Subgroups — #11660834

Order 768.

1716 conjugacy classes of subgroups.

The subgroup lattice has 1122 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#3480	C₂	1	1	yes	maximal, characteristic
2	#83280	C₂	1	1	yes	maximal, characteristic, complemented
3	#83280	C₂	1	2	yes	maximal, complemented
4	#83279	C₂	1	2	yes	maximal, complemented
5	#83278	C₂	1	1	yes	maximal, characteristic, complemented
6	#83133	C₂	1	2	yes	maximal, complemented
7	#83132	C₂	1	1	yes	maximal, characteristic, complemented
8	#83131	C₂	1	1	yes	maximal, characteristic, complemented
9	#83130	C₂	1	2	yes	maximal, complemented
10	#83129	C₂	1	1	yes	maximal, characteristic, complemented
11	#83128	C₂	1	2	yes	maximal, complemented
12	#83127	C₂	1	2	yes	maximal, complemented
13	#83126	C₂	1	1	yes	maximal, characteristic, complemented
14	#82522	C₂	1	1	yes	maximal, characteristic, complemented
15	#82521	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	#82515	C₂	1	1	yes	maximal, characteristic, complemented
19	#82515	C₂	1	2	yes	maximal, complemented
20	#82514	C₂	1	2	yes	maximal, complemented
21	#82513	C₂	1	1	yes	maximal, characteristic, complemented
22	#82437	C₂	1	1	yes	maximal, characteristic, complemented
23	#82436	C₂	1	1	yes	maximal, characteristic, complemented
24	#60302	—	3	1	no	maximal, Sylow
25	C₃×#559	C₄	1	2	yes	—
26	C₃×#559	C₄	1	1	yes	characteristic
27	C₃×#557	C₄	1	1	yes	characteristic
28	C₃×#556	C₄	1	1	yes	characteristic
29	C₃×#556	C₄	1	2	yes	—
30	C₃×#553	C₄	1	1	yes	characteristic
31	C₃×#553	C₄	1	1	yes	characteristic
32	C₃×#553	C₄	1	2	yes	—
33	C₃×#553	C₄	1	2	yes	—
34	C₃×#550	C₄	1	1	yes	characteristic
35	C₃×#548	C₄	1	1	yes	characteristic
36	C₃×#548	C₄	1	1	yes	characteristic
37	C₃×#532	C₂²	1	1	yes	characteristic
38	C₃×#532	C₂²	1	2	yes	—
39	C₃×#529	C₂²	1	1	yes	characteristic
40	C₃×#529	C₂²	1	2	yes	—
41	C₃×#529	C₂²	1	2	yes	—
42	C₃×#529	C₂²	1	1	yes	characteristic
43	C₃×C₄×#41	C₂²	1	1	yes	characteristic
44	C₃×C₄×#41	C₂²	1	1	yes	characteristic
45	C₃×C₄×#41	C₂²	1	1	yes	characteristic
46	C₃×C₄×#41	C₂²	1	2	yes	—
47	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
48	#5234	C₂²	1	2	yes	—
49	#5234	C₂²	1	2	yes	—
50	#5234	C₂²	1	1	yes	characteristic
51	#5234	C₂²	1	2	yes	—
52	#5234	C₂²	1	2	yes	—
53	#5234	C₂²	1	1	yes	characteristic
54	#5234	C₂²	1	2	yes	—
55	#5024	C₂²	1	1	yes	characteristic
56	#5024	C₂²	1	1	yes	characteristic
57	#5024	C₂²	1	1	yes	characteristic
58	#5024	C₂²	1	2	yes	—
59	#5024	C₂²	1	2	yes	—
60	#5024	C₂²	1	1	yes	characteristic
61	#5024	C₂²	1	1	yes	characteristic
62	#5024	C₂²	1	1	yes	characteristic
63	#5024	C₂²	1	2	yes	—
64	#5024	C₂²	1	2	yes	—
65	Q₈×C₃⋊C₈	C₂²	1	1	yes	characteristic
66	Q₈×C₃⋊C₈	C₂²	1	1	yes	characteristic
67	#5012	C₂²	1	1	yes	characteristic
68	#5012	C₂²	1	1	yes	characteristic
69	#5012	C₂²	1	2	yes	—
70	#5012	C₂²	1	1	yes	characteristic
71	#5012	C₂²	1	1	yes	characteristic
72	#5012	C₂²	1	2	yes	—
73	#5012	C₂²	1	2	yes	—
74	#5011	C₂²	1	2	yes	—
75	#5011	C₂²	1	2	yes	—
76	#5011	C₂²	1	2	yes	—
77	#5011	C₂²	1	2	yes	—
78	#5011	C₂²	1	2	yes	—
79	#5011	C₂²	1	2	yes	—
80	#5011	C₂²	1	2	yes	—
81	#5011	C₂²	1	2	yes	—
82	#5011	C₂²	1	2	yes	—
83	#5011	C₂²	1	2	yes	—
84	#5011	C₂²	1	2	yes	—
85	#5011	C₂²	1	2	yes	—
86	#5011	C₂²	1	2	yes	—
87	#5011	C₂²	1	2	yes	—
88	D₄×C₃⋊C₈	C₂²	1	1	yes	characteristic
89	D₄×C₃⋊C₈	C₂²	1	1	yes	characteristic
90	D₄×C₃⋊C₈	C₂²	1	2	yes	—
91	D₄×C₃⋊C₈	C₂²	1	1	yes	characteristic
92	D₄×C₃⋊C₈	C₂²	1	1	yes	characteristic
93	D₄×C₃⋊C₈	C₂²	1	2	yes	—
94	D₄×C₃⋊C₈	C₂²	1	2	yes	—
95	#5000	C₂²	1	1	yes	characteristic
96	#5000	C₂²	1	1	yes	characteristic
97	#5000	C₂²	1	1	yes	characteristic
98	#5000	C₂²	1	1	yes	characteristic
99	#5000	C₂²	1	2	yes	—
100	#5000	C₂²	1	2	yes	—
101	#5000	C₂²	1	2	yes	—
102	#5000	C₂²	1	2	yes	—
103	#5000	C₂²	1	2	yes	—
104	#5000	C₂²	1	2	yes	—
105	#4999	C₂²	1	1	yes	characteristic
106	#4999	C₂²	1	1	yes	characteristic
107	#4999	C₂²	1	2	yes	—
108	#4999	C₂²	1	2	yes	—
109	#4997	C₂²	1	2	yes	—
110	#4997	C₂²	1	2	yes	—
111	#4997	C₂²	1	2	yes	—
112	#4926	C₂²	1	2	yes	—
113	#4926	C₂²	1	2	yes	—
114	#4926	C₂²	1	2	yes	—
115	#4926	C₂²	1	1	yes	characteristic
116	#4926	C₂²	1	2	yes	—
117	#4926	C₂²	1	2	yes	—
118	#4926	C₂²	1	1	yes	characteristic
119	#4926	C₂²	1	2	yes	—
120	#4925	C₂²	1	1	yes	characteristic
121	#4925	C₂²	1	1	yes	characteristic
122	#4925	C₂²	1	1	yes	characteristic
123	#4925	C₂²	1	2	yes	—
124	#4925	C₂²	1	1	yes	characteristic
125	#4925	C₂²	1	1	yes	characteristic
