Subgroups — C₃×#42460 #10661067

Order 768.

1880 conjugacy classes of subgroups.

The subgroup lattice has 1078 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#2837	C₂	1	2	yes	maximal, complemented
2	C₃×#2780	C₂	1	2	yes	maximal, complemented
3	C₃×#2711	C₂	1	2	yes	maximal, complemented
4	C₃×#2707	C₂	1	2	yes	maximal, complemented
5	C₃×#2701	C₂	1	2	yes	maximal, complemented
6	C₃×#2667	C₂	1	2	yes	maximal, complemented
7	C₃×#2630	C₂	1	2	yes	maximal, complemented
8	C₃×#2620	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#2552	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#2540	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#2538	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#2537	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#2502	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#2501	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#2464	C₂	1	2	yes	maximal, complemented
16	C₃×#2421	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×#2420	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃×#2417	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃×#2416	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃×#2392	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃×#2367	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃×D₄×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃×#2314	C₂	1	1	yes	maximal, characteristic, complemented
24	#42460	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂×C₃×#125	C₂²	1	2	yes	—
26	C₂×C₃×#124	C₂²	1	1	yes	characteristic
27	C₂×C₃×#123	C₂²	1	2	yes	—
28	C₂×C₃×#123	C₂²	1	2	yes	—
29	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
30	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
31	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
32	C₂×C₃×#121	C₂²	1	1	yes	characteristic
33	C₂×C₃×#121	C₂²	1	1	yes	characteristic
34	C₂×C₃×#121	C₂²	1	2	yes	—
35	C₂×C₃×#121	C₂²	1	2	yes	—
36	C₂×C₃×#121	C₂²	1	1	yes	characteristic
37	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
38	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
39	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
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×#117	C₂²	1	1	yes	characteristic
44	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
45	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
46	C₃×#400	C₂²	1	2	yes	—
47	C₃×#399	C₂²	1	2	yes	—
48	C₃×#399	C₂²	1	2	yes	—
49	C₃×#399	C₂²	1	2	yes	—
50	C₃×#398	C₂²	1	2	yes	—
51	C₃×#398	C₂²	1	1	yes	characteristic
52	C₃×#398	C₂²	1	2	yes	—
53	C₃×#398	C₂²	1	2	yes	—
54	C₃×#398	C₂²	1	2	yes	—
55	C₃×#398	C₂²	1	2	yes	—
56	C₃×#397	C₂²	1	2	yes	—
57	C₃×#397	C₂²	1	1	yes	characteristic
58	C₃×#397	C₂²	1	2	yes	—
59	C₃×#396	C₂²	1	2	yes	—
60	C₃×#396	C₂²	1	2	yes	—
61	C₃×#396	C₂²	1	2	yes	—
62	C₃×#396	C₂²	1	1	yes	characteristic
63	C₃×#396	C₂²	1	1	yes	characteristic
64	C₃×#396	C₂²	1	2	yes	—
65	C₃×#396	C₂²	1	2	yes	—
66	C₃×#396	C₂²	1	2	yes	—
67	C₃×#394	C₂²	1	2	yes	—
68	C₃×#394	C₂²	1	2	yes	—
69	C₃×#394	C₂²	1	1	yes	characteristic
70	C₃×#394	C₂²	1	2	yes	—
71	C₃×#394	C₂²	1	2	yes	—
72	C₃×#394	C₂²	1	1	yes	characteristic
73	C₃×#394	C₂²	1	1	yes	characteristic
74	C₃×#394	C₂²	1	2	yes	—
75	C₃×#394	C₂²	1	2	yes	—
76	C₃×#392	C₂²	1	2	yes	—
77	C₃×#392	C₂²	1	1	yes	characteristic
78	C₃×#391	C₂²	1	1	yes	characteristic
79	C₃×#391	C₂²	1	1	yes	characteristic
80	C₃×#390	C₂²	1	1	yes	characteristic
81	C₃×#390	C₂²	1	1	yes	characteristic
82	C₃×#390	C₂²	1	2	yes	—
83	C₃×#390	C₂²	1	2	yes	—
84	C₃×#390	C₂²	1	2	yes	—
85	C₃×#389	C₂²	1	2	yes	—
86	C₃×#389	C₂²	1	2	yes	—
87	C₃×#389	C₂²	1	1	yes	characteristic
88	C₃×#389	C₂²	1	1	yes	characteristic
89	C₃×#389	C₂²	1	2	yes	—
90	C₃×#388	C₂²	1	2	yes	—
91	C₃×#388	C₂²	1	2	yes	—
92	C₃×#388	C₂²	1	2	yes	—
93	C₃×#388	C₂²	1	2	yes	—
94	C₃×#388	C₂²	1	2	yes	—
95	C₃×#387	C₂²	1	2	yes	—
96	C₃×#387	C₂²	1	2	yes	—
97	C₃×#387	C₂²	1	2	yes	—
98	C₃×#386	C₂²	1	2	yes	—
99	C₃×#386	C₂²	1	2	yes	—
100	C₃×#386	C₂²	1	2	yes	—
101	C₃×#385	C₂²	1	2	yes	—
102	C₃×#385	C₂²	1	2	yes	—
103	C₃×#385	C₂²	1	2	yes	—
104	C₃×#385	C₂²	1	2	yes	—
105	C₃×#385	C₂²	1	2	yes	—
106	C₃×#384	C₂²	1	1	yes	characteristic
107	C₃×#384	C₂²	1	1	yes	characteristic
108	C₃×#384	C₂²	1	1	yes	characteristic
109	C₃×#384	C₂²	1	1	yes	characteristic
110	C₃×#382	C₂²	1	1	yes	characteristic
