Subgroups — #8898065

Order 512.

7680 conjugacy classes of subgroups.

The subgroup lattice has 1059 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#56344	C₂	1	4	yes	maximal, complemented
2	#56324	C₂	1	8	yes	maximal, complemented
3	#47878	C₂	1	8	yes	maximal, complemented
4	#47827	C₂	1	4	yes	maximal, complemented
5	#47170	C₂	1	4	yes	maximal, complemented
6	#47042	C₂	1	8	yes	maximal, complemented
7	#46387	C₂	1	2	yes	maximal, complemented
8	#46386	C₂	1	2	yes	maximal, complemented
9	#46384	C₂	1	2	yes	maximal, complemented
10	#37744	C₂	1	4	yes	maximal, complemented
11	#37644	C₂	1	8	yes	maximal, complemented
12	#36717	C₂	1	1	yes	maximal, characteristic, complemented
13	#36714	C₂	1	2	yes	maximal, complemented
14	#35512	C₂	1	1	yes	maximal, characteristic, complemented
15	#35347	C₂	1	1	yes	maximal, characteristic, complemented
16	#35346	C₂	1	2	yes	maximal, complemented
17	#35346	C₂	1	2	yes	maximal, complemented
18	C₂²×H(5,𝔽₂)	C₂²	1	1	yes	characteristic, complemented
19	C₂²×H(5,𝔽₂)	C₂²	1	1	yes	characteristic, complemented
20	C₂×D₄²	C₂²	1	4	yes	complemented
21	C₂×#534	C₂²	1	4	yes	complemented
22	C₂×#534	C₂²	1	1	yes	characteristic, complemented
23	C₂×#534	C₂²	1	2	yes	complemented
24	C₂×#525	C₂²	1	2	yes	complemented
25	C₂²×#121	C₂²	1	1	yes	characteristic, complemented
26	C₂²×#120	C₂²	1	4	yes	complemented
27	C₂²×#120	C₂²	1	4	yes	complemented
28	C₂²×#120	C₂²	1	2	yes	complemented
29	#2847	C₂²	1	2	yes	complemented
30	#2846	C₂²	1	4	yes	complemented
31	#2842	C₂²	1	2	yes	complemented
32	#2832	C₂²	1	4	yes	complemented
33	#2824	C₂²	1	8	yes	complemented
34	#2824	C₂²	1	4	yes	complemented
35	#2784	C₂²	1	4	yes	complemented
36	#2752	C₂²	1	8	yes	complemented
37	#2751	C₂²	1	8	yes	complemented
38	#2750	C₂²	1	8	yes	complemented
39	#2749	C₂²	1	8	yes	complemented
40	#2749	C₂²	1	8	yes	complemented
41	#2749	C₂²	1	8	yes	complemented
42	#2749	C₂²	1	8	yes	complemented
43	#2743	C₂²	1	8	yes	complemented
44	#2743	C₂²	1	8	yes	complemented
45	#2737	C₂²	1	8	yes	complemented
46	#2736	C₂²	1	4	yes	complemented
47	#2709	C₂²	1	4	yes	complemented
48	#2703	C₂²	1	8	yes	complemented
49	#2703	C₂²	1	8	yes	complemented
50	#2697	C₂²	1	8	yes	complemented
51	#2697	C₂²	1	4	yes	complemented
52	#2696	C₂²	1	8	yes	complemented
53	#2693	C₂²	1	8	yes	complemented
54	#2693	C₂²	1	4	yes	complemented
55	#2688	C₂²	1	8	yes	complemented
56	#2679	C₂²	1	8	yes	complemented
57	#2679	C₂²	1	4	yes	complemented
58	#2678	C₂²	1	8	yes	complemented
59	#2678	C₂²	1	8	yes	complemented
60	#2678	C₂²	1	8	yes	complemented
61	#2678	C₂²	1	8	yes	complemented
62	#2678	C₂²	1	8	yes	complemented
63	#2669	C₂²	1	8	yes	complemented
64	#2669	C₂²	1	8	yes	complemented
65	#2668	C₂²	1	8	yes	complemented
66	#2668	C₂²	1	8	yes	complemented
67	#2639	C₂²	1	4	yes	complemented
68	#2626	C₂²	1	4	yes	complemented
69	#2622	C₂²	1	4	yes	complemented
70	#2617	C₂²	1	8	yes	complemented
71	#2617	C₂²	1	2	yes	complemented
72	#2613	C₂²	1	8	yes	complemented
73	#2598	C₂²	1	8	yes	complemented
74	#2591	C₂²	1	2	yes	complemented
75	#2572	C₂²	1	4	yes	complemented
76	#2539	C₂²	1	8	yes	complemented
77	#2534	C₂²	1	8	yes	complemented
78	#2471	C₂²	1	8	yes	complemented
79	#2471	C₂²	1	8	yes	complemented
80	#2457	C₂²	1	8	yes	complemented
81	#2457	C₂²	1	8	yes	complemented
82	#2456	C₂²	1	8	yes	complemented
83	#2444	C₂²	1	8	yes	complemented
84	#2433	C₂²	1	2	yes	complemented
85	#2430	C₂²	1	8	yes	complemented
86	#2424	C₂²	1	8	yes	complemented
87	#2424	C₂²	1	8	yes	complemented
88	#2424	C₂²	1	8	yes	complemented
89	#2418	C₂²	1	8	yes	complemented
90	#2418	C₂²	1	8	yes	complemented
91	#2412	C₂²	1	8	yes	complemented
92	#2411	C₂²	1	4	yes	complemented
93	#2411	C₂²	1	4	yes	complemented
94	#2410	C₂²	1	8	yes	complemented
95	#2408	C₂²	1	8	yes	complemented
96	#2408	C₂²	1	8	yes	complemented
97	#2407	C₂²	1	8	yes	complemented
98	#2406	C₂²	1	2	yes	complemented
99	#2405	C₂²	1	2	yes	complemented
100	#2405	C₂²	1	2	yes	complemented
101	#2405	C₂²	1	8	yes	complemented
102	#2405	C₂²	1	2	yes	complemented
103	#2404	C₂²	1	4	yes	complemented
104	#2404	C₂²	1	4	yes	complemented
105	#2404	C₂²	1	8	yes	complemented
106	#2404	C₂²	1	8	yes	complemented
107	#2404	C₂²	1	4	yes	complemented
108	#2404	C₂²	1	8	yes	complemented
109	#2404	C₂²	1	8	yes	complemented
110	#2404	C₂²	1	4	yes	complemented
111	#2404	C₂²	1	2	yes	complemented
112	#2403	C₂²	1	2	yes	—
113	#2403	C₂²	1	8	yes	complemented
114	#2403	C₂²	1	4	yes	complemented
115	#2403	C₂²	1	8	yes	complemented
116	#2403	C₂²	1	2	yes	complemented
117	#2403	C₂²	1	2	yes	complemented
118	#2403	C₂²	1	2	yes	complemented
119	#2403	C₂²	1	2	yes	complemented
