Subgroups — #12117111

Order 1280.

868 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×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
2	#10602323	C₂	1	1	yes	maximal, characteristic
3	#10602323	C₂	1	1	yes	maximal, characteristic
4	#10602323	C₂	1	1	yes	maximal, characteristic
5	#10602322	C₂	1	1	yes	maximal, characteristic
6	#10602322	C₂	1	1	yes	maximal, characteristic
7	C₄×C₂²⋊#168	C₂	1	1	yes	maximal, characteristic
8	#10600278	C₂	1	2	yes	maximal, complemented
9	#10600276	C₂	1	2	yes	maximal, complemented
10	#10600275	C₂	1	2	yes	maximal, complemented
11	#10600271	C₂	1	2	yes	maximal, complemented
12	C₂²×C₅×C₄⋊C₄	C₄	1	1	yes	characteristic
13	C₂²×C₅×C₄⋊C₄	C₄	1	1	yes	characteristic
14	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
15	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
17	C₄×C₅×C₄⋊C₄	C₄	1	1	yes	characteristic
18	C₄×C₅×C₄⋊C₄	C₄	1	1	yes	characteristic
19	C₄×C₅×C₄⋊C₄	C₄	1	1	yes	characteristic
20	C₄×C₅×C₄⋊C₄	C₄	1	1	yes	characteristic
21	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
23	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₂×C₅×#95	C₄	1	1	yes	characteristic
26	C₂×C₅×#95	C₄	1	1	yes	characteristic
27	C₂×C₂²⋊#168	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊#168	C₂²	1	1	yes	characteristic
29	C₂×C₂²⋊#168	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊#168	C₂²	1	1	yes	characteristic
31	C₂×C₄⋊#168	C₂²	1	2	yes	—
32	C₂×C₄⋊#168	C₂²	1	2	yes	—
33	C₂×C₄⋊#168	C₂²	1	2	yes	—
34	C₂×#3935	C₂²	1	2	yes	—
35	C₂×#3935	C₂²	1	2	yes	—
36	C₂×C₄×#168	C₂²	1	2	yes	—
37	#64744	C₂²	1	2	yes	—
38	#64744	C₂²	1	2	yes	—
39	#64744	C₂²	1	2	yes	—
40	#64744	C₂²	1	2	yes	—
41	#64744	C₂²	1	2	yes	—
42	#64744	C₂²	1	2	yes	—
43	#22627	—	5	1	no	maximal, Sylow
44	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
45	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
46	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
47	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
48	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
49	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
50	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
51	C₂×C₅×C₄⋊C₄	—	2	4	no	—
52	C₂×C₅×C₄⋊C₄	—	2	4	no	—
53	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
54	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
55	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
56	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
57	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
58	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
59	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
60	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄²×C₅	—	2	4	no	—
62	C₂×C₄²×C₅	—	4	2	no	—
63	C₂×C₄²×C₅	—	4	2	no	—
64	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