126	#4925	C₂²	1	2	yes	—
127	#4925	C₂²	1	1	yes	characteristic
128	#4924	C₂²	1	2	yes	—
129	#4924	C₂²	1	1	yes	characteristic
130	C₂×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
131	C₂×C₄⋊(C₃⋊C₈)	C₂²	1	2	yes	—
132	C₄×#208	C₂²	1	1	yes	characteristic
133	C₄×#208	C₂²	1	2	yes	—
134	C₂×#803	C₂²	1	2	yes	—
135	C₂×C₄×C₃⋊C₈	C₂²	1	1	yes	characteristic
136	#3480	D₃	1	1	yes	characteristic
137	#2995	—	3	2	no	—
138	#2994	—	3	1	no	—
139	#2993	—	3	1	no	—
140	#2992	—	3	2	no	—
141	#2990	—	3	1	no	—
142	#2989	—	3	1	no	—
143	#2984	—	3	1	no	—
144	#2983	—	3	1	no	—
145	#2981	—	3	1	no	—
146	#2981	—	3	2	no	—
147	#2980	—	3	2	no	—
148	#2979	—	3	1	no	—
149	#2970	—	3	1	no	—
150	#2969	—	3	1	no	—
151	#2968	—	3	2	no	—
152	#2967	—	3	2	no	—
153	#2966	—	3	1	no	—
154	#2965	—	3	1	no	—
155	#2925	—	3	1	no	—
156	#2925	—	3	2	no	—
157	#2923	—	3	2	no	—
158	#2922	—	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	C₂×C₃×#41	C₂³	1	1	yes	characteristic
163	C₂²×C₃×Q₈	C₂×C₄	1	1	yes	characteristic
164	C₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
165	C₃×C₄⋊Q₈	C₂×C₄	1	2	yes	—
166	C₃×#127	C₂×C₄	1	1	yes	characteristic
167	C₃×#127	C₂×C₄	1	2	yes	—
168	C₃×#126	C₂×C₄	1	2	yes	—
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×#126	C₂×C₄	1	2	yes	—
174	C₃×#125	C₂×C₄	1	1	yes	characteristic
175	C₃×#125	C₂×C₄	1	2	yes	—
176	C₃×#125	C₂×C₄	1	2	yes	—
177	C₃×#125	C₂×C₄	1	1	yes	characteristic
178	C₃×#124	C₂×C₄	1	1	yes	characteristic
179	C₃×#124	C₂×C₄	1	1	yes	characteristic
180	C₃×#124	C₂×C₄	1	2	yes	—
181	C₃×#124	C₂×C₄	1	2	yes	—
182	C₃×#124	C₂×C₄	1	2	yes	—
183	C₃×#124	C₂×C₄	1	2	yes	—
184	C₃×#124	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×#123	C₂×C₄	1	2	yes	—
189	C₃×#123	C₂×C₄	1	2	yes	—
190	C₃×#123	C₂×C₄	1	2	yes	—
191	C₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
192	C₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
193	C₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
194	C₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
195	C₃×#121	C₂×C₄	1	1	yes	characteristic
196	C₃×#121	C₂×C₄	1	1	yes	characteristic
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	2	yes	—
203	C₃×#121	C₂×C₄	1	2	yes	—
204	C₃×#121	C₂×C₄	1	2	yes	—
205	C₃×#121	C₂×C₄	1	2	yes	—
206	C₃×C₄×Q₈	C₂×C₄	1	1	yes	characteristic
207	C₃×C₄×Q₈	C₂×C₄	1	2	yes	—
208	C₃×C₄×Q₈	C₂×C₄	1	1	yes	characteristic
209	C₃×C₄×Q₈	C₂×C₄	1	2	yes	—
210	C₃×C₄×Q₈	C₂×C₄	1	1	yes	characteristic
211	C₃×C₄×Q₈	C₂×C₄	1	1	yes	characteristic
212	C₃×C₄×Q₈	C₂×C₄	1	1	yes	characteristic
213	C₃×C₄×Q₈	C₂×C₄	1	1	yes	characteristic
214	C₃×C₄×Q₈	C₂×C₄	1	2	yes	—
215	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
216	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
217	C₃×C₄×Q₈	C₂³	1	2	yes	—
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	1	yes	characteristic
221	C₃×C₄×D₄	C₂×C₄	1	1	yes	characteristic
222	C₃×C₄×D₄	C₂×C₄	1	2	yes	—
223	C₃×C₄×D₄	C₂×C₄	1	2	yes	—
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	2	yes	—
227	C₃×C₄×D₄	C₂×C₄	1	2	yes	—
228	C₃×C₄×D₄	C₂×C₄	1	1	yes	characteristic
229	C₃×C₄×D₄	C₂×C₄	1	2	yes	—
230	C₃×C₄×D₄	C₂×C₄	1	1	yes	characteristic
231	C₃×C₄×D₄	C₂×C₄	1	1	yes	characteristic
232	C₃×C₄×D₄	C₂×C₄	1	2	yes	—
233	C₃×C₄×D₄	C₂×C₄	1	2	yes	—
234	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
235	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
236	C₃×C₄×D₄	C₂³	1	2	yes	—
237	C₃×C₄×D₄	C₂³	1	2	yes	—
238	C₃×C₄×D₄	C₂³	1	2	yes	—
239	C₃×C₄×D₄	C₂³	1	2	yes	—
240	C₃×C₄×D₄	C₂³	1	2	yes	—
241	C₃×#117	C₂×C₄	1	1	yes	characteristic
242	C₃×#117	C₂×C₄	1	1	yes	characteristic
243	C₃×#117	C₂×C₄	1	2	yes	—
244	C₃×#117	C₂×C₄	1	2	yes	—
245	C₃×#117	C₂³	1	2	yes	—
246	C₃×#117	C₂³	1	1	yes	characteristic
247	C₃×#117	C₂³	1	1	yes	characteristic
248	C₃×#117	C₂³	1	2	yes	—
249	C₃×#117	C₂³	1	1	yes	characteristic
250	C₂×C₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
251	C₂×C₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
252	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
253	C₂×C₃×C₄²	C₂³	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	2	yes	—
258	C₂×#208	C₂³	1	1	yes	characteristic
259	C₂×#208	C₂³	1	1	yes	characteristic
260	C₂×#208	C₂³	1	2	yes	—
261	C₂×#208	C₂³	1	2	yes	—
262	C₂×#208	C₂³	1	2	yes	—
263	C₂×#208	C₂³	1	2	yes	—
264	C₂×#208	C₂³	1	2	yes	—
265	C₂²×C₃⋊C₈	C₂³	1	1	yes	characteristic
266	C₂²×C₃⋊C₈	C₂³	1	1	yes	characteristic
267	C₂²×C₃⋊C₈	C₂³	1	2	yes	—
268	C₂²×C₃⋊C₈	C₂³	1	2	yes	—
