Subgroups — #10617772

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×#518	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×C₂²⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×C₂²⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
4	#65896	C₂	1	1	yes	maximal, characteristic, complemented
5	#65894	C₂	1	2	yes	maximal, complemented
6	#65892	C₂	1	1	yes	maximal, characteristic, complemented
7	#65887	C₂	1	1	yes	maximal, characteristic, complemented
8	#65884	C₂	1	2	yes	maximal, complemented
9	D₄×D₂₀	C₂	1	1	yes	maximal, characteristic, complemented
10	#65882	C₂	1	1	yes	maximal, characteristic, complemented
11	#65881	C₂	1	2	yes	maximal, complemented
12	#65879	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×D₄×D₅	C₂	1	1	yes	maximal, characteristic, complemented
14	#65874	C₂	1	2	yes	maximal, complemented
15	#65873	C₂	1	1	yes	maximal, characteristic, complemented
16	#65869	C₂	1	1	yes	maximal, characteristic, complemented
17	#65866	C₂	1	1	yes	maximal, characteristic, complemented
18	#65864	C₂	1	1	yes	maximal, characteristic, complemented
19	#65862	C₂	1	1	yes	maximal, characteristic, complemented
20	#65828	C₂	1	2	yes	maximal, complemented
21	#65824	C₂	1	2	yes	maximal, complemented
22	#65824	C₂	1	2	yes	maximal, complemented
23	C₂×#4030	C₂	1	2	yes	maximal, complemented
24	C₂²×C₅×D₄	C₂²	1	1	yes	characteristic
25	C₂²×C₂²⋊D₅	C₂²	1	2	yes	complemented
26	C₂²×C₂²⋊D₅	C₂²	1	2	yes	complemented
27	C₂×D₄×D₅	C₂²	1	1	yes	characteristic
28	C₂×D₄×D₅	C₂²	1	1	yes	characteristic
29	C₂×#709	C₂²	1	2	yes	complemented
30	C₂×#709	C₂²	1	2	yes	complemented
31	C₂²×D₂₀	C₂²	1	2	yes	complemented
32	C₂²×C₄×D₅	C₂²	1	2	yes	complemented
33	C₄×C₅×D₄	C₂²	1	1	yes	characteristic
34	C₄×C₅×D₄	C₂²	1	1	yes	characteristic
35	C₄×C₅×D₄	C₂²	1	2	yes	complemented
36	C₄×C₅×D₄	C₂²	1	2	yes	complemented
37	C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
38	C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
39	C₅×#117	C₂²	1	1	yes	characteristic, complemented
40	C₅×#117	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
42	C₂×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
43	#4099	C₂²	1	2	yes	complemented
44	#4099	C₂²	1	2	yes	complemented
45	#4086	C₂²	1	1	yes	characteristic, complemented
46	#4086	C₂²	1	1	yes	characteristic, complemented
47	#4085	C₂²	1	2	yes	complemented
48	#4085	C₂²	1	2	yes	complemented
49	#4084	C₂²	1	1	yes	characteristic, complemented
50	#4084	C₂²	1	1	yes	characteristic, complemented
51	#4083	C₂²	1	2	yes	complemented
52	#4083	C₂²	1	2	yes	complemented
53	D₄×Dic₅	C₂²	1	1	yes	characteristic
54	D₄×Dic₅	C₂²	1	1	yes	characteristic
55	#4076	C₂²	1	2	yes	complemented
56	#4076	C₂²	1	2	yes	complemented
57	#4076	C₂²	1	2	yes	complemented
58	#4076	C₂²	1	1	yes	characteristic, complemented
59	#4076	C₂²	1	1	yes	characteristic, complemented
60	#4075	C₂²	1	2	yes	complemented
61	#4075	C₂²	1	2	yes	complemented
62	C₄×C₂²⋊D₅	C₂²	1	2	yes	complemented
