Subgroups — #10618052

Order 640.

1132 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#529	C₂	1	1	yes	maximal, characteristic, complemented
2	#66042	C₂	1	2	yes	maximal, complemented
3	#66039	C₂	1	2	yes	maximal, complemented
4	#66028	C₂	1	1	yes	maximal, characteristic, complemented
5	#66024	C₂	1	1	yes	maximal, characteristic, complemented
6	#66010	C₂	1	1	yes	maximal, characteristic, complemented
7	#66005	C₂	1	1	yes	maximal, characteristic, complemented
8	#65995	C₂	1	2	yes	maximal, complemented
9	#65993	C₂	1	2	yes	maximal, complemented
10	#65973	C₂	1	1	yes	maximal, characteristic, complemented
11	#65965	C₂	1	1	yes	maximal, characteristic, complemented
12	#65950	C₂	1	1	yes	maximal, characteristic, complemented
13	#65946	C₂	1	1	yes	maximal, characteristic, complemented
14	#65912	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×#713	C₂	1	1	yes	maximal, characteristic, complemented
16	#65891	C₂	1	1	yes	maximal, characteristic, complemented
17	#65891	C₂	1	2	yes	maximal, complemented
18	#65881	C₂	1	2	yes	maximal, complemented
19	C₄×D₄×D₅	C₂	1	1	yes	maximal, characteristic, complemented
20	#65862	C₂	1	2	yes	maximal, complemented
21	D₅×#117	C₂	1	2	yes	maximal, complemented
22	C₄×#709	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×#709	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#713	C₂²	1	1	yes	characteristic
25	C₂×D₄×D₅	C₂²	1	1	yes	characteristic
26	C₂×#709	C₂²	1	1	yes	characteristic
27	C₂×#709	C₂²	1	1	yes	characteristic
28	C₂²×C₄×D₅	C₂²	1	2	yes	—
29	C₅×#126	C₂²	1	2	yes	complemented
30	C₅×#125	C₂²	1	1	yes	characteristic, complemented
31	C₅×#124	C₂²	1	1	yes	characteristic
32	C₅×#123	C₂²	1	2	yes	complemented
33	C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
34	C₅×#121	C₂²	1	1	yes	characteristic
35	C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
36	C₄×C₅×D₄	C₂²	1	1	yes	characteristic
37	C₄×C₅×D₄	C₂²	1	2	yes	complemented
38	C₅×#117	C₂²	1	2	yes	complemented
39	C₂×C₄²×C₅	C₂²	1	1	yes	characteristic, complemented
40	#4092	C₂²	1	1	yes	characteristic
41	Q₈×Dic₅	C₂²	1	1	yes	characteristic, complemented
42	#4090	C₂²	1	1	yes	characteristic, complemented
43	#4085	C₂²	1	2	yes	complemented
44	#4084	C₂²	1	2	yes	—
45	#4084	C₂²	1	1	yes	characteristic
46	#4083	C₂²	1	2	yes	—
47	#4082	C₂²	1	1	yes	characteristic
48	#4082	C₂²	1	2	yes	complemented
49	D₄×Dic₅	C₂²	1	1	yes	characteristic
50	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic
51	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic
52	C₄×C₂²⋊D₅	C₂²	1	2	yes	—
53	C₄×C₂²⋊D₅	C₂²	1	2	yes	complemented
54	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic, complemented
55	C₄×C₂²⋊D₅	C₂²	1	2	yes	complemented
56	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic, complemented
57	C₄×C₂²⋊D₅	C₂²	1	2	yes	complemented