269	C₂²×C₃⋊C₈	C₂³	1	2	yes	—
270	C₂²×C₃⋊C₈	C₂³	1	2	yes	—
271	C₂²×C₃⋊C₈	C₂³	1	2	yes	—
272	#830	C₂³	1	1	yes	characteristic
273	#830	C₂³	1	2	yes	—
274	#830	C₂³	1	1	yes	characteristic
275	#830	C₂³	1	1	yes	characteristic
276	#830	C₂³	1	1	yes	characteristic
277	#830	C₂³	1	2	yes	—
278	#830	C₂³	1	1	yes	characteristic
279	#830	C₂³	1	2	yes	—
280	#830	C₂³	1	1	yes	characteristic
281	#830	C₂³	1	1	yes	characteristic
282	#830	C₂³	1	2	yes	—
283	#830	C₂³	1	2	yes	—
284	#830	C₂³	1	1	yes	characteristic
285	#830	C₂³	1	2	yes	—
286	#830	C₂³	1	2	yes	—
287	#830	C₂³	1	2	yes	—
288	#830	C₂³	1	2	yes	—
289	#830	C₂³	1	2	yes	—
290	#830	C₂³	1	2	yes	—
291	#830	C₂³	1	2	yes	—
292	C₄⋊(C₃⋊C₈)	C₂³	1	1	yes	characteristic
293	C₄⋊(C₃⋊C₈)	C₂³	1	2	yes	—
294	C₄⋊(C₃⋊C₈)	C₂³	1	2	yes	—
295	C₄⋊(C₃⋊C₈)	C₂³	1	2	yes	—
296	C₄⋊(C₃⋊C₈)	C₂³	1	1	yes	characteristic
297	C₄⋊(C₃⋊C₈)	C₂³	1	1	yes	characteristic
298	C₄⋊(C₃⋊C₈)	C₂³	1	2	yes	—
299	C₄⋊(C₃⋊C₈)	C₂³	1	1	yes	characteristic
300	C₄⋊(C₃⋊C₈)	C₂³	1	1	yes	characteristic
301	C₄⋊(C₃⋊C₈)	C₂³	1	1	yes	characteristic
302	C₄⋊(C₃⋊C₈)	C₂³	1	2	yes	—
303	C₄⋊(C₃⋊C₈)	C₂³	1	2	yes	—
304	C₄⋊(C₃⋊C₈)	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
309	C₄⋊(C₃⋊C₈)	C₂³	1	1	yes	characteristic
310	C₄⋊(C₃⋊C₈)	C₂³	1	2	yes	—
311	C₄⋊(C₃⋊C₈)	C₂³	1	2	yes	—
312	C₄⋊(C₃⋊C₈)	C₂³	1	2	yes	—
313	C₄⋊(C₃⋊C₈)	C₂³	1	2	yes	—
314	#803	C₂³	1	1	yes	characteristic
315	#803	C₂³	1	2	yes	—
316	#803	C₂³	1	2	yes	—
317	#803	C₂³	1	2	yes	—
318	#803	C₂³	1	1	yes	characteristic
319	#803	C₂³	1	2	yes	—
320	#803	C₂³	1	2	yes	—
321	#803	C₂³	1	2	yes	—
322	#803	C₂³	1	2	yes	—
323	#803	C₂³	1	2	yes	—
324	C₄×C₃⋊C₈	C₂³	1	1	yes	characteristic
325	C₄×C₃⋊C₈	C₂³	1	1	yes	characteristic
326	C₄×C₃⋊C₈	C₂³	1	1	yes	characteristic
327	C₄×C₃⋊C₈	C₂³	1	1	yes	characteristic
328	C₄×C₃⋊C₈	C₂³	1	2	yes	—
329	C₄×C₃⋊C₈	C₂³	1	1	yes	characteristic
330	C₄×C₃⋊C₈	C₂³	1	1	yes	characteristic
331	C₄×C₃⋊C₈	C₂³	1	2	yes	—
332	C₄×C₃⋊C₈	C₂³	1	2	yes	—
333	C₄×C₃⋊C₈	C₂³	1	2	yes	—
334	#559	Dic₃	1	1	yes	characteristic
335	#559	Dic₃	1	2	yes	—
336	#557	Dic₃	1	1	yes	characteristic
337	#556	Dic₃	1	1	yes	characteristic
338	#556	Dic₃	1	2	yes	—
339	#553	Dic₃	1	1	yes	characteristic
340	#553	Dic₃	1	1	yes	characteristic
341	#553	Dic₃	1	2	yes	—
342	#553	Dic₃	1	2	yes	—
343	#550	Dic₃	1	1	yes	characteristic
344	#548	Dic₃	1	1	yes	characteristic
345	#548	Dic₃	1	1	yes	characteristic
346	#532	C₂×D₃	1	1	yes	characteristic
347	#532	C₂×D₃	1	2	yes	—
348	#529	C₂×D₃	1	1	yes	characteristic
349	#529	C₂×D₃	1	2	yes	—
350	#529	C₂×D₃	1	2	yes	—
351	#529	C₂×D₃	1	1	yes	characteristic
352	C₄×#41	C₂×D₃	1	1	yes	characteristic
353	C₄×#41	C₂×D₃	1	1	yes	characteristic
354	C₄×#41	C₂×D₃	1	1	yes	characteristic
355	C₄×#41	C₂×D₃	1	2	yes	—
356	C₂×C₄×Q₈	C₂×D₃	1	1	yes	characteristic
357	#446	—	3	1	no	—
358	#446	—	3	1	no	—
359	#446	—	3	1	no	—
360	#446	—	3	2	no	—
361	#446	—	3	2	no	—
362	#446	—	3	2	no	—
363	#446	—	3	2	no	—
364	#446	—	3	1	no	—
365	#446	—	3	1	no	—
366	#446	—	3	1	no	—
367	C₈×Q₈	—	3	1	no	—
368	C₈×Q₈	—	3	1	no	—
369	#436	—	3	1	no	—
370	#436	—	3	1	no	—
371	#436	—	3	1	no	—
372	#436	—	3	2	no	—
373	#436	—	3	2	no	—
374	#436	—	3	1	no	—
375	#436	—	3	2	no	—
376	#435	—	3	2	no	—
377	#435	—	3	2	no	—
378	#435	—	3	2	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	2	no	—
387	#435	—	3	2	no	—
388	#435	—	3	2	no	—
389	#435	—	3	2	no	—
390	C₈×D₄	—	3	1	no	—
391	C₈×D₄	—	3	2	no	—
392	C₈×D₄	—	3	2	no	—
393	C₈×D₄	—	3	2	no	—
394	C₈×D₄	—	3	1	no	—
395	C₈×D₄	—	3	1	no	—
396	C₈×D₄	—	3	1	no	—
397	#433	—	3	1	no	—
398	#433	—	3	1	no	—
399	#433	—	3	1	no	—
400	#433	—	3	1	no	—
401	#433	—	3	2	no	—
402	#433	—	3	2	no	—
403	#433	—	3	2	no	—
404	#433	—	3	2	no	—
405	#433	—	3	2	no	—
406	#433	—	3	2	no	—
407	#432	—	3	2	no	—
408	#432	—	3	2	no	—
409	#432	—	3	2	no	—
410	#432	—	3	2	no	—
411	#432	—	3	1	no	—
412	#432	—	3	2	no	—
413	#432	—	3	2	no	—
414	#432	—	3	1	no	—
415	#431	—	3	1	no	—
416	#431	—	3	1	no	—
417	#431	—	3	1	no	—
418	#431	—	3	1	no	—
419	#431	—	3	2	no	—
420	#431	—	3	1	no	—
421	#431	—	3	1	no	—
422	#431	—	3	2	no	—
423	#424	—	3	1	no	—
424	#424	—	3	1	no	—
425	#424	—	3	2	no	—
426	#424	—	3	2	no	—
427	#423	—	3	2	no	—
428	#423	—	3	1	no	—
429	C₂×C₄⋊C₈	—	3	1	no	—
430	C₂×C₄⋊C₈	—	3	2	no	—
431	#408	—	3	1	no	—
432	#408	—	3	1	no	—
433	#408	—	3	2	no	—
434	#408	—	3	2	no	—
435	#408	—	3	2	no	—
436	#408	—	3	2	no	—
437	#408	—	3	2	no	—
438	#405	—	3	2	no	—
439	#405	—	3	2	no	—
440	#405	—	3	2	no	—
441	C₄×M₁₆	—	3	1	no	—
442	C₄×M₁₆	—	3	2	no	—
