Subgroups — #10618850

Order 640.

1100 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#554	C₂	1	1	yes	maximal, characteristic, complemented
2	#66063	C₂	1	1	yes	maximal, characteristic, complemented
3	#66061	C₂	1	1	yes	maximal, characteristic, complemented
4	#66024	C₂	1	1	yes	maximal, characteristic, complemented
5	#66024	C₂	1	1	yes	maximal, characteristic, complemented
6	#66023	C₂	1	1	yes	maximal, characteristic, complemented
7	#66022	C₂	1	1	yes	maximal, characteristic, complemented
8	#65970	C₂	1	2	yes	maximal, complemented
9	#65970	C₂	1	2	yes	maximal, complemented
10	#65968	C₂	1	2	yes	maximal, complemented
11	#65968	C₂	1	2	yes	maximal, complemented
12	#65966	C₂	1	2	yes	maximal, complemented
13	D₅×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
14	#65913	C₂	1	1	yes	maximal, characteristic, complemented
15	#65912	C₂	1	1	yes	maximal, characteristic, complemented
16	#65879	C₂	1	1	yes	maximal, characteristic
17	#65879	C₂	1	1	yes	maximal, characteristic
18	C₄×D₄×D₅	C₂	1	1	yes	maximal, characteristic
19	#65873	C₂	1	1	yes	maximal, characteristic, complemented
20	#65873	C₂	1	1	yes	maximal, characteristic, complemented
21	D₄×Dic₁₀	C₂	1	1	yes	maximal, characteristic, complemented
22	#65845	C₂	1	2	yes	maximal, complemented
23	C₂×#4042	C₂	1	2	yes	maximal, complemented
24	C₂×Q₈×D₅	C₂²	1	2	yes	complemented
25	C₂×D₄×D₅	C₂²	1	1	yes	characteristic
26	C₂²×C₄×D₅	C₂²	1	2	yes	—
27	C₂²×Dic₁₀	C₂²	1	2	yes	complemented
28	C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
29	C₅×#125	C₂²	1	1	yes	characteristic, complemented
30	C₅×#125	C₂²	1	1	yes	characteristic, complemented
31	C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
32	C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
33	C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
34	C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
35	C₄×C₅×D₄	C₂²	1	1	yes	characteristic
36	C₄×C₅×D₄	C₂²	1	1	yes	characteristic
37	C₄×C₅×D₄	C₂²	1	1	yes	characteristic
38	C₂×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
39	#4092	C₂²	1	2	yes	—
40	#4092	C₂²	1	1	yes	characteristic
41	#4092	C₂²	1	2	yes	complemented
42	#4092	C₂²	1	2	yes	complemented
43	#4090	C₂²	1	2	yes	complemented
44	#4090	C₂²	1	1	yes	characteristic, complemented
45	D₄×Dic₅	C₂²	1	1	yes	characteristic
46	D₄×Dic₅	C₂²	1	1	yes	characteristic
47	D₄×Dic₅	C₂²	1	1	yes	characteristic
48	C₄×C₂²⋊D₅	C₂²	1	2	yes	—
49	C₄×C₂²⋊D₅	C₂²	1	2	yes	—
50	C₄×C₂²⋊D₅	C₂²	1	2	yes	—
51	C₂×#685	C₂²	1	2	yes	—
52	C₂×#685	C₂²	1	2	yes	—
53	#4070	C₂²	1	2	yes	complemented
54	#4070	C₂²	1	2	yes	complemented
55	#4070	C₂²	1	2	yes	complemented
56	C₂×#683	C₂²	1	2	yes	complemented
57	C₂×#683	C₂²	1	2	yes	complemented
58	#4043	C₂²	1	1	yes	characteristic
59	#4043	C₂²	1	2	yes	—
60	#4043	C₂²	1	2	yes	complemented
61	#4043	C₂²	1	2	yes	complemented
62	#4042	C₂²	1	2	yes	—
