Subgroups — #34261

Order 256.

1359 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#518	C₂	1	1	yes	maximal, characteristic
2	#2357	C₂	1	1	yes	maximal, characteristic, complemented
3	#2354	C₂	1	1	yes	maximal, characteristic, complemented
4	#2353	C₂	1	2	yes	maximal, complemented
5	#2352	C₂	1	2	yes	maximal, complemented
6	#2349	C₂	1	1	yes	maximal, characteristic, complemented
7	D₄×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
8	#2347	C₂	1	1	yes	maximal, characteristic, complemented
9	#2346	C₂	1	1	yes	maximal, characteristic, complemented
10	#2342	C₂	1	2	yes	maximal, complemented
11	#2342	C₂	1	2	yes	maximal, complemented
12	D₄×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
13	D₄×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
14	#2319	C₂	1	1	yes	maximal, characteristic, complemented
15	#2318	C₂	1	2	yes	maximal, complemented
16	#2314	C₂	1	1	yes	maximal, characteristic, complemented
17	#2312	C₂	1	2	yes	maximal, complemented
18	#2298	C₂	1	1	yes	maximal, characteristic, complemented
19	#2293	C₂	1	1	yes	maximal, characteristic, complemented
20	#2290	C₂	1	2	yes	maximal, complemented
21	C₂×#388	C₂	1	2	yes	maximal, complemented
22	#2275	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄²×D₄	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂³×D₄	C₂²	1	1	yes	characteristic
25	#518	C₄	1	16	yes	complemented
26	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄	C₂²	1	2	yes	—
33	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄	C₂²	1	2	yes	—
35	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
36	C₂×#117	C₂²	1	1	yes	characteristic
37	C₂×#117	C₂²	1	1	yes	characteristic
38	C₂×#117	C₂²	1	2	yes	complemented
39	C₂×#117	C₂²	1	2	yes	complemented
40	C₂²×C₄⋊C₄	C₂²	1	2	yes	complemented
41	C₂²×C₂²⋊C₄	C₂²	1	2	yes	—
42	C₂²×C₂²⋊C₄	C₂²	1	2	yes	—
43	C₂²×C₂²⋊C₄	C₂²	1	2	yes	—
44	C₂²×C₂²⋊C₄	C₂²	1	2	yes	—
45	C₂²×C₄²	C₂²	1	2	yes	complemented
46	#390	C₂²	1	1	yes	characteristic
47	#390	C₂²	1	1	yes	characteristic
48	#390	C₂²	1	1	yes	characteristic
49	#390	C₂²	1	1	yes	characteristic
50	#389	C₂²	1	1	yes	characteristic, complemented
51	#389	C₂²	1	1	yes	characteristic, complemented
52	#389	C₂²	1	1	yes	characteristic, complemented
53	#389	C₂²	1	1	yes	characteristic, complemented
54	#388	C₂²	1	1	yes	characteristic
55	#388	C₂²	1	2	yes	—
56	#388	C₂²	1	2	yes	—
57	#388	C₂²	1	2	yes	—
58	#388	C₂²	1	2	yes	—
59	#388	C₂²	1	1	yes	characteristic
60	#388	C₂²	1	1	yes	characteristic
61	#388	C₂²	1	2	yes	—
62	#388	C₂²	1	2	yes	—
63	#388	C₂²	1	1	yes	characteristic
64	#388	C₂²	1	2	yes	complemented
65	#388	C₂²	1	2	yes	complemented
