Subgroups — #11660422

Order 768.

1832 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#85764	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#435	C₂	1	1	yes	maximal, characteristic, complemented
3	#83756	C₂	1	1	yes	maximal, characteristic, complemented
4	#83750	C₂	1	1	yes	maximal, characteristic, complemented
5	#83734	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#5102	C₂	1	1	yes	maximal, characteristic, complemented
7	D₄×#208	C₂	1	1	yes	maximal, characteristic, complemented
8	#79468	C₂	1	2	yes	maximal, complemented
9	#79467	C₂	1	2	yes	maximal, complemented
10	#79466	C₂	1	2	yes	maximal, complemented
11	#79465	C₂	1	2	yes	maximal, complemented
12	#79464	C₂	1	2	yes	maximal, complemented
13	#79463	C₂	1	2	yes	maximal, complemented
14	#79462	C₂	1	2	yes	maximal, complemented
15	#79461	C₂	1	2	yes	maximal, complemented
16	#79012	C₂	1	1	yes	maximal, characteristic, complemented
17	#79008	C₂	1	1	yes	maximal, characteristic, complemented
18	#78596	C₂	1	1	yes	maximal, characteristic, complemented
19	#78596	C₂	1	1	yes	maximal, characteristic, complemented
20	#78584	C₂	1	1	yes	maximal, characteristic, complemented
21	#78584	C₂	1	1	yes	maximal, characteristic, complemented
22	#78489	C₂	1	1	yes	maximal, characteristic, complemented
23	#78480	C₂	1	1	yes	maximal, characteristic, complemented
24	#60272	—	3	1	no	maximal, Sylow
25	C₂²×C₃×M₁₆	C₂²	1	1	yes	characteristic
26	C₂³×C₃×C₈	C₂²	1	1	yes	characteristic
27	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
28	#5806	C₄	1	2	yes	—
29	#5791	C₂²	1	1	yes	characteristic
30	#5791	C₂²	1	1	yes	characteristic
31	C₂×#926	C₂²	1	1	yes	characteristic
32	C₂×#926	C₂²	1	1	yes	characteristic
33	C₂²×#208	C₂²	1	1	yes	characteristic
34	C₂²×#208	C₂²	1	1	yes	characteristic
35	C₂×#901	C₂²	1	1	yes	characteristic
36	C₂×#901	C₂²	1	1	yes	characteristic
37	#5565	C₄	1	1	yes	characteristic
38	#5565	C₄	1	1	yes	characteristic
39	#5563	C₄	1	1	yes	characteristic
40	#5557	C₂²	1	2	yes	—
41	#5555	C₄	1	1	yes	characteristic
42	#5543	C₄	1	1	yes	characteristic
43	#5542	C₄	1	1	yes	characteristic
44	#5541	C₄	1	1	yes	characteristic
45	#5541	C₄	1	1	yes	characteristic
46	#5538	C₂²	1	2	yes	—
47	#5538	C₂²	1	2	yes	—
48	C₄×#237	C₂²	1	2	yes	—
49	#5513	C₄	1	2	yes	—
50	#5495	C₄	1	2	yes	—
51	#5495	C₄	1	2	yes	—
52	C₄×#235	C₂²	1	1	yes	characteristic
53	#5470	C₂²	1	1	yes	characteristic
54	C₃×#435	C₂²	1	1	yes	characteristic
55	C₃×#435	C₂²	1	1	yes	characteristic
56	C₃×#435	C₂²	1	1	yes	characteristic
57	C₃×#435	C₂²	1	1	yes	characteristic
58	C₃×#435	C₂²	1	1	yes	characteristic
59	C₃×#435	C₂²	1	1	yes	characteristic
60	C₃×#435	C₂²	1	1	yes	characteristic
61	C₃×#435	C₂²	1	1	yes	characteristic
62	C₂×C₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
63	C₂×C₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
64	C₂×C₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
65	C₂×C₃×#97	C₂²	1	1	yes	characteristic
66	#5207	C₂²	1	1	yes	characteristic
67	#5207	C₂²	1	1	yes	characteristic
68	#5128	C₂²	1	2	yes	complemented
69	#5128	C₂²	1	2	yes	complemented
70	#5127	C₂²	1	2	yes	complemented
71	#5127	C₂²	1	2	yes	complemented
72	#5119	C₂²	1	2	yes	complemented
73	#5119	C₂²	1	2	yes	complemented
74	#5118	C₂²	1	2	yes	complemented
75	#5118	C₂²	1	2	yes	complemented
76	#5111	C₂²	1	2	yes	complemented
77	#5111	C₂²	1	2	yes	complemented
78	#5110	C₂²	1	1	yes	characteristic
79	#5110	C₂²	1	1	yes	characteristic
80	C₈×#67	C₂²	1	2	yes	complemented
81	C₈×#67	C₂²	1	2	yes	complemented
82	#5102	C₂²	1	1	yes	characteristic
83	#5102	C₂²	1	1	yes	characteristic
84	#5102	C₂²	1	1	yes	characteristic
85	#5102	C₂²	1	1	yes	characteristic
86	#5102	C₂²	1	1	yes	characteristic
87	#5102	C₂²	1	1	yes	characteristic
88	#5102	C₂²	1	1	yes	characteristic
89	#5102	C₂²	1	1	yes	characteristic
90	#5102	C₂²	1	2	yes	complemented
91	#5102	C₂²	1	2	yes	complemented
92	#5101	C₂²	1	1	yes	characteristic
93	#5101	C₂²	1	1	yes	characteristic
94	#5101	C₂²	1	1	yes	characteristic
95	#5101	C₂²	1	1	yes	characteristic
96	C₂×Dic₃⋊C₈	C₂²	1	2	yes	complemented
97	C₂×Dic₃⋊C₈	C₂²	1	2	yes	complemented
98	#5012	C₂²	1	2	yes	—
99	#5011	C₂²	1	2	yes	—
100	#5011	C₂²	1	2	yes	—
101	D₄×C₃⋊C₈	C₂²	1	2	yes	—
102	#4924	C₂²	1	1	yes	characteristic
103	C₄×#208	C₂²	1	1	yes	characteristic
104	#4839	C₂²	1	2	yes	complemented
105	#4839	C₂²	1	2	yes	complemented
106	#4837	C₂²	1	2	yes	complemented
107	D₃×C₄⋊C₈	C₂²	1	2	yes	complemented
108	#4831	C₂²	1	2	yes	complemented
109	#4830	C₂²	1	2	yes	complemented
110	#4828	C₂²	1	2	yes	complemented
111	#4828	C₂²	1	2	yes	complemented
112	#4730	C₂²	1	2	yes	complemented
113	#4730	C₂²	1	2	yes	complemented
114	#4729	C₂²	1	2	yes	complemented
115	#4729	C₂²	1	2	yes	complemented
116	#4728	C₂²	1	2	yes	complemented
117	#4728	C₂²	1	2	yes	complemented