120	#2403	C₂²	1	8	yes	complemented
121	#2403	C₂²	1	2	yes	complemented
122	#2403	C₂²	1	2	yes	complemented
123	#2403	C₂²	1	2	yes	complemented
124	#2403	C₂²	1	8	yes	complemented
125	#2375	C₂²	1	4	yes	complemented
126	D₄×C₂²⋊C₄	C₂²	1	8	yes	complemented
127	#2325	C₂²	1	4	yes	complemented
128	#2321	C₂²	1	8	yes	complemented
129	#2312	C₂²	1	1	yes	characteristic, complemented
130	#2311	C₂²	1	2	yes	complemented
131	#2309	C₂²	1	2	yes	complemented
132	#2309	C₂²	1	1	yes	characteristic, complemented
133	#2308	C₂²	1	4	yes	complemented
134	#2308	C₂²	1	2	yes	complemented
135	#2308	C₂²	1	2	yes	complemented
136	#2308	C₂²	1	4	yes	complemented
137	#2308	C₂²	1	1	yes	characteristic, complemented
138	C₂×#386	C₂²	1	2	yes	complemented
139	C₂⁶	C₂³	1	2	yes	complemented
140	C₂×H(5,𝔽₂)	—	4	4	no	—
141	C₂×H(5,𝔽₂)	—	4	4	no	—
142	C₂×H(5,𝔽₂)	—	4	8	no	—
143	C₂×H(5,𝔽₂)	—	4	8	no	—
144	C₂²×#41	C₂³	1	2	yes	—
145	C₂²×#41	C₂³	1	2	yes	—
146	C₂²×#41	C₂³	1	4	yes	—
147	C₂²×#41	C₂³	1	4	yes	—
148	C₂³×D₄	C₂³	1	2	yes	—
149	C₂³×D₄	C₂³	1	2	yes	—
150	C₂³×D₄	C₂³	1	1	yes	characteristic
151	C₂³×D₄	C₂³	1	4	yes	—
152	C₂³×D₄	C₂³	1	4	yes	—
153	C₂³×D₄	C₂³	1	1	yes	characteristic
154	C₂³×D₄	C₂³	1	2	yes	—
155	C₂³×D₄	C₂³	1	8	yes	—
156	C₂³×D₄	C₂³	1	2	yes	—
157	C₂³×D₄	C₂³	1	2	yes	—
158	C₂³×D₄	C₂³	1	8	yes	—
159	C₂³×D₄	C₂³	1	1	yes	characteristic, complemented
160	C₂⁴×C₄	C₂³	1	1	yes	characteristic, complemented
161	D₄²	—	4	16	no	—
162	#534	—	4	4	no	—
163	#534	—	4	16	no	—
164	#534	—	4	8	no	—
165	C₂×#127	C₂³	1	4	yes	—
166	#525	—	4	8	no	—
167	C₂×#123	C₂³	1	8	yes	—
168	C₂×#123	C₂³	1	4	yes	—
169	C₂×#123	C₂³	1	8	yes	—
170	C₂×#123	C₂³	1	4	yes	complemented
171	C₂×#123	C₂³	1	4	yes	complemented
172	C₂×#123	C₂³	1	4	yes	complemented
173	C₂×#123	C₂³	1	8	yes	complemented
174	C₂×C₂²⋊Q₈	C₂³	1	4	yes	complemented
175	C₂×#121	—	4	4	no	—
176	C₂×#121	C₂³	1	4	yes	—
177	C₂×#121	C₂³	1	2	yes	—
178	C₂×#121	C₂³	1	2	yes	—
179	C₂×#121	C₂³	1	4	yes	—
180	C₂×#121	C₂³	1	8	yes	—
181	C₂×#121	C₂³	1	8	yes	—
182	C₂×#121	C₂³	1	8	yes	—
183	C₂×#121	C₂³	1	8	yes	complemented
184	C₂×#121	C₂³	1	8	yes	complemented
185	C₂×#120	—	4	16	no	—
186	C₂×#120	—	4	8	no	—
187	C₂×#120	—	4	16	no	—
188	C₂×#120	C₂³	1	8	yes	—
189	C₂×#120	C₂³	1	4	yes	—
190	C₂×#120	C₂³	1	8	yes	—
191	C₂×#120	C₂³	1	4	yes	—
192	C₂×#120	C₂³	1	8	yes	—
193	C₂×#120	C₂³	1	4	yes	—
194	C₂×#120	C₂³	1	4	yes	—
195	C₂×#120	C₂³	1	8	yes	—
196	C₂×#120	C₂³	1	8	yes	—
197	C₂×#120	C₂³	1	4	yes	—
198	C₂×#120	C₂³	1	4	yes	—
199	C₂×#120	C₂³	1	4	yes	—
200	C₂×#120	C₂³	1	4	yes	—
201	C₂×#120	C₂³	1	4	yes	—
202	C₂×#120	C₂³	1	8	yes	complemented
203	C₂×#120	C₂³	1	4	yes	complemented
204	C₂×#120	C₂³	1	4	yes	complemented
205	C₂×#120	C₂³	1	8	yes	complemented
206	C₂×#120	C₂³	1	4	yes	complemented
207	C₂×#120	C₂³	1	8	yes	complemented
208	C₂×#120	C₂³	1	4	yes	complemented
209	C₂×#120	C₂³	1	4	yes	complemented
210	C₂×#120	C₂³	1	4	yes	complemented
211	C₂×#120	C₂³	1	4	yes	complemented
212	C₂×#120	C₂³	1	4	yes	complemented
213	C₂×C₄×D₄	C₂³	1	8	yes	—
214	C₂×C₄×D₄	C₂³	1	8	yes	complemented
215	C₂×C₄×D₄	C₂³	1	8	yes	complemented
216	C₂×#117	C₂³	1	2	yes	complemented
217	C₂×#117	C₂³	1	4	yes	complemented
218	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic, complemented
219	C₂²×C₂²⋊C₄	C₂³	1	1	yes	characteristic
220	C₂²×C₂²⋊C₄	C₂³	1	4	yes	—
221	C₂²×C₂²⋊C₄	C₂³	1	2	yes	complemented
222	C₂²×C₂²⋊C₄	C₂³	1	2	yes	complemented
223	C₂²×C₂²⋊C₄	C₂³	1	4	yes	complemented
224	C₂²×C₂²⋊C₄	C₂³	1	4	yes	complemented
225	C₂²×C₂²⋊C₄	C₂³	1	2	yes	complemented
226	C₂²×C₂²⋊C₄	C₂³	1	8	yes	complemented
227	C₂²×C₂²⋊C₄	C₂³	1	8	yes	complemented
228	C₂²×C₂²⋊C₄	C₂³	1	1	yes	characteristic, complemented
229	C₂²×C₂²⋊C₄	C₂³	1	2	yes	complemented
230	#400	C₂³	1	8	yes	complemented
231	#400	C₂³	1	8	yes	complemented
232	#400	C₂³	1	8	yes	complemented
233	#400	C₂³	1	4	yes	complemented
234	#400	C₂³	1	8	yes	complemented
235	#399	C₂³	1	8	yes	complemented
236	#399	C₂³	1	8	yes	complemented
237	#397	C₂³	1	8	yes	complemented
238	#397	C₂³	1	8	yes	complemented
239	#397	C₂³	1	8	yes	complemented
240	#397	C₂³	1	8	yes	complemented
241	#397	C₂³	1	8	yes	complemented
242	#397	C₂³	1	4	yes	complemented
243	#397	C₂³	1	8	yes	complemented
244	#397	C₂³	1	8	yes	complemented
245	#396	C₂³	1	8	yes	complemented
246	#396	C₂³	1	8	yes	complemented
247	#396	C₂³	1	8	yes	complemented
248	#396	C₂³	1	8	yes	complemented
249	#396	C₂³	1	8	yes	complemented
250	#395	C₂³	1	4	yes	complemented
251	#394	C₂³	1	8	yes	—
252	#394	C₂³	1	8	yes	—
253	#394	C₂³	1	4	yes	—
254	#394	C₂³	1	4	yes	—
255	#394	C₂³	1	8	yes	—
256	#394	C₂³	1	8	yes	—
257	#394	C₂³	1	8	yes	—
258	#394	C₂³	1	8	yes	—
259	#394	C₂³	1	8	yes	—
260	#394	C₂³	1	8	yes	—