58	#4072	C₂²	1	1	yes	characteristic, complemented
59	#4072	C₂²	1	1	yes	characteristic, complemented
60	#4072	C₂²	1	2	yes	complemented
61	#4044	C₂²	1	2	yes	complemented
62	#4043	C₂²	1	1	yes	characteristic
63	#4043	C₂²	1	1	yes	characteristic, complemented
64	#4043	C₂²	1	2	yes	complemented
65	#4042	C₂²	1	2	yes	—
66	#4042	C₂²	1	2	yes	complemented
67	#4042	C₂²	1	2	yes	complemented
68	#4040	C₂²	1	2	yes	—
69	#4040	C₂²	1	2	yes	complemented
70	#4039	C₂²	1	1	yes	characteristic
71	#4039	C₂²	1	1	yes	characteristic
72	#4039	C₂²	1	2	yes	complemented
73	#4038	C₂²	1	2	yes	—
74	#4038	C₂²	1	2	yes	—
75	#4038	C₂²	1	1	yes	characteristic, complemented
76	#4038	C₂²	1	2	yes	complemented
77	D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
78	D₅×C₄⋊C₄	C₂²	1	2	yes	complemented
79	D₅×C₄⋊C₄	C₂²	1	2	yes	complemented
80	#4036	C₂²	1	1	yes	characteristic, complemented
81	#4036	C₂²	1	2	yes	complemented
82	#4035	C₂²	1	2	yes	complemented
83	#4035	C₂²	1	2	yes	complemented
84	#4034	C₂²	1	1	yes	characteristic, complemented
85	#4031	C₂²	1	2	yes	complemented
86	#4030	C₂²	1	2	yes	—
87	#4030	C₂²	1	2	yes	complemented
88	#4029	C₂²	1	2	yes	—
89	#4029	C₂²	1	2	yes	—
90	#4029	C₂²	1	2	yes	—
91	#4029	C₂²	1	2	yes	complemented
92	#4029	C₂²	1	2	yes	complemented
93	#4028	C₂²	1	2	yes	—
94	#4027	C₂²	1	2	yes	—
95	D₅×C₂²⋊C₄	C₂²	1	2	yes	—
96	D₅×C₂²⋊C₄	C₂²	1	2	yes	—
97	D₅×C₂²⋊C₄	C₂²	1	2	yes	—
98	#4025	C₂²	1	2	yes	complemented
99	#4025	C₂²	1	2	yes	complemented
100	#4025	C₂²	1	2	yes	complemented
101	#4025	C₂²	1	2	yes	complemented
102	#4024	C₂²	1	2	yes	complemented
103	#4023	C₂²	1	2	yes	complemented
104	#4023	C₂²	1	2	yes	complemented
105	C₄×D₂₀	C₂²	1	1	yes	characteristic
106	C₄×D₂₀	C₂²	1	1	yes	characteristic
107	C₄×D₂₀	C₂²	1	1	yes	characteristic
108	C₄×D₂₀	C₂²	1	1	yes	characteristic
109	C₄×D₂₀	C₂²	1	2	yes	complemented
110	#4018	C₂²	1	1	yes	characteristic
111	#4018	C₂²	1	2	yes	—
112	#4018	C₂²	1	1	yes	characteristic, complemented
113	#4018	C₂²	1	2	yes	complemented
114	C₄²×D₅	C₂²	1	1	yes	characteristic
115	C₄²×D₅	C₂²	1	2	yes	complemented
116	C₄²×D₅	C₂²	1	1	yes	characteristic, complemented
117	C₄²×D₅	C₂²	1	2	yes	complemented
118	C₄×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
119	C₄×Dic₁₀	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	2	yes	complemented
123	#3475	—	5	1	no	maximal, Sylow
124	C₂³×D₅	C₂³	1	2	yes	—
125	C₂×C₅×Q₈	C₂³	1	1	yes	characteristic
126	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
127	C₂×C₅×D₄	C₂³	1	2	yes	—
128	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
129	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
130	C₂²×C₄×C₅	C₂³	1	2	yes	—
131	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
132	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
133	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