118	#67⋊C₈	C₂²	1	2	yes	complemented
119	#67⋊C₈	C₂²	1	2	yes	complemented
120	#4720	C₂²	1	2	yes	complemented
121	#4720	C₂²	1	2	yes	complemented
122	#4720	C₂²	1	2	yes	complemented
123	#4720	C₂²	1	2	yes	complemented
124	#4719	C₂²	1	2	yes	complemented
125	#4719	C₂²	1	2	yes	complemented
126	#4718	C₂²	1	2	yes	complemented
127	#4718	C₂²	1	2	yes	complemented
128	#4709	C₂²	1	2	yes	complemented
129	#4709	C₂²	1	2	yes	complemented
130	#4705	C₂²	1	2	yes	complemented
131	#4705	C₂²	1	2	yes	complemented
132	#4701	C₂²	1	2	yes	complemented
133	#4701	C₂²	1	2	yes	complemented
134	#4701	C₂²	1	2	yes	complemented
135	#4701	C₂²	1	2	yes	complemented
136	#3475	—	3	1	no	—
137	#2995	—	3	2	no	—
138	#2995	—	3	2	no	—
139	#2994	—	3	2	no	—
140	#2993	—	3	2	no	—
141	#2992	—	3	2	no	—
142	#2992	—	3	2	no	—
143	#2990	—	3	2	no	—
144	#2989	—	3	2	no	—
145	#2962	—	3	1	no	—
146	#2961	—	3	1	no	—
147	D₄×M₁₆	—	3	1	no	—
148	#2933	—	3	1	no	—
149	#2933	—	3	1	no	—
150	#2930	—	3	1	no	—
151	#2929	—	3	1	no	—
152	C₂×#435	D₃	1	1	yes	characteristic, complemented
153	#2924	—	3	1	no	—
154	#2924	—	3	1	no	—
155	#2923	—	3	1	no	—
156	#2906	—	3	1	no	—
157	#2905	—	3	1	no	—
158	C₂×#424	—	3	1	no	—
159	C₂²×C₃×D₄	C₂×C₄	1	1	yes	characteristic
160	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
161	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
162	C₂×#237	C₂×C₄	1	2	yes	—
163	C₂×#235	C₂³	1	1	yes	characteristic
164	C₂×C₃×M₁₆	—	4	2	no	—
165	C₂×C₃×M₁₆	C₂³	1	1	yes	characteristic
166	C₂×C₃×M₁₆	C₂³	1	1	yes	characteristic
167	C₂×C₃×M₁₆	C₂³	1	1	yes	characteristic
168	C₂×C₃×M₁₆	C₂³	1	1	yes	characteristic
169	C₂²×C₃×C₈	—	4	2	no	—
170	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
171	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
172	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
173	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
174	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
175	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
176	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
177	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
178	C₃×C₄×D₄	C₂×C₄	1	1	yes	characteristic
179	C₃×C₄×D₄	C₂×C₄	1	1	yes	characteristic
180	C₃×C₄×D₄	C₂×C₄	1	1	yes	characteristic
181	C₃×C₄×D₄	C₂×C₄	1	1	yes	characteristic
182	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
183	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
184	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
185	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
186	C₂×C₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
187	C₂×C₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
188	C₂×C₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
189	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
190	#953	C₂×C₄	1	2	yes	—
191	#953	C₂×C₄	1	2	yes	—
192	C₂×#217	C₂×C₄	1	2	yes	—
193	C₂×#217	C₂×C₄	1	2	yes	—
194	#939	C₂×C₄	1	2	yes	—
195	#939	C₂×C₄	1	2	yes	—
196	#938	C₂×C₄	1	2	yes	—
197	#936	C₂×C₄	1	2	yes	—
198	#935	C₂×C₄	1	2	yes	—
199	#935	C₂×C₄	1	2	yes	—
200	D₄×Dic₃	C₂×C₄	1	2	yes	—
201	#930	C₂×C₄	1	1	yes	characteristic
202	#930	C₂×C₄	1	1	yes	characteristic
203	#930	C₂×C₄	1	1	yes	characteristic
204	#930	C₂×C₄	1	1	yes	characteristic
205	#929	C₂×C₄	1	2	yes	—
206	#929	C₂×C₄	1	2	yes	—
207	C₄×#67	C₂×C₄	1	2	yes	—
208	C₄×#67	C₂×C₄	1	2	yes	—
209	C₄×#67	C₂³	1	2	yes	—
210	C₄×#67	C₂³	1	2	yes	—
211	C₄×#67	C₂³	1	2	yes	—
212	C₄×#67	C₂³	1	2	yes	—
213	#926	C₂×C₄	1	2	yes	—
214	#926	C₂×C₄	1	2	yes	—
215	#926	C₂×C₄	1	1	yes	characteristic
216	#926	C₂×C₄	1	1	yes	characteristic
217	#926	C₂×C₄	1	1	yes	characteristic
218	#926	C₂×C₄	1	1	yes	characteristic
219	#926	C₂³	1	1	yes	characteristic
220	#926	C₂³	1	1	yes	characteristic
221	#926	C₂³	1	1	yes	characteristic
222	#926	C₂³	1	2	yes	—
223	#926	C₂³	1	2	yes	—
224	C₂×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
225	C₂×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
226	C₂×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
227	C₂×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
228	#924	C₂×C₄	1	2	yes	—
229	#924	C₂×C₄	1	2	yes	—
230	#924	C₂×C₄	1	1	yes	characteristic
231	#924	C₂×C₄	1	1	yes	characteristic
232	#924	C₂×C₄	1	1	yes	characteristic
233	#924	C₂×C₄	1	1	yes	characteristic
234	C₂×C₄×Dic₃	C₂³	1	2	yes	—
235	C₂×C₄×Dic₃	C₂³	1	2	yes	—
236	C₂×#208	—	4	2	no	—
237	C₂×#208	—	4	2	no	—
238	C₂×#208	C₂³	1	1	yes	characteristic
239	C₂×#208	C₂³	1	1	yes	characteristic
240	C₂×#208	C₂³	1	1	yes	characteristic
241	C₂×#208	C₂³	1	1	yes	characteristic
242	C₂×#208	C₂³	1	2	yes	—
243	C₂×#208	C₂³	1	2	yes	—
244	C₂²×C₃⋊C₈	C₂³	1	2	yes	—
245	C₂²×C₃⋊C₈	C₂³	1	2	yes	—
246	#901	—	4	2	no	—
247	#901	—	4	2	no	—
248	C₂×ΓL(1,𝔽₂₅)	C₂³	1	2	yes	—
249	C₂×ΓL(1,𝔽₂₅)	C₂³	1	2	yes	—
250	C₂×D₃×C₈	C₂³	1	2	yes	—