443	C₂×#97	—	3	2	no	—
444	C₂×C₄×C₈	—	3	1	no	—
445	C₃×#41	—	4	2	no	—
446	C₃×#41	—	4	1	no	—
447	C₃×#41	—	4	2	no	—
448	C₃×#41	—	4	1	no	—
449	C₃×#41	—	4	2	no	—
450	C₃×#41	—	4	2	no	—
451	C₂×C₃×Q₈	—	4	2	no	—
452	C₂×C₃×Q₈	C₂²×C₄	1	1	yes	characteristic
453	C₂×C₃×Q₈	C₂²×C₄	1	1	yes	characteristic
454	C₂×C₃×Q₈	C₂²×C₄	1	1	yes	characteristic
455	C₂×C₃×Q₈	C₂²×C₄	1	2	yes	—
456	C₂×C₃×Q₈	C₂²×C₄	1	2	yes	—
457	C₂×C₃×D₄	C₂²×C₄	1	1	yes	characteristic
458	C₂×C₃×D₄	C₂²×C₄	1	1	yes	characteristic
459	C₂×C₃×D₄	C₂²×C₄	1	1	yes	characteristic
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	2	yes	—
463	C₂×C₃×D₄	C₂²×C₄	1	1	yes	characteristic
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	2	yes	—
467	C₂×C₃×D₄	C₂²×C₄	1	2	yes	—
468	C₂×C₃×D₄	C₂²×C₄	1	2	yes	—
469	C₂×C₃×D₄	C₂²×C₄	1	2	yes	—
470	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
471	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
472	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
473	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
474	C₂²×C₃×C₄	C₂²×C₄	1	2	yes	—
475	C₂²×C₃×C₄	C₂²×C₄	1	2	yes	—
476	C₂²×C₃×C₄	C₂²×C₄	1	2	yes	—
477	C₂²×C₃×C₄	C₂²×C₄	1	2	yes	—
478	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
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	2	yes	—
482	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
483	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
484	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
485	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
486	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
487	C₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
488	C₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
489	C₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
490	C₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
491	C₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
492	C₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
493	C₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
494	C₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
495	C₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
496	C₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
497	C₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
498	C₃×C₄⋊C₄	C₂²×C₄	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	2	yes	—
504	C₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
505	C₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
506	C₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
507	C₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
508	C₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
509	C₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
510	C₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
511	C₃×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
512	C₃×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
513	C₃×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
514	C₃×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
515	C₃×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
516	C₃×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
517	C₃×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
518	C₃×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
519	C₃×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
520	C₃×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
521	C₃×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
522	C₃×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
523	C₃×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
524	C₃×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
525	C₃×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
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×C₄²	C₂²×C₄	1	1	yes	characteristic
534	C₃×C₄²	C₂²×C₄	1	2	yes	—
535	C₃×C₄²	C₂²×C₄	1	1	yes	characteristic
536	C₃×C₄²	C₂²×C₄	1	2	yes	—
537	C₃×C₄²	C₂²×C₄	1	2	yes	—
538	C₃×C₄²	C₂²×C₄	1	2	yes	—
539	C₃×C₄²	C₂²×C₄	1	1	yes	characteristic
540	C₃×C₄²	C₂²×C₄	1	1	yes	characteristic
541	C₃×C₄²	C₂²×C₄	1	1	yes	characteristic
542	C₃×C₄²	C₂²×C₄	1	2	yes	—
543	C₃×C₄²	C₂²×C₄	1	2	yes	—
544	C₃×C₄²	C₂²×C₄	1	1	yes	characteristic
545	C₃×C₄²	C₂⁴	1	1	yes	characteristic
546	C₃×C₄²	C₂⁴	1	1	yes	characteristic
547	C₃×C₄²	C₂⁴	1	2	yes	—
548	C₃×C₄²	C₂⁴	1	1	yes	characteristic
549	C₃×C₄²	C₂⁴	1	2	yes	—
550	C₃×C₄²	C₂⁴	1	1	yes	characteristic
551	#208	—	4	1	no	—