111	C₃×#381	C₂²	1	2	yes	—
112	C₃×#380	C₂²	1	2	yes	—
113	C₃×#380	C₂²	1	2	yes	—
114	C₃×#380	C₂²	1	1	yes	characteristic
115	C₃×#380	C₂²	1	1	yes	characteristic
116	C₃×#380	C₂²	1	1	yes	characteristic
117	C₃×#380	C₂²	1	1	yes	characteristic
118	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
119	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
120	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
121	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
122	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
123	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
124	#2837	C₂×C₃	1	2	yes	complemented
125	#2780	C₂×C₃	1	2	yes	complemented
126	#2711	C₂×C₃	1	2	yes	complemented
127	#2707	C₂×C₃	1	2	yes	complemented
128	#2701	C₂×C₃	1	2	yes	complemented
129	#2667	C₂×C₃	1	2	yes	complemented
130	#2630	C₂×C₃	1	2	yes	complemented
131	#2620	C₂×C₃	1	1	yes	characteristic, complemented
132	#2552	C₂×C₃	1	1	yes	characteristic, complemented
133	#2540	C₂×C₃	1	1	yes	characteristic, complemented
134	#2538	C₂×C₃	1	1	yes	characteristic, complemented
135	#2537	C₂×C₃	1	1	yes	characteristic, complemented
136	#2502	C₂×C₃	1	1	yes	characteristic, complemented
137	#2501	C₂×C₃	1	1	yes	characteristic, complemented
138	#2464	C₂×C₃	1	2	yes	complemented
139	#2421	C₂×C₃	1	1	yes	characteristic, complemented
140	#2420	C₂×C₃	1	1	yes	characteristic, complemented
141	#2417	C₂×C₃	1	1	yes	characteristic, complemented
142	#2416	C₂×C₃	1	1	yes	characteristic, complemented
143	#2392	C₂×C₃	1	1	yes	characteristic, complemented
144	#2367	C₂×C₃	1	1	yes	characteristic, complemented
145	D₄×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
146	#2314	C₂×C₃	1	1	yes	characteristic, complemented
147	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
148	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
149	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
150	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
151	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
152	C₂²×C₃×D₄	C₂³	1	2	yes	—
153	C₂²×C₃×D₄	C₂³	1	2	yes	—
154	C₂²×C₃×D₄	C₂³	1	2	yes	—
155	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
156	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
157	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
158	C₂³×C₃×C₄	C₂³	1	2	yes	—
159	C₂³×C₃×C₄	C₂³	1	2	yes	—
160	C₂³×C₃×C₄	C₂³	1	2	yes	—
161	C₃×#125	—	4	4	no	—
162	C₃×#124	—	2	4	no	—
163	C₃×#123	—	4	4	no	—
164	C₃×#123	—	4	4	no	—
165	C₃×C₂²⋊Q₈	—	4	2	no	—
166	C₃×C₂²⋊Q₈	—	4	2	no	—
167	C₃×C₂²⋊Q₈	—	4	2	no	—
168	C₃×#121	—	4	4	no	—
169	C₃×#121	—	4	4	no	—
170	C₃×#121	—	4	2	no	—
171	C₃×#121	—	4	2	no	—
172	C₃×#121	—	4	2	no	—
173	C₃×C₄×Q₈	—	4	2	no	—
174	C₃×C₄×D₄	—	2	4	no	—
175	C₃×C₄×D₄	—	4	2	no	—
176	C₃×C₄×D₄	—	4	2	no	—
177	C₃×C₄×D₄	—	4	2	no	—
178	C₃×C₄×D₄	—	4	4	no	—
179	C₃×#117	—	2	4	no	—
180	C₂×C₃×C₄⋊C₄	—	4	2	no	—
181	C₂×C₃×C₄⋊C₄	—	4	2	no	—
182	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
187	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
188	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
189	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
190	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
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	2	yes	—
198	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
199	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
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×C₄⋊C₄	C₂³	1	2	yes	—
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×C₂²⋊C₄	C₂³	1	1	yes	characteristic
219	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
220	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
221	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
228	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
229	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
230	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
231	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
232	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
233	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
234	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
235	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
236	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
237	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