251	C₂×D₃×C₈	C₂³	1	2	yes	—
252	#898	C₂×C₄	1	2	yes	—
253	#898	C₂×C₄	1	2	yes	—
254	#897	C₂×C₄	1	2	yes	—
255	#892	C₂×C₄	1	2	yes	—
256	#890	C₂×C₄	1	2	yes	—
257	#889	C₂×C₄	1	2	yes	—
258	#889	C₂×C₄	1	2	yes	—
259	#887	C₂×C₄	1	2	yes	—
260	#886	C₂×C₄	1	2	yes	—
261	#886	C₂×C₄	1	2	yes	—
262	#885	C₂×C₄	1	2	yes	—
263	#885	C₂×C₄	1	2	yes	—
264	#883	C₂×C₄	1	2	yes	—
265	#883	C₂×C₄	1	2	yes	—
266	#67⋊C₄	C₂×C₄	1	2	yes	—
267	#67⋊C₄	C₂×C₄	1	2	yes	—
268	#879	C₂×C₄	1	2	yes	—
269	#879	C₂×C₄	1	2	yes	—
270	#879	C₂×C₄	1	2	yes	—
271	#879	C₂×C₄	1	2	yes	—
272	#878	C₂×C₄	1	2	yes	—
273	#878	C₂×C₄	1	2	yes	—
274	#877	C₂×C₄	1	2	yes	—
275	#877	C₂×C₄	1	2	yes	—
276	C₄×D₁₂	C₂×C₄	1	1	yes	characteristic
277	C₄×D₁₂	C₂×C₄	1	1	yes	characteristic
278	#872	C₂³	1	2	yes	—
279	C₄²×D₃	C₂³	1	2	yes	—
280	#870	C₂×C₄	1	1	yes	characteristic
281	#870	C₂×C₄	1	1	yes	characteristic
282	#869	C₂×C₄	1	1	yes	characteristic
283	#869	C₂×C₄	1	1	yes	characteristic
284	C₄×Dic₆	C₂×C₄	1	1	yes	characteristic
285	C₄×Dic₆	C₂×C₄	1	1	yes	characteristic
286	C₄×Dic₆	C₂³	1	2	yes	—
287	C₄×Dic₆	C₂³	1	2	yes	—
288	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
289	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
290	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
291	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
292	C₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
293	C₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
294	C₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
295	C₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
296	C₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
297	C₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
298	C₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
299	C₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
300	C₃×#97	C₂³	1	1	yes	characteristic
301	C₃×#97	C₂³	1	1	yes	characteristic
302	C₃×#97	C₂³	1	1	yes	characteristic
303	C₃×#97	C₂³	1	1	yes	characteristic
304	#830	C₂³	1	2	yes	—
305	#830	C₂³	1	2	yes	—
306	#830	C₂³	1	2	yes	—
307	#830	C₂³	1	2	yes	—
308	(C₂×D₃)⋊C₈	C₂³	1	2	yes	—
309	(C₂×D₃)⋊C₈	C₂³	1	2	yes	—
310	(C₂×D₃)⋊C₈	C₂³	1	2	yes	—
311	(C₂×D₃)⋊C₈	C₂³	1	2	yes	—
312	#815	C₂³	1	2	yes	—
313	#815	C₂³	1	2	yes	—
314	#815	C₂³	1	2	yes	—
315	#815	C₂³	1	2	yes	—
316	Dic₃⋊C₈	C₂³	1	2	yes	—
317	Dic₃⋊C₈	C₂³	1	2	yes	—
318	Dic₃⋊C₈	C₂³	1	2	yes	—
319	Dic₃⋊C₈	C₂³	1	2	yes	—
320	Dic₃⋊C₈	C₂³	1	2	yes	—
321	Dic₃⋊C₈	C₂³	1	2	yes	—
322	Dic₃⋊C₈	C₂³	1	2	yes	—
323	Dic₃⋊C₈	C₂³	1	2	yes	—
324	Dic₃⋊C₈	C₂³	1	2	yes	—
325	Dic₃⋊C₈	C₂³	1	2	yes	—
326	Dic₃⋊C₈	C₂³	1	2	yes	—
327	Dic₃⋊C₈	C₂³	1	2	yes	—
328	Dic₃⋊C₈	C₂³	1	2	yes	—
329	Dic₃⋊C₈	C₂³	1	2	yes	—
330	Dic₃⋊C₈	C₂³	1	2	yes	—
331	Dic₃⋊C₈	C₂³	1	2	yes	—
332	C₈×Dic₃	C₂³	1	2	yes	—
333	C₈×Dic₃	C₂³	1	2	yes	—
334	C₈×Dic₃	C₂³	1	2	yes	—
335	C₈×Dic₃	C₂³	1	2	yes	—
336	C₄⋊(C₃⋊C₈)	C₂³	1	2	yes	—
337	C₄⋊(C₃⋊C₈)	C₂³	1	2	yes	—
338	#803	C₂³	1	2	yes	—
339	C₄×C₃⋊C₈	C₂³	1	2	yes	—
340	C₂×#131	—	3	1	no	—
341	C₂×#131	—	3	1	no	—
342	C₂²×M₁₆	—	3	1	no	—
343	C₂²×M₁₆	—	3	1	no	—
344	C₂²×M₁₆	C₂×D₃	1	1	yes	characteristic
345	C₂³×C₈	C₂×D₃	1	1	yes	characteristic
346	#556	—	3	1	no	—
347	#555	—	3	1	no	—
348	#554	—	3	1	no	—
349	#553	—	3	1	no	—
350	#553	—	3	1	no	—
351	#552	—	3	1	no	—
352	#552	—	3	1	no	—
353	#552	—	3	2	no	—
354	#551	—	3	2	no	—
355	#551	—	3	2	no	—
356	#547	—	3	1	no	—
357	#546	—	3	2	no	—
358	#533	—	3	1	no	—
359	#529	—	3	2	no	—
360	#529	—	3	2	no	—
361	#529	—	3	2	no	—
362	#525	—	3	1	no	—
363	#525	—	3	1	no	—
364	C₄×#41	—	3	2	no	—
365	C₄×#41	—	3	1	no	—
366	C₂×C₄×D₄	C₂×D₃	1	1	yes	characteristic
367	C₂×#117	—	3	1	no	—
368	C₂×#117	—	3	1	no	—
369	#446	—	3	2	no	—
370	#446	—	3	2	no	—
371	#446	—	3	2	no	—
372	#446	—	3	2	no	—
373	#446	—	3	2	no	—
374	#446	—	3	2	no	—
375	#446	—	3	2	no	—
376	C₈×Q₈	—	3	2	no	—
377	#436	—	3	2	no	—
378	#436	—	3	2	no	—
379	#436	—	3	2	no	—
380	#436	—	3	2	no	—
381	#436	—	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	#435	—	3	2	no	—
391	#435	—	3	2	no	—
392	#435	C₂×D₃	1	1	yes	characteristic
393	#435	C₂×D₃	1	1	yes	characteristic
394	#435	C₂×D₃	1	1	yes	characteristic
395	#435	C₂×D₃	1	1	yes	characteristic
396	#435	C₂×D₃	1	1	yes	characteristic
397	#435	C₂×D₃	1	1	yes	characteristic
398	#435	C₂×D₃	1	1	yes	characteristic
399	#435	C₂×D₃	1	1	yes	characteristic
400	C₈×D₄	—	3	2	no	—
401	C₈×D₄	—	3	2	no	—
402	C₈×D₄	—	3	2	no	—
403	C₈×D₄	—	3	2	no	—
404	C₈×D₄	—	3	2	no	—
405	#433	—	3	2	no	—
406	#433	—	3	2	no	—
407	#433	—	3	2	no	—
408	#433	—	3	2	no	—
409	#433	—	3	2	no	—
410	#433	—	3	2	no	—
411	#432	—	3	2	no	—
412	#432	—	3	2	no	—
413	#432	—	3	2	no	—
414	#432	—	3	2	no	—
415	#431	—	3	2	no	—
416	#431	—	3	2	no	—
417	#424	—	3	2	no	—
418	#424	—	3	2	no	—
419	#424	—	3	1	no	—
420	#424	—	3	1	no	—
421	#424	—	3	1	no	—
422	#424	—	3	1	no	—
423	#424	—	3	2	no	—
424	#424	—	3	2	no	—
