Subgroups — #61642

Order 256.

1021 conjugacy classes of subgroups.

The subgroup lattice has 925 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3541	C₂	1	1	yes	maximal, characteristic, complemented
2	#3489	C₂	1	1	yes	maximal, characteristic, complemented
3	#3320	C₂	1	1	yes	maximal, characteristic, complemented
4	#3315	C₂	1	1	yes	maximal, characteristic, complemented
5	#3314	C₂	1	1	yes	maximal, characteristic, complemented
6	#3313	C₂	1	1	yes	maximal, characteristic, complemented
7	#3302	C₂	1	1	yes	maximal, characteristic, complemented
8	#3300	C₂	1	1	yes	maximal, characteristic, complemented
9	#3299	C₂	1	1	yes	maximal, characteristic, complemented
10	#3297	C₂	1	1	yes	maximal, characteristic, complemented
11	D₄×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	#3285	C₂	1	1	yes	maximal, characteristic, complemented
13	#3283	C₂	1	1	yes	maximal, characteristic, complemented
14	#3282	C₂	1	1	yes	maximal, characteristic, complemented
15	#3270	C₂	1	1	yes	maximal, characteristic, complemented
16	#3269	C₂	1	1	yes	maximal, characteristic, complemented
17	#3269	C₂	1	1	yes	maximal, characteristic, complemented
18	#3266	C₂	1	1	yes	maximal, characteristic, complemented
19	#3225	C₂	1	1	yes	maximal, characteristic, complemented
20	#3223	C₂	1	1	yes	maximal, characteristic, complemented
21	#3203	C₂	1	1	yes	maximal, characteristic, complemented
22	#3201	C₂	1	1	yes	maximal, characteristic, complemented
23	#3190	C₂	1	1	yes	maximal, characteristic, complemented
24	#3189	C₂	1	1	yes	maximal, characteristic, complemented
25	#3124	C₂	1	1	yes	maximal, characteristic, complemented
26	#3120	C₂	1	1	yes	maximal, characteristic, complemented
27	#3013	C₂	1	1	yes	maximal, characteristic, complemented
28	#3011	C₂	1	1	yes	maximal, characteristic, complemented
29	#3002	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂×#452	C₂	1	1	yes	maximal, characteristic, complemented
31	#2977	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
33	C₂²×#41	C₂²	1	1	yes	characteristic
34	C₂×#137	C₂²	1	1	yes	characteristic, complemented
35	C₂×#137	C₂²	1	1	yes	characteristic, complemented
36	C₂×#135	C₂²	1	1	yes	characteristic
37	C₂×#135	C₂²	1	1	yes	characteristic
38	C₂×#135	C₂²	1	1	yes	characteristic, complemented
39	C₂²×Q₁₆	C₂²	1	1	yes	characteristic
40	C₂²×Q₁₆	C₂²	1	1	yes	characteristic, complemented
41	C₂²×SD₁₆	C₂²	1	1	yes	characteristic
42	#563	—	2	1	no	—
43	#562	—	2	1	no	—
44	#556	C₂²	1	1	yes	characteristic, complemented
45	#554	—	2	1	no	—
46	#554	C₂²	1	1	yes	characteristic
47	#553	—	2	1	no	—
48	#553	C₂²	1	1	yes	characteristic
49	#552	C₂²	1	1	yes	characteristic, complemented
50	D₄×Q₈	C₂²	1	1	yes	characteristic
51	D₄×Q₈	C₂²	1	1	yes	characteristic
52	D₄×Q₈	C₂²	1	1	yes	characteristic
53	#548	C₂²	1	1	yes	characteristic
54	#548	C₂²	1	1	yes	characteristic
55	#548	C₂²	1	1	yes	characteristic
56	#548	C₂²	1	1	yes	characteristic, complemented
57	#547	—	2	1	no	—
58	#547	—	2	1	no	—
59	#547	C₂²	1	1	yes	characteristic
60	#547	C₂²	1	1	yes	characteristic
61	#547	C₂²	1	1	yes	characteristic, complemented
62	#546	—	2	1	no	—
63	#546	—	2	1	no	—
64	#546	C₂²	1	1	yes	characteristic
65	#546	C₂²	1	1	yes	characteristic
66	#542	—	2	1	no	—
67	#542	C₂²	1	1	yes	characteristic, complemented
68	#541	C₂²	1	1	yes	characteristic, complemented
69	#539	—	2	1	no	—
70	#538	—	2	1	no	—
71	#538	—	2	1	no	—
72	#537	—	2	1	no	—
73	#537	C₂²	1	1	yes	characteristic
74	#537	C₂²	1	1	yes	characteristic, complemented
75	#536	—	2	1	no	—
76	#536	C₂²	1	1	yes	characteristic
77	#536	C₂²	1	1	yes	characteristic, complemented
78	#525	—	2	1	no	—
79	#525	C₂²	1	1	yes	characteristic
80	#525	C₂²	1	1	yes	characteristic
81	C₂×C₂²⋊Q₈	—	2	1	no	—
82	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
83	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
84	#520	C₂²	1	1	yes	characteristic
85	#497	C₂²	1	1	yes	characteristic, complemented
86	#497	C₂²	1	1	yes	characteristic, complemented
87	#495	C₂²	1	1	yes	characteristic, complemented
88	#494	C₂²	1	1	yes	characteristic, complemented
89	#491	C₂²	1	1	yes	characteristic, complemented
90	#489	C₂²	1	1	yes	characteristic, complemented