135	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
137	C₂²×Dic₅	C₂³	1	2	yes	—
138	#713	—	2	4	no	—
139	D₄×D₅	—	2	4	no	—
140	#709	—	2	4	no	—
141	#709	—	2	4	no	—
142	C₂×D₂₀	C₂³	1	1	yes	characteristic
143	C₂×D₂₀	C₂³	1	2	yes	—
144	C₂×D₂₀	C₂³	1	1	yes	characteristic
145	C₂×C₄×D₅	—	2	8	no	—
146	C₂×C₄×D₅	C₂³	1	2	yes	—
147	C₂×C₄×D₅	C₂³	1	2	yes	—
148	C₂×C₄×D₅	C₂³	1	2	yes	—
149	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
150	C₂×C₄×D₅	C₂³	1	2	yes	—
151	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
152	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
153	C₂×C₄×D₅	C₂³	1	2	yes	—
154	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
155	C₂×C₄×D₅	C₂³	1	2	yes	—
156	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
157	C₂×C₄×D₅	C₂³	1	2	yes	—
158	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
159	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
160	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
161	C₂×Dic₁₀	C₂³	1	2	yes	—
162	C₅×C₄⋊C₄	C₂³	1	2	yes	—
163	C₅×C₄⋊C₄	C₂³	1	2	yes	—
164	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
165	C₅×C₄⋊C₄	C₂³	1	2	yes	—
166	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
167	C₅×C₄⋊C₄	C₂³	1	2	yes	—
168	C₅×C₂²⋊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	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
173	C₄²×C₅	C₂³	1	1	yes	characteristic
174	C₄²×C₅	C₂³	1	1	yes	characteristic
175	C₄²×C₅	C₂³	1	1	yes	characteristic
176	C₄²×C₅	C₂³	1	1	yes	characteristic
177	C₄²×C₅	C₂³	1	2	yes	—
178	C₂²⋊Dic₅	C₂³	1	2	yes	—
179	C₂²⋊Dic₅	C₂³	1	2	yes	—
180	C₂²⋊Dic₅	C₂³	1	2	yes	—
181	C₂²⋊Dic₅	C₂³	1	2	yes	—
182	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
183	C₂²⋊Dic₅	C₂³	1	2	yes	—
184	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
185	#685	C₂³	1	1	yes	characteristic
186	#685	C₂³	1	1	yes	characteristic
187	#685	C₂³	1	2	yes	—
188	#685	C₂³	1	2	yes	—
189	#685	C₂³	1	2	yes	—
190	#685	C₂³	1	2	yes	—
191	#685	C₂³	1	1	yes	characteristic
192	#685	C₂³	1	1	yes	characteristic
193	#685	C₂³	1	2	yes	—
194	#685	C₂³	1	2	yes	—
195	#685	C₂³	1	2	yes	—
196	#685	C₂³	1	2	yes	—
197	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
198	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
199	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
200	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
201	C₄⋊Dic₅	C₂³	1	2	yes	—
202	C₄⋊Dic₅	C₂³	1	2	yes	—
203	C₄⋊Dic₅	C₂³	1	2	yes	—
204	C₄⋊Dic₅	C₂³	1	2	yes	—
205	#683	C₂³	1	1	yes	characteristic
206	#683	C₂³	1	1	yes	characteristic
207	#683	C₂³	1	2	yes	—
208	#683	C₂³	1	1	yes	characteristic
209	#683	C₂³	1	2	yes	—
210	#683	C₂³	1	1	yes	characteristic
211	#683	C₂³	1	2	yes	—
212	#683	C₂³	1	2	yes	—
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	C₄×Dic₅	C₂³	1	1	yes	characteristic
