Subgroups — #49473

Order 256.

796 conjugacy classes of subgroups.

The subgroup lattice has 709 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2786	C₂	1	1	yes	maximal, characteristic, complemented
2	#2777	C₂	1	1	yes	maximal, characteristic, complemented
3	#2772	C₂	1	1	yes	maximal, characteristic, complemented
4	#2770	C₂	1	1	yes	maximal, characteristic, complemented
5	#2757	C₂	1	1	yes	maximal, characteristic, complemented
6	#2738	C₂	1	1	yes	maximal, characteristic, complemented
7	#2735	C₂	1	1	yes	maximal, characteristic, complemented
8	#2735	C₂	1	1	yes	maximal, characteristic, complemented
9	#2725	C₂	1	1	yes	maximal, characteristic, complemented
10	#2725	C₂	1	1	yes	maximal, characteristic, complemented
11	#2724	C₂	1	1	yes	maximal, characteristic, complemented
12	#2697	C₂	1	1	yes	maximal, characteristic
13	#2649	C₂	1	1	yes	maximal, characteristic, complemented
14	#2643	C₂	1	1	yes	maximal, characteristic, complemented
15	#2601	C₂	1	1	yes	maximal, characteristic, complemented
16	#2594	C₂	1	1	yes	maximal, characteristic, complemented
17	#2594	C₂	1	1	yes	maximal, characteristic, complemented
18	#2573	C₂	1	1	yes	maximal, characteristic, complemented
19	#2534	C₂	1	1	yes	maximal, characteristic
20	#2525	C₂	1	1	yes	maximal, characteristic, complemented
21	#2525	C₂	1	1	yes	maximal, characteristic, complemented
22	#2518	C₂	1	1	yes	maximal, characteristic, complemented
23	#2510	C₂	1	1	yes	maximal, characteristic, complemented
24	#2494	C₂	1	1	yes	maximal, characteristic, complemented
25	#2480	C₂	1	1	yes	maximal, characteristic, complemented
26	#2480	C₂	1	1	yes	maximal, characteristic, complemented
27	#2479	C₂	1	1	yes	maximal, characteristic, complemented
28	#2454	C₂	1	1	yes	maximal, characteristic, complemented
29	#2375	C₂	1	1	yes	maximal, characteristic
30	#2359	C₂	1	1	yes	maximal, characteristic, complemented
31	#2335	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#126	C₂²	1	1	yes	characteristic
33	C₂×#126	C₂²	1	1	yes	characteristic
34	C₂×#125	C₂²	1	1	yes	characteristic, complemented
35	C₂×#123	C₂²	1	1	yes	characteristic
36	C₂×#123	C₂²	1	1	yes	characteristic
37	C₂×#120	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
39	C₂×#117	C₂²	1	1	yes	characteristic, complemented
40	C₂²×C₂²⋊C₄	C₂²	1	1	yes	characteristic
41	#401	C₂²	1	1	yes	characteristic, complemented
42	#401	C₂²	1	1	yes	characteristic, complemented
43	#400	C₂²	1	1	yes	characteristic, complemented
44	#400	C₂²	1	1	yes	characteristic, complemented
45	#400	C₂²	1	1	yes	characteristic, complemented
46	#400	C₂²	1	1	yes	characteristic, complemented
47	#400	C₂²	1	1	yes	characteristic, complemented
48	#400	C₂²	1	1	yes	characteristic, complemented
49	#399	C₂²	1	1	yes	characteristic
50	#399	C₂²	1	1	yes	characteristic
51	#399	C₂²	1	1	yes	characteristic, complemented
52	#398	C₂²	1	1	yes	characteristic, complemented
53	#398	C₂²	1	1	yes	characteristic, complemented
54	#398	C₂²	1	1	yes	characteristic, complemented
55	#398	C₂²	1	1	yes	characteristic, complemented
56	#398	C₂²	1	1	yes	characteristic, complemented
57	#398	C₂²	1	1	yes	characteristic, complemented
58	#397	C₂²	1	1	yes	characteristic
59	#397	C₂²	1	1	yes	characteristic
60	#397	C₂²	1	1	yes	characteristic
61	#397	C₂²	1	1	yes	characteristic
62	#397	C₂²	1	1	yes	characteristic
63	#397	C₂²	1	1	yes	characteristic
64	#397	C₂²	1	1	yes	characteristic
65	#397	C₂²	1	1	yes	characteristic
