Subgroups — #10618512

Order 640.

1252 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₄²	C₂	1	1	yes	maximal, characteristic, complemented
2	#66140	C₂	1	2	yes	maximal, complemented
3	C₂×#4085	C₂	1	2	yes	maximal, complemented
4	D₄×C₂²⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
5	D₄×C₂²⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
6	#66132	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×D₄×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
8	#66053	C₂	1	1	yes	maximal, characteristic, complemented
9	#66052	C₂	1	1	yes	maximal, characteristic, complemented
10	#65953	C₂	1	1	yes	maximal, characteristic, complemented
11	#65952	C₂	1	1	yes	maximal, characteristic, complemented
12	#65951	C₂	1	2	yes	maximal, complemented
13	#65950	C₂	1	1	yes	maximal, characteristic, complemented
14	#65935	C₂	1	2	yes	maximal, complemented
15	#65930	C₂	1	1	yes	maximal, characteristic, complemented
16	#65927	C₂	1	2	yes	maximal, complemented
17	#65925	C₂	1	2	yes	maximal, complemented
18	#65925	C₂	1	2	yes	maximal, complemented
19	#65920	C₂	1	2	yes	maximal, complemented
20	#65899	C₂	1	1	yes	maximal, characteristic, complemented
21	#65879	C₂	1	1	yes	maximal, characteristic, complemented
22	#65873	C₂	1	1	yes	maximal, characteristic, complemented
23	#65872	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×C₅×D₄	C₂²	1	1	yes	characteristic
25	C₂²×C₅×D₄	C₂²	1	1	yes	characteristic
26	C₂²×C₅×D₄	C₂²	1	2	yes	complemented
27	C₂²×C₂²⋊D₅	C₂²	1	2	yes	complemented
28	C₂²×C₂²⋊D₅	C₂²	1	2	yes	complemented
29	C₂³×Dic₅	C₂²	1	2	yes	complemented
30	C₂×#711	C₂²	1	2	yes	complemented
31	C₂×#711	C₂²	1	2	yes	complemented
32	C₂×D₄×D₅	C₂²	1	1	yes	characteristic
33	C₅×#127	C₂²	1	1	yes	characteristic, complemented
34	C₅×#121	C₂²	1	1	yes	characteristic, complemented
35	C₅×#121	C₂²	1	2	yes	complemented
36	C₅×#121	C₂²	1	1	yes	characteristic, complemented
37	C₅×#120	C₂²	1	2	yes	complemented
38	C₅×#120	C₂²	1	2	yes	complemented
39	C₄×C₅×D₄	C₂²	1	1	yes	characteristic
40	C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
41	#4099	C₂²	1	2	yes	complemented
42	#4099	C₂²	1	2	yes	complemented
43	C₂×C₂²⋊Dic₅	C₂²	1	2	yes	complemented
44	C₂×C₂²⋊Dic₅	C₂²	1	2	yes	complemented
45	C₂×C₂²⋊Dic₅	C₂²	1	2	yes	complemented
46	#4086	C₂²	1	1	yes	characteristic, complemented
47	#4086	C₂²	1	1	yes	characteristic, complemented
48	#4085	C₂²	1	1	yes	characteristic
49	#4085	C₂²	1	2	yes	complemented
50	#4085	C₂²	1	2	yes	complemented
51	#4085	C₂²	1	2	yes	complemented
52	#4085	C₂²	1	2	yes	complemented
53	#4085	C₂²	1	2	yes	complemented
54	#4085	C₂²	1	2	yes	complemented
55	#4085	C₂²	1	2	yes	complemented
56	#4085	C₂²	1	2	yes	complemented
57	#4085	C₂²	1	2	yes	complemented
58	#4085	C₂²	1	2	yes	complemented
59	#4085	C₂²	1	2	yes	complemented
60	#4084	C₂²	1	2	yes	complemented
61	#4084	C₂²	1	1	yes	characteristic, complemented
62	#4084	C₂²	1	1	yes	characteristic, complemented
63	#4084	C₂²	1	2	yes	complemented
64	#4083	C₂²	1	2	yes	complemented
65	#4083	C₂²	1	2	yes	complemented
66	#4082	C₂²	1	2	yes	complemented
67	#4081	C₂²	1	2	yes	complemented
68	#4081	C₂²	1	2	yes	complemented
69	#4081	C₂²	1	1	yes	characteristic, complemented
70	D₄×Dic₅	C₂²	1	1	yes	characteristic