552	#208	—	4	2	no	—
553	#208	—	4	2	no	—
554	#208	—	4	1	no	—
555	#208	—	4	2	no	—
556	#208	—	4	2	no	—
557	#208	—	4	2	no	—
558	C₂×C₃⋊C₈	—	4	2	no	—
559	C₂×C₃⋊C₈	—	4	1	no	—
560	C₂×C₃⋊C₈	—	4	2	no	—
561	C₂×C₃⋊C₈	—	4	2	no	—
562	C₂×C₃⋊C₈	—	4	2	no	—
563	C₂×C₃⋊C₈	—	4	2	no	—
564	C₂×C₃⋊C₈	—	4	1	no	—
565	C₂×C₃⋊C₈	C₂⁴	1	1	yes	characteristic
566	C₂×C₃⋊C₈	C₂⁴	1	1	yes	characteristic
567	C₂×C₃⋊C₈	C₂⁴	1	1	yes	characteristic
568	C₂×C₃⋊C₈	C₂⁴	1	1	yes	characteristic
569	C₂×C₃⋊C₈	C₂⁴	1	1	yes	characteristic
570	C₂×C₃⋊C₈	C₂⁴	1	2	yes	—
571	C₂×C₃⋊C₈	C₂⁴	1	2	yes	—
572	C₂×C₃⋊C₈	C₂⁴	1	1	yes	characteristic
573	C₂×C₃⋊C₈	C₂⁴	1	1	yes	characteristic
574	C₂×C₃⋊C₈	C₂⁴	1	1	yes	characteristic
575	C₂×C₃⋊C₈	C₂⁴	1	2	yes	—
576	C₂×C₃⋊C₈	C₂⁴	1	2	yes	—
577	C₂×#41	C₂×Dic₃	1	1	yes	characteristic
578	C₂×#41	C₂×Dic₃	1	1	yes	characteristic
579	C₂×#41	C₂²×D₃	1	1	yes	characteristic
580	C₂×#41	C₂²×D₃	1	2	yes	—
581	C₂²×Q₈	C₂×Dic₃	1	1	yes	characteristic
582	C₂×M₁₆	—	3	1	no	—
583	C₂×M₁₆	—	3	1	no	—
584	C₂×M₁₆	—	3	2	no	—
585	C₂×M₁₆	—	3	2	no	—
586	C₂×M₁₆	—	3	2	no	—
587	C₂×M₁₆	—	3	2	no	—
588	C₂×M₁₆	—	3	2	no	—
589	C₂²×C₈	—	3	1	no	—
590	C₂²×C₈	—	3	1	no	—
591	C₂²×C₈	—	3	2	no	—
592	C₂²×C₈	—	3	2	no	—
593	C₂²×C₈	—	3	2	no	—
594	C₂²×C₈	—	3	2	no	—
595	C₂²×C₈	—	3	2	no	—
596	C₄⋊Q₈	C₂×Dic₃	1	1	yes	characteristic
597	C₄⋊Q₈	C₂×Dic₃	1	2	yes	—
598	#127	C₂×Dic₃	1	1	yes	characteristic
599	#127	C₂×Dic₃	1	2	yes	—
600	#126	C₂×Dic₃	1	2	yes	—
601	#126	C₂×Dic₃	1	2	yes	—
602	#126	C₂×Dic₃	1	2	yes	—
603	#126	C₂×Dic₃	1	2	yes	—
604	#126	C₂×Dic₃	1	2	yes	—
605	#126	C₂×Dic₃	1	2	yes	—
606	#125	C₂×Dic₃	1	1	yes	characteristic
607	#125	C₂×Dic₃	1	2	yes	—
608	#125	C₂×Dic₃	1	2	yes	—
609	#125	C₂×Dic₃	1	1	yes	characteristic
610	#124	C₂×Dic₃	1	1	yes	characteristic
611	#124	C₂×Dic₃	1	1	yes	characteristic
612	#124	C₂×Dic₃	1	2	yes	—
613	#124	C₂×Dic₃	1	2	yes	—
614	#124	C₂×Dic₃	1	2	yes	—
615	#124	C₂×Dic₃	1	2	yes	—
616	#124	C₂×Dic₃	1	2	yes	—
617	#123	C₂×Dic₃	1	2	yes	—
618	#123	C₂×Dic₃	1	2	yes	—
619	#123	C₂×Dic₃	1	2	yes	—
620	#123	C₂×Dic₃	1	2	yes	—
621	#123	C₂×Dic₃	1	2	yes	—
622	#123	C₂×Dic₃	1	2	yes	—
623	C₂²⋊Q₈	C₂×Dic₃	1	1	yes	characteristic
624	C₂²⋊Q₈	C₂×Dic₃	1	1	yes	characteristic
625	C₂²⋊Q₈	C₂×Dic₃	1	2	yes	—
626	C₂²⋊Q₈	C₂×Dic₃	1	2	yes	—
627	#121	C₂×Dic₃	1	1	yes	characteristic
628	#121	C₂×Dic₃	1	1	yes	characteristic
629	#121	C₂×Dic₃	1	2	yes	—
630	#121	C₂×Dic₃	1	2	yes	—
631	#121	C₂×Dic₃	1	1	yes	characteristic
632	#121	C₂×Dic₃	1	1	yes	characteristic
633	#121	C₂×Dic₃	1	2	yes	—
634	#121	C₂×Dic₃	1	2	yes	—
635	#121	C₂×Dic₃	1	2	yes	—
636	#121	C₂×Dic₃	1	2	yes	—
637	#121	C₂×Dic₃	1	2	yes	—
638	C₄×Q₈	C₂×Dic₃	1	1	yes	characteristic
639	C₄×Q₈	C₂×Dic₃	1	1	yes	characteristic
640	C₄×Q₈	C₂×Dic₃	1	2	yes	—
641	C₄×Q₈	C₂×Dic₃	1	1	yes	characteristic
642	C₄×Q₈	C₂×Dic₃	1	1	yes	characteristic
643	C₄×Q₈	C₂×Dic₃	1	1	yes	characteristic
644	C₄×Q₈	C₂×Dic₃	1	2	yes	—
645	C₄×Q₈	C₂×Dic₃	1	1	yes	characteristic
646	C₄×Q₈	C₂×Dic₃	1	2	yes	—
647	C₄×Q₈	C₂²×D₃	1	1	yes	characteristic
648	C₄×Q₈	C₂²×D₃	1	1	yes	characteristic
649	C₄×Q₈	C₂²×D₃	1	2	yes	—
650	C₄×D₄	C₂×Dic₃	1	1	yes	characteristic
651	C₄×D₄	C₂×Dic₃	1	1	yes	characteristic
652	C₄×D₄	C₂×Dic₃	1	2	yes	—
653	C₄×D₄	C₂×Dic₃	1	2	yes	—
654	C₄×D₄	C₂×Dic₃	1	1	yes	characteristic
655	C₄×D₄	C₂×Dic₃	1	2	yes	—
656	C₄×D₄	C₂×Dic₃	1	1	yes	characteristic
657	C₄×D₄	C₂×Dic₃	1	1	yes	characteristic
658	C₄×D₄	C₂×Dic₃	1	2	yes	—
659	C₄×D₄	C₂×Dic₃	1	2	yes	—
660	C₄×D₄	C₂×Dic₃	1	1	yes	characteristic
661	C₄×D₄	C₂×Dic₃	1	1	yes	characteristic
662	C₄×D₄	C₂×Dic₃	1	2	yes	—
663	C₄×D₄	C₂×Dic₃	1	2	yes	—
664	C₄×D₄	C₂×Dic₃	1	1	yes	characteristic
665	C₄×D₄	C₂×Dic₃	1	2	yes	—
666	C₄×D₄	C₂²×D₃	1	1	yes	characteristic
667	C₄×D₄	C₂²×D₃	1	1	yes	characteristic
668	C₄×D₄	C₂²×D₃	1	2	yes	—
669	C₄×D₄	C₂²×D₃	1	2	yes	—
670	C₄×D₄	C₂²×D₃	1	2	yes	—
671	C₄×D₄	C₂²×D₃	1	2	yes	—
672	C₄×D₄	C₂²×D₃	1	2	yes	—
673	#117	C₂×Dic₃	1	1	yes	characteristic
674	#117	C₂×Dic₃	1	1	yes	characteristic
675	#117	C₂×Dic₃	1	2	yes	—
676	#117	C₂×Dic₃	1	2	yes	—
677	#117	C₂²×D₃	1	1	yes	characteristic
678	#117	C₂²×D₃	1	1	yes	characteristic
679	#117	C₂²×D₃	1	2	yes	—
680	#117	C₂²×D₃	1	1	yes	characteristic
681	#117	C₂²×D₃	1	2	yes	—
682	C₂×C₄⋊C₄	C₂×Dic₃	1	1	yes	characteristic
683	C₂×C₄⋊C₄	C₂×Dic₃	1	2	yes	—
684	C₂×C₄²	C₂²×D₃	1	1	yes	characteristic
685	C₂×C₄²	C₂²×D₃	1	2	yes	—
686	C₂×C₄²	C₂²×D₃	1	1	yes	characteristic
687	C₂×C₄²	C₂²×D₃	1	2	yes	—
688	C₂×C₄²	C₂²×D₃	1	1	yes	characteristic
689	C₂×C₄²	C₂²×D₃	1	2	yes	—