66	#397	C₂²	1	1	yes	characteristic
67	#397	C₂²	1	1	yes	characteristic
68	#397	C₂²	1	1	yes	characteristic
69	#397	C₂²	1	1	yes	characteristic
70	#397	C₂²	1	1	yes	characteristic
71	#397	C₂²	1	1	yes	characteristic
72	#397	C₂²	1	1	yes	characteristic, complemented
73	#397	C₂²	1	1	yes	characteristic, complemented
74	#396	C₂²	1	1	yes	characteristic
75	#396	C₂²	1	1	yes	characteristic
76	#396	C₂²	1	1	yes	characteristic
77	#396	C₂²	1	1	yes	characteristic
78	#396	C₂²	1	1	yes	characteristic
79	#396	C₂²	1	1	yes	characteristic
80	#396	C₂²	1	1	yes	characteristic
81	#396	C₂²	1	1	yes	characteristic
82	#396	C₂²	1	1	yes	characteristic
83	#396	C₂²	1	1	yes	characteristic
84	#396	C₂²	1	1	yes	characteristic, complemented
85	#394	C₂²	1	1	yes	characteristic
86	#394	C₂²	1	1	yes	characteristic
87	#394	C₂²	1	1	yes	characteristic
88	#394	C₂²	1	1	yes	characteristic
89	#390	C₂²	1	1	yes	characteristic
90	#390	C₂²	1	1	yes	characteristic
91	#390	C₂²	1	1	yes	characteristic
92	#390	C₂²	1	1	yes	characteristic
93	#389	C₂²	1	1	yes	characteristic, complemented
94	#389	C₂²	1	1	yes	characteristic, complemented
95	#389	C₂²	1	1	yes	characteristic, complemented
96	#389	C₂²	1	1	yes	characteristic, complemented
97	#389	C₂²	1	1	yes	characteristic, complemented
98	#389	C₂²	1	1	yes	characteristic, complemented
99	#389	C₂²	1	1	yes	characteristic, complemented
100	#389	C₂²	1	1	yes	characteristic, complemented
101	#389	C₂²	1	1	yes	characteristic, complemented
102	#389	C₂²	1	1	yes	characteristic, complemented
103	#389	C₂²	1	1	yes	characteristic, complemented
104	#388	C₂²	1	1	yes	characteristic
105	#388	C₂²	1	1	yes	characteristic
106	#388	C₂²	1	1	yes	characteristic
107	#388	C₂²	1	1	yes	characteristic
108	#388	C₂²	1	1	yes	characteristic
109	#388	C₂²	1	1	yes	characteristic
110	#388	C₂²	1	1	yes	characteristic
111	#388	C₂²	1	1	yes	characteristic
112	#388	C₂²	1	1	yes	characteristic
113	#388	C₂²	1	1	yes	characteristic
114	#388	C₂²	1	1	yes	characteristic
115	#388	C₂²	1	1	yes	characteristic
116	#388	C₂²	1	1	yes	characteristic
117	#388	C₂²	1	1	yes	characteristic
118	#388	C₂²	1	1	yes	characteristic
119	#388	C₂²	1	1	yes	characteristic
120	#388	C₂²	1	1	yes	characteristic
121	#388	C₂²	1	1	yes	characteristic
122	#388	C₂²	1	1	yes	characteristic
123	#388	C₂²	1	1	yes	characteristic
124	#388	C₂²	1	1	yes	characteristic
125	#388	C₂²	1	1	yes	characteristic
126	#388	C₂²	1	1	yes	characteristic
127	#388	C₂²	1	1	yes	characteristic
128	#388	C₂²	1	1	yes	characteristic
129	#388	C₂²	1	1	yes	characteristic
130	#388	C₂²	1	1	yes	characteristic
131	#388	C₂²	1	1	yes	characteristic
132	#388	C₂²	1	1	yes	characteristic, complemented
133	#388	C₂²	1	1	yes	characteristic, complemented
134	#387	C₂²	1	1	yes	characteristic, complemented
135	#387	C₂²	1	1	yes	characteristic, complemented
136	#387	C₂²	1	1	yes	characteristic, complemented
137	#387	C₂²	1	1	yes	characteristic, complemented
138	#387	C₂²	1	1	yes	characteristic, complemented
139	#387	C₂²	1	1	yes	characteristic, complemented
140	#387	C₂²	1	1	yes	characteristic, complemented
141	#387	C₂²	1	1	yes	characteristic, complemented
142	#387	C₂²	1	1	yes	characteristic, complemented
143	#387	C₂²	1	1	yes	characteristic, complemented
144	#387	C₂²	1	1	yes	characteristic, complemented
145	#387	C₂²	1	1	yes	characteristic, complemented
146	#387	C₂²	1	1	yes	characteristic, complemented