71	D₄×Dic₅	C₂²	1	1	yes	characteristic
72	D₄×Dic₅	C₂²	1	1	yes	characteristic
73	D₄×Dic₅	C₂²	1	1	yes	characteristic, complemented
74	D₄×Dic₅	C₂²	1	1	yes	characteristic, complemented
75	D₄×Dic₅	C₂²	1	1	yes	characteristic, complemented
76	D₄×Dic₅	C₂²	1	1	yes	characteristic, complemented
77	D₄×Dic₅	C₂²	1	2	yes	complemented
78	D₄×Dic₅	C₂²	1	2	yes	complemented
79	D₄×Dic₅	C₂²	1	2	yes	complemented
80	D₄×Dic₅	C₂²	1	2	yes	complemented
81	D₄×Dic₅	C₂²	1	2	yes	complemented
82	#4076	C₂²	1	1	yes	characteristic, complemented
83	#4076	C₂²	1	1	yes	characteristic, complemented
84	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic, complemented
85	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic, complemented
86	C₄×C₂²⋊D₅	C₂²	1	2	yes	complemented
87	C₂×#685	C₂²	1	2	yes	complemented
88	#4072	C₂²	1	1	yes	characteristic, complemented
89	#4072	C₂²	1	1	yes	characteristic, complemented
90	C₂×C₄⋊Dic₅	C₂²	1	1	yes	characteristic, complemented
91	#4070	C₂²	1	2	yes	complemented
92	C₂×#683	C₂²	1	2	yes	complemented
93	C₂×C₄×Dic₅	C₂²	1	1	yes	characteristic, complemented
94	#4044	C₂²	1	1	yes	characteristic, complemented
95	#4044	C₂²	1	2	yes	complemented
96	#4039	C₂²	1	1	yes	characteristic, complemented
97	#4038	C₂²	1	1	yes	characteristic, complemented
98	#4036	C₂²	1	1	yes	characteristic, complemented
99	#4035	C₂²	1	1	yes	characteristic, complemented
100	#4034	C₂²	1	1	yes	characteristic, complemented
101	#4032	C₂²	1	1	yes	characteristic, complemented
102	#4032	C₂²	1	2	yes	complemented
103	#4032	C₂²	1	2	yes	complemented
104	#4031	C₂²	1	1	yes	characteristic, complemented
105	#4031	C₂²	1	2	yes	complemented
106	#4031	C₂²	1	2	yes	complemented
107	#4029	C₂²	1	2	yes	complemented
108	#4029	C₂²	1	2	yes	complemented
109	#4027	C₂²	1	2	yes	complemented
110	#4027	C₂²	1	2	yes	complemented
111	#4027	C₂²	1	2	yes	complemented
112	D₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
113	#4025	C₂²	1	1	yes	characteristic, complemented
114	#4025	C₂²	1	2	yes	complemented
115	#4024	C₂²	1	1	yes	characteristic, complemented
116	#4024	C₂²	1	2	yes	complemented
117	#4024	C₂²	1	2	yes	complemented
118	#4023	C₂²	1	2	yes	complemented
119	C₄×D₂₀	C₂²	1	1	yes	characteristic, complemented
120	#4018	C₂²	1	1	yes	characteristic, complemented
121	#4016	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
123	#3519	—	5	1	no	maximal, Sylow
124	C₂⁴×C₅	C₂³	1	2	yes	—
125	C₂⁴×C₅	C₂³	1	2	yes	—
126	C₂³×D₅	C₂³	1	2	yes	—
127	C₂×C₅×D₄	—	2	4	no	—
128	C₂×C₅×D₄	—	2	4	no	—
129	C₂×C₅×D₄	—	4	4	no	—
130	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
131	C₂×C₅×D₄	C₂³	1	2	yes	—
132	C₂×C₅×D₄	C₂³	1	2	yes	—
133	C₂×C₅×D₄	C₂³	1	2	yes	—
134	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
135	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
136	C₂×C₅×D₄	C₂³	1	2	yes	—
137	C₂×C₅×D₄	C₂³	1	2	yes	—
138	C₂×C₅×D₄	C₂³	1	2	yes	—
139	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
140	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
141	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
142	C₂²×C₄×C₅	C₂³	1	2	yes	—
143	C₂×C₂²⋊D₅	—	4	4	no	—
144	C₂×C₂²⋊D₅	—	4	4	no	—
145	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
146	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