425	#424	—	3	1	no	—
426	#424	—	3	1	no	—
427	#424	—	3	1	no	—
428	#424	—	3	1	no	—
429	#424	—	3	2	no	—
430	#424	—	3	2	no	—
431	#423	—	3	2	no	—
432	#423	—	3	2	no	—
433	#423	—	3	1	no	—
434	#423	—	3	2	no	—
435	C₂×C₄⋊C₈	—	3	2	no	—
436	C₂×C₄⋊C₈	—	3	2	no	—
437	C₂×C₄⋊C₈	—	3	2	no	—
438	C₂×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
439	#408	—	3	1	no	—
440	#408	—	3	1	no	—
441	#407	—	3	1	no	—
442	#407	—	3	1	no	—
443	C₂×C₂²⋊C₈	C₂×D₃	1	1	yes	characteristic
444	C₂×C₂²⋊C₈	C₂×D₃	1	1	yes	characteristic
445	#405	—	3	1	no	—
446	#405	—	3	1	no	—
447	#405	—	3	1	no	—
448	#405	—	3	1	no	—
449	C₄×M₁₆	—	3	1	no	—
450	C₂×#97	C₂×D₃	1	1	yes	characteristic
451	C₂⁴×C₃	C₂²×C₄	1	1	yes	characteristic
452	C₂⁴×C₃	C₂²×C₄	1	1	yes	characteristic
453	C₂×C₃×D₄	—	4	2	no	—
454	C₂×C₃×D₄	C₂²×C₄	1	1	yes	characteristic
455	C₂×C₃×D₄	C₂²×C₄	1	1	yes	characteristic
456	C₂×C₃×D₄	C₂²×C₄	1	1	yes	characteristic
457	C₂×C₃×D₄	C₂²×C₄	1	1	yes	characteristic
458	C₂²×C₃×C₄	—	2	2	no	—
459	C₂²×C₃×C₄	—	2	2	no	—
460	C₂²×C₃×C₄	—	2	2	no	—
461	C₂²×C₃×C₄	—	2	2	no	—
462	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
463	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
464	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
465	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
466	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
467	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
468	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
469	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
470	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
471	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
472	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
473	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
474	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
475	C₂×#67	C₂²×C₄	1	2	yes	—
476	C₂×#67	C₂²×C₄	1	2	yes	—
477	C₂×#67	C₂²×C₄	1	2	yes	—
478	C₂×#67	C₂²×C₄	1	2	yes	—
479	C₂×#67	C₂²×C₄	1	2	yes	—
480	C₂²×Dic₃	C₂²×C₄	1	2	yes	—
481	C₂²×Dic₃	C₂²×C₄	1	2	yes	—
482	C₂²×Dic₃	C₂²×C₄	1	2	yes	—
483	C₂²×Dic₃	C₂²×C₄	1	2	yes	—
484	#237	—	4	4	no	—
485	#235	—	2	2	no	—
486	#235	—	2	2	no	—
487	C₂×D₁₂	C₂²×C₄	1	1	yes	characteristic
488	C₂×C₄×D₃	C₂²×C₄	1	2	yes	—
489	C₂×C₄×D₃	C₂²×C₄	1	2	yes	—
490	C₂×C₄×D₃	C₂⁴	1	2	yes	—
491	C₂×Dic₆	C₂²×C₄	1	1	yes	characteristic
492	C₂×Dic₆	C₂²×C₄	1	2	yes	—
493	C₂×Dic₆	C₂²×C₄	1	2	yes	—
494	C₃×M₁₆	—	4	1	no	—
495	C₃×M₁₆	—	4	1	no	—
496	C₃×M₁₆	—	4	1	no	—
497	C₃×M₁₆	—	4	1	no	—
498	C₂×C₃×C₈	—	2	2	no	—
499	C₂×C₃×C₈	—	2	2	no	—
500	C₂×C₃×C₈	—	2	2	no	—
501	C₂×C₃×C₈	—	2	2	no	—
502	C₂×C₃×C₈	—	4	1	no	—
503	C₂×C₃×C₈	—	4	1	no	—
504	C₂×C₃×C₈	—	4	1	no	—
505	C₂×C₃×C₈	—	4	1	no	—
506	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
507	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
508	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
509	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
510	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
511	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
512	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
513	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
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	1	yes	characteristic
517	C₃×C₄⋊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	1	yes	characteristic
521	C₃×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
522	C₃×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
523	C₃×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
524	C₃×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
525	C₃×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
526	C₃×C₄²	C₂²×C₄	1	1	yes	characteristic
527	C₃×C₄²	C₂²×C₄	1	1	yes	characteristic
528	C₃×C₄²	C₂⁴	1	1	yes	characteristic
529	C₃×C₄²	C₂⁴	1	1	yes	characteristic
530	#217	C₂²×C₄	1	2	yes	—
531	#217	C₂²×C₄	1	2	yes	—
532	#217	C₂²×C₄	1	2	yes	—
533	#217	C₂²×C₄	1	2	yes	—
534	#217	C₂²×C₄	1	2	yes	—
535	#217	C₂²×C₄	1	2	yes	—
536	#217	C₂²×C₄	1	2	yes	—
537	#217	C₂²×C₄	1	2	yes	—
538	#217	C₂²×C₄	1	2	yes	—
539	#217	C₂²×C₄	1	2	yes	—
540	#217	C₂²×C₄	1	2	yes	—
541	(C₂×D₃)⋊C₄	C₂²×C₄	1	2	yes	—
542	(C₂×D₃)⋊C₄	C₂²×C₄	1	2	yes	—
543	(C₂×D₃)⋊C₄	C₂²×C₄	1	2	yes	—
544	(C₂×D₃)⋊C₄	C₂²×C₄	1	2	yes	—
545	(C₂×D₃)⋊C₄	C₂²×C₄	1	2	yes	—
546	(C₂×D₃)⋊C₄	C₂²×C₄	1	2	yes	—
547	C₄⋊Dic₃	C₂²×C₄	1	1	yes	characteristic
548	C₄⋊Dic₃	C₂²×C₄	1	1	yes	characteristic
549	C₄⋊Dic₃	C₂²×C₄	1	2	yes	—
550	C₄⋊Dic₃	C₂²×C₄	1	2	yes	—
551	C₄⋊Dic₃	C₂²×C₄	1	1	yes	characteristic
552	C₄⋊Dic₃	C₂²×C₄	1	1	yes	characteristic
553	C₄⋊Dic₃	C₂²×C₄	1	1	yes	characteristic
554	C₄⋊Dic₃	C₂²×C₄	1	1	yes	characteristic
555	C₄⋊Dic₃	C₂²×C₄	1	2	yes	—
556	C₄⋊Dic₃	C₂²×C₄	1	2	yes	—
557	C₄⋊Dic₃	C₂²×C₄	1	2	yes	—
558	C₄⋊Dic₃	C₂²×C₄	1	2	yes	—
559	Dic₃⋊C₄	C₂²×C₄	1	2	yes	—
560	Dic₃⋊C₄	C₂²×C₄	1	2	yes	—
