Subgroups — #55192

Order 256.

810 conjugacy classes of subgroups.

The subgroup lattice has 685 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2844	C₂	1	1	yes	maximal, characteristic, complemented
2	#2838	C₂	1	1	yes	maximal, characteristic, complemented
3	#2821	C₂	1	1	yes	maximal, characteristic, complemented
4	#2805	C₂	1	1	yes	maximal, characteristic, complemented
5	#2792	C₂	1	1	yes	maximal, characteristic, complemented
6	#2774	C₂	1	1	yes	maximal, characteristic, complemented
7	#2771	C₂	1	1	yes	maximal, characteristic, complemented
8	#2765	C₂	1	1	yes	maximal, characteristic, complemented
9	#2762	C₂	1	1	yes	maximal, characteristic, complemented
10	#2742	C₂	1	1	yes	maximal, characteristic, complemented
11	#2734	C₂	1	1	yes	maximal, characteristic, complemented
12	#2734	C₂	1	1	yes	maximal, characteristic, complemented
13	#2718	C₂	1	1	yes	maximal, characteristic
14	#2717	C₂	1	1	yes	maximal, characteristic
15	#2716	C₂	1	1	yes	maximal, characteristic, complemented
16	#2698	C₂	1	1	yes	maximal, characteristic, complemented
17	#2689	C₂	1	1	yes	maximal, characteristic, complemented
18	#2674	C₂	1	1	yes	maximal, characteristic
19	#2674	C₂	1	1	yes	maximal, characteristic
20	#2650	C₂	1	1	yes	maximal, characteristic, complemented
21	#2628	C₂	1	1	yes	maximal, characteristic, complemented
22	#2614	C₂	1	1	yes	maximal, characteristic
23	#2575	C₂	1	1	yes	maximal, characteristic, complemented
24	#2574	C₂	1	1	yes	maximal, characteristic, complemented
25	#2573	C₂	1	1	yes	maximal, characteristic, complemented
26	#2553	C₂	1	1	yes	maximal, characteristic
27	#2551	C₂	1	1	yes	maximal, characteristic, complemented
28	#2470	C₂	1	1	yes	maximal, characteristic
29	#2439	C₂	1	1	yes	maximal, characteristic, complemented
30	#2434	C₂	1	1	yes	maximal, characteristic, complemented
31	#2434	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂³×Q₈	C₂²	1	1	yes	characteristic
33	C₂×C₄⋊Q₈	C₂²	1	1	yes	characteristic
34	C₂×C₄⋊Q₈	C₂²	1	1	yes	characteristic
35	C₂×C₄⋊Q₈	C₂²	1	1	yes	characteristic
36	C₂×C₄⋊Q₈	C₂²	1	1	yes	characteristic
37	C₂×C₄⋊Q₈	C₂²	1	1	yes	characteristic
38	C₂×C₄⋊Q₈	C₂²	1	1	yes	characteristic
39	C₂×#126	C₂²	1	1	yes	characteristic
40	C₂×#126	C₂²	1	1	yes	characteristic
41	C₂×#124	C₂²	1	1	yes	characteristic
42	C₂×#123	C₂²	1	1	yes	characteristic
43	C₂×#123	C₂²	1	1	yes	characteristic
44	C₂×#123	C₂²	1	1	yes	characteristic
45	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
46	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
47	C₂×#117	C₂²	1	1	yes	characteristic
48	#401	C₂²	1	1	yes	characteristic
49	#400	C₂²	1	1	yes	characteristic
50	#400	C₂²	1	1	yes	characteristic
51	#400	C₂²	1	1	yes	characteristic
