Subgroups — #11660924

Order 768.

1950 conjugacy classes of subgroups.

The subgroup lattice has 1180 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#3481	C₂	1	1	yes	maximal, characteristic
2	#83280	C₂	1	1	yes	maximal, characteristic, complemented
3	#83277	C₂	1	1	yes	maximal, characteristic, complemented
4	#83132	C₂	1	1	yes	maximal, characteristic, complemented
5	#83131	C₂	1	1	yes	maximal, characteristic, complemented
6	#83130	C₂	1	2	yes	maximal, complemented
7	#83129	C₂	1	1	yes	maximal, characteristic, complemented
8	#83128	C₂	1	2	yes	maximal, complemented
9	#83126	C₂	1	1	yes	maximal, characteristic, complemented
10	#82920	C₂	1	2	yes	maximal, complemented
11	#82919	C₂	1	2	yes	maximal, complemented
12	#82918	C₂	1	2	yes	maximal, complemented
13	#82916	C₂	1	2	yes	maximal, complemented
14	#82522	C₂	1	1	yes	maximal, characteristic, complemented
15	#82520	C₂	1	1	yes	maximal, characteristic, complemented
16	#82518	C₂	1	1	yes	maximal, characteristic, complemented
17	#82517	C₂	1	1	yes	maximal, characteristic, complemented
18	#82303	C₂	1	1	yes	maximal, characteristic, complemented
19	#82303	C₂	1	2	yes	maximal, complemented
20	#82301	C₂	1	1	yes	maximal, characteristic, complemented
21	D₄×#208	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#5011	C₂	1	2	yes	maximal, complemented
23	C₂×D₄×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
24	#60311	—	3	1	no	maximal, Sylow
25	C₃×#559	C₄	1	1	yes	characteristic
26	C₃×#554	C₄	1	1	yes	characteristic
27	C₃×#554	C₄	1	1	yes	characteristic
28	C₃×#553	C₄	1	1	yes	characteristic
29	C₃×#553	C₄	1	1	yes	characteristic
30	C₃×#553	C₄	1	2	yes	—
31	C₃×#551	C₄	1	2	yes	—
32	C₃×#551	C₄	1	2	yes	—
33	C₃×#546	C₄	1	1	yes	characteristic
34	C₃×#546	C₄	1	1	yes	characteristic
35	C₃×#546	C₄	1	2	yes	—
36	C₃×D₄²	C₄	1	1	yes	characteristic
37	C₃×#532	C₂²	1	1	yes	characteristic
38	C₃×#529	C₂²	1	1	yes	characteristic
39	C₃×#529	C₂²	1	2	yes	—
40	C₃×#529	C₂²	1	1	yes	characteristic
41	C₃×#525	C₂²	1	2	yes	—
42	C₃×#525	C₂²	1	2	yes	—
43	C₃×C₄×#41	C₂²	1	1	yes	characteristic
44	C₃×C₄×#41	C₂²	1	1	yes	characteristic
45	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
46	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
47	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
48	C₂×#948	C₂²	1	2	yes	complemented
49	C₂²×#208	C₂²	1	2	yes	complemented
50	C₂³×C₃⋊C₈	C₂²	1	2	yes	complemented
51	#5234	C₂²	1	2	yes	complemented
52	#5234	C₂²	1	2	yes	complemented
53	#5234	C₂²	1	2	yes	complemented
54	#5207	C₂²	1	2	yes	complemented
55	#5207	C₂²	1	2	yes	complemented
56	C₂×#830	C₂²	1	2	yes	complemented
57	C₂×#830	C₂²	1	2	yes	complemented
58	C₂×#830	C₂²	1	2	yes	complemented
59	C₂×#830	C₂²	1	2	yes	complemented
60	#5024	C₂²	1	1	yes	characteristic, complemented
61	#5024	C₂²	1	1	yes	characteristic, complemented
62	#5024	C₂²	1	1	yes	characteristic, complemented
63	#5024	C₂²	1	1	yes	characteristic, complemented
64	#5024	C₂²	1	2	yes	complemented
65	Q₈×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
66	Q₈×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
67	#5012	C₂²	1	1	yes	characteristic, complemented
68	#5012	C₂²	1	1	yes	characteristic, complemented
69	#5012	C₂²	1	1	yes	characteristic, complemented
70	#5012	C₂²	1	1	yes	characteristic, complemented
71	#5012	C₂²	1	1	yes	characteristic, complemented
72	#5012	C₂²	1	1	yes	characteristic, complemented
73	#5012	C₂²	1	2	yes	complemented
74	#5012	C₂²	1	2	yes	complemented
75	#5011	C₂²	1	1	yes	characteristic
76	#5011	C₂²	1	1	yes	characteristic
77	#5011	C₂²	1	2	yes	—
78	#5011	C₂²	1	2	yes	complemented
79	#5011	C₂²	1	2	yes	complemented
80	#5011	C₂²	1	2	yes	complemented
81	#5011	C₂²	1	2	yes	complemented
82	#5011	C₂²	1	1	yes	characteristic, complemented
83	#5011	C₂²	1	1	yes	characteristic, complemented
84	#5011	C₂²	1	2	yes	complemented
85	#5011	C₂²	1	2	yes	complemented
86	#5011	C₂²	1	2	yes	complemented
87	#5011	C₂²	1	2	yes	complemented
88	#5011	C₂²	1	2	yes	complemented
89	#5011	C₂²	1	2	yes	complemented
90	#5011	C₂²	1	2	yes	complemented
91	#5011	C₂²	1	2	yes	complemented
92	#5011	C₂²	1	2	yes	complemented
93	#5011	C₂²	1	2	yes	complemented
94	#5011	C₂²	1	2	yes	complemented
95	D₄×C₃⋊C₈	C₂²	1	1	yes	characteristic
96	D₄×C₃⋊C₈	C₂²	1	1	yes	characteristic
97	D₄×C₃⋊C₈	C₂²	1	1	yes	characteristic
98	D₄×C₃⋊C₈	C₂²	1	1	yes	characteristic
99	D₄×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
100	D₄×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
101	D₄×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
102	D₄×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
103	D₄×C₃⋊C₈	C₂²	1	2	yes	complemented
104	D₄×C₃⋊C₈	C₂²	1	2	yes	complemented
105	D₄×C₃⋊C₈	C₂²	1	2	yes	complemented
106	D₄×C₃⋊C₈	C₂²	1	2	yes	complemented
107	D₄×C₃⋊C₈	C₂²	1	2	yes	complemented
108	D₄×C₃⋊C₈	C₂²	1	2	yes	complemented
109	D₄×C₃⋊C₈	C₂²	1	2	yes	complemented
110	D₄×C₃⋊C₈	C₂²	1	2	yes	complemented
111	D₄×C₃⋊C₈	C₂²	1	2	yes	complemented
112	#5000	C₂²	1	2	yes	complemented
113	#5000	C₂²	1	2	yes	complemented
114	#5000	C₂²	1	2	yes	complemented
115	#5000	C₂²	1	2	yes	complemented
116	#4999	C₂²	1	2	yes	complemented
117	#4999	C₂²	1	2	yes	complemented
118	#4997	C₂²	1	2	yes	complemented
119	#4997	C₂²	1	2	yes	complemented
120	#4926	C₂²	1	1	yes	characteristic, complemented