218	C₄×Dic₅	C₂³	1	2	yes	—
219	C₄×Dic₅	C₂³	1	1	yes	characteristic
220	C₄×Dic₅	C₂³	1	1	yes	characteristic
221	C₄×Dic₅	C₂³	1	2	yes	—
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	C₄×Dic₅	C₂³	1	2	yes	—
228	#556	—	5	1	no	—
229	#555	—	5	1	no	—
230	#554	—	5	1	no	—
231	#553	—	5	2	no	—
232	#552	—	5	2	no	—
233	#552	—	5	1	no	—
234	#552	—	5	1	no	—
235	#551	—	5	2	no	—
236	#551	—	5	2	no	—
237	#547	—	5	1	no	—
238	#546	—	5	1	no	—
239	#546	—	5	1	no	—
240	#533	—	5	1	no	—
241	#529	—	5	1	no	—
242	#529	—	5	2	no	—
243	#529	—	5	2	no	—
244	#529	D₅	1	1	yes	characteristic, complemented
245	#525	—	5	2	no	—
246	C₄×#41	—	5	1	no	—
247	C₄×#41	—	5	1	no	—
248	C₄×#41	—	5	1	no	—
249	C₂×C₄×D₄	—	5	1	no	—
250	C₂×#117	—	5	2	no	—
251	C₂³×C₅	C₂⁴	1	2	yes	—
252	C₂³×C₅	C₂⁴	1	1	yes	characteristic
253	C₂²×D₅	—	2	4	no	—
254	C₂²×D₅	—	2	4	no	—
255	C₂²×D₅	—	4	2	no	—
256	C₂²×D₅	C₂⁴	1	1	yes	characteristic
257	C₂²×D₅	C₂⁴	1	1	yes	characteristic
258	C₂²×D₅	C₂⁴	1	2	yes	—
259	C₅×Q₈	—	2	2	no	—
260	C₅×D₄	—	2	2	no	—
261	C₅×D₄	—	4	2	no	—
262	C₂×C₄×C₅	—	2	4	no	—
263	C₂×C₄×C₅	—	2	2	no	—
264	C₂×C₄×C₅	—	2	2	no	—
265	C₂×C₄×C₅	—	4	1	no	—
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	2	yes	—
271	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
272	C₂×C₄×C₅	C₂⁴	1	2	yes	—
273	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
274	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
275	C₂²⋊D₅	—	2	2	no	—
276	C₂²⋊D₅	—	2	4	no	—
277	C₂²⋊D₅	—	2	4	no	—
278	C₂²⋊D₅	—	2	2	no	—
279	C₂²⋊D₅	—	4	2	no	—
280	C₂×Dic₅	—	2	4	no	—
281	C₂×Dic₅	C₂⁴	1	2	yes	—
282	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
283	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
284	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
285	C₂×Dic₅	C₂⁴	1	2	yes	—
286	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
287	C₂×Dic₅	C₂⁴	1	2	yes	—
288	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
289	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
290	D₂₀	—	2	2	no	—
291	D₂₀	—	2	4	no	—
292	D₂₀	#41	1	4	yes	complemented
293	C₄×D₅	—	2	4	no	—
294	C₄×D₅	—	2	4	no	—
295	C₄×D₅	—	2	4	no	—
296	C₄×D₅	—	2	4	no	—
297	C₄×D₅	—	2	2	no	—
298	C₄×D₅	—	2	2	no	—
299	C₄×D₅	—	2	2	no	—
300	C₄×D₅	—	2	4	no	—
301	C₄×D₅	—	4	1	no	—
302	C₄×D₅	—	4	2	no	—
303	C₄×D₅	—	4	2	no	—
304	C₄×D₅	—	4	1	no	—
305	C₄×D₅	#41	1	4	yes	complemented
306	Dic₁₀	—	2	2	no	—
307	Dic₁₀	—	2	2	no	—
308	Dic₁₀	—	4	2	no	—
309	C₂×#41	—	5	1	no	—
310	C₂×#41	—	5	1	no	—
311	C₂×#41	—	5	1	no	—
312	C₂²×D₄	—	5	1	no	—
313	C₂³×C₄	—	5	2	no	—
314	C₄⋊Q₈	—	5	1	no	—
315	C₄⋊Q₈	—	5	1	no	—
316	#126	—	5	2	no	—
317	#126	—	5	2	no	—
318	#126	—	5	2	no	—
319	#126	—	5	2	no	—
320	#126	—	5	2	no	—
321	#126	C₂×D₅	1	2	yes	complemented
322	#125	—	5	2	no	—
323	#125	—	5	2	no	—
324	#125	—	5	1	no	—
325	#125	—	5	2	no	—