147	#386	C₂²	1	1	yes	characteristic
148	#386	C₂²	1	1	yes	characteristic
149	#386	C₂²	1	1	yes	characteristic
150	#386	C₂²	1	1	yes	characteristic
151	#386	C₂²	1	1	yes	characteristic
152	#386	C₂²	1	1	yes	characteristic
153	#386	C₂²	1	1	yes	characteristic
154	#385	C₂²	1	1	yes	characteristic
155	#385	C₂²	1	1	yes	characteristic
156	#385	C₂²	1	1	yes	characteristic
157	#385	C₂²	1	1	yes	characteristic
158	#385	C₂²	1	1	yes	characteristic, complemented
159	#385	C₂²	1	1	yes	characteristic, complemented
160	#385	C₂²	1	1	yes	characteristic, complemented
161	#385	C₂²	1	1	yes	characteristic, complemented
162	#385	C₂²	1	1	yes	characteristic, complemented
163	#383	C₂²	1	1	yes	characteristic, complemented
164	#383	C₂²	1	1	yes	characteristic, complemented
165	#383	C₂²	1	1	yes	characteristic, complemented
166	#382	C₂²	1	1	yes	characteristic, complemented
167	#381	C₂²	1	1	yes	characteristic
168	#380	C₂²	1	1	yes	characteristic
169	#380	C₂²	1	1	yes	characteristic
170	#380	C₂²	1	1	yes	characteristic
171	#380	C₂²	1	1	yes	characteristic, complemented
172	#379	C₂²	1	1	yes	characteristic
173	#379	C₂²	1	1	yes	characteristic
174	#379	C₂²	1	1	yes	characteristic
175	#379	C₂²	1	1	yes	characteristic
176	#379	C₂²	1	1	yes	characteristic
177	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
178	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
179	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
180	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
181	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
182	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
183	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
184	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
185	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
186	C₂×#95	C₂²	1	1	yes	characteristic, complemented
187	C₂⁵	C₂³	1	1	yes	characteristic
188	C₂²×D₄	C₂³	1	1	yes	characteristic
189	C₂²×D₄	C₂³	1	1	yes	characteristic
190	C₂²×D₄	C₂³	1	1	yes	characteristic
191	C₂³×C₄	C₂³	1	1	yes	characteristic
192	C₂³×C₄	C₂³	1	1	yes	characteristic
193	C₂³×C₄	C₂³	1	1	yes	characteristic
194	C₂³×C₄	C₂³	1	1	yes	characteristic
195	C₂³×C₄	C₂³	1	1	yes	characteristic
196	#126	—	4	2	no	—
197	#126	—	4	2	no	—
198	#125	—	4	2	no	—
199	#123	—	2	4	no	—
200	#123	—	2	4	no	—
201	#120	—	2	4	no	—
202	C₄×D₄	—	4	2	no	—
203	#117	—	4	2	no	—
204	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
205	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
206	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
207	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
208	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
209	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
210	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
211	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
212	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
213	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
214	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
215	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
216	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
217	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
218	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
219	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
220	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
221	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