261	#394	C₂³	1	8	yes	complemented
262	#394	C₂³	1	8	yes	complemented
263	#394	C₂³	1	8	yes	complemented
264	#394	C₂³	1	8	yes	complemented
265	#394	C₂³	1	8	yes	complemented
266	#394	C₂³	1	8	yes	complemented
267	#393	C₂³	1	4	yes	complemented
268	#393	C₂³	1	8	yes	complemented
269	#393	C₂³	1	8	yes	complemented
270	#393	C₂³	1	8	yes	complemented
271	#393	C₂³	1	8	yes	complemented
272	#392	C₂³	1	4	yes	—
273	#392	C₂³	1	8	yes	—
274	#392	C₂³	1	8	yes	—
275	#392	C₂³	1	8	yes	—
276	#392	C₂³	1	8	yes	—
277	#392	C₂³	1	8	yes	—
278	#392	C₂³	1	8	yes	—
279	#392	C₂³	1	8	yes	—
280	#392	C₂³	1	8	yes	—
281	#392	C₂³	1	8	yes	—
282	#392	C₂³	1	8	yes	—
283	#392	C₂³	1	8	yes	—
284	#392	C₂³	1	8	yes	—
285	#392	C₂³	1	4	yes	—
286	#392	C₂³	1	8	yes	complemented
287	#392	C₂³	1	8	yes	complemented
288	#391	C₂³	1	4	yes	complemented
289	#390	C₂³	1	8	yes	—
290	#390	C₂³	1	4	yes	—
291	#390	C₂³	1	8	yes	—
292	#390	C₂³	1	8	yes	—
293	#390	C₂³	1	8	yes	—
294	#390	C₂³	1	8	yes	complemented
295	#390	C₂³	1	8	yes	complemented
296	#390	C₂³	1	8	yes	complemented
297	#390	C₂³	1	4	yes	complemented
298	#388	C₂³	1	8	yes	complemented
299	#388	C₂³	1	8	yes	complemented
300	#388	C₂³	1	8	yes	complemented
301	#388	C₂³	1	8	yes	complemented
302	#388	C₂³	1	8	yes	complemented
303	#388	C₂³	1	8	yes	complemented
304	#388	C₂³	1	8	yes	complemented
305	#388	C₂³	1	8	yes	complemented
306	#388	C₂³	1	8	yes	complemented
307	#388	C₂³	1	8	yes	complemented
308	#387	C₂³	1	8	yes	complemented
309	#387	C₂³	1	8	yes	complemented
310	#387	C₂³	1	8	yes	complemented
311	#386	C₂³	1	8	yes	—
312	#386	C₂³	1	8	yes	—
313	#386	C₂³	1	4	yes	—
314	#386	C₂³	1	8	yes	—
315	#386	C₂³	1	4	yes	—
316	#386	C₂³	1	4	yes	—
317	#386	C₂³	1	8	yes	—
318	#386	C₂³	1	4	yes	—
319	#386	C₂³	1	8	yes	—
320	#386	C₂³	1	8	yes	—
321	#386	C₂³	1	8	yes	—
322	#386	C₂³	1	8	yes	—
323	#386	C₂³	1	8	yes	—
324	#386	C₂³	1	4	yes	—
325	#386	C₂³	1	4	yes	—
326	#386	C₂³	1	8	yes	—
327	#386	C₂³	1	8	yes	complemented
328	#386	C₂³	1	4	yes	complemented
329	#386	C₂³	1	8	yes	complemented
330	#386	C₂³	1	4	yes	complemented
331	#386	C₂³	1	8	yes	complemented
332	#386	C₂³	1	8	yes	complemented
333	#386	C₂³	1	4	yes	complemented
334	#386	C₂³	1	8	yes	complemented
335	#386	C₂³	1	4	yes	complemented
336	#386	C₂³	1	4	yes	complemented
337	#386	C₂³	1	4	yes	complemented
338	#386	C₂³	1	8	yes	complemented
339	#386	C₂³	1	8	yes	complemented
340	#386	C₂³	1	4	yes	complemented
341	#386	C₂³	1	4	yes	complemented
342	#386	C₂³	1	8	yes	complemented
343	#386	C₂³	1	8	yes	complemented
344	#386	C₂³	1	8	yes	complemented
345	#386	C₂³	1	8	yes	complemented
346	#386	C₂³	1	4	yes	complemented
347	#386	C₂³	1	8	yes	complemented
348	#386	C₂³	1	4	yes	complemented
349	#386	C₂³	1	4	yes	complemented
350	#386	C₂³	1	8	yes	complemented
351	#385	C₂³	1	8	yes	complemented
352	#385	C₂³	1	4	yes	complemented
353	#385	C₂³	1	8	yes	complemented
354	#385	C₂³	1	8	yes	complemented
355	#385	C₂³	1	8	yes	complemented
356	#385	C₂³	1	4	yes	complemented
357	#385	C₂³	1	4	yes	complemented
358	#383	C₂³	1	8	yes	complemented
359	#381	C₂³	1	8	yes	complemented
360	#381	C₂³	1	4	yes	complemented
361	#381	C₂³	1	8	yes	complemented
362	#381	C₂³	1	4	yes	complemented
363	#381	C₂³	1	2	yes	complemented
364	#381	C₂³	1	8	yes	complemented
365	#380	C₂³	1	8	yes	complemented
366	#380	C₂³	1	2	yes	complemented
367	#380	C₂³	1	4	yes	complemented
368	#380	C₂³	1	8	yes	complemented
369	#380	C₂³	1	8	yes	complemented
370	#379	C₂³	1	2	yes	—
371	#379	C₂³	1	2	yes	—
372	#379	C₂³	1	2	yes	—
373	#379	C₂³	1	8	yes	—
374	#379	C₂³	1	8	yes	—
375	#379	C₂³	1	4	yes	—
376	#379	C₂³	1	4	yes	complemented
377	#379	C₂³	1	2	yes	complemented
378	#379	C₂³	1	8	yes	complemented
379	#379	C₂³	1	8	yes	complemented
380	#379	C₂³	1	4	yes	complemented
381	#379	C₂³	1	4	yes	complemented
382	C₄×C₂²⋊C₄	C₂³	1	2	yes	complemented
383	C₄×C₂²⋊C₄	C₂³	1	8	yes	complemented
384	C₂×#95	C₂³	1	4	yes	complemented
385	C₂⁵	—	4	4	no	—
386	C₂⁵	—	4	8	no	—
387	C₂⁵	—	4	8	no	—
388	C₂⁵	—	8	4	no	—
389	C₂⁵	C₂⁴	1	2	yes	—
390	C₂⁵	C₂⁴	1	2	yes	—
391	C₂⁵	C₂⁴	1	1	yes	characteristic
392	C₂⁵	C₂⁴	1	8	yes	—
393	C₂⁵	C₂⁴	1	2	yes	—
394	C₂⁵	C₂⁴	1	2	yes	—
395	C₂⁵	C₂⁴	1	1	yes	characteristic
396	C₂⁵	C₂⁴	1	1	yes	characteristic
397	C₂⁵	C₂⁴	1	2	yes	—
398	H(5,𝔽₂)	—	4	64	no	—
399	H(5,𝔽₂)	—	4	64	no	—
400	C₂×#41	—	2	8	no	—
401	C₂×#41	—	4	4	no	—
402	C₂×#41	—	4	4	no	—
403	C₂×#41	—	4	8	no	—
404	C₂×#41	—	4	8	no	—
405	C₂×#41	—	4	8	no	—
406	C₂×#41	—	4	8	no	—
407	C₂×#41	—	4	4	no	—
408	C₂×#41	—	4	8	no	—
409	C₂×#41	—	4	8	no	—
410	C₂×#41	—	4	8	no	—
411	C₂²×Q₈	C₂⁴	1	2	yes	—
412	C₂²×Q₈	C₂⁴	1	2	yes	—
413	C₂²×D₄	—	2	8	no	—
414	C₂²×D₄	—	2	8	no	—
415	C₂²×D₄	—	2	4	no	—