66	#388	C₂²	1	2	yes	complemented
67	#388	C₂²	1	2	yes	complemented
68	#388	C₂²	1	2	yes	complemented
69	#388	C₂²	1	2	yes	complemented
70	#388	C₂²	1	2	yes	complemented
71	#388	C₂²	1	2	yes	complemented
72	#387	C₂²	1	2	yes	complemented
73	#387	C₂²	1	2	yes	complemented
74	#387	C₂²	1	1	yes	characteristic, complemented
75	#387	C₂²	1	1	yes	characteristic, complemented
76	#387	C₂²	1	1	yes	characteristic, complemented
77	#387	C₂²	1	1	yes	characteristic, complemented
78	#386	C₂²	1	2	yes	—
79	#386	C₂²	1	2	yes	—
80	#386	C₂²	1	2	yes	—
81	#386	C₂²	1	2	yes	—
82	#385	C₂²	1	2	yes	complemented
83	#385	C₂²	1	2	yes	complemented
84	#385	C₂²	1	2	yes	complemented
85	#385	C₂²	1	2	yes	complemented
86	#384	C₂²	1	1	yes	characteristic, complemented
87	#383	C₂²	1	2	yes	complemented
88	#382	C₂²	1	1	yes	characteristic, complemented
89	#382	C₂²	1	2	yes	complemented
90	#381	C₂²	1	2	yes	complemented
91	#381	C₂²	1	2	yes	complemented
92	#380	C₂²	1	1	yes	characteristic
93	#380	C₂²	1	1	yes	characteristic
94	#380	C₂²	1	2	yes	complemented
95	#380	C₂²	1	2	yes	complemented
96	#380	C₂²	1	2	yes	complemented
97	#380	C₂²	1	2	yes	complemented
98	#379	C₂²	1	2	yes	—
99	#379	C₂²	1	2	yes	—
100	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
101	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
102	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
103	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
104	C₄×C₄⋊C₄	C₂²	1	2	yes	complemented
105	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
106	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
107	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
108	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
109	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
110	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
111	C₄×C₂²⋊C₄	C₂²	1	2	yes	complemented
112	C₄×C₂²⋊C₄	C₂²	1	2	yes	complemented
113	C₄×C₂²⋊C₄	C₂²	1	2	yes	complemented
114	C₄×C₂²⋊C₄	C₂²	1	2	yes	complemented
115	C₄×C₂²⋊C₄	C₂²	1	2	yes	complemented
116	C₄×C₂²⋊C₄	C₂²	1	2	yes	complemented
117	C₄×C₂²⋊C₄	C₂²	1	2	yes	complemented
118	C₄×C₂²⋊C₄	C₂²	1	2	yes	complemented
119	#376	C₂²	1	1	yes	characteristic, complemented
120	#376	C₂²	1	2	yes	complemented
121	C₂×#95	C₂²	1	2	yes	complemented
122	C₂×#95	C₂²	1	2	yes	complemented
123	C₄³	C₂²	1	1	yes	characteristic, complemented
124	C₂⁵	C₂³	1	2	yes	—
125	C₂²×D₄	—	2	4	no	—
126	C₂²×D₄	—	2	4	no	—
127	C₂²×D₄	C₂×C₄	1	8	yes	—
128	C₂²×D₄	C₂³	1	2	yes	—
129	C₂²×D₄	C₂³	1	1	yes	characteristic
130	C₂²×D₄	C₂³	1	1	yes	characteristic
131	C₂³×C₄	C₂³	1	2	yes	—
132	C₂³×C₄	C₂³	1	2	yes	—
133	C₂³×C₄	C₂³	1	1	yes	characteristic