63	C₄×C₂²⋊D₅	C₂²	1	2	yes	complemented
64	C₄×C₂²⋊D₅	C₂²	1	2	yes	complemented
65	C₄×C₂²⋊D₅	C₂²	1	2	yes	complemented
66	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic, complemented
67	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic, complemented
68	C₂×#685	C₂²	1	2	yes	complemented
69	#4070	C₂²	1	2	yes	complemented
70	C₂×#683	C₂²	1	2	yes	complemented
71	#4044	C₂²	1	1	yes	characteristic, complemented
72	#4042	C₂²	1	1	yes	characteristic, complemented
73	#4041	C₂²	1	1	yes	characteristic, complemented
74	#4041	C₂²	1	1	yes	characteristic, complemented
75	#4040	C₂²	1	1	yes	characteristic, complemented
76	#4040	C₂²	1	2	yes	complemented
77	#4040	C₂²	1	2	yes	complemented
78	#4039	C₂²	1	1	yes	characteristic, complemented
79	#4039	C₂²	1	1	yes	characteristic, complemented
80	#4038	C₂²	1	1	yes	characteristic, complemented
81	D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
82	#4036	C₂²	1	1	yes	characteristic, complemented
83	#4035	C₂²	1	1	yes	characteristic, complemented
84	#4034	C₂²	1	1	yes	characteristic, complemented
85	#4031	C₂²	1	1	yes	characteristic, complemented
86	#4031	C₂²	1	2	yes	complemented
87	#4031	C₂²	1	2	yes	complemented
88	#4030	C₂²	1	1	yes	characteristic
89	#4030	C₂²	1	2	yes	complemented
90	#4030	C₂²	1	2	yes	complemented
91	#4030	C₂²	1	2	yes	complemented
92	#4030	C₂²	1	2	yes	complemented
93	#4030	C₂²	1	2	yes	complemented
94	#4030	C₂²	1	2	yes	complemented
95	#4030	C₂²	1	2	yes	complemented
96	#4030	C₂²	1	2	yes	complemented
97	#4030	C₂²	1	2	yes	complemented
98	#4029	C₂²	1	1	yes	characteristic, complemented
99	#4029	C₂²	1	2	yes	complemented
100	#4029	C₂²	1	2	yes	complemented
101	#4028	C₂²	1	2	yes	complemented
102	#4028	C₂²	1	2	yes	complemented
103	#4027	C₂²	1	2	yes	complemented
104	#4027	C₂²	1	2	yes	complemented
105	D₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
106	D₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
107	#4025	C₂²	1	1	yes	characteristic, complemented
108	#4025	C₂²	1	2	yes	complemented
109	#4024	C₂²	1	2	yes	complemented
110	#4024	C₂²	1	2	yes	complemented
111	#4022	C₂²	1	2	yes	complemented
112	#4021	C₂²	1	2	yes	complemented
113	#4020	C₂²	1	1	yes	characteristic, complemented
114	C₄×D₂₀	C₂²	1	1	yes	characteristic, complemented
115	C₄×D₂₀	C₂²	1	2	yes	complemented
116	C₄×D₂₀	C₂²	1	1	yes	characteristic, complemented
117	C₄×D₂₀	C₂²	1	1	yes	characteristic, complemented
118	#4018	C₂²	1	1	yes	characteristic, complemented
119	#4018	C₂²	1	2	yes	complemented
120	C₄²×D₅	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	C₂³×D₅	C₂³	1	2	yes	—
126	C₂³×D₅	C₂³	1	2	yes	—
127	C₂×C₅×D₄	—	2	4	no	—
128	C₂×C₅×D₄	C₂³	1	2	yes	—
129	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
130	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
131	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
132	C₂²×C₄×C₅	C₂³	1	2	yes	—
133	C₂²×C₄×C₅	C₂³	1	2	yes	—
134	C₂²×C₄×C₅	C₂³	1	2	yes	—