52	#400	C₂²	1	1	yes	characteristic
53	#400	C₂²	1	1	yes	characteristic
54	#400	C₂²	1	1	yes	characteristic
55	#400	C₂²	1	1	yes	characteristic
56	#400	C₂²	1	1	yes	characteristic
57	#400	C₂²	1	1	yes	characteristic
58	#400	C₂²	1	1	yes	characteristic
59	#400	C₂²	1	1	yes	characteristic
60	#400	C₂²	1	1	yes	characteristic
61	#400	C₂²	1	1	yes	characteristic
62	#400	C₂²	1	1	yes	characteristic
63	#399	C₂²	1	1	yes	characteristic
64	#399	C₂²	1	1	yes	characteristic
65	#399	C₂²	1	1	yes	characteristic
66	#399	C₂²	1	1	yes	characteristic
67	#398	C₂²	1	1	yes	characteristic
68	#398	C₂²	1	1	yes	characteristic
69	#398	C₂²	1	1	yes	characteristic
70	#398	C₂²	1	1	yes	characteristic
71	#398	C₂²	1	1	yes	characteristic
72	#398	C₂²	1	1	yes	characteristic
73	#398	C₂²	1	1	yes	characteristic
74	#397	C₂²	1	1	yes	characteristic
75	#397	C₂²	1	1	yes	characteristic
76	#397	C₂²	1	1	yes	characteristic
77	#397	C₂²	1	1	yes	characteristic
78	#397	C₂²	1	1	yes	characteristic
79	#397	C₂²	1	1	yes	characteristic
80	#397	C₂²	1	1	yes	characteristic
81	#397	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
85	#396	C₂²	1	1	yes	characteristic
86	#395	C₂²	1	1	yes	characteristic
87	#395	C₂²	1	1	yes	characteristic
88	#395	C₂²	1	1	yes	characteristic
89	#395	C₂²	1	1	yes	characteristic
90	#395	C₂²	1	1	yes	characteristic
91	#395	C₂²	1	1	yes	characteristic
92	#395	C₂²	1	1	yes	characteristic
93	#395	C₂²	1	1	yes	characteristic
94	#395	C₂²	1	1	yes	characteristic
95	#395	C₂²	1	1	yes	characteristic
96	#395	C₂²	1	1	yes	characteristic
97	#395	C₂²	1	1	yes	characteristic
98	#395	C₂²	1	1	yes	characteristic
99	#395	C₂²	1	1	yes	characteristic
100	#395	C₂²	1	1	yes	characteristic
101	#395	C₂²	1	1	yes	characteristic
102	#395	C₂²	1	1	yes	characteristic
103	#395	C₂²	1	1	yes	characteristic
104	#394	C₂²	1	1	yes	characteristic
105	#394	C₂²	1	1	yes	characteristic
106	#393	C₂²	1	1	yes	characteristic
107	#393	C₂²	1	1	yes	characteristic
108	#393	C₂²	1	1	yes	characteristic
109	#393	C₂²	1	1	yes	characteristic
110	#393	C₂²	1	1	yes	characteristic
111	#393	C₂²	1	1	yes	characteristic
112	#391	C₂²	1	1	yes	characteristic
113	#391	C₂²	1	1	yes	characteristic
114	#391	C₂²	1	1	yes	characteristic
115	#391	C₂²	1	1	yes	characteristic
116	#391	C₂²	1	1	yes	characteristic
117	#391	C₂²	1	1	yes	characteristic
118	#389	C₂²	1	1	yes	characteristic
119	#389	C₂²	1	1	yes	characteristic
120	#389	C₂²	1	1	yes	characteristic
121	#389	C₂²	1	1	yes	characteristic
122	#389	C₂²	1	1	yes	characteristic
123	#389	C₂²	1	1	yes	characteristic
124	#389	C₂²	1	1	yes	characteristic
125	#389	C₂²	1	1	yes	characteristic
126	#389	C₂²	1	1	yes	characteristic
127	#389	C₂²	1	1	yes	characteristic
128	#389	C₂²	1	1	yes	characteristic
