Subgroups — C₃×#35016 #10653623

Order 768.

1880 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#2863	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#2862	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#2857	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#2855	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#2666	C₂	1	2	yes	maximal, complemented
6	C₃×#2665	C₂	1	2	yes	maximal, complemented
7	C₃×#2586	C₂	1	2	yes	maximal, complemented
8	C₃×#2574	C₂	1	2	yes	maximal, complemented
9	C₃×#2511	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#2505	C₂	1	2	yes	maximal, complemented
11	C₃×#2492	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#2450	C₂	1	2	yes	maximal
13	C₃×#2446	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#2440	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#2434	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#2429	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×#2417	C₂	1	1	yes	maximal, characteristic
18	C₃×#2409	C₂	1	1	yes	maximal, characteristic
19	C₃×#2329	C₂	1	2	yes	maximal, complemented
20	C₃×#2318	C₂	1	2	yes	maximal
21	C₃×C₄×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₃×#391	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃×C₄²×D₄	C₂	1	1	yes	maximal, characteristic
24	#35016	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂³×C₃×Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
27	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
28	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
29	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
30	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
31	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
32	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
33	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
34	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
35	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
36	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
37	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
38	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
39	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
40	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
41	C₃×#400	C₂²	1	2	yes	—
42	C₃×#400	C₂²	1	2	yes	—
43	C₃×#400	C₂²	1	2	yes	—
44	C₃×#400	C₂²	1	2	yes	—
45	C₃×#398	C₂²	1	2	yes	—
46	C₃×#398	C₂²	1	2	yes	—
47	C₃×#398	C₂²	1	2	yes	—
48	C₃×#398	C₂²	1	2	yes	—
49	C₃×#396	C₂²	1	2	yes	—
50	C₃×#396	C₂²	1	2	yes	—
51	C₃×#395	C₂²	1	2	yes	—
52	C₃×#395	C₂²	1	2	yes	—
53	C₃×#395	C₂²	1	2	yes	—
54	C₃×#395	C₂²	1	2	yes	—
55	C₃×#393	C₂²	1	2	yes	—
56	C₃×#393	C₂²	1	2	yes	—
57	C₃×#391	C₂²	1	1	yes	characteristic
58	C₃×#391	C₂²	1	1	yes	characteristic
59	C₃×#391	C₂²	1	2	yes	—
60	C₃×#391	C₂²	1	2	yes	—
61	C₃×#391	C₂²	1	1	yes	characteristic
62	C₃×#391	C₂²	1	1	yes	characteristic
63	C₃×#391	C₂²	1	1	yes	characteristic
64	C₃×#391	C₂²	1	1	yes	characteristic
65	C₃×#391	C₂²	1	1	yes	characteristic
66	C₃×#391	C₂²	1	2	yes	—
67	C₃×#391	C₂²	1	2	yes	—
68	C₃×#391	C₂²	1	2	yes	—
69	C₃×#391	C₂²	1	1	yes	characteristic
70	C₃×#391	C₂²	1	1	yes	characteristic
71	C₃×#391	C₂²	1	1	yes	characteristic
72	C₃×#389	C₂²	1	2	yes	—
73	C₃×#389	C₂²	1	1	yes	characteristic
74	C₃×#389	C₂²	1	1	yes	characteristic
75	C₃×#389	C₂²	1	2	yes	—
76	C₃×#389	C₂²	1	1	yes	characteristic
77	C₃×#389	C₂²	1	2	yes	—
78	C₃×#389	C₂²	1	1	yes	characteristic
79	C₃×#388	C₂²	1	2	yes	—
80	C₃×#388	C₂²	1	2	yes	—
81	C₃×#387	C₂²	1	2	yes	—
82	C₃×#387	C₂²	1	2	yes	—
83	C₃×#387	C₂²	1	2	yes	—
84	C₃×#387	C₂²	1	2	yes	—
85	C₃×#387	C₂²	1	2	yes	—
86	C₃×#387	C₂²	1	2	yes	—
87	C₃×#387	C₂²	1	2	yes	—
88	C₃×#387	C₂²	1	2	yes	—
89	C₃×#387	C₂²	1	2	yes	—
90	C₃×#387	C₂²	1	2	yes	—
91	C₃×#386	C₂²	1	2	yes	—
92	C₃×#386	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	2	yes	—
97	C₃×#385	C₂²	1	2	yes	—
98	C₃×#385	C₂²	1	2	yes	—
99	C₃×#384	C₂²	1	1	yes	characteristic
100	C₃×#383	C₂²	1	2	yes	—
101	C₃×#382	C₂²	1	2	yes	—
102	C₃×#382	C₂²	1	2	yes	—
103	C₃×#381	C₂²	1	2	yes	—
104	C₃×#380	C₂²	1	1	yes	characteristic
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	2	yes	—
109	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