561	Dic₃⋊C₄	C₂²×C₄	1	2	yes	—
562	Dic₃⋊C₄	C₂²×C₄	1	2	yes	—
563	Dic₃⋊C₄	C₂²×C₄	1	2	yes	—
564	Dic₃⋊C₄	C₂²×C₄	1	2	yes	—
565	Dic₃⋊C₄	C₂²×C₄	1	2	yes	—
566	Dic₃⋊C₄	C₂²×C₄	1	2	yes	—
567	Dic₃⋊C₄	C₂²×C₄	1	2	yes	—
568	Dic₃⋊C₄	C₂²×C₄	1	2	yes	—
569	C₄×Dic₃	C₂²×C₄	1	2	yes	—
570	C₄×Dic₃	C₂²×C₄	1	2	yes	—
571	C₄×Dic₃	C₂²×C₄	1	2	yes	—
572	C₄×Dic₃	C₂²×C₄	1	2	yes	—
573	C₄×Dic₃	C₂²×C₄	1	2	yes	—
574	C₄×Dic₃	C₂²×C₄	1	2	yes	—
575	C₄×Dic₃	C₂⁴	1	2	yes	—
576	C₄×Dic₃	C₂⁴	1	2	yes	—
577	C₄×Dic₃	C₂⁴	1	2	yes	—
578	#208	—	2	2	no	—
579	#208	—	2	2	no	—
580	#208	—	2	2	no	—
581	#208	—	2	2	no	—
582	#208	—	4	2	no	—
583	#208	—	4	2	no	—
584	C₂×C₃⋊C₈	—	4	2	no	—
585	C₂×C₃⋊C₈	—	4	2	no	—
586	C₂×C₃⋊C₈	C₂⁴	1	2	yes	—
587	C₂×C₃⋊C₈	C₂⁴	1	2	yes	—
588	C₂×C₃⋊C₈	C₂⁴	1	2	yes	—
589	C₂×C₃⋊C₈	C₂⁴	1	2	yes	—
590	ΓL(1,𝔽₂₅)	—	4	2	no	—
591	ΓL(1,𝔽₂₅)	—	4	2	no	—
592	D₃×C₈	—	4	2	no	—
593	D₃×C₈	—	4	2	no	—
594	C₂×#41	—	3	2	no	—
595	C₂×#41	—	3	1	no	—
596	C₂²×D₄	C₄×D₃	1	1	yes	characteristic
597	C₂³×C₄	C₂²×D₃	1	1	yes	characteristic
598	C₂³×C₄	C₂²×D₃	1	1	yes	characteristic
599	#131	—	12	2	no	—
600	#131	—	12	2	no	—
601	C₂×M₁₆	—	3	1	no	—
602	C₂×M₁₆	—	3	1	no	—
603	C₂×M₁₆	—	3	1	no	—
604	C₂×M₁₆	—	3	1	no	—
605	C₂×M₁₆	—	3	2	no	—
606	C₂×M₁₆	—	3	2	no	—
607	C₂×M₁₆	—	3	2	no	—
608	C₂×M₁₆	—	3	2	no	—
609	C₂×M₁₆	—	4	2	no	—
610	C₂×M₁₆	—	12	2	no	—
611	C₂×M₁₆	—	12	2	no	—
612	C₂×M₁₆	C₂²×D₃	1	1	yes	characteristic
613	C₂×M₁₆	C₂²×D₃	1	1	yes	characteristic
614	C₂×M₁₆	C₂²×D₃	1	1	yes	characteristic
615	C₂×M₁₆	C₂²×D₃	1	1	yes	characteristic
616	C₂²×C₈	—	3	2	no	—
617	C₂²×C₈	—	3	2	no	—
618	C₂²×C₈	—	3	2	no	—
619	C₂²×C₈	—	3	2	no	—
620	C₂²×C₈	—	4	2	no	—
621	C₂²×C₈	C₂²×D₃	1	1	yes	characteristic
622	C₂²×C₈	C₂²×D₃	1	1	yes	characteristic
623	C₂²×C₈	C₂²×D₃	1	1	yes	characteristic
624	C₂²×C₈	C₂²×D₃	1	1	yes	characteristic
625	C₂²×C₈	C₂²×D₃	1	1	yes	characteristic
626	C₂²×C₈	C₂²×D₃	1	1	yes	characteristic
627	C₂²×C₈	C₂²×D₃	1	1	yes	characteristic
628	C₂²×C₈	C₂²×D₃	1	1	yes	characteristic
629	C₄⋊Q₈	—	3	1	no	—
630	C₄⋊Q₈	—	3	1	no	—
631	#126	—	3	2	no	—
632	#126	—	3	2	no	—
633	#126	—	3	2	no	—
634	#126	—	3	2	no	—
635	#126	—	3	2	no	—
636	#126	—	3	2	no	—
637	#125	—	3	2	no	—
638	#125	—	3	2	no	—
639	#125	—	3	2	no	—
640	#125	—	3	1	no	—
641	#125	—	3	1	no	—
642	#124	—	3	2	no	—
643	#124	—	3	2	no	—
644	#124	—	3	2	no	—
645	#123	—	3	2	no	—
646	#123	—	3	2	no	—
647	#123	—	3	2	no	—
648	#123	—	3	2	no	—
649	#123	—	3	2	no	—
650	#123	—	3	2	no	—
651	#123	—	3	2	no	—
652	#123	—	3	2	no	—
653	C₂²⋊Q₈	—	3	1	no	—
654	C₂²⋊Q₈	—	3	1	no	—
655	C₂²⋊Q₈	—	3	1	no	—
656	C₂²⋊Q₈	—	3	1	no	—
657	C₂²⋊Q₈	—	3	2	no	—
658	C₂²⋊Q₈	—	3	2	no	—
659	C₂²⋊Q₈	—	3	2	no	—
660	C₂²⋊Q₈	—	3	2	no	—
661	C₂²⋊Q₈	—	3	2	no	—
662	#121	—	3	2	no	—
663	#121	—	3	2	no	—
664	#121	—	3	2	no	—
665	#121	—	3	1	no	—
666	#121	—	3	1	no	—
667	#121	—	3	1	no	—
668	#121	—	3	1	no	—
669	#120	—	3	2	no	—
670	#120	—	3	2	no	—
671	C₄×Q₈	—	3	2	no	—
672	C₄×Q₈	—	3	1	no	—
673	C₄×Q₈	—	3	1	no	—
674	C₄×Q₈	—	3	2	no	—
675	C₄×Q₈	—	3	2	no	—
676	C₄×D₄	—	3	2	no	—
677	C₄×D₄	—	3	2	no	—
678	C₄×D₄	—	3	2	no	—
679	C₄×D₄	—	3	2	no	—
680	C₄×D₄	—	3	2	no	—
681	C₄×D₄	—	3	2	no	—
682	C₄×D₄	—	3	2	no	—
683	C₄×D₄	—	3	2	no	—
684	C₄×D₄	—	3	2	no	—
685	C₄×D₄	—	3	1	no	—
686	C₄×D₄	—	3	1	no	—
687	C₄×D₄	C₄×D₃	1	1	yes	characteristic
688	C₄×D₄	C₄×D₃	1	1	yes	characteristic
689	C₄×D₄	C₄×D₃	1	1	yes	characteristic
690	C₄×D₄	C₄×D₃	1	1	yes	characteristic
691	C₄×D₄	C₂²×D₃	1	1	yes	characteristic
692	C₄×D₄	C₂²×D₃	1	1	yes	characteristic
693	C₄×D₄	C₂²×D₃	1	1	yes	characteristic
694	C₄×D₄	C₂²×D₃	1	1	yes	characteristic
695	#117	—	3	2	no	—
696	#117	—	3	2	no	—
697	#117	—	3	1	no	—
698	#117	—	3	1	no	—
699	#117	—	3	1	no	—
700	#117	—	3	1	no	—
701	#117	—	3	1	no	—
702	#117	—	3	1	no	—
703	#117	—	3	1	no	—
704	#117	—	3	2	no	—
705	#117	—	3	2	no	—
706	#117	—	3	2	no	—
707	#117	—	3	2	no	—
708	#117	—	3	2	no	—
709	#117	—	3	2	no	—
710	C₂×C₄⋊C₄	—	3	1	no	—
711	C₂×C₄⋊C₄	—	3	1	no	—
712	C₂×C₄⋊C₄	—	3	1	no	—
713	C₂×C₄⋊C₄	—	3	1	no	—
714	C₂×C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
715	C₂×C₂²⋊C₄	—	3	2	no	—
716	C₂×C₂²⋊C₄	—	3	2	no	—
717	C₂×C₂²⋊C₄	C₄×D₃	1	1	yes	characteristic
718	C₂×C₂²⋊C₄	C₄×D₃	1	1	yes	characteristic
719	C₂×C₄²	—	3	2	no	—
720	C₂×C₄²	—	3	2	no	—
721	C₂×C₄²	—	3	2	no	—
722	C₂×C₄²	C₂²×D₃	1	1	yes	characteristic
723	C₄⋊C₈	—	3	2	no	—
724	C₄⋊C₈	—	3	2	no	—
725	C₄⋊C₈	—	3	2	no	—
726	C₄⋊C₈	—	3	2	no	—
727	C₄⋊C₈	—	3	2	no	—
728	C₄⋊C₈	—	3	2	no	—
729	C₄⋊C₈	—	3	2	no	—
730	C₄⋊C₈	—	3	2	no	—
731	C₄⋊C₈	—	3	2	no	—
732	C₄⋊C₈	—	3	2	no	—
733	C₄⋊C₈	—	3	2	no	—
734	C₄⋊C₈	—	3	2	no	—
735	C₄⋊C₈	—	3	2	no	—
736	C₄⋊C₈	—	3	2	no	—
737	C₄⋊C₈	—	3	2	no	—
738	C₄⋊C₈	—	3	2	no	—
739	C₄⋊C₈	—	3	2	no	—
740	C₄⋊C₈	—	3	2	no	—
741	C₄⋊C₈	C₂²×D₃	1	1	yes	characteristic
742	C₄⋊C₈	C₂²×D₃	1	1	yes	characteristic
743	C₄⋊C₈	C₂²×D₃	1	1	yes	characteristic
744	C₄⋊C₈	C₂²×D₃	1	1	yes	characteristic
