	4	2	no	—
423	C₂²×C₃×C₄	—	4	2	no	—
424	C₂²×C₃×C₄	—	4	2	no	—
425	C₂²×C₃×C₄	C₂²×C₄	1	4	yes	—
426	C₂²×C₃×C₄	C₂²×C₄	1	4	yes	—
427	C₂²×C₃×C₄	C₂²×C₄	1	8	yes	—
428	C₂²×C₃×C₄	C₂²×C₄	1	8	yes	—
429	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
430	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
431	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
432	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
433	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
434	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
435	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
436	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
437	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
438	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
439	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
440	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
441	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
442	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
443	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
444	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
445	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
446	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
447	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
448	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
449	C₃×C₄⋊C₄	—	2	2	no	—
450	C₃×C₄⋊C₄	—	2	2	no	—
451	C₃×C₄⋊C₄	—	2	2	no	—
452	C₃×C₄⋊C₄	—	2	2	no	—
453	C₃×C₄⋊C₄	—	2	2	no	—
454	C₃×C₄⋊C₄	—	4	2	no	—
455	C₃×C₄⋊C₄	—	4	2	no	—
456	C₃×C₄⋊C₄	—	4	1	no	—
457	C₃×C₄⋊C₄	—	4	2	no	—
458	C₃×C₄⋊C₄	—	4	1	no	—
459	C₃×C₄⋊C₄	—	4	1	no	—
460	C₃×C₄⋊C₄	—	4	2	no	—
461	C₃×C₄⋊C₄	—	4	2	no	—
462	C₃×C₄⋊C₄	—	4	2	no	—
463	C₃×C₄⋊C₄	—	4	2	no	—
464	C₃×C₄⋊C₄	—	4	2	no	—
465	C₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
466	C₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
467	C₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
468	C₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
469	C₃×C₂²⋊C₄	—	2	2	no	—
470	C₃×C₂²⋊C₄	—	2	4	no	—
471	C₃×C₂²⋊C₄	—	2	2	no	—
472	C₃×C₂²⋊C₄	—	2	2	no	—
473	C₃×C₂²⋊C₄	—	4	2	no	—
474	C₃×C₂²⋊C₄	—	4	2	no	—
475	C₃×C₂²⋊C₄	—	4	1	no	—
476	C₃×C₂²⋊C₄	—	4	1	no	—
477	C₃×C₂²⋊C₄	—	4	1	no	—
478	C₃×C₂²⋊C₄	—	4	2	no	—
479	C₃×C₂²⋊C₄	—	4	2	no	—
480	C₃×C₂²⋊C₄	—	4	2	no	—
481	C₃×C₂²⋊C₄	—	4	2	no	—
482	C₃×C₂²⋊C₄	—	4	2	no	—
483	C₃×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
484	C₃×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
485	C₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
486	C₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
487	C₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
488	C₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
489	C₃×C₄²	—	2	2	no	—
490	C₃×C₄²	—	2	2	no	—
491	C₃×C₄²	—	2	2	no	—
492	C₃×C₄²	—	2	2	no	—
493	C₃×C₄²	—	4	1	no	—
494	C₃×C₄²	—	4	1	no	—
495	C₃×C₄²	—	4	2	no	—
496	C₃×C₄²	—	4	2	no	—