121	#4926	C₂²	1	2	yes	complemented
122	#4926	C₂²	1	1	yes	characteristic, complemented
123	#4925	C₂²	1	1	yes	characteristic, complemented
124	#4925	C₂²	1	1	yes	characteristic, complemented
125	#4925	C₂²	1	1	yes	characteristic, complemented
126	#4925	C₂²	1	2	yes	complemented
127	#4925	C₂²	1	1	yes	characteristic, complemented
128	#4924	C₂²	1	1	yes	characteristic, complemented
129	C₂×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
130	C₂×C₄⋊(C₃⋊C₈)	C₂²	1	2	yes	complemented
131	C₂×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
132	C₄×#208	C₂²	1	1	yes	characteristic, complemented
133	C₄×#208	C₂²	1	1	yes	characteristic, complemented
134	C₂×#803	C₂²	1	2	yes	complemented
135	C₂×C₄×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
136	#3481	D₃	1	1	yes	characteristic
137	#2994	—	3	1	no	—
138	#2993	—	3	1	no	—
139	#2992	—	3	2	no	—
140	#2990	—	3	1	no	—
141	#2988	—	3	1	no	—
142	#2981	—	3	1	no	—
143	#2977	—	3	2	no	—
144	#2976	—	3	2	no	—
145	#2974	—	3	1	no	—
146	#2974	—	3	2	no	—
147	#2972	—	3	1	no	—
148	#2970	—	3	1	no	—
149	#2969	—	3	1	no	—
150	#2968	—	3	2	no	—
151	#2966	—	3	1	no	—
152	#2965	—	3	1	no	—
153	#2935	—	3	1	no	—
154	D₄×M₁₆	—	3	1	no	—
155	#2933	—	3	2	no	—
156	#2929	—	3	2	no	—
157	C₂×#435	—	3	2	no	—
158	C₂×C₈×D₄	—	3	1	no	—
159	C₂×C₃×#41	C₂×C₄	1	1	yes	characteristic
160	C₂×C₃×#41	C₂×C₄	1	1	yes	characteristic
161	C₂×C₃×#41	C₂³	1	2	yes	—
162	C₂²×C₃×D₄	C₂×C₄	1	1	yes	characteristic
163	C₂²×C₃×D₄	C₂×C₄	1	1	yes	characteristic
164	C₂²×C₃×D₄	C₂×C₄	1	2	yes	—
165	C₂³×C₃×C₄	C₂³	1	2	yes	—
166	C₂³×C₃×C₄	C₂³	1	2	yes	—
167	C₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
168	C₃×#127	C₂×C₄	1	1	yes	characteristic
169	C₃×#126	C₂×C₄	1	2	yes	—
170	C₃×#126	C₂×C₄	1	2	yes	—
171	C₃×#126	C₂×C₄	1	2	yes	—
172	C₃×#126	C₂×C₄	1	2	yes	—
173	C₃×#125	C₂×C₄	1	1	yes	characteristic
174	C₃×#125	C₂×C₄	1	2	yes	—
175	C₃×#125	C₂×C₄	1	1	yes	characteristic
176	C₃×#124	C₂×C₄	1	1	yes	characteristic
177	C₃×#124	C₂×C₄	1	1	yes	characteristic
178	C₃×#124	C₂×C₄	1	2	yes	—
179	C₃×#124	C₂×C₄	1	2	yes	—
180	C₃×#123	C₂×C₄	1	2	yes	—
181	C₃×#123	C₂×C₄	1	2	yes	—
182	C₃×#123	C₂×C₄	1	2	yes	—
183	C₃×#123	C₂×C₄	1	2	yes	—
184	C₃×#123	C₂×C₄	1	2	yes	—
185	C₃×#123	C₂×C₄	1	2	yes	—
186	C₃×#123	C₂×C₄	1	2	yes	—
187	C₃×#123	C₂×C₄	1	2	yes	—
188	C₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
189	C₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
190	C₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
191	C₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
192	C₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
193	C₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
194	C₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
195	C₃×#121	C₂×C₄	1	2	yes	—
196	C₃×#121	C₂×C₄	1	2	yes	—
197	C₃×#121	C₂×C₄	1	2	yes	—
198	C₃×#121	C₂×C₄	1	2	yes	—
199	C₃×#121	C₂×C₄	1	1	yes	characteristic
200	C₃×#121	C₂×C₄	1	1	yes	characteristic
201	C₃×#121	C₂×C₄	1	2	yes	—
202	C₃×#121	C₂×C₄	1	1	yes	characteristic
203	C₃×#121	C₂×C₄	1	1	yes	characteristic
204	C₃×#121	C₂×C₄	1	2	yes	—
205	C₃×#120	C₂×C₄	1	2	yes	—
206	C₃×#120	C₂×C₄	1	2	yes	—
207	C₃×#120	C₂×C₄	1	2	yes	—
208	C₃×#120	C₂×C₄	1	2	yes	—
209	C₃×C₄×Q₈	C₂×C₄	1	1	yes	characteristic
210	C₃×C₄×Q₈	C₂×C₄	1	1	yes	characteristic
211	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
212	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
213	C₃×C₄×D₄	C₂×C₄	1	1	yes	characteristic
214	C₃×C₄×D₄	C₂×C₄	1	1	yes	characteristic
215	C₃×C₄×D₄	C₂×C₄	1	2	yes	—
216	C₃×C₄×D₄	C₂×C₄	1	2	yes	—
217	C₃×C₄×D₄	C₂×C₄	1	1	yes	characteristic
218	C₃×C₄×D₄	C₂×C₄	1	1	yes	characteristic
219	C₃×C₄×D₄	C₂×C₄	1	2	yes	—
220	C₃×C₄×D₄	C₂×C₄	1	2	yes	—
221	C₃×C₄×D₄	C₂×C₄	1	2	yes	—
222	C₃×C₄×D₄	C₂×C₄	1	2	yes	—
223	C₃×C₄×D₄	C₂×C₄	1	1	yes	characteristic
224	C₃×C₄×D₄	C₂×C₄	1	1	yes	characteristic
225	C₃×C₄×D₄	C₂×C₄	1	1	yes	characteristic
226	C₃×C₄×D₄	C₂×C₄	1	1	yes	characteristic
227	C₃×C₄×D₄	C₂×C₄	1	2	yes	—
228	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
229	C₃×C₄×D₄	C₂³	1	2	yes	—
230	C₃×C₄×D₄	C₂³	1	2	yes	—
231	C₃×C₄×D₄	C₂³	1	2	yes	—
232	C₃×C₄×D₄	C₂³	1	2	yes	—
233	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
234	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
235	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
236	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
237	C₃×C₄×D₄	C₂³	1	2	yes	—
238	C₃×C₄×D₄	C₂³	1	2	yes	—
239	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
240	C₃×#117	C₂×C₄	1	1	yes	characteristic
241	C₃×#117	C₂×C₄	1	2	yes	—
242	C₃×#117	C₂×C₄	1	1	yes	characteristic
243	C₃×#117	C₂×C₄	1	1	yes	characteristic
244	C₃×#117	C₂×C₄	1	1	yes	characteristic
245	C₃×#117	C₂³	1	2	yes	—
246	C₃×#117	C₂³	1	2	yes	—
247	C₂×C₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
248	C₂×C₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
249	C₂×C₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
250	C₂×C₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
251	C₂×C₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
252	C₂×C₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
253	C₂×C₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
254	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
255	C₂×C₃×C₄²	C₂³	1	2	yes	—
256	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