91	#488	C₂²	1	1	yes	characteristic, complemented
92	#487	C₂²	1	1	yes	characteristic, complemented
93	#485	C₂²	1	1	yes	characteristic, complemented
94	#485	C₂²	1	1	yes	characteristic, complemented
95	#485	C₂²	1	1	yes	characteristic, complemented
96	#484	C₂²	1	1	yes	characteristic
97	#484	C₂²	1	1	yes	characteristic
98	#484	C₂²	1	1	yes	characteristic, complemented
99	#484	C₂²	1	1	yes	characteristic, complemented
100	#484	C₂²	1	1	yes	characteristic, complemented
101	#483	C₂²	1	1	yes	characteristic, complemented
102	#482	C₂²	1	1	yes	characteristic, complemented
103	#480	C₂²	1	1	yes	characteristic, complemented
104	#480	C₂²	1	1	yes	characteristic, complemented
105	#479	C₂²	1	1	yes	characteristic, complemented
106	#478	C₂²	1	1	yes	characteristic, complemented
107	#477	C₂²	1	1	yes	characteristic, complemented
108	#474	C₂²	1	1	yes	characteristic, complemented
109	#470	C₂²	1	1	yes	characteristic, complemented
110	#468	C₂²	1	1	yes	characteristic, complemented
111	#468	C₂²	1	1	yes	characteristic, complemented
112	#468	C₂²	1	1	yes	characteristic, complemented
113	#467	C₂²	1	1	yes	characteristic
114	#467	C₂²	1	1	yes	characteristic
115	#467	C₂²	1	1	yes	characteristic, complemented
116	#467	C₂²	1	1	yes	characteristic, complemented
117	#467	C₂²	1	1	yes	characteristic, complemented
118	#467	C₂²	1	1	yes	characteristic, complemented
119	#467	C₂²	1	1	yes	characteristic, complemented
120	#467	C₂²	1	1	yes	characteristic, complemented
121	#466	C₂²	1	1	yes	characteristic, complemented
122	#465	C₂²	1	1	yes	characteristic
123	#465	C₂²	1	1	yes	characteristic
124	#465	C₂²	1	1	yes	characteristic, complemented
125	#464	C₂²	1	1	yes	characteristic, complemented
126	#464	C₂²	1	1	yes	characteristic, complemented
127	#464	C₂²	1	1	yes	characteristic, complemented
128	#464	C₂²	1	1	yes	characteristic, complemented
129	#463	C₂²	1	1	yes	characteristic, complemented
130	#463	C₂²	1	1	yes	characteristic, complemented
131	#462	C₂²	1	1	yes	characteristic, complemented
132	#462	C₂²	1	1	yes	characteristic, complemented
133	#462	C₂²	1	1	yes	characteristic, complemented
134	#462	C₂²	1	1	yes	characteristic, complemented
135	#461	C₂²	1	1	yes	characteristic, complemented
136	#461	C₂²	1	1	yes	characteristic, complemented
137	#452	C₂²	1	1	yes	characteristic
138	#452	C₂²	1	1	yes	characteristic
139	#452	C₂²	1	1	yes	characteristic
140	#452	C₂²	1	1	yes	characteristic
141	#452	C₂²	1	1	yes	characteristic
142	#452	C₂²	1	1	yes	characteristic
143	#452	C₂²	1	1	yes	characteristic
144	#452	C₂²	1	1	yes	characteristic
145	#452	C₂²	1	1	yes	characteristic
146	#452	C₂²	1	1	yes	characteristic
147	#452	C₂²	1	1	yes	characteristic, complemented
148	#452	C₂²	1	1	yes	characteristic, complemented
149	#452	C₂²	1	1	yes	characteristic, complemented
150	#452	C₂²	1	1	yes	characteristic, complemented
151	#452	C₂²	1	1	yes	characteristic, complemented
152	#452	C₂²	1	1	yes	characteristic, complemented
153	#451	C₂²	1	1	yes	characteristic
154	#451	C₂²	1	1	yes	characteristic
155	#451	C₂²	1	1	yes	characteristic
156	#451	C₂²	1	1	yes	characteristic, complemented
157	#451	C₂²	1	1	yes	characteristic, complemented
158	#451	C₂²	1	1	yes	characteristic, complemented
159	#451	C₂²	1	1	yes	characteristic, complemented
160	#451	C₂²	1	1	yes	characteristic, complemented
161	#451	C₂²	1	1	yes	characteristic, complemented
162	#451	C₂²	1	1	yes	characteristic, complemented
163	#450	C₂²	1	1	yes	characteristic
164	#449	C₂²	1	1	yes	characteristic
165	#449	C₂²	1	1	yes	characteristic
166	#449	C₂²	1	1	yes	characteristic, complemented
167	#449	C₂²	1	1	yes	characteristic, complemented
168	#448	C₂²	1	1	yes	characteristic
169	#448	C₂²	1	1	yes	characteristic, complemented
170	#448	C₂²	1	1	yes	characteristic, complemented
171	#448	C₂²	1	1	yes	characteristic, complemented
172	#447	C₂²	1	1	yes	characteristic
173	#441	C₂²	1	1	yes	characteristic, complemented
174	#440	C₂²	1	1	yes	characteristic, complemented
175	#440	C₂²	1	1	yes	characteristic, complemented
176	#440	C₂²	1	1	yes	characteristic, complemented
177	C₄×Q₁₆	C₂²	1	1	yes	characteristic, complemented
178	C₄×Q₁₆	C₂²	1	1	yes	characteristic, complemented