238	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
239	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
240	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
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	C₂×C₃×C₄²	C₂³	1	2	yes	—
245	C₂×C₃×C₄²	C₂³	1	2	yes	—
246	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
247	C₃×#95	C₂³	1	1	yes	characteristic
248	C₃×#95	C₂³	1	1	yes	characteristic
249	C₃×#95	C₂³	1	2	yes	—
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	1	yes	characteristic
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	C₃×#95	C₂³	1	2	yes	—
265	C₃×#95	C₂³	1	2	yes	—
266	C₃×#95	C₂³	1	2	yes	—
267	C₂×#125	C₂²×C₃	1	2	yes	—
268	C₂×#124	C₂²×C₃	1	1	yes	characteristic
269	C₂×#123	C₂²×C₃	1	2	yes	—
270	C₂×#123	C₂²×C₃	1	2	yes	—
271	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
272	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
273	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
274	C₂×#121	C₂²×C₃	1	1	yes	characteristic
275	C₂×#121	C₂²×C₃	1	1	yes	characteristic
276	C₂×#121	C₂²×C₃	1	2	yes	—
277	C₂×#121	C₂²×C₃	1	2	yes	—
278	C₂×#121	C₂²×C₃	1	1	yes	characteristic
279	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
280	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
281	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
282	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
283	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
284	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
285	C₂×#117	C₂²×C₃	1	1	yes	characteristic
286	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
287	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
288	#400	C₂²×C₃	1	2	yes	—
289	#399	C₂²×C₃	1	2	yes	—
290	#399	C₂²×C₃	1	2	yes	—
291	#399	C₂²×C₃	1	2	yes	—
292	#398	C₂²×C₃	1	2	yes	—
293	#398	C₂²×C₃	1	2	yes	—
294	#398	C₂²×C₃	1	1	yes	characteristic
295	#398	C₂²×C₃	1	2	yes	—
296	#398	C₂²×C₃	1	2	yes	—
297	#398	C₂²×C₃	1	2	yes	—
298	#397	C₂²×C₃	1	1	yes	characteristic
299	#397	C₂²×C₃	1	2	yes	—
300	#397	C₂²×C₃	1	2	yes	—
301	#396	C₂²×C₃	1	2	yes	—
302	#396	C₂²×C₃	1	2	yes	—
303	#396	C₂²×C₃	1	2	yes	—
304	#396	C₂²×C₃	1	2	yes	—
305	#396	C₂²×C₃	1	2	yes	—
306	#396	C₂²×C₃	1	1	yes	characteristic
307	#396	C₂²×C₃	1	1	yes	characteristic
308	#396	C₂²×C₃	1	2	yes	—
309	#394	C₂²×C₃	1	2	yes	—
310	#394	C₂²×C₃	1	2	yes	—
311	#394	C₂²×C₃	1	2	yes	—
312	#394	C₂²×C₃	1	2	yes	—
313	#394	C₂²×C₃	1	1	yes	characteristic
314	#394	C₂²×C₃	1	2	yes	—
315	#394	C₂²×C₃	1	2	yes	—
316	#394	C₂²×C₃	1	1	yes	characteristic
317	#394	C₂²×C₃	1	1	yes	characteristic
318	#392	C₂²×C₃	1	2	yes	—
319	#392	C₂²×C₃	1	1	yes	characteristic
320	#391	C₂²×C₃	1	1	yes	characteristic
321	#391	C₂²×C₃	1	1	yes	characteristic
322	#390	C₂²×C₃	1	1	yes	characteristic
323	#390	C₂²×C₃	1	1	yes	characteristic
324	#390	C₂²×C₃	1	2	yes	—
325	#390	C₂²×C₃	1	2	yes	—
326	#390	C₂²×C₃	1	2	yes	—
327	#389	C₂²×C₃	1	2	yes	—
328	#389	C₂²×C₃	1	2	yes	—
329	#389	C₂²×C₃	1	1	yes	characteristic
330	#389	C₂²×C₃	1	1	yes	characteristic
331	#389	C₂²×C₃	1	2	yes	—
332	#388	C₂²×C₃	1	2	yes	—
333	#388	C₂²×C₃	1	2	yes	—
334	#388	C₂²×C₃	1	2	yes	—
335	#388	C₂²×C₃	1	2	yes	—
336	#388	C₂²×C₃	1	2	yes	—
337	#387	C₂²×C₃	1	2	yes	—
338	#387	C₂²×C₃	1	2	yes	—
339	#387	C₂²×C₃	1	2	yes	—
340	#386	C₂²×C₃	1	2	yes	—
341	#386	C₂²×C₃	1	2	yes	—
342	#386	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	2	yes	—
348	#384	C₂²×C₃	1	1	yes	characteristic
349	#384	C₂²×C₃	1	1	yes	characteristic
350	#384	C₂²×C₃	1	1	yes	characteristic
351	#384	C₂²×C₃	1	1	yes	characteristic
352	#382	C₂²×C₃	1	1	yes	characteristic
353	#381	C₂²×C₃	1	2	yes	—
354	#380	C₂²×C₃	1	1	yes	characteristic
355	#380	C₂²×C₃	1	1	yes	characteristic
356	#380	C₂²×C₃	1	1	yes	characteristic
357	#380	C₂²×C₃	1	1	yes	characteristic
358	#380	C₂²×C₃	1	2	yes	—
359	#380	C₂²×C₃	1	2	yes	—
360	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
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	1	yes	characteristic
365	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
366	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
367	C₂⁴×C₃	C₂⁴	1	2	yes	—
368	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
369	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
370	C₂×C₃×Q₈	—	2	2	no	—
371	C₂×C₃×Q₈	—	2	2	no	—
372	C₂×C₃×Q₈	—	2	2	no	—