147	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
148	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
149	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
150	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
151	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
152	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
153	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
154	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
155	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
156	C₂²×Dic₅	—	4	4	no	—
157	C₂²×Dic₅	C₂³	1	1	yes	characteristic
158	C₂²×Dic₅	C₂³	1	2	yes	—
159	C₂²×Dic₅	C₂³	1	1	yes	characteristic
160	C₂²×Dic₅	C₂³	1	2	yes	—
161	C₂²×Dic₅	C₂³	1	2	yes	—
162	C₂²×Dic₅	C₂³	1	2	yes	—
163	C₂²×Dic₅	C₂³	1	2	yes	—
164	C₂²×Dic₅	C₂³	1	2	yes	—
165	C₂²×Dic₅	C₂³	1	2	yes	—
166	C₂²×Dic₅	C₂³	1	2	yes	—
167	#711	—	4	4	no	—
168	#711	—	4	4	no	—
169	D₄×D₅	—	2	4	no	—
170	C₂×D₂₀	C₂³	1	1	yes	characteristic
171	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
172	C₂×C₄×D₅	C₂³	1	2	yes	—
173	C₂×C₄×D₅	C₂³	1	2	yes	—
174	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
175	C₂×Dic₁₀	C₂³	1	2	yes	—
176	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
177	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
178	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
179	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
180	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
181	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
182	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
183	C₄²×C₅	C₂³	1	1	yes	characteristic
184	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
185	C₂²⋊Dic₅	C₂³	1	2	yes	—
186	C₂²⋊Dic₅	C₂³	1	2	yes	—
187	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
188	C₂²⋊Dic₅	C₂³	1	2	yes	—
189	C₂²⋊Dic₅	C₂³	1	2	yes	—
190	C₂²⋊Dic₅	C₂³	1	2	yes	—
191	C₂²⋊Dic₅	C₂³	1	2	yes	—
192	C₂²⋊Dic₅	C₂³	1	2	yes	—
193	C₂²⋊Dic₅	C₂³	1	2	yes	—
194	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
195	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
196	C₂²⋊Dic₅	C₂³	1	2	yes	—
197	C₂²⋊Dic₅	C₂³	1	2	yes	—
198	#685	C₂³	1	1	yes	characteristic
199	#685	C₂³	1	1	yes	characteristic
200	#685	C₂³	1	2	yes	—
201	#685	C₂³	1	2	yes	—
202	#685	C₂³	1	2	yes	—
203	#685	C₂³	1	2	yes	—
204	#685	C₂³	1	2	yes	—
205	#685	C₂³	1	1	yes	characteristic
206	#685	C₂³	1	1	yes	characteristic
207	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
208	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
209	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
210	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
211	C₄⋊Dic₅	C₂³	1	2	yes	—
212	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
213	C₄⋊Dic₅	C₂³	1	2	yes	—
214	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
215	#683	C₂³	1	1	yes	characteristic
216	#683	C₂³	1	1	yes	characteristic
217	#683	C₂³	1	2	yes	—
218	#683	C₂³	1	2	yes	—
219	#683	C₂³	1	1	yes	characteristic
220	#683	C₂³	1	1	yes	characteristic
221	#683	C₂³	1	1	yes	characteristic
222	#683	C₂³	1	2	yes	—
223	#683	C₂³	1	2	yes	—
224	#683	C₂³	1	1	yes	characteristic
225	C₄×Dic₅	C₂³	1	1	yes	characteristic
226	C₄×Dic₅	C₂³	1	1	yes	characteristic