135	C₂²×C₄×C₅	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₅	—	4	4	no	—
137	C₂×C₂²⋊D₅	—	4	4	no	—
138	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
139	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
140	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
141	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
142	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
143	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
144	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
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	2	yes	—
149	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
150	C₂²×Dic₅	C₂³	1	2	yes	—
151	C₂²×Dic₅	C₂³	1	2	yes	—
152	D₄×D₅	—	2	4	no	—
153	D₄×D₅	—	2	4	no	—
154	#709	—	4	4	no	—
155	#709	—	4	4	no	—
156	C₂×D₂₀	—	4	4	no	—
157	C₂×D₂₀	C₂³	1	1	yes	characteristic
158	C₂×D₂₀	C₂³	1	2	yes	—
159	C₂×D₂₀	C₂³	1	1	yes	characteristic
160	C₂×D₂₀	C₂³	1	1	yes	characteristic
161	C₂×D₂₀	C₂³	1	2	yes	—
162	C₂×D₂₀	C₂³	1	2	yes	—
163	C₂×D₂₀	C₂³	1	2	yes	—
164	C₂×C₄×D₅	—	4	4	no	—
165	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
166	C₂×C₄×D₅	C₂³	1	2	yes	—
167	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
168	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
169	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
170	C₂×C₄×D₅	C₂³	1	2	yes	—
171	C₂×C₄×D₅	C₂³	1	2	yes	—
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×C₄⋊C₄	C₂³	1	1	yes	characteristic
179	C₅×C₄⋊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	1	yes	characteristic
183	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
184	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
185	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
186	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
187	C₄²×C₅	C₂³	1	1	yes	characteristic
188	C₄²×C₅	C₂³	1	1	yes	characteristic
189	C₄²×C₅	C₂³	1	2	yes	—
190	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
191	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
192	C₂²⋊Dic₅	C₂³	1	2	yes	—
193	C₂²⋊Dic₅	C₂³	1	2	yes	—
194	C₂²⋊Dic₅	C₂³	1	2	yes	—
195	C₂²⋊Dic₅	C₂³	1	2	yes	—
196	#685	C₂³	1	2	yes	—
197	#685	C₂³	1	1	yes	characteristic
198	#685	C₂³	1	2	yes	—
199	#685	C₂³	1	1	yes	characteristic
200	#685	C₂³	1	1	yes	characteristic
201	#685	C₂³	1	2	yes	—
202	#685	C₂³	1	2	yes	—
203	#685	C₂³	1	1	yes	characteristic
204	#685	C₂³	1	1	yes	characteristic
205	#685	C₂³	1	2	yes	—
206	#685	C₂³	1	1	yes	characteristic
207	#685	C₂³	1	2	yes	—
208	#685	C₂³	1	2	yes	—
209	#685	C₂³	1	2	yes	—
210	#685	C₂³	1	2	yes	—
211	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
212	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
213	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
214	C₄⋊Dic₅	C₂³	1	2	yes	—
215	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
216	#683	C₂³	1	1	yes	characteristic
217	#683	C₂³	1	1	yes	characteristic
218	#683	C₂³	1	2	yes	—
219	#683	C₂³	1	2	yes	—