373	C₂×C₃×D₄	—	2	2	no	—
374	C₂×C₃×D₄	—	2	2	no	—
375	C₂×C₃×D₄	—	2	2	no	—
376	C₂×C₃×D₄	—	2	2	no	—
377	C₂×C₃×D₄	—	2	4	no	—
378	C₂×C₃×D₄	—	2	4	no	—
379	C₂×C₃×D₄	—	2	2	no	—
380	C₂×C₃×D₄	—	2	2	no	—
381	C₂×C₃×D₄	—	2	2	no	—
382	C₂×C₃×D₄	—	2	2	no	—
383	C₂×C₃×D₄	—	2	2	no	—
384	C₂×C₃×D₄	—	2	2	no	—
385	C₂×C₃×D₄	—	4	1	no	—
386	C₂×C₃×D₄	—	4	1	no	—
387	C₂×C₃×D₄	—	4	2	no	—
388	C₂×C₃×D₄	—	4	2	no	—
389	C₂×C₃×D₄	—	4	2	no	—
390	C₂×C₃×D₄	—	4	2	no	—
391	C₂×C₃×D₄	—	4	2	no	—
392	C₂×C₃×D₄	—	4	2	no	—
393	C₂×C₃×D₄	—	4	2	no	—
394	C₂²×C₃×C₄	—	2	4	no	—
395	C₂²×C₃×C₄	—	2	2	no	—
396	C₂²×C₃×C₄	—	2	2	no	—
397	C₂²×C₃×C₄	—	2	2	no	—
398	C₂²×C₃×C₄	—	2	2	no	—
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	4	no	—
405	C₂²×C₃×C₄	—	4	2	no	—
406	C₂²×C₃×C₄	—	4	2	no	—
407	C₂²×C₃×C₄	—	4	2	no	—
408	C₂²×C₃×C₄	—	4	2	no	—
409	C₂²×C₃×C₄	—	4	2	no	—
410	C₂²×C₃×C₄	—	4	2	no	—
411	C₂²×C₃×C₄	—	4	2	no	—
412	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
413	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
414	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
415	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
416	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
417	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
418	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
419	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
420	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
421	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
422	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
423	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
424	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
425	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
426	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
427	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
428	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
429	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
430	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
431	C₃×C₄⋊C₄	—	2	2	no	—
432	C₃×C₄⋊C₄	—	2	2	no	—
433	C₃×C₄⋊C₄	—	2	2	no	—
434	C₃×C₄⋊C₄	—	2	2	no	—
435	C₃×C₄⋊C₄	—	2	2	no	—
436	C₃×C₄⋊C₄	—	2	2	no	—
437	C₃×C₄⋊C₄	—	2	2	no	—
438	C₃×C₄⋊C₄	—	2	2	no	—
439	C₃×C₄⋊C₄	—	2	2	no	—
440	C₃×C₄⋊C₄	—	2	4	no	—
441	C₃×C₄⋊C₄	—	2	4	no	—
442	C₃×C₄⋊C₄	—	2	2	no	—
443	C₃×C₄⋊C₄	—	2	2	no	—
444	C₃×C₄⋊C₄	—	4	2	no	—
445	C₃×C₄⋊C₄	—	4	2	no	—
446	C₃×C₄⋊C₄	—	4	1	no	—
447	C₃×C₄⋊C₄	—	4	1	no	—
448	C₃×C₄⋊C₄	—	4	2	no	—
449	C₃×C₄⋊C₄	—	4	2	no	—
450	C₃×C₄⋊C₄	—	4	2	no	—
451	C₃×C₄⋊C₄	—	4	2	no	—
452	C₃×C₄⋊C₄	—	4	2	no	—
453	C₃×C₄⋊C₄	—	4	2	no	—
454	C₃×C₄⋊C₄	—	4	2	no	—
455	C₃×C₄⋊C₄	—	4	2	no	—
456	C₃×C₄⋊C₄	—	4	2	no	—
457	C₃×C₄⋊C₄	—	4	2	no	—
458	C₃×C₄⋊C₄	—	4	2	no	—
459	C₃×C₄⋊C₄	—	4	2	no	—
460	C₃×C₂²⋊C₄	—	2	4	no	—
461	C₃×C₂²⋊C₄	—	2	2	no	—
462	C₃×C₂²⋊C₄	—	2	2	no	—
463	C₃×C₂²⋊C₄	—	2	2	no	—
464	C₃×C₂²⋊C₄	—	2	2	no	—
465	C₃×C₂²⋊C₄	—	2	2	no	—
466	C₃×C₂²⋊C₄	—	2	2	no	—
467	C₃×C₂²⋊C₄	—	2	4	no	—
468	C₃×C₂²⋊C₄	—	2	4	no	—
469	C₃×C₂²⋊C₄	—	2	4	no	—
470	C₃×C₂²⋊C₄	—	2	2	no	—
471	C₃×C₂²⋊C₄	—	2	2	no	—
472	C₃×C₂²⋊C₄	—	4	2	no	—
473	C₃×C₂²⋊C₄	—	4	1	no	—
474	C₃×C₂²⋊C₄	—	4	1	no	—
475	C₃×C₂²⋊C₄	—	4	1	no	—
476	C₃×C₂²⋊C₄	—	4	1	no	—
477	C₃×C₂²⋊C₄	—	4	2	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	—	4	2	no	—
484	C₃×C₂²⋊C₄	—	4	2	no	—
485	C₃×C₂²⋊C₄	—	4	2	no	—
486	C₃×C₂²⋊C₄	—	4	2	no	—
487	C₃×C₂²⋊C₄	—	4	2	no	—
488	C₃×C₂²⋊C₄	—	4	2	no	—
489	C₃×C₄²	—	2	2	no	—
490	C₃×C₄²	—	2	2	no	—
491	C₃×C₄²	—	2	2	no	—
492	C₃×C₄²	—	4	2	no	—
493	C₃×C₄²	—	4	2	no	—
494	C₃×C₄²	—	4	2	no	—
495	C₃×C₄²	#41	1	4	yes	—
496	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
497	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
498	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
499	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
500	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
501	C₂²×D₄	C₂³×C₃	1	2	yes	—
502	C₂²×D₄	C₂³×C₃	1	2	yes	—
503	C₂²×D₄	C₂³×C₃	1	2	yes	—
504	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
505	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
506	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
507	C₂³×C₄	C₂³×C₃	1	2	yes	—
508	C₂³×C₄	C₂³×C₃	1	2	yes	—
509	C₂³×C₄	C₂³×C₃	1	2	yes	—
510	#125	—	4	4	no	—
511	#124	—	2	4	no	—
512	#123	—	4	4	no	—
513	#123	—	4	4	no	—
514	C₂²⋊Q₈	—	4	2	no	—