179	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
180	C₄×D₈	C₂²	1	1	yes	characteristic, complemented
181	#435	C₂²	1	1	yes	characteristic
182	#435	C₂²	1	1	yes	characteristic
183	#435	C₂²	1	1	yes	characteristic, complemented
184	#435	C₂²	1	1	yes	characteristic, complemented
185	C₈×D₄	C₂²	1	1	yes	characteristic
186	C₈×D₄	C₂²	1	1	yes	characteristic
187	C₈×D₄	C₂²	1	1	yes	characteristic, complemented
188	C₈×D₄	C₂²	1	1	yes	characteristic, complemented
189	#433	C₂²	1	1	yes	characteristic, complemented
190	#433	C₂²	1	1	yes	characteristic, complemented
191	#419	C₂²	1	1	yes	characteristic, complemented
192	#417	C₂²	1	1	yes	characteristic, complemented
193	#416	C₂²	1	1	yes	characteristic
194	#416	C₂²	1	1	yes	characteristic
195	#416	C₂²	1	1	yes	characteristic, complemented
196	C₂×#103	C₂²	1	1	yes	characteristic
197	C₂×#103	C₂²	1	1	yes	characteristic, complemented
198	C₂×#102	C₂²	1	1	yes	characteristic
199	#408	C₂²	1	1	yes	characteristic, complemented
200	#408	C₂²	1	1	yes	characteristic, complemented
201	C₂×C₂²⋊C₈	C₂²	1	1	yes	characteristic
202	C₂×C₂²⋊C₈	C₂²	1	1	yes	characteristic
203	2₋¹⁺⁴	—	4	2	no	—
204	2₋¹⁺⁴	—	4	2	no	—
205	C₂×#41	—	2	1	no	—
206	C₂×#41	—	2	1	no	—
207	C₂×#41	—	2	1	no	—
208	C₂×#41	—	2	1	no	—
209	C₂×#41	—	2	1	no	—
210	C₂×#41	—	4	2	no	—
211	C₂×#41	—	4	2	no	—
212	C₂×#41	C₂³	1	1	yes	characteristic
213	C₂×#41	C₂³	1	1	yes	characteristic
214	C₂×#41	C₂³	1	1	yes	characteristic
215	C₂×#41	C₂³	1	1	yes	characteristic
216	C₂×#41	C₂³	1	1	yes	characteristic
217	C₂×#41	C₂³	1	1	yes	characteristic
218	C₂×#41	C₂³	1	1	yes	characteristic
219	C₂×#41	C₂³	1	1	yes	characteristic
220	C₂×#41	C₂³	1	1	yes	characteristic
221	C₂²×Q₈	—	2	1	no	—
222	C₂²×Q₈	C₂³	1	1	yes	characteristic
223	C₂²×Q₈	C₂³	1	1	yes	characteristic
224	C₂²×Q₈	C₂³	1	1	yes	characteristic
225	C₂²×Q₈	C₂³	1	1	yes	characteristic
226	C₂²×Q₈	C₂³	1	1	yes	characteristic
227	C₂²×Q₈	C₂³	1	1	yes	characteristic
228	C₂²×D₄	—	2	1	no	—
229	C₂²×D₄	C₂³	1	1	yes	characteristic
230	C₂³×C₄	—	2	1	no	—
231	C₂³×C₄	C₂³	1	1	yes	characteristic
232	#137	—	4	2	no	—
233	#137	—	4	2	no	—
234	#135	—	4	2	no	—
235	#135	—	4	2	no	—
236	#135	—	4	2	no	—
237	C₂×Q₁₆	—	4	2	no	—
238	C₂×Q₁₆	—	4	2	no	—
239	C₂×Q₁₆	C₂³	1	1	yes	characteristic
240	C₂×Q₁₆	C₂³	1	1	yes	characteristic
241	C₂×Q₁₆	C₂³	1	1	yes	characteristic
242	C₂×Q₁₆	C₂³	1	1	yes	characteristic
243	C₂×Q₁₆	C₂³	1	1	yes	characteristic
244	C₂×Q₁₆	C₂³	1	1	yes	characteristic
245	C₂×Q₁₆	C₂³	1	1	yes	characteristic
246	C₂×Q₁₆	C₂³	1	1	yes	characteristic
247	C₂×Q₁₆	C₂³	1	1	yes	characteristic
248	C₂×Q₁₆	C₂³	1	1	yes	characteristic
249	C₂×Q₁₆	C₂³	1	1	yes	characteristic
250	C₂×Q₁₆	C₂³	1	1	yes	characteristic
251	C₂×SD₁₆	—	4	2	no	—
252	C₂×SD₁₆	C₂³	1	1	yes	characteristic
253	C₂×SD₁₆	C₂³	1	1	yes	characteristic
254	C₂×SD₁₆	C₂³	1	1	yes	characteristic
255	C₂×SD₁₆	C₂³	1	1	yes	characteristic
256	C₂×SD₁₆	C₂³	1	1	yes	characteristic
257	C₂×SD₁₆	C₂³	1	1	yes	characteristic
258	C₂×SD₁₆	C₂³	1	1	yes	characteristic
259	C₂×SD₁₆	C₂³	1	1	yes	characteristic
260	C₂×SD₁₆	C₂³	1	1	yes	characteristic
261	C₂×SD₁₆	C₂³	1	1	yes	characteristic
262	C₂×D₈	C₂³	1	1	yes	characteristic
263	C₂×D₈	C₂³	1	1	yes	characteristic
264	C₂×M₁₆	C₂³	1	1	yes	characteristic
265	C₂×M₁₆	C₂³	1	1	yes	characteristic
266	C₂²×C₈	C₂³	1	1	yes	characteristic
267	C₂²×C₈	C₂³	1	1	yes	characteristic
268	C₂²×C₈	C₂³	1	1	yes	characteristic
269	C₂²×C₈	C₂³	1	1	yes	characteristic
270	C₂²×C₈	C₂³	1	1	yes	characteristic
271	C₂²×C₈	C₂³	1	1	yes	characteristic
272	C₄⋊Q₈	—	2	1	no	—
273	C₄⋊Q₈	—	2	1	no	—
274	C₄⋊Q₈	—	2	1	no	—
275	C₄⋊Q₈	—	2	1	no	—
276	C₄⋊Q₈	C₂³	1	1	yes	characteristic
277	C₄⋊Q₈	C₂³	1	1	yes	characteristic
278	C₄⋊Q₈	C₂³	1	1	yes	characteristic
279	C₄⋊Q₈	C₂³	1	1	yes	characteristic
280	#126	—	2	1	no	—
281	#126	—	2	1	no	—
282	#126	—	2	1	no	—
283	#126	—	2	1	no	—
284	#126	—	2	1	no	—
285	#126	—	2	1	no	—
286	#126	—	2	1	no	—
287	#125	—	2	1	no	—
288	#125	—	2	1	no	—
289	#125	—	2	1	no	—
290	#125	—	2	1	no	—
291	#125	C₂³	1	1	yes	characteristic
292	#124	—	2	1	no	—
293	#124	—	2	1	no	—
294	#124	—	2	1	no	—
295	#124	—	2	1	no	—
296	#124	—	2	1	no	—
297	#124	—	2	1	no	—
298	#124	—	2	1	no	—
299	#124	C₂³	1	1	yes	characteristic
300	#124	C₂³	1	1	yes	characteristic