71	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
72	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
73	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
74	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
76	C₂²×#168	C₂³	1	2	yes	—
77	C₂²×#168	C₂³	1	2	yes	—
78	C₂²×#168	C₂³	1	2	yes	—
79	C₂²×#168	C₂³	1	2	yes	—
80	C₅×#95	C₂×C₄	1	1	yes	characteristic
81	C₅×#95	C₂×C₄	1	1	yes	characteristic
82	C₅×#95	C₂×C₄	1	1	yes	characteristic
83	C₅×#95	C₂×C₄	1	1	yes	characteristic
84	C₅×#95	C₂×C₄	1	1	yes	characteristic
85	C₅×#95	C₂×C₄	1	1	yes	characteristic
86	C₅×#95	C₂×C₄	1	1	yes	characteristic
87	C₅×#95	C₂×C₄	1	1	yes	characteristic
88	C₂²⋊#168	—	2	2	no	—
89	C₂²⋊#168	—	2	2	no	—
90	C₂²⋊#168	—	2	2	no	—
91	C₂²⋊#168	Q₈	1	4	yes	—
92	C₄⋊#168	—	2	4	no	—
93	C₄⋊#168	—	4	2	no	—
94	C₄⋊#168	—	4	2	no	—
95	#3935	—	2	4	no	—
96	#3935	—	4	2	no	—
97	C₄×#168	—	4	2	no	—
98	C₂×C₄×C₄⋊C₄	D₅	1	1	yes	characteristic
99	#1940	—	5	2	no	—
100	#1917	—	5	2	no	—
101	#1916	—	5	2	no	—
102	#1797	—	5	1	no	—
103	#1797	—	5	1	no	—
104	#1797	—	5	1	no	—
105	#1771	—	5	2	no	—
106	#1749	—	5	1	no	—
107	#1749	—	5	1	no	—
108	C₄×C₂²⋊C₈	—	5	1	no	—
109	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₅	—	2	2	no	—
111	C₂²×C₄×C₅	—	2	2	no	—
112	C₂²×C₄×C₅	—	2	2	no	—
113	C₂²×C₄×C₅	—	2	2	no	—
114	C₂²×C₄×C₅	—	2	2	no	—
115	C₂²×C₄×C₅	—	2	2	no	—
116	C₂²×C₄×C₅	—	2	2	no	—
117	C₂²×C₄×C₅	—	2	2	no	—
118	C₂²×C₄×C₅	—	2	2	no	—
119	C₂²×C₄×C₅	—	2	2	no	—
120	C₂²×C₄×C₅	—	2	2	no	—
121	C₂²×C₄×C₅	—	2	2	no	—
122	C₂²×C₄×C₅	—	4	1	no	—
123	C₂²×C₄×C₅	—	4	1	no	—
124	C₂²×C₄×C₅	—	4	1	no	—
125	C₂²×C₄×C₅	—	4	1	no	—
126	C₂²×C₄×C₅	—	4	1	no	—
127	C₂²×C₄×C₅	—	4	1	no	—
128	C₂²×C₄×C₅	—	4	1	no	—
129	C₂²×C₄×C₅	M₁₆	1	4	yes	—
130	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
131	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
132	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
133	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
134	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
135	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
136	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
137	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
138	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
140	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
141	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
142	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
143	C₂²×C₄×C₅	C₂×Q₈	1	2	yes	—
144	C₂²×C₄×C₅	#41	1	2	yes	—
145	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
146	C₅×C₄⋊C₄	—	2	2	no	—
147	C₅×C₄⋊C₄	—	2	2	no	—
148	C₅×C₄⋊C₄	—	2	2	no	—
149	C₅×C₄⋊C₄	—	2	2	no	—
150	C₅×C₄⋊C₄	—	2	2	no	—
151	C₅×C₄⋊C₄	—	2	2	no	—
152	C₅×C₄⋊C₄	—	2	2	no	—
153	C₅×C₄⋊C₄	M₁₆	1	4	yes	—
154	C₄²×C₅	—	2	2	no	—