63	#4042	C₂²	1	1	yes	characteristic
64	#4042	C₂²	1	2	yes	—
65	#4042	C₂²	1	2	yes	—
66	#4042	C₂²	1	1	yes	characteristic
67	#4042	C₂²	1	2	yes	—
68	#4042	C₂²	1	2	yes	complemented
69	#4042	C₂²	1	2	yes	complemented
70	#4042	C₂²	1	2	yes	complemented
71	#4042	C₂²	1	2	yes	complemented
72	#4042	C₂²	1	2	yes	complemented
73	#4042	C₂²	1	2	yes	complemented
74	#4042	C₂²	1	2	yes	complemented
75	#4042	C₂²	1	2	yes	complemented
76	#4039	C₂²	1	1	yes	characteristic
77	#4039	C₂²	1	1	yes	characteristic
78	#4039	C₂²	1	1	yes	characteristic
79	#4038	C₂²	1	1	yes	characteristic
80	#4038	C₂²	1	1	yes	characteristic
81	D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
82	D₅×C₄⋊C₄	C₂²	1	2	yes	complemented
83	D₅×C₄⋊C₄	C₂²	1	2	yes	complemented
84	D₅×C₄⋊C₄	C₂²	1	2	yes	complemented
85	#4036	C₂²	1	1	yes	characteristic, complemented
86	#4036	C₂²	1	1	yes	characteristic, complemented
87	#4035	C₂²	1	2	yes	complemented
88	#4035	C₂²	1	1	yes	characteristic, complemented
89	#4035	C₂²	1	1	yes	characteristic, complemented
90	#4035	C₂²	1	2	yes	complemented
91	#4034	C₂²	1	1	yes	characteristic, complemented
92	#4034	C₂²	1	1	yes	characteristic, complemented
93	#4034	C₂²	1	1	yes	characteristic, complemented
94	#4034	C₂²	1	2	yes	complemented
95	#4034	C₂²	1	1	yes	characteristic, complemented
96	#4034	C₂²	1	1	yes	characteristic, complemented
97	#4033	C₂²	1	2	yes	complemented
98	#4033	C₂²	1	2	yes	complemented
99	#4027	C₂²	1	2	yes	—
100	#4027	C₂²	1	2	yes	—
101	#4027	C₂²	1	2	yes	—
102	D₅×C₂²⋊C₄	C₂²	1	2	yes	—
103	D₅×C₂²⋊C₄	C₂²	1	2	yes	—
104	D₅×C₂²⋊C₄	C₂²	1	2	yes	—
105	#4024	C₂²	1	2	yes	complemented
106	#4024	C₂²	1	2	yes	complemented
107	#4024	C₂²	1	2	yes	complemented
108	#4024	C₂²	1	2	yes	complemented
109	#4024	C₂²	1	2	yes	complemented
110	#4024	C₂²	1	2	yes	complemented
111	C₄×D₂₀	C₂²	1	1	yes	characteristic
112	C₄×D₂₀	C₂²	1	1	yes	characteristic
113	C₄×D₂₀	C₂²	1	1	yes	characteristic
114	#4018	C₂²	1	1	yes	characteristic
115	#4018	C₂²	1	1	yes	characteristic
116	C₄²×D₅	C₂²	1	1	yes	characteristic
117	#4016	C₂²	1	1	yes	characteristic, complemented
118	#4016	C₂²	1	1	yes	characteristic, complemented
119	#4015	C₂²	1	1	yes	characteristic, complemented
120	C₄×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
121	C₄×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
123	#3501	—	5	1	no	maximal, Sylow
124	C₂³×D₅	C₂³	1	2	yes	—
125	C₂×C₅×Q₈	C₂³	1	1	yes	characteristic
126	C₂×C₅×Q₈	C₂³	1	2	yes	—
127	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
128	C₂²×C₄×C₅	C₂³	1	2	yes	—
129	C₂²×C₄×C₅	C₂³	1	2	yes	—
130	C₂²×C₄×C₅	C₂³	1	2	yes	—
131	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
132	C₂²×Dic₅	C₂³	1	2	yes	—
133	C₂²×Dic₅	C₂³	1	2	yes	—
134	C₂²×Dic₅	C₂³	1	2	yes	—
135	Q₈×D₅	—	4	4	no	—
136	D₄×D₅	Q₈	1	8	yes	complemented
137	C₂×D₂₀	C₂³	1	1	yes	characteristic
138	C₂×C₄×D₅	—	4	4	no	—
139	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