326	#125	C₂×D₅	1	1	yes	characteristic, complemented
327	#124	—	5	1	no	—
328	#124	—	5	2	no	—
329	#124	—	5	2	no	—
330	#124	C₂×D₅	1	1	yes	characteristic
331	#123	—	5	2	no	—
332	#123	—	5	2	no	—
333	#123	—	5	2	no	—
334	#123	—	5	2	no	—
335	#123	—	5	2	no	—
336	#123	—	5	2	no	—
337	#123	—	5	2	no	—
338	#123	C₂×D₅	1	2	yes	complemented
339	C₂²⋊Q₈	—	5	1	no	—
340	C₂²⋊Q₈	—	5	2	no	—
341	C₂²⋊Q₈	—	5	1	no	—
342	C₂²⋊Q₈	—	5	2	no	—
343	C₂²⋊Q₈	—	5	2	no	—
344	C₂²⋊Q₈	—	5	1	no	—
345	C₂²⋊Q₈	—	5	2	no	—
346	C₂²⋊Q₈	—	5	2	no	—
347	C₂²⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
348	#121	—	5	2	no	—
349	#121	—	5	2	no	—
350	#121	—	5	1	no	—
351	#121	—	5	2	no	—
352	#121	—	5	2	no	—
353	#121	C₂×D₅	1	1	yes	characteristic
354	#120	—	5	2	no	—
355	#120	—	5	2	no	—
356	C₄×Q₈	—	5	1	no	—
357	C₄×Q₈	—	5	1	no	—
358	C₄×Q₈	—	5	1	no	—
359	C₄×Q₈	—	5	1	no	—
360	C₄×Q₈	—	5	1	no	—
361	C₄×Q₈	—	5	2	no	—
362	C₄×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
363	C₄×D₄	—	5	1	no	—
364	C₄×D₄	—	5	2	no	—
365	C₄×D₄	—	5	2	no	—
366	C₄×D₄	—	5	1	no	—
367	C₄×D₄	—	5	1	no	—
368	C₄×D₄	—	5	1	no	—
369	C₄×D₄	—	5	2	no	—
370	C₄×D₄	—	5	1	no	—
371	C₄×D₄	—	5	2	no	—
372	C₄×D₄	—	5	1	no	—
373	C₄×D₄	—	5	1	no	—
374	C₄×D₄	—	5	2	no	—
375	C₄×D₄	—	5	2	no	—
376	C₄×D₄	—	5	1	no	—
377	C₄×D₄	—	5	2	no	—
378	C₄×D₄	—	5	1	no	—
379	C₄×D₄	—	5	1	no	—
380	C₄×D₄	—	5	1	no	—
381	C₄×D₄	C₂×D₅	1	1	yes	characteristic
382	C₄×D₄	C₂×D₅	1	2	yes	complemented
383	#117	—	5	2	no	—
384	#117	—	5	1	no	—
385	#117	—	5	1	no	—
386	#117	—	5	2	no	—
387	#117	—	5	2	no	—
388	#117	—	5	2	no	—
389	#117	—	5	1	no	—
390	#117	—	5	2	no	—
391	#117	—	5	2	no	—
392	#117	—	5	1	no	—
393	#117	—	5	2	no	—
394	#117	—	5	1	no	—
395	#117	—	5	2	no	—
396	#117	C₂×D₅	1	2	yes	complemented
397	C₂×C₄⋊C₄	—	5	2	no	—
398	C₂×C₄⋊C₄	—	5	2	no	—
399	C₂×C₄⋊C₄	—	5	1	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	2	no	—
404	C₂×C₄²	—	5	2	no	—
405	C₂×C₄²	—	5	1	no	—
406	C₂×C₄²	—	5	1	no	—
407	C₂×C₄²	C₂×D₅	1	1	yes	characteristic, complemented
408	C₂²×C₅	—	2	2	no	—
409	C₂²×C₅	—	2	1	no	—
410	C₂²×C₅	—	2	1	no	—
411	C₂²×C₅	—	2	2	no	—
412	C₂²×C₅	—	2	2	no	—
413	C₂²×C₅	—	2	1	no	—
414	C₂²×C₅	C₂⁵	1	1	yes	characteristic
415	C₂×D₅	—	2	2	no	—
416	C₂×D₅	—	2	1	no	—
417	C₂×D₅	—	2	2	no	—
418	C₂×D₅	—	2	1	no	—
419	C₂×D₅	—	2	1	no	—
420	C₂×D₅	—	2	1	no	—
421	C₂×D₅	—	2	1	no	—
422	C₂×D₅	—	4	8	no	—
423	C₂×D₅	C₂×#41	1	2	yes	—
424	C₂×D₅	C₂×#41	1	4	yes	—
425	C₄×C₅	—	2	1	no	—
426	C₄×C₅	—	2	1	no	—
427	C₄×C₅	—	2	2	no	—
428	C₄×C₅	—	2	2	no	—
429	C₄×C₅	—	2	2	no	—
430	C₄×C₅	—	2	1	no	—
431	C₄×C₅	—	2	1	no	—
432	C₄×C₅	C₂×#41	1	2	yes	—
433	C₄×C₅	C₂×#41	1	2	yes	—
434	Dic₅	—	2	2	no	—
435	Dic₅	—	2	1	no	—
436	Dic₅	—	2	1	no	—
437	Dic₅	—	2	2	no	—
438	Dic₅	—	2	1	no	—
439	Dic₅	—	2	1	no	—
440	Dic₅	—	2	2	no	—
441	Dic₅	—	2	1	no	—
442	Dic₅	C₂×#41	1	2	yes	—
443	C₂⁴	—	5	2	no	—
444	#41	—	10	4	no	—
445	#41	—	10	4	no	—