745	C₂²⋊C₈	—	3	2	no	—
746	C₂²⋊C₈	—	3	2	no	—
747	C₂²⋊C₈	—	3	2	no	—
748	C₂²⋊C₈	—	3	2	no	—
749	C₂²⋊C₈	—	3	2	no	—
750	C₂²⋊C₈	—	3	2	no	—
751	C₂²⋊C₈	—	3	2	no	—
752	C₂²⋊C₈	—	3	2	no	—
753	C₂²⋊C₈	C₂²×D₃	1	1	yes	characteristic
754	C₂²⋊C₈	C₂²×D₃	1	1	yes	characteristic
755	C₂²⋊C₈	C₂²×D₃	1	1	yes	characteristic
756	C₂²⋊C₈	C₂²×D₃	1	1	yes	characteristic
757	C₂²⋊C₈	C₂²×D₃	1	1	yes	characteristic
758	C₂²⋊C₈	C₂²×D₃	1	1	yes	characteristic
759	C₂²⋊C₈	C₂²×D₃	1	1	yes	characteristic
760	C₂²⋊C₈	C₂²×D₃	1	1	yes	characteristic
761	#97	—	3	2	no	—
762	#97	—	3	2	no	—
763	#97	—	3	2	no	—
764	#97	—	3	2	no	—
765	#97	—	3	2	no	—
766	#97	C₂²×D₃	1	1	yes	characteristic
767	#97	C₂²×D₃	1	1	yes	characteristic
768	#97	C₂²×D₃	1	1	yes	characteristic
769	#97	C₂²×D₃	1	1	yes	characteristic
770	C₄×C₈	—	3	2	no	—
771	C₄×C₈	—	3	2	no	—
772	C₄×C₈	—	3	2	no	—
773	C₄×C₈	—	3	2	no	—
774	C₄×C₈	—	3	2	no	—
775	C₂³×C₃	—	2	2	no	—
776	C₂³×C₃	—	2	2	no	—
777	C₂³×C₃	—	2	2	no	—
778	C₂³×C₃	—	4	1	no	—
779	C₂³×C₃	—	4	1	no	—
780	C₂³×C₃	—	4	1	no	—
781	C₂³×C₃	C₂³×C₄	1	1	yes	characteristic
782	C₂³×C₃	C₂³×C₄	1	1	yes	characteristic
783	C₂³×C₃	C₂³×C₄	1	1	yes	characteristic
784	C₂³×C₃	C₂³×C₄	1	1	yes	characteristic
785	C₂³×C₃	C₂³×C₄	1	1	yes	characteristic
786	C₂²×D₃	C₂³×C₄	1	2	yes	—
787	C₃×D₄	—	2	2	no	—
788	C₃×D₄	—	2	2	no	—
789	C₃×D₄	—	4	1	no	—
790	C₃×D₄	—	4	1	no	—
791	C₂×C₃×C₄	—	2	2	no	—
792	C₂×C₃×C₄	—	2	2	no	—
793	C₂×C₃×C₄	—	2	2	no	—
794	C₂×C₃×C₄	—	2	2	no	—
795	C₂×C₃×C₄	—	2	2	no	—
796	C₂×C₃×C₄	—	2	2	no	—
797	C₂×C₃×C₄	—	2	1	no	—
798	C₂×C₃×C₄	—	2	1	no	—
799	C₂×C₃×C₄	—	2	1	no	—
800	C₂×C₃×C₄	—	2	1	no	—
801	C₂×C₃×C₄	—	2	1	no	—
802	C₂×C₃×C₄	—	2	1	no	—
803	C₂×C₃×C₄	—	2	1	no	—
804	C₂×C₃×C₄	—	2	1	no	—
805	C₂×C₃×C₄	—	4	1	no	—
806	C₂×C₃×C₄	—	4	1	no	—
807	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
808	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
809	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
810	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
811	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
812	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
813	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
814	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
815	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
816	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
817	C₂×C₃×C₄	2₋¹⁺⁴	1	2	yes	—
818	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
819	#67	—	2	4	no	—
820	#67	—	2	4	no	—
821	#67	—	4	2	no	—
822	#67	—	4	2	no	—
823	#67	—	4	2	no	—
824	C₂×Dic₃	—	2	4	no	—
825	C₂×Dic₃	—	4	2	no	—
826	C₂×Dic₃	—	4	2	no	—
827	C₂×Dic₃	—	4	2	no	—
828	C₂×Dic₃	C₂³×C₄	1	2	yes	—
829	C₂×Dic₃	C₂³×C₄	1	2	yes	—
830	C₂×Dic₃	C₂³×C₄	1	2	yes	—
831	C₂×Dic₃	C₂³×C₄	1	2	yes	—
832	C₂×Dic₃	C₂³×C₄	1	2	yes	—
833	C₂×Dic₃	C₂³×C₄	1	2	yes	—
834	C₂×Dic₃	C₂³×C₄	1	2	yes	—
835	D₁₂	—	2	2	no	—
836	C₄×D₃	—	2	2	no	—
837	C₄×D₃	—	2	2	no	—
838	C₄×D₃	—	4	2	no	—
839	C₄×D₃	—	4	2	no	—
840	Dic₆	—	2	2	no	—
841	Dic₆	—	4	2	no	—
842	Dic₆	—	4	2	no	—
843	C₃×C₈	—	2	1	no	—
844	C₃×C₈	—	2	1	no	—
845	C₃×C₈	—	2	1	no	—
846	C₃×C₈	—	2	1	no	—
847	C₃×C₈	—	2	1	no	—
848	C₃×C₈	—	2	1	no	—
849	C₃×C₈	—	2	1	no	—
850	C₃×C₈	—	2	1	no	—
851	C₃⋊C₈	—	2	2	no	—
852	C₃⋊C₈	—	2	2	no	—
853	C₃⋊C₈	—	2	2	no	—
854	C₃⋊C₈	—	2	2	no	—
855	C₂⁴	C₂×C₄×D₃	1	1	yes	characteristic
856	C₂⁴	C₂×C₄×D₃	1	1	yes	characteristic
857	#41	—	6	2	no	—
858	#41	—	6	2	no	—
859	#41	—	12	4	no	—
860	C₂×Q₈	—	3	1	no	—
861	C₂×Q₈	—	3	2	no	—
862	C₂×Q₈	—	3	2	no	—
863	C₂×D₄	—	3	2	no	—
864	C₂×D₄	—	3	2	no	—
865	C₂×D₄	—	3	2	no	—
866	C₂×D₄	—	3	2	no	—
867	C₂×D₄	—	3	2	no	—
868	C₂×D₄	—	3	1	no	—
869	C₂×D₄	—	4	2	no	—
870	C₂×D₄	C₂×C₄×D₃	1	1	yes	characteristic
871	C₂×D₄	C₂×C₄×D₃	1	1	yes	characteristic
872	C₂×D₄	C₂×C₄×D₃	1	1	yes	characteristic
873	C₂×D₄	C₂×C₄×D₃	1	1	yes	characteristic
874	C₂²×C₄	—	2	2	no	—
875	C₂²×C₄	—	2	2	no	—
876	C₂²×C₄	—	2	2	no	—
877	C₂²×C₄	—	2	2	no	—
878	C₂²×C₄	—	3	2	no	—
879	C₂²×C₄	—	3	2	no	—
880	C₂²×C₄	—	3	2	no	—
881	C₂²×C₄	—	3	2	no	—
882	C₂²×C₄	—	3	2	no	—
883	C₂²×C₄	—	3	2	no	—
884	C₂²×C₄	—	3	2	no	—
885	C₂²×C₄	C₂×C₄×D₃	1	1	yes	characteristic
886	C₂²×C₄	C₂×C₄×D₃	1	1	yes	characteristic
887	C₂²×C₄	C₂×C₄×D₃	1	1	yes	characteristic
888	C₂²×C₄	C₂×C₄×D₃	1	1	yes	characteristic
889	C₂²×C₄	C₂×C₄×D₃	1	1	yes	characteristic
890	C₂²×C₄	C₂×C₄×D₃	1	1	yes	characteristic
891	C₂²×C₄	C₂×C₄×D₃	1	1	yes	characteristic
892	C₂²×C₄	C₂×C₄×D₃	1	1	yes	characteristic
893	C₂²×C₄	C₂³×D₃	1	1	yes	characteristic
894	C₂²×C₄	C₂³×D₃	1	1	yes	characteristic
895	C₂²×C₄	C₂³×D₃	1	1	yes	characteristic
896	C₂²×C₄	C₂³×D₃	1	1	yes	characteristic
897	C₂²×C₄	C₂³×D₃	1	1	yes	characteristic
898	M₁₆	—	4	1	no	—
899	M₁₆	—	4	1	no	—
900	M₁₆	—	4	1	no	—
901	M₁₆	—	4	1	no	—
902	M₁₆	—	6	2	no	—
903	M₁₆	—	6	2	no	—
904	M₁₆	—	6	2	no	—
905	M₁₆	—	6	2	no	—
906	M₁₆	—	12	2	no	—