129	#389	C₂²	1	1	yes	characteristic
130	#389	C₂²	1	1	yes	characteristic
131	#388	C₂²	1	1	yes	characteristic
132	#388	C₂²	1	1	yes	characteristic
133	#388	C₂²	1	1	yes	characteristic
134	#388	C₂²	1	1	yes	characteristic
135	#388	C₂²	1	1	yes	characteristic
136	#388	C₂²	1	1	yes	characteristic
137	#388	C₂²	1	1	yes	characteristic
138	#388	C₂²	1	1	yes	characteristic
139	#388	C₂²	1	1	yes	characteristic
140	#388	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	#387	C₂²	1	1	yes	characteristic
153	#387	C₂²	1	1	yes	characteristic
154	#387	C₂²	1	1	yes	characteristic
155	#387	C₂²	1	1	yes	characteristic
156	#387	C₂²	1	1	yes	characteristic
157	#387	C₂²	1	1	yes	characteristic
158	#387	C₂²	1	1	yes	characteristic
159	#387	C₂²	1	1	yes	characteristic
160	#386	C₂²	1	1	yes	characteristic
161	#385	C₂²	1	1	yes	characteristic
162	#385	C₂²	1	1	yes	characteristic
163	#385	C₂²	1	1	yes	characteristic
164	#385	C₂²	1	1	yes	characteristic
165	#385	C₂²	1	1	yes	characteristic
166	#385	C₂²	1	1	yes	characteristic
167	#385	C₂²	1	1	yes	characteristic
168	#385	C₂²	1	1	yes	characteristic
169	#385	C₂²	1	1	yes	characteristic
170	#384	C₂²	1	1	yes	characteristic
171	#383	C₂²	1	1	yes	characteristic
172	#382	C₂²	1	1	yes	characteristic
173	#382	C₂²	1	1	yes	characteristic
174	#382	C₂²	1	1	yes	characteristic
175	#382	C₂²	1	1	yes	characteristic
176	#381	C₂²	1	1	yes	characteristic
177	#381	C₂²	1	1	yes	characteristic
178	#381	C₂²	1	1	yes	characteristic
179	#380	C₂²	1	1	yes	characteristic
180	#380	C₂²	1	1	yes	characteristic
181	#380	C₂²	1	1	yes	characteristic
182	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
183	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
184	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
185	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
186	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
187	C₂²×Q₈	—	4	2	no	—
188	C₂²×Q₈	—	4	2	no	—
189	C₂²×Q₈	—	4	2	no	—
190	C₂²×Q₈	C₂³	1	1	yes	characteristic
191	C₂²×Q₈	C₂³	1	1	yes	characteristic
192	C₂²×Q₈	C₂³	1	1	yes	characteristic
193	C₂²×Q₈	C₂³	1	1	yes	characteristic
194	C₂²×Q₈	C₂³	1	1	yes	characteristic
195	C₂²×Q₈	C₂³	1	1	yes	characteristic
196	C₂²×Q₈	C₂³	1	1	yes	characteristic
197	C₂²×D₄	C₂³	1	1	yes	characteristic
198	C₂³×C₄	C₂³	1	1	yes	characteristic
199	C₂³×C₄	C₂³	1	1	yes	characteristic
200	C₂³×C₄	C₂³	1	1	yes	characteristic
201	C₂³×C₄	C₂³	1	1	yes	characteristic
202	C₄⋊Q₈	—	4	2	no	—
203	C₄⋊Q₈	—	4	2	no	—
204	C₄⋊Q₈	—	4	2	no	—
205	C₄⋊Q₈	—	4	2	no	—
206	C₄⋊Q₈	—	4	2	no	—
207	C₄⋊Q₈	—	4	2	no	—
208	#126	—	4	2	no	—
209	#126	—	4	2	no	—
210	#124	—	4	2	no	—
211	#123	—	4	2	no	—
212	#123	—	4	2	no	—
213	#123	—	4	2	no	—
214	C₂²⋊Q₈	—	4	2	no	—