690	C₄⋊C₈	—	3	1	no	—
691	C₄⋊C₈	—	3	2	no	—
692	C₄⋊C₈	—	3	2	no	—
693	C₄⋊C₈	—	3	2	no	—
694	C₄⋊C₈	—	3	1	no	—
695	C₄⋊C₈	—	3	1	no	—
696	C₄⋊C₈	—	3	2	no	—
697	C₄⋊C₈	—	3	1	no	—
698	C₄⋊C₈	—	3	1	no	—
699	C₄⋊C₈	—	3	1	no	—
700	C₄⋊C₈	—	3	2	no	—
701	C₄⋊C₈	—	3	2	no	—
702	C₄⋊C₈	—	3	1	no	—
703	C₄⋊C₈	—	3	1	no	—
704	C₄⋊C₈	—	3	1	no	—
705	C₄⋊C₈	—	3	1	no	—
706	C₄⋊C₈	—	3	1	no	—
707	C₄⋊C₈	—	3	1	no	—
708	C₄⋊C₈	—	3	2	no	—
709	C₄⋊C₈	—	3	2	no	—
710	C₄⋊C₈	—	3	2	no	—
711	C₄⋊C₈	—	3	2	no	—
712	C₂²⋊C₈	—	3	1	no	—
713	C₂²⋊C₈	—	3	1	no	—
714	C₂²⋊C₈	—	3	1	no	—
715	C₂²⋊C₈	—	3	1	no	—
716	C₂²⋊C₈	—	3	2	no	—
717	C₂²⋊C₈	—	3	2	no	—
718	C₂²⋊C₈	—	3	1	no	—
719	C₂²⋊C₈	—	3	2	no	—
720	C₂²⋊C₈	—	3	1	no	—
721	C₂²⋊C₈	—	3	1	no	—
722	C₂²⋊C₈	—	3	2	no	—
723	C₂²⋊C₈	—	3	2	no	—
724	C₂²⋊C₈	—	3	1	no	—
725	C₂²⋊C₈	—	3	2	no	—
726	C₂²⋊C₈	—	3	2	no	—
727	C₂²⋊C₈	—	3	2	no	—
728	C₂²⋊C₈	—	3	2	no	—
729	C₂²⋊C₈	—	3	2	no	—
730	C₂²⋊C₈	—	3	2	no	—
731	C₂²⋊C₈	—	3	2	no	—
732	#97	—	3	1	no	—
733	#97	—	3	2	no	—
734	#97	—	3	2	no	—
735	#97	—	3	2	no	—
736	#97	—	3	1	no	—
737	#97	—	3	2	no	—
738	#97	—	3	2	no	—
739	#97	—	3	2	no	—
740	#97	—	3	2	no	—
741	#97	—	3	2	no	—
742	C₄×C₈	—	3	1	no	—
743	C₄×C₈	—	3	1	no	—
744	C₄×C₈	—	3	1	no	—
745	C₄×C₈	—	3	1	no	—
746	C₄×C₈	—	3	2	no	—
747	C₄×C₈	—	3	1	no	—
748	C₄×C₈	—	3	1	no	—
749	C₄×C₈	—	3	2	no	—
750	C₄×C₈	—	3	2	no	—
751	C₄×C₈	—	3	2	no	—
752	C₂³×C₃	C₂³×C₄	1	1	yes	characteristic
753	C₂³×C₃	C₂³×C₄	1	1	yes	characteristic
754	C₂³×C₃	C₂³×C₄	1	2	yes	—
755	C₂³×C₃	C₂³×C₄	1	2	yes	—
756	C₂³×C₃	C₂³×C₄	1	1	yes	characteristic
757	C₃×Q₈	—	2	2	no	—
758	C₃×Q₈	—	2	2	no	—
759	C₃×Q₈	—	4	2	no	—
760	C₃×Q₈	—	4	1	no	—
761	C₃×Q₈	—	4	2	no	—
762	C₃×D₄	—	2	2	no	—
763	C₃×D₄	—	2	2	no	—
764	C₃×D₄	—	4	2	no	—
765	C₃×D₄	—	4	2	no	—
766	C₃×D₄	—	4	2	no	—
767	C₃×D₄	—	4	1	no	—
768	C₃×D₄	—	4	2	no	—
769	C₃×D₄	—	4	1	no	—
770	C₃×D₄	—	4	2	no	—
771	C₃×D₄	—	4	1	no	—
772	C₃×D₄	—	4	2	no	—
773	C₃×D₄	—	4	2	no	—
774	C₃×D₄	—	4	2	no	—
775	C₂×C₃×C₄	—	2	2	no	—
776	C₂×C₃×C₄	—	2	2	no	—
777	C₂×C₃×C₄	—	2	2	no	—
778	C₂×C₃×C₄	—	2	2	no	—
779	C₂×C₃×C₄	—	2	1	no	—
780	C₂×C₃×C₄	—	2	1	no	—
781	C₂×C₃×C₄	—	2	2	no	—
782	C₂×C₃×C₄	—	2	2	no	—
783	C₂×C₃×C₄	—	2	1	no	—
784	C₂×C₃×C₄	—	2	1	no	—
785	C₂×C₃×C₄	—	2	2	no	—
786	C₂×C₃×C₄	—	2	1	no	—
787	C₂×C₃×C₄	—	2	1	no	—
788	C₂×C₃×C₄	—	4	1	no	—
789	C₂×C₃×C₄	—	4	2	no	—
790	C₂×C₃×C₄	—	4	1	no	—
791	C₂×C₃×C₄	—	4	2	no	—
792	C₂×C₃×C₄	—	4	1	no	—
793	C₂×C₃×C₄	—	4	2	no	—
794	C₂×C₃×C₄	—	4	2	no	—
795	C₂×C₃×C₄	—	4	2	no	—
796	C₂×C₃×C₄	—	4	2	no	—
797	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
798	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
799	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
800	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
801	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
802	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
803	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
804	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
805	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
806	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
807	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
808	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
809	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
810	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
811	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
812	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
813	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
814	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
815	C₃⋊C₈	—	2	1	no	—
816	C₃⋊C₈	—	2	2	no	—
817	C₃⋊C₈	—	2	1	no	—
818	C₃⋊C₈	—	2	1	no	—
819	C₃⋊C₈	—	2	1	no	—
820	C₃⋊C₈	—	2	2	no	—
821	C₃⋊C₈	—	2	1	no	—
822	C₃⋊C₈	—	2	2	no	—
823	C₃⋊C₈	—	2	2	no	—
824	C₃⋊C₈	—	2	1	no	—
825	C₃⋊C₈	—	2	1	no	—
826	C₃⋊C₈	—	2	1	no	—
827	#41	—	4	1	no	—
828	#41	—	4	2	no	—
829	#41	—	4	1	no	—
830	#41	—	4	2	no	—
831	#41	—	4	2	no	—
832	#41	—	4	2	no	—
833	C₂×Q₈	—	4	2	no	—
834	C₂×Q₈	C₂²×Dic₃	1	1	yes	characteristic
835	C₂×Q₈	C₂²×Dic₃	1	1	yes	characteristic
836	C₂×Q₈	C₂²×Dic₃	1	1	yes	characteristic
837	C₂×Q₈	C₂²×Dic₃	1	2	yes	—
838	C₂×Q₈	C₂²×Dic₃	1	2	yes	—
839	C₂×D₄	C₂²×Dic₃	1	1	yes	characteristic
840	C₂×D₄	C₂²×Dic₃	1	1	yes	characteristic
841	C₂×D₄	C₂²×Dic₃	1	1	yes	characteristic
842	C₂×D₄	C₂²×Dic₃	1	1	yes	characteristic
843	C₂×D₄	C₂²×Dic₃	1	2	yes	—
844	C₂×D₄	C₂²×Dic₃	1	2	yes	—
845	C₂×D₄	C₂²×Dic₃	1	1	yes	characteristic
846	C₂×D₄	C₂²×Dic₃	1	2	yes	—