140	C₂×C₄×D₅	C₂³	1	2	yes	—
141	C₂×C₄×D₅	C₂³	1	2	yes	—
142	C₂×C₄×D₅	C₂³	1	2	yes	—
143	C₂×C₄×D₅	C₂³	1	2	yes	—
144	C₂×C₄×D₅	C₂³	1	2	yes	—
145	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
146	C₂×C₄×D₅	C₂³	1	2	yes	—
147	C₂×C₄×D₅	C₂³	1	2	yes	—
148	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
149	C₂×Dic₁₀	—	4	4	no	—
150	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
151	C₂×Dic₁₀	C₂³	1	2	yes	—
152	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
153	C₂×Dic₁₀	C₂³	1	2	yes	—
154	C₂×Dic₁₀	C₂³	1	2	yes	—
155	C₂×Dic₁₀	C₂³	1	2	yes	—
156	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
157	C₂×Dic₁₀	C₂³	1	2	yes	—
158	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
159	C₅×C₄⋊C₄	C₂³	1	2	yes	—
160	C₅×C₄⋊C₄	C₂³	1	2	yes	—
161	C₅×C₄⋊C₄	C₂³	1	2	yes	—
162	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
163	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
164	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
165	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
166	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
167	C₅×C₄⋊C₄	C₂³	1	2	yes	—
168	C₅×C₄⋊C₄	C₂³	1	2	yes	—
169	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
170	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
171	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
172	C₄²×C₅	C₂³	1	1	yes	characteristic
173	C₄²×C₅	C₂³	1	1	yes	characteristic
174	C₄²×C₅	C₂³	1	1	yes	characteristic
175	C₂²⋊Dic₅	C₂³	1	2	yes	—
176	C₂²⋊Dic₅	C₂³	1	2	yes	—
177	C₂²⋊Dic₅	C₂³	1	2	yes	—
178	#685	C₂³	1	1	yes	characteristic
179	#685	C₂³	1	1	yes	characteristic
180	#685	C₂³	1	1	yes	characteristic
181	#685	C₂³	1	1	yes	characteristic
182	#685	C₂³	1	2	yes	—
183	#685	C₂³	1	2	yes	—
184	#685	C₂³	1	2	yes	—
185	#685	C₂³	1	2	yes	—
186	#685	C₂³	1	2	yes	—
187	#685	C₂³	1	2	yes	—
188	#685	C₂³	1	2	yes	—
189	#685	C₂³	1	2	yes	—
190	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
191	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
192	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
193	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
194	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
195	C₄⋊Dic₅	C₂³	1	2	yes	—
196	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
197	C₄⋊Dic₅	C₂³	1	2	yes	—
198	C₄⋊Dic₅	C₂³	1	2	yes	—
199	#683	C₂³	1	1	yes	characteristic
200	#683	C₂³	1	1	yes	characteristic
201	#683	C₂³	1	1	yes	characteristic
202	#683	C₂³	1	1	yes	characteristic
203	#683	C₂³	1	1	yes	characteristic
204	#683	C₂³	1	1	yes	characteristic
205	#683	C₂³	1	2	yes	—
206	#683	C₂³	1	2	yes	—
207	#683	C₂³	1	2	yes	—
208	#683	C₂³	1	2	yes	—
209	#683	C₂³	1	1	yes	characteristic
210	#683	C₂³	1	1	yes	characteristic
211	#683	C₂³	1	1	yes	characteristic
212	#683	C₂³	1	1	yes	characteristic
213	#683	C₂³	1	2	yes	—
214	#683	C₂³	1	2	yes	—
215	#683	C₂³	1	2	yes	—