155	C₄²×C₅	—	2	2	no	—
156	C₄²×C₅	—	2	2	no	—
157	C₄²×C₅	—	2	2	no	—
158	C₄²×C₅	—	2	2	no	—
159	C₄²×C₅	—	2	2	no	—
160	C₄²×C₅	—	2	2	no	—
161	C₄²×C₅	—	4	1	no	—
162	C₄²×C₅	—	4	1	no	—
163	C₄²×C₅	—	4	1	no	—
164	C₄²×C₅	—	4	1	no	—
165	C₄²×C₅	#41	1	4	yes	—
166	C₂×#168	—	2	2	no	—
167	C₂×#168	—	2	2	no	—
168	C₂×#168	—	2	2	no	—
169	C₂×#168	—	2	2	no	—
170	C₂×#168	—	2	2	no	—
171	C₂×#168	—	2	2	no	—
172	C₂×#168	—	2	2	no	—
173	C₂×#168	—	2	2	no	—
174	C₂×#168	—	2	2	no	—
175	C₂×#168	—	2	2	no	—
176	C₂×#168	—	2	2	no	—
177	C₂×#168	C₂×Q₈	1	4	yes	—
178	C₂²×C₄⋊C₄	Dic₅	1	1	yes	characteristic
179	C₂²×C₄⋊C₄	Dic₅	1	1	yes	characteristic
180	C₂²×C₄²	C₂×D₅	1	1	yes	characteristic
181	C₂²×C₄²	C₂×D₅	1	1	yes	characteristic
182	C₂²×C₄²	C₂×D₅	1	1	yes	characteristic
183	C₂×C₄⋊C₈	—	5	2	no	—
184	C₂×C₄⋊C₈	—	5	2	no	—
185	C₂×C₄⋊C₈	—	5	2	no	—
186	C₂×C₂²⋊C₈	—	5	1	no	—
187	C₂×C₂²⋊C₈	—	5	1	no	—
188	C₂×C₂²⋊C₈	—	5	1	no	—
189	C₂×C₂²⋊C₈	—	5	1	no	—
190	C₂×#97	—	5	2	no	—
191	C₂×#97	—	5	2	no	—
192	C₂×C₄×C₈	—	5	2	no	—
193	C₄×C₄⋊C₄	Dic₅	1	1	yes	characteristic
194	C₄×C₄⋊C₄	Dic₅	1	1	yes	characteristic
195	C₄×C₄⋊C₄	Dic₅	1	1	yes	characteristic
196	C₄×C₄⋊C₄	Dic₅	1	1	yes	characteristic
197	C₄×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
198	C₄×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
199	C₄×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
200	C₄×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
201	C₂×#95	Dic₅	1	1	yes	characteristic
202	C₂×#95	Dic₅	1	1	yes	characteristic
203	#336	—	5	2	no	—
204	#336	—	5	2	no	—
205	#336	—	5	2	no	—
206	#336	—	5	2	no	—
207	#336	—	5	2	no	—
208	#336	—	5	2	no	—
209	C₂³×C₅	—	2	1	no	—
210	C₂³×C₅	—	2	1	no	—
211	C₂³×C₅	—	2	1	no	—
212	C₂³×C₅	—	2	1	no	—
213	C₂³×C₅	C₄×Q₈	1	2	yes	—
214	C₂³×C₅	C₂×M₁₆	1	2	yes	—
215	C₂³×C₅	#131	1	2	yes	—
216	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
217	C₂×C₄×C₅	—	2	8	no	—
218	C₂×C₄×C₅	—	2	1	no	—
219	C₂×C₄×C₅	—	2	1	no	—
220	C₂×C₄×C₅	—	2	1	no	—
221	C₂×C₄×C₅	—	2	1	no	—
222	C₂×C₄×C₅	—	2	1	no	—
223	C₂×C₄×C₅	—	2	1	no	—
224	C₂×C₄×C₅	—	2	1	no	—
225	C₂×C₄×C₅	—	2	1	no	—
226	C₂×C₄×C₅	—	2	1	no	—
227	C₂×C₄×C₅	—	2	1	no	—
228	C₂×C₄×C₅	—	2	1	no	—
229	C₂×C₄×C₅	—	2	1	no	—
230	C₂×C₄×C₅	—	2	1	no	—
231	C₂×C₄×C₅	—	2	1	no	—
232	C₂×C₄×C₅	—	2	1	no	—
233	C₂×C₄×C₅	—	2	1	no	—
234	C₂×C₄×C₅	—	2	4	no	—
235	C₂×C₄×C₅	—	2	4	no	—
236	C₂×C₄×C₅	—	2	1	no	—
237	C₂×C₄×C₅	—	2	1	no	—
238	C₂×C₄×C₅	—	2	1	no	—
239	C₂×C₄×C₅	—	2	1	no	—
240	C₂×C₄×C₅	—	2	1	no	—
241	C₂×C₄×C₅	—	2	1	no	—
242	C₂×C₄×C₅	—	2	1	no	—
243	C₂×C₄×C₅	—	2	1	no	—
244	C₂×C₄×C₅	—	2	1	no	—
245	C₂×C₄×C₅	—	2	1	no	—
246	C₂×C₄×C₅	—	2	1	no	—
247	C₂×C₄×C₅	—	2	1	no	—
248	C₂×C₄×C₅	—	2	1	no	—
249	C₂×C₄×C₅	—	2	1	no	—
250	C₂×C₄×C₅	—	2	1	no	—
251	C₂×C₄×C₅	—	4	4	no	—
252	C₂×C₄×C₅	—	4	4	no	—
253	C₂×C₄×C₅	—	4	4	no	—
254	C₂×C₄×C₅	—	4	4	no	—