497	C₃×C₄²	—	4	2	no	—
498	C₃×C₄²	—	4	2	no	—
499	C₃×C₄²	—	4	2	no	—
500	C₃×C₄²	C₂²×C₄	1	8	yes	—
501	C₃×C₄²	C₂²×C₄	1	4	yes	—
502	C₂×#41	—	4	2	no	—
503	C₂×#41	—	4	2	no	—
504	C₂×#41	C₂×C₃×C₄	1	8	yes	complemented
505	C₂²×Q₈	—	4	2	no	—
506	C₂²×Q₈	—	4	2	no	—
507	C₂²×Q₈	C₂×C₃×C₄	1	8	yes	complemented
508	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
509	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
510	C₂²×Q₈	C₂³×C₃	1	2	yes	—
511	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
512	C₂²×D₄	C₂³×C₃	1	2	yes	—
513	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
514	C₂²×D₄	C₂³×C₃	1	2	yes	—
515	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
516	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
517	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
518	C₂³×C₄	C₂³×C₃	1	2	yes	—
519	C₂³×C₄	C₂³×C₃	1	2	yes	—
520	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
521	C₂³×C₄	C₂³×C₃	1	2	yes	—
522	C₂³×C₄	C₂³×C₃	1	2	yes	—
523	C₂³×C₄	C₂³×C₃	1	2	yes	—
524	C₂³×C₄	C₂³×C₃	1	2	yes	—
525	#124	C₂×C₃×C₄	1	8	yes	complemented
526	#124	C₂×C₃×C₄	1	16	yes	complemented
527	C₂²⋊Q₈	C₂×C₃×C₄	1	8	yes	complemented
528	C₂²⋊Q₈	C₂×C₃×C₄	1	16	yes	complemented
529	#121	C₂×C₃×C₄	1	8	yes	complemented
530	#121	C₂×C₃×C₄	1	16	yes	complemented
531	C₄×Q₈	—	4	2	no	—
532	C₄×Q₈	—	4	2	no	—
533	C₄×Q₈	C₂×C₃×C₄	1	8	yes	complemented
534	C₄×D₄	—	4	2	no	—
535	C₄×D₄	—	4	2	no	—
536	C₄×D₄	—	4	4	no	—
537	C₄×D₄	—	4	4	no	—
538	C₄×D₄	—	4	4	no	—
539	C₄×D₄	C₂×C₃×C₄	1	8	yes	complemented
540	C₄×D₄	C₂×C₃×C₄	1	16	yes	complemented
541	#117	—	4	2	no	—
542	C₂×C₄⋊C₄	—	4	2	no	—
543	C₂×C₄⋊C₄	—	4	2	no	—
544	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
545	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
546	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
547	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
548	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
549	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
550	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
551	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
552	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
553	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
554	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
555	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
556	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
557	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
558	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
559	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
560	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
561	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
562	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
563	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
564	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
565	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