301	#124	C₂³	1	1	yes	characteristic
302	#123	—	2	1	no	—
303	#123	—	2	1	no	—
304	#123	—	2	1	no	—
305	#123	—	2	1	no	—
306	#123	—	2	1	no	—
307	#123	—	2	1	no	—
308	#123	—	2	1	no	—
309	#123	—	2	1	no	—
310	#123	—	2	1	no	—
311	#123	—	2	1	no	—
312	#123	—	2	1	no	—
313	#123	—	2	1	no	—
314	#123	—	2	1	no	—
315	#123	—	2	1	no	—
316	#123	—	2	1	no	—
317	#123	—	2	1	no	—
318	#123	D₄	1	1	yes	characteristic
319	#123	D₄	1	1	yes	characteristic
320	C₂²⋊Q₈	—	2	1	no	—
321	C₂²⋊Q₈	—	2	1	no	—
322	C₂²⋊Q₈	—	2	1	no	—
323	C₂²⋊Q₈	—	2	1	no	—
324	C₂²⋊Q₈	—	2	1	no	—
325	C₂²⋊Q₈	—	2	1	no	—
326	C₂²⋊Q₈	—	2	1	no	—
327	C₂²⋊Q₈	—	2	1	no	—
328	C₂²⋊Q₈	—	2	1	no	—
329	C₂²⋊Q₈	—	2	1	no	—
330	C₂²⋊Q₈	—	2	1	no	—
331	C₂²⋊Q₈	—	2	1	no	—
332	C₂²⋊Q₈	—	2	1	no	—
333	C₂²⋊Q₈	—	2	1	no	—
334	C₂²⋊Q₈	—	2	1	no	—
335	C₂²⋊Q₈	—	2	1	no	—
336	C₂²⋊Q₈	—	2	1	no	—
337	C₂²⋊Q₈	—	2	1	no	—
338	C₂²⋊Q₈	—	2	1	no	—
339	C₂²⋊Q₈	—	2	1	no	—
340	C₂²⋊Q₈	—	2	1	no	—
341	C₂²⋊Q₈	D₄	1	1	yes	characteristic
342	C₂²⋊Q₈	D₄	1	1	yes	characteristic
343	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
344	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
345	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
346	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
347	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
348	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
349	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
350	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
351	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
352	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
353	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
354	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
355	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
356	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
357	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
358	#121	—	2	1	no	—
359	#121	—	2	1	no	—
360	#121	—	2	1	no	—
361	#121	—	2	1	no	—
362	#121	—	2	1	no	—
363	#121	—	2	1	no	—
364	#121	—	2	1	no	—
365	#121	—	2	1	no	—
366	#121	—	2	1	no	—
367	#121	—	2	1	no	—
368	#121	—	2	1	no	—
369	#121	—	2	1	no	—
370	#121	—	2	1	no	—
371	#121	—	2	1	no	—
372	#121	—	2	1	no	—
373	#121	—	2	1	no	—
374	#121	D₄	1	1	yes	characteristic
375	#121	D₄	1	1	yes	characteristic
376	#121	C₂³	1	1	yes	characteristic
377	#121	C₂³	1	1	yes	characteristic
378	#121	C₂³	1	1	yes	characteristic
379	#121	C₂³	1	1	yes	characteristic
380	#121	C₂³	1	1	yes	characteristic
381	#120	—	2	1	no	—
382	#120	—	2	1	no	—
383	#120	—	2	1	no	—
384	#120	D₄	1	1	yes	characteristic
385	#120	D₄	1	1	yes	characteristic
386	C₄×Q₈	—	2	1	no	—
387	C₄×Q₈	C₂³	1	1	yes	characteristic
388	C₄×Q₈	C₂³	1	1	yes	characteristic
389	C₄×Q₈	C₂³	1	1	yes	characteristic
390	C₄×Q₈	C₂³	1	1	yes	characteristic
391	C₄×Q₈	C₂³	1	1	yes	characteristic
392	C₄×D₄	—	2	1	no	—
393	C₄×D₄	—	2	1	no	—
394	C₄×D₄	—	2	1	no	—
395	C₄×D₄	—	2	1	no	—
396	C₄×D₄	—	2	1	no	—
397	C₄×D₄	—	2	1	no	—
398	C₄×D₄	—	2	1	no	—
399	C₄×D₄	—	2	1	no	—
400	C₄×D₄	—	2	1	no	—
401	C₄×D₄	—	2	1	no	—
402	C₄×D₄	—	2	1	no	—
403	C₄×D₄	—	2	1	no	—
404	C₄×D₄	—	2	1	no	—
405	C₄×D₄	C₂³	1	1	yes	characteristic
406	C₄×D₄	C₂³	1	1	yes	characteristic
407	C₄×D₄	C₂³	1	1	yes	characteristic
408	C₄×D₄	C₂³	1	1	yes	characteristic
409	C₄×D₄	C₂³	1	1	yes	characteristic
410	C₄×D₄	C₂³	1	1	yes	characteristic
411	C₄×D₄	C₂³	1	1	yes	characteristic
412	#117	—	2	1	no	—
413	#117	—	2	1	no	—
414	#117	C₂³	1	1	yes	characteristic
415	#117	C₂³	1	1	yes	characteristic
416	#117	C₂³	1	1	yes	characteristic
417	C₂×C₄⋊C₄	—	2	1	no	—
418	C₂×C₄⋊C₄	—	2	1	no	—
419	C₂×C₄⋊C₄	—	2	1	no	—
420	C₂×C₄⋊C₄	—	2	1	no	—
421	C₂×C₄⋊C₄	—	2	1	no	—
422	C₂×C₄⋊C₄	—	2	1	no	—
423	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
424	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
425	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
426	C₂×C₂²⋊C₄	—	2	1	no	—
427	C₂×C₂²⋊C₄	—	2	1	no	—
428	C₂×C₂²⋊C₄	—	2	1	no	—
429	C₂×C₂²⋊C₄	—	2	1	no	—
430	#107	C₂³	1	1	yes	characteristic
431	#107	C₂³	1	1	yes	characteristic
432	#107	C₂³	1	1	yes	characteristic
433	#107	C₂³	1	1	yes	characteristic
434	#107	C₂³	1	1	yes	characteristic
435	#107	C₂³	1	1	yes	characteristic
436	#106	C₂³	1	1	yes	characteristic