220	#683	C₂³	1	1	yes	characteristic
221	#683	C₂³	1	2	yes	—
222	#683	C₂³	1	1	yes	characteristic
223	#683	C₂³	1	1	yes	characteristic
224	#683	C₂³	1	1	yes	characteristic
225	#683	C₂³	1	2	yes	—
226	#683	C₂³	1	2	yes	—
227	C₄×Dic₅	C₂³	1	1	yes	characteristic
228	C₄×Dic₅	C₂³	1	1	yes	characteristic
229	C₄×Dic₅	C₂³	1	1	yes	characteristic
230	C₄×Dic₅	C₂³	1	1	yes	characteristic
231	C₄×Dic₅	C₂³	1	2	yes	—
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	—	5	1	no	—
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	D₅	1	1	yes	characteristic, complemented
254	C₂×C₄×D₄	—	5	1	no	—
255	C₂³×C₅	—	2	4	no	—
256	C₂³×C₅	—	4	2	no	—
257	C₂³×C₅	—	4	2	no	—
258	C₂³×C₅	C₂⁴	1	1	yes	characteristic
259	C₂³×C₅	C₂⁴	1	2	yes	—
260	C₂³×C₅	C₂⁴	1	2	yes	—
261	C₂²×D₅	—	2	4	no	—
262	C₂²×D₅	—	2	4	no	—
263	C₂²×D₅	—	2	4	no	—
264	C₂²×D₅	—	4	2	no	—
265	C₂²×D₅	—	4	2	no	—
266	C₂²×D₅	—	4	2	no	—
267	C₂²×D₅	C₂⁴	1	1	yes	characteristic
268	C₂²×D₅	C₂⁴	1	2	yes	—
269	C₂²×D₅	C₂⁴	1	2	yes	—
270	C₂²×D₅	C₂⁴	1	1	yes	characteristic
271	C₅×D₄	—	2	4	no	—
272	C₅×D₄	—	2	2	no	—
273	C₅×D₄	#41	1	4	yes	complemented
274	C₂×C₄×C₅	—	2	2	no	—
275	C₂×C₄×C₅	—	4	2	no	—
276	C₂×C₄×C₅	—	4	2	no	—
277	C₂×C₄×C₅	—	4	2	no	—
278	C₂×C₄×C₅	—	4	2	no	—
279	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
280	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
281	C₂×C₄×C₅	C₂⁴	1	2	yes	—
282	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
283	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
284	C₂×C₄×C₅	C₂⁴	1	2	yes	—
285	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
286	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
287	C₂²⋊D₅	—	2	4	no	—
288	C₂²⋊D₅	—	2	4	no	—
289	C₂²⋊D₅	—	2	4	no	—
290	C₂²⋊D₅	—	2	2	no	—
291	C₂²⋊D₅	—	2	4	no	—
292	C₂²⋊D₅	—	2	2	no	—
293	C₂²⋊D₅	—	4	2	no	—
294	C₂²⋊D₅	—	4	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	C₂×Dic₅	—	2	4	no	—
300	C₂×Dic₅	—	4	2	no	—
301	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
302	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
303	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
304	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
305	C₂×Dic₅	C₂⁴	1	2	yes	—
306	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
307	C₂×Dic₅	C₂⁴	1	2	yes	—
308	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
309	D₂₀	—	2	2	no	—
310	D₂₀	—	2	4	no	—
311	D₂₀	—	2	2	no	—
312	D₂₀	—	2	2	no	—
313	D₂₀	—	4	2	no	—
314	D₂₀	—	4	2	no	—
315	D₂₀	—	4	2	no	—
316	C₄×D₅	—	2	2	no	—
317	C₄×D₅	—	2	2	no	—
318	C₄×D₅	—	2	2	no	—
319	C₄×D₅	—	2	2	no	—
320	C₄×D₅	—	2	4	no	—
321	C₄×D₅	—	4	2	no	—
322	C₄×D₅	—	4	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	—	5	1	no	—
333	C₂²×D₄	—	5	2	no	—
334	C₂²×D₄	C₂×D₅	1	1	yes	characteristic
335	C₂³×C₄	—	5	2	no	—
336	C₄⋊Q₈	—	5	1	no	—
337	#127	—	5	1	no	—
338	#127	—	5	1	no	—
339	#127	—	5	1	no	—
340	#126	—	5	1	no	—
341	#126	—	5	1	no	—
342	#126	—	5	2	no	—
343	#126	—	5	2	no	—
344	#125	—	5	1	no	—