255	C₂×C₄×C₅	—	4	4	no	—
256	C₂×C₄×C₅	#117	1	2	yes	—
257	C₂×C₄×C₅	#117	1	2	yes	—
258	C₂×C₄×C₅	C₄×Q₈	1	2	yes	—
259	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
260	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
261	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
262	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
263	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
264	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
265	C₂×C₄×C₅	C₂×#41	1	2	yes	—
266	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
267	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
268	#168	—	2	4	no	—
269	#168	—	4	2	no	—
270	#168	—	4	2	no	—
271	#168	—	4	2	no	—
272	C₂³×C₄	C₂×Dic₅	1	1	yes	characteristic
273	C₂³×C₄	C₂×Dic₅	1	1	yes	characteristic
274	C₂³×C₄	C₂×Dic₅	1	1	yes	characteristic
275	C₂³×C₄	C₂×Dic₅	1	1	yes	characteristic
276	C₂³×C₄	C₂×Dic₅	1	1	yes	characteristic
277	C₂³×C₄	C₂×Dic₅	1	1	yes	characteristic
278	C₂³×C₄	C₂²×D₅	1	1	yes	characteristic
279	C₂²×C₈	—	5	2	no	—
280	C₂²×C₈	—	5	2	no	—
281	C₂²×C₈	—	5	2	no	—
282	C₂²×C₈	—	5	2	no	—
283	C₂×C₄⋊C₄	—	2	4	no	—
284	C₂×C₄⋊C₄	—	2	4	no	—
285	C₂×C₄⋊C₄	C₂×Dic₅	1	1	yes	characteristic
286	C₂×C₄⋊C₄	C₂×Dic₅	1	1	yes	characteristic
287	C₂×C₄⋊C₄	C₂×Dic₅	1	1	yes	characteristic
288	C₂×C₄⋊C₄	C₂×Dic₅	1	1	yes	characteristic
289	C₂×C₄⋊C₄	C₂×Dic₅	1	1	yes	characteristic
290	C₂×C₄⋊C₄	C₂×Dic₅	1	1	yes	characteristic
291	C₂×C₄⋊C₄	C₂×Dic₅	1	1	yes	characteristic
292	C₂×C₄⋊C₄	C₂×Dic₅	1	1	yes	characteristic
293	C₂×C₄²	—	2	4	no	—
294	C₂×C₄²	—	4	2	no	—
295	C₂×C₄²	—	4	2	no	—
296	C₂×C₄²	C₂×Dic₅	1	1	yes	characteristic
297	C₂×C₄²	C₂×Dic₅	1	1	yes	characteristic
298	C₂×C₄²	C₂×Dic₅	1	1	yes	characteristic
299	C₂×C₄²	C₂×Dic₅	1	1	yes	characteristic
300	C₂×C₄²	C₂×Dic₅	1	1	yes	characteristic
301	C₂×C₄²	C₂×Dic₅	1	1	yes	characteristic
302	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
303	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
304	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
305	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
306	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
307	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
308	C₄⋊C₈	—	10	4	no	—
309	C₄⋊C₈	—	20	2	no	—
310	C₄⋊C₈	—	20	2	no	—
311	C₂²⋊C₈	—	5	4	no	—
312	C₂²⋊C₈	—	10	2	no	—
313	C₂²⋊C₈	—	10	2	no	—
314	C₂²⋊C₈	—	10	2	no	—
315	#97	—	10	4	no	—
316	#97	—	20	2	no	—
317	C₄×C₈	—	20	2	no	—
318	#95	C₂×Dic₅	1	1	yes	characteristic
319	#95	C₂×Dic₅	1	1	yes	characteristic
320	#95	C₂×Dic₅	1	1	yes	characteristic
321	#95	C₂×Dic₅	1	1	yes	characteristic
322	#95	C₂×Dic₅	1	1	yes	characteristic
323	#95	C₂×Dic₅	1	1	yes	characteristic
324	#95	C₂×Dic₅	1	1	yes	characteristic
325	#95	C₂×Dic₅	1	1	yes	characteristic
326	C₂²×C₅	—	2	2	no	—
327	C₂²×C₅	—	2	2	no	—
328	C₂²×C₅	—	2	2	no	—