215	C₂²⋊Q₈	—	4	2	no	—
216	#117	—	4	2	no	—
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×C₄⋊C₄	C₂³	1	1	yes	characteristic
242	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
243	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
244	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
245	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
246	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
247	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
248	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
249	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
250	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
251	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
252	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
253	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
254	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
255	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
256	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
257	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
258	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
259	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
260	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
261	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
262	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
263	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
264	C₂×C₄⋊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×C₂²⋊C₄	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	#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	#95	C₂³	1	1	yes	characteristic
349	#95	C₂³	1	1	yes	characteristic
350	#95	C₂³	1	1	yes	characteristic
351	#95	C₂³	1	1	yes	characteristic
352	#95	C₂³	1	1	yes	characteristic
353	#95	C₂³	1	1	yes	characteristic
354	#95	C₂³	1	1	yes	characteristic
355	#95	C₂³	1	1	yes	characteristic
356	#95	C₂³	1	1	yes	characteristic
357	#95	C₂³	1	1	yes	characteristic
358	#95	C₂³	1	1	yes	characteristic
359	#95	C₂³	1	1	yes	characteristic
360	C₂⁴	C₂⁴	1	1	yes	characteristic
361	C₂⁴	C₂⁴	1	1	yes	characteristic
362	C₂×Q₈	—	2	2	no	—
363	C₂×Q₈	—	2	2	no	—
364	C₂×Q₈	—	2	2	no	—
365	C₂×Q₈	—	2	2	no	—
366	C₂×Q₈	—	2	2	no	—
367	C₂×Q₈	—	2	2	no	—
368	C₂×Q₈	—	4	1	no	—
369	C₂×Q₈	—	4	1	no	—
370	C₂×Q₈	—	4	1	no	—
371	C₂×Q₈	—	4	1	no	—
372	C₂×Q₈	—	4	1	no	—
373	C₂×Q₈	—	4	1	no	—
374	C₂×Q₈	—	4	1	no	—
375	C₂×Q₈	—	4	1	no	—
376	C₂×Q₈	—	4	1	no	—
377	C₂×Q₈	—	4	1	no	—
378	C₂×Q₈	—	4	1	no	—
379	C₂×Q₈	—	4	1	no	—
380	C₂×Q₈	—	4	1	no	—
381	C₂×Q₈	—	4	1	no	—
382	C₂×Q₈	—	4	1	no	—
383	C₂×Q₈	—	4	16	no	—
384	C₂×D₄	—	2	2	no	—
385	C₂×D₄	—	4	1	no	—
386	C₂×D₄	—	4	1	no	—
387	C₂²×C₄	—	2	2	no	—