345	#125	—	5	1	no	—
346	#125	—	5	1	no	—
347	#124	—	5	1	no	—
348	#124	—	5	2	no	—
349	#124	—	5	2	no	—
350	#124	—	5	2	no	—
351	#123	—	5	2	no	—
352	#123	—	5	2	no	—
353	#123	—	5	2	no	—
354	#123	—	5	1	no	—
355	#123	—	5	2	no	—
356	#123	—	5	2	no	—
357	#123	—	5	1	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	2	no	—
364	#121	—	5	1	no	—
365	#121	—	5	2	no	—
366	#121	—	5	1	no	—
367	#121	—	5	2	no	—
368	#121	—	5	2	no	—
369	#121	—	5	1	no	—
370	#121	—	5	1	no	—
371	#121	—	5	2	no	—
372	#121	—	5	1	no	—
373	#121	—	5	1	no	—
374	#121	—	5	1	no	—
375	#121	—	5	2	no	—
376	#121	—	5	2	no	—
377	#121	—	5	2	no	—
378	#121	—	5	2	no	—
379	#121	—	5	2	no	—
380	#121	—	5	2	no	—
381	#121	—	5	2	no	—
382	#121	—	5	2	no	—
383	#121	—	5	2	no	—
384	#120	—	5	2	no	—
385	#120	—	5	2	no	—
386	#120	—	5	2	no	—
387	#120	—	5	2	no	—
388	#120	—	5	2	no	—
389	#120	—	5	2	no	—
390	C₄×Q₈	—	5	1	no	—
391	C₄×D₄	—	5	1	no	—
392	C₄×D₄	—	5	1	no	—
393	C₄×D₄	—	5	2	no	—
394	C₄×D₄	—	5	2	no	—
395	C₄×D₄	—	5	2	no	—
396	C₄×D₄	—	5	1	no	—
397	C₄×D₄	—	5	1	no	—
398	C₄×D₄	—	5	2	no	—
399	C₄×D₄	—	5	1	no	—
400	C₄×D₄	—	5	1	no	—
401	C₄×D₄	—	5	2	no	—
402	C₄×D₄	—	5	2	no	—
403	C₄×D₄	—	5	1	no	—
404	C₄×D₄	—	5	1	no	—
405	C₄×D₄	—	5	2	no	—
406	C₄×D₄	—	5	1	no	—
407	C₄×D₄	C₂×D₅	1	1	yes	characteristic
408	C₄×D₄	C₂×D₅	1	1	yes	characteristic
409	C₄×D₄	C₂×D₅	1	2	yes	complemented
410	C₄×D₄	C₂×D₅	1	1	yes	characteristic, complemented
411	C₄×D₄	C₂×D₅	1	2	yes	complemented
412	C₄×D₄	C₂×D₅	1	1	yes	characteristic, complemented
413	#117	—	5	1	no	—
414	#117	—	5	1	no	—
415	#117	—	5	2	no	—
416	#117	C₂×D₅	1	1	yes	characteristic, complemented
417	#117	C₂×D₅	1	1	yes	characteristic, complemented
418	C₂×C₄⋊C₄	—	5	2	no	—
419	C₂×C₄⋊C₄	—	5	1	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	C₂×D₅	1	2	yes	complemented
424	C₂×C₂²⋊C₄	C₂×D₅	1	2	yes	complemented
425	C₂×C₄²	—	5	1	no	—
426	C₂²×C₅	—	2	2	no	—
427	C₂²×C₅	—	2	2	no	—
428	C₂²×C₅	—	2	1	no	—
429	C₂²×C₅	—	2	2	no	—
430	C₂²×C₅	—	2	2	no	—
431	C₂²×C₅	—	2	2	no	—
432	C₂²×C₅	—	2	1	no	—
433	C₂²×C₅	—	2	1	no	—
434	C₂²×C₅	—	8	4	no	—
435	C₂²×C₅	C₂×#41	1	4	yes	—
436	C₂²×C₅	C₂⁵	1	1	yes	characteristic
437	C₂×D₅	—	2	1	no	—
438	C₂×D₅	—	2	1	no	—
439	C₂×D₅	—	2	1	no	—
440	C₂×D₅	—	2	2	no	—
441	C₂×D₅	—	2	2	no	—
442	C₂×D₅	—	2	2	no	—
443	C₂×D₅	—	2	2	no	—
444	C₂×D₅	—	2	2	no	—
445	C₂×D₅	—	2	1	no	—
446	C₂×D₅	—	2	2	no	—
447	C₂×D₅	—	2	1	no	—
448	C₂×D₅	—	4	8	no	—
449	C₂×D₅	—	8	4	no	—
450	C₂×D₅	H(5,𝔽₂)	1	2	yes	—
451	C₄×C₅	—	2	1	no	—
452	C₄×C₅	—	2	1	no	—
453	C₄×C₅	—	2	2	no	—
454	C₄×C₅	—	2	1	no	—
455	C₄×C₅	—	2	1	no	—
456	C₄×C₅	—	2	2	no	—
457	C₄×C₅	—	2	1	no	—
458	C₄×C₅	C₂×#41	1	2	yes	—
459	Dic₅	—	2	1	no	—
460	Dic₅	—	2	1	no	—
461	Dic₅	—	2	1	no	—
462	Dic₅	—	2	1	no	—
463	Dic₅	—	2	2	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	—	5	2	no	—
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	—	5	2	no	—
476	C₂×D₄	—	5	2	no	—
477	C₂×D₄	—	5	2	no	—
478	C₂×D₄	—	5	1	no	—
479	C₂×D₄	—	5	1	no	—
