Subgroups — #39329

Order 256.

735 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2863	C₂	1	1	yes	maximal, characteristic, complemented
2	#2801	C₂	1	1	yes	maximal, characteristic
3	#2776	C₂	1	1	yes	maximal, characteristic, complemented
4	#2759	C₂	1	1	yes	maximal, characteristic, complemented
5	#2755	C₂	1	1	yes	maximal, characteristic, complemented
6	#2754	C₂	1	1	yes	maximal, characteristic, complemented
7	#2727	C₂	1	1	yes	maximal, characteristic
8	#2716	C₂	1	1	yes	maximal, characteristic, complemented
9	#2716	C₂	1	1	yes	maximal, characteristic, complemented
10	#2654	C₂	1	1	yes	maximal, characteristic, complemented
11	#2653	C₂	1	1	yes	maximal, characteristic
12	#2607	C₂	1	1	yes	maximal, characteristic, complemented
13	#2606	C₂	1	1	yes	maximal, characteristic, complemented
14	#2597	C₂	1	1	yes	maximal, characteristic
15	#2594	C₂	1	1	yes	maximal, characteristic, complemented
16	#2573	C₂	1	1	yes	maximal, characteristic, complemented
17	#2573	C₂	1	1	yes	maximal, characteristic, complemented
18	#2572	C₂	1	1	yes	maximal, characteristic
19	#2560	C₂	1	1	yes	maximal, characteristic
20	#2556	C₂	1	1	yes	maximal, characteristic, complemented
21	#2532	C₂	1	1	yes	maximal, characteristic, complemented
22	#2519	C₂	1	1	yes	maximal, characteristic, complemented
23	#2518	C₂	1	1	yes	maximal, characteristic
24	#2514	C₂	1	1	yes	maximal, characteristic, complemented
25	#2514	C₂	1	1	yes	maximal, characteristic, complemented
26	#2373	C₂	1	1	yes	maximal, characteristic, complemented
27	#2369	C₂	1	1	yes	maximal, characteristic, complemented
28	#2336	C₂	1	1	yes	maximal, characteristic, complemented
29	#2332	C₂	1	1	yes	maximal, characteristic, complemented
30	C₄×#126	C₂	1	1	yes	maximal, characteristic, complemented
31	C₄×#126	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×C₄⋊Q₈	C₂²	1	1	yes	characteristic
33	C₂×#126	C₂²	1	1	yes	characteristic
34	C₂×#126	C₂²	1	1	yes	characteristic
35	C₂×#126	C₂²	1	1	yes	characteristic
36	C₂×#125	C₂²	1	1	yes	characteristic
37	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
38	#401	C₂²	1	1	yes	characteristic
39	#401	C₂²	1	1	yes	characteristic
40	#401	C₂²	1	1	yes	characteristic
41	#400	C₂²	1	1	yes	characteristic
42	#400	C₂²	1	1	yes	characteristic
43	#400	C₂²	1	1	yes	characteristic
44	#400	C₂²	1	1	yes	characteristic
45	#400	C₂²	1	1	yes	characteristic
46	#400	C₂²	1	1	yes	characteristic
47	#400	C₂²	1	1	yes	characteristic
48	#399	C₂²	1	1	yes	characteristic
49	#399	C₂²	1	1	yes	characteristic
50	#399	C₂²	1	1	yes	characteristic
51	#398	C₂²	1	1	yes	characteristic
52	#398	C₂²	1	1	yes	characteristic
53	#398	C₂²	1	1	yes	characteristic
54	#398	C₂²	1	1	yes	characteristic
55	#398	C₂²	1	1	yes	characteristic
56	#398	C₂²	1	1	yes	characteristic
57	#398	C₂²	1	1	yes	characteristic
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	#396	C₂²	1	1	yes	characteristic
65	#396	C₂²	1	1	yes	characteristic
66	#396	C₂²	1	1	yes	characteristic
67	#396	C₂²	1	1	yes	characteristic
68	#395	C₂²	1	1	yes	characteristic