110	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
111	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
112	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
113	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
114	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
115	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
119	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
120	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
121	C₂×C₃×#95	C₂²	1	2	yes	—
122	C₂×C₃×#95	C₂²	1	2	yes	—
123	C₃×C₄³	C₂²	1	1	yes	characteristic
124	#2863	C₂×C₃	1	1	yes	characteristic, complemented
125	#2862	C₂×C₃	1	1	yes	characteristic, complemented
126	#2857	C₂×C₃	1	1	yes	characteristic, complemented
127	#2855	C₂×C₃	1	1	yes	characteristic, complemented
128	#2666	C₂×C₃	1	2	yes	complemented
129	#2665	C₂×C₃	1	2	yes	complemented
130	#2586	C₂×C₃	1	2	yes	complemented
131	#2574	C₂×C₃	1	2	yes	complemented
132	#2511	C₂×C₃	1	1	yes	characteristic, complemented
133	#2505	C₂×C₃	1	2	yes	complemented
134	#2492	C₂×C₃	1	1	yes	characteristic, complemented
135	#2450	C₂×C₃	1	2	yes	—
136	#2446	C₂×C₃	1	1	yes	characteristic, complemented
137	#2440	C₂×C₃	1	1	yes	characteristic, complemented
138	#2434	C₂×C₃	1	1	yes	characteristic, complemented
139	#2429	C₂×C₃	1	1	yes	characteristic, complemented
140	#2417	C₂×C₃	1	1	yes	characteristic
141	#2409	C₂×C₃	1	1	yes	characteristic
142	#2329	C₂×C₃	1	2	yes	complemented
143	#2318	C₂×C₃	1	2	yes	—
144	C₄×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
145	C₂×#391	C₂×C₃	1	1	yes	characteristic, complemented
146	C₄²×D₄	C₂×C₃	1	1	yes	characteristic
147	C₂²×C₃×Q₈	—	2	4	no	—
148	C₂²×C₃×Q₈	—	4	2	no	—
149	C₂²×C₃×Q₈	—	4	2	no	—
150	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
151	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
152	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
153	C₂²×C₃×Q₈	C₂³	1	2	yes	—
154	C₂²×C₃×Q₈	C₂³	1	2	yes	—
155	C₂²×C₃×D₄	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	1	yes	characteristic
159	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
160	C₂³×C₃×C₄	C₂³	1	2	yes	—
161	C₂³×C₃×C₄	C₂³	1	2	yes	—
162	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
163	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
164	C₃×C₄⋊Q₈	—	4	2	no	—
165	C₃×C₄⋊Q₈	—	4	2	no	—
166	C₃×C₄⋊Q₈	—	4	2	no	—
167	C₃×C₂²⋊Q₈	—	2	4	no	—
168	C₃×C₂²⋊Q₈	—	2	8	no	—
169	C₃×C₂²⋊Q₈	—	4	2	no	—
170	C₃×C₂²⋊Q₈	—	4	2	no	—
171	C₃×C₂²⋊Q₈	—	4	2	no	—
172	C₃×C₄×Q₈	—	4	2	no	—
173	C₃×C₄×D₄	—	2	4	no	—
174	C₃×C₄×D₄	—	2	4	no	—
175	C₃×C₄×D₄	Q₈	1	8	yes	complemented
176	C₂×C₃×C₄⋊C₄	—	4	2	no	—
177	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
178	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
182	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
183	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
188	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
189	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
202	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
203	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
204	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
205	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
209	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
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×C₄²	—	4	2	no	—
215	C₂×C₃×C₄²	—	4	2	no	—
216	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
217	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
218	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
219	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
220	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
221	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
222	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
223	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
224	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
225	C₂×C₃×C₄²	C₂³	1	2	yes	—
226	C₂×C₃×C₄²	C₂³	1	2	yes	—
227	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
228	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
229	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
230	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