437	#106	C₂³	1	1	yes	characteristic
438	C₄⋊C₈	C₂³	1	1	yes	characteristic
439	C₄⋊C₈	C₂³	1	1	yes	characteristic
440	C₄⋊C₈	C₂³	1	1	yes	characteristic
441	C₄⋊C₈	C₂³	1	1	yes	characteristic
442	#103	C₂³	1	1	yes	characteristic
443	#103	C₂³	1	1	yes	characteristic
444	#103	C₂³	1	1	yes	characteristic
445	#103	C₂³	1	1	yes	characteristic
446	#103	C₂³	1	1	yes	characteristic
447	#103	C₂³	1	1	yes	characteristic
448	#103	C₂³	1	1	yes	characteristic
449	#103	C₂³	1	1	yes	characteristic
450	#103	C₂³	1	1	yes	characteristic
451	#103	C₂³	1	1	yes	characteristic
452	#103	C₂³	1	1	yes	characteristic
453	#103	C₂³	1	1	yes	characteristic
454	#103	C₂³	1	1	yes	characteristic
455	#103	C₂³	1	1	yes	characteristic
456	#103	C₂³	1	1	yes	characteristic
457	#103	C₂³	1	1	yes	characteristic
458	#103	C₂³	1	1	yes	characteristic
459	#103	C₂³	1	1	yes	characteristic
460	#103	C₂³	1	1	yes	characteristic
461	#103	C₂³	1	1	yes	characteristic
462	#103	C₂³	1	1	yes	characteristic
463	#103	C₂³	1	1	yes	characteristic
464	#102	C₂³	1	1	yes	characteristic
465	#102	C₂³	1	1	yes	characteristic
466	#102	C₂³	1	1	yes	characteristic
467	#102	C₂³	1	1	yes	characteristic
468	#102	C₂³	1	1	yes	characteristic
469	#102	C₂³	1	1	yes	characteristic
470	#102	C₂³	1	1	yes	characteristic
471	#102	C₂³	1	1	yes	characteristic
472	#102	C₂³	1	1	yes	characteristic
473	#102	C₂³	1	1	yes	characteristic
474	C₂²⋊C₈	C₂³	1	1	yes	characteristic
475	C₂²⋊C₈	C₂³	1	1	yes	characteristic
476	C₂²⋊C₈	C₂³	1	1	yes	characteristic
477	C₂²⋊C₈	C₂³	1	1	yes	characteristic
478	C₂²⋊C₈	C₂³	1	1	yes	characteristic
479	C₂²⋊C₈	C₂³	1	1	yes	characteristic
480	C₂²⋊C₈	C₂³	1	1	yes	characteristic
481	C₂²⋊C₈	C₂³	1	1	yes	characteristic
482	C₂²⋊C₈	C₂³	1	1	yes	characteristic
483	C₂²⋊C₈	C₂³	1	1	yes	characteristic
484	C₂²⋊C₈	C₂³	1	1	yes	characteristic
485	C₂²⋊C₈	C₂³	1	1	yes	characteristic
486	#97	C₂³	1	1	yes	characteristic
487	#97	C₂³	1	1	yes	characteristic
488	C₄×C₈	C₂³	1	1	yes	characteristic
489	C₄×C₈	C₂³	1	1	yes	characteristic
490	C₂⁴	—	2	1	no	—
491	C₂⁴	C₂×D₄	1	1	yes	characteristic
492	#41	—	2	2	no	—
493	#41	—	2	2	no	—
494	#41	—	2	2	no	—
495	#41	—	2	2	no	—
496	#41	—	2	2	no	—
497	#41	—	2	2	no	—
498	#41	—	4	1	no	—
499	#41	—	4	1	no	—
500	#41	—	4	1	no	—
501	#41	—	4	1	no	—
502	#41	—	4	1	no	—
503	#41	—	4	1	no	—
504	#41	—	4	1	no	—
505	#41	—	4	1	no	—
506	#41	—	4	4	no	—
507	#41	—	4	4	no	—
508	#41	—	4	1	no	—
509	#41	—	4	1	no	—
510	#41	—	4	1	no	—
511	#41	—	4	1	no	—
512	#41	—	4	4	no	—
513	#41	—	4	4	no	—
514	#41	—	4	4	no	—
515	C₂×Q₈	—	2	1	no	—
516	C₂×Q₈	—	2	1	no	—
517	C₂×Q₈	—	2	1	no	—
518	C₂×Q₈	—	2	1	no	—
519	C₂×Q₈	—	2	1	no	—
520	C₂×Q₈	—	2	1	no	—
521	C₂×Q₈	—	2	1	no	—
522	C₂×Q₈	—	2	2	no	—
523	C₂×Q₈	—	2	2	no	—
524	C₂×Q₈	—	2	2	no	—
525	C₂×Q₈	—	4	1	no	—
526	C₂×Q₈	—	4	1	no	—
527	C₂×Q₈	—	4	1	no	—
528	C₂×Q₈	—	4	1	no	—
529	C₂×Q₈	—	4	1	no	—
530	C₂×Q₈	—	4	4	no	—
531	C₂×Q₈	—	4	1	no	—
532	C₂×Q₈	—	4	1	no	—
533	C₂×Q₈	—	4	1	no	—
534	C₂×Q₈	—	4	1	no	—
535	C₂×Q₈	C₂×D₄	1	1	yes	characteristic
536	C₂×Q₈	C₂⁴	1	1	yes	characteristic
537	C₂×Q₈	C₂⁴	1	1	yes	characteristic
538	C₂×Q₈	C₂⁴	1	1	yes	characteristic
539	C₂×Q₈	C₂⁴	1	1	yes	characteristic
540	C₂×Q₈	C₂⁴	1	1	yes	characteristic
541	C₂×Q₈	C₂⁴	1	1	yes	characteristic
542	C₂×Q₈	C₂⁴	1	1	yes	characteristic
543	C₂×D₄	—	2	1	no	—
544	C₂×D₄	—	2	2	no	—
545	C₂×D₄	—	2	1	no	—
546	C₂×D₄	—	2	1	no	—
547	C₂×D₄	—	2	1	no	—
548	C₂×D₄	—	2	1	no	—
549	C₂×D₄	—	2	1	no	—
550	C₂×D₄	—	2	1	no	—
551	C₂×D₄	—	2	1	no	—
552	C₂×D₄	—	2	1	no	—
553	C₂×D₄	—	2	1	no	—
554	C₂×D₄	—	2	1	no	—
555	C₂×D₄	—	2	1	no	—
556	C₂×D₄	—	2	1	no	—
557	C₂×D₄	—	2	1	no	—
558	C₂×D₄	—	4	1	no	—
559	C₂×D₄	—	4	4	no	—
560	C₂×D₄	C₂×D₄	1	1	yes	characteristic
561	C₂×D₄	C₂×D₄	1	1	yes	characteristic
562	C₂×D₄	C₂×D₄	1	1	yes	characteristic
563	C₂×D₄	C₂×D₄	1	1	yes	characteristic
564	C₂×D₄	C₂×D₄	1	1	yes	characteristic
565	C₂×D₄	C₂×D₄	1	1	yes	characteristic
566	C₂×D₄	C₂×D₄	1	1	yes	characteristic
567	C₂×D₄	C₂⁴	1	1	yes	characteristic
568	C₂×D₄	C₂⁴	1	1	yes	characteristic
569	C₂×D₄	C₂⁴	1	1	yes	characteristic
570	C₂²×C₄	—	2	1	no	—
571	C₂²×C₄	—	2	1	no	—
572	C₂²×C₄	—	2	1	no	—
573	C₂²×C₄	—	2	1	no	—
574	C₂²×C₄	—	2	1	no	—
575	C₂²×C₄	—	2	1	no	—
576	C₂²×C₄	—	2	1	no	—
577	C₂²×C₄	—	2	1	no	—