222	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
223	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
224	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
225	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
226	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
227	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
228	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
229	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
230	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
231	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
232	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
233	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
234	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
235	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
236	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
237	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
238	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
239	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
240	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
241	C₂×C₂²⋊C₄	—	4	2	no	—
242	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
243	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
244	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
245	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
246	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
247	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
248	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
249	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
250	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
251	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
252	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
253	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
254	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
255	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
256	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
257	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
258	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
259	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
260	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
261	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
262	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
263	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
264	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
265	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
266	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
267	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
268	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
269	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
270	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
271	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
272	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
273	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
274	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
275	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
276	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
277	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
278	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
279	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
280	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
281	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
282	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
283	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
284	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
285	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
286	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
287	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
288	C₂×C₄²	C₂³	1	1	yes	characteristic
289	C₂×C₄²	C₂³	1	1	yes	characteristic
290	C₂×C₄²	C₂³	1	1	yes	characteristic
291	C₂×C₄²	C₂³	1	1	yes	characteristic
292	C₂×C₄²	C₂³	1	1	yes	characteristic
293	C₂×C₄²	C₂³	1	1	yes	characteristic
294	C₂×C₄²	C₂³	1	1	yes	characteristic
295	C₂×C₄²	C₂³	1	1	yes	characteristic
296	C₂×C₄²	C₂³	1	1	yes	characteristic
297	C₂×C₄²	C₂³	1	1	yes	characteristic
298	C₂×C₄²	C₂³	1	1	yes	characteristic
299	C₂×C₄²	C₂³	1	1	yes	characteristic
300	C₂×C₄²	C₂³	1	1	yes	characteristic
301	#95	C₂³	1	1	yes	characteristic
302	#95	C₂³	1	1	yes	characteristic
303	#95	C₂³	1	1	yes	characteristic
304	#95	C₂³	1	1	yes	characteristic
305	#95	C₂³	1	1	yes	characteristic
306	#95	C₂³	1	1	yes	characteristic
307	#95	C₂³	1	1	yes	characteristic
308	#95	C₂³	1	1	yes	characteristic
309	#95	C₂³	1	1	yes	characteristic
310	#95	C₂³	1	1	yes	characteristic
311	#95	C₂³	1	1	yes	characteristic
312	#95	C₂³	1	1	yes	characteristic
313	#95	C₂³	1	1	yes	characteristic
314	#95	C₂³	1	1	yes	characteristic
315	#95	C₂³	1	1	yes	characteristic
316	#95	C₂³	1	1	yes	characteristic
317	#95	C₂³	1	1	yes	characteristic
318	#95	C₂³	1	1	yes	characteristic
319	#95	C₂³	1	1	yes	characteristic
320	#95	C₂³	1	1	yes	characteristic
321	#95	C₂³	1	1	yes	characteristic
322	#95	C₂³	1	1	yes	characteristic
323	#95	C₂³	1	1	yes	characteristic
324	#95	C₂³	1	1	yes	characteristic
325	#95	C₂³	1	1	yes	characteristic
326	#95	C₂³	1	1	yes	characteristic
327	#95	C₂³	1	1	yes	characteristic
328	#95	C₂³	1	1	yes	characteristic
329	#95	C₂³	1	1	yes	characteristic
330	#95	C₂³	1	1	yes	characteristic
331	#95	C₂³	1	1	yes	characteristic
332	#95	C₂³	1	1	yes	characteristic
333	#95	C₂³	1	1	yes	characteristic
334	#95	C₂³	1	1	yes	characteristic
335	#95	C₂³	1	1	yes	characteristic
336	#95	C₂³	1	1	yes	characteristic
337	#95	C₂³	1	1	yes	characteristic
338	#95	C₂³	1	1	yes	characteristic
339	#95	C₂³	1	1	yes	characteristic
340	#95	C₂³	1	1	yes	characteristic
341	#95	C₂³	1	1	yes	characteristic
342	#95	C₂³	1	1	yes	characteristic
343	#95	C₂³	1	1	yes	characteristic
344	#95	C₂³	1	1	yes	characteristic
345	#95	C₂³	1	1	yes	characteristic
346	#95	C₂³	1	1	yes	characteristic
347	#95	C₂³	1	1	yes	characteristic
348	#95	C₂³	1	1	yes	characteristic
349	#95	C₂³	1	1	yes	characteristic
350	#95	C₂³	1	1	yes	characteristic
351	C₂⁴	—	2	2	no	—
352	C₂⁴	—	4	1	no	—
353	C₂⁴	—	4	1	no	—
354	C₂⁴	—	4	1	no	—
355	C₂⁴	—	4	1	no	—
356	C₂⁴	—	4	1	no	—
357	C₂⁴	—	4	1	no	—
358	C₂⁴	C₂⁴	1	1	yes	characteristic
359	C₂⁴	C₂⁴	1	1	yes	characteristic
360	C₂⁴	C₂⁴	1	1	yes	characteristic
361	C₂⁴	C₂⁴	1	1	yes	characteristic
362	C₂×D₄	—	2	2	no	—
363	C₂×D₄	—	2	2	no	—
364	C₂×D₄	—	4	1	no	—
365	C₂×D₄	—	4	1	no	—
366	C₂×D₄	—	4	1	no	—
367	C₂×D₄	—	4	1	no	—
368	C₂×D₄	—	4	1	no	—
369	C₂×D₄	—	4	1	no	—
370	C₂×D₄	#41	1	4	yes	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	4	1	no	—
375	C₂²×C₄	—	4	1	no	—
376	C₂²×C₄	—	4	1	no	—
377	C₂²×C₄	—	4	1	no	—
378	C₂²×C₄	—	4	1	no	—
