Subgroups — C₃×#42454 #10661061

Order 768.

1804 conjugacy classes of subgroups.

The subgroup lattice has 1064 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#2836	C₂	1	2	yes	maximal, complemented
2	C₃×#2780	C₂	1	2	yes	maximal, complemented
3	C₃×#2761	C₂	1	2	yes	maximal, complemented
4	C₃×#2753	C₂	1	2	yes	maximal, complemented
5	C₃×#2701	C₂	1	2	yes	maximal, complemented
6	C₃×#2649	C₂	1	2	yes	maximal, complemented
7	C₃×#2635	C₂	1	2	yes	maximal, complemented
8	C₃×#2620	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#2571	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#2540	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#2536	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#2535	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#2504	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#2503	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#2457	C₂	1	2	yes	maximal, complemented
16	C₃×#2423	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×#2422	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	#42454	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂×C₃×#124	C₂²	1	1	yes	characteristic
26	C₂×C₃×#123	C₂²	1	2	yes	—
27	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
28	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
29	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
30	C₂×C₃×#121	C₂²	1	1	yes	characteristic
31	C₂×C₃×#121	C₂²	1	2	yes	—
32	C₂×C₃×#121	C₂²	1	1	yes	characteristic
33	C₂×C₃×#121	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×C₄×D₄	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	1	yes	characteristic
40	C₂×C₃×#117	C₂²	1	1	yes	characteristic
41	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
42	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
43	C₃×#400	C₂²	1	2	yes	—
44	C₃×#400	C₂²	1	2	yes	—
45	C₃×#400	C₂²	1	2	yes	—
46	C₃×#400	C₂²	1	2	yes	—
47	C₃×#399	C₂²	1	2	yes	—
48	C₃×#399	C₂²	1	2	yes	—
49	C₃×#398	C₂²	1	1	yes	characteristic
50	C₃×#398	C₂²	1	2	yes	—
51	C₃×#398	C₂²	1	2	yes	—
52	C₃×#398	C₂²	1	2	yes	—
53	C₃×#397	C₂²	1	1	yes	characteristic
54	C₃×#397	C₂²	1	2	yes	—
55	C₃×#397	C₂²	1	2	yes	—
56	C₃×#397	C₂²	1	2	yes	—
57	C₃×#397	C₂²	1	2	yes	—
58	C₃×#396	C₂²	1	2	yes	—
59	C₃×#396	C₂²	1	2	yes	—
60	C₃×#396	C₂²	1	1	yes	characteristic
61	C₃×#396	C₂²	1	1	yes	characteristic
62	C₃×#396	C₂²	1	2	yes	—
63	C₃×#396	C₂²	1	2	yes	—
64	C₃×#394	C₂²	1	2	yes	—
65	C₃×#394	C₂²	1	2	yes	—
66	C₃×#394	C₂²	1	2	yes	—
67	C₃×#394	C₂²	1	2	yes	—
68	C₃×#394	C₂²	1	1	yes	characteristic
69	C₃×#394	C₂²	1	1	yes	characteristic
70	C₃×#394	C₂²	1	1	yes	characteristic
71	C₃×#394	C₂²	1	2	yes	—
72	C₃×#392	C₂²	1	1	yes	characteristic
73	C₃×#392	C₂²	1	2	yes	—
74	C₃×#392	C₂²	1	2	yes	—
75	C₃×#391	C₂²	1	1	yes	characteristic
76	C₃×#391	C₂²	1	1	yes	characteristic
77	C₃×#390	C₂²	1	1	yes	characteristic
78	C₃×#390	C₂²	1	1	yes	characteristic
79	C₃×#390	C₂²	1	2	yes	—
80	C₃×#390	C₂²	1	2	yes	—
81	C₃×#389	C₂²	1	2	yes	—
82	C₃×#389	C₂²	1	1	yes	characteristic
83	C₃×#389	C₂²	1	1	yes	characteristic
84	C₃×#389	C₂²	1	2	yes	—
85	C₃×#388	C₂²	1	2	yes	—
86	C₃×#388	C₂²	1	2	yes	—
87	C₃×#388	C₂²	1	2	yes	—
88	C₃×#388	C₂²	1	2	yes	—
89	C₃×#388	C₂²	1	2	yes	—
90	C₃×#388	C₂²	1	2	yes	—
91	C₃×#388	C₂²	1	2	yes	—
92	C₃×#387	C₂²	1	2	yes	—
93	C₃×#387	C₂²	1	2	yes	—
94	C₃×#387	C₂²	1	2	yes	—
95	C₃×#386	C₂²	1	2	yes	—
96	C₃×#386	C₂²	1	2	yes	—
97	C₃×#386	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×#384	C₂²	1	1	yes	characteristic
106	C₃×#384	C₂²	1	1	yes	characteristic
107	C₃×#382	C₂²	1	2	yes	—
108	C₃×#382	C₂²	1	1	yes	characteristic
109	C₃×#382	C₂²	1	1	yes	characteristic
110	C₃×#382	C₂²	1	1	yes	characteristic
111	C₃×#381	C₂²	1	2	yes	—
112	C₃×#381	C₂²	1	2	yes	—
113	C₃×#380	C₂²	1	1	yes	characteristic
114	C₃×#380	C₂²	1	2	yes	—
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	#2836	C₂×C₃	1	2	yes	complemented