257	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
258	#948	—	4	4	no	—
259	C₂×#208	—	4	4	no	—
260	C₂×#208	C₂³	1	1	yes	characteristic
261	C₂×#208	C₂³	1	1	yes	characteristic
262	C₂×#208	C₂³	1	2	yes	—
263	C₂×#208	C₂³	1	1	yes	characteristic
264	C₂×#208	C₂³	1	1	yes	characteristic
265	C₂×#208	C₂³	1	2	yes	—
266	C₂×#208	C₂³	1	2	yes	—
267	C₂×#208	C₂³	1	2	yes	—
268	C₂×#208	C₂³	1	2	yes	—
269	C₂²×C₃⋊C₈	—	4	4	no	—
270	C₂²×C₃⋊C₈	C₂³	1	1	yes	characteristic
271	C₂²×C₃⋊C₈	C₂³	1	2	yes	—
272	C₂²×C₃⋊C₈	C₂³	1	2	yes	—
273	C₂²×C₃⋊C₈	C₂³	1	1	yes	characteristic
274	C₂²×C₃⋊C₈	C₂³	1	2	yes	—
275	C₂²×C₃⋊C₈	C₂³	1	2	yes	—
276	C₂²×C₃⋊C₈	C₂³	1	2	yes	—
277	C₂²×C₃⋊C₈	C₂³	1	2	yes	—
278	C₂²×C₃⋊C₈	C₂³	1	2	yes	—
279	C₂²×C₃⋊C₈	C₂³	1	2	yes	—
280	C₂²×C₃⋊C₈	C₂³	1	2	yes	—
281	C₂²×C₃⋊C₈	C₂³	1	2	yes	—
282	#830	C₂³	1	2	yes	—
283	#830	C₂³	1	1	yes	characteristic
284	#830	C₂³	1	1	yes	characteristic
285	#830	C₂³	1	2	yes	—
286	#830	C₂³	1	1	yes	characteristic
287	#830	C₂³	1	2	yes	—
288	#830	C₂³	1	1	yes	characteristic
289	#830	C₂³	1	1	yes	characteristic
290	#830	C₂³	1	1	yes	characteristic
291	#830	C₂³	1	2	yes	—
292	#830	C₂³	1	2	yes	—
293	#830	C₂³	1	2	yes	—
294	#830	C₂³	1	2	yes	—
295	#830	C₂³	1	2	yes	—
296	#830	C₂³	1	2	yes	—
297	#830	C₂³	1	2	yes	—
298	#830	C₂³	1	2	yes	—
299	#830	C₂³	1	2	yes	—
300	#830	C₂³	1	2	yes	—
301	#830	C₂³	1	2	yes	—
302	#830	C₂³	1	2	yes	—
303	C₄⋊(C₃⋊C₈)	C₂³	1	1	yes	characteristic
304	C₄⋊(C₃⋊C₈)	C₂³	1	2	yes	—
305	C₄⋊(C₃⋊C₈)	C₂³	1	1	yes	characteristic
306	C₄⋊(C₃⋊C₈)	C₂³	1	1	yes	characteristic
307	C₄⋊(C₃⋊C₈)	C₂³	1	1	yes	characteristic
308	C₄⋊(C₃⋊C₈)	C₂³	1	2	yes	—
309	C₄⋊(C₃⋊C₈)	C₂³	1	2	yes	—
310	C₄⋊(C₃⋊C₈)	C₂³	1	2	yes	—
311	C₄⋊(C₃⋊C₈)	C₂³	1	2	yes	—
312	C₄⋊(C₃⋊C₈)	C₂³	1	1	yes	characteristic
313	C₄⋊(C₃⋊C₈)	C₂³	1	1	yes	characteristic
314	C₄⋊(C₃⋊C₈)	C₂³	1	1	yes	characteristic
315	C₄⋊(C₃⋊C₈)	C₂³	1	1	yes	characteristic
316	C₄⋊(C₃⋊C₈)	C₂³	1	1	yes	characteristic
317	C₄⋊(C₃⋊C₈)	C₂³	1	1	yes	characteristic
318	C₄⋊(C₃⋊C₈)	C₂³	1	2	yes	—
319	C₄⋊(C₃⋊C₈)	C₂³	1	2	yes	—
320	#803	C₂³	1	1	yes	characteristic
321	#803	C₂³	1	2	yes	—
322	#803	C₂³	1	2	yes	—
323	#803	C₂³	1	2	yes	—
324	#803	C₂³	1	1	yes	characteristic
325	#803	C₂³	1	1	yes	characteristic
326	#803	C₂³	1	1	yes	characteristic
327	#803	C₂³	1	2	yes	—
328	C₄×C₃⋊C₈	C₂³	1	1	yes	characteristic
329	C₄×C₃⋊C₈	C₂³	1	1	yes	characteristic
330	C₄×C₃⋊C₈	C₂³	1	1	yes	characteristic
331	C₄×C₃⋊C₈	C₂³	1	1	yes	characteristic
332	C₄×C₃⋊C₈	C₂³	1	1	yes	characteristic
333	C₄×C₃⋊C₈	C₂³	1	1	yes	characteristic
334	C₄×C₃⋊C₈	C₂³	1	2	yes	—
335	C₄×C₃⋊C₈	C₂³	1	2	yes	—
336	C₄×C₃⋊C₈	C₂³	1	2	yes	—
337	C₂×#131	—	3	2	no	—
338	C₂²×M₁₆	—	3	2	no	—
339	C₂³×C₈	—	3	2	no	—
340	#559	Dic₃	1	1	yes	characteristic
341	#554	Dic₃	1	1	yes	characteristic
342	#554	Dic₃	1	1	yes	characteristic
343	#553	Dic₃	1	1	yes	characteristic
344	#553	Dic₃	1	1	yes	characteristic
345	#553	Dic₃	1	2	yes	—
346	#551	Dic₃	1	2	yes	—
347	#551	Dic₃	1	2	yes	—
348	#546	Dic₃	1	1	yes	characteristic
349	#546	Dic₃	1	1	yes	characteristic
350	#546	Dic₃	1	2	yes	—
351	D₄²	Dic₃	1	1	yes	characteristic
352	#532	C₂×D₃	1	1	yes	characteristic
353	#529	C₂×D₃	1	1	yes	characteristic
354	#529	C₂×D₃	1	2	yes	—
355	#529	C₂×D₃	1	1	yes	characteristic
356	#525	C₂×D₃	1	2	yes	—
357	#525	C₂×D₃	1	2	yes	—
358	C₄×#41	C₂×D₃	1	1	yes	characteristic
359	C₄×#41	C₂×D₃	1	1	yes	characteristic
360	C₂×C₄×D₄	C₂×D₃	1	1	yes	characteristic
361	C₂×C₄×D₄	C₂×D₃	1	2	yes	—
362	C₂×C₄×D₄	C₂×D₃	1	1	yes	characteristic
363	#446	—	3	1	no	—
364	#446	—	3	1	no	—
365	#446	—	3	1	no	—
366	#446	—	3	2	no	—
367	#446	—	3	1	no	—
368	C₈×Q₈	—	3	1	no	—
369	C₈×Q₈	—	3	1	no	—
370	#436	—	3	1	no	—
371	#436	—	3	2	no	—
372	#436	—	3	1	no	—
373	#436	—	3	1	no	—
374	#436	—	3	1	no	—
375	#436	—	3	1	no	—
376	#436	—	3	2	no	—
377	#436	—	3	1	no	—
378	#435	—	3	1	no	—
379	#435	—	3	2	no	—
380	#435	—	3	2	no	—
381	#435	—	3	2	no	—
382	#435	—	3	2	no	—
383	#435	—	3	2	no	—
384	#435	—	3	2	no	—
385	#435	—	3	2	no	—
386	#435	—	3	1	no	—
387	#435	—	3	2	no	—
388	#435	—	3	2	no	—
389	#435	—	3	2	no	—
390	#435	—	3	2	no	—
391	#435	—	3	2	no	—
392	#435	—	3	2	no	—
393	#435	—	3	1	no	—
394	#435	—	3	1	no	—
395	#435	—	3	2	no	—
396	#435	—	3	2	no	—
397	#435	—	3	2	no	—
398	C₈×D₄	—	3	2	no	—
399	C₈×D₄	—	3	1	no	—
400	C₈×D₄	—	3	1	no	—
401	C₈×D₄	—	3	1	no	—
402	C₈×D₄	—	3	2	no	—
403	C₈×D₄	—	3	1	no	—
404	C₈×D₄	—	3	2	no	—
405	C₈×D₄	—	3	2	no	—
406	C₈×D₄	—	3	2	no	—
407	C₈×D₄	—	3	2	no	—
408	C₈×D₄	—	3	2	no	—
409	C₈×D₄	—	3	1	no	—
410	C₈×D₄	—	3	1	no	—
411	C₈×D₄	—	3	1	no	—
412	C₈×D₄	—	3	1	no	—
413	C₈×D₄	—	3	2	no	—
414	C₈×D₄	—	3	2	no	—
415	#433	—	3	2	no	—
416	#433	—	3	2	no	—
417	#433	—	3	2	no	—
418	#433	—	3	2	no	—
419	#432	—	3	1	no	—
420	#432	—	3	2	no	—
421	#432	—	3	1	no	—
422	#431	—	3	1	no	—
423	#431	—	3	1	no	—
424	#431	—	3	1	no	—
425	#431	—	3	2	no	—
426	#431	—	3	1	no	—
427	#424	—	3	2	no	—
428	#424	—	3	2	no	—
429	#423	—	3	1	no	—
430	C₂×C₄⋊C₈	—	3	1	no	—
431	C₂×C₄⋊C₈	—	3	2	no	—
432	C₂×C₄⋊C₈	—	3	1	no	—
433	#408	—	3	2	no	—
434	#408	—	3	2	no	—
435	#408	—	3	2	no	—
436	#407	—	3	2	no	—
437	#407	—	3	2	no	—
438	C₂×C₂²⋊C₈	—	3	2	no	—
439	C₂×C₂²⋊C₈	—	3	2	no	—
440	C₂×C₂²⋊C₈	—	3	2	no	—
441	C₂×C₂²⋊C₈	—	3	2	no	—
442	#405	—	3	2	no	—
443	#405	—	3	2	no	—
444	C₄×M₁₆	—	3	1	no	—
445	C₄×M₁₆	—	3	1	no	—
446	C₂×#97	—	3	2	no	—
447	C₂×C₄×C₈	—	3	1	no	—
448	C₂⁴×C₃	C₂²×C₄	1	2	yes	—
449	C₂⁴×C₃	C₂²×C₄	1	2	yes	—
450	C₃×#41	—	2	4	no	—