388	C₂²×C₄	—	2	2	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	2	2	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	2	2	no	—
394	C₂²×C₄	—	4	1	no	—
395	C₂²×C₄	—	4	1	no	—
396	C₂²×C₄	—	4	1	no	—
397	C₂²×C₄	—	4	1	no	—
398	C₂²×C₄	—	4	1	no	—
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	C₂²×C₄	C₂⁴	1	1	yes	characteristic
414	C₂²×C₄	C₂⁴	1	1	yes	characteristic
415	C₂²×C₄	C₂⁴	1	1	yes	characteristic
416	C₂²×C₄	C₂⁴	1	1	yes	characteristic
417	C₂²×C₄	C₂⁴	1	1	yes	characteristic
418	C₂²×C₄	C₂⁴	1	1	yes	characteristic
419	C₂²×C₄	C₂⁴	1	1	yes	characteristic
420	C₂²×C₄	C₂⁴	1	1	yes	characteristic
421	C₂²×C₄	C₂⁴	1	1	yes	characteristic
422	C₂²×C₄	C₂⁴	1	1	yes	characteristic
423	C₂²×C₄	C₂⁴	1	1	yes	characteristic
424	C₂²×C₄	C₂⁴	1	1	yes	characteristic
425	C₂²×C₄	C₂⁴	1	1	yes	characteristic
426	C₂²×C₄	C₂⁴	1	1	yes	characteristic
427	C₂²×C₄	C₂⁴	1	1	yes	characteristic
428	C₄⋊C₄	—	2	2	no	—
429	C₄⋊C₄	—	2	2	no	—
430	C₄⋊C₄	—	2	2	no	—
431	C₄⋊C₄	—	2	2	no	—
432	C₄⋊C₄	—	2	2	no	—
433	C₄⋊C₄	—	2	2	no	—
434	C₄⋊C₄	—	2	2	no	—
435	C₄⋊C₄	—	2	2	no	—
436	C₄⋊C₄	—	2	2	no	—
437	C₄⋊C₄	—	2	2	no	—
438	C₄⋊C₄	—	2	2	no	—
439	C₄⋊C₄	—	2	2	no	—
440	C₄⋊C₄	—	2	2	no	—
441	C₄⋊C₄	—	2	2	no	—
442	C₄⋊C₄	—	2	2	no	—
443	C₄⋊C₄	—	2	2	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	C₄⋊C₄	—	4	1	no	—
451	C₄⋊C₄	—	4	1	no	—
452	C₄⋊C₄	—	4	1	no	—
453	C₄⋊C₄	—	4	1	no	—
454	C₄⋊C₄	—	4	1	no	—
455	C₄⋊C₄	—	4	1	no	—
456	C₄⋊C₄	—	4	1	no	—
457	C₄⋊C₄	—	4	1	no	—
458	C₄⋊C₄	—	4	1	no	—
459	C₄⋊C₄	—	4	1	no	—
460	C₄⋊C₄	—	4	1	no	—
461	C₄⋊C₄	—	4	1	no	—
462	C₄⋊C₄	—	4	1	no	—
463	C₄⋊C₄	—	4	1	no	—
464	C₄⋊C₄	—	4	1	no	—
465	C₄⋊C₄	—	4	1	no	—
466	C₄⋊C₄	—	4	1	no	—
467	C₄⋊C₄	—	4	1	no	—
468	C₄⋊C₄	—	4	1	no	—
469	C₄⋊C₄	—	4	1	no	—
470	C₄⋊C₄	—	4	1	no	—
471	C₄⋊C₄	—	4	1	no	—
472	C₄⋊C₄	—	4	1	no	—
473	C₄⋊C₄	—	4	1	no	—
474	C₄⋊C₄	—	4	1	no	—
475	C₄⋊C₄	—	4	1	no	—
476	C₂²⋊C₄	—	2	2	no	—
477	C₂²⋊C₄	—	2	2	no	—
478	C₂²⋊C₄	—	2	2	no	—
479	C₂²⋊C₄	—	2	2	no	—
480	C₂²⋊C₄	—	2	2	no	—
481	C₂²⋊C₄	—	2	2	no	—
482	C₂²⋊C₄	—	2	2	no	—
483	C₂²⋊C₄	—	2	2	no	—
484	C₂²⋊C₄	—	2	2	no	—
485	C₂²⋊C₄	—	2	2	no	—
486	C₂²⋊C₄	—	2	2	no	—
487	C₂²⋊C₄	—	2	2	no	—
488	C₂²⋊C₄	—	2	2	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	C₂²⋊C₄	—	4	1	no	—
497	C₂²⋊C₄	—	4	1	no	—
498	C₂²⋊C₄	—	4	1	no	—
499	C₂²⋊C₄	—	4	1	no	—
500	C₄²	—	2	2	no	—
501	C₄²	—	2	2	no	—
502	C₄²	—	2	2	no	—
503	C₄²	—	2	2	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	C₄²	—	4	1	no	—
510	C₄²	—	4	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	H(5,𝔽₂)	1	2	yes	—
525	C₂³	C₂⁵	1	1	yes	characteristic
526	Q₈	—	4	4	no	—
527	Q₈	—	4	4	no	—
528	Q₈	—	4	4	no	—
529	Q₈	—	4	4	no	—
530	Q₈	—	8	2	no	—
531	Q₈	—	8	2	no	—
532	Q₈	—	8	2	no	—