134	C₂³×C₄	C₂³	1	2	yes	—
135	C₂³×C₄	C₂³	1	2	yes	—
136	C₂³×C₄	C₂³	1	2	yes	—
137	C₂³×C₄	C₂³	1	2	yes	—
138	C₂³×C₄	C₂³	1	2	yes	—
139	C₂³×C₄	C₂³	1	2	yes	—
140	C₄×D₄	—	2	4	no	—
141	C₄×D₄	—	2	4	no	—
142	C₄×D₄	—	2	4	no	—
143	C₄×D₄	—	2	4	no	—
144	C₄×D₄	C₂×C₄	1	8	yes	—
145	C₄×D₄	C₂×C₄	1	8	yes	—
146	C₄×D₄	C₂×C₄	1	8	yes	complemented
147	C₄×D₄	C₂×C₄	1	8	yes	complemented
148	C₄×D₄	C₂×C₄	1	16	yes	complemented
149	C₄×D₄	C₂×C₄	1	16	yes	complemented
150	#117	—	4	4	no	—
151	#117	—	4	4	no	—
152	#117	C₂×C₄	1	8	yes	complemented
153	#117	C₂×C₄	1	8	yes	complemented
154	C₂×C₄⋊C₄	—	4	4	no	—
155	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
156	C₂×C₄⋊C₄	C₂³	1	2	yes	—
157	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
158	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
159	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
160	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
161	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
162	C₂×C₄⋊C₄	C₂³	1	2	yes	—
163	C₂×C₄⋊C₄	C₂³	1	2	yes	—
164	C₂×C₄⋊C₄	C₂³	1	2	yes	—
165	C₂×C₄⋊C₄	C₂³	1	2	yes	—
166	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
167	C₂×C₄⋊C₄	C₂³	1	2	yes	—
168	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
169	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
170	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
171	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
172	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
173	C₂×C₂²⋊C₄	—	4	4	no	—
174	C₂×C₂²⋊C₄	—	4	4	no	—
175	C₂×C₂²⋊C₄	C₂×C₄	1	16	yes	complemented
176	C₂×C₂²⋊C₄	C₂×C₄	1	16	yes	complemented
177	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
178	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
179	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
180	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
181	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
182	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
183	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
184	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
185	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
186	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
187	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
188	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
189	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
190	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
191	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
192	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
193	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