69	#394	C₂²	1	1	yes	characteristic
70	#394	C₂²	1	1	yes	characteristic
71	#394	C₂²	1	1	yes	characteristic
72	#394	C₂²	1	1	yes	characteristic
73	#393	C₂²	1	1	yes	characteristic
74	#393	C₂²	1	1	yes	characteristic
75	#393	C₂²	1	1	yes	characteristic
76	#393	C₂²	1	1	yes	characteristic
77	#393	C₂²	1	1	yes	characteristic
78	#391	C₂²	1	1	yes	characteristic
79	#391	C₂²	1	1	yes	characteristic
80	#391	C₂²	1	1	yes	characteristic
81	#391	C₂²	1	1	yes	characteristic
82	#391	C₂²	1	1	yes	characteristic
83	#391	C₂²	1	1	yes	characteristic
84	#391	C₂²	1	1	yes	characteristic
85	#391	C₂²	1	1	yes	characteristic
86	#391	C₂²	1	1	yes	characteristic
87	#391	C₂²	1	1	yes	characteristic
88	#391	C₂²	1	1	yes	characteristic
89	#391	C₂²	1	1	yes	characteristic
90	#390	C₂²	1	1	yes	characteristic
91	#389	C₂²	1	1	yes	characteristic
92	#389	C₂²	1	1	yes	characteristic
93	#389	C₂²	1	1	yes	characteristic
94	#389	C₂²	1	1	yes	characteristic
95	#389	C₂²	1	1	yes	characteristic
96	#389	C₂²	1	1	yes	characteristic
97	#389	C₂²	1	1	yes	characteristic
98	#389	C₂²	1	1	yes	characteristic
99	#389	C₂²	1	1	yes	characteristic
100	#389	C₂²	1	1	yes	characteristic
101	#389	C₂²	1	1	yes	characteristic
102	#389	C₂²	1	1	yes	characteristic
103	#388	C₂²	1	1	yes	characteristic
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	#387	C₂²	1	1	yes	characteristic
127	#387	C₂²	1	1	yes	characteristic
128	#387	C₂²	1	1	yes	characteristic
129	#387	C₂²	1	1	yes	characteristic
130	#387	C₂²	1	1	yes	characteristic
131	#387	C₂²	1	1	yes	characteristic
132	#387	C₂²	1	1	yes	characteristic
133	#387	C₂²	1	1	yes	characteristic
134	#387	C₂²	1	1	yes	characteristic
135	#387	C₂²	1	1	yes	characteristic
136	#387	C₂²	1	1	yes	characteristic
137	#387	C₂²	1	1	yes	characteristic
138	#387	C₂²	1	1	yes	characteristic
139	#387	C₂²	1	1	yes	characteristic
140	#387	C₂²	1	1	yes	characteristic
141	#387	C₂²	1	1	yes	characteristic
142	#387	C₂²	1	1	yes	characteristic
143	#387	C₂²	1	1	yes	characteristic
144	#387	C₂²	1	1	yes	characteristic
145	#387	C₂²	1	1	yes	characteristic
146	#387	C₂²	1	1	yes	characteristic
147	#387	C₂²	1	1	yes	characteristic
148	#387	C₂²	1	1	yes	characteristic
149	#387	C₂²	1	1	yes	characteristic
150	#387	C₂²	1	1	yes	characteristic
151	#387	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	#383	C₂²	1	1	yes	characteristic
157	#383	C₂²	1	1	yes	characteristic
158	#383	C₂²	1	1	yes	characteristic
159	#383	C₂²	1	1	yes	characteristic
160	#383	C₂²	1	1	yes	characteristic
161	#383	C₂²	1	1	yes	characteristic
162	#382	C₂²	1	1	yes	characteristic
163	#382	C₂²	1	1	yes	characteristic
164	#381	C₂²	1	1	yes	characteristic
165	#381	C₂²	1	1	yes	characteristic
166	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
167	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
168	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
169	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
170	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
171	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