566	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
567	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
568	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
569	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
570	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
571	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
572	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
573	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
574	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
575	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
576	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
577	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
578	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
579	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
580	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
581	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
582	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
583	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
584	C₂×C₄²	—	4	2	no	—
585	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
586	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
587	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
588	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
589	C₂×C₄²	C₂³×C₃	1	2	yes	—
590	C₂×C₄²	C₂³×C₃	1	2	yes	—
591	C₂×C₄²	C₂³×C₃	1	2	yes	—
592	C₂×C₄²	C₂³×C₃	1	2	yes	—
593	C₂×C₄²	C₂³×C₃	1	2	yes	—
594	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
595	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
596	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
597	C₂×C₄²	C₂³×C₃	1	2	yes	—
598	#95	C₂³×C₃	1	1	yes	characteristic
599	#95	C₂³×C₃	1	2	yes	—
600	#95	C₂³×C₃	1	2	yes	—
601	#95	C₂³×C₃	1	2	yes	—
602	#95	C₂³×C₃	1	2	yes	—
603	#95	C₂³×C₃	1	2	yes	—
604	#95	C₂³×C₃	1	2	yes	—
605	#95	C₂³×C₃	1	2	yes	—
606	#95	C₂³×C₃	1	2	yes	—
607	#95	C₂³×C₃	1	2	yes	—
608	#95	C₂³×C₃	1	2	yes	—
609	#95	C₂³×C₃	1	1	yes	characteristic
610	#95	C₂³×C₃	1	1	yes	characteristic
611	#95	C₂³×C₃	1	1	yes	characteristic
612	#95	C₂³×C₃	1	1	yes	characteristic
613	#95	C₂³×C₃	1	1	yes	characteristic
614	#95	C₂³×C₃	1	2	yes	—
615	#95	C₂³×C₃	1	2	yes	—
616	#95	C₂³×C₃	1	1	yes	characteristic
617	#95	C₂³×C₃	1	2	yes	—
618	#95	C₂³×C₃	1	2	yes	—
619	#95	C₂³×C₃	1	2	yes	—
620	#95	C₂³×C₃	1	1	yes	characteristic
621	#95	C₂³×C₃	1	1	yes	characteristic
622	#95	C₂³×C₃	1	2	yes	—
623	#95	C₂³×C₃	1	2	yes	—
624	#95	C₂³×C₃	1	2	yes	—
625	#95	C₂³×C₃	1	2	yes	—
626	#95	C₂³×C₃	1	1	yes	characteristic
627	C₂³×C₃	—	2	1	no	—
628	C₂³×C₃	—	2	1	no	—
629	C₂³×C₃	—	2	1	no	—
630	C₂³×C₃	—	2	1	no	—
631	C₂³×C₃	—	2	1	no	—
632	C₂³×C₃	—	2	2	no	—
633	C₂³×C₃	—	2	1	no	—
634	C₂³×C₃	—	2	2	no	—
635	C₂³×C₃	—	2	2	no	—
636	C₂³×C₃	—	2	1	no	—
637	C₂³×C₃	—	2	1	no	—
638	C₂³×C₃	—	2	2	no	—
639	C₂³×C₃	—	2	1	no	—
640	C₂³×C₃	—	2	2	no	—
641	C₂³×C₃	—	2	2	no	—