227	C₄×Dic₅	C₂³	1	1	yes	characteristic
228	C₄×Dic₅	C₂³	1	2	yes	—
229	C₄×Dic₅	C₂³	1	2	yes	—
230	C₄×Dic₅	C₂³	1	1	yes	characteristic
231	C₄×Dic₅	C₂³	1	1	yes	characteristic
232	#555	—	5	1	no	—
233	#554	—	5	1	no	—
234	#553	—	5	2	no	—
235	#553	—	5	1	no	—
236	#553	—	5	1	no	—
237	#550	—	5	1	no	—
238	#546	—	5	2	no	—
239	#546	—	5	2	no	—
240	#546	—	5	2	no	—
241	D₄²	—	5	1	no	—
242	D₄²	—	5	1	no	—
243	D₄²	D₅	1	1	yes	characteristic, complemented
244	#540	—	5	1	no	—
245	#540	—	5	1	no	—
246	#538	—	5	2	no	—
247	#538	—	5	2	no	—
248	#532	—	5	1	no	—
249	#529	—	5	1	no	—
250	#525	—	5	2	no	—
251	C₂×#121	—	5	2	no	—
252	#518	—	5	1	no	—
253	#518	—	5	1	no	—
254	C₂×C₄×D₄	—	5	1	no	—
255	C₂³×C₅	—	2	4	no	—
256	C₂³×C₅	—	2	4	no	—
257	C₂³×C₅	—	2	4	no	—
258	C₂³×C₅	—	4	2	no	—
259	C₂³×C₅	—	4	2	no	—
260	C₂³×C₅	—	4	2	no	—
261	C₂³×C₅	C₂⁴	1	1	yes	characteristic
262	C₂³×C₅	C₂⁴	1	2	yes	—
263	C₂³×C₅	C₂⁴	1	2	yes	—
264	C₂³×C₅	C₂⁴	1	2	yes	—
265	C₂³×C₅	C₂⁴	1	1	yes	characteristic
266	C₂²×D₅	—	2	4	no	—
267	C₂²×D₅	—	4	2	no	—
268	C₂²×D₅	—	4	2	no	—
269	C₂²×D₅	C₂⁴	1	1	yes	characteristic
270	C₂²×D₅	C₂⁴	1	2	yes	—
271	C₅×D₄	—	2	4	no	—
272	C₅×D₄	—	2	4	no	—
273	C₅×D₄	—	2	4	no	—
274	C₅×D₄	—	2	2	no	—
275	C₅×D₄	—	2	2	no	—
276	C₅×D₄	—	2	2	no	—
277	C₅×D₄	—	4	2	no	—
278	C₅×D₄	—	4	2	no	—
279	C₅×D₄	—	4	2	no	—
280	C₅×D₄	#41	1	4	yes	complemented
281	C₂×C₄×C₅	—	2	2	no	—
282	C₂×C₄×C₅	—	2	2	no	—
283	C₂×C₄×C₅	—	4	2	no	—
284	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
285	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
286	C₂×C₄×C₅	C₂⁴	1	2	yes	—
287	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
288	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
289	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
290	C₂²⋊D₅	—	2	4	no	—
291	C₂²⋊D₅	—	2	4	no	—
292	C₂²⋊D₅	—	2	2	no	—
293	C₂²⋊D₅	—	2	4	no	—
294	C₂²⋊D₅	—	2	2	no	—
295	C₂²⋊D₅	—	4	2	no	—
296	C₂²⋊D₅	—	4	2	no	—
297	C₂²⋊D₅	—	4	2	no	—
298	C₂²⋊D₅	—	4	2	no	—
299	C₂²⋊D₅	—	4	2	no	—
300	C₂²⋊D₅	—	4	2	no	—
301	C₂×Dic₅	—	2	2	no	—
302	C₂×Dic₅	—	2	4	no	—
303	C₂×Dic₅	—	2	2	no	—
304	C₂×Dic₅	—	2	4	no	—
305	C₂×Dic₅	—	4	2	no	—
306	C₂×Dic₅	—	4	2	no	—
307	C₂×Dic₅	—	4	2	no	—
308	C₂×Dic₅	—	4	2	no	—
309	C₂×Dic₅	—	4	2	no	—
310	C₂×Dic₅	—	4	2	no	—
311	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
312	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
313	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
314	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
315	C₂×Dic₅	C₂⁴	1	2	yes	—
316	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
317	C₂×Dic₅	C₂⁴	1	2	yes	—
318	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
319	C₂×Dic₅	C₂⁴	1	2	yes	—
320	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
321	D₂₀	—	2	2	no	—
322	C₄×D₅	—	2	2	no	—
323	C₄×D₅	—	4	2	no	—
324	C₄×D₅	—	4	2	no	—
325	Dic₁₀	—	2	2	no	—
326	Dic₁₀	—	4	2	no	—
327	C₂×#41	—	5	2	no	—
328	C₂×#41	—	5	2	no	—
329	C₂²×D₄	—	5	2	no	—
330	C₂²×D₄	—	5	2	no	—
331	C₂²×D₄	—	5	1	no	—
332	C₂²×D₄	C₂×D₅	1	1	yes	characteristic
333	C₂²×D₄	C₂×D₅	1	1	yes	characteristic
334	C₂²×D₄	C₂×D₅	1	2	yes	complemented
335	C₂³×C₄	—	5	2	no	—
336	C₄⋊Q₈	—	5	1	no	—
337	#127	—	5	1	no	—
338	#127	—	5	1	no	—
339	#127	C₂×D₅	1	1	yes	characteristic, complemented
340	#126	—	5	1	no	—