515	C₂²⋊Q₈	—	4	2	no	—
516	C₂²⋊Q₈	—	4	2	no	—
517	#121	—	4	4	no	—
518	#121	—	4	4	no	—
519	#121	—	4	2	no	—
520	#121	—	4	2	no	—
521	#121	—	4	2	no	—
522	C₄×Q₈	—	4	2	no	—
523	C₄×D₄	—	2	4	no	—
524	C₄×D₄	—	4	2	no	—
525	C₄×D₄	—	4	2	no	—
526	C₄×D₄	—	4	2	no	—
527	C₄×D₄	—	4	4	no	—
528	#117	—	2	4	no	—
529	C₂×C₄⋊C₄	—	4	2	no	—
530	C₂×C₄⋊C₄	—	4	2	no	—
531	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
532	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
533	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
534	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
535	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
536	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
537	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
538	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
539	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
540	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
541	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
542	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
543	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
544	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
545	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
546	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
547	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
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	2	yes	—
552	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
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	2	yes	—
559	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
560	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
561	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
562	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
563	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
564	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
565	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
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	2	yes	—
569	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
570	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
571	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
572	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
573	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
574	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
575	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
576	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
577	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
578	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
579	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
580	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
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×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
585	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
586	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
587	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
588	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
589	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
590	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
591	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
592	C₂×C₄²	C₂³×C₃	1	2	yes	—
593	C₂×C₄²	C₂³×C₃	1	2	yes	—
594	C₂×C₄²	C₂³×C₃	1	2	yes	—
595	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
596	#95	C₂³×C₃	1	1	yes	characteristic
597	#95	C₂³×C₃	1	1	yes	characteristic
598	#95	C₂³×C₃	1	2	yes	—
599	#95	C₂³×C₃	1	1	yes	characteristic
600	#95	C₂³×C₃	1	1	yes	characteristic
601	#95	C₂³×C₃	1	1	yes	characteristic
602	#95	C₂³×C₃	1	2	yes	—
603	#95	C₂³×C₃	1	2	yes	—
604	#95	C₂³×C₃	1	1	yes	characteristic
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	2	yes	—
610	#95	C₂³×C₃	1	2	yes	—
611	#95	C₂³×C₃	1	2	yes	—
612	#95	C₂³×C₃	1	2	yes	—
613	#95	C₂³×C₃	1	2	yes	—
614	#95	C₂³×C₃	1	2	yes	—
615	#95	C₂³×C₃	1	2	yes	—
616	C₂³×C₃	—	2	1	no	—
617	C₂³×C₃	—	2	1	no	—
618	C₂³×C₃	—	2	1	no	—
619	C₂³×C₃	—	2	1	no	—
620	C₂³×C₃	—	2	1	no	—
621	C₂³×C₃	—	2	1	no	—
622	C₂³×C₃	—	2	1	no	—
623	C₂³×C₃	—	2	1	no	—
624	C₂³×C₃	—	2	1	no	—
625	C₂³×C₃	—	2	1	no	—
626	C₂³×C₃	—	2	1	no	—
627	C₂³×C₃	—	2	1	no	—
628	C₂³×C₃	—	2	1	no	—
629	C₂³×C₃	—	2	2	no	—
630	C₂³×C₃	—	2	2	no	—
631	C₂³×C₃	—	2	1	no	—