533	D₄	—	8	2	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	—	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	—	4	4	no	—
616	C₂×C₄	—	4	4	no	—
617	C₂×C₄	—	4	4	no	—
618	C₂×C₄	—	4	4	no	—
619	C₂×C₄	H(5,𝔽₂)	1	2	yes	—
620	C₂×C₄	H(5,𝔽₂)	1	2	yes	—
621	C₂×C₄	2₋¹⁺⁴	1	2	yes	—
622	C₂×C₄	2₋¹⁺⁴	1	2	yes	—
623	C₂×C₄	2₋¹⁺⁴	1	2	yes	—
624	C₂×C₄	2₋¹⁺⁴	1	2	yes	—
625	C₂²	—	2	2	no	—
626	C₂²	—	2	2	no	—
627	C₂²	—	2	2	no	—
628	C₂²	—	4	1	no	—
629	C₂²	—	4	1	no	—
630	C₂²	—	4	1	no	—
631	C₂²	—	4	1	no	—
632	C₂²	—	4	1	no	—
633	C₂²	—	4	1	no	—
634	C₂²	—	4	1	no	—
635	C₂²	—	4	1	no	—
636	C₂²	—	4	1	no	—
637	C₂²	—	4	1	no	—
638	C₂²	—	4	1	no	—
639	C₂²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
640	C₂²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
641	C₂²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
642	C₂²	C₂×2₋¹⁺⁴	1	1	yes	characteristic
643	C₂²	C₂×2₋¹⁺⁴	1	1	yes	characteristic
644	C₂²	C₂×2₋¹⁺⁴	1	1	yes	characteristic
645	C₂²	C₂×2₋¹⁺⁴	1	1	yes	characteristic
646	C₄	—	2	2	no	—
647	C₄	—	2	2	no	—
648	C₄	—	2	2	no	—
649	C₄	—	2	2	no	—
650	C₄	—	2	2	no	—
651	C₄	—	2	2	no	—
652	C₄	—	4	1	no	—
653	C₄	—	4	1	no	—
654	C₄	—	4	1	no	—
655	C₄	—	4	1	no	—
656	C₄	—	4	1	no	—
657	C₄	—	4	1	no	—
658	C₄	—	4	1	no	—
659	C₄	—	4	1	no	—
660	C₄	—	4	1	no	—
661	C₄	—	4	1	no	—
662	C₄	—	4	1	no	—
663	C₄	—	4	1	no	—
664	C₄	—	4	1	no	—
665	C₄	—	4	1	no	—
666	C₄	—	4	1	no	—
667	C₄	—	4	1	no	—
668	C₄	—	4	1	no	—
669	C₄	—	4	1	no	—
670	C₄	—	4	1	no	—
671	C₄	—	4	1	no	—
672	C₄	—	4	1	no	—
673	C₄	—	4	1	no	—
674	C₄	—	4	1	no	—
675	C₂	—	4	2	no	—
676	C₂	—	8	1	no	—
677	C₂	#3532	1	1	yes	characteristic
678	C₂	#3538	1	1	yes	characteristic
679	C₂	#3544	1	1	yes	characteristic
680	C₂	#3544	1	1	yes	characteristic
681	C₂	#3550	1	1	yes	characteristic
682	C₂	#3552	1	1	yes	characteristic
683	C₂	#3552	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. #2844	C₂	semidirect
2. #2838	C₂	semidirect
3. #2821	C₂	semidirect
4. #2805	C₂	semidirect
5. #2792	C₂	semidirect
6. #2774	C₂	semidirect
7. #2771	C₂	semidirect
8. #2765	C₂	semidirect
9. #2762	C₂	semidirect
10. #2742	C₂	semidirect
11. #2734	C₂	semidirect
12. #2734	C₂	semidirect
15. #2716	C₂	semidirect
16. #2698	C₂	semidirect
17. #2689	C₂	semidirect
20. #2650	C₂	semidirect
21. #2628	C₂	semidirect
23. #2575	C₂	semidirect
24. #2574	C₂	semidirect
25. #2573	C₂	semidirect
27. #2551	C₂	semidirect
29. #2439	C₂	semidirect
30. #2434	C₂	semidirect
31. #2434	C₂	semidirect

Maximal subgroups

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

subgroup	index
#2844	2
#2838	2
#2821	2
#2805	2
#2792	2
#2774	2
#2771	2
#2765	2
#2762	2
#2742	2
#2734	2
#2718	2
#2717	2
#2716	2
#2698	2
#2689	2
#2674	2
#2650	2
#2628	2
#2614	2
#2575	2
#2574	2
#2573	2
#2553	2
#2551	2
#2470	2
#2439	2
#2434	2