416	C₂²×D₄	—	2	4	no	—
417	C₂²×D₄	—	2	16	no	—
418	C₂²×D₄	—	2	8	no	—
419	C₂²×D₄	—	2	8	no	—
420	C₂²×D₄	—	2	32	no	—
421	C₂²×D₄	—	2	16	no	—
422	C₂²×D₄	—	4	4	no	—
423	C₂²×D₄	—	4	8	no	—
424	C₂²×D₄	—	4	2	no	—
425	C₂²×D₄	—	4	4	no	—
426	C₂²×D₄	—	4	4	no	—
427	C₂²×D₄	—	4	4	no	—
428	C₂²×D₄	—	4	4	no	—
429	C₂²×D₄	—	4	8	no	—
430	C₂²×D₄	—	4	8	no	—
431	C₂²×D₄	—	4	8	no	—
432	C₂²×D₄	—	4	8	no	—
433	C₂²×D₄	—	4	8	no	—
434	C₂²×D₄	—	4	8	no	—
435	C₂²×D₄	—	4	16	no	—
436	C₂²×D₄	—	4	16	no	—
437	C₂²×D₄	—	4	4	no	—
438	C₂²×D₄	—	4	16	no	—
439	C₂²×D₄	—	8	4	no	—
440	C₂²×D₄	—	8	8	no	—
441	C₂²×D₄	—	8	8	no	—
442	C₂²×D₄	C₂⁴	1	8	yes	—
443	C₂²×D₄	C₂⁴	1	8	yes	—
444	C₂²×D₄	C₂⁴	1	4	yes	—
445	C₂²×D₄	C₂⁴	1	4	yes	—
446	C₂²×D₄	C₂⁴	1	2	yes	—
447	C₂²×D₄	C₂⁴	1	4	yes	—
448	C₂²×D₄	C₂⁴	1	4	yes	—
449	C₂²×D₄	C₂⁴	1	4	yes	—
450	C₂²×D₄	C₂⁴	1	4	yes	—
451	C₂²×D₄	C₂⁴	1	4	yes	—
452	C₂²×D₄	C₂⁴	1	8	yes	—
453	C₂²×D₄	C₂⁴	1	8	yes	—
454	C₂²×D₄	C₂⁴	1	4	yes	—
455	C₂²×D₄	C₂⁴	1	4	yes	—
456	C₂²×D₄	C₂⁴	1	8	yes	—
457	C₂²×D₄	C₂⁴	1	4	yes	—
458	C₂²×D₄	C₂⁴	1	8	yes	—
459	C₂²×D₄	C₂⁴	1	4	yes	—
460	C₂²×D₄	C₂⁴	1	2	yes	—
461	C₂²×D₄	C₂⁴	1	2	yes	—
462	C₂²×D₄	C₂⁴	1	8	yes	—
463	C₂²×D₄	C₂⁴	1	2	yes	—
464	C₂³×C₄	—	4	4	no	—
465	C₂³×C₄	—	4	2	no	—
466	C₂³×C₄	C₂⁴	1	1	yes	characteristic
467	C₂³×C₄	C₂⁴	1	4	yes	—
468	C₂³×C₄	C₂⁴	1	1	yes	characteristic
469	C₂³×C₄	C₂⁴	1	1	yes	characteristic
470	C₂³×C₄	C₂⁴	1	4	yes	—
471	C₂³×C₄	C₂⁴	1	2	yes	—
472	C₂³×C₄	C₂⁴	1	8	yes	—
473	C₂³×C₄	C₂⁴	1	2	yes	—
474	C₂³×C₄	C₂⁴	1	2	yes	—
475	C₂³×C₄	C₂⁴	1	4	yes	—
476	C₂³×C₄	C₂⁴	1	1	yes	characteristic
477	C₂³×C₄	C₂⁴	1	2	yes	—
478	C₂³×C₄	C₂⁴	1	4	yes	—
479	C₂³×C₄	C₂⁴	1	8	yes	—
480	C₂³×C₄	C₂⁴	1	2	yes	—
481	#127	—	4	8	no	—
482	#123	—	4	16	no	—
483	#123	—	4	16	no	—
484	#123	—	4	8	no	—
485	#123	—	4	8	no	—
486	#123	—	4	8	no	—
487	#123	—	4	8	no	—
488	#123	—	8	8	no	—
489	C₂²⋊Q₈	—	4	8	no	—
490	#121	—	2	16	no	—
491	#121	—	4	8	no	—
492	#121	—	4	16	no	—
493	#121	—	4	16	no	—
494	#121	—	4	16	no	—
495	#121	—	4	16	no	—
496	#121	—	4	4	no	—
497	#121	—	4	4	no	—
498	#121	—	4	16	no	—
499	#120	—	2	16	no	—
500	#120	—	2	32	no	—
501	#120	—	4	8	no	—
502	#120	—	4	8	no	—
503	#120	—	4	16	no	—
504	#120	—	4	8	no	—
505	#120	—	4	16	no	—
506	#120	—	4	16	no	—
507	#120	—	4	8	no	—
508	#120	—	4	16	no	—
509	#120	—	4	8	no	—
510	#120	—	4	16	no	—
511	#120	—	4	8	no	—
512	#120	—	4	8	no	—
513	#120	—	4	8	no	—
514	#120	—	4	16	no	—
515	#120	—	4	16	no	—
516	#120	—	4	8	no	—
517	#120	—	4	8	no	—
518	#120	—	4	8	no	—
519	#120	—	4	8	no	—
520	#120	—	8	4	no	—
521	#120	—	8	4	no	—
522	#120	—	8	4	no	—
523	#120	—	8	4	no	—
524	C₄×D₄	—	4	16	no	—
525	C₄×D₄	—	4	16	no	—
526	C₄×D₄	—	8	8	no	—
527	#117	—	4	4	no	—
528	#117	—	8	4	no	—
529	C₂×C₄⋊C₄	—	4	2	no	—
530	C₂×C₄⋊C₄	C₂⁴	1	4	yes	—
531	C₂×C₄⋊C₄	C₂⁴	1	4	yes	—
532	C₂×C₄⋊C₄	C₂⁴	1	8	yes	—
533	C₂×C₄⋊C₄	C₂⁴	1	8	yes	—
534	C₂×C₄⋊C₄	C₂⁴	1	8	yes	—
535	C₂×C₄⋊C₄	C₂⁴	1	8	yes	—
536	C₂×C₄⋊C₄	C₂⁴	1	4	yes	—
537	C₂×C₄⋊C₄	C₂⁴	1	2	yes	—
538	C₂×C₄⋊C₄	C₂⁴	1	8	yes	—
539	C₂×C₄⋊C₄	C₂⁴	1	2	yes	—
540	C₂×C₄⋊C₄	C₂⁴	1	8	yes	—
541	C₂×C₂²⋊C₄	—	2	4	no	—
542	C₂×C₂²⋊C₄	—	4	8	no	—
543	C₂×C₂²⋊C₄	—	4	16	no	—
544	C₂×C₂²⋊C₄	—	4	8	no	—
545	C₂×C₂²⋊C₄	—	4	4	no	—
546	C₂×C₂²⋊C₄	—	4	4	no	—
547	C₂×C₂²⋊C₄	—	4	4	no	—
548	C₂×C₂²⋊C₄	—	4	4	no	—
549	C₂×C₂²⋊C₄	—	4	16	no	—
550	C₂×C₂²⋊C₄	—	4	8	no	—
551	C₂×C₂²⋊C₄	—	4	2	no	—
552	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
553	C₂×C₂²⋊C₄	C₂⁴	1	4	yes	—
554	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
555	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
556	C₂×C₂²⋊C₄	C₂⁴	1	4	yes	—
557	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
558	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
559	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
560	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
561	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
562	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
563	C₂×C₂²⋊C₄	C₂⁴	1	4	yes	—
564	C₂×C₂²⋊C₄	C₂⁴	1	4	yes	—
565	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
566	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
567	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
568	C₂×C₂²⋊C₄	C₂⁴	1	4	yes	—
569	C₂×C₂²⋊C₄	C₂⁴	1	4	yes	—
570	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
571	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
572	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
573	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
574	C₂×C₂²⋊C₄	C₂⁴	1	4	yes	—
575	C₂×C₂²⋊C₄	C₂⁴	1	4	yes	—
576	C₂×C₂²⋊C₄	C₂⁴	1	4	yes	—
577	C₂×C₂²⋊C₄	C₂⁴	1	4	yes	—
578	C₂×C₂²⋊C₄	C₂⁴	1	4	yes	—
579	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
580	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