642	C₂³×C₃	—	2	1	no	—
643	C₂³×C₃	C₂³×C₄	1	2	yes	—
644	C₂³×C₃	C₂³×C₄	1	4	yes	—
645	C₂³×C₃	C₂³×C₄	1	2	yes	—
646	C₂³×C₃	H(5,𝔽₂)	1	2	yes	—
647	C₂³×C₃	2₋¹⁺⁴	1	2	yes	—
648	C₂³×C₃	C₂⁵	1	1	yes	characteristic
649	C₃×Q₈	—	2	8	no	—
650	C₃×Q₈	—	2	8	no	—
651	C₃×Q₈	—	4	8	no	—
652	C₃×D₄	—	2	8	no	—
653	C₃×D₄	—	2	16	no	—
654	C₃×D₄	—	2	8	no	—
655	C₃×D₄	—	4	8	no	—
656	C₂×C₃×C₄	—	2	1	no	—
657	C₂×C₃×C₄	—	2	2	no	—
658	C₂×C₃×C₄	—	2	1	no	—
659	C₂×C₃×C₄	—	2	1	no	—
660	C₂×C₃×C₄	—	2	1	no	—
661	C₂×C₃×C₄	—	2	2	no	—
662	C₂×C₃×C₄	—	2	2	no	—
663	C₂×C₃×C₄	—	2	1	no	—
664	C₂×C₃×C₄	—	2	1	no	—
665	C₂×C₃×C₄	—	2	1	no	—
666	C₂×C₃×C₄	—	2	2	no	—
667	C₂×C₃×C₄	—	2	2	no	—
668	C₂×C₃×C₄	—	2	1	no	—
669	C₂×C₃×C₄	—	2	1	no	—
670	C₂×C₃×C₄	—	2	2	no	—
671	C₂×C₃×C₄	—	2	1	no	—
672	C₂×C₃×C₄	—	2	8	no	—
673	C₂×C₃×C₄	—	2	8	no	—
674	C₂×C₃×C₄	—	2	1	no	—
675	C₂×C₃×C₄	—	2	1	no	—
676	C₂×C₃×C₄	—	2	1	no	—
677	C₂×C₃×C₄	—	2	1	no	—
678	C₂×C₃×C₄	—	2	1	no	—
679	C₂×C₃×C₄	—	2	1	no	—
680	C₂×C₃×C₄	—	2	1	no	—
681	C₂×C₃×C₄	—	2	1	no	—
682	C₂×C₃×C₄	—	2	2	no	—
683	C₂×C₃×C₄	—	2	2	no	—
684	C₂×C₃×C₄	—	2	2	no	—
685	C₂×C₃×C₄	—	2	2	no	—
686	C₂×C₃×C₄	—	2	2	no	—
687	C₂×C₃×C₄	—	2	2	no	—
688	C₂×C₃×C₄	—	2	1	no	—
689	C₂×C₃×C₄	—	2	1	no	—
690	C₂×C₃×C₄	—	2	2	no	—
691	C₂×C₃×C₄	—	2	2	no	—
692	C₂×C₃×C₄	—	2	1	no	—
693	C₂×C₃×C₄	—	2	1	no	—
694	C₂×C₃×C₄	—	2	1	no	—
695	C₂×C₃×C₄	—	2	1	no	—
696	C₂×C₃×C₄	—	2	1	no	—
697	C₂×C₃×C₄	—	2	2	no	—
698	C₂×C₃×C₄	—	2	1	no	—
699	C₂×C₃×C₄	—	2	1	no	—
700	C₂×C₃×C₄	—	2	1	no	—
701	C₂×C₃×C₄	—	2	1	no	—
702	C₂×C₃×C₄	—	2	1	no	—
703	C₂×C₃×C₄	—	2	2	no	—
704	C₂×C₃×C₄	—	2	1	no	—
705	C₂×C₃×C₄	—	2	2	no	—
706	C₂×C₃×C₄	—	2	2	no	—
707	C₂×C₃×C₄	—	4	8	no	—
708	C₂×C₃×C₄	—	4	8	no	—
709	C₂×C₃×C₄	—	4	4	no	—
710	C₂×C₃×C₄	—	4	4	no	—
711	C₂×C₃×C₄	—	8	4	no	—
712	C₂×C₃×C₄	—	8	4	no	—
713	C₂×C₃×C₄	—	8	4	no	—
714	C₂×C₃×C₄	—	8	4	no	—
715	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
716	C₂×C₃×C₄	C₂³×C₄	1	4	yes	—
717	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
718	C₂×C₃×C₄	C₂³×C₄	1	4	yes	—
719	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
720	C₂×C₃×C₄	C₂³×C₄	1	4	yes	—
721	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
722	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
723	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
724	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
725	C₂×C₃×C₄	2₋¹⁺⁴	1	2	yes	—
726	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
727	C₂⁴	C₂⁴×C₃	1	2	yes	—
728	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
729	#41	—	4	16	no	—
730	C₂×Q₈	—	2	2	no	—
731	C₂×Q₈	—	2	2	no	—
732	C₂×Q₈	—	2	2	no	—
733	C₂×Q₈	—	2	2	no	—
734	C₂×Q₈	—	4	2	no	—
735	C₂×Q₈	—	4	2	no	—
736	C₂×Q₈	—	4	16	no	—
737	C₂×Q₈	C₂²×C₃×C₄	1	4	yes	—
738	C₂×Q₈	C₂²×C₃×C₄	1	4	yes	—
739	C₂×Q₈	C₂²×C₃×C₄	1	8	yes	—
740	C₂×D₄	—	2	4	no	—
741	C₂×D₄	—	2	2	no	—
742	C₂×D₄	—	2	2	no	—
743	C₂×D₄	—	2	4	no	—
744	C₂×D₄	—	2	2	no	—
745	C₂×D₄	—	2	2	no	—
746	C₂×D₄	—	4	2	no	—