125	#2780	C₂×C₃	1	2	yes	complemented
126	#2761	C₂×C₃	1	2	yes	complemented
127	#2753	C₂×C₃	1	2	yes	complemented
128	#2701	C₂×C₃	1	2	yes	complemented
129	#2649	C₂×C₃	1	2	yes	complemented
130	#2635	C₂×C₃	1	2	yes	complemented
131	#2620	C₂×C₃	1	1	yes	characteristic, complemented
132	#2571	C₂×C₃	1	1	yes	characteristic, complemented
133	#2540	C₂×C₃	1	1	yes	characteristic, complemented
134	#2536	C₂×C₃	1	1	yes	characteristic, complemented
135	#2535	C₂×C₃	1	1	yes	characteristic, complemented
136	#2504	C₂×C₃	1	1	yes	characteristic, complemented
137	#2503	C₂×C₃	1	1	yes	characteristic, complemented
138	#2457	C₂×C₃	1	2	yes	complemented
139	#2423	C₂×C₃	1	1	yes	characteristic, complemented
140	#2422	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	2	yes	—
151	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
152	C₂²×C₃×D₄	C₂³	1	2	yes	—
153	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
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×#124	—	2	4	no	—
162	C₃×#123	—	4	4	no	—
163	C₃×C₂²⋊Q₈	—	4	2	no	—
164	C₃×C₂²⋊Q₈	—	4	2	no	—
165	C₃×C₂²⋊Q₈	—	4	2	no	—
166	C₃×#121	—	4	2	no	—
167	C₃×#121	—	4	2	no	—
168	C₃×#121	—	4	2	no	—
169	C₃×#121	—	4	4	no	—
170	C₃×C₄×Q₈	—	4	2	no	—
171	C₃×C₄×D₄	—	2	4	no	—
172	C₃×C₄×D₄	—	4	2	no	—
173	C₃×C₄×D₄	—	4	2	no	—
174	C₃×C₄×D₄	—	4	2	no	—
175	C₃×C₄×D₄	—	4	4	no	—
176	C₃×#117	—	2	4	no	—
177	C₂×C₃×C₄⋊C₄	—	4	2	no	—
178	C₂×C₃×C₄⋊C₄	—	4	2	no	—
179	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
180	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
181	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
192	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
193	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
194	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
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	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	1	yes	characteristic
203	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
204	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
208	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
209	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
210	C₂×C₃×C₂²⋊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	1	yes	characteristic
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	2	yes	—
223	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
224	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
225	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
226	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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	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	1	yes	characteristic
236	C₂×C₃×C₄²	C₂³	1	2	yes	—
237	C₂×C₃×C₄²	C₂³	1	2	yes	—
238	C₂×C₃×C₄²	C₂³	1	2	yes	—
239	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
240	C₃×#95	C₂³	1	1	yes	characteristic
241	C₃×#95	C₂³	1	2	yes	—
242	C₃×#95	C₂³	1	1	yes	characteristic
243	C₃×#95	C₂³	1	1	yes	characteristic
244	C₃×#95	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	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	C₂×#124	C₂²×C₃	1	1	yes	characteristic
265	C₂×#123	C₂²×C₃	1	2	yes	—
266	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
267	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
268	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
269	C₂×#121	C₂²×C₃	1	1	yes	characteristic
270	C₂×#121	C₂²×C₃	1	2	yes	—
271	C₂×#121	C₂²×C₃	1	1	yes	characteristic
272	C₂×#121	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×C₄×D₄	C₂²×C₃	1	2	yes	—
276	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
277	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
278	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
279	C₂×#117	C₂²×C₃	1	1	yes	characteristic
280	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