446	#41	—	10	4	no	—
447	C₂×Q₈	—	5	1	no	—
448	C₂×Q₈	—	5	1	no	—
449	C₂×Q₈	—	5	2	no	—
450	C₂×Q₈	C₂²×D₅	1	1	yes	characteristic
451	C₂×D₄	—	5	1	no	—
452	C₂×D₄	—	5	2	no	—
453	C₂×D₄	—	5	1	no	—
454	C₂×D₄	—	5	2	no	—
455	C₂×D₄	—	5	2	no	—
456	C₂×D₄	—	5	1	no	—
457	C₂×D₄	—	5	1	no	—
458	C₂×D₄	—	5	2	no	—
459	C₂×D₄	—	10	4	no	—
460	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
461	C₂×D₄	C₂²×D₅	1	2	yes	—
462	C₂²×C₄	—	5	1	no	—
463	C₂²×C₄	—	5	2	no	—
464	C₂²×C₄	—	5	2	no	—
465	C₂²×C₄	—	5	2	no	—
466	C₂²×C₄	—	5	1	no	—
467	C₂²×C₄	—	5	1	no	—
468	C₂²×C₄	—	5	2	no	—
469	C₂²×C₄	—	5	2	no	—
470	C₂²×C₄	—	5	2	no	—
471	C₂²×C₄	—	5	1	no	—
472	C₂²×C₄	—	5	1	no	—
473	C₂²×C₄	—	5	2	no	—
474	C₂²×C₄	—	5	2	no	—
475	C₂²×C₄	—	5	1	no	—
476	C₂²×C₄	—	10	8	no	—
477	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
478	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
479	C₂²×C₄	C₂²×D₅	1	2	yes	—
480	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
481	C₄⋊C₄	—	5	1	no	—
482	C₄⋊C₄	—	5	1	no	—
483	C₄⋊C₄	—	5	1	no	—
484	C₄⋊C₄	—	5	2	no	—
485	C₄⋊C₄	—	5	2	no	—
486	C₄⋊C₄	—	5	2	no	—
487	C₄⋊C₄	—	5	2	no	—
488	C₄⋊C₄	—	5	2	no	—
489	C₄⋊C₄	—	5	1	no	—
490	C₄⋊C₄	—	5	1	no	—
491	C₄⋊C₄	—	5	1	no	—
492	C₄⋊C₄	—	5	2	no	—
493	C₄⋊C₄	—	5	2	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	2	no	—
499	C₄⋊C₄	—	5	2	no	—
500	C₄⋊C₄	—	5	2	no	—
501	C₄⋊C₄	C₂²×D₅	1	2	yes	—
502	C₄⋊C₄	C₂²×D₅	1	2	yes	—
503	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
504	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
505	C₄⋊C₄	C₂²×D₅	1	2	yes	—
506	C₄⋊C₄	C₂²×D₅	1	2	yes	—
507	C₂²⋊C₄	—	5	2	no	—
508	C₂²⋊C₄	—	5	2	no	—
509	C₂²⋊C₄	—	5	2	no	—
510	C₂²⋊C₄	—	5	1	no	—
511	C₂²⋊C₄	—	5	2	no	—
512	C₂²⋊C₄	—	5	1	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	2	no	—
518	C₂²⋊C₄	—	5	2	no	—
519	C₂²⋊C₄	—	5	2	no	—
520	C₂²⋊C₄	—	5	2	no	—
521	C₂²⋊C₄	—	5	2	no	—
522	C₂²⋊C₄	—	5	1	no	—
523	C₂²⋊C₄	—	5	2	no	—
524	C₂²⋊C₄	—	5	1	no	—
525	C₂²⋊C₄	—	5	2	no	—
526	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
527	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
528	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
529	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
530	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
531	C₄²	—	5	2	no	—
532	C₄²	—	5	2	no	—
533	C₄²	—	5	2	no	—
534	C₄²	—	5	2	no	—
535	C₄²	—	5	1	no	—
536	C₄²	—	5	1	no	—
537	C₄²	—	5	1	no	—
538	C₄²	—	5	1	no	—
539	C₄²	—	5	1	no	—
540	C₄²	—	5	1	no	—
541	C₄²	—	5	2	no	—
542	C₄²	C₂²×D₅	1	1	yes	characteristic
543	C₄²	C₂²×D₅	1	1	yes	characteristic
544	C₄²	C₂²×D₅	1	1	yes	characteristic
545	C₄²	C₂²×D₅	1	1	yes	characteristic
546	C₄²	C₂²×D₅	1	2	yes	—
547	C₂×C₅	—	4	2	no	—
548	C₂×C₅	—	4	1	no	—
549	C₂×C₅	C₂²×#41	1	1	yes	characteristic
550	C₂×C₅	C₂²×#41	1	1	yes	characteristic
551	C₂×C₅	#585	1	1	yes	characteristic