451	C₃×#41	—	4	2	no	—
452	C₃×#41	—	4	2	no	—
453	C₃×#41	—	4	2	no	—
454	C₂×C₃×Q₈	C₂²×C₄	1	1	yes	characteristic
455	C₂×C₃×Q₈	C₂²×C₄	1	1	yes	characteristic
456	C₂×C₃×Q₈	C₂²×C₄	1	2	yes	—
457	C₂×C₃×D₄	—	2	4	no	—
458	C₂×C₃×D₄	—	2	4	no	—
459	C₂×C₃×D₄	—	4	4	no	—
460	C₂×C₃×D₄	C₂²×C₄	1	1	yes	characteristic
461	C₂×C₃×D₄	C₂²×C₄	1	2	yes	—
462	C₂×C₃×D₄	C₂²×C₄	1	1	yes	characteristic
463	C₂×C₃×D₄	C₂²×C₄	1	2	yes	—
464	C₂×C₃×D₄	C₂²×C₄	1	2	yes	—
465	C₂×C₃×D₄	C₂²×C₄	1	2	yes	—
466	C₂×C₃×D₄	C₂²×C₄	1	1	yes	characteristic
467	C₂×C₃×D₄	C₂²×C₄	1	1	yes	characteristic
468	C₂×C₃×D₄	C₂²×C₄	1	1	yes	characteristic
469	C₂×C₃×D₄	C₂²×C₄	1	2	yes	—
470	C₂×C₃×D₄	C₂²×C₄	1	2	yes	—
471	C₂×C₃×D₄	C₂²×C₄	1	2	yes	—
472	C₂×C₃×D₄	C₂²×C₄	1	2	yes	—
473	C₂×C₃×D₄	C₂²×C₄	1	2	yes	—
474	C₂×C₃×D₄	C₂²×C₄	1	1	yes	characteristic
475	C₂²×C₃×C₄	—	4	2	no	—
476	C₂²×C₃×C₄	—	4	2	no	—
477	C₂²×C₃×C₄	—	4	2	no	—
478	C₂²×C₃×C₄	—	4	2	no	—
479	C₂²×C₃×C₄	C₂²×C₄	1	2	yes	—
480	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
481	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
482	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
483	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
484	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
485	C₂²×C₃×C₄	C₂²×C₄	1	2	yes	—
486	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
487	C₂²×C₃×C₄	C₂²×C₄	1	2	yes	—
488	C₂²×C₃×C₄	C₂²×C₄	1	2	yes	—
489	C₂²×C₃×C₄	C₂²×C₄	1	2	yes	—
490	C₂²×C₃×C₄	C₂²×C₄	1	2	yes	—
491	C₂²×C₃×C₄	C₂²×C₄	1	2	yes	—
492	C₂²×C₃×C₄	C₂²×C₄	1	2	yes	—
493	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
494	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
495	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
496	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
497	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
498	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
499	C₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
500	C₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
501	C₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
502	C₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
503	C₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
504	C₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
505	C₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
506	C₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
507	C₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
508	C₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
509	C₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
510	C₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
511	C₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
512	C₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
513	C₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
514	C₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
515	C₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
516	C₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
517	C₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
518	C₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
519	C₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
520	C₃×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
521	C₃×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
522	C₃×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
523	C₃×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
524	C₃×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
525	C₃×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
526	C₃×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
527	C₃×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
528	C₃×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
529	C₃×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
530	C₃×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
531	C₃×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
532	C₃×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
533	C₃×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
534	C₃×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
535	C₃×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
536	C₃×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
537	C₃×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
538	C₃×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
539	C₃×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
540	C₃×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
541	C₃×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
542	C₃×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
543	C₃×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
544	C₃×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
545	C₃×C₄²	C₂²×C₄	1	1	yes	characteristic
546	C₃×C₄²	C₂²×C₄	1	1	yes	characteristic
547	C₃×C₄²	C₂²×C₄	1	2	yes	—
548	C₃×C₄²	C₂²×C₄	1	1	yes	characteristic
549	C₃×C₄²	C₂²×C₄	1	2	yes	—
550	C₃×C₄²	C₂²×C₄	1	1	yes	characteristic
551	C₃×C₄²	C₂²×C₄	1	1	yes	characteristic
552	C₃×C₄²	C₂²×C₄	1	1	yes	characteristic
553	C₃×C₄²	C₂⁴	1	1	yes	characteristic
554	C₃×C₄²	C₂⁴	1	1	yes	characteristic
555	C₃×C₄²	C₂⁴	1	1	yes	characteristic
556	C₃×C₄²	C₂⁴	1	2	yes	—
557	C₃×C₄²	C₂⁴	1	1	yes	characteristic
558	#208	—	2	2	no	—
559	#208	—	2	4	no	—
560	#208	—	2	2	no	—
561	#208	—	4	2	no	—