281	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
282	#400	C₂²×C₃	1	2	yes	—
283	#400	C₂²×C₃	1	2	yes	—
284	#400	C₂²×C₃	1	2	yes	—
285	#400	C₂²×C₃	1	2	yes	—
286	#399	C₂²×C₃	1	2	yes	—
287	#399	C₂²×C₃	1	2	yes	—
288	#398	C₂²×C₃	1	1	yes	characteristic
289	#398	C₂²×C₃	1	2	yes	—
290	#398	C₂²×C₃	1	2	yes	—
291	#398	C₂²×C₃	1	2	yes	—
292	#397	C₂²×C₃	1	2	yes	—
293	#397	C₂²×C₃	1	2	yes	—
294	#397	C₂²×C₃	1	2	yes	—
295	#397	C₂²×C₃	1	1	yes	characteristic
296	#397	C₂²×C₃	1	2	yes	—
297	#396	C₂²×C₃	1	2	yes	—
298	#396	C₂²×C₃	1	2	yes	—
299	#396	C₂²×C₃	1	2	yes	—
300	#396	C₂²×C₃	1	1	yes	characteristic
301	#396	C₂²×C₃	1	1	yes	characteristic
302	#396	C₂²×C₃	1	2	yes	—
303	#394	C₂²×C₃	1	2	yes	—
304	#394	C₂²×C₃	1	2	yes	—
305	#394	C₂²×C₃	1	2	yes	—
306	#394	C₂²×C₃	1	2	yes	—
307	#394	C₂²×C₃	1	1	yes	characteristic
308	#394	C₂²×C₃	1	1	yes	characteristic
309	#394	C₂²×C₃	1	1	yes	characteristic
310	#394	C₂²×C₃	1	2	yes	—
311	#392	C₂²×C₃	1	1	yes	characteristic
312	#392	C₂²×C₃	1	2	yes	—
313	#392	C₂²×C₃	1	2	yes	—
314	#391	C₂²×C₃	1	1	yes	characteristic
315	#391	C₂²×C₃	1	1	yes	characteristic
316	#390	C₂²×C₃	1	1	yes	characteristic
317	#390	C₂²×C₃	1	1	yes	characteristic
318	#390	C₂²×C₃	1	2	yes	—
319	#390	C₂²×C₃	1	2	yes	—
320	#389	C₂²×C₃	1	1	yes	characteristic
321	#389	C₂²×C₃	1	1	yes	characteristic
322	#389	C₂²×C₃	1	2	yes	—
323	#389	C₂²×C₃	1	2	yes	—
324	#388	C₂²×C₃	1	2	yes	—
325	#388	C₂²×C₃	1	2	yes	—
326	#388	C₂²×C₃	1	2	yes	—
327	#388	C₂²×C₃	1	2	yes	—
328	#388	C₂²×C₃	1	2	yes	—
329	#388	C₂²×C₃	1	2	yes	—
330	#388	C₂²×C₃	1	2	yes	—
331	#387	C₂²×C₃	1	2	yes	—
332	#387	C₂²×C₃	1	2	yes	—
333	#387	C₂²×C₃	1	2	yes	—
334	#386	C₂²×C₃	1	2	yes	—
335	#386	C₂²×C₃	1	2	yes	—
336	#386	C₂²×C₃	1	2	yes	—
337	#386	C₂²×C₃	1	2	yes	—
338	#386	C₂²×C₃	1	2	yes	—
339	#386	C₂²×C₃	1	2	yes	—
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	#384	C₂²×C₃	1	1	yes	characteristic
345	#384	C₂²×C₃	1	1	yes	characteristic
346	#382	C₂²×C₃	1	1	yes	characteristic
347	#382	C₂²×C₃	1	2	yes	—
348	#382	C₂²×C₃	1	1	yes	characteristic
349	#382	C₂²×C₃	1	1	yes	characteristic
350	#381	C₂²×C₃	1	2	yes	—
351	#381	C₂²×C₃	1	2	yes	—
352	#380	C₂²×C₃	1	1	yes	characteristic
353	#380	C₂²×C₃	1	1	yes	characteristic
354	#380	C₂²×C₃	1	1	yes	characteristic
355	#380	C₂²×C₃	1	1	yes	characteristic
356	#380	C₂²×C₃	1	2	yes	—
357	C₄×C₄⋊C₄	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×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
361	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
362	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
363	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
364	C₂⁴×C₃	C₂⁴	1	2	yes	—
365	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
366	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
367	C₂×C₃×Q₈	—	2	2	no	—
368	C₂×C₃×Q₈	—	2	2	no	—
369	C₂×C₃×Q₈	—	2	2	no	—
370	C₂×C₃×D₄	—	2	2	no	—
371	C₂×C₃×D₄	—	2	2	no	—
372	C₂×C₃×D₄	—	2	2	no	—
373	C₂×C₃×D₄	—	2	2	no	—
374	C₂×C₃×D₄	—	2	4	no	—
375	C₂×C₃×D₄	—	2	4	no	—
376	C₂×C₃×D₄	—	2	2	no	—
377	C₂×C₃×D₄	—	2	2	no	—
378	C₂×C₃×D₄	—	2	2	no	—
379	C₂×C₃×D₄	—	2	2	no	—
380	C₂×C₃×D₄	—	4	1	no	—
381	C₂×C₃×D₄	—	4	1	no	—
382	C₂×C₃×D₄	—	4	1	no	—
383	C₂×C₃×D₄	—	4	1	no	—
384	C₂×C₃×D₄	—	4	2	no	—
385	C₂×C₃×D₄	—	4	2	no	—
386	C₂×C₃×D₄	—	4	2	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	C₂²×C₃×C₄	—	2	4	no	—
392	C₂²×C₃×C₄	—	2	2	no	—
393	C₂²×C₃×C₄	—	2	2	no	—
394	C₂²×C₃×C₄	—	2	2	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	—	4	2	no	—
402	C₂²×C₃×C₄	—	4	2	no	—
403	C₂²×C₃×C₄	—	4	2	no	—
404	C₂²×C₃×C₄	—	4	2	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	C₂⁴	1	1	yes	characteristic
410	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
411	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
412	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
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	2	yes	—