216	#683	C₂³	1	2	yes	—
217	#683	C₂³	1	2	yes	—
218	#683	C₂³	1	2	yes	—
219	#683	C₂³	1	2	yes	—
220	C₄×Dic₅	C₂³	1	1	yes	characteristic
221	C₄×Dic₅	C₂³	1	1	yes	characteristic
222	C₄×Dic₅	C₂³	1	1	yes	characteristic
223	C₄×Dic₅	C₂³	1	1	yes	characteristic
224	C₄×Dic₅	C₂³	1	1	yes	characteristic
225	C₄×Dic₅	C₂³	1	2	yes	—
226	C₄×Dic₅	C₂³	1	2	yes	—
227	#554	—	5	1	no	—
228	#554	—	5	1	no	—
229	#554	—	5	2	no	—
230	#554	—	5	2	no	—
231	#554	—	5	1	no	—
232	#554	—	5	1	no	—
233	#554	—	5	1	no	—
234	#554	—	5	2	no	—
235	#554	D₅	1	1	yes	characteristic, complemented
236	D₄×Q₈	—	5	1	no	—
237	D₄×Q₈	—	5	2	no	—
238	D₄×Q₈	—	5	1	no	—
239	#544	—	5	1	no	—
240	#544	—	5	1	no	—
241	#543	—	5	2	no	—
242	#543	—	5	2	no	—
243	#533	—	5	1	no	—
244	#533	—	5	1	no	—
245	C₂×C₂²⋊Q₈	—	5	2	no	—
246	C₂×C₂²⋊Q₈	—	5	2	no	—
247	#518	—	5	1	no	—
248	#518	—	5	1	no	—
249	C₂×C₄×D₄	—	5	1	no	—
250	C₂³×C₅	C₂⁴	1	2	yes	—
251	C₂²×D₅	—	4	2	no	—
252	C₂²×D₅	—	4	2	no	—
253	C₂²×D₅	C₂×Q₈	1	8	yes	complemented
254	C₂²×D₅	C₂⁴	1	1	yes	characteristic
255	C₂²×D₅	C₂⁴	1	2	yes	—
256	C₅×Q₈	—	4	2	no	—
257	C₅×Q₈	—	4	1	no	—
258	C₅×D₄	C₂×Q₈	1	4	yes	complemented
259	C₂×C₄×C₅	—	4	2	no	—
260	C₂×C₄×C₅	—	4	2	no	—
261	C₂×C₄×C₅	—	4	2	no	—
262	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
263	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
264	C₂×C₄×C₅	C₂⁴	1	2	yes	—
265	C₂×C₄×C₅	C₂⁴	1	2	yes	—
266	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
267	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
268	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
269	C₂×C₄×C₅	C₂⁴	1	2	yes	—
270	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
271	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
272	C₂²⋊D₅	C₂×Q₈	1	8	yes	complemented
273	C₂×Dic₅	—	2	4	no	—
274	C₂×Dic₅	—	4	2	no	—
275	C₂×Dic₅	—	4	2	no	—
276	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
277	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
278	C₂×Dic₅	C₂⁴	1	2	yes	—
279	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
280	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
281	C₂×Dic₅	C₂⁴	1	2	yes	—
282	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
283	C₂×Dic₅	C₂⁴	1	2	yes	—
284	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
285	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
286	D₂₀	C₂×Q₈	1	4	yes	complemented
287	C₄×D₅	—	2	2	no	—
288	C₄×D₅	—	2	4	no	—
289	C₄×D₅	—	4	2	no	—
290	C₄×D₅	—	4	2	no	—
291	C₄×D₅	—	4	1	no	—
292	C₄×D₅	—	4	2	no	—
293	C₄×D₅	—	4	2	no	—
294	C₄×D₅	—	4	2	no	—
295	C₄×D₅	—	4	2	no	—
296	C₄×D₅	C₂×Q₈	1	4	yes	complemented
297	Dic₁₀	—	2	2	no	—
298	Dic₁₀	—	2	4	no	—
299	Dic₁₀	—	2	2	no	—
300	Dic₁₀	—	4	2	no	—
301	Dic₁₀	—	4	2	no	—
302	Dic₁₀	—	4	2	no	—
303	Dic₁₀	—	4	1	no	—
304	Dic₁₀	—	4	2	no	—
305	C₂²×Q₈	—	5	2	no	—
306	C₂²×Q₈	—	5	2	no	—
307	C₂²×D₄	—	5	1	no	—
308	C₂³×C₄	—	5	2	no	—
309	C₄⋊Q₈	—	5	1	no	—
310	C₄⋊Q₈	—	5	2	no	—