480	C₂×D₄	—	5	2	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	1	no	—
488	C₂×D₄	—	5	1	no	—
489	C₂×D₄	—	5	2	no	—
490	C₂×D₄	—	5	1	no	—
491	C₂×D₄	—	5	2	no	—
492	C₂×D₄	—	5	2	no	—
493	C₂×D₄	—	5	2	no	—
494	C₂×D₄	—	10	4	no	—
495	C₂×D₄	—	10	4	no	—
496	C₂×D₄	—	20	4	no	—
497	C₂×D₄	—	20	4	no	—
498	C₂×D₄	—	20	4	no	—
499	C₂×D₄	C₂²×D₅	1	2	yes	—
500	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
501	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
502	C₂²×C₄	—	5	2	no	—
503	C₂²×C₄	—	5	2	no	—
504	C₂²×C₄	—	5	1	no	—
505	C₂²×C₄	—	5	1	no	—
506	C₂²×C₄	—	5	1	no	—
507	C₂²×C₄	—	5	1	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	2	no	—
513	C₂²×C₄	—	20	4	no	—
514	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
515	C₂²×C₄	C₂²×D₅	1	2	yes	—
516	C₂²×C₄	C₂²×D₅	1	2	yes	—
517	C₂²×C₄	C₂²×D₅	1	2	yes	—
518	C₂²×C₄	C₂²×D₅	1	2	yes	—
519	C₄⋊C₄	—	5	1	no	—
520	C₄⋊C₄	—	5	2	no	—
521	C₄⋊C₄	—	5	1	no	—
522	C₄⋊C₄	—	5	2	no	—
523	C₄⋊C₄	—	5	2	no	—
524	C₄⋊C₄	—	5	2	no	—
525	C₄⋊C₄	—	5	1	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	2	no	—
532	C₄⋊C₄	—	5	2	no	—
533	C₄⋊C₄	—	5	1	no	—
534	C₄⋊C₄	—	5	1	no	—
535	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
536	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
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	2	no	—
541	C₂²⋊C₄	—	5	1	no	—
542	C₂²⋊C₄	—	5	1	no	—
543	C₂²⋊C₄	—	5	2	no	—
544	C₂²⋊C₄	—	5	2	no	—
545	C₂²⋊C₄	—	5	1	no	—
546	C₂²⋊C₄	—	5	2	no	—
547	C₂²⋊C₄	—	5	1	no	—
548	C₂²⋊C₄	—	5	2	no	—
549	C₂²⋊C₄	—	5	2	no	—
550	C₂²⋊C₄	—	5	2	no	—
551	C₂²⋊C₄	—	5	2	no	—
552	C₂²⋊C₄	—	5	2	no	—
553	C₂²⋊C₄	—	5	2	no	—
554	C₂²⋊C₄	—	5	1	no	—
555	C₂²⋊C₄	—	5	1	no	—
556	C₂²⋊C₄	—	5	1	no	—
557	C₂²⋊C₄	—	5	1	no	—
558	C₂²⋊C₄	—	5	2	no	—
559	C₂²⋊C₄	—	5	2	no	—
560	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
561	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
562	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
563	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
564	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
565	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
566	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
567	C₄²	—	5	1	no	—
568	C₄²	—	5	1	no	—
569	C₄²	—	5	1	no	—
570	C₄²	—	5	2	no	—
571	C₄²	—	5	1	no	—
572	C₄²	C₂²×D₅	1	1	yes	characteristic
573	C₄²	C₂²×D₅	1	2	yes	—
574	C₄²	C₂²×D₅	1	1	yes	characteristic
575	C₂×C₅	—	2	4	no	—
576	C₂×C₅	—	4	2	no	—
577	C₂×C₅	—	4	1	no	—
578	C₂×C₅	C₂²×#41	1	1	yes	characteristic
579	C₂×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
580	C₂×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
581	D₅	—	2	2	no	—
582	D₅	—	4	2	no	—
583	D₅	—	4	2	no	—
584	D₅	—	4	1	no	—
585	C₂³	—	2	4	no	—
586	C₂³	—	4	2	no	—
587	C₂³	—	4	2	no	—
588	C₂³	—	5	1	no	—
589	C₂³	—	5	1	no	—
590	C₂³	—	5	2	no	—
591	C₂³	—	5	2	no	—
592	C₂³	—	10	4	no	—
593	C₂³	—	10	4	no	—
594	C₂³	—	10	4	no	—
595	C₂³	—	20	2	no	—
596	C₂³	—	20	2	no	—
597	C₂³	—	20	2	no	—
598	C₂³	C₂³×D₅	1	1	yes	characteristic