417	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
418	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
419	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
420	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
421	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
422	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
423	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
424	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
425	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
426	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
427	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
428	C₃×C₄⋊C₄	—	2	2	no	—
429	C₃×C₄⋊C₄	—	2	2	no	—
430	C₃×C₄⋊C₄	—	2	2	no	—
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	—	4	2	no	—
438	C₃×C₄⋊C₄	—	4	2	no	—
439	C₃×C₄⋊C₄	—	4	1	no	—
440	C₃×C₄⋊C₄	—	4	1	no	—
441	C₃×C₄⋊C₄	—	4	2	no	—
442	C₃×C₄⋊C₄	—	4	2	no	—
443	C₃×C₄⋊C₄	—	4	2	no	—
444	C₃×C₄⋊C₄	—	4	1	no	—
445	C₃×C₄⋊C₄	—	4	1	no	—
446	C₃×C₄⋊C₄	—	4	2	no	—
447	C₃×C₄⋊C₄	—	4	2	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×C₂²⋊C₄	—	2	4	no	—
454	C₃×C₂²⋊C₄	—	2	2	no	—
455	C₃×C₂²⋊C₄	—	2	2	no	—
456	C₃×C₂²⋊C₄	—	2	2	no	—
457	C₃×C₂²⋊C₄	—	2	2	no	—
458	C₃×C₂²⋊C₄	—	2	2	no	—
459	C₃×C₂²⋊C₄	—	2	2	no	—
460	C₃×C₂²⋊C₄	—	2	4	no	—
461	C₃×C₂²⋊C₄	—	2	4	no	—
462	C₃×C₂²⋊C₄	—	4	2	no	—
463	C₃×C₂²⋊C₄	—	4	2	no	—
464	C₃×C₂²⋊C₄	—	4	1	no	—
465	C₃×C₂²⋊C₄	—	4	2	no	—
466	C₃×C₂²⋊C₄	—	4	1	no	—
467	C₃×C₂²⋊C₄	—	4	1	no	—
468	C₃×C₂²⋊C₄	—	4	1	no	—
469	C₃×C₂²⋊C₄	—	4	2	no	—
470	C₃×C₂²⋊C₄	—	4	1	no	—
471	C₃×C₂²⋊C₄	—	4	1	no	—
472	C₃×C₂²⋊C₄	—	4	2	no	—
473	C₃×C₂²⋊C₄	—	4	2	no	—
474	C₃×C₂²⋊C₄	—	4	2	no	—
475	C₃×C₂²⋊C₄	—	4	2	no	—
476	C₃×C₂²⋊C₄	—	4	2	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×C₄²	—	2	2	no	—
483	C₃×C₄²	—	2	2	no	—
484	C₃×C₄²	—	2	2	no	—
485	C₃×C₄²	—	4	2	no	—
486	C₃×C₄²	—	4	2	no	—
487	C₃×C₄²	—	4	2	no	—
488	C₃×C₄²	#41	1	4	yes	—
489	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
490	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
491	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
492	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
493	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
494	C₂²×D₄	C₂³×C₃	1	2	yes	—
495	C₂²×D₄	C₂³×C₃	1	2	yes	—
496	C₂²×D₄	C₂³×C₃	1	2	yes	—
497	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
498	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
499	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
500	C₂³×C₄	C₂³×C₃	1	2	yes	—
501	C₂³×C₄	C₂³×C₃	1	2	yes	—
502	C₂³×C₄	C₂³×C₃	1	2	yes	—
503	#124	—	2	4	no	—
504	#123	—	4	4	no	—
505	C₂²⋊Q₈	—	4	2	no	—
506	C₂²⋊Q₈	—	4	2	no	—
507	C₂²⋊Q₈	—	4	2	no	—
508	#121	—	4	2	no	—
509	#121	—	4	2	no	—
510	#121	—	4	2	no	—
511	#121	—	4	4	no	—
512	C₄×Q₈	—	4	2	no	—
513	C₄×D₄	—	2	4	no	—
514	C₄×D₄	—	4	2	no	—
515	C₄×D₄	—	4	2	no	—
516	C₄×D₄	—	4	2	no	—
517	C₄×D₄	—	4	4	no	—
518	#117	—	2	4	no	—
519	C₂×C₄⋊C₄	—	4	2	no	—
520	C₂×C₄⋊C₄	—	4	2	no	—
521	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
522	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
523	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
524	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
525	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
526	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
527	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
528	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
529	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
530	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
531	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
532	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
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	2	yes	—
536	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
537	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