632	C₂³×C₃	—	2	1	no	—
633	C₂³×C₃	—	2	2	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	1	no	—
642	C₂³×C₃	H(5,𝔽₂)	1	2	yes	—
643	C₂³×C₃	2₋¹⁺⁴	1	2	yes	—
644	C₂³×C₃	C₂⁵	1	1	yes	characteristic
645	C₃×Q₈	—	4	4	no	—
646	C₃×D₄	—	2	8	no	—
647	C₃×D₄	—	4	4	no	—
648	C₃×D₄	—	4	4	no	—
649	C₃×D₄	—	4	4	no	—
650	C₃×D₄	—	8	4	no	—
651	C₃×D₄	—	8	4	no	—
652	C₃×D₄	—	8	4	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	1	no	—
657	C₂×C₃×C₄	—	2	1	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	1	no	—
662	C₂×C₃×C₄	—	2	1	no	—
663	C₂×C₃×C₄	—	2	2	no	—
664	C₂×C₃×C₄	—	2	1	no	—
665	C₂×C₃×C₄	—	2	1	no	—
666	C₂×C₃×C₄	—	2	1	no	—
667	C₂×C₃×C₄	—	2	1	no	—
668	C₂×C₃×C₄	—	2	1	no	—
669	C₂×C₃×C₄	—	2	2	no	—
670	C₂×C₃×C₄	—	2	2	no	—
671	C₂×C₃×C₄	—	2	2	no	—
672	C₂×C₃×C₄	—	2	2	no	—
673	C₂×C₃×C₄	—	2	2	no	—
674	C₂×C₃×C₄	—	2	2	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	2	no	—
679	C₂×C₃×C₄	—	2	2	no	—
680	C₂×C₃×C₄	—	2	1	no	—
681	C₂×C₃×C₄	—	2	2	no	—
682	C₂×C₃×C₄	—	2	2	no	—
683	C₂×C₃×C₄	—	2	1	no	—
684	C₂×C₃×C₄	—	2	1	no	—
685	C₂×C₃×C₄	—	2	1	no	—
686	C₂×C₃×C₄	—	2	2	no	—
687	C₂×C₃×C₄	—	2	2	no	—
688	C₂×C₃×C₄	—	2	2	no	—
689	C₂×C₃×C₄	—	2	2	no	—
690	C₂×C₃×C₄	—	2	2	no	—
691	C₂×C₃×C₄	—	2	1	no	—
692	C₂×C₃×C₄	—	2	2	no	—
693	C₂×C₃×C₄	—	2	1	no	—
694	C₂×C₃×C₄	—	2	2	no	—
695	C₂×C₃×C₄	—	2	2	no	—
696	C₂×C₃×C₄	—	2	1	no	—
697	C₂×C₃×C₄	—	2	1	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	2	no	—
702	C₂×C₃×C₄	—	2	2	no	—
703	C₂×C₃×C₄	—	4	4	no	—
704	C₂×C₃×C₄	—	4	4	no	—
705	C₂×C₃×C₄	—	4	4	no	—
706	C₂×C₃×C₄	—	8	4	no	—
707	C₂×C₃×C₄	—	8	4	no	—
708	C₂×C₃×C₄	—	8	4	no	—
709	C₂×C₃×C₄	C₂×#41	1	2	yes	—
710	C₂×C₃×C₄	C₂×#41	1	2	yes	—
711	C₂×C₃×C₄	C₂×#41	1	2	yes	—
712	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
713	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
714	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
715	C₂×C₃×C₄	2₋¹⁺⁴	1	2	yes	—
716	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
717	C₂⁴	C₂⁴×C₃	1	2	yes	—
718	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
719	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
720	C₂×Q₈	—	2	2	no	—
721	C₂×Q₈	—	2	2	no	—
722	C₂×Q₈	—	2	2	no	—
723	C₂×D₄	—	2	2	no	—
724	C₂×D₄	—	2	2	no	—
725	C₂×D₄	—	2	2	no	—
726	C₂×D₄	—	2	2	no	—
727	C₂×D₄	—	2	4	no	—
728	C₂×D₄	—	2	4	no	—
729	C₂×D₄	—	2	2	no	—
730	C₂×D₄	—	2	2	no	—
731	C₂×D₄	—	2	2	no	—
732	C₂×D₄	—	2	2	no	—
733	C₂×D₄	—	2	2	no	—
734	C₂×D₄	—	2	2	no	—
735	C₂×D₄	—	4	1	no	—
736	C₂×D₄	—	4	1	no	—
737	C₂×D₄	—	4	2	no	—
738	C₂×D₄	—	4	2	no	—
739	C₂×D₄	—	4	2	no	—
740	C₂×D₄	—	4	2	no	—
741	C₂×D₄	—	4	2	no	—
742	C₂×D₄	—	4	2	no	—
743	C₂×D₄	—	4	2	no	—
744	C₂²×C₄	—	2	4	no	—
745	C₂²×C₄	—	2	2	no	—
746	C₂²×C₄	—	2	2	no	—
747	C₂²×C₄	—	2	2	no	—
748	C₂²×C₄	—	2	2	no	—
749	C₂²×C₄	—	2	2	no	—
750	C₂²×C₄	—	2	2	no	—
751	C₂²×C₄	—	2	2	no	—
752	C₂²×C₄	—	2	2	no	—
753	C₂²×C₄	—	2	2	no	—
754	C₂²×C₄	—	2	4	no	—
755	C₂²×C₄	—	4	2	no	—
756	C₂²×C₄	—	4	2	no	—
757	C₂²×C₄	—	4	2	no	—
758	C₂²×C₄	—	4	2	no	—
759	C₂²×C₄	—	4	2	no	—
760	C₂²×C₄	—	4	2	no	—
761	C₂²×C₄	—	4	2	no	—
762	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
763	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
764	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
765	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
766	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
767	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
768	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
769	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
770	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
771	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
772	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
773	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
774	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
775	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
776	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
777	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
778	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
779	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
780	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
781	C₄⋊C₄	—	2	2	no	—
782	C₄⋊C₄	—	2	2	no	—
783	C₄⋊C₄	—	2	2	no	—
784	C₄⋊C₄	—	2	2	no	—
785	C₄⋊C₄	—	2	2	no	—
786	C₄⋊C₄	—	2	2	no	—
787	C₄⋊C₄	—	2	2	no	—