907	M₁₆	—	12	2	no	—
908	M₁₆	—	12	2	no	—
909	M₁₆	—	12	2	no	—
910	C₂×C₈	—	2	2	no	—
911	C₂×C₈	—	2	2	no	—
912	C₂×C₈	—	2	2	no	—
913	C₂×C₈	—	2	2	no	—
914	C₂×C₈	—	3	2	no	—
915	C₂×C₈	—	3	2	no	—
916	C₂×C₈	—	3	2	no	—
917	C₂×C₈	—	3	2	no	—
918	C₂×C₈	—	4	1	no	—
919	C₂×C₈	—	4	1	no	—
920	C₂×C₈	—	4	1	no	—
921	C₂×C₈	—	4	1	no	—
922	C₂×C₈	—	12	2	no	—
923	C₂×C₈	—	12	2	no	—
924	C₂×C₈	—	12	2	no	—
925	C₂×C₈	—	12	2	no	—
926	C₂×C₈	C₂³×D₃	1	1	yes	characteristic
927	C₂×C₈	C₂³×D₃	1	1	yes	characteristic
928	C₂×C₈	C₂³×D₃	1	1	yes	characteristic
929	C₂×C₈	C₂³×D₃	1	1	yes	characteristic
930	C₂×C₈	C₂³×D₃	1	1	yes	characteristic
931	C₂×C₈	C₂³×D₃	1	1	yes	characteristic
932	C₂×C₈	C₂³×D₃	1	1	yes	characteristic
933	C₂×C₈	C₂³×D₃	1	1	yes	characteristic
934	C₄⋊C₄	—	3	1	no	—
935	C₄⋊C₄	—	3	1	no	—
936	C₄⋊C₄	—	3	1	no	—
937	C₄⋊C₄	—	3	1	no	—
938	C₄⋊C₄	—	3	1	no	—
939	C₄⋊C₄	—	3	1	no	—
940	C₄⋊C₄	—	3	2	no	—
941	C₄⋊C₄	—	3	2	no	—
942	C₄⋊C₄	—	3	2	no	—
943	C₄⋊C₄	—	3	2	no	—
944	C₄⋊C₄	—	3	2	no	—
945	C₄⋊C₄	—	3	2	no	—
946	C₄⋊C₄	—	3	2	no	—
947	C₄⋊C₄	—	3	2	no	—
948	C₄⋊C₄	—	3	2	no	—
949	C₄⋊C₄	—	3	2	no	—
950	C₄⋊C₄	—	3	2	no	—
951	C₄⋊C₄	—	3	2	no	—
952	C₄⋊C₄	—	3	2	no	—
953	C₄⋊C₄	—	3	2	no	—
954	C₄⋊C₄	—	3	2	no	—
955	C₄⋊C₄	—	3	2	no	—
956	C₄⋊C₄	C₂×C₄×D₃	1	1	yes	characteristic
957	C₄⋊C₄	C₂×C₄×D₃	1	1	yes	characteristic
958	C₄⋊C₄	C₂×C₄×D₃	1	1	yes	characteristic
959	C₄⋊C₄	C₂×C₄×D₃	1	1	yes	characteristic
960	C₂²⋊C₄	—	3	2	no	—
961	C₂²⋊C₄	—	3	2	no	—
962	C₂²⋊C₄	—	3	2	no	—
963	C₂²⋊C₄	—	3	2	no	—
964	C₂²⋊C₄	—	3	2	no	—
965	C₂²⋊C₄	—	3	2	no	—
966	C₂²⋊C₄	—	3	2	no	—
967	C₂²⋊C₄	—	3	2	no	—
968	C₂²⋊C₄	—	3	2	no	—
969	C₂²⋊C₄	—	3	2	no	—
970	C₂²⋊C₄	—	3	2	no	—
971	C₂²⋊C₄	—	3	2	no	—
972	C₂²⋊C₄	—	3	2	no	—
973	C₂²⋊C₄	—	3	2	no	—
974	C₂²⋊C₄	—	3	2	no	—
975	C₂²⋊C₄	—	3	2	no	—
976	C₂²⋊C₄	—	3	2	no	—
977	C₂²⋊C₄	C₂×C₄×D₃	1	1	yes	characteristic
978	C₂²⋊C₄	C₂×C₄×D₃	1	1	yes	characteristic
979	C₂²⋊C₄	C₂×C₄×D₃	1	1	yes	characteristic
980	C₂²⋊C₄	C₂×C₄×D₃	1	1	yes	characteristic
981	C₂²⋊C₄	C₂×C₄×D₃	1	1	yes	characteristic
982	C₂²⋊C₄	C₂×C₄×D₃	1	1	yes	characteristic
983	C₂²⋊C₄	C₂×C₄×D₃	1	1	yes	characteristic
984	C₂²⋊C₄	C₂×C₄×D₃	1	1	yes	characteristic
985	C₄²	—	3	2	no	—
986	C₄²	—	3	2	no	—
987	C₄²	—	3	2	no	—
988	C₄²	—	3	2	no	—
989	C₄²	—	3	2	no	—
990	C₄²	—	3	2	no	—
991	C₄²	—	3	2	no	—
992	C₄²	—	3	2	no	—
993	C₄²	—	3	2	no	—
994	C₄²	C₂×C₄×D₃	1	1	yes	characteristic
995	C₄²	C₂×C₄×D₃	1	1	yes	characteristic
996	C₄²	C₂³×D₃	1	1	yes	characteristic
997	C₄²	C₂³×D₃	1	1	yes	characteristic
998	C₂²×C₃	—	2	1	no	—
999	C₂²×C₃	—	2	1	no	—
1000	C₂²×C₃	—	2	1	no	—
1001	C₂²×C₃	—	2	1	no	—
1002	C₂²×C₃	—	2	1	no	—
1003	C₂²×C₃	—	2	1	no	—
1004	C₂²×C₃	—	2	1	no	—
1005	C₂²×C₃	—	2	1	no	—
1006	C₂²×C₃	—	2	1	no	—
1007	C₂²×C₃	—	2	1	no	—
1008	C₂²×C₃	—	2	1	no	—
1009	C₂²×C₃	—	2	1	no	—
1010	C₂²×C₃	—	2	1	no	—
1011	C₂²×C₃	—	4	4	no	—
1012	C₂²×C₃	—	8	2	no	—
1013	C₂²×C₃	#520	1	2	yes	—
1014	C₂²×C₃	#568	1	2	yes	—
1015	C₂²×C₃	C₂⁴×C₄	1	1	yes	characteristic
1016	C₂×D₃	—	2	2	no	—
1017	C₂×D₃	—	2	2	no	—
1018	C₂×D₃	—	2	2	no	—
1019	C₃×C₄	—	2	1	no	—
1020	C₃×C₄	—	2	1	no	—
1021	C₃×C₄	—	2	1	no	—
1022	C₃×C₄	—	2	1	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	#520	1	2	yes	—
1028	C₃×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1029	C₃×C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
1030	Dic₃	—	2	2	no	—
1031	Dic₃	—	2	2	no	—
1032	Dic₃	—	2	2	no	—
1033	Dic₃	—	2	2	no	—
1034	Dic₃	—	2	2	no	—
1035	Dic₃	—	2	2	no	—
1036	Dic₃	—	2	2	no	—
1037	C₂³	—	2	2	no	—
1038	C₂³	—	2	2	no	—
1039	C₂³	—	2	2	no	—
1040	C₂³	—	3	2	no	—
1041	C₂³	—	4	1	no	—
1042	C₂³	—	4	1	no	—
1043	C₂³	—	4	1	no	—
1044	C₂³	C₂²×C₄×D₃	1	1	yes	characteristic
1045	C₂³	C₂²×C₄×D₃	1	1	yes	characteristic
1046	C₂³	C₂²×C₄×D₃	1	1	yes	characteristic
1047	C₂³	C₂²×C₄×D₃	1	1	yes	characteristic
1048	C₂³	C₂²×C₄×D₃	1	1	yes	characteristic
1049	Q₈	—	6	2	no	—
1050	Q₈	—	12	2	no	—
1051	Q₈	—	12	2	no	—
1052	D₄	—	2	2	no	—
1053	D₄	—	2	2	no	—
1054	D₄	—	4	1	no	—
1055	D₄	—	4	1	no	—
1056	D₄	—	6	4	no	—
1057	D₄	—	6	4	no	—
1058	D₄	—	6	2	no	—
1059	D₄	—	12	2	no	—
1060	D₄	—	12	2	no	—
1061	D₄	—	12	2	no	—
1062	C₂×C₄	—	2	2	no	—
1063	C₂×C₄	—	2	2	no	—
1064	C₂×C₄	—	2	1	no	—
1065	C₂×C₄	—	2	1	no	—
1066	C₂×C₄	—	2	1	no	—
1067	C₂×C₄	—	2	1	no	—
1068	C₂×C₄	—	2	1	no	—
1069	C₂×C₄	—	2	1	no	—
1070	C₂×C₄	—	2	1	no	—
1071	C₂×C₄	—	2	1	no	—
1072	C₂×C₄	—	2	2	no	—
1073	C₂×C₄	—	2	2	no	—
1074	C₂×C₄	—	2	2	no	—
1075	C₂×C₄	—	2	2	no	—
1076	C₂×C₄	—	3	2	no	—
1077	C₂×C₄	—	3	2	no	—
1078	C₂×C₄	—	3	2	no	—
1079	C₂×C₄	—	3	2	no	—
1080	C₂×C₄	—	3	2	no	—
1081	C₂×C₄	—	3	2	no	—
1082	C₂×C₄	—	3	2	no	—
1083	C₂×C₄	—	4	1	no	—
1084	C₂×C₄	—	4	1	no	—
1085	C₂×C₄	—	6	4	no	—
1086	C₂×C₄	—	6	2	no	—
1087	C₂×C₄	—	6	2	no	—
1088	C₂×C₄	—	12	2	no	—
1089	C₂×C₄	—	12	2	no	—
1090	C₂×C₄	—	12	2	no	—
1091	C₂×C₄	—	12	2	no	—
1092	C₂×C₄	—	12	2	no	—
1093	C₂×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