311	C₄⋊Q₈	—	5	1	no	—
312	C₄⋊Q₈	—	5	1	no	—
313	C₄⋊Q₈	—	5	1	no	—
314	C₄⋊Q₈	—	5	2	no	—
315	C₄⋊Q₈	—	5	1	no	—
316	C₄⋊Q₈	—	5	1	no	—
317	C₄⋊Q₈	—	5	1	no	—
318	C₄⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
319	#125	—	5	1	no	—
320	#125	—	5	1	no	—
321	#125	—	5	2	no	—
322	#125	—	5	2	no	—
323	#125	—	5	1	no	—
324	#125	—	5	1	no	—
325	#125	—	5	1	no	—
326	#125	—	5	1	no	—
327	#125	C₂×D₅	1	1	yes	characteristic, complemented
328	#125	C₂×D₅	1	1	yes	characteristic, complemented
329	C₂²⋊Q₈	—	5	2	no	—
330	C₂²⋊Q₈	—	5	1	no	—
331	C₂²⋊Q₈	—	5	2	no	—
332	C₂²⋊Q₈	—	5	2	no	—
333	C₂²⋊Q₈	—	5	2	no	—
334	C₂²⋊Q₈	—	5	2	no	—
335	C₂²⋊Q₈	—	5	2	no	—
336	C₂²⋊Q₈	—	5	1	no	—
337	C₂²⋊Q₈	—	5	2	no	—
338	C₂²⋊Q₈	—	5	1	no	—
339	C₂²⋊Q₈	—	5	2	no	—
340	C₂²⋊Q₈	—	5	2	no	—
341	C₂²⋊Q₈	—	5	2	no	—
342	C₂²⋊Q₈	—	5	2	no	—
343	C₂²⋊Q₈	—	5	2	no	—
344	C₂²⋊Q₈	—	5	2	no	—
345	C₂²⋊Q₈	—	5	2	no	—
346	C₂²⋊Q₈	—	5	2	no	—
347	C₂²⋊Q₈	—	5	1	no	—
348	C₂²⋊Q₈	—	5	2	no	—
349	C₂²⋊Q₈	—	5	2	no	—
350	C₂²⋊Q₈	—	5	2	no	—
351	C₂²⋊Q₈	—	5	2	no	—
352	C₂²⋊Q₈	—	5	2	no	—
353	C₂²⋊Q₈	—	5	2	no	—
354	C₂²⋊Q₈	—	5	2	no	—
355	C₂²⋊Q₈	—	5	2	no	—
356	C₂²⋊Q₈	—	5	2	no	—
357	C₂²⋊Q₈	—	5	2	no	—
358	C₂²⋊Q₈	—	5	2	no	—
359	C₂²⋊Q₈	—	5	2	no	—
360	C₂²⋊Q₈	C₂×D₅	1	2	yes	complemented
361	C₂²⋊Q₈	C₂×D₅	1	2	yes	complemented
362	C₂²⋊Q₈	C₂×D₅	1	2	yes	complemented
363	C₄×Q₈	—	5	2	no	—
364	C₄×Q₈	—	5	2	no	—
365	C₄×Q₈	—	5	1	no	—
366	C₄×Q₈	—	5	1	no	—
367	C₄×Q₈	—	5	1	no	—
368	C₄×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
369	C₄×D₄	—	5	1	no	—
370	C₄×D₄	—	5	1	no	—
371	C₄×D₄	—	5	1	no	—
372	C₄×D₄	—	5	2	no	—
373	C₄×D₄	—	5	2	no	—
374	C₄×D₄	—	5	2	no	—
375	C₄×D₄	—	5	1	no	—
376	C₄×D₄	—	5	1	no	—
377	C₄×D₄	—	5	1	no	—
378	C₄×D₄	—	5	2	no	—
379	C₄×D₄	—	5	2	no	—
380	C₄×D₄	—	5	2	no	—
381	C₄×D₄	—	5	1	no	—
382	C₄×D₄	—	5	1	no	—
383	C₄×D₄	—	5	1	no	—
384	C₄×D₄	C₂×D₅	1	1	yes	characteristic
385	C₄×D₄	C₂×D₅	1	1	yes	characteristic
386	C₄×D₄	C₂×D₅	1	1	yes	characteristic
387	#117	—	5	1	no	—
388	#117	—	5	1	no	—
389	#117	—	5	1	no	—
390	#117	—	5	1	no	—
391	C₂×C₄⋊C₄	—	5	2	no	—
392	C₂×C₄⋊C₄	—	5	2	no	—
393	C₂×C₄⋊C₄	—	5	1	no	—
394	C₂×C₄⋊C₄	—	5	2	no	—
395	C₂×C₄⋊C₄	—	5	2	no	—
396	C₂×C₄⋊C₄	—	5	2	no	—
397	C₂×C₄⋊C₄	C₂×D₅	1	2	yes	complemented
398	C₂×C₂²⋊C₄	—	5	2	no	—
399	C₂×C₂²⋊C₄	—	5	2	no	—
400	C₂×C₂²⋊C₄	—	5	2	no	—
401	C₂×C₂²⋊C₄	—	5	2	no	—
402	C₂×C₂²⋊C₄	—	5	2	no	—
403	C₂×C₄²	—	5	1	no	—
404	C₂²×C₅	—	2	2	no	—
405	C₂²×C₅	—	2	2	no	—
406	C₂²×C₅	C₂²×Q₈	1	4	yes	—
407	C₂²×C₅	C₂⁵	1	1	yes	characteristic
408	C₂×D₅	—	2	2	no	—
409	C₂×D₅	—	2	1	no	—
410	C₂×D₅	—	2	2	no	—
411	C₂×D₅	—	2	1	no	—
412	C₂×D₅	—	4	8	no	—
413	C₂×D₅	C₂²×Q₈	1	2	yes	—
414	C₂×D₅	C₂²×Q₈	1	4	yes	—
415	C₄×C₅	—	2	1	no	—
416	C₄×C₅	—	2	2	no	—
417	C₄×C₅	—	2	1	no	—
418	C₄×C₅	—	2	2	no	—
419	C₄×C₅	—	2	1	no	—
420	C₄×C₅	—	2	2	no	—
421	C₄×C₅	—	2	1	no	—
422	C₄×C₅	—	2	1	no	—
423	C₄×C₅	—	2	1	no	—
424	C₄×C₅	C₂²×Q₈	1	2	yes	—
425	Dic₅	—	2	1	no	—