747	C₂×D₄	—	4	2	no	—
748	C₂×D₄	C₂²×C₃×C₄	1	4	yes	—
749	C₂×D₄	C₂²×C₃×C₄	1	8	yes	—
750	C₂×D₄	C₂²×C₃×C₄	1	4	yes	—
751	C₂×D₄	C₂²×C₃×C₄	1	8	yes	—
752	C₂²×C₄	—	2	2	no	—
753	C₂²×C₄	—	2	2	no	—
754	C₂²×C₄	—	2	2	no	—
755	C₂²×C₄	—	2	2	no	—
756	C₂²×C₄	—	2	2	no	—
757	C₂²×C₄	—	2	2	no	—
758	C₂²×C₄	—	2	4	no	—
759	C₂²×C₄	—	2	2	no	—
760	C₂²×C₄	—	2	4	no	—
761	C₂²×C₄	—	4	1	no	—
762	C₂²×C₄	—	4	1	no	—
763	C₂²×C₄	—	4	2	no	—
764	C₂²×C₄	—	4	2	no	—
765	C₂²×C₄	—	4	2	no	—
766	C₂²×C₄	—	4	2	no	—
767	C₂²×C₄	—	4	1	no	—
768	C₂²×C₄	—	4	2	no	—
769	C₂²×C₄	—	4	2	no	—
770	C₂²×C₄	—	4	2	no	—
771	C₂²×C₄	—	4	2	no	—
772	C₂²×C₄	—	4	2	no	—
773	C₂²×C₄	—	4	2	no	—
774	C₂²×C₄	—	4	2	no	—
775	C₂²×C₄	—	4	2	no	—
776	C₂²×C₄	—	4	2	no	—
777	C₂²×C₄	—	4	2	no	—
778	C₂²×C₄	C₂²×C₃×C₄	1	4	yes	—
779	C₂²×C₄	C₂²×C₃×C₄	1	4	yes	—
780	C₂²×C₄	C₂²×C₃×C₄	1	8	yes	—
781	C₂²×C₄	C₂²×C₃×C₄	1	8	yes	—
782	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
783	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
784	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
785	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
786	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
787	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
788	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
789	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
790	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
791	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
792	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
793	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
794	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
795	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
796	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
797	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
798	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
799	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
800	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
801	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
802	C₄⋊C₄	—	2	2	no	—
803	C₄⋊C₄	—	2	2	no	—
804	C₄⋊C₄	—	2	2	no	—
805	C₄⋊C₄	—	2	2	no	—
806	C₄⋊C₄	—	2	2	no	—
807	C₄⋊C₄	—	4	2	no	—
808	C₄⋊C₄	—	4	2	no	—
809	C₄⋊C₄	—	4	1	no	—
810	C₄⋊C₄	—	4	1	no	—
811	C₄⋊C₄	—	4	2	no	—
812	C₄⋊C₄	—	4	2	no	—
813	C₄⋊C₄	—	4	2	no	—
814	C₄⋊C₄	—	4	2	no	—
815	C₄⋊C₄	—	4	2	no	—
816	C₄⋊C₄	—	4	1	no	—
817	C₄⋊C₄	—	4	2	no	—
818	C₄⋊C₄	C₂²×C₃×C₄	1	4	yes	—
819	C₄⋊C₄	C₂²×C₃×C₄	1	8	yes	—
820	C₄⋊C₄	C₂²×C₃×C₄	1	8	yes	—
821	C₄⋊C₄	C₂²×C₃×C₄	1	4	yes	—
822	C₂²⋊C₄	—	2	2	no	—
823	C₂²⋊C₄	—	2	4	no	—
824	C₂²⋊C₄	—	2	2	no	—
825	C₂²⋊C₄	—	2	2	no	—
826	C₂²⋊C₄	—	4	1	no	—
827	C₂²⋊C₄	—	4	1	no	—
828	C₂²⋊C₄	—	4	2	no	—
829	C₂²⋊C₄	—	4	2	no	—
830	C₂²⋊C₄	—	4	2	no	—
831	C₂²⋊C₄	—	4	2	no	—
832	C₂²⋊C₄	—	4	2	no	—
833	C₂²⋊C₄	—	4	2	no	—
834	C₂²⋊C₄	—	4	2	no	—
835	C₂²⋊C₄	—	4	1	no	—
836	C₂²⋊C₄	C₂²×C₃×C₄	1	4	yes	—
837	C₂²⋊C₄	C₂²×C₃×C₄	1	4	yes	—
838	C₂²⋊C₄	C₂²×C₃×C₄	1	8	yes	—