231	C₃×#95	C₂³	1	2	yes	—
232	C₃×#95	C₂³	1	2	yes	—
233	C₃×#95	C₂³	1	2	yes	—
234	C₃×#95	C₂³	1	2	yes	—
235	C₃×#95	C₂³	1	2	yes	—
236	C₃×#95	C₂³	1	2	yes	—
237	C₃×#95	C₂³	1	2	yes	—
238	C₃×#95	C₂³	1	2	yes	—
239	C₃×#95	C₂³	1	1	yes	characteristic
240	C₃×#95	C₂³	1	1	yes	characteristic
241	C₃×#95	C₂³	1	1	yes	characteristic
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	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	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	C₂³×Q₈	C₂²×C₃	1	1	yes	characteristic
265	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
266	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
267	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
268	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
269	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
270	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
271	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
272	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
273	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
274	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
275	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
276	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
277	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
278	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
279	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
280	#400	C₂²×C₃	1	2	yes	—
281	#400	C₂²×C₃	1	2	yes	—
282	#400	C₂²×C₃	1	2	yes	—
283	#400	C₂²×C₃	1	2	yes	—
284	#398	C₂²×C₃	1	2	yes	—
285	#398	C₂²×C₃	1	2	yes	—
286	#398	C₂²×C₃	1	2	yes	—
287	#398	C₂²×C₃	1	2	yes	—
288	#396	C₂²×C₃	1	2	yes	—
289	#396	C₂²×C₃	1	2	yes	—
290	#395	C₂²×C₃	1	2	yes	—
291	#395	C₂²×C₃	1	2	yes	—
292	#395	C₂²×C₃	1	2	yes	—
293	#395	C₂²×C₃	1	2	yes	—
294	#393	C₂²×C₃	1	2	yes	—
295	#393	C₂²×C₃	1	2	yes	—
296	#391	C₂²×C₃	1	2	yes	—
297	#391	C₂²×C₃	1	2	yes	—
298	#391	C₂²×C₃	1	2	yes	—
299	#391	C₂²×C₃	1	2	yes	—
300	#391	C₂²×C₃	1	1	yes	characteristic
301	#391	C₂²×C₃	1	1	yes	characteristic
302	#391	C₂²×C₃	1	1	yes	characteristic
303	#391	C₂²×C₃	1	1	yes	characteristic
304	#391	C₂²×C₃	1	1	yes	characteristic
305	#391	C₂²×C₃	1	1	yes	characteristic
306	#391	C₂²×C₃	1	1	yes	characteristic
307	#391	C₂²×C₃	1	1	yes	characteristic
308	#391	C₂²×C₃	1	2	yes	—
309	#391	C₂²×C₃	1	1	yes	characteristic
310	#391	C₂²×C₃	1	1	yes	characteristic
311	#389	C₂²×C₃	1	2	yes	—
312	#389	C₂²×C₃	1	2	yes	—
313	#389	C₂²×C₃	1	2	yes	—
314	#389	C₂²×C₃	1	1	yes	characteristic
315	#389	C₂²×C₃	1	1	yes	characteristic
316	#389	C₂²×C₃	1	1	yes	characteristic
317	#389	C₂²×C₃	1	1	yes	characteristic
318	#388	C₂²×C₃	1	2	yes	—
319	#388	C₂²×C₃	1	2	yes	—
320	#387	C₂²×C₃	1	2	yes	—
321	#387	C₂²×C₃	1	2	yes	—
322	#387	C₂²×C₃	1	2	yes	—
323	#387	C₂²×C₃	1	2	yes	—
324	#387	C₂²×C₃	1	2	yes	—
325	#387	C₂²×C₃	1	2	yes	—
326	#387	C₂²×C₃	1	2	yes	—
327	#387	C₂²×C₃	1	2	yes	—
328	#387	C₂²×C₃	1	2	yes	—
329	#387	C₂²×C₃	1	2	yes	—
330	#386	C₂²×C₃	1	2	yes	—
331	#386	C₂²×C₃	1	2	yes	—
332	#385	C₂²×C₃	1	2	yes	—
333	#385	C₂²×C₃	1	2	yes	—
334	#385	C₂²×C₃	1	2	yes	—
335	#385	C₂²×C₃	1	2	yes	—
336	#385	C₂²×C₃	1	2	yes	—
337	#385	C₂²×C₃	1	2	yes	—
338	#384	C₂²×C₃	1	1	yes	characteristic
339	#383	C₂²×C₃	1	2	yes	—
340	#382	C₂²×C₃	1	2	yes	—
341	#382	C₂²×C₃	1	2	yes	—
342	#381	C₂²×C₃	1	2	yes	—
343	#380	C₂²×C₃	1	2	yes	—
344	#380	C₂²×C₃	1	2	yes	—
345	#380	C₂²×C₃	1	2	yes	—
346	#380	C₂²×C₃	1	1	yes	characteristic
347	#380	C₂²×C₃	1	1	yes	characteristic
348	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
349	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
350	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
351	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
352	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
353	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
354	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
355	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
356	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
357	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
358	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
359	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
360	C₂×#95	C₂²×C₃	1	2	yes	—