194	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
195	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
196	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
197	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
198	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
199	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
200	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
201	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
202	C₂×C₄²	—	4	4	no	—
203	C₂×C₄²	C₂³	1	1	yes	characteristic
204	C₂×C₄²	C₂³	1	2	yes	—
205	C₂×C₄²	C₂³	1	1	yes	characteristic
206	C₂×C₄²	C₂³	1	1	yes	characteristic
207	C₂×C₄²	C₂³	1	1	yes	characteristic
208	C₂×C₄²	C₂³	1	1	yes	characteristic
209	C₂×C₄²	C₂³	1	1	yes	characteristic
210	C₂×C₄²	C₂³	1	2	yes	—
211	C₂×C₄²	C₂³	1	2	yes	—
212	C₂×C₄²	C₂³	1	1	yes	characteristic
213	C₂×C₄²	C₂³	1	1	yes	characteristic
214	C₂×C₄²	C₂³	1	2	yes	—
215	C₂×C₄²	C₂³	1	2	yes	—
216	C₂×C₄²	C₂³	1	2	yes	—
217	C₂×C₄²	C₂³	1	1	yes	characteristic
218	C₂×C₄²	C₂³	1	2	yes	—
219	C₂×C₄²	C₂³	1	1	yes	characteristic
220	#95	C₂³	1	1	yes	characteristic
221	#95	C₂³	1	1	yes	characteristic
222	#95	C₂³	1	2	yes	—
223	#95	C₂³	1	2	yes	—
224	#95	C₂³	1	2	yes	—
225	#95	C₂³	1	2	yes	—
226	#95	C₂³	1	2	yes	—
227	#95	C₂³	1	2	yes	—
228	#95	C₂³	1	1	yes	characteristic
229	#95	C₂³	1	1	yes	characteristic
230	#95	C₂³	1	1	yes	characteristic
231	#95	C₂³	1	1	yes	characteristic
232	#95	C₂³	1	2	yes	—
233	#95	C₂³	1	2	yes	—
234	#95	C₂³	1	1	yes	characteristic
235	#95	C₂³	1	1	yes	characteristic
236	#95	C₂³	1	1	yes	characteristic
237	#95	C₂³	1	2	yes	—
238	#95	C₂³	1	2	yes	—
239	#95	C₂³	1	2	yes	—
240	#95	C₂³	1	1	yes	characteristic
241	#95	C₂³	1	2	yes	—
242	#95	C₂³	1	2	yes	—
243	#95	C₂³	1	2	yes	—
244	#95	C₂³	1	1	yes	characteristic
245	#95	C₂³	1	1	yes	characteristic
246	C₂⁴	—	2	4	no	—
247	C₂⁴	—	2	4	no	—
248	C₂⁴	—	4	2	no	—
249	C₂⁴	—	4	2	no	—
250	C₂⁴	—	4	2	no	—
251	C₂⁴	—	4	2	no	—
252	C₂⁴	C₂²×C₄	1	8	yes	—
253	C₂⁴	C₂⁴	1	1	yes	characteristic
254	C₂⁴	C₂⁴	1	2	yes	—
255	C₂⁴	C₂⁴	1	2	yes	—
256	C₂×D₄	—	2	4	no	—
257	C₂×D₄	—	2	4	no	—
258	C₂×D₄	—	2	32	no	—
259	C₂×D₄	—	2	2	no	—
260	C₂×D₄	—	2	2	no	—
261	C₂×D₄	C₂²×C₄	1	8	yes	—
262	C₂×D₄	C₂²×C₄	1	4	yes	—
263	C₂×D₄	C₂²×C₄	1	4	yes	—
264	C₂×D₄	#41	1	4	yes	—
265	C₂×D₄	#41	1	4	yes	—
266	C₂²×C₄	—	2	2	no	—
267	C₂²×C₄	—	2	2	no	—
268	C₂²×C₄	—	2	4	no	—
269	C₂²×C₄	—	2	4	no	—
270	C₂²×C₄	—	2	4	no	—
271	C₂²×C₄	—	2	4	no	—
272	C₂²×C₄	—	2	4	no	—
273	C₂²×C₄	—	2	4	no	—
274	C₂²×C₄	—	4	2	no	—
275	C₂²×C₄	—	4	2	no	—
276	C₂²×C₄	—	4	2	no	—
277	C₂²×C₄	—	4	2	no	—
278	C₂²×C₄	—	4	2	no	—
279	C₂²×C₄	—	4	2	no	—
280	C₂²×C₄	—	4	2	no	—
281	C₂²×C₄	—	4	2	no	—
282	C₂²×C₄	—	4	2	no	—