847	C₂×D₄	C₂²×Dic₃	1	2	yes	—
848	C₂×D₄	C₂²×Dic₃	1	2	yes	—
849	C₂×D₄	C₂²×Dic₃	1	2	yes	—
850	C₂×D₄	C₂²×Dic₃	1	2	yes	—
851	C₂×D₄	C₂²×Dic₃	1	2	yes	—
852	C₂²×C₄	C₂²×Dic₃	1	1	yes	characteristic
853	C₂²×C₄	C₂²×Dic₃	1	1	yes	characteristic
854	C₂²×C₄	C₂²×Dic₃	1	1	yes	characteristic
855	C₂²×C₄	C₂²×Dic₃	1	1	yes	characteristic
856	C₂²×C₄	C₂²×Dic₃	1	2	yes	—
857	C₂²×C₄	C₂²×Dic₃	1	2	yes	—
858	C₂²×C₄	C₂²×Dic₃	1	2	yes	—
859	C₂²×C₄	C₂²×Dic₃	1	2	yes	—
860	C₂²×C₄	C₂²×Dic₃	1	1	yes	characteristic
861	C₂²×C₄	C₂²×Dic₃	1	2	yes	—
862	C₂²×C₄	C₂²×Dic₃	1	1	yes	characteristic
863	C₂²×C₄	C₂²×Dic₃	1	2	yes	—
864	C₂²×C₄	C₂³×D₃	1	1	yes	characteristic
865	C₂²×C₄	C₂³×D₃	1	1	yes	characteristic
866	C₂²×C₄	C₂³×D₃	1	2	yes	—
867	C₂²×C₄	C₂³×D₃	1	2	yes	—
868	C₂²×C₄	C₂³×D₃	1	1	yes	characteristic
869	M₁₆	—	12	1	no	—
870	M₁₆	—	12	2	no	—
871	M₁₆	—	12	2	no	—
872	M₁₆	—	12	1	no	—
873	M₁₆	—	12	2	no	—
874	M₁₆	—	12	2	no	—
875	M₁₆	—	12	2	no	—
876	C₂×C₈	—	3	1	no	—
877	C₂×C₈	—	3	1	no	—
878	C₂×C₈	—	3	1	no	—
879	C₂×C₈	—	3	1	no	—
880	C₂×C₈	—	3	1	no	—
881	C₂×C₈	—	3	2	no	—
882	C₂×C₈	—	3	2	no	—
883	C₂×C₈	—	3	1	no	—
884	C₂×C₈	—	3	1	no	—
885	C₂×C₈	—	3	1	no	—
886	C₂×C₈	—	3	2	no	—
887	C₂×C₈	—	3	2	no	—
888	C₂×C₈	—	12	2	no	—
889	C₂×C₈	—	12	1	no	—
890	C₂×C₈	—	12	2	no	—
891	C₂×C₈	—	12	2	no	—
892	C₂×C₈	—	12	2	no	—
893	C₂×C₈	—	12	2	no	—
894	C₂×C₈	—	12	1	no	—
895	C₄⋊C₄	C₂²×Dic₃	1	2	yes	—
896	C₄⋊C₄	C₂²×Dic₃	1	1	yes	characteristic
897	C₄⋊C₄	C₂²×Dic₃	1	2	yes	—
898	C₄⋊C₄	C₂²×Dic₃	1	1	yes	characteristic
899	C₄⋊C₄	C₂²×Dic₃	1	2	yes	—
900	C₄⋊C₄	C₂²×Dic₃	1	2	yes	—
901	C₄⋊C₄	C₂²×Dic₃	1	2	yes	—
902	C₄⋊C₄	C₂²×Dic₃	1	2	yes	—
903	C₄⋊C₄	C₂²×Dic₃	1	2	yes	—
904	C₄⋊C₄	C₂²×Dic₃	1	1	yes	characteristic
905	C₄⋊C₄	C₂²×Dic₃	1	1	yes	characteristic
906	C₄⋊C₄	C₂²×Dic₃	1	1	yes	characteristic
907	C₄⋊C₄	C₂²×Dic₃	1	1	yes	characteristic
908	C₄⋊C₄	C₂²×Dic₃	1	1	yes	characteristic
909	C₄⋊C₄	C₂²×Dic₃	1	2	yes	—
910	C₄⋊C₄	C₂²×Dic₃	1	1	yes	characteristic
911	C₄⋊C₄	C₂²×Dic₃	1	2	yes	—
912	C₄⋊C₄	C₂²×Dic₃	1	1	yes	characteristic
913	C₄⋊C₄	C₂²×Dic₃	1	2	yes	—
914	C₄⋊C₄	C₂²×Dic₃	1	1	yes	characteristic
915	C₄⋊C₄	C₂²×Dic₃	1	2	yes	—
916	C₄⋊C₄	C₂²×Dic₃	1	2	yes	—
917	C₄⋊C₄	C₂²×Dic₃	1	2	yes	—
918	C₄⋊C₄	C₂²×Dic₃	1	2	yes	—
919	C₂²⋊C₄	C₂²×Dic₃	1	2	yes	—
920	C₂²⋊C₄	C₂²×Dic₃	1	2	yes	—
921	C₂²⋊C₄	C₂²×Dic₃	1	2	yes	—
922	C₂²⋊C₄	C₂²×Dic₃	1	2	yes	—
923	C₂²⋊C₄	C₂²×Dic₃	1	2	yes	—
924	C₂²⋊C₄	C₂²×Dic₃	1	2	yes	—
925	C₂²⋊C₄	C₂²×Dic₃	1	1	yes	characteristic
926	C₂²⋊C₄	C₂²×Dic₃	1	1	yes	characteristic
927	C₂²⋊C₄	C₂²×Dic₃	1	1	yes	characteristic
928	C₂²⋊C₄	C₂²×Dic₃	1	2	yes	—
929	C₂²⋊C₄	C₂²×Dic₃	1	1	yes	characteristic
930	C₂²⋊C₄	C₂²×Dic₃	1	2	yes	—
931	C₂²⋊C₄	C₂²×Dic₃	1	1	yes	characteristic
932	C₂²⋊C₄	C₂²×Dic₃	1	2	yes	—
933	C₂²⋊C₄	C₂²×Dic₃	1	1	yes	characteristic
934	C₂²⋊C₄	C₂²×Dic₃	1	2	yes	—
935	C₂²⋊C₄	C₂²×Dic₃	1	2	yes	—
936	C₂²⋊C₄	C₂²×Dic₃	1	2	yes	—
937	C₂²⋊C₄	C₂²×Dic₃	1	2	yes	—
938	C₂²⋊C₄	C₂²×Dic₃	1	2	yes	—
939	C₂²⋊C₄	C₂²×Dic₃	1	2	yes	—
940	C₂²⋊C₄	C₂²×Dic₃	1	2	yes	—
941	C₄²	C₂²×Dic₃	1	1	yes	characteristic
942	C₄²	C₂²×Dic₃	1	2	yes	—
943	C₄²	C₂²×Dic₃	1	1	yes	characteristic
944	C₄²	C₂²×Dic₃	1	2	yes	—
945	C₄²	C₂²×Dic₃	1	2	yes	—
946	C₄²	C₂²×Dic₃	1	2	yes	—
947	C₄²	C₂²×Dic₃	1	1	yes	characteristic
948	C₄²	C₂²×Dic₃	1	1	yes	characteristic
949	C₄²	C₂²×Dic₃	1	1	yes	characteristic
950	C₄²	C₂²×Dic₃	1	2	yes	—
951	C₄²	C₂²×Dic₃	1	2	yes	—
952	C₄²	C₂²×Dic₃	1	1	yes	characteristic
953	C₄²	C₂³×D₃	1	1	yes	characteristic
954	C₄²	C₂³×D₃	1	1	yes	characteristic
955	C₄²	C₂³×D₃	1	2	yes	—
956	C₄²	C₂³×D₃	1	1	yes	characteristic
957	C₄²	C₂³×D₃	1	2	yes	—
958	C₄²	C₂³×D₃	1	1	yes	characteristic
959	C₂²×C₃	—	2	1	no	—
960	C₂²×C₃	—	2	1	no	—
961	C₂²×C₃	—	2	2	no	—
962	C₂²×C₃	—	2	1	no	—
963	C₂²×C₃	—	2	2	no	—
964	C₂²×C₃	—	2	1	no	—
965	C₂²×C₃	—	2	1	no	—
966	C₂²×C₃	—	2	1	no	—
967	C₂²×C₃	—	2	2	no	—
968	C₂²×C₃	—	2	2	no	—
969	C₂²×C₃	—	2	1	no	—
970	C₂²×C₃	—	2	1	no	—
971	C₂²×C₃	—	2	1	no	—
972	C₂²×C₃	—	2	2	no	—
973	C₂²×C₃	—	2	2	no	—
974	C₂²×C₃	C₂⁴×C₄	1	1	yes	characteristic
975	C₃×C₄	—	2	1	no	—
976	C₃×C₄	—	2	2	no	—
977	C₃×C₄	—	2	1	no	—
978	C₃×C₄	—	2	1	no	—
979	C₃×C₄	—	2	2	no	—
980	C₃×C₄	—	2	1	no	—
981	C₃×C₄	—	2	1	no	—
982	C₃×C₄	—	2	1	no	—
983	C₃×C₄	—	2	2	no	—
984	C₃×C₄	—	2	2	no	—
985	C₃×C₄	—	2	1	no	—
986	C₃×C₄	—	2	1	no	—
987	C₃×C₄	—	2	1	no	—
988	C₃×C₄	—	2	2	no	—
989	C₃×C₄	—	2	1	no	—
990	C₃×C₄	—	2	2	no	—
991	C₃×C₄	#568	1	2	yes	—
992	C₃×C₄	#585	1	1	yes	characteristic
993	C₃×C₄	#585	1	1	yes	characteristic
994	C₂³	C₂³×Dic₃	1	1	yes	characteristic