581	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
582	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
583	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
584	C₂×C₂²⋊C₄	C₂⁴	1	4	yes	—
585	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
586	C₂×C₂²⋊C₄	C₂⁴	1	4	yes	—
587	C₂×C₂²⋊C₄	C₂⁴	1	4	yes	—
588	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
589	C₂×C₂²⋊C₄	C₂⁴	1	4	yes	—
590	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
591	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
592	C₂×C₂²⋊C₄	C₂⁴	1	4	yes	—
593	C₂×C₄²	C₂⁴	1	4	yes	—
594	C₂×C₄²	C₂⁴	1	8	yes	—
595	C₂×C₄²	C₂⁴	1	4	yes	—
596	#95	C₂⁴	1	8	yes	—
597	#95	C₂⁴	1	8	yes	—
598	#95	C₂⁴	1	4	yes	—
599	#95	C₂⁴	1	8	yes	—
600	#95	C₂⁴	1	8	yes	—
601	#95	C₂⁴	1	4	yes	—
602	#95	C₂⁴	1	8	yes	—
603	#95	C₂⁴	1	8	yes	—
604	#95	C₂⁴	1	8	yes	—
605	#95	C₂⁴	1	8	yes	—
606	#95	C₂⁴	1	8	yes	—
607	#95	C₂⁴	1	8	yes	—
608	#95	C₂⁴	1	4	yes	—
609	#95	C₂⁴	1	8	yes	—
610	#95	C₂⁴	1	8	yes	—
611	#95	C₂⁴	1	4	yes	—
612	#95	C₂⁴	1	8	yes	—
613	#95	C₂⁴	1	8	yes	—
614	C₂⁴	—	2	4	no	—
615	C₂⁴	—	2	4	no	—
616	C₂⁴	—	2	4	no	—
617	C₂⁴	—	2	8	no	—
618	C₂⁴	—	2	8	no	—
619	C₂⁴	—	2	2	no	—
620	C₂⁴	—	2	16	no	—
621	C₂⁴	—	2	4	no	—
622	C₂⁴	—	2	2	no	—
623	C₂⁴	—	2	16	no	—
624	C₂⁴	—	2	8	no	—
625	C₂⁴	—	4	8	no	—
626	C₂⁴	—	4	4	no	—
627	C₂⁴	—	4	8	no	—
628	C₂⁴	—	4	8	no	—
629	C₂⁴	—	4	4	no	—
630	C₂⁴	—	4	2	no	—
631	C₂⁴	—	4	2	no	—
632	C₂⁴	—	4	2	no	—
633	C₂⁴	—	4	2	no	—
634	C₂⁴	—	4	2	no	—
635	C₂⁴	—	4	2	no	—
636	C₂⁴	—	4	4	no	—
637	C₂⁴	—	4	2	no	—
638	C₂⁴	—	4	2	no	—
639	C₂⁴	—	4	4	no	—
640	C₂⁴	—	4	4	no	—
641	C₂⁴	—	4	8	no	—
642	C₂⁴	—	4	8	no	—
643	C₂⁴	—	4	4	no	—
644	C₂⁴	—	4	4	no	—
645	C₂⁴	—	4	2	no	—
646	C₂⁴	—	4	4	no	—
647	C₂⁴	—	4	4	no	—
648	C₂⁴	—	4	4	no	—
649	C₂⁴	—	4	4	no	—
650	C₂⁴	—	4	2	no	—
651	C₂⁴	—	4	2	no	—
652	C₂⁴	—	8	16	no	—
653	C₂⁴	—	8	16	no	—
654	C₂⁴	—	8	64	no	—
655	C₂⁴	—	8	16	no	—
656	C₂⁴	H(5,𝔽₂)	1	4	yes	—
657	C₂⁴	H(5,𝔽₂)	1	8	yes	complemented
658	C₂⁴	C₂⁵	1	4	yes	—
659	C₂⁴	C₂⁵	1	2	yes	—
660	C₂⁴	C₂⁵	1	4	yes	—
661	C₂⁴	C₂⁵	1	4	yes	—
662	C₂⁴	C₂⁵	1	2	yes	—
663	C₂⁴	C₂⁵	1	1	yes	characteristic
664	C₂⁴	C₂⁵	1	2	yes	—
665	#41	—	4	32	no	—
666	#41	—	4	64	no	—
667	#41	—	4	32	no	—
668	#41	—	4	64	no	—
669	C₂×Q₈	—	2	4	no	—
670	C₂×Q₈	—	4	2	no	—
671	C₂×Q₈	—	4	2	no	—
672	C₂×Q₈	—	4	2	no	—
673	C₂×Q₈	—	4	4	no	—
674	C₂×D₄	—	2	16	no	—
675	C₂×D₄	—	2	16	no	—
676	C₂×D₄	—	2	16	no	—
677	C₂×D₄	—	2	16	no	—
678	C₂×D₄	—	2	8	no	—
679	C₂×D₄	—	2	8	no	—
680	C₂×D₄	—	2	8	no	—
681	C₂×D₄	—	2	8	no	—
682	C₂×D₄	—	2	8	no	—
683	C₂×D₄	—	2	8	no	—
684	C₂×D₄	—	2	8	no	—
685	C₂×D₄	—	2	8	no	—
686	C₂×D₄	—	2	8	no	—
687	C₂×D₄	—	2	8	no	—
688	C₂×D₄	—	2	8	no	—
689	C₂×D₄	—	2	8	no	—
690	C₂×D₄	—	2	8	no	—
691	C₂×D₄	—	2	8	no	—
692	C₂×D₄	—	2	8	no	—
693	C₂×D₄	—	2	16	no	—
694	C₂×D₄	—	2	16	no	—
695	C₂×D₄	—	2	8	no	—
696	C₂×D₄	—	2	16	no	—
697	C₂×D₄	—	2	8	no	—
698	C₂×D₄	—	2	8	no	—
699	C₂×D₄	—	2	16	no	—
700	C₂×D₄	—	2	8	no	—
701	C₂×D₄	—	4	8	no	—
702	C₂×D₄	—	4	2	no	—
703	C₂×D₄	—	4	4	no	—
704	C₂×D₄	—	4	2	no	—
705	C₂×D₄	—	4	4	no	—
706	C₂×D₄	—	4	4	no	—
707	C₂×D₄	—	4	4	no	—
708	C₂×D₄	—	4	4	no	—
709	C₂×D₄	—	4	4	no	—
710	C₂×D₄	—	4	2	no	—
711	C₂×D₄	—	4	4	no	—
712	C₂×D₄	—	4	4	no	—
713	C₂×D₄	—	4	4	no	—
714	C₂×D₄	—	4	8	no	—
715	C₂×D₄	—	4	16	no	—
716	C₂×D₄	—	4	8	no	—
717	C₂×D₄	—	4	8	no	—
718	C₂×D₄	—	4	8	no	—
719	C₂×D₄	—	4	8	no	—
720	C₂×D₄	—	4	4	no	—
721	C₂×D₄	—	4	4	no	—
722	C₂×D₄	—	4	8	no	—
723	C₂×D₄	—	4	8	no	—
724	C₂×D₄	—	4	4	no	—
725	C₂×D₄	—	4	4	no	—
726	C₂×D₄	—	4	8	no	—
727	C₂×D₄	—	4	8	no	—
728	C₂×D₄	—	4	4	no	—
729	C₂×D₄	—	4	4	no	—
730	C₂×D₄	—	4	8	no	—
731	C₂×D₄	—	4	8	no	—
732	C₂×D₄	—	4	8	no	—
733	C₂×D₄	—	4	2	no	—
734	C₂×D₄	—	4	4	no	—
735	C₂×D₄	—	4	2	no	—
736	C₂×D₄	—	4	4	no	—
737	C₂×D₄	—	4	64	no	—
738	C₂×D₄	—	4	16	no	—
739	C₂×D₄	—	4	32	no	—
740	C₂×D₄	—	4	32	no	—
741	C₂×D₄	—	4	32	no	—
742	C₂×D₄	—	4	64	no	—
743	C₂×D₄	—	4	32	no	—
744	C₂×D₄	—	8	16	no	—
745	C₂×D₄	—	8	64	no	—
746	C₂×D₄	—	8	64	no	—
747	C₂×D₄	—	8	8	no	—
748	C₂×D₄	H(5,𝔽₂)	1	8	yes	complemented
749	C₂²×C₄	—	2	2	no	—
750	C₂²×C₄	—	2	4	no	—
751	C₂²×C₄	—	2	4	no	—
752	C₂²×C₄	—	2	4	no	—
753	C₂²×C₄	—	2	4	no	—
754	C₂²×C₄	—	2	8	no	—
755	C₂²×C₄	—	2	2	no	—
756	C₂²×C₄	—	2	8	no	—
757	C₂²×C₄	—	2	4	no	—
758	C₂²×C₄	—	2	2	no	—
759	C₂²×C₄	—	2	2	no	—
760	C₂²×C₄	—	2	16	no	—
761	C₂²×C₄	—	2	8	no	—
762	C₂²×C₄	—	2	8	no	—
763	C₂²×C₄	—	4	4	no	—
764	C₂²×C₄	—	4	4	no	—
765	C₂²×C₄	—	4	2	no	—
766	C₂²×C₄	—	4	2	no	—
767	C₂²×C₄	—	4	2	no	—
768	C₂²×C₄	—	4	2	no	—
769	C₂²×C₄	—	4	4	no	—
770	C₂²×C₄	—	4	4	no	—
771	C₂²×C₄	—	4	4	no	—
772	C₂²×C₄	—	4	4	no	—
773	C₂²×C₄	—	4	4	no	—
774	C₂²×C₄	—	4	8	no	—
775	C₂²×C₄	—	4	4	no	—
776	C₂²×C₄	—	4	8	no	—
777	C₂²×C₄	—	4	8	no	—