379	C₂²×C₄	—	4	1	no	—
380	C₂²×C₄	—	4	1	no	—
381	C₂²×C₄	—	4	1	no	—
382	C₂²×C₄	—	4	1	no	—
383	C₂²×C₄	—	4	1	no	—
384	C₂²×C₄	—	4	1	no	—
385	C₂²×C₄	—	4	1	no	—
386	C₂²×C₄	C₂⁴	1	1	yes	characteristic
387	C₂²×C₄	C₂⁴	1	1	yes	characteristic
388	C₂²×C₄	C₂⁴	1	1	yes	characteristic
389	C₂²×C₄	C₂⁴	1	1	yes	characteristic
390	C₂²×C₄	C₂⁴	1	1	yes	characteristic
391	C₂²×C₄	C₂⁴	1	1	yes	characteristic
392	C₂²×C₄	C₂⁴	1	1	yes	characteristic
393	C₂²×C₄	C₂⁴	1	1	yes	characteristic
394	C₂²×C₄	C₂⁴	1	1	yes	characteristic
395	C₂²×C₄	C₂⁴	1	1	yes	characteristic
396	C₂²×C₄	C₂⁴	1	1	yes	characteristic
397	C₂²×C₄	C₂⁴	1	1	yes	characteristic
398	C₂²×C₄	C₂⁴	1	1	yes	characteristic
399	C₂²×C₄	C₂⁴	1	1	yes	characteristic
400	C₂²×C₄	C₂⁴	1	1	yes	characteristic
401	C₂²×C₄	C₂⁴	1	1	yes	characteristic
402	C₂²×C₄	C₂⁴	1	1	yes	characteristic
403	C₂²×C₄	C₂⁴	1	1	yes	characteristic
404	C₂²×C₄	C₂⁴	1	1	yes	characteristic
405	C₂²×C₄	C₂⁴	1	1	yes	characteristic
406	C₂²×C₄	C₂⁴	1	1	yes	characteristic
407	C₂²×C₄	C₂⁴	1	1	yes	characteristic
408	C₂²×C₄	C₂⁴	1	1	yes	characteristic
409	C₂²×C₄	C₂⁴	1	1	yes	characteristic
410	C₂²×C₄	C₂⁴	1	1	yes	characteristic
411	C₂²×C₄	C₂⁴	1	1	yes	characteristic
412	C₂²×C₄	C₂⁴	1	1	yes	characteristic
413	C₄⋊C₄	—	2	2	no	—
414	C₄⋊C₄	—	2	2	no	—
415	C₄⋊C₄	—	2	2	no	—
416	C₄⋊C₄	—	2	2	no	—
417	C₄⋊C₄	—	2	2	no	—
418	C₄⋊C₄	—	2	2	no	—
419	C₄⋊C₄	—	2	2	no	—
420	C₄⋊C₄	—	2	2	no	—
421	C₄⋊C₄	—	4	1	no	—
422	C₄⋊C₄	—	4	1	no	—
423	C₄⋊C₄	—	4	1	no	—
424	C₄⋊C₄	—	4	1	no	—
425	C₄⋊C₄	—	4	1	no	—
426	C₄⋊C₄	—	4	1	no	—
427	C₄⋊C₄	—	4	1	no	—
428	C₄⋊C₄	—	4	1	no	—
429	C₄⋊C₄	—	4	1	no	—
430	C₄⋊C₄	—	4	1	no	—
431	C₄⋊C₄	—	4	1	no	—
432	C₄⋊C₄	—	4	1	no	—
433	C₄⋊C₄	—	4	1	no	—
434	C₄⋊C₄	—	4	1	no	—
435	C₄⋊C₄	—	4	1	no	—
436	C₄⋊C₄	—	4	1	no	—
437	C₄⋊C₄	—	4	1	no	—
438	C₄⋊C₄	—	4	1	no	—
439	C₄⋊C₄	—	4	1	no	—
440	C₄⋊C₄	—	4	1	no	—
441	C₄⋊C₄	—	4	1	no	—
442	C₄⋊C₄	—	4	1	no	—
443	C₄⋊C₄	—	4	1	no	—
444	C₄⋊C₄	—	4	1	no	—
445	C₄⋊C₄	—	4	1	no	—
446	C₄⋊C₄	—	4	1	no	—
447	C₄⋊C₄	—	4	1	no	—
448	C₄⋊C₄	—	4	1	no	—
449	C₄⋊C₄	—	4	1	no	—
450	C₂²⋊C₄	—	2	2	no	—
451	C₂²⋊C₄	—	2	2	no	—
452	C₂²⋊C₄	—	2	2	no	—
453	C₂²⋊C₄	—	2	2	no	—
454	C₂²⋊C₄	—	2	2	no	—
455	C₂²⋊C₄	—	2	2	no	—
456	C₂²⋊C₄	—	2	2	no	—
457	C₂²⋊C₄	—	2	2	no	—
458	C₂²⋊C₄	—	2	2	no	—
459	C₂²⋊C₄	—	2	2	no	—
460	C₂²⋊C₄	—	2	2	no	—
461	C₂²⋊C₄	—	2	2	no	—
462	C₂²⋊C₄	—	4	1	no	—
463	C₂²⋊C₄	—	4	1	no	—
464	C₂²⋊C₄	—	4	1	no	—
465	C₂²⋊C₄	—	4	1	no	—
466	C₂²⋊C₄	—	4	1	no	—
467	C₂²⋊C₄	—	4	1	no	—
468	C₂²⋊C₄	—	4	1	no	—
469	C₂²⋊C₄	—	4	1	no	—
470	C₂²⋊C₄	—	4	1	no	—
471	C₂²⋊C₄	—	4	1	no	—
472	C₂²⋊C₄	—	4	1	no	—
473	C₂²⋊C₄	—	4	1	no	—
474	C₂²⋊C₄	—	4	1	no	—
475	C₂²⋊C₄	—	4	1	no	—
476	C₂²⋊C₄	—	4	1	no	—
477	C₂²⋊C₄	—	4	1	no	—
478	C₂²⋊C₄	—	4	1	no	—
479	C₂²⋊C₄	—	4	1	no	—
480	C₂²⋊C₄	—	4	1	no	—
481	C₂²⋊C₄	—	4	1	no	—
482	C₂²⋊C₄	—	4	1	no	—
483	C₂²⋊C₄	—	4	1	no	—
484	C₂²⋊C₄	—	4	1	no	—
485	C₂²⋊C₄	—	4	1	no	—
486	C₂²⋊C₄	—	4	1	no	—
487	C₂²⋊C₄	—	4	1	no	—
488	C₂²⋊C₄	—	4	1	no	—
489	C₂²⋊C₄	—	4	1	no	—
490	C₂²⋊C₄	—	4	1	no	—
491	C₂²⋊C₄	—	4	1	no	—
492	C₂²⋊C₄	—	4	1	no	—
493	C₂²⋊C₄	—	4	1	no	—
494	C₂²⋊C₄	—	4	1	no	—
495	C₂²⋊C₄	—	4	1	no	—
496	C₄²	—	2	2	no	—
497	C₄²	—	4	1	no	—
498	C₄²	—	4	1	no	—
499	C₄²	—	4	1	no	—
500	C₄²	—	4	1	no	—
501	C₄²	—	4	1	no	—
502	C₄²	—	4	1	no	—
503	C₄²	—	4	1	no	—
504	C₄²	—	4	1	no	—
505	C₄²	—	4	1	no	—
506	C₄²	—	4	1	no	—
507	C₄²	—	4	1	no	—
508	C₄²	—	4	1	no	—
509	C₂³	—	2	1	no	—
510	C₂³	—	2	1	no	—
511	C₂³	—	2	1	no	—
512	C₂³	—	2	1	no	—
513	C₂³	—	2	1	no	—