562	#208	—	4	2	no	—
563	#208	—	4	1	no	—
564	#208	—	4	2	no	—
565	#208	—	4	1	no	—
566	#208	—	4	2	no	—
567	C₂×C₃⋊C₈	—	2	2	no	—
568	C₂×C₃⋊C₈	—	2	4	no	—
569	C₂×C₃⋊C₈	—	2	4	no	—
570	C₂×C₃⋊C₈	—	4	2	no	—
571	C₂×C₃⋊C₈	—	4	2	no	—
572	C₂×C₃⋊C₈	—	4	2	no	—
573	C₂×C₃⋊C₈	—	4	2	no	—
574	C₂×C₃⋊C₈	—	4	1	no	—
575	C₂×C₃⋊C₈	—	4	2	no	—
576	C₂×C₃⋊C₈	—	4	2	no	—
577	C₂×C₃⋊C₈	—	4	2	no	—
578	C₂×C₃⋊C₈	—	4	2	no	—
579	C₂×C₃⋊C₈	C₂⁴	1	1	yes	characteristic
580	C₂×C₃⋊C₈	C₂⁴	1	1	yes	characteristic
581	C₂×C₃⋊C₈	C₂⁴	1	1	yes	characteristic
582	C₂×C₃⋊C₈	C₂⁴	1	1	yes	characteristic
583	C₂×C₃⋊C₈	C₂⁴	1	2	yes	—
584	C₂×C₃⋊C₈	C₂⁴	1	1	yes	characteristic
585	C₂×C₃⋊C₈	C₂⁴	1	2	yes	—
586	C₂×C₃⋊C₈	C₂⁴	1	1	yes	characteristic
587	C₂×C₃⋊C₈	C₂⁴	1	1	yes	characteristic
588	C₂×C₃⋊C₈	C₂⁴	1	2	yes	—
589	C₂×C₃⋊C₈	C₂⁴	1	2	yes	—
590	C₂×C₃⋊C₈	C₂⁴	1	1	yes	characteristic
591	C₂×#41	C₂×Dic₃	1	1	yes	characteristic
592	C₂×#41	C₂×Dic₃	1	1	yes	characteristic
593	C₂×#41	C₂²×D₃	1	2	yes	—
594	C₂²×D₄	C₂×Dic₃	1	1	yes	characteristic
595	C₂²×D₄	C₂×Dic₃	1	1	yes	characteristic
596	C₂²×D₄	C₂×Dic₃	1	2	yes	—
597	C₂³×C₄	C₂²×D₃	1	2	yes	—
598	C₂³×C₄	C₂²×D₃	1	2	yes	—
599	#131	—	12	4	no	—
600	C₂×M₁₆	—	3	1	no	—
601	C₂×M₁₆	—	3	2	no	—
602	C₂×M₁₆	—	3	1	no	—
603	C₂×M₁₆	—	3	2	no	—
604	C₂×M₁₆	—	3	2	no	—
605	C₂×M₁₆	—	3	2	no	—
606	C₂×M₁₆	—	3	1	no	—
607	C₂×M₁₆	—	3	1	no	—
608	C₂×M₁₆	—	3	2	no	—
609	C₂×M₁₆	—	12	4	no	—
610	C₂²×C₈	—	3	1	no	—
611	C₂²×C₈	—	3	2	no	—
612	C₂²×C₈	—	3	2	no	—
613	C₂²×C₈	—	3	2	no	—
614	C₂²×C₈	—	3	2	no	—
615	C₂²×C₈	—	3	2	no	—
616	C₂²×C₈	—	3	2	no	—
617	C₂²×C₈	—	3	2	no	—
618	C₂²×C₈	—	3	2	no	—
619	C₂²×C₈	—	3	1	no	—
620	C₂²×C₈	—	3	2	no	—
621	C₂²×C₈	—	3	2	no	—
622	C₂²×C₈	—	12	4	no	—
623	C₄⋊Q₈	C₂×Dic₃	1	1	yes	characteristic
624	#127	C₂×Dic₃	1	1	yes	characteristic
625	#126	C₂×Dic₃	1	2	yes	—
626	#126	C₂×Dic₃	1	2	yes	—
627	#126	C₂×Dic₃	1	2	yes	—
628	#126	C₂×Dic₃	1	2	yes	—
629	#125	C₂×Dic₃	1	1	yes	characteristic
630	#125	C₂×Dic₃	1	2	yes	—
631	#125	C₂×Dic₃	1	1	yes	characteristic
632	#124	C₂×Dic₃	1	1	yes	characteristic
633	#124	C₂×Dic₃	1	1	yes	characteristic
634	#124	C₂×Dic₃	1	2	yes	—
635	#124	C₂×Dic₃	1	2	yes	—
636	#123	C₂×Dic₃	1	2	yes	—
637	#123	C₂×Dic₃	1	2	yes	—
638	#123	C₂×Dic₃	1	2	yes	—
639	#123	C₂×Dic₃	1	2	yes	—
640	#123	C₂×Dic₃	1	2	yes	—
641	#123	C₂×Dic₃	1	2	yes	—
642	#123	C₂×Dic₃	1	2	yes	—
643	#123	C₂×Dic₃	1	2	yes	—
644	C₂²⋊Q₈	C₂×Dic₃	1	2	yes	—
645	C₂²⋊Q₈	C₂×Dic₃	1	2	yes	—
646	C₂²⋊Q₈	C₂×Dic₃	1	2	yes	—
647	C₂²⋊Q₈	C₂×Dic₃	1	2	yes	—
648	C₂²⋊Q₈	C₂×Dic₃	1	1	yes	characteristic
649	C₂²⋊Q₈	C₂×Dic₃	1	1	yes	characteristic
650	C₂²⋊Q₈	C₂×Dic₃	1	2	yes	—
651	#121	C₂×Dic₃	1	2	yes	—
652	#121	C₂×Dic₃	1	2	yes	—
653	#121	C₂×Dic₃	1	2	yes	—
654	#121	C₂×Dic₃	1	2	yes	—
655	#121	C₂×Dic₃	1	1	yes	characteristic
656	#121	C₂×Dic₃	1	1	yes	characteristic
657	#121	C₂×Dic₃	1	2	yes	—
658	#121	C₂×Dic₃	1	1	yes	characteristic
659	#121	C₂×Dic₃	1	1	yes	characteristic
660	#121	C₂×Dic₃	1	2	yes	—
661	#120	C₂×Dic₃	1	2	yes	—
662	#120	C₂×Dic₃	1	2	yes	—
663	#120	C₂×Dic₃	1	2	yes	—
664	#120	C₂×Dic₃	1	2	yes	—
665	C₄×Q₈	C₂×Dic₃	1	1	yes	characteristic
666	C₄×Q₈	C₂×Dic₃	1	1	yes	characteristic
667	C₄×Q₈	C₂²×D₃	1	1	yes	characteristic
668	C₄×Q₈	C₂²×D₃	1	1	yes	characteristic
669	C₄×D₄	C₂×Dic₃	1	2	yes	—
670	C₄×D₄	C₂×Dic₃	1	1	yes	characteristic
671	C₄×D₄	C₂×Dic₃	1	1	yes	characteristic
672	C₄×D₄	C₂×Dic₃	1	2	yes	—
673	C₄×D₄	C₂×Dic₃	1	2	yes	—
674	C₄×D₄	C₂×Dic₃	1	2	yes	—
675	C₄×D₄	C₂×Dic₃	1	2	yes	—
676	C₄×D₄	C₂×Dic₃	1	1	yes	characteristic
677	C₄×D₄	C₂×Dic₃	1	1	yes	characteristic
678	C₄×D₄	C₂×Dic₃	1	2	yes	—
679	C₄×D₄	C₂×Dic₃	1	1	yes	characteristic
680	C₄×D₄	C₂×Dic₃	1	1	yes	characteristic
681	C₄×D₄	C₂×Dic₃	1	1	yes	characteristic
682	C₄×D₄	C₂×Dic₃	1	1	yes	characteristic
683	C₄×D₄	C₂×Dic₃	1	2	yes	—
684	C₄×D₄	C₂²×D₃	1	1	yes	characteristic
685	C₄×D₄	C₂²×D₃	1	1	yes	characteristic
686	C₄×D₄	C₂²×D₃	1	2	yes	—
687	C₄×D₄	C₂²×D₃	1	2	yes	—
688	C₄×D₄	C₂²×D₃	1	2	yes	—
689	C₄×D₄	C₂²×D₃	1	2	yes	—
690	C₄×D₄	C₂²×D₃	1	1	yes	characteristic
691	C₄×D₄	C₂²×D₃	1	1	yes	characteristic
692	C₄×D₄	C₂²×D₃	1	2	yes	—
693	C₄×D₄	C₂²×D₃	1	1	yes	characteristic
694	C₄×D₄	C₂²×D₃	1	2	yes	—
695	C₄×D₄	C₂²×D₃	1	1	yes	characteristic
696	#117	C₂×Dic₃	1	1	yes	characteristic
697	#117	C₂×Dic₃	1	2	yes	—
698	#117	C₂×Dic₃	1	1	yes	characteristic
699	#117	C₂×Dic₃	1	1	yes	characteristic
700	#117	C₂×Dic₃	1	1	yes	characteristic
701	#117	C₂²×D₃	1	2	yes	—
702	#117	C₂²×D₃	1	2	yes	—
703	C₂×C₄⋊C₄	C₂×Dic₃	1	1	yes	characteristic
704	C₂×C₄⋊C₄	C₂×Dic₃	1	1	yes	characteristic
705	C₂×C₄⋊C₄	C₂×Dic₃	1	2	yes	—
706	C₂×C₂²⋊C₄	C₂×Dic₃	1	2	yes	—
707	C₂×C₂²⋊C₄	C₂×Dic₃	1	2	yes	—
708	C₂×C₂²⋊C₄	C₂×Dic₃	1	2	yes	—
709	C₂×C₂²⋊C₄	C₂×Dic₃	1	2	yes	—
710	C₂×C₄²	C₂²×D₃	1	1	yes	characteristic
711	C₂×C₄²	C₂²×D₃	1	2	yes	—
712	C₂×C₄²	C₂²×D₃	1	1	yes	characteristic
713	C₂×C₄²	C₂²×D₃	1	1	yes	characteristic
714	C₄⋊C₈	—	3	1	no	—
715	C₄⋊C₈	—	3	1	no	—
716	C₄⋊C₈	—	3	2	no	—
717	C₄⋊C₈	—	3	1	no	—
718	C₄⋊C₈	—	3	1	no	—
719	C₄⋊C₈	—	3	2	no	—
720	C₄⋊C₈	—	3	2	no	—
721	C₄⋊C₈	—	3	2	no	—
722	C₄⋊C₈	—	3	2	no	—
723	C₄⋊C₈	—	3	1	no	—
724	C₄⋊C₈	—	3	1	no	—
725	C₄⋊C₈	—	3	2	no	—
726	C₄⋊C₈	—	3	1	no	—
727	C₄⋊C₈	—	3	1	no	—
728	C₄⋊C₈	—	3	1	no	—
729	C₄⋊C₈	—	3	1	no	—
730	C₄⋊C₈	—	3	2	no	—
731	C₂²⋊C₈	—	3	2	no	—
732	C₂²⋊C₈	—	3	1	no	—
733	C₂²⋊C₈	—	3	1	no	—
734	C₂²⋊C₈	—	3	2	no	—
735	C₂²⋊C₈	—	3	1	no	—
736	C₂²⋊C₈	—	3	2	no	—
737	C₂²⋊C₈	—	3	2	no	—