599	C₂³	C₂³×D₅	1	2	yes	—
600	C₂³	C₂³×D₅	1	2	yes	—
601	Q₈	—	10	2	no	—
602	Q₈	—	20	2	no	—
603	D₄	—	2	4	no	—
604	D₄	—	2	2	no	—
605	D₄	—	10	2	no	—
606	D₄	—	10	4	no	—
607	D₄	—	10	2	no	—
608	D₄	—	10	4	no	—
609	D₄	—	10	2	no	—
610	D₄	—	10	4	no	—
611	D₄	—	10	4	no	—
612	D₄	—	10	4	no	—
613	D₄	—	10	2	no	—
614	D₄	—	10	2	no	—
615	D₄	—	20	2	no	—
616	D₄	—	20	2	no	—
617	D₄	—	20	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	#709	1	4	yes	complemented
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	4	2	no	—
627	C₂×C₄	—	4	2	no	—
628	C₂×C₄	—	4	2	no	—
629	C₂×C₄	—	4	2	no	—
630	C₂×C₄	—	5	1	no	—
631	C₂×C₄	—	5	1	no	—
632	C₂×C₄	—	5	1	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	2	no	—
641	C₂×C₄	—	10	4	no	—
642	C₂×C₄	—	10	2	no	—
643	C₂×C₄	—	10	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	C₂³×D₅	1	1	yes	characteristic
650	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
651	C₂×C₄	C₂³×D₅	1	2	yes	—
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	2	no	—
659	C₂²	—	2	2	no	—
660	C₂²	—	2	1	no	—
661	C₂²	—	2	2	no	—
662	C₂²	—	2	2	no	—
663	C₂²	—	2	2	no	—
664	C₂²	—	2	1	no	—
665	C₂²	—	2	1	no	—
666	C₂²	—	5	2	no	—
667	C₂²	—	8	4	no	—
668	C₂²	—	10	1	no	—
669	C₂²	—	10	1	no	—
670	C₂²	—	10	1	no	—
671	C₂²	—	10	2	no	—
672	C₂²	—	10	2	no	—
673	C₂²	—	10	2	no	—
674	C₂²	—	10	2	no	—
675	C₂²	—	10	2	no	—
676	C₂²	—	10	1	no	—
677	C₂²	—	10	1	no	—
678	C₂²	—	10	2	no	—
679	C₂²	—	20	8	no	—
680	C₂²	—	40	4	no	—
681	C₂²	C₂×#709	1	4	yes	—
682	C₂²	C₂⁴×D₅	1	1	yes	characteristic
683	C₄	—	2	1	no	—
684	C₄	—	2	1	no	—
685	C₄	—	2	2	no	—
686	C₄	—	2	1	no	—
687	C₄	—	2	1	no	—
688	C₄	—	2	2	no	—
689	C₄	—	2	1	no	—
690	C₄	—	5	2	no	—
691	C₄	—	10	1	no	—
692	C₄	—	10	1	no	—
693	C₄	—	10	2	no	—
694	C₄	—	10	1	no	—
695	C₄	—	10	1	no	—
696	C₄	—	10	2	no	—
697	C₄	—	10	1	no	—
698	C₄	C₂×#709	1	2	yes	—
699	C₂	—	2	4	no	—
700	C₂	—	4	1	no	—
701	C₂	—	4	2	no	—
702	C₂	—	10	2	no	—
703	C₂	—	20	2	no	—
704	C₂	—	20	1	no	—
705	C₂	—	20	2	no	—
706	C₂	C₂²×#709	1	1	yes	characteristic
707	C₂	D₅×H(5,𝔽₂)	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×#518	C₂
hypercenter	#518	D₅
hypocenter	C₅	#3519
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ #518

Complements

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

N	H ≅ G/N	type
1. C₅×#518	C₂	semidirect
2. D₄×C₂²⋊D₅	C₂	semidirect
3. D₄×C₂²⋊D₅	C₂	semidirect
4. #65896	C₂	semidirect
5. #65894	C₂	semidirect
6. #65892	C₂	semidirect
7. #65887	C₂	semidirect
8. #65884	C₂	semidirect
9. D₄×D₂₀	C₂	semidirect
10. #65882	C₂	semidirect
11. #65881	C₂	semidirect
12. #65879	C₂	semidirect
13. C₄×D₄×D₅	C₂	semidirect
14. #65874	C₂	semidirect
15. #65873	C₂	semidirect
16. #65869	C₂	semidirect
17. #65866	C₂	semidirect
18. #65864	C₂	semidirect
19. #65862	C₂	semidirect
20. #65828	C₂	semidirect
21. #65824	C₂	semidirect
22. #65824	C₂	semidirect
23. C₂×#4030	C₂	semidirect
25. C₂²×C₂²⋊D₅	C₂²	semidirect
26. C₂²×C₂²⋊D₅	C₂²	semidirect
29. C₂×#709	C₂²	semidirect