341	#126	—	5	2	no	—
342	#126	—	5	1	no	—
343	#126	—	5	2	no	—
344	#125	—	5	1	no	—
345	#125	—	5	1	no	—
346	#125	—	5	1	no	—
347	#124	—	5	2	no	—
348	#124	—	5	1	no	—
349	#124	—	5	2	no	—
350	#124	—	5	2	no	—
351	#123	—	5	2	no	—
352	#123	—	5	1	no	—
353	#123	—	5	2	no	—
354	#123	—	5	2	no	—
355	#123	—	5	1	no	—
356	#123	—	5	2	no	—
357	#123	—	5	2	no	—
358	#123	—	5	2	no	—
359	C₂²⋊Q₈	—	5	2	no	—
360	C₂²⋊Q₈	—	5	1	no	—
361	C₂²⋊Q₈	—	5	2	no	—
362	C₂²⋊Q₈	—	5	2	no	—
363	#121	—	5	1	no	—
364	#121	—	5	2	no	—
365	#121	—	5	2	no	—
366	#121	—	5	2	no	—
367	#121	—	5	2	no	—
368	#121	—	5	2	no	—
369	#121	—	5	2	no	—
370	#121	—	5	2	no	—
371	#121	—	5	2	no	—
372	#121	—	5	2	no	—
373	#121	—	5	2	no	—
374	#121	—	5	2	no	—
375	#121	—	5	1	no	—
376	#121	—	5	1	no	—
377	#121	—	5	2	no	—
378	#121	—	5	2	no	—
379	#121	—	5	1	no	—
380	#121	—	5	1	no	—
381	#121	C₂×D₅	1	1	yes	characteristic, complemented
382	#121	C₂×D₅	1	2	yes	complemented
383	#121	C₂×D₅	1	1	yes	characteristic, complemented
384	#120	—	5	2	no	—
385	#120	—	5	2	no	—
386	#120	—	5	2	no	—
387	#120	—	5	2	no	—
388	#120	C₂×D₅	1	2	yes	complemented
389	#120	C₂×D₅	1	2	yes	complemented
390	C₄×Q₈	—	5	1	no	—
391	C₄×D₄	—	5	1	no	—
392	C₄×D₄	—	5	2	no	—
393	C₄×D₄	—	5	1	no	—
394	C₄×D₄	—	5	1	no	—
395	C₄×D₄	—	5	2	no	—
396	C₄×D₄	—	5	1	no	—
397	C₄×D₄	—	5	2	no	—
398	C₄×D₄	—	5	1	no	—
399	C₄×D₄	—	5	1	no	—
400	C₄×D₄	—	5	2	no	—
401	C₄×D₄	—	5	1	no	—
402	C₄×D₄	—	5	2	no	—
403	C₄×D₄	—	5	2	no	—
404	C₄×D₄	—	5	1	no	—
405	C₄×D₄	—	5	1	no	—
406	C₄×D₄	—	5	1	no	—
407	C₄×D₄	—	5	2	no	—
408	C₄×D₄	—	5	2	no	—
409	C₄×D₄	—	5	2	no	—
410	C₄×D₄	—	5	1	no	—
411	C₄×D₄	C₂×D₅	1	1	yes	characteristic
412	C₄×D₄	C₂×D₅	1	1	yes	characteristic, complemented
413	#117	—	5	1	no	—
414	#117	—	5	1	no	—
415	#117	—	5	1	no	—
416	#117	—	5	2	no	—
417	#117	—	5	1	no	—
418	C₂×C₄⋊C₄	—	5	1	no	—
419	C₂×C₄⋊C₄	—	5	2	no	—
420	C₂×C₂²⋊C₄	—	5	2	no	—
421	C₂×C₂²⋊C₄	—	5	2	no	—
422	C₂×C₂²⋊C₄	—	5	2	no	—
423	C₂×C₂²⋊C₄	—	5	2	no	—
424	C₂×C₂²⋊C₄	—	5	2	no	—
425	C₂×C₄²	—	5	1	no	—
426	C₂²×C₅	—	2	1	no	—
427	C₂²×C₅	—	2	1	no	—
428	C₂²×C₅	—	2	2	no	—
429	C₂²×C₅	—	2	2	no	—
430	C₂²×C₅	—	2	1	no	—
431	C₂²×C₅	—	2	2	no	—
432	C₂²×C₅	—	2	2	no	—
433	C₂²×C₅	—	2	2	no	—
434	C₂²×C₅	—	2	2	no	—
435	C₂²×C₅	—	2	2	no	—
436	C₂²×C₅	—	2	1	no	—
437	C₂²×C₅	—	2	2	no	—
438	C₂²×C₅	—	2	1	no	—
439	C₂²×C₅	—	4	8	no	—
440	C₂²×C₅	—	8	4	no	—
441	C₂²×C₅	C₂×#41	1	4	yes	—
442	C₂²×C₅	H(5,𝔽₂)	1	2	yes	—
443	C₂²×C₅	C₂⁵	1	1	yes	characteristic
444	C₂×D₅	—	2	1	no	—
445	C₂×D₅	—	2	2	no	—
446	C₂×D₅	—	2	2	no	—
447	C₂×D₅	—	2	2	no	—
448	C₂×D₅	—	2	1	no	—
449	C₂×D₅	—	2	1	no	—
450	C₂×D₅	—	8	4	no	—
451	C₄×C₅	—	2	1	no	—
452	C₄×C₅	—	2	1	no	—
453	C₄×C₅	—	2	1	no	—
454	C₄×C₅	—	2	2	no	—
455	C₄×C₅	—	2	1	no	—
456	C₄×C₅	C₂×#41	1	2	yes	—
457	Dic₅	—	2	1	no	—
458	Dic₅	—	2	1	no	—
459	Dic₅	—	2	1	no	—
460	Dic₅	—	2	2	no	—
461	Dic₅	—	2	1	no	—
462	Dic₅	—	2	2	no	—
463	Dic₅	—	2	1	no	—
464	Dic₅	—	2	2	no	—
465	Dic₅	—	2	1	no	—
466	Dic₅	H(5,𝔽₂)	1	2	yes	—
467	C₂⁴	—	5	2	no	—
468	C₂⁴	C₂²×D₅	1	2	yes	—
469	C₂⁴	C₂²×D₅	1	2	yes	—
470	#41	—	20	4	no	—
471	#41	—	20	4	no	—
472	C₂×Q₈	—	5	1	no	—
473	C₂×Q₈	—	5	2	no	—
474	C₂×D₄	—	2	4	no	—
475	C₂×D₄	—	2	4	no	—
476	C₂×D₄	—	4	4	no	—
477	C₂×D₄	—	5	2	no	—
478	C₂×D₄	—	5	2	no	—
479	C₂×D₄	—	5	1	no	—
480	C₂×D₄	—	5	1	no	—
481	C₂×D₄	—	5	2	no	—