361	C₂×#95	C₂²×C₃	1	2	yes	—
362	C₄³	C₂²×C₃	1	1	yes	characteristic
363	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
364	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
365	C₂×C₃×Q₈	—	2	2	no	—
366	C₂×C₃×Q₈	—	2	4	no	—
367	C₂×C₃×Q₈	—	2	2	no	—
368	C₂×C₃×Q₈	—	2	2	no	—
369	C₂×C₃×Q₈	—	2	4	no	—
370	C₂×C₃×Q₈	—	2	2	no	—
371	C₂×C₃×Q₈	—	2	2	no	—
372	C₂×C₃×Q₈	—	2	2	no	—
373	C₂×C₃×Q₈	—	2	2	no	—
374	C₂×C₃×Q₈	—	2	2	no	—
375	C₂×C₃×Q₈	—	2	2	no	—
376	C₂×C₃×Q₈	—	4	2	no	—
377	C₂×C₃×Q₈	—	4	2	no	—
378	C₂×C₃×Q₈	—	4	2	no	—
379	C₂×C₃×Q₈	—	4	2	no	—
380	C₂×C₃×Q₈	—	4	16	no	—
381	C₂×C₃×D₄	—	2	2	no	—
382	C₂×C₃×D₄	—	2	2	no	—
383	C₂×C₃×D₄	C₂×Q₈	1	4	yes	—
384	C₂²×C₃×C₄	—	2	2	no	—
385	C₂²×C₃×C₄	—	2	2	no	—
386	C₂²×C₃×C₄	—	2	2	no	—
387	C₂²×C₃×C₄	—	2	4	no	—
388	C₂²×C₃×C₄	—	2	4	no	—
389	C₂²×C₃×C₄	—	2	2	no	—
390	C₂²×C₃×C₄	—	2	2	no	—
391	C₂²×C₃×C₄	—	2	2	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	—	4	1	no	—
396	C₂²×C₃×C₄	—	4	1	no	—
397	C₂²×C₃×C₄	—	4	1	no	—
398	C₂²×C₃×C₄	—	4	1	no	—
399	C₂²×C₃×C₄	—	4	1	no	—
400	C₂²×C₃×C₄	—	4	1	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	C₂×Q₈	1	4	yes	—
406	C₂²×C₃×C₄	C₂×Q₈	1	4	yes	complemented
407	C₂²×C₃×C₄	#41	1	4	yes	—
408	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
409	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
410	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
411	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
412	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
413	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
414	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
415	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
416	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
417	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
418	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
419	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
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	1	yes	characteristic
424	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
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	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
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	4	no	—
433	C₃×C₄⋊C₄	—	2	4	no	—
434	C₃×C₄⋊C₄	—	2	4	no	—
435	C₃×C₄⋊C₄	—	2	4	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	—	4	2	no	—
442	C₃×C₄⋊C₄	—	4	2	no	—
443	C₃×C₄⋊C₄	—	4	2	no	—
444	C₃×C₄⋊C₄	—	4	2	no	—
445	C₃×C₄⋊C₄	—	4	2	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×C₄⋊C₄	C₂×Q₈	1	4	yes	complemented
454	C₃×C₂²⋊C₄	—	2	2	no	—
455	C₃×C₂²⋊C₄	—	2	4	no	—
456	C₃×C₂²⋊C₄	—	2	4	no	—
457	C₃×C₂²⋊C₄	—	2	2	no	—
458	C₃×C₂²⋊C₄	—	2	2	no	—
459	C₃×C₂²⋊C₄	—	4	2	no	—
460	C₃×C₂²⋊C₄	—	4	2	no	—
461	C₃×C₂²⋊C₄	—	4	2	no	—
462	C₃×C₂²⋊C₄	—	4	2	no	—
463	C₃×C₂²⋊C₄	C₂×Q₈	1	4	yes	—
464	C₃×C₂²⋊C₄	C₂×Q₈	1	4	yes	complemented
465	C₃×C₂²⋊C₄	#41	1	4	yes	—
466	C₃×C₄²	—	2	2	no	—
467	C₃×C₄²	—	2	2	no	—
468	C₃×C₄²	—	2	2	no	—
469	C₃×C₄²	—	2	2	no	—
470	C₃×C₄²	—	2	2	no	—
471	C₃×C₄²	—	2	2	no	—
472	C₃×C₄²	—	2	2	no	—
473	C₃×C₄²	—	4	1	no	—
474	C₃×C₄²	—	4	1	no	—
475	C₃×C₄²	—	4	1	no	—
476	C₃×C₄²	—	4	1	no	—
477	C₃×C₄²	—	4	2	no	—
478	C₃×C₄²	—	4	1	no	—
479	C₃×C₄²	—	4	2	no	—
480	C₃×C₄²	C₂×Q₈	1	4	yes	complemented
481	C₂²×Q₈	—	2	4	no	—
482	C₂²×Q₈	—	4	2	no	—
483	C₂²×Q₈	—	4	2	no	—
484	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
485	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
486	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
487	C₂²×Q₈	C₂³×C₃	1	2	yes	—
488	C₂²×Q₈	C₂³×C₃	1	2	yes	—
489	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
490	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
491	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
492	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
493	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
494	C₂³×C₄	C₂³×C₃	1	2	yes	—
495	C₂³×C₄	C₂³×C₃	1	2	yes	—
496	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
497	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
498	C₄⋊Q₈	—	4	2	no	—
499	C₄⋊Q₈	—	4	2	no	—
500	C₄⋊Q₈	—	4	2	no	—
501	C₂²⋊Q₈	—	2	4	no	—
502	C₂²⋊Q₈	—	2	8	no	—
503	C₂²⋊Q₈	—	4	2	no	—
504	C₂²⋊Q₈	—	4	2	no	—
505	C₂²⋊Q₈	—	4	2	no	—