283	C₂²×C₄	—	4	2	no	—
284	C₂²×C₄	—	4	2	no	—
285	C₂²×C₄	—	4	2	no	—
286	C₂²×C₄	—	4	2	no	—
287	C₂²×C₄	—	4	2	no	—
288	C₂²×C₄	C₂²×C₄	1	4	yes	—
289	C₂²×C₄	C₂²×C₄	1	8	yes	—
290	C₂²×C₄	C₂²×C₄	1	8	yes	—
291	C₂²×C₄	C₂²×C₄	1	8	yes	—
292	C₂²×C₄	C₂²×C₄	1	8	yes	—
293	C₂²×C₄	C₂⁴	1	1	yes	characteristic
294	C₂²×C₄	C₂⁴	1	1	yes	characteristic
295	C₂²×C₄	C₂⁴	1	1	yes	characteristic
296	C₂²×C₄	C₂⁴	1	2	yes	—
297	C₂²×C₄	C₂⁴	1	2	yes	—
298	C₂²×C₄	C₂⁴	1	1	yes	characteristic
299	C₂²×C₄	C₂⁴	1	1	yes	characteristic
300	C₂²×C₄	C₂⁴	1	1	yes	characteristic
301	C₂²×C₄	C₂⁴	1	2	yes	—
302	C₂²×C₄	C₂⁴	1	2	yes	—
303	C₂²×C₄	C₂⁴	1	1	yes	characteristic
304	C₂²×C₄	C₂⁴	1	1	yes	characteristic
305	C₂²×C₄	C₂⁴	1	2	yes	—
306	C₂²×C₄	C₂⁴	1	1	yes	characteristic
307	C₂²×C₄	C₂⁴	1	1	yes	characteristic
308	C₂²×C₄	C₂⁴	1	2	yes	—
309	C₂²×C₄	C₂⁴	1	1	yes	characteristic
310	C₂²×C₄	C₂⁴	1	1	yes	characteristic
311	C₂²×C₄	C₂⁴	1	1	yes	characteristic
312	C₂²×C₄	C₂⁴	1	1	yes	characteristic
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	—	2	2	no	—
315	C₄⋊C₄	—	2	2	no	—
316	C₄⋊C₄	—	2	2	no	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	2	4	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	—	4	2	no	—
321	C₄⋊C₄	—	4	2	no	—
322	C₄⋊C₄	—	4	1	no	—
323	C₄⋊C₄	—	4	1	no	—
324	C₄⋊C₄	—	4	2	no	—
325	C₄⋊C₄	—	4	2	no	—
326	C₄⋊C₄	—	4	2	no	—
327	C₄⋊C₄	C₂²×C₄	1	4	yes	—
328	C₄⋊C₄	C₂²×C₄	1	4	yes	—
329	C₄⋊C₄	C₂²×C₄	1	4	yes	—
330	C₄⋊C₄	C₂²×C₄	1	4	yes	—
331	C₂²⋊C₄	—	2	4	no	—
332	C₂²⋊C₄	—	2	4	no	—
333	C₂²⋊C₄	—	2	4	no	—
334	C₂²⋊C₄	—	2	4	no	—
335	C₂²⋊C₄	—	2	2	no	—
336	C₂²⋊C₄	—	2	2	no	—
337	C₂²⋊C₄	—	2	4	no	—
338	C₂²⋊C₄	—	2	4	no	—
339	C₂²⋊C₄	—	4	2	no	—
340	C₂²⋊C₄	—	4	2	no	—
341	C₂²⋊C₄	—	4	2	no	—
342	C₂²⋊C₄	—	4	2	no	—
343	C₂²⋊C₄	—	4	1	no	—
344	C₂²⋊C₄	—	4	2	no	—
345	C₂²⋊C₄	—	4	1	no	—
346	C₂²⋊C₄	—	4	2	no	—
347	C₂²⋊C₄	—	4	2	no	—
348	C₂²⋊C₄	—	4	2	no	—
349	C₂²⋊C₄	C₂²×C₄	1	4	yes	—
350	C₂²⋊C₄	C₂²×C₄	1	4	yes	—
351	C₂²⋊C₄	C₂²×C₄	1	8	yes	—
352	C₂²⋊C₄	C₂²×C₄	1	8	yes	—
353	C₂²⋊C₄	C₂²×C₄	1	8	yes	—
354	C₂²⋊C₄	C₂²×C₄	1	8	yes	—
355	C₂²⋊C₄	C₂²×C₄	1	8	yes	—
356	C₄²	—	2	2	no	—
357	C₄²	—	2	2	no	—
358	C₄²	—	2	2	no	—
359	C₄²	—	2	2	no	—
360	C₄²	—	2	2	no	—
361	C₄²	—	2	4	no	—
362	C₄²	—	2	2	no	—
363	C₄²	—	4	2	no	—
364	C₄²	—	4	2	no	—
365	C₄²	—	4	1	no	—
366	C₄²	—	4	2	no	—
367	C₄²	—	4	1	no	—
368	C₄²	—	4	2	no	—
369	C₄²	—	4	2	no	—
370	C₄²	C₂²×C₄	1	4	yes	—
371	C₄²	C₂²×C₄	1	4	yes	—
372	C₄²	C₂²×C₄	1	8	yes	—
373	C₂³	—	2	2	no	—
374	C₂³	—	2	2	no	—
375	C₂³	—	2	2	no	—
376	C₂³	—	2	2	no	—
377	C₂³	—	2	1	no	—
378	C₂³	—	2	1	no	—
379	C₂³	—	2	2	no	—
380	C₂³	—	2	2	no	—
381	C₂³	—	2	2	no	—
382	C₂³	—	2	2	no	—
383	C₂³	—	2	1	no	—
384	C₂³	—	2	1	no	—
385	C₂³	—	2	2	no	—