172	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
173	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
174	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
175	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
176	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
177	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
178	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
179	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
180	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
181	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
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
185	#376	C₂²	1	1	yes	characteristic
186	C₄³	C₂²	1	1	yes	characteristic
187	C₂²×Q₈	C₂³	1	1	yes	characteristic
188	C₂²×Q₈	C₂³	1	1	yes	characteristic
189	C₂²×Q₈	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	C₄⋊Q₈	—	2	4	no	—
194	#126	—	2	4	no	—
195	#126	—	2	4	no	—
196	#126	—	2	4	no	—
197	#125	—	2	4	no	—
198	C₂²⋊Q₈	—	2	4	no	—
199	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
200	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
201	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
202	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
203	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄	C₂³	1	1	yes	characteristic
238	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
239	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
240	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
241	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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×C₄²	C₂³	1	1	yes	characteristic
264	C₂×C₄²	C₂³	1	1	yes	characteristic
265	C₂×C₄²	C₂³	1	1	yes	characteristic
266	C₂×C₄²	C₂³	1	1	yes	characteristic
267	C₂×C₄²	C₂³	1	1	yes	characteristic
268	C₂×C₄²	C₂³	1	1	yes	characteristic
269	C₂×C₄²	C₂³	1	1	yes	characteristic
270	C₂×C₄²	C₂³	1	1	yes	characteristic
271	C₂×C₄²	C₂³	1	1	yes	characteristic
272	C₂×C₄²	C₂³	1	1	yes	characteristic
273	C₂×C₄²	C₂³	1	1	yes	characteristic
274	C₂×C₄²	C₂³	1	1	yes	characteristic
275	C₂×C₄²	C₂³	1	1	yes	characteristic
276	C₂×C₄²	C₂³	1	1	yes	characteristic
277	C₂×C₄²	C₂³	1	1	yes	characteristic
278	C₂×C₄²	C₂³	1	1	yes	characteristic
279	C₂×C₄²	C₂³	1	1	yes	characteristic
280	C₂×C₄²	C₂³	1	1	yes	characteristic
281	C₂×C₄²	C₂³	1	1	yes	characteristic
282	C₂×C₄²	C₂³	1	1	yes	characteristic
283	C₂×C₄²	C₂³	1	1	yes	characteristic
284	#95	C₂³	1	1	yes	characteristic
285	#95	C₂³	1	1	yes	characteristic
286	#95	C₂³	1	1	yes	characteristic
287	#95	C₂³	1	1	yes	characteristic
288	#95	C₂³	1	1	yes	characteristic
289	#95	C₂³	1	1	yes	characteristic
290	#95	C₂³	1	1	yes	characteristic
291	#95	C₂³	1	1	yes	characteristic
292	#95	C₂³	1	1	yes	characteristic
293	#95	C₂³	1	1	yes	characteristic
294	#95	C₂³	1	1	yes	characteristic
295	#95	C₂³	1	1	yes	characteristic
296	#95	C₂³	1	1	yes	characteristic
297	#95	C₂³	1	1	yes	characteristic
298	#95	C₂³	1	1	yes	characteristic
299	#95	C₂³	1	1	yes	characteristic