538	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
539	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
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×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
547	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
548	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
549	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
550	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
551	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
552	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
553	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
554	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
555	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
556	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
557	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
558	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
559	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
560	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
561	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
562	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
563	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
564	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
565	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
566	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
567	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
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	2	yes	—
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	2	yes	—
575	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
576	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
577	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
578	C₂×C₄²	C₂³×C₃	1	2	yes	—
579	C₂×C₄²	C₂³×C₃	1	2	yes	—
580	C₂×C₄²	C₂³×C₃	1	2	yes	—
581	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
582	#95	C₂³×C₃	1	1	yes	characteristic
583	#95	C₂³×C₃	1	2	yes	—
584	#95	C₂³×C₃	1	1	yes	characteristic
585	#95	C₂³×C₃	1	1	yes	characteristic
586	#95	C₂³×C₃	1	1	yes	characteristic
587	#95	C₂³×C₃	1	1	yes	characteristic
588	#95	C₂³×C₃	1	2	yes	—
589	#95	C₂³×C₃	1	2	yes	—
590	#95	C₂³×C₃	1	1	yes	characteristic
591	#95	C₂³×C₃	1	2	yes	—
592	#95	C₂³×C₃	1	2	yes	—
593	#95	C₂³×C₃	1	2	yes	—
594	#95	C₂³×C₃	1	2	yes	—
595	#95	C₂³×C₃	1	2	yes	—
596	#95	C₂³×C₃	1	2	yes	—
597	#95	C₂³×C₃	1	2	yes	—
598	#95	C₂³×C₃	1	2	yes	—
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	C₂³×C₃	—	2	1	no	—
607	C₂³×C₃	—	2	1	no	—
608	C₂³×C₃	—	2	1	no	—
609	C₂³×C₃	—	2	1	no	—
610	C₂³×C₃	—	2	1	no	—
611	C₂³×C₃	—	2	1	no	—
612	C₂³×C₃	—	2	1	no	—
613	C₂³×C₃	—	2	1	no	—
614	C₂³×C₃	—	2	1	no	—
615	C₂³×C₃	—	2	1	no	—
616	C₂³×C₃	—	2	1	no	—
617	C₂³×C₃	—	2	1	no	—
618	C₂³×C₃	—	2	1	no	—
619	C₂³×C₃	—	2	2	no	—
620	C₂³×C₃	—	2	1	no	—
621	C₂³×C₃	—	2	1	no	—
622	C₂³×C₃	—	2	2	no	—
623	C₂³×C₃	—	2	2	no	—
624	C₂³×C₃	—	2	2	no	—
625	C₂³×C₃	—	2	1	no	—
626	C₂³×C₃	—	2	1	no	—
627	C₂³×C₃	—	2	2	no	—
628	C₂³×C₃	—	2	2	no	—
629	C₂³×C₃	—	2	1	no	—
630	C₂³×C₃	—	2	2	no	—
631	C₂³×C₃	—	2	1	no	—
632	C₂³×C₃	H(5,𝔽₂)	1	2	yes	—
633	C₂³×C₃	2₋¹⁺⁴	1	2	yes	—
634	C₂³×C₃	C₂⁵	1	1	yes	characteristic
635	C₃×Q₈	—	4	4	no	—
636	C₃×D₄	—	2	8	no	—
637	C₃×D₄	—	4	4	no	—
638	C₃×D₄	—	4	4	no	—
639	C₃×D₄	—	4	4	no	—
640	C₃×D₄	—	8	4	no	—
641	C₃×D₄	—	8	4	no	—
642	C₃×D₄	—	8	4	no	—
643	C₂×C₃×C₄	—	2	1	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	1	no	—
649	C₂×C₃×C₄	—	2	2	no	—
650	C₂×C₃×C₄	—	2	1	no	—
651	C₂×C₃×C₄	—	2	1	no	—
652	C₂×C₃×C₄	—	2	1	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	2	no	—
658	C₂×C₃×C₄	—	2	2	no	—
659	C₂×C₃×C₄	—	2	2	no	—
660	C₂×C₃×C₄	—	2	2	no	—
661	C₂×C₃×C₄	—	2	1	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	2	no	—
666	C₂×C₃×C₄	—	2	2	no	—
667	C₂×C₃×C₄	—	2	1	no	—
668	C₂×C₃×C₄	—	2	1	no	—