329	C₂²×C₅	—	2	2	no	—
330	C₂²×C₅	—	2	2	no	—
331	C₂²×C₅	—	2	2	no	—
332	C₂²×C₅	#446	1	4	yes	—
333	C₂²×C₅	C₂×#117	1	1	yes	characteristic
334	C₂²×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
335	C₂²×C₅	#518	1	1	yes	characteristic
336	C₂²×C₅	C₂²×M₁₆	1	1	yes	characteristic
337	C₂²×C₅	C₂²×M₁₆	1	1	yes	characteristic
338	C₂²×C₅	C₂×#131	1	1	yes	characteristic
339	C₂²×C₅	#568	1	1	yes	characteristic
340	C₄×C₅	—	2	2	no	—
341	C₄×C₅	—	2	2	no	—
342	C₄×C₅	—	2	2	no	—
343	C₄×C₅	—	2	2	no	—
344	C₄×C₅	—	2	2	no	—
345	C₄×C₅	—	2	2	no	—
346	C₄×C₅	—	2	2	no	—
347	C₄×C₅	—	2	2	no	—
348	C₄×C₅	—	4	1	no	—
349	C₄×C₅	—	4	1	no	—
350	C₄×C₅	—	4	1	no	—
351	C₄×C₅	—	4	1	no	—
352	C₄×C₅	—	4	1	no	—
353	C₄×C₅	#553	1	2	yes	—
354	C₄×C₅	#554	1	2	yes	—
355	C₂⁴	C₂²×Dic₅	1	1	yes	characteristic
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	4	1	no	—
369	C₂²×C₄	—	4	1	no	—
370	C₂²×C₄	—	4	1	no	—
371	C₂²×C₄	—	4	1	no	—
372	C₂²×C₄	—	4	1	no	—
373	C₂²×C₄	—	4	1	no	—
374	C₂²×C₄	—	4	1	no	—
375	C₂²×C₄	#681	1	4	yes	—
376	C₂²×C₄	Q₈×D₅	1	2	yes	—
377	C₂²×C₄	#713	1	2	yes	—
378	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
379	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
380	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
381	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
382	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
383	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
384	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
385	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
386	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
387	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
388	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
389	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
390	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
391	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
392	C₂×C₈	—	5	4	no	—
393	C₂×C₈	—	10	2	no	—
394	C₂×C₈	—	10	2	no	—
395	C₂×C₈	—	10	2	no	—
396	C₂×C₈	—	10	2	no	—
397	C₂×C₈	—	10	2	no	—
398	C₂×C₈	—	10	2	no	—
399	C₂×C₈	—	10	2	no	—
400	C₂×C₈	—	10	2	no	—
401	C₂×C₈	—	10	2	no	—
402	C₂×C₈	—	10	2	no	—
403	C₂×C₈	—	10	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	#681	1	4	yes	—
412	C₄²	—	2	2	no	—
413	C₄²	—	2	2	no	—
414	C₄²	—	2	2	no	—
415	C₄²	—	2	2	no	—
416	C₄²	—	2	2	no	—
417	C₄²	—	2	2	no	—
418	C₄²	—	2	2	no	—
419	C₄²	—	4	1	no	—
420	C₄²	—	4	1	no	—
421	C₄²	—	4	1	no	—
422	C₄²	—	4	1	no	—
423	C₄²	#709	1	4	yes	—
424	C₂×C₅	—	2	4	no	—
425	C₂×C₅	#2345	1	1	yes	characteristic
426	C₂×C₅	#2920	1	1	yes	characteristic
427	C₂×C₅	#2924	1	1	yes	characteristic
428	C₂×C₅	C₂×#446	1	1	yes	characteristic
429	C₂×C₅	Q₈×M₁₆	1	1	yes	characteristic
430	C₂×C₅	#2973	1	1	yes	characteristic
431	C₂×C₅	#2974	1	1	yes	characteristic