300	#95	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	C₂⁴	C₂⁴	1	1	yes	characteristic
349	C₂⁴	C₂⁴	1	1	yes	characteristic
350	C₂×Q₈	—	2	2	no	—
351	C₂×Q₈	—	2	2	no	—
352	C₂×Q₈	—	2	2	no	—
353	C₂×Q₈	—	4	1	no	—
354	C₂×Q₈	—	4	1	no	—
355	C₂×Q₈	—	4	1	no	—
356	C₂×Q₈	—	4	1	no	—
357	C₂×Q₈	—	4	1	no	—
358	C₂×Q₈	—	4	1	no	—
359	C₂×D₄	—	4	1	no	—
360	C₂×D₄	—	4	1	no	—
361	C₂×D₄	—	4	1	no	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	4	1	no	—
365	C₂²×C₄	—	4	1	no	—
366	C₂²×C₄	—	4	1	no	—
367	C₂²×C₄	—	4	1	no	—
368	C₂²×C₄	C₂⁴	1	1	yes	characteristic
369	C₂²×C₄	C₂⁴	1	1	yes	characteristic
370	C₂²×C₄	C₂⁴	1	1	yes	characteristic
371	C₂²×C₄	C₂⁴	1	1	yes	characteristic
372	C₂²×C₄	C₂⁴	1	1	yes	characteristic
373	C₂²×C₄	C₂⁴	1	1	yes	characteristic
374	C₂²×C₄	C₂⁴	1	1	yes	characteristic
375	C₂²×C₄	C₂⁴	1	1	yes	characteristic
376	C₂²×C₄	C₂⁴	1	1	yes	characteristic
377	C₂²×C₄	C₂⁴	1	1	yes	characteristic
378	C₂²×C₄	C₂⁴	1	1	yes	characteristic
379	C₂²×C₄	C₂⁴	1	1	yes	characteristic
380	C₂²×C₄	C₂⁴	1	1	yes	characteristic
381	C₂²×C₄	C₂⁴	1	1	yes	characteristic
382	C₂²×C₄	C₂⁴	1	1	yes	characteristic
383	C₂²×C₄	C₂⁴	1	1	yes	characteristic
384	C₂²×C₄	C₂⁴	1	1	yes	characteristic
385	C₂²×C₄	C₂⁴	1	1	yes	characteristic
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	C₄⋊C₄	—	2	2	no	—
398	C₄⋊C₄	—	2	2	no	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	—	2	2	no	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	—	2	2	no	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	—	2	2	no	—
408	C₄⋊C₄	—	2	2	no	—
409	C₄⋊C₄	—	2	2	no	—
410	C₄⋊C₄	—	2	2	no	—
411	C₄⋊C₄	—	2	2	no	—
412	C₄⋊C₄	—	2	2	no	—
413	C₄⋊C₄	—	2	2	no	—
414	C₄⋊C₄	—	4	1	no	—
415	C₄⋊C₄	—	4	1	no	—
416	C₄⋊C₄	—	4	1	no	—
417	C₄⋊C₄	—	4	1	no	—
418	C₄⋊C₄	—	4	1	no	—
419	C₄⋊C₄	—	4	1	no	—
420	C₄⋊C₄	—	4	1	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	#41	1	4	yes	—
434	C₄⋊C₄	#41	1	4	yes	—
435	C₂²⋊C₄	—	2	2	no	—
436	C₂²⋊C₄	—	2	2	no	—
437	C₂²⋊C₄	—	2	2	no	—
438	C₂²⋊C₄	—	2	2	no	—
439	C₂²⋊C₄	—	2	2	no	—
440	C₂²⋊C₄	—	2	2	no	—
441	C₂²⋊C₄	—	2	2	no	—
442	C₂²⋊C₄	—	2	2	no	—
443	C₂²⋊C₄	—	2	2	no	—
444	C₂²⋊C₄	—	2	2	no	—
445	C₂²⋊C₄	—	2	2	no	—
446	C₂²⋊C₄	—	2	2	no	—
447	C₂²⋊C₄	—	4	1	no	—
448	C₂²⋊C₄	—	4	1	no	—
449	C₂²⋊C₄	—	4	1	no	—
450	C₂²⋊C₄	—	4	1	no	—
451	C₂²⋊C₄	—	4	1	no	—
452	C₂²⋊C₄	—	4	1	no	—
453	C₂²⋊C₄	—	4	1	no	—
454	C₂²⋊C₄	—	4	1	no	—
455	C₂²⋊C₄	—	4	1	no	—
456	C₂²⋊C₄	—	4	1	no	—
457	C₂²⋊C₄	—	4	1	no	—
458	C₂²⋊C₄	—	4	1	no	—
459	C₂²⋊C₄	—	4	1	no	—
460	C₂²⋊C₄	—	4	1	no	—
461	C₄²	—	2	2	no	—
462	C₄²	—	2	2	no	—
463	C₄²	—	2	2	no	—
464	C₄²	—	2	2	no	—
465	C₄²	—	2	2	no	—
466	C₄²	—	2	2	no	—
467	C₄²	—	2	2	no	—
468	C₄²	—	4	1	no	—
469	C₄²	—	4	1	no	—
470	C₄²	—	4	1	no	—
471	C₄²	—	4	1	no	—
472	C₄²	—	4	1	no	—
473	C₄²	—	4	1	no	—
474	C₄²	—	4	1	no	—
475	C₄²	—	4	1	no	—
476	C₄²	—	4	1	no	—
477	C₄²	—	4	1	no	—
478	C₄²	—	4	1	no	—
479	C₄²	—	4	1	no	—
480	C₄²	—	4	1	no	—
481	C₄²	—	4	1	no	—
482	C₂³	—	2	1	no	—
483	C₂³	—	2	1	no	—
484	C₂³	—	2	1	no	—
485	C₂³	—	2	1	no	—
486	C₂³	—	2	1	no	—
487	C₂³	—	2	1	no	—
488	C₂³	—	2	1	no	—