778	C₂²×C₄	—	4	4	no	—
779	C₂²×C₄	—	4	2	no	—
780	C₂²×C₄	—	4	2	no	—
781	C₂²×C₄	—	4	8	no	—
782	C₂²×C₄	—	4	8	no	—
783	C₂²×C₄	—	4	4	no	—
784	C₂²×C₄	—	4	4	no	—
785	C₂²×C₄	—	4	4	no	—
786	C₂²×C₄	—	8	8	no	—
787	C₂²×C₄	C₂⁵	1	4	yes	—
788	C₂²×C₄	C₂⁵	1	2	yes	—
789	C₂²×C₄	C₂⁵	1	4	yes	—
790	C₂²×C₄	C₂⁵	1	8	yes	—
791	C₂²×C₄	C₂⁵	1	4	yes	—
792	C₂²×C₄	C₂⁵	1	8	yes	—
793	C₂²×C₄	C₂⁵	1	8	yes	—
794	C₂²×C₄	C₂⁵	1	2	yes	—
795	C₂²×C₄	C₂⁵	1	2	yes	—
796	C₂²×C₄	C₂⁵	1	2	yes	—
797	C₄⋊C₄	—	2	8	no	—
798	C₄⋊C₄	—	4	4	no	—
799	C₄⋊C₄	—	4	8	no	—
800	C₄⋊C₄	—	4	8	no	—
801	C₄⋊C₄	—	4	8	no	—
802	C₄⋊C₄	—	4	8	no	—
803	C₄⋊C₄	—	4	8	no	—
804	C₄⋊C₄	—	4	8	no	—
805	C₄⋊C₄	—	4	2	no	—
806	C₄⋊C₄	—	4	4	no	—
807	C₄⋊C₄	—	4	2	no	—
808	C₂²⋊C₄	—	2	8	no	—
809	C₂²⋊C₄	—	2	16	no	—
810	C₂²⋊C₄	—	2	8	no	—
811	C₂²⋊C₄	—	2	16	no	—
812	C₂²⋊C₄	—	2	16	no	—
813	C₂²⋊C₄	—	2	16	no	—
814	C₂²⋊C₄	—	2	16	no	—
815	C₂²⋊C₄	—	4	4	no	—
816	C₂²⋊C₄	—	4	8	no	—
817	C₂²⋊C₄	—	4	8	no	—
818	C₂²⋊C₄	—	4	8	no	—
819	C₂²⋊C₄	—	4	4	no	—
820	C₂²⋊C₄	—	4	8	no	—
821	C₂²⋊C₄	—	4	4	no	—
822	C₂²⋊C₄	—	4	8	no	—
823	C₂²⋊C₄	—	4	4	no	—
824	C₂²⋊C₄	—	4	8	no	—
825	C₂²⋊C₄	—	4	8	no	—
826	C₂²⋊C₄	—	4	8	no	—
827	C₂²⋊C₄	—	4	8	no	—
828	C₂²⋊C₄	—	4	8	no	—
829	C₂²⋊C₄	—	4	8	no	—
830	C₂²⋊C₄	—	4	4	no	—
831	C₂²⋊C₄	—	4	4	no	—
832	C₂²⋊C₄	—	4	4	no	—
833	C₂²⋊C₄	—	4	4	no	—
834	C₂²⋊C₄	—	4	4	no	—
835	C₂²⋊C₄	—	4	8	no	—
836	C₂²⋊C₄	—	4	8	no	—
837	C₂²⋊C₄	—	4	8	no	—
838	C₂²⋊C₄	—	4	8	no	—
839	C₂²⋊C₄	—	4	8	no	—
840	C₂²⋊C₄	—	4	4	no	—
841	C₂²⋊C₄	—	4	8	no	—
842	C₂²⋊C₄	—	4	4	no	—
843	C₂²⋊C₄	—	4	8	no	—
844	C₂²⋊C₄	—	4	4	no	—
845	C₂²⋊C₄	—	4	4	no	—
846	C₂²⋊C₄	—	4	8	no	—
847	C₂²⋊C₄	—	4	8	no	—
848	C₂²⋊C₄	—	4	4	no	—
849	C₄²	—	4	4	no	—
850	C₄²	—	4	8	no	—
851	C₄²	—	4	4	no	—
852	C₂³	—	2	8	no	—
853	C₂³	—	2	16	no	—
854	C₂³	—	2	16	no	—
855	C₂³	—	2	8	no	—
856	C₂³	—	2	8	no	—
857	C₂³	—	2	4	no	—
858	C₂³	—	2	2	no	—
859	C₂³	—	2	2	no	—
860	C₂³	—	2	4	no	—
861	C₂³	—	2	4	no	—
862	C₂³	—	2	4	no	—
863	C₂³	—	2	4	no	—
864	C₂³	—	2	4	no	—
865	C₂³	—	2	4	no	—
866	C₂³	—	2	2	no	—
867	C₂³	—	2	2	no	—
868	C₂³	—	2	4	no	—
869	C₂³	—	2	4	no	—
870	C₂³	—	2	2	no	—
871	C₂³	—	2	8	no	—
872	C₂³	—	2	8	no	—
873	C₂³	—	2	8	no	—
874	C₂³	—	2	4	no	—
875	C₂³	—	2	4	no	—
876	C₂³	—	2	8	no	—
877	C₂³	—	2	2	no	—
878	C₂³	—	2	4	no	—
879	C₂³	—	2	4	no	—
880	C₂³	—	2	4	no	—
881	C₂³	—	2	4	no	—
882	C₂³	—	4	4	no	—
883	C₂³	—	4	4	no	—
884	C₂³	—	4	8	no	—
885	C₂³	—	4	4	no	—
886	C₂³	—	4	16	no	—
887	C₂³	—	4	32	no	—
888	C₂³	—	4	8	no	—
889	C₂³	—	4	8	no	—
890	C₂³	—	4	32	no	—
891	C₂³	—	4	4	no	—
892	C₂³	—	8	2	no	—
893	C₂³	—	8	2	no	—
894	C₂³	—	8	8	no	—
895	C₂³	—	8	4	no	—
896	C₂³	—	8	4	no	—
897	C₂³	—	8	16	no	—
898	C₂³	—	8	16	no	—
899	C₂³	—	8	4	no	—
900	C₂³	—	8	4	no	—
901	C₂³	—	8	4	no	—
902	C₂³	—	8	4	no	—
903	C₂³	—	8	16	no	—
904	C₂³	—	8	16	no	—
905	C₂³	—	8	16	no	—
906	C₂³	—	8	2	no	—
907	C₂³	—	8	16	no	—
908	C₂³	—	8	2	no	—
909	C₂³	—	8	16	no	—
910	C₂³	—	8	16	no	—
911	C₂³	—	8	16	no	—
912	C₂³	—	8	128	no	—
913	C₂³	—	16	2	no	—
914	C₂³	—	16	2	no	—
915	C₂³	—	16	2	no	—
916	C₂³	—	16	2	no	—
917	C₂³	—	16	4	no	—
918	C₂³	—	16	4	no	—
919	C₂³	—	16	4	no	—
920	C₂³	C₂×H(5,𝔽₂)	1	8	yes	—
921	C₂³	C₂×H(5,𝔽₂)	1	4	yes	—
922	C₂³	C₂×H(5,𝔽₂)	1	8	yes	—
923	C₂³	C₂×H(5,𝔽₂)	1	4	yes	—
924	C₂³	C₂×H(5,𝔽₂)	1	2	yes	—
925	C₂³	C₂⁶	1	1	yes	characteristic
926	Q₈	—	4	8	no	—
927	Q₈	—	4	8	no	—
928	D₄	—	4	8	no	—
929	D₄	—	4	16	no	—
930	D₄	—	4	16	no	—
931	D₄	—	4	16	no	—
932	D₄	—	4	16	no	—
933	D₄	—	4	16	no	—
934	D₄	—	4	16	no	—
935	D₄	—	4	16	no	—
936	D₄	—	4	8	no	—
937	D₄	—	4	32	no	—
938	D₄	—	4	32	no	—
939	D₄	—	4	16	no	—
940	D₄	—	8	8	no	—
941	D₄	—	8	8	no	—
942	D₄	—	8	8	no	—
943	D₄	—	8	16	no	—
944	D₄	—	8	16	no	—
945	D₄	—	8	16	no	—
946	D₄	—	8	16	no	—
947	D₄	—	8	16	no	—
948	D₄	—	16	2	no	—
949	D₄	—	16	2	no	—
950	C₂×C₄	—	2	8	no	—
951	C₂×C₄	—	2	2	no	—
952	C₂×C₄	—	2	2	no	—
953	C₂×C₄	—	2	4	no	—
954	C₂×C₄	—	2	8	no	—
955	C₂×C₄	—	2	8	no	—
956	C₂×C₄	—	2	2	no	—
957	C₂×C₄	—	2	8	no	—
958	C₂×C₄	—	2	8	no	—
959	C₂×C₄	—	2	4	no	—
960	C₂×C₄	—	2	2	no	—
961	C₂×C₄	—	2	8	no	—
962	C₂×C₄	—	2	8	no	—
963	C₂×C₄	—	2	4	no	—
964	C₂×C₄	—	2	4	no	—
965	C₂×C₄	—	2	4	no	—
966	C₂×C₄	—	2	4	no	—
967	C₂×C₄	—	2	4	no	—
968	C₂×C₄	—	2	4	no	—
969	C₂×C₄	—	2	2	no	—
970	C₂×C₄	—	2	4	no	—
971	C₂×C₄	—	2	4	no	—
972	C₂×C₄	—	2	4	no	—
973	C₂×C₄	—	2	8	no	—
974	C₂×C₄	—	2	8	no	—
975	C₂×C₄	—	2	4	no	—
976	C₂×C₄	—	2	8	no	—
977	C₂×C₄	—	4	16	no	—
978	C₂×C₄	—	4	4	no	—
979	C₂×C₄	—	4	8	no	—
980	C₂×C₄	—	4	8	no	—
981	C₂×C₄	—	4	8	no	—
982	C₂×C₄	—	4	16	no	—
983	C₂×C₄	—	4	8	no	—
984	C₂×C₄	—	4	8	no	—
985	C₂×C₄	—	8	8	no	—
986	C₂×C₄	—	8	2	no	—
987	C₂×C₄	—	8	2	no	—
988	C₂×C₄	—	8	16	no	—
989	C₂×C₄	—	8	16	no	—
990	C₂×C₄	—	16	4	no	—
991	C₂×C₄	C₂×H(5,𝔽₂)	1	4	yes	—
992	C₂²	—	2	2	no	—