482	C₂×D₄	—	5	2	no	—
483	C₂×D₄	—	5	2	no	—
484	C₂×D₄	—	5	2	no	—
485	C₂×D₄	—	5	2	no	—
486	C₂×D₄	—	5	2	no	—
487	C₂×D₄	—	5	2	no	—
488	C₂×D₄	—	5	1	no	—
489	C₂×D₄	—	10	4	no	—
490	C₂×D₄	—	20	4	no	—
491	C₂×D₄	—	20	4	no	—
492	C₂×D₄	C₂²×D₅	1	2	yes	—
493	C₂×D₄	C₂²×D₅	1	2	yes	—
494	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
495	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
496	C₂×D₄	C₂²×D₅	1	2	yes	—
497	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
498	C₂×D₄	C₂²×D₅	1	2	yes	—
499	C₂×D₄	C₂²×D₅	1	2	yes	—
500	C₂×D₄	C₂²×D₅	1	2	yes	—
501	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
502	C₂²×C₄	—	5	1	no	—
503	C₂²×C₄	—	5	1	no	—
504	C₂²×C₄	—	5	2	no	—
505	C₂²×C₄	—	5	2	no	—
506	C₂²×C₄	—	5	2	no	—
507	C₂²×C₄	—	5	2	no	—
508	C₂²×C₄	—	5	2	no	—
509	C₂²×C₄	—	5	2	no	—
510	C₂²×C₄	—	5	2	no	—
511	C₂²×C₄	—	5	2	no	—
512	C₂²×C₄	—	5	1	no	—
513	C₂²×C₄	—	5	2	no	—
514	C₂²×C₄	—	5	2	no	—
515	C₂²×C₄	—	20	4	no	—
516	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
517	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
518	C₂²×C₄	C₂²×D₅	1	2	yes	—
519	C₄⋊C₄	—	5	1	no	—
520	C₄⋊C₄	—	5	1	no	—
521	C₄⋊C₄	—	5	2	no	—
522	C₄⋊C₄	—	5	1	no	—
523	C₄⋊C₄	—	5	2	no	—
524	C₄⋊C₄	—	5	2	no	—
525	C₄⋊C₄	—	5	2	no	—
526	C₄⋊C₄	—	5	1	no	—
527	C₄⋊C₄	—	5	1	no	—
528	C₄⋊C₄	—	5	1	no	—
529	C₄⋊C₄	—	5	1	no	—
530	C₄⋊C₄	—	5	1	no	—
531	C₄⋊C₄	—	5	1	no	—
532	C₄⋊C₄	—	5	1	no	—
533	C₄⋊C₄	—	5	2	no	—
534	C₄⋊C₄	—	5	2	no	—
535	C₄⋊C₄	—	5	1	no	—
536	C₄⋊C₄	—	5	1	no	—
537	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
538	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
539	C₂²⋊C₄	—	5	2	no	—
540	C₂²⋊C₄	—	5	1	no	—
541	C₂²⋊C₄	—	5	2	no	—
542	C₂²⋊C₄	—	5	1	no	—
543	C₂²⋊C₄	—	5	2	no	—
544	C₂²⋊C₄	—	5	2	no	—
545	C₂²⋊C₄	—	5	2	no	—
546	C₂²⋊C₄	—	5	2	no	—
547	C₂²⋊C₄	—	5	2	no	—
548	C₂²⋊C₄	—	5	2	no	—
549	C₂²⋊C₄	—	5	2	no	—
550	C₂²⋊C₄	—	5	1	no	—
551	C₂²⋊C₄	—	5	1	no	—
552	C₂²⋊C₄	—	5	2	no	—
553	C₂²⋊C₄	—	5	1	no	—
554	C₂²⋊C₄	—	5	2	no	—
555	C₂²⋊C₄	—	5	1	no	—
556	C₂²⋊C₄	—	5	2	no	—
557	C₂²⋊C₄	—	5	2	no	—
558	C₂²⋊C₄	—	5	1	no	—
559	C₂²⋊C₄	—	5	1	no	—
560	C₂²⋊C₄	—	5	2	no	—
561	C₂²⋊C₄	—	5	2	no	—
562	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
563	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
564	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
565	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
566	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
567	C₄²	—	5	1	no	—
568	C₄²	—	5	1	no	—
569	C₄²	—	5	1	no	—
570	C₄²	—	5	1	no	—
571	C₄²	—	5	2	no	—
572	C₄²	—	5	2	no	—
573	C₄²	—	5	1	no	—
574	C₄²	C₂²×D₅	1	1	yes	characteristic
575	C₂×C₅	—	2	4	no	—
576	C₂×C₅	—	2	2	no	—
577	C₂×C₅	—	4	2	no	—
578	C₂×C₅	—	4	2	no	—
579	C₂×C₅	—	4	1	no	—
580	C₂×C₅	C₂²×#41	1	1	yes	characteristic
581	C₂×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
582	C₂×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
583	D₅	—	4	2	no	—
584	D₅	—	4	1	no	—
585	C₂³	—	2	4	no	—
586	C₂³	—	2	4	no	—
587	C₂³	—	2	4	no	—
588	C₂³	—	4	2	no	—
589	C₂³	—	4	2	no	—
590	C₂³	—	4	2	no	—
591	C₂³	—	5	1	no	—
592	C₂³	—	5	2	no	—
593	C₂³	—	10	4	no	—
594	C₂³	—	20	2	no	—
595	C₂³	—	20	2	no	—
596	C₂³	C₂³×D₅	1	1	yes	characteristic
597	C₂³	C₂³×D₅	1	2	yes	—
598	C₂³	C₂³×D₅	1	2	yes	—
599	C₂³	C₂³×D₅	1	2	yes	—