669	C₂×C₃×C₄	—	2	1	no	—
670	C₂×C₃×C₄	—	2	1	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	1	no	—
675	C₂×C₃×C₄	—	2	2	no	—
676	C₂×C₃×C₄	—	2	2	no	—
677	C₂×C₃×C₄	—	2	2	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	1	no	—
686	C₂×C₃×C₄	—	2	1	no	—
687	C₂×C₃×C₄	—	2	1	no	—
688	C₂×C₃×C₄	—	2	2	no	—
689	C₂×C₃×C₄	—	2	2	no	—
690	C₂×C₃×C₄	—	2	1	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	—	4	4	no	—
696	C₂×C₃×C₄	—	4	4	no	—
697	C₂×C₃×C₄	—	4	4	no	—
698	C₂×C₃×C₄	—	8	4	no	—
699	C₂×C₃×C₄	—	8	4	no	—
700	C₂×C₃×C₄	—	8	4	no	—
701	C₂×C₃×C₄	C₂×#41	1	2	yes	—
702	C₂×C₃×C₄	C₂×#41	1	2	yes	—
703	C₂×C₃×C₄	C₂×#41	1	2	yes	—
704	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
705	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
706	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
707	C₂⁴	C₂⁴×C₃	1	2	yes	—
708	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
709	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
710	C₂×Q₈	—	2	2	no	—
711	C₂×Q₈	—	2	2	no	—
712	C₂×Q₈	—	2	2	no	—
713	C₂×D₄	—	2	2	no	—
714	C₂×D₄	—	2	2	no	—
715	C₂×D₄	—	2	2	no	—
716	C₂×D₄	—	2	2	no	—
717	C₂×D₄	—	2	4	no	—
718	C₂×D₄	—	2	4	no	—
719	C₂×D₄	—	2	2	no	—
720	C₂×D₄	—	2	2	no	—
721	C₂×D₄	—	2	2	no	—
722	C₂×D₄	—	2	2	no	—
723	C₂×D₄	—	4	1	no	—
724	C₂×D₄	—	4	1	no	—
725	C₂×D₄	—	4	1	no	—
726	C₂×D₄	—	4	1	no	—
727	C₂×D₄	—	4	2	no	—
728	C₂×D₄	—	4	2	no	—
729	C₂×D₄	—	4	2	no	—
730	C₂×D₄	—	4	2	no	—
731	C₂×D₄	—	4	2	no	—
732	C₂×D₄	—	4	2	no	—
733	C₂×D₄	—	4	2	no	—
734	C₂²×C₄	—	2	4	no	—
735	C₂²×C₄	—	2	2	no	—
736	C₂²×C₄	—	2	2	no	—
737	C₂²×C₄	—	2	2	no	—
738	C₂²×C₄	—	2	2	no	—
739	C₂²×C₄	—	2	2	no	—
740	C₂²×C₄	—	2	2	no	—
741	C₂²×C₄	—	2	2	no	—
742	C₂²×C₄	—	2	2	no	—
743	C₂²×C₄	—	2	2	no	—
744	C₂²×C₄	—	4	2	no	—
745	C₂²×C₄	—	4	2	no	—
746	C₂²×C₄	—	4	2	no	—
747	C₂²×C₄	—	4	2	no	—
748	C₂²×C₄	—	4	2	no	—
749	C₂²×C₄	—	4	2	no	—
750	C₂²×C₄	—	4	2	no	—
751	C₂²×C₄	—	4	2	no	—
752	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
753	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
754	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
755	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
756	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
757	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
758	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
759	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
760	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
761	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
762	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
763	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
764	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
765	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
766	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
767	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
768	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
769	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
770	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
771	C₄⋊C₄	—	2	2	no	—
772	C₄⋊C₄	—	2	2	no	—
773	C₄⋊C₄	—	2	2	no	—
774	C₄⋊C₄	—	2	2	no	—
775	C₄⋊C₄	—	2	2	no	—
776	C₄⋊C₄	—	2	2	no	—
777	C₄⋊C₄	—	2	2	no	—
778	C₄⋊C₄	—	2	2	no	—
779	C₄⋊C₄	—	2	2	no	—
780	C₄⋊C₄	—	4	2	no	—
781	C₄⋊C₄	—	4	2	no	—
782	C₄⋊C₄	—	4	2	no	—
783	C₄⋊C₄	—	4	1	no	—
784	C₄⋊C₄	—	4	1	no	—
785	C₄⋊C₄	—	4	2	no	—
786	C₄⋊C₄	—	4	2	no	—
787	C₄⋊C₄	—	4	2	no	—
788	C₄⋊C₄	—	4	2	no	—
789	C₄⋊C₄	—	4	2	no	—
790	C₄⋊C₄	—	4	2	no	—
791	C₄⋊C₄	—	4	2	no	—
792	C₄⋊C₄	—	4	1	no	—
793	C₄⋊C₄	—	4	1	no	—
794	C₄⋊C₄	—	4	2	no	—
795	C₄⋊C₄	—	4	2	no	—
796	C₂²⋊C₄	—	2	4	no	—
797	C₂²⋊C₄	—	2	2	no	—
798	C₂²⋊C₄	—	2	2	no	—
799	C₂²⋊C₄	—	2	2	no	—
800	C₂²⋊C₄	—	2	2	no	—
801	C₂²⋊C₄	—	2	2	no	—
802	C₂²⋊C₄	—	2	2	no	—
803	C₂²⋊C₄	—	2	4	no	—
804	C₂²⋊C₄	—	2	4	no	—
805	C₂²⋊C₄	—	4	1	no	—
806	C₂²⋊C₄	—	4	1	no	—
807	C₂²⋊C₄	—	4	2	no	—