432	C₂³	—	2	1	no	—
433	C₂³	—	2	1	no	—
434	C₂³	—	2	1	no	—
435	C₂³	—	2	1	no	—
436	C₂³	C₂×#681	1	2	yes	—
437	C₂³	Q₈×Dic₅	1	2	yes	—
438	C₂³	#4094	1	2	yes	—
439	C₂³	C₂³×Dic₅	1	1	yes	characteristic
440	C₂×C₄	—	2	8	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	1	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	1	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	1	no	—
456	C₂×C₄	—	2	1	no	—
457	C₂×C₄	—	2	4	no	—
458	C₂×C₄	—	2	4	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	1	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	1	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	4	4	no	—
475	C₂×C₄	—	4	4	no	—
476	C₂×C₄	—	4	4	no	—
477	C₂×C₄	—	4	4	no	—
478	C₂×C₄	—	4	4	no	—
479	C₂×C₄	C₂×#681	1	2	yes	—
480	C₂×C₄	C₂×#681	1	2	yes	—
481	C₂×C₄	C₂×#681	1	2	yes	—
482	C₂×C₄	C₂×#681	1	2	yes	—
483	C₂×C₄	C₂×#681	1	2	yes	—
484	C₂×C₄	#4072	1	2	yes	—
485	C₂×C₄	#4072	1	2	yes	—
486	C₂×C₄	Q₈×Dic₅	1	2	yes	—
487	C₂×C₄	C₂×#709	1	2	yes	—
488	C₂×C₄	#4144	1	2	yes	—
489	C₂×C₄	C₂×Q₈×D₅	1	1	yes	characteristic
490	C₂×C₄	C₂×#713	1	1	yes	characteristic
491	C₈	—	10	4	no	—
492	C₈	—	20	2	no	—
493	C₈	—	20	2	no	—
494	C₈	—	20	2	no	—
495	C₅	#22627	1	1	yes	characteristic, complemented, Sylow
496	C₂²	—	2	2	no	—
497	C₂²	—	2	2	no	—
498	C₂²	—	2	2	no	—
499	C₂²	—	2	2	no	—
500	C₂²	—	2	2	no	—
501	C₂²	—	2	2	no	—
502	C₂²	#65313	1	4	yes	—
503	C₂²	C₂²×#681	1	1	yes	characteristic
504	C₂²	C₂²×#681	1	1	yes	characteristic
505	C₂²	C₂×#4072	1	1	yes	characteristic
506	C₂²	#66132	1	1	yes	characteristic
507	C₂²	C₂×Q₈×Dic₅	1	1	yes	characteristic
508	C₂²	C₂×#4094	1	1	yes	characteristic
509	C₂²	#66153	1	1	yes	characteristic
510	C₄	—	2	2	no	—
511	C₄	—	2	2	no	—
512	C₄	—	2	2	no	—
513	C₄	—	2	2	no	—
514	C₄	—	2	2	no	—
515	C₄	—	2	2	no	—
516	C₄	—	2	2	no	—
517	C₄	—	2	2	no	—
518	C₄	—	4	1	no	—
519	C₄	—	4	1	no	—
520	C₄	—	4	1	no	—
521	C₄	—	4	1	no	—
522	C₄	—	4	1	no	—
523	C₄	#65845	1	2	yes	—
524	C₄	#65848	1	2	yes	—
525	C₂	—	2	4	no	—
526	C₂	#10613780	1	1	yes	characteristic
527	C₂	#10613891	1	1	yes	characteristic
528	C₂	#10613941	1	1	yes	characteristic
529	C₂	#10614033	1	1	yes	characteristic
530	C₂	#10614034	1	1	yes	characteristic
531	C₂	C₂×#65313	1	1	yes	characteristic
532	C₂	Q₈×#681	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₅
commutator, socle	C₂³×C₅	C₂³×C₄
Fitting	C₂×C₄×C₅×C₄⋊C₄	C₂
prime radical	C₂⁴×C₅	C₂²×C₄
cosocle	C₂²×C₄×C₅	C₂⁴
hypercenter	C₂×C₄×C₄⋊C₄	D₅
hypocenter	C₅	#22627
LCS	G ▷ C₂³×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
8. #10600278	C₂	semidirect
9. #10600276	C₂	semidirect
10. #10600275	C₂	semidirect
11. #10600271	C₂	semidirect
495. C₅	#22627	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×C₅×C₄⋊C₄	2
#10602323	2
#10602322	2
C₄×C₂²⋊#168	2
#10600278	2
#10600276	2
#10600275	2
#10600271	2
#22627	5