386	C₂³	—	2	2	no	—
387	C₂³	—	2	1	no	—
388	C₂³	—	2	1	no	—
389	C₂³	—	2	16	no	—
390	C₂³	—	4	8	no	—
391	C₂³	—	4	8	no	—
392	C₂³	—	8	4	no	—
393	C₂³	—	8	4	no	—
394	C₂³	—	8	4	no	—
395	C₂³	—	8	4	no	—
396	C₂³	C₂³×C₄	1	2	yes	—
397	C₂³	C₂³×C₄	1	4	yes	—
398	C₂³	C₂³×C₄	1	4	yes	—
399	C₂³	C₂×#41	1	4	yes	—
400	C₂³	C₂×#41	1	4	yes	—
401	C₂³	C₂⁵	1	1	yes	characteristic
402	D₄	—	2	16	no	—
403	D₄	—	2	8	no	—
404	D₄	#117	1	16	yes	complemented
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	8	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	4	8	no	—
455	C₂×C₄	—	4	8	no	—
456	C₂×C₄	—	4	8	no	—
457	C₂×C₄	—	4	8	no	—
458	C₂×C₄	—	4	8	no	—
459	C₂×C₄	—	4	8	no	—
460	C₂×C₄	—	8	4	no	—
461	C₂×C₄	—	8	4	no	—
462	C₂×C₄	C₂³×C₄	1	2	yes	—
463	C₂×C₄	C₂³×C₄	1	2	yes	—
464	C₂×C₄	C₂³×C₄	1	2	yes	—
465	C₂×C₄	C₂³×C₄	1	2	yes	—
466	C₂×C₄	C₂³×C₄	1	2	yes	—
467	C₂×C₄	C₂³×C₄	1	4	yes	—
468	C₂×C₄	C₂³×C₄	1	4	yes	—
469	C₂×C₄	C₂³×C₄	1	2	yes	—
470	C₂×C₄	C₂×#41	1	2	yes	—
471	C₂×C₄	C₂×#41	1	2	yes	—
472	C₂×C₄	H(5,𝔽₂)	1	2	yes	—
473	C₂×C₄	H(5,𝔽₂)	1	2	yes	—
474	C₂²	—	2	4	no	—
475	C₂²	—	2	4	no	—
476	C₂²	—	2	4	no	—
477	C₂²	—	2	4	no	—
478	C₂²	—	2	4	no	—
479	C₂²	—	2	4	no	—
480	C₂²	—	2	2	no	—
481	C₂²	—	2	4	no	—
482	C₂²	—	2	4	no	—
483	C₂²	—	2	4	no	—
484	C₂²	—	2	2	no	—
485	C₂²	—	2	2	no	—
486	C₂²	—	4	2	no	—
487	C₂²	—	4	1	no	—
488	C₂²	—	4	2	no	—
489	C₂²	—	4	1	no	—
490	C₂²	—	4	2	no	—
491	C₂²	—	4	1	no	—
492	C₂²	—	4	2	no	—
493	C₂²	—	4	1	no	—
494	C₂²	—	8	16	no	—
495	C₂²	C₂×#117	1	8	yes	—
496	C₂²	C₂⁴×C₄	1	1	yes	characteristic
497	C₂²	C₂²×#41	1	1	yes	characteristic
498	C₂²	C₂²×#41	1	1	yes	characteristic
499	C₂²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
500	C₂²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
501	C₂²	#585	1	1	yes	characteristic
502	C₂²	#585	1	1	yes	characteristic
503	C₄	—	2	2	no	—
504	C₄	—	2	2	no	—
505	C₄	—	2	4	no	—
506	C₄	—	2	2	no	—
507	C₄	—	2	2	no	—
508	C₄	—	2	2	no	—
509	C₄	—	2	4	no	—
510	C₄	—	2	2	no	—
511	C₄	—	2	2	no	—
512	C₄	—	4	1	no	—
513	C₄	—	4	2	no	—
514	C₄	—	4	1	no	—
515	C₄	—	4	2	no	—
516	C₄	—	4	1	no	—
517	C₄	—	4	2	no	—
518	C₄	—	4	2	no	—
519	C₄	—	4	1	no	—
520	C₄	—	4	1	no	—
521	C₄	—	4	1	no	—
522	C₄	C₂×#117	1	4	yes	—
523	C₂	—	2	8	no	—
524	C₂	—	4	4	no	—
525	C₂	—	4	2	no	—
526	C₂	C₂²×#117	1	1	yes	characteristic
527	C₂	C₄×H(5,𝔽₂)	1	1	yes	characteristic
528	C₂	C₄×H(5,𝔽₂)	1	1	yes	characteristic
529	C₂	#3513	1	1	yes	characteristic
530	C₂	#3514	1	1	yes	characteristic
531	C₂	#3519	1	1	yes	characteristic
532	C₂	#3521	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, socle, cosocle	C₂³	C₂⁵
commutator	C₂²	C₂⁴×C₄
prime radical	C₂³×D₄	C₂²