839	C₂²⋊C₄	C₂²×C₃×C₄	1	8	yes	—
840	C₂²⋊C₄	C₂²×C₃×C₄	1	8	yes	—
841	C₂²⋊C₄	C₂²×C₃×C₄	1	8	yes	—
842	C₄²	—	2	2	no	—
843	C₄²	—	2	2	no	—
844	C₄²	—	2	2	no	—
845	C₄²	—	2	2	no	—
846	C₄²	—	4	1	no	—
847	C₄²	—	4	1	no	—
848	C₄²	—	4	2	no	—
849	C₄²	—	4	2	no	—
850	C₄²	—	4	2	no	—
851	C₄²	—	4	2	no	—
852	C₄²	—	4	2	no	—
853	C₄²	C₂²×C₃×C₄	1	8	yes	—
854	C₄²	C₂²×C₃×C₄	1	4	yes	—
855	C₂²×C₃	—	2	2	no	—
856	C₂²×C₃	—	2	2	no	—
857	C₂²×C₃	—	2	2	no	—
858	C₂²×C₃	—	2	2	no	—
859	C₂²×C₃	—	2	2	no	—
860	C₂²×C₃	—	2	2	no	—
861	C₂²×C₃	—	2	2	no	—
862	C₂²×C₃	—	2	4	no	—
863	C₂²×C₃	—	2	2	no	—
864	C₂²×C₃	—	2	4	no	—
865	C₂²×C₃	—	2	2	no	—
866	C₂²×C₃	—	2	4	no	—
867	C₂²×C₃	—	4	2	no	—
868	C₂²×C₃	—	4	1	no	—
869	C₂²×C₃	—	4	1	no	—
870	C₂²×C₃	—	4	2	no	—
871	C₂²×C₃	—	4	2	no	—
872	C₂²×C₃	—	4	1	no	—
873	C₂²×C₃	—	4	1	no	—
874	C₂²×C₃	—	4	2	no	—
875	C₂²×C₃	#520	1	4	yes	—
876	C₂²×C₃	C₂⁴×C₄	1	1	yes	characteristic
877	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
878	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
879	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
880	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
881	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
882	C₂²×C₃	#585	1	1	yes	characteristic
883	C₃×C₄	—	2	2	no	—
884	C₃×C₄	—	2	2	no	—
885	C₃×C₄	—	2	4	no	—
886	C₃×C₄	—	2	4	no	—
887	C₃×C₄	—	2	4	no	—
888	C₃×C₄	—	2	2	no	—
889	C₃×C₄	—	2	2	no	—
890	C₃×C₄	—	2	2	no	—
891	C₃×C₄	—	4	1	no	—
892	C₃×C₄	—	4	1	no	—
893	C₃×C₄	—	4	2	no	—
894	C₃×C₄	—	4	1	no	—
895	C₃×C₄	—	4	1	no	—
896	C₃×C₄	—	4	1	no	—
897	C₃×C₄	—	4	1	no	—
898	C₃×C₄	—	4	2	no	—
899	C₃×C₄	—	4	1	no	—
900	C₃×C₄	—	4	2	no	—
901	C₃×C₄	—	4	2	no	—
902	C₃×C₄	#518	1	4	yes	—
903	C₂³	—	2	1	no	—
904	C₂³	—	2	1	no	—
905	C₂³	—	2	1	no	—
906	C₂³	—	2	1	no	—
907	C₂³	—	2	1	no	—
908	C₂³	—	2	2	no	—
909	C₂³	—	2	1	no	—
910	C₂³	—	2	2	no	—
911	C₂³	—	2	2	no	—
912	C₂³	—	2	1	no	—
913	C₂³	—	2	1	no	—
914	C₂³	—	2	2	no	—
915	C₂³	—	2	1	no	—
916	C₂³	—	2	2	no	—
917	C₂³	—	2	2	no	—
918	C₂³	—	2	1	no	—
919	C₂³	C₂³×C₃×C₄	1	2	yes	—
920	C₂³	C₂³×C₃×C₄	1	4	yes	—
921	C₂³	C₂³×C₃×C₄	1	2	yes	—
922	C₂³	C₃×H(5,𝔽₂)	1	2	yes	—
923	C₂³	C₃×2₋¹⁺⁴	1	2	yes	—
924	C₂³	C₂⁵×C₃	1	1	yes	characteristic
925	Q₈	—	2	8	no	—
926	Q₈	—	2	8	no	—
927	Q₈	—	4	8	no	—
928	D₄	—	2	8	no	—
929	D₄	—	2	16	no	—
930	D₄	—	2	8	no	—
931	D₄	—	4	8	no	—
932	C₂×C₄	—	2	1	no	—
933	C₂×C₄	—	2	2	no	—
934	C₂×C₄	—	2	1	no	—
935	C₂×C₄	—	2	1	no	—
936	C₂×C₄	—	2	1	no	—
937	C₂×C₄	—	2	2	no	—
938	C₂×C₄	—	2	2	no	—
939	C₂×C₄	—	2	1	no	—
940	C₂×C₄	—	2	1	no	—
941	C₂×C₄	—	2	1	no	—
942	C₂×C₄	—	2	2	no	—
943	C₂×C₄	—	2	2	no	—
944	C₂×C₄	—	2	1	no	—
945	C₂×C₄	—	2	1	no	—
946	C₂×C₄	—	2	2	no	—
947	C₂×C₄	—	2	1	no	—
948	C₂×C₄	—	2	8	no	—
949	C₂×C₄	—	2	8	no	—
950	C₂×C₄	—	2	1	no	—
951	C₂×C₄	—	2	1	no	—
952	C₂×C₄	—	2	1	no	—
953	C₂×C₄	—	2	1	no	—
954	C₂×C₄	—	2	1	no	—
955	C₂×C₄	—	2	1	no	—
956	C₂×C₄	—	2	1	no	—
957	C₂×C₄	—	2	1	no	—
958	C₂×C₄	—	2	2	no	—
959	C₂×C₄	—	2	2	no	—
960	C₂×C₄	—	2	2	no	—