738	C₂²⋊C₈	—	3	2	no	—
739	C₂²⋊C₈	—	3	2	no	—
740	C₂²⋊C₈	—	3	2	no	—
741	C₂²⋊C₈	—	3	2	no	—
742	C₂²⋊C₈	—	3	2	no	—
743	C₂²⋊C₈	—	3	2	no	—
744	C₂²⋊C₈	—	3	2	no	—
745	C₂²⋊C₈	—	3	2	no	—
746	C₂²⋊C₈	—	3	1	no	—
747	C₂²⋊C₈	—	3	2	no	—
748	C₂²⋊C₈	—	3	2	no	—
749	C₂²⋊C₈	—	3	1	no	—
750	C₂²⋊C₈	—	3	1	no	—
751	C₂²⋊C₈	—	3	2	no	—
752	#97	—	3	1	no	—
753	#97	—	3	2	no	—
754	#97	—	3	2	no	—
755	#97	—	3	2	no	—
756	#97	—	3	1	no	—
757	#97	—	3	1	no	—
758	#97	—	3	1	no	—
759	#97	—	3	2	no	—
760	C₄×C₈	—	3	1	no	—
761	C₄×C₈	—	3	1	no	—
762	C₄×C₈	—	3	1	no	—
763	C₄×C₈	—	3	1	no	—
764	C₄×C₈	—	3	1	no	—
765	C₄×C₈	—	3	1	no	—
766	C₄×C₈	—	3	2	no	—
767	C₄×C₈	—	3	2	no	—
768	C₄×C₈	—	3	2	no	—
769	C₂³×C₃	—	2	4	no	—
770	C₂³×C₃	—	2	4	no	—
771	C₂³×C₃	—	2	4	no	—
772	C₂³×C₃	—	4	2	no	—
773	C₂³×C₃	—	4	2	no	—
774	C₂³×C₃	—	4	2	no	—
775	C₂³×C₃	C₂³×C₄	1	2	yes	—
776	C₂³×C₃	C₂³×C₄	1	2	yes	—
777	C₂³×C₃	C₂³×C₄	1	1	yes	characteristic
778	C₂³×C₃	C₂³×C₄	1	1	yes	characteristic
779	C₂³×C₃	C₂³×C₄	1	2	yes	—
780	C₂³×C₃	C₂³×C₄	1	1	yes	characteristic
781	C₃×Q₈	—	2	2	no	—
782	C₃×Q₈	—	4	2	no	—
783	C₃×Q₈	—	4	1	no	—
784	C₃×D₄	—	2	4	no	—
785	C₃×D₄	—	2	4	no	—
786	C₃×D₄	—	2	4	no	—
787	C₃×D₄	—	2	2	no	—
788	C₃×D₄	—	2	4	no	—
789	C₃×D₄	—	2	2	no	—
790	C₃×D₄	—	2	2	no	—
791	C₃×D₄	—	2	2	no	—
792	C₃×D₄	—	4	2	no	—
793	C₃×D₄	—	4	2	no	—
794	C₃×D₄	—	4	2	no	—
795	C₃×D₄	—	4	2	no	—
796	C₃×D₄	—	4	2	no	—
797	C₃×D₄	—	4	1	no	—
798	C₃×D₄	#131	1	4	yes	complemented
799	C₂×C₃×C₄	—	2	4	no	—
800	C₂×C₃×C₄	—	2	2	no	—
801	C₂×C₃×C₄	—	2	2	no	—
802	C₂×C₃×C₄	—	2	2	no	—
803	C₂×C₃×C₄	—	2	2	no	—
804	C₂×C₃×C₄	—	2	1	no	—
805	C₂×C₃×C₄	—	2	2	no	—
806	C₂×C₃×C₄	—	2	2	no	—
807	C₂×C₃×C₄	—	2	1	no	—
808	C₂×C₃×C₄	—	2	2	no	—
809	C₂×C₃×C₄	—	2	1	no	—
810	C₂×C₃×C₄	—	2	1	no	—
811	C₂×C₃×C₄	—	2	2	no	—
812	C₂×C₃×C₄	—	2	2	no	—
813	C₂×C₃×C₄	—	2	1	no	—
814	C₂×C₃×C₄	—	2	2	no	—
815	C₂×C₃×C₄	—	2	1	no	—
816	C₂×C₃×C₄	—	4	2	no	—
817	C₂×C₃×C₄	—	4	2	no	—
818	C₂×C₃×C₄	—	4	2	no	—
819	C₂×C₃×C₄	—	4	2	no	—
820	C₂×C₃×C₄	—	4	2	no	—
821	C₂×C₃×C₄	—	4	2	no	—
822	C₂×C₃×C₄	—	4	2	no	—
823	C₂×C₃×C₄	—	4	1	no	—
824	C₂×C₃×C₄	—	4	1	no	—
825	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
826	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
827	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
828	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
829	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
830	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
831	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
832	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
833	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
834	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
835	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
836	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
837	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
838	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
839	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
840	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
841	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
842	C₃⋊C₈	—	2	1	no	—
843	C₃⋊C₈	—	2	2	no	—
844	C₃⋊C₈	—	2	2	no	—
845	C₃⋊C₈	—	2	1	no	—
846	C₃⋊C₈	—	2	2	no	—
847	C₃⋊C₈	—	2	1	no	—
848	C₃⋊C₈	—	2	1	no	—
849	C₃⋊C₈	—	2	2	no	—
850	C₃⋊C₈	—	2	1	no	—
851	C₃⋊C₈	—	2	1	no	—
852	C₃⋊C₈	—	2	1	no	—
853	C₃⋊C₈	H(5,𝔽₂)	1	2	yes	—
854	C₂⁴	C₂²×Dic₃	1	2	yes	—
855	C₂⁴	C₂²×Dic₃	1	2	yes	—
856	#41	—	2	4	no	—
857	#41	—	4	2	no	—
858	#41	—	4	2	no	—
859	#41	—	4	2	no	—
860	C₂×Q₈	C₂²×Dic₃	1	1	yes	characteristic
861	C₂×Q₈	C₂²×Dic₃	1	1	yes	characteristic
862	C₂×Q₈	C₂²×Dic₃	1	2	yes	—
863	C₂×D₄	—	2	4	no	—
864	C₂×D₄	—	2	4	no	—
865	C₂×D₄	—	4	4	no	—
866	C₂×D₄	C₂²×Dic₃	1	1	yes	characteristic
867	C₂×D₄	C₂²×Dic₃	1	2	yes	—
868	C₂×D₄	C₂²×Dic₃	1	1	yes	characteristic
869	C₂×D₄	C₂²×Dic₃	1	2	yes	—
870	C₂×D₄	C₂²×Dic₃	1	2	yes	—
871	C₂×D₄	C₂²×Dic₃	1	2	yes	—
872	C₂×D₄	C₂²×Dic₃	1	1	yes	characteristic
873	C₂×D₄	C₂²×Dic₃	1	1	yes	characteristic
874	C₂×D₄	C₂²×Dic₃	1	1	yes	characteristic
875	C₂×D₄	C₂²×Dic₃	1	2	yes	—
876	C₂×D₄	C₂²×Dic₃	1	2	yes	—
877	C₂×D₄	C₂²×Dic₃	1	2	yes	—
878	C₂×D₄	C₂²×Dic₃	1	2	yes	—
879	C₂×D₄	C₂²×Dic₃	1	2	yes	—
880	C₂×D₄	C₂²×Dic₃	1	1	yes	characteristic
881	C₂²×C₄	—	4	2	no	—
882	C₂²×C₄	—	4	2	no	—
883	C₂²×C₄	—	4	2	no	—
884	C₂²×C₄	—	4	2	no	—
885	C₂²×C₄	C₂²×Dic₃	1	2	yes	—
886	C₂²×C₄	C₂²×Dic₃	1	1	yes	characteristic
887	C₂²×C₄	C₂²×Dic₃	1	1	yes	characteristic
888	C₂²×C₄	C₂²×Dic₃	1	1	yes	characteristic
889	C₂²×C₄	C₂²×Dic₃	1	1	yes	characteristic
890	C₂²×C₄	C₂²×Dic₃	1	1	yes	characteristic
891	C₂²×C₄	C₂²×Dic₃	1	2	yes	—
892	C₂²×C₄	C₂²×Dic₃	1	1	yes	characteristic
893	C₂²×C₄	C₂²×Dic₃	1	2	yes	—
894	C₂²×C₄	C₂²×Dic₃	1	2	yes	—
895	C₂²×C₄	C₂²×Dic₃	1	2	yes	—
896	C₂²×C₄	C₂²×Dic₃	1	2	yes	—
897	C₂²×C₄	C₂²×Dic₃	1	2	yes	—
898	C₂²×C₄	C₂²×Dic₃	1	2	yes	—
899	C₂²×C₄	C₂³×D₃	1	2	yes	—
900	C₂²×C₄	C₂³×D₃	1	1	yes	characteristic
901	C₂²×C₄	C₂³×D₃	1	1	yes	characteristic
902	C₂²×C₄	C₂³×D₃	1	1	yes	characteristic
903	C₂²×C₄	C₂³×D₃	1	2	yes	—
904	C₂²×C₄	C₂³×D₃	1	2	yes	—
905	M₁₆	—	6	2	no	—
906	M₁₆	—	6	4	no	—
907	M₁₆	—	6	2	no	—
908	M₁₆	—	12	2	no	—
909	M₁₆	—	12	2	no	—
910	M₁₆	—	12	2	no	—
911	M₁₆	—	12	1	no	—
912	M₁₆	—	12	2	no	—
913	M₁₆	—	12	1	no	—
914	C₂×C₈	—	3	1	no	—
915	C₂×C₈	—	3	1	no	—
916	C₂×C₈	—	3	1	no	—
917	C₂×C₈	—	3	1	no	—
918	C₂×C₈	—	3	1	no	—
919	C₂×C₈	—	3	2	no	—