506	C₄×Q₈	—	4	2	no	—
507	C₄×D₄	—	2	4	no	—
508	C₄×D₄	—	2	4	no	—
509	C₄×D₄	C₃×Q₈	1	8	yes	complemented
510	C₂×C₄⋊C₄	—	4	2	no	—
511	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
512	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
513	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
514	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
515	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
516	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
517	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
518	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
519	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
520	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
521	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
522	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
523	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
524	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
525	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
526	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
527	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
528	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
529	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
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	2	yes	—
534	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
535	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
536	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
537	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
538	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
539	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
540	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
541	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
542	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
543	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
544	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
545	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
546	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
547	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
548	C₂×C₄²	—	4	2	no	—
549	C₂×C₄²	—	4	2	no	—
550	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
551	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
552	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
553	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
554	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
555	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
556	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
557	C₂×C₄²	C₂³×C₃	1	2	yes	—
558	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
559	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
560	C₂×C₄²	C₂³×C₃	1	2	yes	—
561	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
562	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
563	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
564	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
565	#95	C₂³×C₃	1	2	yes	—
566	#95	C₂³×C₃	1	2	yes	—
567	#95	C₂³×C₃	1	2	yes	—
568	#95	C₂³×C₃	1	2	yes	—
569	#95	C₂³×C₃	1	2	yes	—
570	#95	C₂³×C₃	1	2	yes	—
571	#95	C₂³×C₃	1	2	yes	—
572	#95	C₂³×C₃	1	2	yes	—
573	#95	C₂³×C₃	1	1	yes	characteristic
574	#95	C₂³×C₃	1	1	yes	characteristic
575	#95	C₂³×C₃	1	1	yes	characteristic
576	#95	C₂³×C₃	1	1	yes	characteristic
577	#95	C₂³×C₃	1	1	yes	characteristic
578	#95	C₂³×C₃	1	1	yes	characteristic
579	#95	C₂³×C₃	1	2	yes	—
580	#95	C₂³×C₃	1	2	yes	—
581	#95	C₂³×C₃	1	2	yes	—
582	#95	C₂³×C₃	1	2	yes	—
583	#95	C₂³×C₃	1	2	yes	—
584	#95	C₂³×C₃	1	2	yes	—
585	#95	C₂³×C₃	1	2	yes	—
586	#95	C₂³×C₃	1	2	yes	—
587	#95	C₂³×C₃	1	2	yes	—
588	#95	C₂³×C₃	1	2	yes	—
589	#95	C₂³×C₃	1	2	yes	—
590	#95	C₂³×C₃	1	2	yes	—
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	C₂³×C₃	—	2	1	no	—
599	C₂³×C₃	—	2	1	no	—
600	C₂³×C₃	—	2	1	no	—
601	C₂³×C₃	—	2	1	no	—
602	C₂³×C₃	—	2	1	no	—
603	C₂³×C₃	—	2	1	no	—
604	C₂³×C₃	—	2	1	no	—
605	C₂³×C₃	—	2	1	no	—
606	C₂³×C₃	—	2	1	no	—
607	C₂³×C₃	—	2	1	no	—
608	C₂³×C₃	C₂²×Q₈	1	2	yes	—
609	C₂³×C₃	C₂²×Q₈	1	2	yes	—
610	C₂³×C₃	C₂×#41	1	2	yes	—
611	C₂³×C₃	C₂×#41	1	2	yes	—
612	C₂³×C₃	C₂⁵	1	1	yes	characteristic