788	C₄⋊C₄	—	2	2	no	—
789	C₄⋊C₄	—	2	2	no	—
790	C₄⋊C₄	—	2	4	no	—
791	C₄⋊C₄	—	2	4	no	—
792	C₄⋊C₄	—	2	2	no	—
793	C₄⋊C₄	—	2	2	no	—
794	C₄⋊C₄	—	4	2	no	—
795	C₄⋊C₄	—	4	2	no	—
796	C₄⋊C₄	—	4	1	no	—
797	C₄⋊C₄	—	4	1	no	—
798	C₄⋊C₄	—	4	2	no	—
799	C₄⋊C₄	—	4	2	no	—
800	C₄⋊C₄	—	4	2	no	—
801	C₄⋊C₄	—	4	2	no	—
802	C₄⋊C₄	—	4	2	no	—
803	C₄⋊C₄	—	4	2	no	—
804	C₄⋊C₄	—	4	2	no	—
805	C₄⋊C₄	—	4	2	no	—
806	C₄⋊C₄	—	4	2	no	—
807	C₄⋊C₄	—	4	2	no	—
808	C₄⋊C₄	—	4	2	no	—
809	C₄⋊C₄	—	4	2	no	—
810	C₂²⋊C₄	—	2	4	no	—
811	C₂²⋊C₄	—	2	2	no	—
812	C₂²⋊C₄	—	2	2	no	—
813	C₂²⋊C₄	—	2	2	no	—
814	C₂²⋊C₄	—	2	2	no	—
815	C₂²⋊C₄	—	2	2	no	—
816	C₂²⋊C₄	—	2	2	no	—
817	C₂²⋊C₄	—	2	4	no	—
818	C₂²⋊C₄	—	2	4	no	—
819	C₂²⋊C₄	—	2	4	no	—
820	C₂²⋊C₄	—	2	2	no	—
821	C₂²⋊C₄	—	2	2	no	—
822	C₂²⋊C₄	—	4	2	no	—
823	C₂²⋊C₄	—	4	1	no	—
824	C₂²⋊C₄	—	4	1	no	—
825	C₂²⋊C₄	—	4	1	no	—
826	C₂²⋊C₄	—	4	1	no	—
827	C₂²⋊C₄	—	4	2	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	2	no	—
836	C₂²⋊C₄	—	4	2	no	—
837	C₂²⋊C₄	—	4	2	no	—
838	C₂²⋊C₄	—	4	2	no	—
839	C₄²	—	2	2	no	—
840	C₄²	—	2	2	no	—
841	C₄²	—	2	2	no	—
842	C₄²	—	4	2	no	—
843	C₄²	—	4	2	no	—
844	C₄²	—	4	2	no	—
845	C₄²	C₃×#41	1	4	yes	—
846	C₂²×C₃	—	2	2	no	—
847	C₂²×C₃	—	2	2	no	—
848	C₂²×C₃	—	2	2	no	—
849	C₂²×C₃	—	2	2	no	—
850	C₂²×C₃	—	2	2	no	—
851	C₂²×C₃	—	2	2	no	—
852	C₂²×C₃	—	4	1	no	—
853	C₂²×C₃	—	4	1	no	—
854	C₂²×C₃	—	4	1	no	—
855	C₂²×C₃	—	4	1	no	—
856	C₂²×C₃	—	4	1	no	—
857	C₂²×C₃	—	4	1	no	—
858	C₂²×C₃	—	4	1	no	—
859	C₂²×C₃	—	4	1	no	—
860	C₂²×C₃	—	4	1	no	—
861	C₂²×C₃	—	4	2	no	—
862	C₂²×C₃	—	4	1	no	—
863	C₂²×C₃	—	4	2	no	—
864	C₂²×C₃	—	4	1	no	—
865	C₂²×C₃	—	4	2	no	—
866	C₂²×C₃	—	4	2	no	—
867	C₂²×C₃	—	4	1	no	—
868	C₂²×C₃	—	4	1	no	—
869	C₂²×C₃	—	4	2	no	—
870	C₂²×C₃	—	4	2	no	—
871	C₂²×C₃	—	4	1	no	—
872	C₂²×C₃	—	4	1	no	—
873	C₂²×C₃	—	4	2	no	—
874	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
875	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
876	C₂²×C₃	C₂×H(5,𝔽₂)	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	C₂×2₋¹⁺⁴	1	1	yes	characteristic
880	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
881	C₃×C₄	—	2	2	no	—
882	C₃×C₄	—	2	2	no	—
883	C₃×C₄	—	2	2	no	—
884	C₃×C₄	—	2	2	no	—
885	C₃×C₄	—	4	1	no	—
886	C₃×C₄	—	4	1	no	—
887	C₃×C₄	—	4	1	no	—
888	C₃×C₄	—	4	2	no	—
889	C₃×C₄	—	4	1	no	—
890	C₃×C₄	—	4	1	no	—
891	C₃×C₄	—	4	1	no	—
892	C₃×C₄	—	4	1	no	—
893	C₃×C₄	—	4	2	no	—
894	C₃×C₄	—	4	2	no	—
895	C₃×C₄	—	4	2	no	—
896	C₃×C₄	—	4	2	no	—
897	C₃×C₄	—	4	2	no	—
898	C₃×C₄	—	4	2	no	—
899	C₃×C₄	#540	1	4	yes	—
900	C₂³	—	2	1	no	—
901	C₂³	—	2	1	no	—
902	C₂³	—	2	1	no	—
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	1	no	—
909	C₂³	—	2	1	no	—
910	C₂³	—	2	1	no	—
911	C₂³	—	2	1	no	—
912	C₂³	—	2	1	no	—
913	C₂³	—	2	2	no	—
914	C₂³	—	2	2	no	—
915	C₂³	—	2	1	no	—
916	C₂³	—	2	1	no	—
917	C₂³	—	2	2	no	—
918	C₂³	—	2	2	no	—
919	C₂³	—	2	2	no	—
920	C₂³	—	2	1	no	—
921	C₂³	—	2	1	no	—
922	C₂³	—	2	2	no	—
923	C₂³	—	2	1	no	—
924	C₂³	—	2	2	no	—
925	C₂³	—	2	1	no	—
926	C₂³	C₃×H(5,𝔽₂)	1	2	yes	—
927	C₂³	C₃×2₋¹⁺⁴	1	2	yes	—
928	C₂³	C₂⁵×C₃	1	1	yes	characteristic
929	Q₈	—	4	4	no	—
930	D₄	—	2	8	no	—
931	D₄	—	4	4	no	—
932	D₄	—	4	4	no	—
933	D₄	—	4	4	no	—
934	D₄	—	8	4	no	—
935	D₄	—	8	4	no	—
936	D₄	—	8	4	no	—
937	C₂×C₄	—	2	1	no	—
938	C₂×C₄	—	2	1	no	—
939	C₂×C₄	—	2	1	no	—
940	C₂×C₄	—	2	1	no	—
941	C₂×C₄	—	2	1	no	—
942	C₂×C₄	—	2	1	no	—
943	C₂×C₄	—	2	1	no	—
944	C₂×C₄	—	2	1	no	—
945	C₂×C₄	—	2	1	no	—
946	C₂×C₄	—	2	1	no	—
947	C₂×C₄	—	2	2	no	—
948	C₂×C₄	—	2	1	no	—
949	C₂×C₄	—	2	1	no	—
950	C₂×C₄	—	2	1	no	—
951	C₂×C₄	—	2	1	no	—
952	C₂×C₄	—	2	1	no	—
953	C₂×C₄	—	2	2	no	—
954	C₂×C₄	—	2	2	no	—
955	C₂×C₄	—	2	2	no	—
956	C₂×C₄	—	2	2	no	—
957	C₂×C₄	—	2	2	no	—
958	C₂×C₄	—	2	2	no	—
959	C₂×C₄	—	2	1	no	—
960	C₂×C₄	—	2	1	no	—
961	C₂×C₄	—	2	1	no	—
962	C₂×C₄	—	2	2	no	—
963	C₂×C₄	—	2	2	no	—
964	C₂×C₄	—	2	1	no	—
965	C₂×C₄	—	2	2	no	—
966	C₂×C₄	—	2	2	no	—
967	C₂×C₄	—	2	1	no	—
968	C₂×C₄	—	2	1	no	—
969	C₂×C₄	—	2	1	no	—
970	C₂×C₄	—	2	2	no	—
971	C₂×C₄	—	2	2	no	—
972	C₂×C₄	—	2	2	no	—
973	C₂×C₄	—	2	2	no	—
974	C₂×C₄	—	2	2	no	—
975	C₂×C₄	—	2	1	no	—
976	C₂×C₄	—	2	2	no	—
977	C₂×C₄	—	2	1	no	—
978	C₂×C₄	—	2	2	no	—
979	C₂×C₄	—	2	2	no	—
980	C₂×C₄	—	2	1	no	—
981	C₂×C₄	—	2	1	no	—
982	C₂×C₄	—	2	1	no	—
983	C₂×C₄	—	2	1	no	—
984	C₂×C₄	—	2	1	no	—
985	C₂×C₄	—	2	2	no	—
986	C₂×C₄	—	2	2	no	—
987	C₂×C₄	—	4	4	no	—
988	C₂×C₄	—	4	4	no	—
989	C₂×C₄	—	4	4	no	—