552	D₅	—	2	2	no	—
553	D₅	—	2	4	no	—
554	D₅	—	4	1	no	—
555	C₂³	—	5	1	no	—
556	C₂³	—	5	2	no	—
557	C₂³	—	5	1	no	—
558	C₂³	—	10	4	no	—
559	C₂³	—	10	4	no	—
560	C₂³	—	20	2	no	—
561	C₂³	C₂³×D₅	1	2	yes	—
562	C₂³	C₂³×D₅	1	1	yes	characteristic
563	Q₈	—	2	2	no	—
564	Q₈	—	10	2	no	—
565	Q₈	—	10	2	no	—
566	Q₈	—	20	2	no	—
567	D₄	—	2	2	no	—
568	D₄	—	4	2	no	—
569	D₄	—	5	4	no	—
570	D₄	—	10	2	no	—
571	D₄	—	10	4	no	—
572	D₄	—	10	2	no	—
573	D₄	—	10	4	no	—
574	D₄	—	10	2	no	—
575	D₄	—	10	4	no	—
576	D₄	—	20	2	no	—
577	C₂×C₄	—	2	4	no	—
578	C₂×C₄	—	2	2	no	—
579	C₂×C₄	—	2	2	no	—
580	C₂×C₄	—	4	1	no	—
581	C₂×C₄	—	5	1	no	—
582	C₂×C₄	—	5	4	no	—
583	C₂×C₄	—	5	2	no	—
584	C₂×C₄	—	5	1	no	—
585	C₂×C₄	—	5	1	no	—
586	C₂×C₄	—	5	1	no	—
587	C₂×C₄	—	5	1	no	—
588	C₂×C₄	—	5	2	no	—
589	C₂×C₄	—	5	2	no	—
590	C₂×C₄	—	5	1	no	—
591	C₂×C₄	—	10	4	no	—
592	C₂×C₄	—	10	4	no	—
593	C₂×C₄	—	10	4	no	—
594	C₂×C₄	—	10	4	no	—
595	C₂×C₄	—	10	4	no	—
596	C₂×C₄	—	10	4	no	—
597	C₂×C₄	—	10	2	no	—
598	C₂×C₄	—	10	2	no	—
599	C₂×C₄	—	10	2	no	—
600	C₂×C₄	—	20	1	no	—
601	C₂×C₄	—	20	2	no	—
602	C₂×C₄	—	20	1	no	—
603	C₂×C₄	—	20	2	no	—
604	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
605	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
606	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
607	C₂×C₄	C₂³×D₅	1	2	yes	—
608	C₂×C₄	C₂³×D₅	1	2	yes	—
609	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
610	C₂×C₄	C₂³×D₅	1	2	yes	—
611	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
612	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
613	C₅	#3475	1	1	yes	characteristic, complemented, Sylow
614	C₂²	—	2	2	no	—
615	C₂²	—	2	1	no	—
616	C₂²	—	2	1	no	—
617	C₂²	—	2	2	no	—
618	C₂²	—	2	1	no	—
619	C₂²	—	2	2	no	—
620	C₂²	—	5	2	no	—
621	C₂²	—	5	4	no	—
622	C₂²	—	10	2	no	—
623	C₂²	—	10	1	no	—
624	C₂²	—	10	2	no	—
625	C₂²	—	10	1	no	—
626	C₂²	—	10	1	no	—
627	C₂²	—	10	1	no	—
628	C₂²	—	10	1	no	—
629	C₂²	—	20	8	no	—
630	C₂²	C₂⁴×D₅	1	1	yes	characteristic
631	C₄	—	2	2	no	—
632	C₄	—	2	1	no	—
633	C₄	—	2	1	no	—
634	C₄	—	2	2	no	—
635	C₄	—	2	1	no	—
636	C₄	—	2	1	no	—
637	C₄	—	2	2	no	—
638	C₄	—	5	2	no	—
639	C₄	—	10	2	no	—
640	C₄	—	10	1	no	—
641	C₄	—	10	1	no	—
642	C₄	—	10	1	no	—
643	C₄	—	10	2	no	—
644	C₄	—	10	1	no	—
645	C₄	—	10	2	no	—
646	C₄	—	10	1	no	—
647	C₄	D₅×#41	1	2	yes	—
648	C₄	D₅×#41	1	2	yes	—
649	C₂	—	4	2	no	—
650	C₂	—	4	1	no	—
651	C₂	—	10	2	no	—
652	C₂	—	10	4	no	—
653	C₂	—	20	1	no	—
654	C₂	C₂×D₅×#41	1	1	yes	characteristic
655	C₂	C₂×D₅×#41	1	1	yes	characteristic
656	C₂	#66283	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₅
commutator, socle, cosocle	C₂²×C₅	C₂⁵
Frattini	C₂²	C₂⁴×D₅
Fitting	C₅×#529	C₂
hypercenter	#529	D₅
hypocenter	C₅	#3475
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ #529

Complements

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