808	C₂²⋊C₄	—	4	1	no	—
809	C₂²⋊C₄	—	4	1	no	—
810	C₂²⋊C₄	—	4	2	no	—
811	C₂²⋊C₄	—	4	2	no	—
812	C₂²⋊C₄	—	4	2	no	—
813	C₂²⋊C₄	—	4	2	no	—
814	C₂²⋊C₄	—	4	2	no	—
815	C₂²⋊C₄	—	4	2	no	—
816	C₂²⋊C₄	—	4	2	no	—
817	C₂²⋊C₄	—	4	2	no	—
818	C₂²⋊C₄	—	4	2	no	—
819	C₂²⋊C₄	—	4	2	no	—
820	C₂²⋊C₄	—	4	2	no	—
821	C₂²⋊C₄	—	4	2	no	—
822	C₂²⋊C₄	—	4	1	no	—
823	C₂²⋊C₄	—	4	2	no	—
824	C₂²⋊C₄	—	4	1	no	—
825	C₄²	—	2	2	no	—
826	C₄²	—	2	2	no	—
827	C₄²	—	2	2	no	—
828	C₄²	—	4	2	no	—
829	C₄²	—	4	2	no	—
830	C₄²	—	4	2	no	—
831	C₄²	C₃×#41	1	4	yes	—
832	C₂²×C₃	—	2	2	no	—
833	C₂²×C₃	—	2	2	no	—
834	C₂²×C₃	—	2	2	no	—
835	C₂²×C₃	—	2	2	no	—
836	C₂²×C₃	—	2	2	no	—
837	C₂²×C₃	—	2	2	no	—
838	C₂²×C₃	—	4	1	no	—
839	C₂²×C₃	—	4	1	no	—
840	C₂²×C₃	—	4	1	no	—
841	C₂²×C₃	—	4	1	no	—
842	C₂²×C₃	—	4	1	no	—
843	C₂²×C₃	—	4	1	no	—
844	C₂²×C₃	—	4	1	no	—
845	C₂²×C₃	—	4	1	no	—
846	C₂²×C₃	—	4	1	no	—
847	C₂²×C₃	—	4	2	no	—
848	C₂²×C₃	—	4	1	no	—
849	C₂²×C₃	—	4	2	no	—
850	C₂²×C₃	—	4	1	no	—
851	C₂²×C₃	—	4	2	no	—
852	C₂²×C₃	—	4	1	no	—
853	C₂²×C₃	—	4	2	no	—
854	C₂²×C₃	—	4	2	no	—
855	C₂²×C₃	—	4	1	no	—
856	C₂²×C₃	—	4	1	no	—
857	C₂²×C₃	—	4	2	no	—
858	C₂²×C₃	—	4	2	no	—
859	C₂²×C₃	—	4	1	no	—
860	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
861	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
862	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
863	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
864	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
865	C₂²×C₃	#585	1	1	yes	characteristic
866	C₂²×C₃	#585	1	1	yes	characteristic
867	C₃×C₄	—	2	2	no	—
868	C₃×C₄	—	2	2	no	—
869	C₃×C₄	—	4	1	no	—
870	C₃×C₄	—	4	1	no	—
871	C₃×C₄	—	4	1	no	—
872	C₃×C₄	—	4	2	no	—
873	C₃×C₄	—	4	1	no	—
874	C₃×C₄	—	4	1	no	—
875	C₃×C₄	—	4	1	no	—
876	C₃×C₄	—	4	1	no	—
877	C₃×C₄	—	4	2	no	—
878	C₃×C₄	—	4	1	no	—
879	C₃×C₄	—	4	1	no	—
880	C₃×C₄	—	4	2	no	—
881	C₃×C₄	—	4	2	no	—
882	C₃×C₄	—	4	2	no	—
883	C₃×C₄	—	4	2	no	—
884	C₃×C₄	—	4	2	no	—
885	C₃×C₄	#540	1	4	yes	—
886	C₂³	—	2	1	no	—
887	C₂³	—	2	1	no	—
888	C₂³	—	2	1	no	—
889	C₂³	—	2	1	no	—
890	C₂³	—	2	1	no	—
891	C₂³	—	2	1	no	—
892	C₂³	—	2	1	no	—
893	C₂³	—	2	1	no	—
894	C₂³	—	2	1	no	—
895	C₂³	—	2	1	no	—
896	C₂³	—	2	1	no	—
897	C₂³	—	2	1	no	—
898	C₂³	—	2	1	no	—
899	C₂³	—	2	2	no	—
900	C₂³	—	2	1	no	—
901	C₂³	—	2	1	no	—
902	C₂³	—	2	2	no	—
903	C₂³	—	2	2	no	—
904	C₂³	—	2	2	no	—
905	C₂³	—	2	1	no	—
906	C₂³	—	2	1	no	—
907	C₂³	—	2	2	no	—
908	C₂³	—	2	2	no	—
909	C₂³	—	2	1	no	—
910	C₂³	—	2	2	no	—
911	C₂³	—	2	1	no	—
912	C₂³	C₃×H(5,𝔽₂)	1	2	yes	—
913	C₂³	C₃×2₋¹⁺⁴	1	2	yes	—
914	C₂³	C₂⁵×C₃	1	1	yes	characteristic
915	Q₈	—	4	4	no	—
916	D₄	—	2	8	no	—
917	D₄	—	4	4	no	—
918	D₄	—	4	4	no	—
919	D₄	—	4	4	no	—
920	D₄	—	8	4	no	—
921	D₄	—	8	4	no	—
922	D₄	—	8	4	no	—
923	C₂×C₄	—	2	1	no	—
924	C₂×C₄	—	2	1	no	—
925	C₂×C₄	—	2	1	no	—
926	C₂×C₄	—	2	1	no	—
927	C₂×C₄	—	2	1	no	—
928	C₂×C₄	—	2	1	no	—
929	C₂×C₄	—	2	2	no	—
930	C₂×C₄	—	2	1	no	—
931	C₂×C₄	—	2	1	no	—
932	C₂×C₄	—	2	1	no	—
933	C₂×C₄	—	2	1	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	2	no	—
940	C₂×C₄	—	2	2	no	—
941	C₂×C₄	—	2	1	no	—
942	C₂×C₄	—	2	2	no	—
943	C₂×C₄	—	2	1	no	—
944	C₂×C₄	—	2	1	no	—
945	C₂×C₄	—	2	2	no	—
946	C₂×C₄	—	2	2	no	—
947	C₂×C₄	—	2	1	no	—
948	C₂×C₄	—	2	1	no	—
949	C₂×C₄	—	2	1	no	—
950	C₂×C₄	—	2	1	no	—
951	C₂×C₄	—	2	2	no	—
952	C₂×C₄	—	2	2	no	—
953	C₂×C₄	—	2	2	no	—
954	C₂×C₄	—	2	1	no	—
955	C₂×C₄	—	2	2	no	—
956	C₂×C₄	—	2	2	no	—
957	C₂×C₄	—	2	2	no	—
958	C₂×C₄	—	2	1	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	2	no	—
965	C₂×C₄	—	2	1	no	—
966	C₂×C₄	—	2	1	no	—
967	C₂×C₄	—	2	1	no	—
968	C₂×C₄	—	2	2	no	—
969	C₂×C₄	—	2	2	no	—
970	C₂×C₄	—	2	1	no	—
971	C₂×C₄	—	2	1	no	—
972	C₂×C₄	—	2	2	no	—
973	C₂×C₄	—	2	1	no	—
974	C₂×C₄	—	2	2	no	—
975	C₂×C₄	—	4	4	no	—
976	C₂×C₄	—	4	4	no	—
977	C₂×C₄	—	4	4	no	—
978	C₂×C₄	—	8	4	no	—
979	C₂×C₄	—	8	4	no	—
980	C₂×C₄	—	8	4	no	—
981	C₂×C₄	C₂×C₃×#41	1	2	yes	—