426	Dic₅	—	2	2	no	—
427	Dic₅	—	2	1	no	—
428	Dic₅	—	2	2	no	—
429	Dic₅	—	2	1	no	—
430	Dic₅	—	2	1	no	—
431	Dic₅	—	2	2	no	—
432	Dic₅	—	2	1	no	—
433	Dic₅	C₂²×Q₈	1	2	yes	—
434	Dic₅	H(5,𝔽₂)	1	2	yes	—
435	C₂⁴	—	5	2	no	—
436	C₂×Q₈	—	5	2	no	—
437	C₂×Q₈	—	5	1	no	—
438	C₂×Q₈	—	5	1	no	—
439	C₂×Q₈	—	5	2	no	—
440	C₂×Q₈	—	5	1	no	—
441	C₂×Q₈	—	5	2	no	—
442	C₂×Q₈	—	5	2	no	—
443	C₂×Q₈	—	5	2	no	—
444	C₂×Q₈	—	20	4	no	—
445	C₂×Q₈	—	20	4	no	—
446	C₂×Q₈	C₂²×D₅	1	1	yes	characteristic
447	C₂×Q₈	C₂²×D₅	1	2	yes	—
448	C₂×D₄	—	5	2	no	—
449	C₂×D₄	—	5	8	no	—
450	C₂×D₄	—	5	1	no	—
451	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
452	C₂²×C₄	—	5	1	no	—
453	C₂²×C₄	—	5	2	no	—
454	C₂²×C₄	—	5	2	no	—
455	C₂²×C₄	—	5	2	no	—
456	C₂²×C₄	—	5	1	no	—
457	C₂²×C₄	—	5	2	no	—
458	C₂²×C₄	—	5	1	no	—
459	C₂²×C₄	—	5	2	no	—
460	C₂²×C₄	—	5	2	no	—
461	C₂²×C₄	—	5	2	no	—
462	C₂²×C₄	—	5	2	no	—
463	C₂²×C₄	—	5	2	no	—
464	C₂²×C₄	—	5	2	no	—
465	C₂²×C₄	—	20	4	no	—
466	C₂²×C₄	C₂²×D₅	1	2	yes	—
467	C₂²×C₄	C₂²×D₅	1	2	yes	—
468	C₂²×C₄	C₂²×D₅	1	2	yes	—
469	C₄⋊C₄	—	5	1	no	—
470	C₄⋊C₄	—	5	2	no	—
471	C₄⋊C₄	—	5	1	no	—
472	C₄⋊C₄	—	5	2	no	—
473	C₄⋊C₄	—	5	1	no	—
474	C₄⋊C₄	—	5	1	no	—
475	C₄⋊C₄	—	5	2	no	—
476	C₄⋊C₄	—	5	1	no	—
477	C₄⋊C₄	—	5	2	no	—
478	C₄⋊C₄	—	5	2	no	—
479	C₄⋊C₄	—	5	2	no	—
480	C₄⋊C₄	—	5	2	no	—
481	C₄⋊C₄	—	5	2	no	—
482	C₄⋊C₄	—	5	2	no	—
483	C₄⋊C₄	—	5	2	no	—
484	C₄⋊C₄	—	5	2	no	—
485	C₄⋊C₄	—	5	2	no	—
486	C₄⋊C₄	—	5	1	no	—
487	C₄⋊C₄	—	5	1	no	—
488	C₄⋊C₄	—	5	1	no	—
489	C₄⋊C₄	—	5	1	no	—
490	C₄⋊C₄	—	5	1	no	—
491	C₄⋊C₄	—	5	1	no	—
492	C₄⋊C₄	—	5	1	no	—
493	C₄⋊C₄	—	5	1	no	—
494	C₄⋊C₄	—	5	2	no	—
495	C₄⋊C₄	—	5	1	no	—
496	C₄⋊C₄	—	5	1	no	—
497	C₄⋊C₄	—	5	2	no	—
498	C₄⋊C₄	—	5	1	no	—
499	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
500	C₄⋊C₄	C₂²×D₅	1	2	yes	—
501	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
502	C₄⋊C₄	C₂²×D₅	1	2	yes	—
503	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
504	C₄⋊C₄	C₂²×D₅	1	2	yes	—
505	C₄⋊C₄	C₂²×D₅	1	2	yes	—
506	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
507	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
508	C₄⋊C₄	C₂²×D₅	1	2	yes	—
509	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
510	C₂²⋊C₄	—	5	2	no	—
511	C₂²⋊C₄	—	5	2	no	—
512	C₂²⋊C₄	—	5	2	no	—
513	C₂²⋊C₄	—	5	2	no	—
514	C₂²⋊C₄	—	5	1	no	—
515	C₂²⋊C₄	—	5	1	no	—
516	C₂²⋊C₄	—	5	2	no	—
517	C₂²⋊C₄	—	5	1	no	—
518	C₂²⋊C₄	—	5	1	no	—
519	C₂²⋊C₄	—	5	2	no	—
520	C₂²⋊C₄	—	5	2	no	—
521	C₂²⋊C₄	—	5	2	no	—
522	C₂²⋊C₄	—	5	2	no	—
523	C₂²⋊C₄	—	5	2	no	—
524	C₂²⋊C₄	—	5	2	no	—
525	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
526	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
527	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
528	C₄²	—	5	1	no	—
529	C₄²	—	5	1	no	—
530	C₄²	—	5	1	no	—
531	C₄²	—	5	2	no	—
532	C₄²	—	5	2	no	—
533	C₄²	—	5	1	no	—
534	C₄²	—	5	1	no	—
535	C₄²	C₂²×D₅	1	1	yes	characteristic