N	H ≅ G/N	type
1. C₅×#529	C₂	semidirect
2. #66042	C₂	semidirect
3. #66039	C₂	semidirect
4. #66028	C₂	semidirect
5. #66024	C₂	semidirect
6. #66010	C₂	semidirect
7. #66005	C₂	semidirect
8. #65995	C₂	semidirect
9. #65993	C₂	semidirect
10. #65973	C₂	semidirect
11. #65965	C₂	semidirect
12. #65950	C₂	semidirect
13. #65946	C₂	semidirect
14. #65912	C₂	semidirect
15. C₄×#713	C₂	semidirect
16. #65891	C₂	semidirect
17. #65891	C₂	semidirect
18. #65881	C₂	semidirect
19. C₄×D₄×D₅	C₂	semidirect
20. #65862	C₂	semidirect
21. D₅×#117	C₂	semidirect
22. C₄×#709	C₂	semidirect
23. C₄×#709	C₂	semidirect
29. C₅×#126	C₂²	semidirect
30. C₅×#125	C₂²	semidirect
32. C₅×#123	C₂²	semidirect
33. C₅×C₂²⋊Q₈	C₂²	semidirect
35. C₄×C₅×Q₈	C₂²	semidirect
37. C₄×C₅×D₄	C₂²	semidirect
38. C₅×#117	C₂²	semidirect
39. C₂×C₄²×C₅	C₂²	semidirect
41. Q₈×Dic₅	C₂²	semidirect
42. #4090	C₂²	semidirect
43. #4085	C₂²	semidirect
48. #4082	C₂²	semidirect
53. C₄×C₂²⋊D₅	C₂²	semidirect
54. C₄×C₂²⋊D₅	C₂²	semidirect
55. C₄×C₂²⋊D₅	C₂²	semidirect
56. C₄×C₂²⋊D₅	C₂²	semidirect
57. C₄×C₂²⋊D₅	C₂²	semidirect
58. #4072	C₂²	semidirect
59. #4072	C₂²	semidirect
60. #4072	C₂²	semidirect
61. #4044	C₂²	semidirect
63. #4043	C₂²	semidirect
64. #4043	C₂²	semidirect
66. #4042	C₂²	semidirect
67. #4042	C₂²	semidirect
69. #4040	C₂²	semidirect
72. #4039	C₂²	semidirect
75. #4038	C₂²	semidirect
76. #4038	C₂²	semidirect
78. D₅×C₄⋊C₄	C₂²	semidirect
79. D₅×C₄⋊C₄	C₂²	semidirect
80. #4036	C₂²	semidirect
81. #4036	C₂²	semidirect
82. #4035	C₂²	semidirect
83. #4035	C₂²	semidirect
84. #4034	C₂²	semidirect
85. #4031	C₂²	semidirect
87. #4030	C₂²	semidirect
91. #4029	C₂²	semidirect
92. #4029	C₂²	semidirect
98. #4025	C₂²	semidirect
99. #4025	C₂²	semidirect
100. #4025	C₂²	semidirect
101. #4025	C₂²	semidirect
102. #4024	C₂²	semidirect
103. #4023	C₂²	semidirect
104. #4023	C₂²	semidirect
109. C₄×D₂₀	C₂²	semidirect
112. #4018	C₂²	semidirect
113. #4018	C₂²	semidirect
115. C₄²×D₅	C₂²	semidirect
116. C₄²×D₅	C₂²	semidirect
117. C₄²×D₅	C₂²	semidirect
118. C₄×Dic₁₀	C₂²	semidirect
119. C₄×Dic₁₀	C₂²	semidirect
120. C₄×Dic₁₀	C₂²	semidirect
121. C₄×Dic₁₀	C₂²	semidirect
122. C₄×Dic₁₀	C₂²	semidirect
244. #529	D₅	semidirect
292. D₂₀	#41	semidirect
305. C₄×D₅	#41	semidirect
321. #126	C₂×D₅	semidirect
326. #125	C₂×D₅	semidirect
338. #123	C₂×D₅	semidirect
347. C₂²⋊Q₈	C₂×D₅	semidirect
362. C₄×Q₈	C₂×D₅	semidirect
382. C₄×D₄	C₂×D₅	semidirect
396. #117	C₂×D₅	semidirect
407. C₂×C₄²	C₂×D₅	semidirect
613. C₅	#3475	semidirect

Maximal subgroups

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

subgroup	index
C₅×#529	2
#66042	2
#66039	2
#66028	2
#66024	2
#66010	2
#66005	2
#65995	2
#65993	2
#65973	2
#65965	2
#65950	2
#65946	2
#65912	2
C₄×#713	2
#65891	2
#65881	2
C₄×D₄×D₅	2
#65862	2
D₅×#117	2
C₄×#709	2
#3475	5