1094	C₂×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
1095	C₂×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
1096	C₂×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
1097	C₂×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
1098	C₂×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
1099	C₂×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
1100	C₂×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
1101	C₂×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
1102	C₂×C₄	#1004	1	2	yes	—
1103	C₂×C₄	#1010	1	2	yes	—
1104	C₂×C₄	C₂⁴×D₃	1	1	yes	characteristic
1105	C₈	—	2	1	no	—
1106	C₈	—	2	1	no	—
1107	C₈	—	2	1	no	—
1108	C₈	—	2	1	no	—
1109	C₈	—	2	1	no	—
1110	C₈	—	2	1	no	—
1111	C₈	—	2	1	no	—
1112	C₈	—	2	1	no	—
1113	C₈	—	6	2	no	—
1114	C₈	—	6	2	no	—
1115	C₈	—	6	2	no	—
1116	C₈	—	6	2	no	—
1117	C₂×C₃	—	2	2	no	—
1118	C₂×C₃	—	2	2	no	—
1119	C₂×C₃	—	4	1	no	—
1120	C₂×C₃	—	4	1	no	—
1121	C₂×C₃	—	4	1	no	—
1122	C₂×C₃	C₂×#520	1	1	yes	characteristic
1123	C₂×C₃	C₂×#568	1	1	yes	characteristic
1124	C₂×C₃	#3573	1	1	yes	characteristic
1125	D₃	—	4	2	no	—
1126	C₂²	—	2	1	no	—
1127	C₂²	—	2	1	no	—
1128	C₂²	—	2	1	no	—
1129	C₂²	—	2	1	no	—
1130	C₂²	—	2	1	no	—
1131	C₂²	—	2	1	no	—
1132	C₂²	—	2	1	no	—
1133	C₂²	—	2	1	no	—
1134	C₂²	—	2	1	no	—
1135	C₂²	—	2	1	no	—
1136	C₂²	—	2	1	no	—
1137	C₂²	—	2	1	no	—
1138	C₂²	—	2	1	no	—
1139	C₂²	—	4	4	no	—
1140	C₂²	—	6	2	no	—
1141	C₂²	—	6	2	no	—
1142	C₂²	—	6	2	no	—
1143	C₂²	—	8	2	no	—
1144	C₂²	#5546	1	2	yes	—
1145	C₂²	#5745	1	2	yes	—
1146	C₂²	C₂³×C₄×D₃	1	1	yes	characteristic
1147	C₄	—	2	1	no	—
1148	C₄	—	2	1	no	—
1149	C₄	—	2	1	no	—
1150	C₄	—	2	1	no	—
1151	C₄	—	2	1	no	—
1152	C₄	—	2	1	no	—
1153	C₄	—	2	1	no	—
1154	C₄	—	2	1	no	—
1155	C₄	—	6	2	no	—
1156	C₄	—	6	2	no	—
1157	C₄	—	6	2	no	—
1158	C₄	—	6	2	no	—
1159	C₄	—	6	2	no	—
1160	C₄	—	6	2	no	—
1161	C₄	—	6	2	no	—
1162	C₄	#5546	1	2	yes	—
1163	C₄	C₂×#1004	1	1	yes	characteristic
1164	C₄	C₂×#1010	1	1	yes	characteristic
1165	C₃	#60272	1	1	yes	characteristic, complemented, Sylow
1166	C₂	—	2	2	no	—
1167	C₂	—	2	2	no	—
1168	C₂	—	4	1	no	—
1169	C₂	—	4	1	no	—
1170	C₂	—	4	1	no	—
1171	C₂	—	12	2	no	—
1172	C₂	C₂×#5546	1	1	yes	characteristic
1173	C₂	C₂×#5745	1	1	yes	characteristic
1174	C₂	#87160	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂⁴×D₃
commutator, socle	C₂²×C₃	C₂⁴×C₄
Fitting	C₂×C₃×#435	C₂
prime radical	#85764	C₂
cosocle	C₂×C₃×C₄	C₂⁵
hypercenter	C₂×#435	D₃
hypocenter	C₃	#60272
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#435

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×#435	C₂	semidirect
3. #83756	C₂	semidirect
4. #83750	C₂	semidirect
5. #83734	C₂	semidirect
6. C₂×#5102	C₂	semidirect
7. D₄×#208	C₂	semidirect
8. #79468	C₂	semidirect
9. #79467	C₂	semidirect
10. #79466	C₂	semidirect
11. #79465	C₂	semidirect
12. #79464	C₂	semidirect
13. #79463	C₂	semidirect
14. #79462	C₂	semidirect
15. #79461	C₂	semidirect
16. #79012	C₂	semidirect
17. #79008	C₂	semidirect
18. #78596	C₂	semidirect
19. #78596	C₂	semidirect
20. #78584	C₂	semidirect
21. #78584	C₂	semidirect
22. #78489	C₂	semidirect
23. #78480	C₂	semidirect
68. #5128	C₂²	semidirect
69. #5128	C₂²	semidirect
70. #5127	C₂²	semidirect
71. #5127	C₂²	semidirect
72. #5119	C₂²	semidirect
73. #5119	C₂²	semidirect
74. #5118	C₂²	semidirect
75. #5118	C₂²	semidirect
76. #5111	C₂²	semidirect
77. #5111	C₂²	semidirect
80. C₈×#67	C₂²	semidirect
81. C₈×#67	C₂²	semidirect
90. #5102	C₂²	semidirect
91. #5102	C₂²	semidirect
96. C₂×Dic₃⋊C₈	C₂²	semidirect
97. C₂×Dic₃⋊C₈	C₂²	semidirect
104. #4839	C₂²	semidirect
105. #4839	C₂²	semidirect
106. #4837	C₂²	semidirect
107. D₃×C₄⋊C₈	C₂²	semidirect
108. #4831	C₂²	semidirect
109. #4830	C₂²	semidirect
110. #4828	C₂²	semidirect
111. #4828	C₂²	semidirect
112. #4730	C₂²	semidirect
113. #4730	C₂²	semidirect
114. #4729	C₂²	semidirect
115. #4729	C₂²	semidirect
116. #4728	C₂²	semidirect
117. #4728	C₂²	semidirect
118. #67⋊C₈	C₂²	semidirect
119. #67⋊C₈	C₂²	semidirect
120. #4720	C₂²	semidirect
121. #4720	C₂²	semidirect
122. #4720	C₂²	semidirect
123. #4720	C₂²	semidirect
124. #4719	C₂²	semidirect
125. #4719	C₂²	semidirect
126. #4718	C₂²	semidirect
127. #4718	C₂²	semidirect
128. #4709	C₂²	semidirect
129. #4709	C₂²	semidirect
130. #4705	C₂²	semidirect
131. #4705	C₂²	semidirect
132. #4701	C₂²	semidirect
133. #4701	C₂²	semidirect
134. #4701	C₂²	semidirect
135. #4701	C₂²	semidirect
152. C₂×#435	D₃	semidirect
1165. C₃	#60272	semidirect

Maximal subgroups

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

subgroup	index
#85764	2
C₂×C₃×#435	2
#83756	2
#83750	2
#83734	2
C₂×#5102	2
D₄×#208	2
#79468	2
#79467	2
#79466	2
#79465	2
#79464	2
#79463	2
#79462	2
#79461	2
#79012	2
#79008	2
#78596	2
#78584	2
#78489	2
#78480	2
#60272	3