489	C₂³	—	2	1	no	—
490	C₂³	—	2	1	no	—
491	C₂³	—	2	1	no	—
492	C₂³	—	2	1	no	—
493	C₂³	—	2	1	no	—
494	C₂³	—	2	1	no	—
495	C₂³	—	2	1	no	—
496	C₂³	C₂⁵	1	1	yes	characteristic
497	Q₈	—	8	2	no	—
498	Q₈	—	8	2	no	—
499	Q₈	—	8	2	no	—
500	D₄	—	8	2	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	1	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	—	8	2	no	—
582	C₂×C₄	—	8	2	no	—
583	C₂×C₄	C₂×#41	1	2	yes	—
584	C₂×C₄	C₂×#41	1	2	yes	—
585	C₂×C₄	C₂×#41	1	2	yes	—
586	C₂×C₄	C₂×#41	1	2	yes	—
587	C₂×C₄	C₂×#41	1	2	yes	—
588	C₂×C₄	C₂×#41	1	2	yes	—
589	C₂×C₄	2₋¹⁺⁴	1	2	yes	—
590	C₂²	—	4	1	no	—
591	C₂²	—	4	1	no	—
592	C₂²	—	4	1	no	—
593	C₂²	—	4	1	no	—
594	C₂²	—	4	1	no	—
595	C₂²	—	4	1	no	—
596	C₂²	—	4	1	no	—
597	C₂²	—	4	1	no	—
598	C₂²	—	4	1	no	—
599	C₂²	—	4	1	no	—
600	C₂²	—	4	1	no	—
601	C₂²	—	4	1	no	—
602	C₂²	—	4	1	no	—
603	C₂²	—	4	1	no	—
604	C₂²	C₂²×#41	1	1	yes	characteristic
605	C₂²	C₂²×#41	1	1	yes	characteristic
606	C₂²	C₂×2₋¹⁺⁴	1	1	yes	characteristic
607	C₂²	#585	1	1	yes	characteristic
608	C₂²	#585	1	1	yes	characteristic
609	C₂²	#585	1	1	yes	characteristic
610	C₂²	#585	1	1	yes	characteristic
611	C₄	—	2	2	no	—
612	C₄	—	2	2	no	—
613	C₄	—	2	2	no	—
614	C₄	—	2	2	no	—
615	C₄	—	2	2	no	—
616	C₄	—	2	2	no	—
617	C₄	—	2	2	no	—
618	C₄	—	4	1	no	—
619	C₄	—	4	1	no	—
620	C₄	—	4	1	no	—
621	C₄	—	4	1	no	—
622	C₄	—	4	1	no	—
623	C₄	—	4	1	no	—
624	C₄	—	4	1	no	—
625	C₄	—	4	1	no	—
626	C₄	—	4	1	no	—
627	C₄	—	4	1	no	—
628	C₄	—	4	1	no	—
629	C₄	—	4	1	no	—
630	C₄	—	4	1	no	—
631	C₄	—	4	1	no	—
632	C₄	—	4	1	no	—
633	C₄	—	4	1	no	—
634	C₄	—	4	1	no	—
635	C₄	—	4	1	no	—
636	C₄	—	4	1	no	—
637	C₄	—	4	1	no	—
638	C₄	—	4	1	no	—
639	C₄	—	4	1	no	—
640	C₂	—	8	1	no	—
641	C₂	—	8	1	no	—
642	C₂	#3461	1	1	yes	characteristic
643	C₂	#3480	1	1	yes	characteristic
644	C₂	#3518	1	1	yes	characteristic
645	C₂	#3521	1	1	yes	characteristic
646	C₂	#3521	1	1	yes	characteristic
647	C₂	#3564	1	1	yes	characteristic
648	C₂	#3566	1	1	yes	characteristic

	subgroup	G/H
center, commutator, Frattini, socle, cosocle	C₂³	C₂⁵
prime radical	C₂²×D₄	C₂³
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. #2863	C₂	semidirect
3. #2776	C₂	semidirect
4. #2759	C₂	semidirect
5. #2755	C₂	semidirect
6. #2754	C₂	semidirect
8. #2716	C₂	semidirect
9. #2716	C₂	semidirect
10. #2654	C₂	semidirect
12. #2607	C₂	semidirect
13. #2606	C₂	semidirect
15. #2594	C₂	semidirect
16. #2573	C₂	semidirect
17. #2573	C₂	semidirect
20. #2556	C₂	semidirect
21. #2532	C₂	semidirect
22. #2519	C₂	semidirect
24. #2514	C₂	semidirect
25. #2514	C₂	semidirect
26. #2373	C₂	semidirect
27. #2369	C₂	semidirect
28. #2336	C₂	semidirect
29. #2332	C₂	semidirect
30. C₄×#126	C₂	semidirect
31. C₄×#126	C₂	semidirect

Maximal subgroups

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

subgroup	index
#2863	2
#2801	2
#2776	2
#2759	2
#2755	2
#2754	2
#2727	2
#2716	2
#2654	2
#2653	2
#2607	2
#2606	2
#2597	2
#2594	2
#2573	2
#2572	2
#2560	2
#2556	2
#2532	2
#2519	2
#2518	2
#2514	2
#2373	2
#2369	2
#2336	2
#2332	2
C₄×#126	2