613	C₃×Q₈	—	4	8	no	—
614	C₃×Q₈	—	4	4	no	—
615	C₃×Q₈	—	4	4	no	—
616	C₃×Q₈	—	4	4	no	—
617	C₃×Q₈	—	8	4	no	—
618	C₃×D₄	—	2	8	no	—
619	C₂×C₃×C₄	—	2	1	no	—
620	C₂×C₃×C₄	—	2	1	no	—
621	C₂×C₃×C₄	—	2	1	no	—
622	C₂×C₃×C₄	—	2	1	no	—
623	C₂×C₃×C₄	—	2	1	no	—
624	C₂×C₃×C₄	—	2	1	no	—
625	C₂×C₃×C₄	—	2	1	no	—
626	C₂×C₃×C₄	—	2	1	no	—
627	C₂×C₃×C₄	—	2	1	no	—
628	C₂×C₃×C₄	—	2	1	no	—
629	C₂×C₃×C₄	—	2	1	no	—
630	C₂×C₃×C₄	—	2	1	no	—
631	C₂×C₃×C₄	—	2	1	no	—
632	C₂×C₃×C₄	—	2	1	no	—
633	C₂×C₃×C₄	—	2	1	no	—
634	C₂×C₃×C₄	—	2	1	no	—
635	C₂×C₃×C₄	—	2	1	no	—
636	C₂×C₃×C₄	—	2	1	no	—
637	C₂×C₃×C₄	—	2	8	no	—
638	C₂×C₃×C₄	—	2	1	no	—
639	C₂×C₃×C₄	—	2	2	no	—
640	C₂×C₃×C₄	—	2	2	no	—
641	C₂×C₃×C₄	—	2	1	no	—
642	C₂×C₃×C₄	—	2	1	no	—
643	C₂×C₃×C₄	—	2	2	no	—
644	C₂×C₃×C₄	—	2	2	no	—
645	C₂×C₃×C₄	—	2	2	no	—
646	C₂×C₃×C₄	—	2	2	no	—
647	C₂×C₃×C₄	—	2	2	no	—
648	C₂×C₃×C₄	—	2	2	no	—
649	C₂×C₃×C₄	—	2	1	no	—
650	C₂×C₃×C₄	—	2	1	no	—
651	C₂×C₃×C₄	—	2	2	no	—
652	C₂×C₃×C₄	—	2	2	no	—
653	C₂×C₃×C₄	—	2	2	no	—
654	C₂×C₃×C₄	—	2	2	no	—
655	C₂×C₃×C₄	—	2	2	no	—
656	C₂×C₃×C₄	—	2	2	no	—
657	C₂×C₃×C₄	—	2	2	no	—
658	C₂×C₃×C₄	—	2	2	no	—
659	C₂×C₃×C₄	—	2	1	no	—
660	C₂×C₃×C₄	—	2	2	no	—
661	C₂×C₃×C₄	—	2	2	no	—
662	C₂×C₃×C₄	—	2	1	no	—
663	C₂×C₃×C₄	—	2	2	no	—
664	C₂×C₃×C₄	—	2	2	no	—
665	C₂×C₃×C₄	—	2	1	no	—
666	C₂×C₃×C₄	—	2	2	no	—
667	C₂×C₃×C₄	—	2	1	no	—
668	C₂×C₃×C₄	—	2	2	no	—
669	C₂×C₃×C₄	—	2	2	no	—
670	C₂×C₃×C₄	—	2	2	no	—
671	C₂×C₃×C₄	—	4	4	no	—
672	C₂×C₃×C₄	—	4	4	no	—
673	C₂×C₃×C₄	—	4	4	no	—
674	C₂×C₃×C₄	—	4	4	no	—
675	C₂×C₃×C₄	—	4	8	no	—
676	C₂×C₃×C₄	—	4	4	no	—
677	C₂×C₃×C₄	—	8	4	no	—
678	C₂×C₃×C₄	C₂²×Q₈	1	2	yes	—
679	C₂×C₃×C₄	C₂²×Q₈	1	2	yes	—
680	C₂×C₃×C₄	C₂²×Q₈	1	2	yes	—
681	C₂×C₃×C₄	C₂²×Q₈	1	2	yes	—
682	C₂×C₃×C₄	C₂²×Q₈	1	2	yes	—
683	C₂×C₃×C₄	C₂×#41	1	2	yes	—
684	C₂×C₃×C₄	C₂×#41	1	2	yes	—
685	C₂×C₃×C₄	C₂×#41	1	2	yes	—
686	C₂×C₃×C₄	C₂×#41	1	2	yes	—
687	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
688	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
689	C₂×C₃×C₄	2₋¹⁺⁴	1	2	yes	—
690	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
691	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
692	C₂×Q₈	—	2	2	no	—
693	C₂×Q₈	—	2	4	no	—
694	C₂×Q₈	—	2	2	no	—
695	C₂×Q₈	—	2	2	no	—
696	C₂×Q₈	—	2	4	no	—
697	C₂×Q₈	—	2	2	no	—
698	C₂×Q₈	—	2	2	no	—
699	C₂×Q₈	—	2	2	no	—
700	C₂×Q₈	—	2	2	no	—
701	C₂×Q₈	—	2	2	no	—
702	C₂×Q₈	—	2	2	no	—
703	C₂×Q₈	—	4	2	no	—
704	C₂×Q₈	—	4	2	no	—
705	C₂×Q₈	—	4	2	no	—
706	C₂×Q₈	—	4	2	no	—
707	C₂×Q₈	—	4	16	no	—
708	C₂×D₄	—	2	2	no	—
709	C₂×D₄	—	2	2	no	—
710	C₂×D₄	C₂×C₃×Q₈	1	4	yes	—
711	C₂²×C₄	—	2	2	no	—
712	C₂²×C₄	—	2	2	no	—
713	C₂²×C₄	—	2	2	no	—
714	C₂²×C₄	—	2	4	no	—
715	C₂²×C₄	—	2	4	no	—
716	C₂²×C₄	—	2	2	no	—
717	C₂²×C₄	—	2	2	no	—
718	C₂²×C₄	—	2	2	no	—
719	C₂²×C₄	—	2	2	no	—
720	C₂²×C₄	—	2	2	no	—
721	C₂²×C₄	—	2	2	no	—
722	C₂²×C₄	—	4	1	no	—
723	C₂²×C₄	—	4	1	no	—
724	C₂²×C₄	—	4	1	no	—
725	C₂²×C₄	—	4	1	no	—
726	C₂²×C₄	—	4	2	no	—
727	C₂²×C₄	—	4	2	no	—
728	C₂²×C₄	—	4	1	no	—
729	C₂²×C₄	—	4	1	no	—
730	C₂²×C₄	—	4	2	no	—
731	C₂²×C₄	—	4	2	no	—
732	C₂²×C₄	C₂×C₃×Q₈	1	4	yes	—
733	C₂²×C₄	C₂×C₃×Q₈	1	4	yes	complemented
734	C₂²×C₄	C₃×#41	1	4	yes	—
735	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
736	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
737	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
738	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
739	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
740	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
741	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
742	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
743	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
744	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
745	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
746	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
747	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
748	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
749	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
750	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
751	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
752	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