982	C₂×C₄	C₂×C₃×#41	1	2	yes	—
983	C₂×C₄	C₂×C₃×#41	1	2	yes	—
984	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
985	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
986	C₂×C₃	—	4	2	no	—
987	C₂×C₃	—	4	2	no	—
988	C₂×C₃	—	8	1	no	—
989	C₂×C₃	—	8	2	no	—
990	C₂×C₃	C₂×#540	1	1	yes	characteristic
991	C₂×C₃	#3492	1	1	yes	characteristic
992	C₂×C₃	#3512	1	1	yes	characteristic
993	C₂×C₃	#3541	1	1	yes	characteristic
994	C₂×C₃	#3542	1	1	yes	characteristic
995	C₂×C₃	#3558	1	1	yes	characteristic
996	C₂×C₃	#3561	1	1	yes	characteristic
997	C₂²	—	2	2	no	—
998	C₂²	—	2	2	no	—
999	C₂²	—	2	2	no	—
1000	C₂²	—	2	2	no	—
1001	C₂²	—	2	2	no	—
1002	C₂²	—	2	2	no	—
1003	C₂²	—	4	1	no	—
1004	C₂²	—	4	1	no	—
1005	C₂²	—	4	1	no	—
1006	C₂²	—	4	1	no	—
1007	C₂²	—	4	1	no	—
1008	C₂²	—	4	1	no	—
1009	C₂²	—	4	1	no	—
1010	C₂²	—	4	1	no	—
1011	C₂²	—	4	1	no	—
1012	C₂²	—	4	2	no	—
1013	C₂²	—	4	1	no	—
1014	C₂²	—	4	2	no	—
1015	C₂²	—	4	1	no	—
1016	C₂²	—	4	2	no	—
1017	C₂²	—	4	1	no	—
1018	C₂²	—	4	2	no	—
1019	C₂²	—	4	2	no	—
1020	C₂²	—	4	1	no	—
1021	C₂²	—	4	1	no	—
1022	C₂²	—	4	2	no	—
1023	C₂²	—	4	2	no	—
1024	C₂²	—	4	1	no	—
1025	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
1026	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1027	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1028	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1029	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
1030	C₂²	C₃×#585	1	1	yes	characteristic
1031	C₂²	C₃×#585	1	1	yes	characteristic
1032	C₄	—	2	2	no	—
1033	C₄	—	2	2	no	—
1034	C₄	—	4	1	no	—
1035	C₄	—	4	1	no	—
1036	C₄	—	4	1	no	—
1037	C₄	—	4	2	no	—
1038	C₄	—	4	1	no	—
1039	C₄	—	4	1	no	—
1040	C₄	—	4	1	no	—
1041	C₄	—	4	1	no	—
1042	C₄	—	4	1	no	—
1043	C₄	—	4	2	no	—
1044	C₄	—	4	1	no	—
1045	C₄	—	4	2	no	—
1046	C₄	—	4	2	no	—
1047	C₄	—	4	2	no	—
1048	C₄	—	4	2	no	—
1049	C₄	—	4	2	no	—
1050	C₄	C₃×#540	1	4	yes	—
1051	C₃	#42454	1	1	yes	characteristic, direct product factor, Sylow
1052	C₂	—	4	2	no	—
1053	C₂	—	4	2	no	—
1054	C₂	—	8	1	no	—
1055	C₂	—	8	2	no	—
1056	C₂	C₂×C₃×#540	1	1	yes	characteristic
1057	C₂	C₃×#3492	1	1	yes	characteristic
1058	C₂	C₃×#3512	1	1	yes	characteristic
1059	C₂	C₃×#3541	1	1	yes	characteristic
1060	C₂	C₃×#3542	1	1	yes	characteristic
1061	C₂	C₃×#3558	1	1	yes	characteristic
1062	C₂	C₃×#3561	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×#2836	C₂	semidirect
2. C₃×#2780	C₂	semidirect
3. C₃×#2761	C₂	semidirect
4. C₃×#2753	C₂	semidirect
5. C₃×#2701	C₂	semidirect
6. C₃×#2649	C₂	semidirect
7. C₃×#2635	C₂	semidirect
8. C₃×#2620	C₂	semidirect
9. C₃×#2571	C₂	semidirect
10. C₃×#2540	C₂	semidirect
11. C₃×#2536	C₂	semidirect
12. C₃×#2535	C₂	semidirect
13. C₃×#2504	C₂	semidirect
14. C₃×#2503	C₂	semidirect
15. C₃×#2457	C₂	semidirect
16. C₃×#2423	C₂	semidirect
17. C₃×#2422	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. #42454	C₃	direct (N × H)
124. #2836	C₂×C₃	semidirect
125. #2780	C₂×C₃	semidirect
126. #2761	C₂×C₃	semidirect
127. #2753	C₂×C₃	semidirect
128. #2701	C₂×C₃	semidirect
129. #2649	C₂×C₃	semidirect
130. #2635	C₂×C₃	semidirect
131. #2620	C₂×C₃	semidirect
132. #2571	C₂×C₃	semidirect
133. #2540	C₂×C₃	semidirect
134. #2536	C₂×C₃	semidirect
135. #2535	C₂×C₃	semidirect
136. #2504	C₂×C₃	semidirect
137. #2503	C₂×C₃	semidirect
138. #2457	C₂×C₃	semidirect
139. #2423	C₂×C₃	semidirect
140. #2422	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
1051. C₃	#42454	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×#2836	2
C₃×#2780	2
C₃×#2761	2
C₃×#2753	2
C₃×#2701	2
C₃×#2649	2
C₃×#2635	2
C₃×#2620	2
C₃×#2571	2
C₃×#2540	2
C₃×#2536	2
C₃×#2535	2
C₃×#2504	2
C₃×#2503	2
C₃×#2457	2
C₃×#2423	2
C₃×#2422	2
C₃×#2417	2
C₃×#2416	2
C₃×#2392	2
C₃×#2367	2
C₃×D₄×C₄⋊C₄	2
C₃×#2314	2
#42454	3

Subgroups — C3×#42454 #10661061

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#42454 #10661061