920	C₂×C₈	—	3	1	no	—
921	C₂×C₈	—	3	2	no	—
922	C₂×C₈	—	3	1	no	—
923	C₂×C₈	—	3	1	no	—
924	C₂×C₈	—	3	2	no	—
925	C₂×C₈	—	3	2	no	—
926	C₂×C₈	—	6	2	no	—
927	C₂×C₈	—	6	4	no	—
928	C₂×C₈	—	6	4	no	—
929	C₂×C₈	—	12	2	no	—
930	C₂×C₈	—	12	2	no	—
931	C₂×C₈	—	12	2	no	—
932	C₂×C₈	—	12	2	no	—
933	C₂×C₈	—	12	2	no	—
934	C₂×C₈	—	12	2	no	—
935	C₂×C₈	—	12	2	no	—
936	C₂×C₈	—	12	1	no	—
937	C₂×C₈	—	12	2	no	—
938	C₄⋊C₄	C₂²×Dic₃	1	1	yes	characteristic
939	C₄⋊C₄	C₂²×Dic₃	1	1	yes	characteristic
940	C₄⋊C₄	C₂²×Dic₃	1	2	yes	—
941	C₄⋊C₄	C₂²×Dic₃	1	1	yes	characteristic
942	C₄⋊C₄	C₂²×Dic₃	1	1	yes	characteristic
943	C₄⋊C₄	C₂²×Dic₃	1	2	yes	—
944	C₄⋊C₄	C₂²×Dic₃	1	2	yes	—
945	C₄⋊C₄	C₂²×Dic₃	1	2	yes	—
946	C₄⋊C₄	C₂²×Dic₃	1	2	yes	—
947	C₄⋊C₄	C₂²×Dic₃	1	1	yes	characteristic
948	C₄⋊C₄	C₂²×Dic₃	1	1	yes	characteristic
949	C₄⋊C₄	C₂²×Dic₃	1	2	yes	—
950	C₄⋊C₄	C₂²×Dic₃	1	1	yes	characteristic
951	C₄⋊C₄	C₂²×Dic₃	1	1	yes	characteristic
952	C₄⋊C₄	C₂²×Dic₃	1	2	yes	—
953	C₄⋊C₄	C₂²×Dic₃	1	1	yes	characteristic
954	C₄⋊C₄	C₂²×Dic₃	1	1	yes	characteristic
955	C₄⋊C₄	C₂²×Dic₃	1	2	yes	—
956	C₄⋊C₄	C₂²×Dic₃	1	2	yes	—
957	C₄⋊C₄	C₂²×Dic₃	1	2	yes	—
958	C₄⋊C₄	C₂²×Dic₃	1	2	yes	—
959	C₂²⋊C₄	C₂²×Dic₃	1	1	yes	characteristic
960	C₂²⋊C₄	C₂²×Dic₃	1	2	yes	—
961	C₂²⋊C₄	C₂²×Dic₃	1	1	yes	characteristic
962	C₂²⋊C₄	C₂²×Dic₃	1	2	yes	—
963	C₂²⋊C₄	C₂²×Dic₃	1	2	yes	—
964	C₂²⋊C₄	C₂²×Dic₃	1	2	yes	—
965	C₂²⋊C₄	C₂²×Dic₃	1	2	yes	—
966	C₂²⋊C₄	C₂²×Dic₃	1	2	yes	—
967	C₂²⋊C₄	C₂²×Dic₃	1	2	yes	—
968	C₂²⋊C₄	C₂²×Dic₃	1	2	yes	—
969	C₂²⋊C₄	C₂²×Dic₃	1	2	yes	—
970	C₂²⋊C₄	C₂²×Dic₃	1	2	yes	—
971	C₂²⋊C₄	C₂²×Dic₃	1	2	yes	—
972	C₂²⋊C₄	C₂²×Dic₃	1	2	yes	—
973	C₂²⋊C₄	C₂²×Dic₃	1	2	yes	—
974	C₂²⋊C₄	C₂²×Dic₃	1	1	yes	characteristic
975	C₂²⋊C₄	C₂²×Dic₃	1	2	yes	—
976	C₂²⋊C₄	C₂²×Dic₃	1	1	yes	characteristic
977	C₂²⋊C₄	C₂²×Dic₃	1	1	yes	characteristic
978	C₂²⋊C₄	C₂²×Dic₃	1	2	yes	—
979	C₂²⋊C₄	C₂²×Dic₃	1	1	yes	characteristic
980	C₂²⋊C₄	C₂²×Dic₃	1	2	yes	—
981	C₂²⋊C₄	C₂²×Dic₃	1	2	yes	—
982	C₂²⋊C₄	C₂²×Dic₃	1	2	yes	—
983	C₂²⋊C₄	C₂²×Dic₃	1	2	yes	—
984	C₄²	C₂²×Dic₃	1	1	yes	characteristic
985	C₄²	C₂²×Dic₃	1	1	yes	characteristic
986	C₄²	C₂²×Dic₃	1	2	yes	—
987	C₄²	C₂²×Dic₃	1	1	yes	characteristic
988	C₄²	C₂²×Dic₃	1	2	yes	—
989	C₄²	C₂²×Dic₃	1	1	yes	characteristic
990	C₄²	C₂²×Dic₃	1	1	yes	characteristic
991	C₄²	C₂²×Dic₃	1	1	yes	characteristic
992	C₄²	C₂³×D₃	1	1	yes	characteristic
993	C₄²	C₂³×D₃	1	1	yes	characteristic
994	C₄²	C₂³×D₃	1	1	yes	characteristic
995	C₄²	C₂³×D₃	1	2	yes	—
996	C₄²	C₂³×D₃	1	1	yes	characteristic
997	C₂²×C₃	—	2	1	no	—
998	C₂²×C₃	—	2	2	no	—
999	C₂²×C₃	—	2	1	no	—
1000	C₂²×C₃	—	2	2	no	—
1001	C₂²×C₃	—	2	1	no	—
1002	C₂²×C₃	—	2	2	no	—
1003	C₂²×C₃	—	2	2	no	—
1004	C₂²×C₃	—	2	1	no	—
1005	C₂²×C₃	—	2	1	no	—
1006	C₂²×C₃	—	2	1	no	—
1007	C₂²×C₃	—	2	2	no	—
1008	C₂²×C₃	—	2	2	no	—
1009	C₂²×C₃	—	2	1	no	—
1010	C₂²×C₃	—	2	1	no	—
1011	C₂²×C₃	—	2	2	no	—
1012	C₂²×C₃	—	2	2	no	—
1013	C₂²×C₃	—	4	8	no	—
1014	C₂²×C₃	—	8	4	no	—
1015	C₂²×C₃	C₂×#131	1	4	yes	—
1016	C₂²×C₃	#568	1	2	yes	—
1017	C₂²×C₃	C₂⁴×C₄	1	1	yes	characteristic
1018	C₃×C₄	—	2	1	no	—
1019	C₃×C₄	—	2	2	no	—
1020	C₃×C₄	—	2	1	no	—
1021	C₃×C₄	—	2	2	no	—
1022	C₃×C₄	—	2	2	no	—
1023	C₃×C₄	—	2	1	no	—
1024	C₃×C₄	—	2	1	no	—
1025	C₃×C₄	—	2	1	no	—
1026	C₃×C₄	—	2	1	no	—
1027	C₃×C₄	—	2	2	no	—
1028	C₃×C₄	—	2	1	no	—
1029	C₃×C₄	—	2	1	no	—
1030	C₃×C₄	—	2	1	no	—
1031	C₃×C₄	—	2	2	no	—
1032	C₃×C₄	—	2	1	no	—
1033	C₃×C₄	C₂×#131	1	2	yes	—
1034	C₃×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1035	C₃×C₄	#585	1	1	yes	characteristic
1036	C₂³	—	2	4	no	—
1037	C₂³	—	2	4	no	—
1038	C₂³	—	2	4	no	—
1039	C₂³	—	4	2	no	—
1040	C₂³	—	4	2	no	—
1041	C₂³	—	4	2	no	—
1042	C₂³	C₂³×Dic₃	1	2	yes	—
1043	C₂³	C₂³×Dic₃	1	2	yes	—
1044	C₂³	C₂³×Dic₃	1	1	yes	characteristic
1045	C₂³	C₂³×Dic₃	1	1	yes	characteristic
1046	C₂³	C₂³×Dic₃	1	2	yes	—
1047	C₂³	C₂³×Dic₃	1	1	yes	characteristic
1048	Q₈	—	2	2	no	—
1049	Q₈	—	4	1	no	—
1050	Q₈	—	4	2	no	—
1051	D₄	—	2	4	no	—
1052	D₄	—	2	4	no	—
1053	D₄	—	2	4	no	—
1054	D₄	—	2	2	no	—
1055	D₄	—	2	4	no	—
1056	D₄	—	2	2	no	—
1057	D₄	—	2	2	no	—
1058	D₄	—	2	2	no	—
1059	D₄	—	4	2	no	—
1060	D₄	—	4	2	no	—
1061	D₄	—	4	1	no	—
1062	D₄	—	4	2	no	—
1063	D₄	—	4	2	no	—
1064	D₄	—	4	2	no	—
1065	D₄	#948	1	4	yes	complemented
1066	C₂×C₄	—	2	4	no	—
1067	C₂×C₄	—	2	2	no	—
1068	C₂×C₄	—	2	1	no	—
1069	C₂×C₄	—	2	2	no	—
1070	C₂×C₄	—	2	2	no	—
1071	C₂×C₄	—	2	1	no	—
1072	C₂×C₄	—	2	2	no	—
1073	C₂×C₄	—	2	1	no	—
1074	C₂×C₄	—	2	1	no	—
1075	C₂×C₄	—	2	2	no	—
1076	C₂×C₄	—	2	2	no	—
1077	C₂×C₄	—	2	1	no	—
1078	C₂×C₄	—	2	2	no	—
1079	C₂×C₄	—	2	1	no	—
1080	C₂×C₄	—	2	2	no	—
1081	C₂×C₄	—	2	2	no	—
1082	C₂×C₄	—	2	2	no	—
1083	C₂×C₄	—	4	2	no	—
1084	C₂×C₄	—	4	2	no	—
1085	C₂×C₄	—	4	2	no	—
1086	C₂×C₄	—	4	2	no	—
1087	C₂×C₄	—	4	2	no	—
1088	C₂×C₄	—	4	2	no	—
1089	C₂×C₄	—	4	2	no	—
1090	C₂×C₄	—	4	1	no	—
1091	C₂×C₄	—	4	1	no	—
1092	C₂×C₄	C₂³×Dic₃	1	1	yes	characteristic
1093	C₂×C₄	C₂³×Dic₃	1	1	yes	characteristic
1094	C₂×C₄	C₂³×Dic₃	1	1	yes	characteristic
1095	C₂×C₄	C₂³×Dic₃	1	1	yes	characteristic
1096	C₂×C₄	C₂³×Dic₃	1	2	yes	—
1097	C₂×C₄	C₂³×Dic₃	1	1	yes	characteristic
1098	C₂×C₄	C₂³×Dic₃	1	1	yes	characteristic
1099	C₂×C₄	C₂³×Dic₃	1	2	yes	—
1100	C₂×C₄	C₂³×Dic₃	1	1	yes	characteristic
1101	C₂×C₄	C₂³×Dic₃	1	1	yes	characteristic
1102	C₂×C₄	C₂³×Dic₃	1	1	yes	characteristic
1103	C₂×C₄	C₂³×Dic₃	1	1	yes	characteristic
1104	C₂×C₄	C₂³×Dic₃	1	2	yes	—