514	C₂³	—	2	1	no	—
515	C₂³	—	2	1	no	—
516	C₂³	—	2	1	no	—
517	C₂³	—	2	1	no	—
518	C₂³	—	2	1	no	—
519	C₂³	—	2	1	no	—
520	C₂³	—	2	1	no	—
521	C₂³	—	2	1	no	—
522	C₂³	—	2	1	no	—
523	C₂³	—	2	1	no	—
524	C₂³	—	2	1	no	—
525	C₂³	—	2	1	no	—
526	C₂³	—	2	1	no	—
527	C₂³	—	2	1	no	—
528	C₂³	—	2	1	no	—
529	C₂³	—	2	1	no	—
530	C₂³	—	2	1	no	—
531	C₂³	—	2	1	no	—
532	C₂³	—	2	1	no	—
533	C₂³	—	2	1	no	—
534	C₂³	—	2	1	no	—
535	C₂³	—	4	4	no	—
536	C₂³	—	8	2	no	—
537	C₂³	—	8	2	no	—
538	C₂³	—	8	2	no	—
539	C₂³	—	8	2	no	—
540	C₂³	—	8	2	no	—
541	C₂³	—	8	2	no	—
542	C₂³	C₂×#41	1	2	yes	—
543	C₂³	C₂×#41	1	2	yes	—
544	C₂³	C₂⁵	1	1	yes	characteristic
545	D₄	—	4	4	no	—
546	D₄	—	8	2	no	—
547	D₄	—	8	2	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	2	1	no	—
552	C₂×C₄	—	2	1	no	—
553	C₂×C₄	—	2	1	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	2	1	no	—
564	C₂×C₄	—	2	1	no	—
565	C₂×C₄	—	2	1	no	—
566	C₂×C₄	—	2	1	no	—
567	C₂×C₄	—	2	1	no	—
568	C₂×C₄	—	2	1	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	—	2	1	no	—
572	C₂×C₄	—	2	1	no	—
573	C₂×C₄	—	2	1	no	—
574	C₂×C₄	—	2	1	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	2	1	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	2	1	no	—
583	C₂×C₄	—	2	1	no	—
584	C₂×C₄	—	2	1	no	—
585	C₂×C₄	—	2	1	no	—
586	C₂×C₄	—	2	1	no	—
587	C₂×C₄	—	2	1	no	—
588	C₂×C₄	—	2	1	no	—
589	C₂×C₄	—	2	1	no	—
590	C₂×C₄	—	2	1	no	—
591	C₂×C₄	—	2	1	no	—
592	C₂×C₄	—	2	1	no	—
593	C₂×C₄	—	2	1	no	—
594	C₂×C₄	—	2	1	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	2	1	no	—
597	C₂×C₄	—	2	1	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	2	1	no	—
600	C₂×C₄	—	2	1	no	—
601	C₂×C₄	—	2	1	no	—
602	C₂×C₄	—	2	1	no	—
603	C₂×C₄	—	2	1	no	—
604	C₂×C₄	—	2	1	no	—
605	C₂×C₄	—	2	1	no	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	2	1	no	—
608	C₂×C₄	—	2	1	no	—
609	C₂×C₄	—	2	1	no	—
610	C₂×C₄	—	2	1	no	—
611	C₂×C₄	—	2	1	no	—
612	C₂×C₄	—	2	1	no	—
613	C₂×C₄	—	2	1	no	—
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	2	1	no	—
616	C₂×C₄	—	2	1	no	—
617	C₂×C₄	—	2	1	no	—
618	C₂×C₄	—	2	1	no	—
619	C₂×C₄	—	2	1	no	—
620	C₂×C₄	—	2	1	no	—
621	C₂×C₄	—	2	1	no	—
622	C₂×C₄	—	2	1	no	—
623	C₂×C₄	—	2	1	no	—
624	C₂×C₄	—	2	1	no	—
625	C₂×C₄	—	2	1	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	4	4	no	—
628	C₂×C₄	—	8	2	no	—
629	C₂×C₄	—	8	2	no	—
630	C₂×C₄	—	8	2	no	—
631	C₂×C₄	—	8	2	no	—
632	C₂×C₄	C₂×#41	1	2	yes	—
633	C₂×C₄	H(5,𝔽₂)	1	2	yes	—
634	C₂²	—	2	2	no	—
635	C₂²	—	2	2	no	—
636	C₂²	—	2	2	no	—
637	C₂²	—	2	2	no	—
638	C₂²	—	2	2	no	—
639	C₂²	—	2	2	no	—
640	C₂²	—	4	1	no	—
641	C₂²	—	4	1	no	—
642	C₂²	—	4	1	no	—
643	C₂²	—	4	1	no	—
644	C₂²	—	4	1	no	—
645	C₂²	—	4	1	no	—
646	C₂²	—	4	1	no	—
647	C₂²	—	4	1	no	—
648	C₂²	—	4	1	no	—
649	C₂²	—	4	1	no	—
650	C₂²	—	4	1	no	—
651	C₂²	—	4	1	no	—
652	C₂²	—	4	1	no	—
653	C₂²	—	4	1	no	—
654	C₂²	—	4	1	no	—
655	C₂²	—	4	1	no	—
656	C₂²	—	4	1	no	—
657	C₂²	—	4	1	no	—
658	C₂²	—	4	1	no	—
659	C₂²	—	4	1	no	—
660	C₂²	—	4	1	no	—
661	C₂²	—	4	1	no	—
662	C₂²	—	8	8	no	—
663	C₂²	C₂²×#41	1	1	yes	characteristic
664	C₂²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
665	C₂²	#585	1	1	yes	characteristic
666	C₂²	#585	1	1	yes	characteristic
667	C₂²	#585	1	1	yes	characteristic
668	C₂²	#585	1	1	yes	characteristic
669	C₂²	#585	1	1	yes	characteristic
670	C₄	—	2	2	no	—
671	C₄	—	2	2	no	—
672	C₄	—	4	1	no	—
673	C₄	—	4	1	no	—
674	C₄	—	4	1	no	—
675	C₄	—	4	1	no	—
676	C₄	—	4	1	no	—
677	C₄	—	4	1	no	—