536	C₄²	C₂²×D₅	1	1	yes	characteristic
537	C₄²	C₂²×D₅	1	1	yes	characteristic
538	C₂×C₅	—	2	4	no	—
539	C₂×C₅	C₂³×Q₈	1	1	yes	characteristic
540	C₂×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
541	C₂×C₅	#585	1	1	yes	characteristic
542	D₅	—	2	2	no	—
543	D₅	—	2	4	no	—
544	C₂³	—	5	1	no	—
545	C₂³	—	5	2	no	—
546	C₂³	—	5	8	no	—
547	C₂³	—	20	2	no	—
548	C₂³	—	20	2	no	—
549	C₂³	C₂³×D₅	1	2	yes	—
550	Q₈	—	4	2	no	—
551	Q₈	—	4	1	no	—
552	Q₈	—	10	2	no	—
553	Q₈	—	10	4	no	—
554	Q₈	—	10	2	no	—
555	Q₈	—	20	2	no	—
556	Q₈	—	20	2	no	—
557	Q₈	—	20	2	no	—
558	Q₈	—	20	2	no	—
559	Q₈	—	20	1	no	—
560	D₄	—	5	8	no	—
561	D₄	—	5	4	no	—
562	D₄	Q₈×D₅	1	4	yes	complemented
563	C₂×C₄	—	4	2	no	—
564	C₂×C₄	—	4	2	no	—
565	C₂×C₄	—	4	2	no	—
566	C₂×C₄	—	5	1	no	—
567	C₂×C₄	—	5	1	no	—
568	C₂×C₄	—	5	4	no	—
569	C₂×C₄	—	5	1	no	—
570	C₂×C₄	—	5	1	no	—
571	C₂×C₄	—	5	2	no	—
572	C₂×C₄	—	5	1	no	—
573	C₂×C₄	—	5	1	no	—
574	C₂×C₄	—	5	2	no	—
575	C₂×C₄	—	5	1	no	—
576	C₂×C₄	—	5	2	no	—
577	C₂×C₄	—	10	2	no	—
578	C₂×C₄	—	10	4	no	—
579	C₂×C₄	—	10	4	no	—
580	C₂×C₄	—	20	2	no	—
581	C₂×C₄	—	20	2	no	—
582	C₂×C₄	—	20	2	no	—
583	C₂×C₄	—	20	2	no	—
584	C₂×C₄	—	20	2	no	—
585	C₂×C₄	—	20	2	no	—
586	C₂×C₄	—	20	1	no	—
587	C₂×C₄	—	20	2	no	—
588	C₂×C₄	—	20	2	no	—
589	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
590	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
591	C₂×C₄	C₂³×D₅	1	2	yes	—
592	C₂×C₄	C₂³×D₅	1	2	yes	—
593	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
594	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
595	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
596	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
597	C₂×C₄	C₂³×D₅	1	2	yes	—
598	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
599	C₅	#3501	1	1	yes	characteristic, complemented, Sylow
600	C₂²	—	2	2	no	—
601	C₂²	—	2	2	no	—
602	C₂²	—	5	2	no	—
603	C₂²	—	5	4	no	—
604	C₂²	—	10	2	no	—
605	C₂²	—	10	1	no	—
606	C₂²	—	10	2	no	—
607	C₂²	—	10	1	no	—
608	C₂²	—	20	8	no	—
609	C₂²	C₂×Q₈×D₅	1	4	yes	—
610	C₂²	C₂⁴×D₅	1	1	yes	characteristic
611	C₄	—	2	1	no	—
612	C₄	—	2	2	no	—
613	C₄	—	2	1	no	—
614	C₄	—	2	1	no	—
615	C₄	—	2	1	no	—
616	C₄	—	2	1	no	—
617	C₄	—	2	2	no	—
618	C₄	—	2	2	no	—
619	C₄	—	2	1	no	—
620	C₄	—	5	2	no	—
621	C₄	—	5	2	no	—
622	C₄	—	10	1	no	—
623	C₄	—	10	2	no	—
624	C₄	—	10	1	no	—
625	C₄	—	10	1	no	—
626	C₄	—	10	2	no	—
627	C₄	—	10	1	no	—
628	C₄	—	10	2	no	—
629	C₄	—	10	1	no	—
630	C₄	C₂×Q₈×D₅	1	2	yes	—
631	C₂	—	2	4	no	—
632	C₂	—	10	2	no	—
633	C₂	—	10	4	no	—
634	C₂	C₂²×Q₈×D₅	1	1	yes	characteristic
635	C₂	#66283	1	1	yes	characteristic
636	C₂	D₅×H(5,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅
commutator, socle, cosocle	C₂²×C₅	C₂⁵
Fitting	C₅×#554	C₂
prime radical	C₂×D₄×D₅	C₂²
hypercenter	#554	D₅
hypocenter	C₅	#3501
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ #554

Complements

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