753	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
754	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
755	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
756	C₄⋊C₄	—	2	2	no	—
757	C₄⋊C₄	—	2	2	no	—
758	C₄⋊C₄	—	2	2	no	—
759	C₄⋊C₄	—	2	4	no	—
760	C₄⋊C₄	—	2	4	no	—
761	C₄⋊C₄	—	2	4	no	—
762	C₄⋊C₄	—	2	4	no	—
763	C₄⋊C₄	—	2	2	no	—
764	C₄⋊C₄	—	2	2	no	—
765	C₄⋊C₄	—	2	2	no	—
766	C₄⋊C₄	—	2	2	no	—
767	C₄⋊C₄	—	2	4	no	—
768	C₄⋊C₄	—	4	2	no	—
769	C₄⋊C₄	—	4	2	no	—
770	C₄⋊C₄	—	4	2	no	—
771	C₄⋊C₄	—	4	2	no	—
772	C₄⋊C₄	—	4	2	no	—
773	C₄⋊C₄	—	4	2	no	—
774	C₄⋊C₄	—	4	2	no	—
775	C₄⋊C₄	—	4	2	no	—
776	C₄⋊C₄	—	4	2	no	—
777	C₄⋊C₄	—	4	2	no	—
778	C₄⋊C₄	—	4	2	no	—
779	C₄⋊C₄	—	4	2	no	—
780	C₄⋊C₄	C₂×C₃×Q₈	1	4	yes	complemented
781	C₂²⋊C₄	—	2	2	no	—
782	C₂²⋊C₄	—	2	4	no	—
783	C₂²⋊C₄	—	2	4	no	—
784	C₂²⋊C₄	—	2	2	no	—
785	C₂²⋊C₄	—	2	2	no	—
786	C₂²⋊C₄	—	4	2	no	—
787	C₂²⋊C₄	—	4	2	no	—
788	C₂²⋊C₄	—	4	2	no	—
789	C₂²⋊C₄	—	4	2	no	—
790	C₂²⋊C₄	C₂×C₃×Q₈	1	4	yes	—
791	C₂²⋊C₄	C₂×C₃×Q₈	1	4	yes	complemented
792	C₂²⋊C₄	C₃×#41	1	4	yes	—
793	C₄²	—	2	2	no	—
794	C₄²	—	2	2	no	—
795	C₄²	—	2	2	no	—
796	C₄²	—	2	2	no	—
797	C₄²	—	2	2	no	—
798	C₄²	—	2	2	no	—
799	C₄²	—	2	2	no	—
800	C₄²	—	4	1	no	—
801	C₄²	—	4	1	no	—
802	C₄²	—	4	1	no	—
803	C₄²	—	4	1	no	—
804	C₄²	—	4	2	no	—
805	C₄²	—	4	2	no	—
806	C₄²	—	4	1	no	—
807	C₄²	C₂×C₃×Q₈	1	4	yes	complemented
808	C₂²×C₃	—	2	2	no	—
809	C₂²×C₃	—	2	2	no	—
810	C₂²×C₃	—	2	2	no	—
811	C₂²×C₃	—	2	2	no	—
812	C₂²×C₃	—	2	2	no	—
813	C₂²×C₃	—	2	2	no	—
814	C₂²×C₃	—	2	2	no	—
815	C₂²×C₃	—	2	2	no	—
816	C₂²×C₃	—	2	2	no	—
817	C₂²×C₃	—	4	1	no	—
818	C₂²×C₃	—	4	1	no	—
819	C₂²×C₃	—	4	1	no	—
820	C₂²×C₃	—	4	1	no	—
821	C₂²×C₃	#533	1	4	yes	—
822	C₂²×C₃	C₂³×Q₈	1	1	yes	characteristic
823	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
824	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
825	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
826	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
827	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
828	C₂²×C₃	#585	1	1	yes	characteristic
829	C₃×C₄	—	2	2	no	—
830	C₃×C₄	—	2	2	no	—
831	C₃×C₄	—	2	2	no	—
832	C₃×C₄	—	2	2	no	—
833	C₃×C₄	—	2	2	no	—
834	C₃×C₄	—	2	2	no	—
835	C₃×C₄	—	2	2	no	—
836	C₃×C₄	—	2	2	no	—
837	C₃×C₄	—	2	2	no	—
838	C₃×C₄	—	4	1	no	—
839	C₃×C₄	—	4	2	no	—
840	C₃×C₄	—	4	2	no	—
841	C₃×C₄	—	4	2	no	—
842	C₃×C₄	—	4	1	no	—
843	C₃×C₄	—	4	2	no	—
844	C₃×C₄	—	4	2	no	—
845	C₃×C₄	—	4	2	no	—
846	C₃×C₄	—	4	2	no	—
847	C₃×C₄	—	4	2	no	—
848	C₃×C₄	—	4	1	no	—
849	C₃×C₄	#538	1	4	yes	—
850	C₂³	—	2	1	no	—
851	C₂³	—	2	1	no	—
852	C₂³	—	2	1	no	—
853	C₂³	—	2	1	no	—
854	C₂³	—	2	1	no	—
855	C₂³	—	2	1	no	—
856	C₂³	—	2	1	no	—
857	C₂³	—	2	1	no	—
858	C₂³	—	2	1	no	—
859	C₂³	—	2	1	no	—
860	C₂³	C₂²×C₃×Q₈	1	2	yes	—
861	C₂³	C₂²×C₃×Q₈	1	2	yes	—
862	C₂³	C₂×C₃×#41	1	2	yes	—
863	C₂³	C₂×C₃×#41	1	2	yes	—
864	C₂³	C₂⁵×C₃	1	1	yes	characteristic
865	Q₈	—	4	8	no	—
866	Q₈	—	4	4	no	—
867	Q₈	—	4	4	no	—
868	Q₈	—	4	4	no	—
869	Q₈	—	8	4	no	—
870	D₄	—	2	8	no	—
871	C₂×C₄	—	2	1	no	—
872	C₂×C₄	—	2	1	no	—
873	C₂×C₄	—	2	1	no	—
874	C₂×C₄	—	2	1	no	—
875	C₂×C₄	—	2	1	no	—
876	C₂×C₄	—	2	1	no	—
877	C₂×C₄	—	2	1	no	—
878	C₂×C₄	—	2	1	no	—
879	C₂×C₄	—	2	1	no	—
880	C₂×C₄	—	2	1	no	—
881	C₂×C₄	—	2	1	no	—
882	C₂×C₄	—	2	1	no	—
883	C₂×C₄	—	2	1	no	—
884	C₂×C₄	—	2	1	no	—
885	C₂×C₄	—	2	1	no	—
886	C₂×C₄	—	2	1	no	—
887	C₂×C₄	—	2	1	no	—
888	C₂×C₄	—	2	1	no	—
889	C₂×C₄	—	2	8	no	—
890	C₂×C₄	—	2	1	no	—
891	C₂×C₄	—	2	2	no	—
892	C₂×C₄	—	2	2	no	—
893	C₂×C₄	—	2	1	no	—
894	C₂×C₄	—	2	1	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	2	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	2	no	—
900	C₂×C₄	—	2	2	no	—
901	C₂×C₄	—	2	1	no	—
902	C₂×C₄	—	2	1	no	—
903	C₂×C₄	—	2	2	no	—
904	C₂×C₄	—	2	2	no	—
905	C₂×C₄	—	2	2	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	2	2	no	—
909	C₂×C₄	—	2	2	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	1	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	2	1	no	—
915	C₂×C₄	—	2	2	no	—
916	C₂×C₄	—	2	2	no	—
917	C₂×C₄	—	2	1	no	—
918	C₂×C₄	—	2	2	no	—
919	C₂×C₄	—	2	1	no	—
920	C₂×C₄	—	2	2	no	—
921	C₂×C₄	—	2	2	no	—
922	C₂×C₄	—	2	2	no	—
923	C₂×C₄	—	4	4	no	—
924	C₂×C₄	—	4	4	no	—
925	C₂×C₄	—	4	4	no	—
926	C₂×C₄	—	4	4	no	—