990	C₂×C₄	—	8	4	no	—
991	C₂×C₄	—	8	4	no	—
992	C₂×C₄	—	8	4	no	—
993	C₂×C₄	C₂×C₃×#41	1	2	yes	—
994	C₂×C₄	C₂×C₃×#41	1	2	yes	—
995	C₂×C₄	C₂×C₃×#41	1	2	yes	—
996	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
997	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
998	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
999	C₂×C₄	C₃×2₋¹⁺⁴	1	2	yes	—
1000	C₂×C₃	—	4	2	no	—
1001	C₂×C₃	—	4	2	no	—
1002	C₂×C₃	—	8	1	no	—
1003	C₂×C₃	—	8	2	no	—
1004	C₂×C₃	C₂×#540	1	1	yes	characteristic
1005	C₂×C₃	#3492	1	1	yes	characteristic
1006	C₂×C₃	#3511	1	1	yes	characteristic
1007	C₂×C₃	#3536	1	1	yes	characteristic
1008	C₂×C₃	#3536	1	1	yes	characteristic
1009	C₂×C₃	#3543	1	1	yes	characteristic
1010	C₂×C₃	#3552	1	1	yes	characteristic
1011	C₂²	—	2	2	no	—
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	—	4	1	no	—
1018	C₂²	—	4	1	no	—
1019	C₂²	—	4	1	no	—
1020	C₂²	—	4	1	no	—
1021	C₂²	—	4	1	no	—
1022	C₂²	—	4	1	no	—
1023	C₂²	—	4	1	no	—
1024	C₂²	—	4	1	no	—
1025	C₂²	—	4	1	no	—
1026	C₂²	—	4	2	no	—
1027	C₂²	—	4	1	no	—
1028	C₂²	—	4	2	no	—
1029	C₂²	—	4	1	no	—
1030	C₂²	—	4	2	no	—
1031	C₂²	—	4	2	no	—
1032	C₂²	—	4	1	no	—
1033	C₂²	—	4	1	no	—
1034	C₂²	—	4	2	no	—
1035	C₂²	—	4	2	no	—
1036	C₂²	—	4	1	no	—
1037	C₂²	—	4	1	no	—
1038	C₂²	—	4	2	no	—
1039	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
1040	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1041	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1042	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1043	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1044	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
1045	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
1046	C₄	—	2	2	no	—
1047	C₄	—	2	2	no	—
1048	C₄	—	2	2	no	—
1049	C₄	—	2	2	no	—
1050	C₄	—	4	1	no	—
1051	C₄	—	4	1	no	—
1052	C₄	—	4	1	no	—
1053	C₄	—	4	2	no	—
1054	C₄	—	4	1	no	—
1055	C₄	—	4	1	no	—
1056	C₄	—	4	2	no	—
1057	C₄	—	4	2	no	—
1058	C₄	—	4	1	no	—
1059	C₄	—	4	1	no	—
1060	C₄	—	4	2	no	—
1061	C₄	—	4	2	no	—
1062	C₄	—	4	2	no	—
1063	C₄	—	4	2	no	—
1064	C₄	C₃×#540	1	4	yes	—
1065	C₃	#42460	1	1	yes	characteristic, direct product factor, Sylow
1066	C₂	—	4	2	no	—
1067	C₂	—	4	2	no	—
1068	C₂	—	8	1	no	—
1069	C₂	—	8	2	no	—
1070	C₂	C₂×C₃×#540	1	1	yes	characteristic
1071	C₂	C₃×#3492	1	1	yes	characteristic
1072	C₂	C₃×#3511	1	1	yes	characteristic
1073	C₂	C₃×#3536	1	1	yes	characteristic
1074	C₂	C₃×#3536	1	1	yes	characteristic
1075	C₂	C₃×#3543	1	1	yes	characteristic
1076	C₂	C₃×#3552	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#2837	C₂	semidirect
2. C₃×#2780	C₂	semidirect
3. C₃×#2711	C₂	semidirect
4. C₃×#2707	C₂	semidirect
5. C₃×#2701	C₂	semidirect
6. C₃×#2667	C₂	semidirect
7. C₃×#2630	C₂	semidirect
8. C₃×#2620	C₂	semidirect
9. C₃×#2552	C₂	semidirect
10. C₃×#2540	C₂	semidirect
11. C₃×#2538	C₂	semidirect
12. C₃×#2537	C₂	semidirect
13. C₃×#2502	C₂	semidirect
14. C₃×#2501	C₂	semidirect
15. C₃×#2464	C₂	semidirect
16. C₃×#2421	C₂	semidirect
17. C₃×#2420	C₂	semidirect
18. C₃×#2417	C₂	semidirect
19. C₃×#2416	C₂	semidirect
20. C₃×#2392	C₂	semidirect
21. C₃×#2367	C₂	semidirect
22. C₃×D₄×C₄⋊C₄	C₂	semidirect
23. C₃×#2314	C₂	semidirect
24. #42460	C₃	direct (N × H)
124. #2837	C₂×C₃	semidirect
125. #2780	C₂×C₃	semidirect
126. #2711	C₂×C₃	semidirect
127. #2707	C₂×C₃	semidirect
128. #2701	C₂×C₃	semidirect
129. #2667	C₂×C₃	semidirect
130. #2630	C₂×C₃	semidirect
131. #2620	C₂×C₃	semidirect
132. #2552	C₂×C₃	semidirect
133. #2540	C₂×C₃	semidirect
134. #2538	C₂×C₃	semidirect
135. #2537	C₂×C₃	semidirect
136. #2502	C₂×C₃	semidirect
137. #2501	C₂×C₃	semidirect
138. #2464	C₂×C₃	semidirect
139. #2421	C₂×C₃	semidirect
140. #2420	C₂×C₃	semidirect
141. #2417	C₂×C₃	semidirect
142. #2416	C₂×C₃	semidirect
143. #2392	C₂×C₃	semidirect
144. #2367	C₂×C₃	semidirect
145. D₄×C₄⋊C₄	C₂×C₃	semidirect
146. #2314	C₂×C₃	semidirect
1065. C₃	#42460	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×#2837	2
C₃×#2780	2
C₃×#2711	2
C₃×#2707	2
C₃×#2701	2
C₃×#2667	2
C₃×#2630	2
C₃×#2620	2
C₃×#2552	2
C₃×#2540	2
C₃×#2538	2
C₃×#2537	2
C₃×#2502	2
C₃×#2501	2
C₃×#2464	2
C₃×#2421	2
C₃×#2420	2
C₃×#2417	2
C₃×#2416	2
C₃×#2392	2
C₃×#2367	2
C₃×D₄×C₄⋊C₄	2
C₃×#2314	2
#42460	3

Subgroups — C3×#42460 #10661067

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#42460 #10661067