995	C₂³	C₂³×Dic₃	1	1	yes	characteristic
996	C₂³	C₂³×Dic₃	1	2	yes	—
997	C₂³	C₂³×Dic₃	1	2	yes	—
998	C₂³	C₂³×Dic₃	1	1	yes	characteristic
999	Q₈	—	2	2	no	—
1000	Q₈	—	2	2	no	—
1001	Q₈	—	4	2	no	—
1002	Q₈	—	4	1	no	—
1003	Q₈	—	4	2	no	—
1004	D₄	—	2	2	no	—
1005	D₄	—	2	2	no	—
1006	D₄	—	4	2	no	—
1007	D₄	—	4	2	no	—
1008	D₄	—	4	1	no	—
1009	D₄	—	4	2	no	—
1010	D₄	—	4	1	no	—
1011	D₄	—	4	2	no	—
1012	D₄	—	4	1	no	—
1013	D₄	—	4	2	no	—
1014	D₄	—	4	2	no	—
1015	D₄	—	4	2	no	—
1016	D₄	—	4	2	no	—
1017	C₂×C₄	—	2	2	no	—
1018	C₂×C₄	—	2	1	no	—
1019	C₂×C₄	—	2	1	no	—
1020	C₂×C₄	—	2	2	no	—
1021	C₂×C₄	—	2	2	no	—
1022	C₂×C₄	—	2	1	no	—
1023	C₂×C₄	—	2	1	no	—
1024	C₂×C₄	—	2	2	no	—
1025	C₂×C₄	—	2	1	no	—
1026	C₂×C₄	—	2	1	no	—
1027	C₂×C₄	—	2	2	no	—
1028	C₂×C₄	—	2	2	no	—
1029	C₂×C₄	—	2	2	no	—
1030	C₂×C₄	—	4	2	no	—
1031	C₂×C₄	—	4	2	no	—
1032	C₂×C₄	—	4	2	no	—
1033	C₂×C₄	—	4	1	no	—
1034	C₂×C₄	—	4	2	no	—
1035	C₂×C₄	—	4	1	no	—
1036	C₂×C₄	—	4	2	no	—
1037	C₂×C₄	—	4	1	no	—
1038	C₂×C₄	—	4	2	no	—
1039	C₂×C₄	C₂³×Dic₃	1	1	yes	characteristic
1040	C₂×C₄	C₂³×Dic₃	1	1	yes	characteristic
1041	C₂×C₄	C₂³×Dic₃	1	2	yes	—
1042	C₂×C₄	C₂³×Dic₃	1	1	yes	characteristic
1043	C₂×C₄	C₂³×Dic₃	1	1	yes	characteristic
1044	C₂×C₄	C₂³×Dic₃	1	1	yes	characteristic
1045	C₂×C₄	C₂³×Dic₃	1	1	yes	characteristic
1046	C₂×C₄	C₂³×Dic₃	1	2	yes	—
1047	C₂×C₄	C₂³×Dic₃	1	1	yes	characteristic
1048	C₂×C₄	C₂³×Dic₃	1	2	yes	—
1049	C₂×C₄	C₂³×Dic₃	1	1	yes	characteristic
1050	C₂×C₄	C₂³×Dic₃	1	2	yes	—
1051	C₂×C₄	C₂³×Dic₃	1	1	yes	characteristic
1052	C₂×C₄	C₂³×Dic₃	1	2	yes	—
1053	C₂×C₄	C₂³×Dic₃	1	2	yes	—
1054	C₂×C₄	C₂³×Dic₃	1	1	yes	characteristic
1055	C₂×C₄	C₂³×Dic₃	1	1	yes	characteristic
1056	C₂×C₄	C₂⁴×D₃	1	1	yes	characteristic
1057	C₈	—	6	1	no	—
1058	C₈	—	6	1	no	—
1059	C₈	—	6	1	no	—
1060	C₈	—	6	2	no	—
1061	C₈	—	6	1	no	—
1062	C₈	—	6	2	no	—
1063	C₈	—	6	1	no	—
1064	C₈	—	6	2	no	—
1065	C₈	—	6	1	no	—
1066	C₈	—	6	1	no	—
1067	C₈	—	6	2	no	—
1068	C₈	—	6	1	no	—
1069	C₂×C₃	—	4	1	no	—
1070	C₂×C₃	—	4	1	no	—
1071	C₂×C₃	—	4	1	no	—
1072	C₂×C₃	—	4	2	no	—
1073	C₂×C₃	—	4	2	no	—
1074	C₂×C₃	#3428	1	1	yes	characteristic
1075	C₂×C₃	C₂×#568	1	1	yes	characteristic
1076	C₂×C₃	#3573	1	1	yes	characteristic
1077	C₂²	—	2	1	no	—
1078	C₂²	—	2	1	no	—
1079	C₂²	—	2	1	no	—
1080	C₂²	—	2	2	no	—
1081	C₂²	—	2	2	no	—
1082	C₂²	—	2	1	no	—
1083	C₂²	—	2	1	no	—
1084	C₂²	—	2	1	no	—
1085	C₂²	—	2	2	no	—
1086	C₂²	—	2	2	no	—
1087	C₂²	—	2	1	no	—
1088	C₂²	—	2	1	no	—
1089	C₂²	—	2	2	no	—
1090	C₂²	—	2	1	no	—
1091	C₂²	—	2	2	no	—
1092	C₂²	C₂⁴×Dic₃	1	1	yes	characteristic
1093	C₄	—	2	1	no	—
1094	C₄	—	2	1	no	—
1095	C₄	—	2	1	no	—
1096	C₄	—	2	2	no	—
1097	C₄	—	2	1	no	—
1098	C₄	—	2	2	no	—
1099	C₄	—	2	1	no	—
1100	C₄	—	2	1	no	—
1101	C₄	—	2	1	no	—
1102	C₄	—	2	2	no	—
1103	C₄	—	2	2	no	—
1104	C₄	—	2	1	no	—
1105	C₄	—	2	2	no	—
1106	C₄	—	2	1	no	—
1107	C₄	—	2	1	no	—
1108	C₄	—	2	2	no	—
1109	C₄	#5819	1	2	yes	—
1110	C₄	#5964	1	1	yes	characteristic
1111	C₄	#5964	1	1	yes	characteristic
1112	C₃	#60302	1	1	yes	characteristic, complemented, Sylow
1113	C₂	—	4	1	no	—
1114	C₂	—	4	1	no	—
1115	C₂	—	4	1	no	—
1116	C₂	—	4	2	no	—
1117	C₂	—	4	2	no	—
1118	C₂	C₂×#5819	1	1	yes	characteristic
1119	C₂	#87260	1	1	yes	characteristic
1120	C₂	#87296	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂⁴×D₃
commutator, socle	C₂²×C₃	C₂⁴×C₄
Fitting, prime radical	C₃×#3480	C₂
cosocle	C₂×C₃×C₄	C₂⁵
hypercenter	#3480	D₃
hypocenter	C₃	#60302
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄ ◁ #3480

Complements

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

N	H ≅ G/N	type
2. #83280	C₂	semidirect
3. #83280	C₂	semidirect
4. #83279	C₂	semidirect
5. #83278	C₂	semidirect
6. #83133	C₂	semidirect
7. #83132	C₂	semidirect
8. #83131	C₂	semidirect
9. #83130	C₂	semidirect
10. #83129	C₂	semidirect
11. #83128	C₂	semidirect
12. #83127	C₂	semidirect
13. #83126	C₂	semidirect
14. #82522	C₂	semidirect
15. #82521	C₂	semidirect
16. #82518	C₂	semidirect
17. #82517	C₂	semidirect
18. #82515	C₂	semidirect
19. #82515	C₂	semidirect
20. #82514	C₂	semidirect
21. #82513	C₂	semidirect
22. #82437	C₂	semidirect
23. #82436	C₂	semidirect
1112. C₃	#60302	semidirect

Maximal subgroups

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

subgroup	index
C₃×#3480	2
#83280	2
#83279	2
#83278	2
#83133	2
#83132	2
#83131	2
#83130	2
#83129	2
#83128	2
#83127	2
#83126	2
#82522	2
#82521	2
#82518	2
#82517	2
#82515	2
#82514	2
#82513	2
#82437	2
#82436	2
#60302	3