LCS	G ▷ C₂² ▷ 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
2. #2357	C₂	semidirect
3. #2354	C₂	semidirect
4. #2353	C₂	semidirect
5. #2352	C₂	semidirect
6. #2349	C₂	semidirect
7. D₄×C₄⋊C₄	C₂	semidirect
8. #2347	C₂	semidirect
9. #2346	C₂	semidirect
10. #2342	C₂	semidirect
11. #2342	C₂	semidirect
14. #2319	C₂	semidirect
15. #2318	C₂	semidirect
16. #2314	C₂	semidirect
17. #2312	C₂	semidirect
18. #2298	C₂	semidirect
19. #2293	C₂	semidirect
20. #2290	C₂	semidirect
21. C₂×#388	C₂	semidirect
22. #2275	C₂	semidirect
23. C₄²×D₄	C₂	semidirect
25. #518	C₄	semidirect
38. C₂×#117	C₂²	semidirect
39. C₂×#117	C₂²	semidirect
40. C₂²×C₄⋊C₄	C₂²	semidirect
45. C₂²×C₄²	C₂²	semidirect
50. #389	C₂²	semidirect
51. #389	C₂²	semidirect
52. #389	C₂²	semidirect
53. #389	C₂²	semidirect
64. #388	C₂²	semidirect
65. #388	C₂²	semidirect
66. #388	C₂²	semidirect
67. #388	C₂²	semidirect
68. #388	C₂²	semidirect
69. #388	C₂²	semidirect
70. #388	C₂²	semidirect
71. #388	C₂²	semidirect
72. #387	C₂²	semidirect
73. #387	C₂²	semidirect
74. #387	C₂²	semidirect
75. #387	C₂²	semidirect
76. #387	C₂²	semidirect
77. #387	C₂²	semidirect
82. #385	C₂²	semidirect
83. #385	C₂²	semidirect
84. #385	C₂²	semidirect
85. #385	C₂²	semidirect
86. #384	C₂²	semidirect
87. #383	C₂²	semidirect
88. #382	C₂²	semidirect
89. #382	C₂²	semidirect
90. #381	C₂²	semidirect
91. #381	C₂²	semidirect
94. #380	C₂²	semidirect
95. #380	C₂²	semidirect
96. #380	C₂²	semidirect
97. #380	C₂²	semidirect
100. C₄×C₄⋊C₄	C₂²	semidirect
101. C₄×C₄⋊C₄	C₂²	semidirect
102. C₄×C₄⋊C₄	C₂²	semidirect
103. C₄×C₄⋊C₄	C₂²	semidirect
104. C₄×C₄⋊C₄	C₂²	semidirect
105. C₄×C₄⋊C₄	C₂²	semidirect
106. C₄×C₄⋊C₄	C₂²	semidirect
107. C₄×C₄⋊C₄	C₂²	semidirect
108. C₄×C₄⋊C₄	C₂²	semidirect
111. C₄×C₂²⋊C₄	C₂²	semidirect
112. C₄×C₂²⋊C₄	C₂²	semidirect
113. C₄×C₂²⋊C₄	C₂²	semidirect
114. C₄×C₂²⋊C₄	C₂²	semidirect
115. C₄×C₂²⋊C₄	C₂²	semidirect
116. C₄×C₂²⋊C₄	C₂²	semidirect
117. C₄×C₂²⋊C₄	C₂²	semidirect
118. C₄×C₂²⋊C₄	C₂²	semidirect
119. #376	C₂²	semidirect
120. #376	C₂²	semidirect
121. C₂×#95	C₂²	semidirect
122. C₂×#95	C₂²	semidirect
123. C₄³	C₂²	semidirect
146. C₄×D₄	C₂×C₄	semidirect
147. C₄×D₄	C₂×C₄	semidirect
148. C₄×D₄	C₂×C₄	semidirect
149. C₄×D₄	C₂×C₄	semidirect
152. #117	C₂×C₄	semidirect
153. #117	C₂×C₄	semidirect
175. C₂×C₂²⋊C₄	C₂×C₄	semidirect
176. C₂×C₂²⋊C₄	C₂×C₄	semidirect
404. D₄	#117	semidirect

Maximal subgroups

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

subgroup	index
C₂×#518	2
#2357	2
#2354	2
#2353	2
#2352	2
#2349	2
D₄×C₄⋊C₄	2
#2347	2
#2346	2
#2342	2
D₄×C₂²⋊C₄	2
#2319	2
#2318	2
#2314	2
#2312	2
#2298	2
#2293	2
#2290	2
C₂×#388	2
#2275	2
C₄²×D₄	2