678	C₄	—	4	1	no	—
679	C₄	—	4	1	no	—
680	C₄	—	4	1	no	—
681	C₄	—	4	1	no	—
682	C₄	—	4	1	no	—
683	C₄	—	4	1	no	—
684	C₄	—	4	1	no	—
685	C₄	—	4	1	no	—
686	C₄	—	4	1	no	—
687	C₄	—	4	1	no	—
688	C₄	—	4	1	no	—
689	C₄	—	4	1	no	—
690	C₄	—	4	1	no	—
691	C₄	—	4	1	no	—
692	C₄	—	4	1	no	—
693	C₄	—	4	1	no	—
694	C₄	—	4	1	no	—
695	C₄	—	4	1	no	—
696	C₄	—	4	1	no	—
697	C₂	—	4	2	no	—
698	C₂	—	4	2	no	—
699	C₂	—	8	1	no	—
700	C₂	—	8	1	no	—
701	C₂	#3505	1	1	yes	characteristic
702	C₂	#3521	1	1	yes	characteristic
703	C₂	#3521	1	1	yes	characteristic
704	C₂	#3539	1	1	yes	characteristic
705	C₂	#3560	1	1	yes	characteristic
706	C₂	#3566	1	1	yes	characteristic
707	C₂	#3568	1	1	yes	characteristic

	subgroup	G/H
center, commutator, Frattini, socle, cosocle	C₂³	C₂⁵
prime radical	C₂×#120	C₂²
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. #2786	C₂	semidirect
2. #2777	C₂	semidirect
3. #2772	C₂	semidirect
4. #2770	C₂	semidirect
5. #2757	C₂	semidirect
6. #2738	C₂	semidirect
7. #2735	C₂	semidirect
8. #2735	C₂	semidirect
9. #2725	C₂	semidirect
10. #2725	C₂	semidirect
11. #2724	C₂	semidirect
13. #2649	C₂	semidirect
14. #2643	C₂	semidirect
15. #2601	C₂	semidirect
16. #2594	C₂	semidirect
17. #2594	C₂	semidirect
18. #2573	C₂	semidirect
20. #2525	C₂	semidirect
21. #2525	C₂	semidirect
22. #2518	C₂	semidirect
23. #2510	C₂	semidirect
24. #2494	C₂	semidirect
25. #2480	C₂	semidirect
26. #2480	C₂	semidirect
27. #2479	C₂	semidirect
28. #2454	C₂	semidirect
30. #2359	C₂	semidirect
31. #2335	C₂	semidirect
34. C₂×#125	C₂²	semidirect
39. C₂×#117	C₂²	semidirect
41. #401	C₂²	semidirect
42. #401	C₂²	semidirect
43. #400	C₂²	semidirect
44. #400	C₂²	semidirect
45. #400	C₂²	semidirect
46. #400	C₂²	semidirect
47. #400	C₂²	semidirect
48. #400	C₂²	semidirect
51. #399	C₂²	semidirect
52. #398	C₂²	semidirect
53. #398	C₂²	semidirect
54. #398	C₂²	semidirect
55. #398	C₂²	semidirect
56. #398	C₂²	semidirect
57. #398	C₂²	semidirect
72. #397	C₂²	semidirect
73. #397	C₂²	semidirect
84. #396	C₂²	semidirect
93. #389	C₂²	semidirect
94. #389	C₂²	semidirect
95. #389	C₂²	semidirect
96. #389	C₂²	semidirect
97. #389	C₂²	semidirect
98. #389	C₂²	semidirect
99. #389	C₂²	semidirect
100. #389	C₂²	semidirect
101. #389	C₂²	semidirect
102. #389	C₂²	semidirect
103. #389	C₂²	semidirect
132. #388	C₂²	semidirect
133. #388	C₂²	semidirect
134. #387	C₂²	semidirect
135. #387	C₂²	semidirect
136. #387	C₂²	semidirect
137. #387	C₂²	semidirect
138. #387	C₂²	semidirect
139. #387	C₂²	semidirect
140. #387	C₂²	semidirect
141. #387	C₂²	semidirect
142. #387	C₂²	semidirect
143. #387	C₂²	semidirect
144. #387	C₂²	semidirect
145. #387	C₂²	semidirect
146. #387	C₂²	semidirect
158. #385	C₂²	semidirect
159. #385	C₂²	semidirect
160. #385	C₂²	semidirect
161. #385	C₂²	semidirect
162. #385	C₂²	semidirect
163. #383	C₂²	semidirect
164. #383	C₂²	semidirect
165. #383	C₂²	semidirect
166. #382	C₂²	semidirect
171. #380	C₂²	semidirect
177. C₄×C₄⋊C₄	C₂²	semidirect
178. C₄×C₄⋊C₄	C₂²	semidirect
179. C₄×C₄⋊C₄	C₂²	semidirect
180. C₄×C₄⋊C₄	C₂²	semidirect
181. C₄×C₄⋊C₄	C₂²	semidirect
184. C₄×C₂²⋊C₄	C₂²	semidirect
185. C₄×C₂²⋊C₄	C₂²	semidirect
186. C₂×#95	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#2786	2
#2777	2
#2772	2
#2770	2
#2757	2
#2738	2
#2735	2
#2725	2
#2724	2
#2697	2
#2649	2
#2643	2
#2601	2
#2594	2
#2573	2
#2534	2
#2525	2
#2518	2
#2510	2
#2494	2
#2480	2
#2479	2
#2454	2
#2375	2
#2359	2
#2335	2