961	C₂×C₄	—	2	2	no	—
962	C₂×C₄	—	2	2	no	—
963	C₂×C₄	—	2	2	no	—
964	C₂×C₄	—	2	1	no	—
965	C₂×C₄	—	2	1	no	—
966	C₂×C₄	—	2	2	no	—
967	C₂×C₄	—	2	2	no	—
968	C₂×C₄	—	2	1	no	—
969	C₂×C₄	—	2	1	no	—
970	C₂×C₄	—	2	1	no	—
971	C₂×C₄	—	2	1	no	—
972	C₂×C₄	—	2	1	no	—
973	C₂×C₄	—	2	2	no	—
974	C₂×C₄	—	2	1	no	—
975	C₂×C₄	—	2	1	no	—
976	C₂×C₄	—	2	1	no	—
977	C₂×C₄	—	2	1	no	—
978	C₂×C₄	—	2	1	no	—
979	C₂×C₄	—	2	2	no	—
980	C₂×C₄	—	2	1	no	—
981	C₂×C₄	—	2	2	no	—
982	C₂×C₄	—	2	2	no	—
983	C₂×C₄	—	4	8	no	—
984	C₂×C₄	—	4	8	no	—
985	C₂×C₄	—	4	4	no	—
986	C₂×C₄	—	4	4	no	—
987	C₂×C₄	—	8	4	no	—
988	C₂×C₄	—	8	4	no	—
989	C₂×C₄	—	8	4	no	—
990	C₂×C₄	—	8	4	no	—
991	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
992	C₂×C₄	C₂³×C₃×C₄	1	4	yes	—
993	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
994	C₂×C₄	C₂³×C₃×C₄	1	4	yes	—
995	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
996	C₂×C₄	C₂³×C₃×C₄	1	4	yes	—
997	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
998	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
999	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
1000	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
1001	C₂×C₄	C₃×2₋¹⁺⁴	1	2	yes	—
1002	C₂×C₃	—	2	4	no	—
1003	C₂×C₃	—	4	2	no	—
1004	C₂×C₃	—	4	4	no	—
1005	C₂×C₃	C₂×#518	1	1	yes	characteristic
1006	C₂×C₃	C₂×#520	1	1	yes	characteristic
1007	C₂×C₃	C₄×2₋¹⁺⁴	1	1	yes	characteristic
1008	C₂×C₃	#3536	1	1	yes	characteristic
1009	C₂×C₃	#3541	1	1	yes	characteristic
1010	C₂×C₃	#3552	1	1	yes	characteristic
1011	C₂×C₃	#3558	1	1	yes	characteristic
1012	C₂²	—	2	2	no	—
1013	C₂²	—	2	2	no	—
1014	C₂²	—	2	2	no	—
1015	C₂²	—	2	2	no	—
1016	C₂²	—	2	2	no	—
1017	C₂²	—	2	2	no	—
1018	C₂²	—	2	2	no	—
1019	C₂²	—	2	4	no	—
1020	C₂²	—	2	2	no	—
1021	C₂²	—	2	4	no	—
1022	C₂²	—	2	2	no	—
1023	C₂²	—	2	4	no	—
1024	C₂²	—	4	2	no	—
1025	C₂²	—	4	1	no	—
1026	C₂²	—	4	1	no	—
1027	C₂²	—	4	2	no	—
1028	C₂²	—	4	2	no	—
1029	C₂²	—	4	1	no	—
1030	C₂²	—	4	1	no	—
1031	C₂²	—	4	2	no	—
1032	C₂²	C₃×#520	1	4	yes	—
1033	C₂²	C₂⁴×C₃×C₄	1	1	yes	characteristic
1034	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1035	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1036	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1037	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
1038	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
1039	C₂²	C₃×#585	1	1	yes	characteristic
1040	C₄	—	2	2	no	—
1041	C₄	—	2	2	no	—
1042	C₄	—	2	4	no	—
1043	C₄	—	2	4	no	—
1044	C₄	—	2	4	no	—
1045	C₄	—	2	2	no	—
1046	C₄	—	2	2	no	—
1047	C₄	—	2	2	no	—
1048	C₄	—	4	1	no	—
1049	C₄	—	4	2	no	—
1050	C₄	—	4	1	no	—
1051	C₄	—	4	1	no	—
1052	C₄	—	4	1	no	—
1053	C₄	—	4	1	no	—
1054	C₄	—	4	1	no	—
1055	C₄	—	4	1	no	—
1056	C₄	—	4	2	no	—
1057	C₄	—	4	2	no	—
1058	C₄	—	4	2	no	—
1059	C₄	C₃×#518	1	4	yes	—
1060	C₃	#34472	1	1	yes	characteristic, direct product factor, Sylow
1061	C₂	—	2	4	no	—
1062	C₂	—	4	2	no	—
1063	C₂	—	4	4	no	—
1064	C₂	C₂×C₃×#518	1	1	yes	characteristic