600	C₂³	C₂³×D₅	1	1	yes	characteristic
601	Q₈	—	10	2	no	—
602	Q₈	—	20	2	no	—
603	D₄	—	2	4	no	—
604	D₄	—	2	4	no	—
605	D₄	—	2	2	no	—
606	D₄	—	2	4	no	—
607	D₄	—	2	2	no	—
608	D₄	—	2	2	no	—
609	D₄	—	4	2	no	—
610	D₄	—	4	2	no	—
611	D₄	—	4	2	no	—
612	D₄	—	10	2	no	—
613	D₄	—	10	4	no	—
614	D₄	—	10	4	no	—
615	D₄	—	10	2	no	—
616	D₄	—	10	4	no	—
617	D₄	—	10	2	no	—
618	D₄	—	20	2	no	—
619	D₄	—	20	2	no	—
620	D₄	—	20	2	no	—
621	D₄	—	20	2	no	—
622	D₄	—	20	2	no	—
623	D₄	—	20	2	no	—
624	D₄	#711	1	4	yes	complemented
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	4	2	no	—
628	C₂×C₄	—	5	1	no	—
629	C₂×C₄	—	5	1	no	—
630	C₂×C₄	—	5	1	no	—
631	C₂×C₄	—	5	1	no	—
632	C₂×C₄	—	5	2	no	—
633	C₂×C₄	—	5	1	no	—
634	C₂×C₄	—	5	2	no	—
635	C₂×C₄	—	5	1	no	—
636	C₂×C₄	—	5	1	no	—
637	C₂×C₄	—	5	2	no	—
638	C₂×C₄	—	10	2	no	—
639	C₂×C₄	—	10	4	no	—
640	C₂×C₄	—	10	4	no	—
641	C₂×C₄	—	10	2	no	—
642	C₂×C₄	—	10	2	no	—
643	C₂×C₄	—	20	2	no	—
644	C₂×C₄	—	20	2	no	—
645	C₂×C₄	—	20	2	no	—
646	C₂×C₄	—	20	2	no	—
647	C₂×C₄	—	20	2	no	—
648	C₂×C₄	—	20	2	no	—
649	C₂×C₄	—	20	2	no	—
650	C₂×C₄	—	20	2	no	—
651	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
652	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
653	C₂×C₄	C₂³×D₅	1	2	yes	—
654	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
655	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
656	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
657	C₅	#3519	1	1	yes	characteristic, complemented, Sylow
658	C₂²	—	2	1	no	—
659	C₂²	—	2	2	no	—
660	C₂²	—	2	1	no	—
661	C₂²	—	2	2	no	—
662	C₂²	—	2	1	no	—
663	C₂²	—	2	2	no	—
664	C₂²	—	2	2	no	—
665	C₂²	—	2	2	no	—
666	C₂²	—	2	1	no	—
667	C₂²	—	2	2	no	—
668	C₂²	—	2	2	no	—
669	C₂²	—	2	2	no	—
670	C₂²	—	2	1	no	—
671	C₂²	—	4	8	no	—
672	C₂²	—	8	4	no	—
673	C₂²	—	10	1	no	—
674	C₂²	—	10	2	no	—
675	C₂²	—	10	2	no	—
676	C₂²	—	10	1	no	—
677	C₂²	—	10	2	no	—
678	C₂²	—	10	1	no	—
679	C₂²	—	40	4	no	—
680	C₂²	C₂×#711	1	4	yes	—
681	C₂²	#4144	1	2	yes	—
682	C₂²	C₂⁴×D₅	1	1	yes	characteristic
683	C₄	—	2	1	no	—
684	C₄	—	2	1	no	—
685	C₄	—	2	1	no	—
686	C₄	—	2	2	no	—
687	C₄	—	2	1	no	—
688	C₄	—	5	2	no	—
689	C₄	—	10	1	no	—
690	C₄	—	10	1	no	—
691	C₄	—	10	1	no	—
692	C₄	—	10	1	no	—
693	C₄	—	10	2	no	—
694	C₄	—	10	1	no	—
695	C₄	—	10	2	no	—
696	C₄	—	10	2	no	—
697	C₄	—	10	1	no	—
698	C₄	C₂×#711	1	2	yes	—
699	C₂	—	2	2	no	—
700	C₂	—	2	4	no	—
701	C₂	—	4	2	no	—
702	C₂	—	4	1	no	—
703	C₂	—	4	2	no	—
704	C₂	—	20	1	no	—
705	C₂	—	20	2	no	—
706	C₂	C₂²×#711	1	1	yes	characteristic
707	C₂	C₂×#4144	1	1	yes	characteristic
708	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×D₄²	C₂
hypercenter	D₄²	D₅
hypocenter	C₅	#3519
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ D₄²

Complements

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

N	H ≅ G/N	type
1. C₅×D₄²	C₂	semidirect
2. #66140	C₂	semidirect
3. C₂×#4085	C₂	semidirect
4. D₄×C₂²⋊D₅	C₂	semidirect
5. D₄×C₂²⋊D₅	C₂	semidirect
6. #66132	C₂	semidirect
7. C₂×D₄×Dic₅	C₂	semidirect
8. #66053	C₂	semidirect
9. #66052	C₂	semidirect
10. #65953	C₂	semidirect
11. #65952	C₂	semidirect
12. #65951	C₂	semidirect
13. #65950	C₂	semidirect
14. #65935	C₂	semidirect
15. #65930	C₂	semidirect
16. #65927	C₂	semidirect
17. #65925	C₂	semidirect
18. #65925	C₂	semidirect