30. C₂×#709	C₂²	semidirect
31. C₂²×D₂₀	C₂²	semidirect
32. C₂²×C₄×D₅	C₂²	semidirect
35. C₄×C₅×D₄	C₂²	semidirect
36. C₄×C₅×D₄	C₂²	semidirect
37. C₄×C₅×D₄	C₂²	semidirect
38. C₄×C₅×D₄	C₂²	semidirect
39. C₅×#117	C₂²	semidirect
40. C₅×#117	C₂²	semidirect
41. C₂×C₅×C₂²⋊C₄	C₂²	semidirect
42. C₂×C₅×C₂²⋊C₄	C₂²	semidirect
43. #4099	C₂²	semidirect
44. #4099	C₂²	semidirect
45. #4086	C₂²	semidirect
46. #4086	C₂²	semidirect
47. #4085	C₂²	semidirect
48. #4085	C₂²	semidirect
49. #4084	C₂²	semidirect
50. #4084	C₂²	semidirect
51. #4083	C₂²	semidirect
52. #4083	C₂²	semidirect
55. #4076	C₂²	semidirect
56. #4076	C₂²	semidirect
57. #4076	C₂²	semidirect
58. #4076	C₂²	semidirect
59. #4076	C₂²	semidirect
60. #4075	C₂²	semidirect
61. #4075	C₂²	semidirect
62. C₄×C₂²⋊D₅	C₂²	semidirect
63. C₄×C₂²⋊D₅	C₂²	semidirect
64. C₄×C₂²⋊D₅	C₂²	semidirect
65. C₄×C₂²⋊D₅	C₂²	semidirect
66. C₄×C₂²⋊D₅	C₂²	semidirect
67. C₄×C₂²⋊D₅	C₂²	semidirect
68. C₂×#685	C₂²	semidirect
69. #4070	C₂²	semidirect
70. C₂×#683	C₂²	semidirect
71. #4044	C₂²	semidirect
72. #4042	C₂²	semidirect
73. #4041	C₂²	semidirect
74. #4041	C₂²	semidirect
75. #4040	C₂²	semidirect
76. #4040	C₂²	semidirect
77. #4040	C₂²	semidirect
78. #4039	C₂²	semidirect
79. #4039	C₂²	semidirect
80. #4038	C₂²	semidirect
81. D₅×C₄⋊C₄	C₂²	semidirect
82. #4036	C₂²	semidirect
83. #4035	C₂²	semidirect
84. #4034	C₂²	semidirect
85. #4031	C₂²	semidirect
86. #4031	C₂²	semidirect
87. #4031	C₂²	semidirect
89. #4030	C₂²	semidirect
90. #4030	C₂²	semidirect
91. #4030	C₂²	semidirect
92. #4030	C₂²	semidirect
93. #4030	C₂²	semidirect
94. #4030	C₂²	semidirect
95. #4030	C₂²	semidirect
96. #4030	C₂²	semidirect
97. #4030	C₂²	semidirect
98. #4029	C₂²	semidirect
99. #4029	C₂²	semidirect
100. #4029	C₂²	semidirect
101. #4028	C₂²	semidirect
102. #4028	C₂²	semidirect
103. #4027	C₂²	semidirect
104. #4027	C₂²	semidirect
105. D₅×C₂²⋊C₄	C₂²	semidirect
106. D₅×C₂²⋊C₄	C₂²	semidirect
107. #4025	C₂²	semidirect
108. #4025	C₂²	semidirect
109. #4024	C₂²	semidirect
110. #4024	C₂²	semidirect
111. #4022	C₂²	semidirect
112. #4021	C₂²	semidirect
113. #4020	C₂²	semidirect
114. C₄×D₂₀	C₂²	semidirect
115. C₄×D₂₀	C₂²	semidirect
116. C₄×D₂₀	C₂²	semidirect
117. C₄×D₂₀	C₂²	semidirect
118. #4018	C₂²	semidirect
119. #4018	C₂²	semidirect
120. C₄²×D₅	C₂²	semidirect
121. #4016	C₂²	semidirect
122. C₄×Dic₁₀	C₂²	semidirect
253. #518	D₅	semidirect
273. C₅×D₄	#41	semidirect
409. C₄×D₄	C₂×D₅	semidirect
410. C₄×D₄	C₂×D₅	semidirect
411. C₄×D₄	C₂×D₅	semidirect
412. C₄×D₄	C₂×D₅	semidirect
416. #117	C₂×D₅	semidirect
417. #117	C₂×D₅	semidirect
423. C₂×C₂²⋊C₄	C₂×D₅	semidirect
424. C₂×C₂²⋊C₄	C₂×D₅	semidirect
624. D₄	#709	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×#518	2
D₄×C₂²⋊D₅	2
#65896	2
#65894	2
#65892	2
#65887	2
#65884	2
D₄×D₂₀	2
#65882	2
#65881	2
#65879	2
C₄×D₄×D₅	2
#65874	2
#65873	2
#65869	2
#65866	2
#65864	2
#65862	2
#65828	2
#65824	2
C₂×#4030	2
#3519	5