1065	C₂	C₂×C₃×#520	1	1	yes	characteristic
1066	C₂	C₃×C₄×2₋¹⁺⁴	1	1	yes	characteristic
1067	C₂	C₃×#3536	1	1	yes	characteristic
1068	C₂	C₃×#3541	1	1	yes	characteristic
1069	C₂	C₃×#3552	1	1	yes	characteristic
1070	C₂	C₃×#3558	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator	C₂²	C₂⁴×C₃×C₄
Frattini, cosocle	C₂³	C₂⁵×C₃
prime radical	C₂×C₃×#548	C₂
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×#2379	C₂	semidirect
3. C₃×#2378	C₂	semidirect
4. C₃×#2367	C₂	semidirect
5. C₃×#2364	C₂	semidirect
6. C₃×#2361	C₂	semidirect
7. C₃×#2360	C₂	semidirect
8. C₃×#2355	C₂	semidirect
9. C₃×#2349	C₂	semidirect
10. C₃×D₄×C₄⋊C₄	C₂	semidirect
11. C₃×Q₈×C₂²⋊C₄	C₂	semidirect
12. C₃×#2339	C₂	semidirect
13. C₃×#2337	C₂	semidirect
14. C₃×#2329	C₂	semidirect
15. C₃×#2326	C₂	semidirect
16. C₃×#2325	C₂	semidirect
17. C₃×#2323	C₂	semidirect
18. C₃×#2320	C₂	semidirect
19. C₃×#2318	C₂	semidirect
20. C₃×#2311	C₂	semidirect
21. C₃×C₄×#121	C₂	semidirect
22. C₂×C₃×#391	C₂	semidirect
23. C₃×#2290	C₂	semidirect
24. #34472	C₃	direct (N × H)
27. C₃×#548	C₄	semidirect
126. #2379	C₂×C₃	semidirect
127. #2378	C₂×C₃	semidirect
128. #2367	C₂×C₃	semidirect
129. #2364	C₂×C₃	semidirect
130. #2361	C₂×C₃	semidirect
131. #2360	C₂×C₃	semidirect
132. #2355	C₂×C₃	semidirect
133. #2349	C₂×C₃	semidirect
134. D₄×C₄⋊C₄	C₂×C₃	semidirect
135. Q₈×C₂²⋊C₄	C₂×C₃	semidirect
136. #2339	C₂×C₃	semidirect
137. #2337	C₂×C₃	semidirect
138. #2329	C₂×C₃	semidirect
139. #2326	C₂×C₃	semidirect
140. #2325	C₂×C₃	semidirect
141. #2323	C₂×C₃	semidirect
142. #2320	C₂×C₃	semidirect
143. #2318	C₂×C₃	semidirect
144. #2311	C₂×C₃	semidirect
145. C₄×#121	C₂×C₃	semidirect
146. C₂×#391	C₂×C₃	semidirect
147. #2290	C₂×C₃	semidirect
150. C₂×C₃×#41	C₂×C₄	semidirect
153. C₂²×C₃×Q₈	C₂×C₄	semidirect
171. C₃×#124	C₂×C₄	semidirect
172. C₃×#124	C₂×C₄	semidirect
173. C₃×C₂²⋊Q₈	C₂×C₄	semidirect
174. C₃×C₂²⋊Q₈	C₂×C₄	semidirect
175. C₃×#121	C₂×C₄	semidirect
176. C₃×#121	C₂×C₄	semidirect
179. C₃×C₄×Q₈	C₂×C₄	semidirect
185. C₃×C₄×D₄	C₂×C₄	semidirect
186. C₃×C₄×D₄	C₂×C₄	semidirect
275. #548	C₃×C₄	semidirect
504. C₂×#41	C₂×C₃×C₄	semidirect
507. C₂²×Q₈	C₂×C₃×C₄	semidirect
525. #124	C₂×C₃×C₄	semidirect
526. #124	C₂×C₃×C₄	semidirect
527. C₂²⋊Q₈	C₂×C₃×C₄	semidirect
528. C₂²⋊Q₈	C₂×C₃×C₄	semidirect
529. #121	C₂×C₃×C₄	semidirect
530. #121	C₂×C₃×C₄	semidirect
533. C₄×Q₈	C₂×C₃×C₄	semidirect
539. C₄×D₄	C₂×C₃×C₄	semidirect
540. C₄×D₄	C₂×C₃×C₄	semidirect
1060. C₃	#34472	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×#548	2
C₃×#2379	2
C₃×#2378	2
C₃×#2367	2
C₃×#2364	2
C₃×#2361	2
C₃×#2360	2
C₃×#2355	2
C₃×#2349	2
C₃×D₄×C₄⋊C₄	2
C₃×Q₈×C₂²⋊C₄	2
C₃×#2339	2
C₃×#2337	2
C₃×#2329	2
C₃×#2326	2
C₃×#2325	2
C₃×#2323	2
C₃×#2320	2
C₃×#2318	2
C₃×#2311	2
C₃×C₄×#121	2
C₂×C₃×#391	2
C₃×#2290	2
#34472	3

Subgroups — C3×#34472 #10653079

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#34472 #10653079