19. #65920	C₂	semidirect
20. #65899	C₂	semidirect
21. #65879	C₂	semidirect
22. #65873	C₂	semidirect
23. #65872	C₂	semidirect
26. C₂²×C₅×D₄	C₂²	semidirect
27. C₂²×C₂²⋊D₅	C₂²	semidirect
28. C₂²×C₂²⋊D₅	C₂²	semidirect
29. C₂³×Dic₅	C₂²	semidirect
30. C₂×#711	C₂²	semidirect
31. C₂×#711	C₂²	semidirect
33. C₅×#127	C₂²	semidirect
34. C₅×#121	C₂²	semidirect
35. C₅×#121	C₂²	semidirect
36. C₅×#121	C₂²	semidirect
37. C₅×#120	C₂²	semidirect
38. C₅×#120	C₂²	semidirect
40. C₄×C₅×D₄	C₂²	semidirect
41. #4099	C₂²	semidirect
42. #4099	C₂²	semidirect
43. C₂×C₂²⋊Dic₅	C₂²	semidirect
44. C₂×C₂²⋊Dic₅	C₂²	semidirect
45. C₂×C₂²⋊Dic₅	C₂²	semidirect
46. #4086	C₂²	semidirect
47. #4086	C₂²	semidirect
49. #4085	C₂²	semidirect
50. #4085	C₂²	semidirect
51. #4085	C₂²	semidirect
52. #4085	C₂²	semidirect
53. #4085	C₂²	semidirect
54. #4085	C₂²	semidirect
55. #4085	C₂²	semidirect
56. #4085	C₂²	semidirect
57. #4085	C₂²	semidirect
58. #4085	C₂²	semidirect
59. #4085	C₂²	semidirect
60. #4084	C₂²	semidirect
61. #4084	C₂²	semidirect
62. #4084	C₂²	semidirect
63. #4084	C₂²	semidirect
64. #4083	C₂²	semidirect
65. #4083	C₂²	semidirect
66. #4082	C₂²	semidirect
67. #4081	C₂²	semidirect
68. #4081	C₂²	semidirect
69. #4081	C₂²	semidirect
73. D₄×Dic₅	C₂²	semidirect
74. D₄×Dic₅	C₂²	semidirect
75. D₄×Dic₅	C₂²	semidirect
76. D₄×Dic₅	C₂²	semidirect
77. D₄×Dic₅	C₂²	semidirect
78. D₄×Dic₅	C₂²	semidirect
79. D₄×Dic₅	C₂²	semidirect
80. D₄×Dic₅	C₂²	semidirect
81. D₄×Dic₅	C₂²	semidirect
82. #4076	C₂²	semidirect
83. #4076	C₂²	semidirect
84. C₄×C₂²⋊D₅	C₂²	semidirect
85. C₄×C₂²⋊D₅	C₂²	semidirect
86. C₄×C₂²⋊D₅	C₂²	semidirect
87. C₂×#685	C₂²	semidirect
88. #4072	C₂²	semidirect
89. #4072	C₂²	semidirect
90. C₂×C₄⋊Dic₅	C₂²	semidirect
91. #4070	C₂²	semidirect
92. C₂×#683	C₂²	semidirect
93. C₂×C₄×Dic₅	C₂²	semidirect
94. #4044	C₂²	semidirect
95. #4044	C₂²	semidirect
96. #4039	C₂²	semidirect
97. #4038	C₂²	semidirect
98. #4036	C₂²	semidirect
99. #4035	C₂²	semidirect
100. #4034	C₂²	semidirect
101. #4032	C₂²	semidirect
102. #4032	C₂²	semidirect
103. #4032	C₂²	semidirect
104. #4031	C₂²	semidirect
105. #4031	C₂²	semidirect
106. #4031	C₂²	semidirect
107. #4029	C₂²	semidirect
108. #4029	C₂²	semidirect
109. #4027	C₂²	semidirect
110. #4027	C₂²	semidirect
111. #4027	C₂²	semidirect
112. D₅×C₂²⋊C₄	C₂²	semidirect
113. #4025	C₂²	semidirect
114. #4025	C₂²	semidirect
115. #4024	C₂²	semidirect
116. #4024	C₂²	semidirect
117. #4024	C₂²	semidirect
118. #4023	C₂²	semidirect
119. C₄×D₂₀	C₂²	semidirect
120. #4018	C₂²	semidirect
121. #4016	C₂²	semidirect
122. C₄×Dic₁₀	C₂²	semidirect
243. D₄²	D₅	semidirect
280. C₅×D₄	#41	semidirect
334. C₂²×D₄	C₂×D₅	semidirect
339. #127	C₂×D₅	semidirect
381. #121	C₂×D₅	semidirect
382. #121	C₂×D₅	semidirect
383. #121	C₂×D₅	semidirect
388. #120	C₂×D₅	semidirect
389. #120	C₂×D₅	semidirect
412. C₄×D₄	C₂×D₅	semidirect
624. D₄	#711	semidirect
657. C₅	#3519	semidirect

Maximal subgroups

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

subgroup	index
C₅×D₄²	2
#66140	2
C₂×#4085	2
D₄×C₂²⋊D₅	2
#66132	2
C₂×D₄×Dic₅	2
#66053	2
#66052	2
#65953	2
#65952	2
#65951	2
#65950	2
#65935	2
#65930	2
#65927	2
#65925	2
#65920	2
#65899	2
#65879	2
#65873	2
#65872	2
#3519	5