993	C₂²	—	2	2	no	—
994	C₂²	—	2	4	no	—
995	C₂²	—	2	8	no	—
996	C₂²	—	2	4	no	—
997	C₂²	—	2	4	no	—
998	C₂²	—	2	8	no	—
999	C₂²	—	2	4	no	—
1000	C₂²	—	2	2	no	—
1001	C₂²	—	2	16	no	—
1002	C₂²	—	2	8	no	—
1003	C₂²	—	2	16	no	—
1004	C₂²	—	4	2	no	—
1005	C₂²	—	4	4	no	—
1006	C₂²	—	4	4	no	—
1007	C₂²	—	4	4	no	—
1008	C₂²	—	4	4	no	—
1009	C₂²	—	4	2	no	—
1010	C₂²	—	4	8	no	—
1011	C₂²	—	4	4	no	—
1012	C₂²	—	4	8	no	—
1013	C₂²	—	4	8	no	—
1014	C₂²	—	4	4	no	—
1015	C₂²	—	4	2	no	—
1016	C₂²	—	4	2	no	—
1017	C₂²	—	4	4	no	—
1018	C₂²	—	4	4	no	—
1019	C₂²	—	4	4	no	—
1020	C₂²	—	4	2	no	—
1021	C₂²	—	4	8	no	—
1022	C₂²	—	4	8	no	—
1023	C₂²	—	4	8	no	—
1024	C₂²	—	8	8	no	—
1025	C₂²	—	8	16	no	—
1026	C₂²	—	8	16	no	—
1027	C₂²	—	8	64	no	—
1028	C₂²	—	8	16	no	—
1029	C₂²	—	16	8	no	—
1030	C₂²	—	16	4	no	—
1031	C₂²	—	16	8	no	—
1032	C₂²	—	16	4	no	—
1033	C₂²	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
1034	C₂²	C₂²×H(5,𝔽₂)	1	2	yes	—
1035	C₂²	C₂²×H(5,𝔽₂)	1	2	yes	—
1036	C₂²	H(7,𝔽₂)	1	2	yes	—
1037	C₄	—	2	4	no	—
1038	C₄	—	4	4	no	—
1039	C₄	—	4	4	no	—
1040	C₄	—	4	2	no	—
1041	C₄	—	4	2	no	—
1042	C₄	—	4	2	no	—
1043	C₄	—	4	4	no	—
1044	C₄	—	4	8	no	—
1045	C₄	—	4	8	no	—
1046	C₄	—	4	8	no	—
1047	C₂	—	4	4	no	—
1048	C₂	—	4	8	no	—
1049	C₂	—	4	8	no	—
1050	C₂	—	4	4	no	—
1051	C₂	—	4	2	no	—
1052	C₂	—	8	4	no	—
1053	C₂	—	8	2	no	—
1054	C₂	#62817	1	1	yes	characteristic
1055	C₂	#62817	1	1	yes	characteristic
1056	C₂	#62862	1	1	yes	characteristic
1057	C₂	#62892	1	4	yes	—

	subgroup	G/H
center, commutator, Frattini, socle, cosocle	C₂³	C₂⁶
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ G
LECS	G ▷ C₂³ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #56344	C₂	semidirect
2. #56324	C₂	semidirect
3. #47878	C₂	semidirect
4. #47827	C₂	semidirect
5. #47170	C₂	semidirect
6. #47042	C₂	semidirect
7. #46387	C₂	semidirect
8. #46386	C₂	semidirect
9. #46384	C₂	semidirect
10. #37744	C₂	semidirect
11. #37644	C₂	semidirect
12. #36717	C₂	semidirect
13. #36714	C₂	semidirect
14. #35512	C₂	semidirect
15. #35347	C₂	semidirect
16. #35346	C₂	semidirect
17. #35346	C₂	semidirect
18. C₂²×H(5,𝔽₂)	C₂²	semidirect
19. C₂²×H(5,𝔽₂)	C₂²	semidirect
20. C₂×D₄²	C₂²	semidirect
21. C₂×#534	C₂²	semidirect
22. C₂×#534	C₂²	semidirect
23. C₂×#534	C₂²	semidirect
24. C₂×#525	C₂²	semidirect
25. C₂²×#121	C₂²	semidirect
26. C₂²×#120	C₂²	semidirect
27. C₂²×#120	C₂²	semidirect
28. C₂²×#120	C₂²	semidirect
29. #2847	C₂²	semidirect
30. #2846	C₂²	semidirect
31. #2842	C₂²	semidirect
32. #2832	C₂²	semidirect
33. #2824	C₂²	semidirect
34. #2824	C₂²	semidirect
35. #2784	C₂²	semidirect
36. #2752	C₂²	semidirect
37. #2751	C₂²	semidirect
38. #2750	C₂²	semidirect
39. #2749	C₂²	semidirect
40. #2749	C₂²	semidirect
41. #2749	C₂²	semidirect
42. #2749	C₂²	semidirect
43. #2743	C₂²	semidirect
44. #2743	C₂²	semidirect
45. #2737	C₂²	semidirect
46. #2736	C₂²	semidirect
47. #2709	C₂²	semidirect
48. #2703	C₂²	semidirect
49. #2703	C₂²	semidirect
50. #2697	C₂²	semidirect
51. #2697	C₂²	semidirect
52. #2696	C₂²	semidirect
53. #2693	C₂²	semidirect
54. #2693	C₂²	semidirect
55. #2688	C₂²	semidirect
56. #2679	C₂²	semidirect
57. #2679	C₂²	semidirect
58. #2678	C₂²	semidirect
59. #2678	C₂²	semidirect
60. #2678	C₂²	semidirect
61. #2678	C₂²	semidirect
62. #2678	C₂²	semidirect
63. #2669	C₂²	semidirect
64. #2669	C₂²	semidirect
65. #2668	C₂²	semidirect
66. #2668	C₂²	semidirect
67. #2639	C₂²	semidirect
68. #2626	C₂²	semidirect
69. #2622	C₂²	semidirect
70. #2617	C₂²	semidirect
71. #2617	C₂²	semidirect
72. #2613	C₂²	semidirect
73. #2598	C₂²	semidirect
74. #2591	C₂²	semidirect
75. #2572	C₂²	semidirect
76. #2539	C₂²	semidirect
77. #2534	C₂²	semidirect
78. #2471	C₂²	semidirect
79. #2471	C₂²	semidirect
80. #2457	C₂²	semidirect
81. #2457	C₂²	semidirect
82. #2456	C₂²	semidirect
83. #2444	C₂²	semidirect
84. #2433	C₂²	semidirect
85. #2430	C₂²	semidirect
86. #2424	C₂²	semidirect
87. #2424	C₂²	semidirect
88. #2424	C₂²	semidirect
89. #2418	C₂²	semidirect
90. #2418	C₂²	semidirect
91. #2412	C₂²	semidirect
92. #2411	C₂²	semidirect
93. #2411	C₂²	semidirect
94. #2410	C₂²	semidirect
95. #2408	C₂²	semidirect
96. #2408	C₂²	semidirect
97. #2407	C₂²	semidirect
98. #2406	C₂²	semidirect
99. #2405	C₂²	semidirect
100. #2405	C₂²	semidirect
101. #2405	C₂²	semidirect
102. #2405	C₂²	semidirect
103. #2404	C₂²	semidirect
104. #2404	C₂²	semidirect
105. #2404	C₂²	semidirect
106. #2404	C₂²	semidirect
107. #2404	C₂²	semidirect
108. #2404	C₂²	semidirect
109. #2404	C₂²	semidirect
110. #2404	C₂²	semidirect
111. #2404	C₂²	semidirect
113. #2403	C₂²	semidirect
114. #2403	C₂²	semidirect
115. #2403	C₂²	semidirect