578	C₂²×C₄	—	2	1	no	—
579	C₂²×C₄	—	2	1	no	—
580	C₂²×C₄	—	2	1	no	—
581	C₂²×C₄	—	2	1	no	—
582	C₂²×C₄	—	2	1	no	—
583	C₂²×C₄	—	2	1	no	—
584	C₂²×C₄	—	2	1	no	—
585	C₂²×C₄	—	2	1	no	—
586	C₂²×C₄	—	2	1	no	—
587	C₂²×C₄	—	2	1	no	—
588	C₂²×C₄	—	2	1	no	—
589	C₂²×C₄	—	2	1	no	—
590	C₂²×C₄	—	4	1	no	—
591	C₂²×C₄	—	4	1	no	—
592	C₂²×C₄	—	4	4	no	—
593	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
594	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
595	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
596	C₂²×C₄	C₂⁴	1	1	yes	characteristic
597	C₂²×C₄	C₂⁴	1	1	yes	characteristic
598	C₂²×C₄	C₂⁴	1	1	yes	characteristic
599	C₂²×C₄	C₂⁴	1	1	yes	characteristic
600	C₂²×C₄	C₂⁴	1	1	yes	characteristic
601	Q₁₆	—	2	2	no	—
602	Q₁₆	—	2	2	no	—
603	Q₁₆	—	2	2	no	—
604	Q₁₆	—	4	1	no	—
605	Q₁₆	—	4	1	no	—
606	Q₁₆	—	4	1	no	—
607	Q₁₆	—	4	1	no	—
608	Q₁₆	—	4	1	no	—
609	Q₁₆	—	4	1	no	—
610	Q₁₆	—	4	1	no	—
611	Q₁₆	—	4	1	no	—
612	Q₁₆	—	4	1	no	—
613	SD₁₆	—	2	2	no	—
614	SD₁₆	—	2	2	no	—
615	SD₁₆	—	2	2	no	—
616	SD₁₆	—	2	2	no	—
617	SD₁₆	—	4	1	no	—
618	SD₁₆	—	4	1	no	—
619	SD₁₆	—	4	1	no	—
620	SD₁₆	—	4	1	no	—
621	SD₁₆	—	4	1	no	—
622	SD₁₆	—	4	1	no	—
623	D₈	—	2	2	no	—
624	D₈	—	4	1	no	—
625	M₁₆	—	4	1	no	—
626	M₁₆	—	4	1	no	—
627	C₂×C₈	—	4	1	no	—
628	C₂×C₈	—	4	1	no	—
629	C₂×C₈	—	4	1	no	—
630	C₂×C₈	—	4	1	no	—
631	C₂×C₈	—	4	1	no	—
632	C₂×C₈	—	4	1	no	—
633	C₂×C₈	C₂⁴	1	1	yes	characteristic
634	C₂×C₈	C₂⁴	1	1	yes	characteristic
635	C₂×C₈	C₂⁴	1	1	yes	characteristic
636	C₂×C₈	C₂⁴	1	1	yes	characteristic
637	C₂×C₈	C₂⁴	1	1	yes	characteristic
638	C₂×C₈	C₂⁴	1	1	yes	characteristic
639	C₂×C₈	C₂⁴	1	1	yes	characteristic
640	C₂×C₈	C₂⁴	1	1	yes	characteristic
641	C₄⋊C₄	—	2	1	no	—
642	C₄⋊C₄	—	2	1	no	—
643	C₄⋊C₄	—	2	1	no	—
644	C₄⋊C₄	—	2	1	no	—
645	C₄⋊C₄	—	2	1	no	—
646	C₄⋊C₄	—	2	1	no	—
647	C₄⋊C₄	—	2	1	no	—
648	C₄⋊C₄	—	2	1	no	—
649	C₄⋊C₄	—	2	1	no	—
650	C₄⋊C₄	—	2	1	no	—
651	C₄⋊C₄	—	2	1	no	—
652	C₄⋊C₄	—	2	1	no	—
653	C₄⋊C₄	—	2	1	no	—
654	C₄⋊C₄	—	2	1	no	—
655	C₄⋊C₄	—	2	1	no	—
656	C₄⋊C₄	—	2	1	no	—
657	C₄⋊C₄	—	2	1	no	—
658	C₄⋊C₄	—	2	1	no	—
659	C₄⋊C₄	—	2	1	no	—
660	C₄⋊C₄	—	2	1	no	—
661	C₄⋊C₄	—	2	1	no	—
662	C₄⋊C₄	—	2	1	no	—
663	C₄⋊C₄	—	2	1	no	—
664	C₄⋊C₄	—	2	1	no	—
665	C₄⋊C₄	—	2	1	no	—
666	C₄⋊C₄	—	2	1	no	—
667	C₄⋊C₄	—	2	1	no	—
668	C₄⋊C₄	—	2	1	no	—
669	C₄⋊C₄	—	2	1	no	—
670	C₄⋊C₄	—	2	1	no	—
671	C₄⋊C₄	—	2	1	no	—
672	C₄⋊C₄	—	2	1	no	—
673	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
674	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
675	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
676	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
677	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
678	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
679	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
680	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
681	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
682	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
683	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
684	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
685	C₂²⋊C₄	—	2	1	no	—
686	C₂²⋊C₄	—	2	1	no	—
687	C₂²⋊C₄	—	2	1	no	—
688	C₂²⋊C₄	—	2	1	no	—
689	C₂²⋊C₄	—	2	1	no	—
690	C₂²⋊C₄	—	2	1	no	—
691	C₂²⋊C₄	—	2	1	no	—
692	C₂²⋊C₄	—	2	1	no	—
693	C₂²⋊C₄	—	2	1	no	—
694	C₂²⋊C₄	—	2	1	no	—
695	C₂²⋊C₄	—	2	1	no	—
696	C₂²⋊C₄	—	2	1	no	—
697	C₂²⋊C₄	—	2	1	no	—
698	C₂²⋊C₄	—	2	1	no	—
699	C₂²⋊C₄	—	2	1	no	—
700	C₂²⋊C₄	—	2	1	no	—
701	C₂²⋊C₄	—	2	1	no	—
702	C₂²⋊C₄	—	2	1	no	—
703	C₂²⋊C₄	—	2	1	no	—
704	C₂²⋊C₄	—	2	1	no	—
705	C₂²⋊C₄	—	2	1	no	—
706	C₂²⋊C₄	—	2	1	no	—
707	C₂²⋊C₄	—	2	1	no	—
708	C₂²⋊C₄	—	2	1	no	—
709	C₂²⋊C₄	—	2	1	no	—
710	C₂²⋊C₄	—	2	1	no	—
711	C₂²⋊C₄	—	2	1	no	—
712	C₂²⋊C₄	—	2	1	no	—
713	C₂²⋊C₄	—	2	1	no	—
714	C₂²⋊C₄	—	2	1	no	—
715	C₂²⋊C₄	—	2	1	no	—
716	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
717	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
718	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
719	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
720	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
721	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
722	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