1105	C₂×C₄	C₂³×Dic₃	1	2	yes	—
1106	C₂×C₄	C₂³×Dic₃	1	2	yes	—
1107	C₂×C₄	C₂³×Dic₃	1	1	yes	characteristic
1108	C₂×C₄	C₂⁴×D₃	1	1	yes	characteristic
1109	C₈	—	3	2	no	—
1110	C₈	—	6	1	no	—
1111	C₈	—	6	2	no	—
1112	C₈	—	6	2	no	—
1113	C₈	—	6	1	no	—
1114	C₈	—	6	2	no	—
1115	C₈	—	6	1	no	—
1116	C₈	—	6	1	no	—
1117	C₈	—	6	1	no	—
1118	C₈	—	6	2	no	—
1119	C₈	—	6	1	no	—
1120	C₈	—	6	1	no	—
1121	C₂×C₃	—	2	2	no	—
1122	C₂×C₃	—	2	4	no	—
1123	C₂×C₃	—	4	1	no	—
1124	C₂×C₃	—	4	2	no	—
1125	C₂×C₃	—	4	2	no	—
1126	C₂×C₃	—	4	1	no	—
1127	C₂×C₃	C₄×H(5,𝔽₂)	1	1	yes	characteristic
1128	C₂×C₃	C₂²×#131	1	1	yes	characteristic
1129	C₂×C₃	C₂×#568	1	1	yes	characteristic
1130	C₂²	—	2	1	no	—
1131	C₂²	—	2	2	no	—
1132	C₂²	—	2	1	no	—
1133	C₂²	—	2	2	no	—
1134	C₂²	—	2	1	no	—
1135	C₂²	—	2	1	no	—
1136	C₂²	—	2	2	no	—
1137	C₂²	—	2	2	no	—
1138	C₂²	—	2	1	no	—
1139	C₂²	—	2	1	no	—
1140	C₂²	—	2	2	no	—
1141	C₂²	—	2	2	no	—
1142	C₂²	—	2	1	no	—
1143	C₂²	—	2	2	no	—
1144	C₂²	—	2	2	no	—
1145	C₂²	—	2	1	no	—
1146	C₂²	—	4	8	no	—
1147	C₂²	—	8	4	no	—
1148	C₂²	C₂×#948	1	4	yes	—
1149	C₂²	#5819	1	2	yes	—
1150	C₂²	C₂⁴×Dic₃	1	1	yes	characteristic
1151	C₄	—	2	1	no	—
1152	C₄	—	2	1	no	—
1153	C₄	—	2	1	no	—
1154	C₄	—	2	2	no	—
1155	C₄	—	2	1	no	—
1156	C₄	—	2	1	no	—
1157	C₄	—	2	1	no	—
1158	C₄	—	2	2	no	—
1159	C₄	—	2	1	no	—
1160	C₄	—	2	1	no	—
1161	C₄	—	2	2	no	—
1162	C₄	—	2	1	no	—
1163	C₄	—	2	2	no	—
1164	C₄	—	2	2	no	—
1165	C₄	—	2	1	no	—
1166	C₄	C₂×#948	1	2	yes	—
1167	C₄	D₃×H(5,𝔽₂)	1	1	yes	characteristic
1168	C₄	#5966	1	1	yes	characteristic
1169	C₃	#60311	1	1	yes	characteristic, complemented, Sylow
1170	C₂	—	2	2	no	—
1171	C₂	—	2	4	no	—
1172	C₂	—	4	2	no	—
1173	C₂	—	4	1	no	—
1174	C₂	—	4	2	no	—
1175	C₂	—	4	1	no	—
1176	C₂	C₂²×#948	1	1	yes	characteristic
1177	C₂	C₂×#5819	1	1	yes	characteristic
1178	C₂	Dic₃×H(5,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂⁴×D₃
commutator, socle	C₂²×C₃	C₂⁴×C₄
Fitting, prime radical	C₃×#3481	C₂
cosocle	C₂×C₃×C₄	C₂⁵
hypercenter	#3481	D₃
hypocenter	C₃	#60311
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄ ◁ #3481

Complements

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

N	H ≅ G/N	type
2. #83280	C₂	semidirect
3. #83277	C₂	semidirect
4. #83132	C₂	semidirect
5. #83131	C₂	semidirect
6. #83130	C₂	semidirect
7. #83129	C₂	semidirect
8. #83128	C₂	semidirect
9. #83126	C₂	semidirect
10. #82920	C₂	semidirect
11. #82919	C₂	semidirect
12. #82918	C₂	semidirect
13. #82916	C₂	semidirect
14. #82522	C₂	semidirect
15. #82520	C₂	semidirect
16. #82518	C₂	semidirect
17. #82517	C₂	semidirect
18. #82303	C₂	semidirect
19. #82303	C₂	semidirect
20. #82301	C₂	semidirect
21. D₄×#208	C₂	semidirect
22. C₂×#5011	C₂	semidirect
23. C₂×D₄×C₃⋊C₈	C₂	semidirect
48. C₂×#948	C₂²	semidirect
49. C₂²×#208	C₂²	semidirect
50. C₂³×C₃⋊C₈	C₂²	semidirect
51. #5234	C₂²	semidirect
52. #5234	C₂²	semidirect
53. #5234	C₂²	semidirect
54. #5207	C₂²	semidirect
55. #5207	C₂²	semidirect
56. C₂×#830	C₂²	semidirect
57. C₂×#830	C₂²	semidirect
58. C₂×#830	C₂²	semidirect
59. C₂×#830	C₂²	semidirect
60. #5024	C₂²	semidirect
61. #5024	C₂²	semidirect
62. #5024	C₂²	semidirect
63. #5024	C₂²	semidirect
64. #5024	C₂²	semidirect
65. Q₈×C₃⋊C₈	C₂²	semidirect
66. Q₈×C₃⋊C₈	C₂²	semidirect
67. #5012	C₂²	semidirect
68. #5012	C₂²	semidirect
69. #5012	C₂²	semidirect
70. #5012	C₂²	semidirect
71. #5012	C₂²	semidirect
72. #5012	C₂²	semidirect
73. #5012	C₂²	semidirect
74. #5012	C₂²	semidirect
78. #5011	C₂²	semidirect
79. #5011	C₂²	semidirect
80. #5011	C₂²	semidirect
81. #5011	C₂²	semidirect
82. #5011	C₂²	semidirect
83. #5011	C₂²	semidirect
84. #5011	C₂²	semidirect
85. #5011	C₂²	semidirect
86. #5011	C₂²	semidirect
87. #5011	C₂²	semidirect
88. #5011	C₂²	semidirect
89. #5011	C₂²	semidirect
90. #5011	C₂²	semidirect
91. #5011	C₂²	semidirect
92. #5011	C₂²	semidirect
93. #5011	C₂²	semidirect
94. #5011	C₂²	semidirect
99. D₄×C₃⋊C₈	C₂²	semidirect
100. D₄×C₃⋊C₈	C₂²	semidirect
101. D₄×C₃⋊C₈	C₂²	semidirect
102. D₄×C₃⋊C₈	C₂²	semidirect
103. D₄×C₃⋊C₈	C₂²	semidirect
104. D₄×C₃⋊C₈	C₂²	semidirect
105. D₄×C₃⋊C₈	C₂²	semidirect
106. D₄×C₃⋊C₈	C₂²	semidirect
107. D₄×C₃⋊C₈	C₂²	semidirect
108. D₄×C₃⋊C₈	C₂²	semidirect
109. D₄×C₃⋊C₈	C₂²	semidirect
110. D₄×C₃⋊C₈	C₂²	semidirect
111. D₄×C₃⋊C₈	C₂²	semidirect
112. #5000	C₂²	semidirect
113. #5000	C₂²	semidirect
114. #5000	C₂²	semidirect
115. #5000	C₂²	semidirect
116. #4999	C₂²	semidirect
117. #4999	C₂²	semidirect
118. #4997	C₂²	semidirect
119. #4997	C₂²	semidirect
120. #4926	C₂²	semidirect
121. #4926	C₂²	semidirect
122. #4926	C₂²	semidirect
123. #4925	C₂²	semidirect
124. #4925	C₂²	semidirect
125. #4925	C₂²	semidirect
126. #4925	C₂²	semidirect
127. #4925	C₂²	semidirect
128. #4924	C₂²	semidirect
129. C₂×C₄⋊(C₃⋊C₈)	C₂²	semidirect
130. C₂×C₄⋊(C₃⋊C₈)	C₂²	semidirect
131. C₂×C₄⋊(C₃⋊C₈)	C₂²	semidirect
132. C₄×#208	C₂²	semidirect
133. C₄×#208	C₂²	semidirect
134. C₂×#803	C₂²	semidirect
135. C₂×C₄×C₃⋊C₈	C₂²	semidirect
798. C₃×D₄	#131	semidirect
1065. D₄	#948	semidirect
1169. C₃	#60311	semidirect

Maximal subgroups

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

subgroup	index
C₃×#3481	2
#83280	2
#83277	2
#83132	2
#83131	2
#83130	2
#83129	2
#83128	2
#83126	2
#82920	2
#82919	2
#82918	2
#82916	2
#82522	2
#82520	2
#82518	2
#82517	2
#82303	2
#82301	2
D₄×#208	2
C₂×#5011	2
C₂×D₄×C₃⋊C₈	2
#60311	3