116. #2403	C₂²	semidirect
117. #2403	C₂²	semidirect
118. #2403	C₂²	semidirect
119. #2403	C₂²	semidirect
120. #2403	C₂²	semidirect
121. #2403	C₂²	semidirect
122. #2403	C₂²	semidirect
123. #2403	C₂²	semidirect
124. #2403	C₂²	semidirect
125. #2375	C₂²	semidirect
126. D₄×C₂²⋊C₄	C₂²	semidirect
127. #2325	C₂²	semidirect
128. #2321	C₂²	semidirect
129. #2312	C₂²	semidirect
130. #2311	C₂²	semidirect
131. #2309	C₂²	semidirect
132. #2309	C₂²	semidirect
133. #2308	C₂²	semidirect
134. #2308	C₂²	semidirect
135. #2308	C₂²	semidirect
136. #2308	C₂²	semidirect
137. #2308	C₂²	semidirect
138. C₂×#386	C₂²	semidirect
139. C₂⁶	C₂³	semidirect
159. C₂³×D₄	C₂³	semidirect
160. C₂⁴×C₄	C₂³	semidirect
170. C₂×#123	C₂³	semidirect
171. C₂×#123	C₂³	semidirect
172. C₂×#123	C₂³	semidirect
173. C₂×#123	C₂³	semidirect
174. C₂×C₂²⋊Q₈	C₂³	semidirect
183. C₂×#121	C₂³	semidirect
184. C₂×#121	C₂³	semidirect
202. C₂×#120	C₂³	semidirect
203. C₂×#120	C₂³	semidirect
204. C₂×#120	C₂³	semidirect
205. C₂×#120	C₂³	semidirect
206. C₂×#120	C₂³	semidirect
207. C₂×#120	C₂³	semidirect
208. C₂×#120	C₂³	semidirect
209. C₂×#120	C₂³	semidirect
210. C₂×#120	C₂³	semidirect
211. C₂×#120	C₂³	semidirect
212. C₂×#120	C₂³	semidirect
214. C₂×C₄×D₄	C₂³	semidirect
215. C₂×C₄×D₄	C₂³	semidirect
216. C₂×#117	C₂³	semidirect
217. C₂×#117	C₂³	semidirect
218. C₂²×C₄⋊C₄	C₂³	semidirect
221. C₂²×C₂²⋊C₄	C₂³	semidirect
222. C₂²×C₂²⋊C₄	C₂³	semidirect
223. C₂²×C₂²⋊C₄	C₂³	semidirect
224. C₂²×C₂²⋊C₄	C₂³	semidirect
225. C₂²×C₂²⋊C₄	C₂³	semidirect
226. C₂²×C₂²⋊C₄	C₂³	semidirect
227. C₂²×C₂²⋊C₄	C₂³	semidirect
228. C₂²×C₂²⋊C₄	C₂³	semidirect
229. C₂²×C₂²⋊C₄	C₂³	semidirect
230. #400	C₂³	semidirect
231. #400	C₂³	semidirect
232. #400	C₂³	semidirect
233. #400	C₂³	semidirect
234. #400	C₂³	semidirect
235. #399	C₂³	semidirect
236. #399	C₂³	semidirect
237. #397	C₂³	semidirect
238. #397	C₂³	semidirect
239. #397	C₂³	semidirect
240. #397	C₂³	semidirect
241. #397	C₂³	semidirect
242. #397	C₂³	semidirect
243. #397	C₂³	semidirect
244. #397	C₂³	semidirect
245. #396	C₂³	semidirect
246. #396	C₂³	semidirect
247. #396	C₂³	semidirect
248. #396	C₂³	semidirect
249. #396	C₂³	semidirect
250. #395	C₂³	semidirect
261. #394	C₂³	semidirect
262. #394	C₂³	semidirect
263. #394	C₂³	semidirect
264. #394	C₂³	semidirect
265. #394	C₂³	semidirect
266. #394	C₂³	semidirect
267. #393	C₂³	semidirect
268. #393	C₂³	semidirect
269. #393	C₂³	semidirect
270. #393	C₂³	semidirect
271. #393	C₂³	semidirect
286. #392	C₂³	semidirect
287. #392	C₂³	semidirect
288. #391	C₂³	semidirect
294. #390	C₂³	semidirect
295. #390	C₂³	semidirect
296. #390	C₂³	semidirect
297. #390	C₂³	semidirect
298. #388	C₂³	semidirect
299. #388	C₂³	semidirect
300. #388	C₂³	semidirect
301. #388	C₂³	semidirect
302. #388	C₂³	semidirect
303. #388	C₂³	semidirect
304. #388	C₂³	semidirect
305. #388	C₂³	semidirect
306. #388	C₂³	semidirect
307. #388	C₂³	semidirect
308. #387	C₂³	semidirect
309. #387	C₂³	semidirect
310. #387	C₂³	semidirect
327. #386	C₂³	semidirect
328. #386	C₂³	semidirect
329. #386	C₂³	semidirect
330. #386	C₂³	semidirect
331. #386	C₂³	semidirect
332. #386	C₂³	semidirect
333. #386	C₂³	semidirect
334. #386	C₂³	semidirect
335. #386	C₂³	semidirect
336. #386	C₂³	semidirect
337. #386	C₂³	semidirect
338. #386	C₂³	semidirect
339. #386	C₂³	semidirect
340. #386	C₂³	semidirect
341. #386	C₂³	semidirect
342. #386	C₂³	semidirect
343. #386	C₂³	semidirect
344. #386	C₂³	semidirect
345. #386	C₂³	semidirect
346. #386	C₂³	semidirect
347. #386	C₂³	semidirect
348. #386	C₂³	semidirect
349. #386	C₂³	semidirect
350. #386	C₂³	semidirect
351. #385	C₂³	semidirect
352. #385	C₂³	semidirect
353. #385	C₂³	semidirect
354. #385	C₂³	semidirect
355. #385	C₂³	semidirect
356. #385	C₂³	semidirect
357. #385	C₂³	semidirect
358. #383	C₂³	semidirect
359. #381	C₂³	semidirect
360. #381	C₂³	semidirect
361. #381	C₂³	semidirect
362. #381	C₂³	semidirect
363. #381	C₂³	semidirect
364. #381	C₂³	semidirect
365. #380	C₂³	semidirect
366. #380	C₂³	semidirect
367. #380	C₂³	semidirect
368. #380	C₂³	semidirect
369. #380	C₂³	semidirect
376. #379	C₂³	semidirect
377. #379	C₂³	semidirect
378. #379	C₂³	semidirect
379. #379	C₂³	semidirect
380. #379	C₂³	semidirect
381. #379	C₂³	semidirect
382. C₄×C₂²⋊C₄	C₂³	semidirect
383. C₄×C₂²⋊C₄	C₂³	semidirect
384. C₂×#95	C₂³	semidirect
657. C₂⁴	H(5,𝔽₂)	semidirect
748. C₂×D₄	H(5,𝔽₂)	semidirect

Maximal subgroups

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

subgroup	index
#56344	2
#56324	2
#47878	2
#47827	2
#47170	2
#47042	2
#46387	2
#46386	2
#46384	2
#37744	2
#37644	2
#36717	2
#36714	2
#35512	2
#35347	2
#35346	2