723	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
724	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
725	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
726	C₄²	—	2	1	no	—
727	C₄²	—	2	1	no	—
728	C₄²	—	2	1	no	—
729	C₄²	—	2	1	no	—
730	C₄²	—	2	1	no	—
731	C₄²	—	2	1	no	—
732	C₄²	—	2	1	no	—
733	C₄²	C₂⁴	1	1	yes	characteristic
734	C₄²	C₂⁴	1	1	yes	characteristic
735	C₂³	—	2	1	no	—
736	C₂³	—	2	2	no	—
737	C₂³	—	2	1	no	—
738	C₂³	—	2	1	no	—
739	C₂³	—	4	1	no	—
740	C₂³	—	4	1	no	—
741	C₂³	—	4	2	no	—
742	C₂³	—	4	2	no	—
743	C₂³	—	8	1	no	—
744	C₂³	C₂²×D₄	1	1	yes	characteristic
745	C₂³	C₂²×D₄	1	1	yes	characteristic
746	C₂³	C₂²×D₄	1	1	yes	characteristic
747	C₂³	C₂²×D₄	1	1	yes	characteristic
748	C₂³	C₂²×D₄	1	1	yes	characteristic
749	Q₈	—	2	1	no	—
750	Q₈	—	2	1	no	—
751	Q₈	—	2	1	no	—
752	Q₈	—	2	1	no	—
753	Q₈	—	2	1	no	—
754	Q₈	—	2	1	no	—
755	Q₈	—	2	1	no	—
756	Q₈	—	2	1	no	—
757	Q₈	—	2	1	no	—
758	Q₈	—	2	1	no	—
759	Q₈	—	2	1	no	—
760	Q₈	—	2	1	no	—
761	Q₈	—	2	1	no	—
762	Q₈	—	4	1	no	—
763	Q₈	—	4	2	no	—
764	Q₈	—	4	2	no	—
765	Q₈	—	4	2	no	—
766	Q₈	—	4	2	no	—
767	Q₈	—	8	1	no	—
768	Q₈	—	8	1	no	—
769	Q₈	—	8	1	no	—
770	Q₈	H(5,𝔽₂)	1	2	yes	—
771	D₄	—	2	4	no	—
772	D₄	—	2	2	no	—
773	D₄	—	2	2	no	—
774	D₄	—	2	1	no	—
775	D₄	—	2	1	no	—
776	D₄	—	2	1	no	—
777	D₄	—	2	1	no	—
778	D₄	—	2	1	no	—
779	D₄	—	4	1	no	—
780	D₄	—	4	1	no	—
781	D₄	—	4	1	no	—
782	D₄	—	4	1	no	—
783	D₄	—	4	1	no	—
784	D₄	—	4	2	no	—
785	D₄	—	4	2	no	—
786	D₄	—	4	2	no	—
787	D₄	—	4	2	no	—
788	D₄	—	4	2	no	—
789	D₄	—	4	2	no	—
790	D₄	—	4	2	no	—
791	D₄	—	8	1	no	—
792	D₄	—	8	1	no	—
793	D₄	—	8	1	no	—
794	D₄	—	8	1	no	—
795	D₄	—	8	1	no	—
796	D₄	—	8	1	no	—
797	D₄	H(5,𝔽₂)	1	2	yes	—
798	C₂×C₄	—	2	4	no	—
799	C₂×C₄	—	2	1	no	—
800	C₂×C₄	—	2	1	no	—
801	C₂×C₄	—	2	1	no	—
802	C₂×C₄	—	2	1	no	—
803	C₂×C₄	—	2	1	no	—
804	C₂×C₄	—	2	1	no	—
805	C₂×C₄	—	2	1	no	—
806	C₂×C₄	—	2	1	no	—
807	C₂×C₄	—	2	1	no	—
808	C₂×C₄	—	2	1	no	—
809	C₂×C₄	—	2	1	no	—
810	C₂×C₄	—	2	1	no	—
811	C₂×C₄	—	2	1	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	2	1	no	—
815	C₂×C₄	—	2	1	no	—
816	C₂×C₄	—	2	1	no	—
817	C₂×C₄	—	2	1	no	—
818	C₂×C₄	—	2	1	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	1	no	—
821	C₂×C₄	—	2	1	no	—
822	C₂×C₄	—	4	1	no	—
823	C₂×C₄	—	4	1	no	—
824	C₂×C₄	—	4	1	no	—
825	C₂×C₄	—	4	2	no	—
826	C₂×C₄	—	4	2	no	—
827	C₂×C₄	—	4	2	no	—
828	C₂×C₄	—	4	2	no	—
829	C₂×C₄	—	4	2	no	—
830	C₂×C₄	—	4	2	no	—
831	C₂×C₄	—	4	2	no	—
832	C₂×C₄	—	4	2	no	—
833	C₂×C₄	—	4	2	no	—
834	C₂×C₄	—	8	1	no	—
835	C₂×C₄	—	8	1	no	—
836	C₂×C₄	—	8	1	no	—
837	C₂×C₄	—	8	1	no	—
838	C₂×C₄	—	8	1	no	—
839	C₂×C₄	—	8	1	no	—
840	C₂×C₄	—	8	1	no	—
841	C₂×C₄	—	8	1	no	—
842	C₂×C₄	—	8	1	no	—
843	C₂×C₄	—	8	1	no	—
844	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
845	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
846	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
847	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
848	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
849	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
850	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
851	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
852	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
853	C₂×C₄	C₂⁵	1	1	yes	characteristic
854	C₈	—	2	1	no	—
855	C₈	—	2	1	no	—
856	C₈	—	2	1	no	—
857	C₈	—	2	1	no	—
858	C₈	—	2	1	no	—
859	C₈	—	2	1	no	—
860	C₈	—	2	1	no	—
861	C₈	—	2	1	no	—
862	C₂²	—	2	1	no	—
863	C₂²	—	2	1	no	—
864	C₂²	—	2	1	no	—
865	C₂²	—	2	1	no	—
866	C₂²	—	2	1	no	—
867	C₂²	—	2	1	no	—
868	C₂²	—	2	1	no	—
869	C₂²	—	2	2	no	—
870	C₂²	—	2	1	no	—
871	C₂²	—	2	1	no	—
872	C₂²	—	2	1	no	—
873	C₂²	—	2	1	no	—
874	C₂²	—	2	1	no	—
875	C₂²	—	2	1	no	—
876	C₂²	—	2	1	no	—
877	C₂²	—	4	1	no	—
878	C₂²	—	4	1	no	—
879	C₂²	—	4	1	no	—
880	C₂²	—	4	1	no	—
881	C₂²	—	4	1	no	—
882	C₂²	—	4	1	no	—
883	C₂²	—	4	1	no	—
884	C₂²	—	4	1	no	—
885	C₂²	—	8	2	no	—
886	C₂²	—	8	4	no	—
887	C₂²	#578	1	2	yes	—
888	C₂²	C₂³×D₄	1	1	yes	characteristic
889	C₄	—	2	1	no	—
890	C₄	—	2	1	no	—
891	C₄	—	2	1	no	—
892	C₄	—	2	2	no	—
893	C₄	—	2	1	no	—
894	C₄	—	2	1	no	—
895	C₄	—	2	1	no	—
896	C₄	—	2	1	no	—
897	C₄	—	2	1	no	—
898	C₄	—	2	1	no	—
899	C₄	—	4	1	no	—