927	C₂×C₄	—	4	8	no	—
928	C₂×C₄	—	4	4	no	—
929	C₂×C₄	—	8	4	no	—
930	C₂×C₄	C₂²×C₃×Q₈	1	2	yes	—
931	C₂×C₄	C₂²×C₃×Q₈	1	2	yes	—
932	C₂×C₄	C₂²×C₃×Q₈	1	2	yes	—
933	C₂×C₄	C₂²×C₃×Q₈	1	2	yes	—
934	C₂×C₄	C₂²×C₃×Q₈	1	2	yes	—
935	C₂×C₄	C₂×C₃×#41	1	2	yes	—
936	C₂×C₄	C₂×C₃×#41	1	2	yes	—
937	C₂×C₄	C₂×C₃×#41	1	2	yes	—
938	C₂×C₄	C₂×C₃×#41	1	2	yes	—
939	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
940	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
941	C₂×C₄	C₃×2₋¹⁺⁴	1	2	yes	—
942	C₂×C₃	—	2	4	no	—
943	C₂×C₃	—	4	2	no	—
944	C₂×C₃	C₂×#533	1	1	yes	characteristic
945	C₂×C₃	C₂×#538	1	1	yes	characteristic
946	C₂×C₃	#3461	1	1	yes	characteristic
947	C₂×C₃	#3501	1	1	yes	characteristic
948	C₂×C₃	#3503	1	1	yes	characteristic
949	C₂×C₃	#3514	1	1	yes	characteristic
950	C₂×C₃	#3520	1	1	yes	characteristic
951	C₂²	—	2	2	no	—
952	C₂²	—	2	2	no	—
953	C₂²	—	2	2	no	—
954	C₂²	—	2	2	no	—
955	C₂²	—	2	2	no	—
956	C₂²	—	2	2	no	—
957	C₂²	—	2	2	no	—
958	C₂²	—	2	2	no	—
959	C₂²	—	2	2	no	—
960	C₂²	—	4	1	no	—
961	C₂²	—	4	1	no	—
962	C₂²	—	4	1	no	—
963	C₂²	—	4	1	no	—
964	C₂²	C₃×#533	1	4	yes	—
965	C₂²	C₂³×C₃×Q₈	1	1	yes	characteristic
966	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
967	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
968	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
969	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
970	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
971	C₂²	C₃×#585	1	1	yes	characteristic
972	C₄	—	2	2	no	—
973	C₄	—	2	2	no	—
974	C₄	—	2	2	no	—
975	C₄	—	2	2	no	—
976	C₄	—	2	2	no	—
977	C₄	—	2	2	no	—
978	C₄	—	2	2	no	—
979	C₄	—	2	2	no	—
980	C₄	—	2	2	no	—
981	C₄	—	4	2	no	—
982	C₄	—	4	2	no	—
983	C₄	—	4	1	no	—
984	C₄	—	4	2	no	—
985	C₄	—	4	1	no	—
986	C₄	—	4	2	no	—
987	C₄	—	4	2	no	—
988	C₄	—	4	2	no	—
989	C₄	—	4	2	no	—
990	C₄	—	4	1	no	—
991	C₄	—	4	2	no	—
992	C₄	C₃×#538	1	4	yes	—
993	C₃	#35016	1	1	yes	characteristic, direct product factor, Sylow
994	C₂	—	2	4	no	—
995	C₂	—	4	2	no	—
996	C₂	C₂×C₃×#533	1	1	yes	characteristic
997	C₂	C₂×C₃×#538	1	1	yes	characteristic
998	C₂	C₃×#3461	1	1	yes	characteristic
999	C₂	C₃×#3501	1	1	yes	characteristic
1000	C₂	C₃×#3503	1	1	yes	characteristic
1001	C₂	C₃×#3514	1	1	yes	characteristic
1002	C₂	C₃×#3520	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
prime radical	C₂²×C₃×D₄	C₂³
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×#2863	C₂	semidirect
2. C₃×#2862	C₂	semidirect
3. C₃×#2857	C₂	semidirect
4. C₃×#2855	C₂	semidirect
5. C₃×#2666	C₂	semidirect
6. C₃×#2665	C₂	semidirect
7. C₃×#2586	C₂	semidirect
8. C₃×#2574	C₂	semidirect
9. C₃×#2511	C₂	semidirect
10. C₃×#2505	C₂	semidirect
11. C₃×#2492	C₂	semidirect
13. C₃×#2446	C₂	semidirect
14. C₃×#2440	C₂	semidirect
15. C₃×#2434	C₂	semidirect
16. C₃×#2429	C₂	semidirect
19. C₃×#2329	C₂	semidirect
21. C₃×C₄×C₂²⋊Q₈	C₂	semidirect
22. C₂×C₃×#391	C₂	semidirect
24. #35016	C₃	direct (N × H)
124. #2863	C₂×C₃	semidirect
125. #2862	C₂×C₃	semidirect
126. #2857	C₂×C₃	semidirect
127. #2855	C₂×C₃	semidirect
128. #2666	C₂×C₃	semidirect
129. #2665	C₂×C₃	semidirect
130. #2586	C₂×C₃	semidirect
131. #2574	C₂×C₃	semidirect
132. #2511	C₂×C₃	semidirect
133. #2505	C₂×C₃	semidirect
134. #2492	C₂×C₃	semidirect
136. #2446	C₂×C₃	semidirect
137. #2440	C₂×C₃	semidirect
138. #2434	C₂×C₃	semidirect
139. #2429	C₂×C₃	semidirect
142. #2329	C₂×C₃	semidirect
144. C₄×C₂²⋊Q₈	C₂×C₃	semidirect
145. C₂×#391	C₂×C₃	semidirect
175. C₃×C₄×D₄	Q₈	semidirect
406. C₂²×C₃×C₄	C₂×Q₈	semidirect
453. C₃×C₄⋊C₄	C₂×Q₈	semidirect
464. C₃×C₂²⋊C₄	C₂×Q₈	semidirect
480. C₃×C₄²	C₂×Q₈	semidirect
509. C₄×D₄	C₃×Q₈	semidirect
733. C₂²×C₄	C₂×C₃×Q₈	semidirect
780. C₄⋊C₄	C₂×C₃×Q₈	semidirect
791. C₂²⋊C₄	C₂×C₃×Q₈	semidirect
807. C₄²	C₂×C₃×Q₈	semidirect
993. C₃	#35016	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×#2863	2
C₃×#2862	2
C₃×#2857	2
C₃×#2855	2
C₃×#2666	2
C₃×#2665	2
C₃×#2586	2
C₃×#2574	2
C₃×#2511	2
C₃×#2505	2
C₃×#2492	2
C₃×#2450	2
C₃×#2446	2
C₃×#2440	2
C₃×#2434	2
C₃×#2429	2
C₃×#2417	2
C₃×#2409	2
C₃×#2329	2
C₃×#2318	2
C₃×C₄×C₂²⋊Q₈	2
C₂×C₃×#391	2
C₃×C₄²×D₄	2
#35016	3

Subgroups — C3×#35016 #10653623

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#35016 #10653623