N	H ≅ G/N	type
1. C₅×#554	C₂	semidirect
2. #66063	C₂	semidirect
3. #66061	C₂	semidirect
4. #66024	C₂	semidirect
5. #66024	C₂	semidirect
6. #66023	C₂	semidirect
7. #66022	C₂	semidirect
8. #65970	C₂	semidirect
9. #65970	C₂	semidirect
10. #65968	C₂	semidirect
11. #65968	C₂	semidirect
12. #65966	C₂	semidirect
13. D₅×C₂²⋊Q₈	C₂	semidirect
14. #65913	C₂	semidirect
15. #65912	C₂	semidirect
19. #65873	C₂	semidirect
20. #65873	C₂	semidirect
21. D₄×Dic₁₀	C₂	semidirect
22. #65845	C₂	semidirect
23. C₂×#4042	C₂	semidirect
24. C₂×Q₈×D₅	C₂²	semidirect
27. C₂²×Dic₁₀	C₂²	semidirect
28. C₅×C₄⋊Q₈	C₂²	semidirect
29. C₅×#125	C₂²	semidirect
30. C₅×#125	C₂²	semidirect
31. C₅×C₂²⋊Q₈	C₂²	semidirect
32. C₅×C₂²⋊Q₈	C₂²	semidirect
33. C₅×C₂²⋊Q₈	C₂²	semidirect
34. C₄×C₅×Q₈	C₂²	semidirect
38. C₂×C₅×C₄⋊C₄	C₂²	semidirect
41. #4092	C₂²	semidirect
42. #4092	C₂²	semidirect
43. #4090	C₂²	semidirect
44. #4090	C₂²	semidirect
53. #4070	C₂²	semidirect
54. #4070	C₂²	semidirect
55. #4070	C₂²	semidirect
56. C₂×#683	C₂²	semidirect
57. C₂×#683	C₂²	semidirect
60. #4043	C₂²	semidirect
61. #4043	C₂²	semidirect
68. #4042	C₂²	semidirect
69. #4042	C₂²	semidirect
70. #4042	C₂²	semidirect
71. #4042	C₂²	semidirect
72. #4042	C₂²	semidirect
73. #4042	C₂²	semidirect
74. #4042	C₂²	semidirect
75. #4042	C₂²	semidirect
82. D₅×C₄⋊C₄	C₂²	semidirect
83. D₅×C₄⋊C₄	C₂²	semidirect
84. D₅×C₄⋊C₄	C₂²	semidirect
85. #4036	C₂²	semidirect
86. #4036	C₂²	semidirect
87. #4035	C₂²	semidirect
88. #4035	C₂²	semidirect
89. #4035	C₂²	semidirect
90. #4035	C₂²	semidirect
91. #4034	C₂²	semidirect
92. #4034	C₂²	semidirect
93. #4034	C₂²	semidirect
94. #4034	C₂²	semidirect
95. #4034	C₂²	semidirect
96. #4034	C₂²	semidirect
97. #4033	C₂²	semidirect
98. #4033	C₂²	semidirect
105. #4024	C₂²	semidirect
106. #4024	C₂²	semidirect
107. #4024	C₂²	semidirect
108. #4024	C₂²	semidirect
109. #4024	C₂²	semidirect
110. #4024	C₂²	semidirect
117. #4016	C₂²	semidirect
118. #4016	C₂²	semidirect
119. #4015	C₂²	semidirect
120. C₄×Dic₁₀	C₂²	semidirect
121. C₄×Dic₁₀	C₂²	semidirect
122. C₄×Dic₁₀	C₂²	semidirect
136. D₄×D₅	Q₈	semidirect
235. #554	D₅	semidirect
253. C₂²×D₅	C₂×Q₈	semidirect
258. C₅×D₄	C₂×Q₈	semidirect
272. C₂²⋊D₅	C₂×Q₈	semidirect
286. D₂₀	C₂×Q₈	semidirect
296. C₄×D₅	C₂×Q₈	semidirect
318. C₄⋊Q₈	C₂×D₅	semidirect
327. #125	C₂×D₅	semidirect
328. #125	C₂×D₅	semidirect
360. C₂²⋊Q₈	C₂×D₅	semidirect
361. C₂²⋊Q₈	C₂×D₅	semidirect
362. C₂²⋊Q₈	C₂×D₅	semidirect
368. C₄×Q₈	C₂×D₅	semidirect
397. C₂×C₄⋊C₄	C₂×D₅	semidirect
562. D₄	Q₈×D₅	semidirect
599. C₅	#3501	semidirect

Maximal subgroups

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

subgroup	index
C₅×#554	2
#66063	2
#66061	2
#66024	2
#66023	2
#66022	2
#65970	2
#65968	2
#65966	2
D₅×C₂²⋊Q₈	2
#65913	2
#65912	2
#65879	2
C₄×D₄×D₅	2
#65873	2
D₄×Dic₁₀	2
#65845	2
C₂×#4042	2
#3501	5