900	C₄	—	4	1	no	—
901	C₄	—	4	1	no	—
902	C₄	—	4	1	no	—
903	C₄	—	4	1	no	—
904	C₄	—	4	1	no	—
905	C₄	—	4	1	no	—
906	C₄	—	4	1	no	—
907	C₄	—	4	1	no	—
908	C₄	—	4	1	no	—
909	C₄	—	4	1	no	—
910	C₄	—	4	1	no	—
911	C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
912	C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
913	C₂	—	2	2	no	—
914	C₂	—	4	1	no	—
915	C₂	—	4	1	no	—
916	C₂	—	4	1	no	—
917	C₂	—	4	1	no	—
918	C₂	—	4	2	no	—
919	C₂	—	8	1	no	—
920	C₂	—	8	1	no	—
921	C₂	#3484	1	1	yes	characteristic
922	C₂	C₂×#578	1	1	yes	characteristic
923	C₂	#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ #525 ◁ G
LECS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #3541	C₂	semidirect
2. #3489	C₂	semidirect
3. #3320	C₂	semidirect
4. #3315	C₂	semidirect
5. #3314	C₂	semidirect
6. #3313	C₂	semidirect
7. #3302	C₂	semidirect
8. #3300	C₂	semidirect
9. #3299	C₂	semidirect
10. #3297	C₂	semidirect
11. D₄×Q₁₆	C₂	semidirect
12. #3285	C₂	semidirect
13. #3283	C₂	semidirect
14. #3282	C₂	semidirect
15. #3270	C₂	semidirect
16. #3269	C₂	semidirect
17. #3269	C₂	semidirect
18. #3266	C₂	semidirect
19. #3225	C₂	semidirect
20. #3223	C₂	semidirect
21. #3203	C₂	semidirect
22. #3201	C₂	semidirect
23. #3190	C₂	semidirect
24. #3189	C₂	semidirect
25. #3124	C₂	semidirect
26. #3120	C₂	semidirect
27. #3013	C₂	semidirect
28. #3011	C₂	semidirect
29. #3002	C₂	semidirect
30. C₂×#452	C₂	semidirect
31. #2977	C₂	semidirect
34. C₂×#137	C₂²	semidirect
35. C₂×#137	C₂²	semidirect
38. C₂×#135	C₂²	semidirect
40. C₂²×Q₁₆	C₂²	semidirect
44. #556	C₂²	semidirect
49. #552	C₂²	semidirect
56. #548	C₂²	semidirect
61. #547	C₂²	semidirect
67. #542	C₂²	semidirect
68. #541	C₂²	semidirect
74. #537	C₂²	semidirect
77. #536	C₂²	semidirect
85. #497	C₂²	semidirect
86. #497	C₂²	semidirect
87. #495	C₂²	semidirect
88. #494	C₂²	semidirect
89. #491	C₂²	semidirect
90. #489	C₂²	semidirect
91. #488	C₂²	semidirect
92. #487	C₂²	semidirect
93. #485	C₂²	semidirect
94. #485	C₂²	semidirect
95. #485	C₂²	semidirect
98. #484	C₂²	semidirect
99. #484	C₂²	semidirect
100. #484	C₂²	semidirect
101. #483	C₂²	semidirect
102. #482	C₂²	semidirect
103. #480	C₂²	semidirect
104. #480	C₂²	semidirect
105. #479	C₂²	semidirect
106. #478	C₂²	semidirect
107. #477	C₂²	semidirect
108. #474	C₂²	semidirect
109. #470	C₂²	semidirect
110. #468	C₂²	semidirect
111. #468	C₂²	semidirect
112. #468	C₂²	semidirect
115. #467	C₂²	semidirect
116. #467	C₂²	semidirect
117. #467	C₂²	semidirect
118. #467	C₂²	semidirect
119. #467	C₂²	semidirect
120. #467	C₂²	semidirect
121. #466	C₂²	semidirect
124. #465	C₂²	semidirect
125. #464	C₂²	semidirect
126. #464	C₂²	semidirect
127. #464	C₂²	semidirect
128. #464	C₂²	semidirect
129. #463	C₂²	semidirect
130. #463	C₂²	semidirect
131. #462	C₂²	semidirect
132. #462	C₂²	semidirect
133. #462	C₂²	semidirect
134. #462	C₂²	semidirect
135. #461	C₂²	semidirect
136. #461	C₂²	semidirect
147. #452	C₂²	semidirect
148. #452	C₂²	semidirect
149. #452	C₂²	semidirect
150. #452	C₂²	semidirect
151. #452	C₂²	semidirect
152. #452	C₂²	semidirect
156. #451	C₂²	semidirect
157. #451	C₂²	semidirect
158. #451	C₂²	semidirect
159. #451	C₂²	semidirect
160. #451	C₂²	semidirect
161. #451	C₂²	semidirect
162. #451	C₂²	semidirect
166. #449	C₂²	semidirect
167. #449	C₂²	semidirect
169. #448	C₂²	semidirect
170. #448	C₂²	semidirect
171. #448	C₂²	semidirect
173. #441	C₂²	semidirect
174. #440	C₂²	semidirect
175. #440	C₂²	semidirect
176. #440	C₂²	semidirect
177. C₄×Q₁₆	C₂²	semidirect
178. C₄×Q₁₆	C₂²	semidirect
179. C₄×SD₁₆	C₂²	semidirect
180. C₄×D₈	C₂²	semidirect
183. #435	C₂²	semidirect
184. #435	C₂²	semidirect
187. C₈×D₄	C₂²	semidirect
188. C₈×D₄	C₂²	semidirect
189. #433	C₂²	semidirect
190. #433	C₂²	semidirect
191. #419	C₂²	semidirect
192. #417	C₂²	semidirect
195. #416	C₂²	semidirect
197. C₂×#103	C₂²	semidirect
199. #408	C₂²	semidirect
200. #408	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#3541	2
#3489	2
#3320	2
#3315	2
#3314	2
#3313	2
#3302	2
#3300	2
#3299	2
#3297	2
D₄×Q₁₆	2
#3285	2
#3283	2
#3282	2
#3270	2
#3269	2
#3266	2
#3225	2
#3223	2
#3203	2
#3201	2
#3190	2
#3189	2
#3124	2
#3120	2
#3013	2
#3011	2
#3002	2
C₂×#452	2
#2977	2