Subgroups — #10618455

Order 640.

1142 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#542	C₂	1	1	yes	maximal, characteristic, complemented
2	#66068	C₂	1	1	yes	maximal, characteristic, complemented
3	#66061	C₂	1	1	yes	maximal, characteristic, complemented
4	#66040	C₂	1	2	yes	maximal, complemented
5	#66038	C₂	1	2	yes	maximal, complemented
6	#66015	C₂	1	1	yes	maximal, characteristic, complemented
7	#66012	C₂	1	2	yes	maximal, complemented
8	#66010	C₂	1	1	yes	maximal, characteristic, complemented
9	D₅×#124	C₂	1	2	yes	maximal, complemented
10	#65993	C₂	1	2	yes	maximal, complemented
11	#65988	C₂	1	2	yes	maximal, complemented
12	#65975	C₂	1	1	yes	maximal, characteristic, complemented
13	#65971	C₂	1	2	yes	maximal, complemented
14	#65967	C₂	1	2	yes	maximal, complemented
15	#65964	C₂	1	1	yes	maximal, characteristic, complemented
16	#65950	C₂	1	1	yes	maximal, characteristic, complemented
17	#65943	C₂	1	1	yes	maximal, characteristic, complemented
18	#65916	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×#713	C₂	1	1	yes	maximal, characteristic, complemented
20	#65882	C₂	1	1	yes	maximal, characteristic, complemented
21	#65879	C₂	1	1	yes	maximal, characteristic, complemented
22	#65862	C₂	1	1	yes	maximal, characteristic, complemented
23	#65855	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#713	C₂²	1	1	yes	characteristic
25	C₂×Q₈×D₅	C₂²	1	2	yes	complemented
26	C₂×D₄×D₅	C₂²	1	1	yes	characteristic
27	C₂×D₄×D₅	C₂²	1	2	yes	—
28	C₂×#709	C₂²	1	2	yes	complemented
29	C₂²×D₂₀	C₂²	1	1	yes	characteristic
30	C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
31	C₅×#126	C₂²	1	2	yes	complemented
32	C₅×#124	C₂²	1	2	yes	complemented
33	C₅×#124	C₂²	1	1	yes	characteristic, complemented
34	C₅×#123	C₂²	1	2	yes	complemented
35	C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
36	C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
37	C₅×#121	C₂²	1	1	yes	characteristic
38	C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
39	C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
40	C₅×#117	C₂²	1	1	yes	characteristic, complemented
41	#4093	C₂²	1	2	yes	complemented
42	#4093	C₂²	1	2	yes	complemented
43	#4093	C₂²	1	1	yes	characteristic, complemented
44	#4092	C₂²	1	2	yes	complemented
45	#4092	C₂²	1	1	yes	characteristic, complemented
46	Q₈×Dic₅	C₂²	1	1	yes	characteristic, complemented
47	#4086	C₂²	1	1	yes	characteristic
48	#4085	C₂²	1	2	yes	complemented
49	#4084	C₂²	1	1	yes	characteristic, complemented
50	#4083	C₂²	1	2	yes	—
51	#4082	C₂²	1	2	yes	complemented
52	D₄×Dic₅	C₂²	1	1	yes	characteristic, complemented
53	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic
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	2	yes	complemented
57	C₂×#685	C₂²	1	2	yes	complemented
58	#4072	C₂²	1	1	yes	characteristic, complemented
59	#4044	C₂²	1	1	yes	characteristic, complemented
60	#4044	C₂²	1	2	yes	complemented
61	#4042	C₂²	1	2	yes	complemented
62	#4042	C₂²	1	2	yes	complemented
63	#4042	C₂²	1	1	yes	characteristic, complemented
64	#4042	C₂²	1	2	yes	complemented
65	#4041	C₂²	1	1	yes	characteristic
66	#4041	C₂²	1	1	yes	characteristic, complemented
67	#4041	C₂²	1	2	yes	complemented
68	#4041	C₂²	1	2	yes	complemented
69	#4040	C₂²	1	1	yes	characteristic, complemented
70	#4040	C₂²	1	2	yes	complemented
71	#4040	C₂²	1	2	yes	complemented
72	#4039	C₂²	1	1	yes	characteristic
73	#4039	C₂²	1	1	yes	characteristic
74	#4039	C₂²	1	2	yes	complemented
75	#4039	C₂²	1	2	yes	complemented
76	#4039	C₂²	1	2	yes	complemented
77	#4038	C₂²	1	1	yes	characteristic, complemented
78	#4038	C₂²	1	1	yes	characteristic, complemented
79	#4038	C₂²	1	2	yes	complemented
80	#4038	C₂²	1	2	yes	complemented
81	#4035	C₂²	1	1	yes	characteristic, complemented
82	#4034	C₂²	1	1	yes	characteristic, complemented
83	#4034	C₂²	1	1	yes	characteristic, complemented
84	#4033	C₂²	1	2	yes	complemented
85	#4032	C₂²	1	2	yes	complemented
86	#4031	C₂²	1	1	yes	characteristic
87	#4031	C₂²	1	2	yes	—
88	#4031	C₂²	1	2	yes	complemented
89	#4031	C₂²	1	2	yes	complemented
90	#4031	C₂²	1	2	yes	complemented
91	#4030	C₂²	1	1	yes	characteristic
92	#4030	C₂²	1	2	yes	—
93	#4030	C₂²	1	2	yes	complemented
94	#4030	C₂²	1	2	yes	complemented
95	#4029	C₂²	1	1	yes	characteristic, complemented
96	#4029	C₂²	1	2	yes	complemented
97	#4029	C₂²	1	2	yes	complemented
98	#4028	C₂²	1	2	yes	—
99	#4028	C₂²	1	2	yes	complemented
100	#4028	C₂²	1	2	yes	complemented
101	#4027	C₂²	1	2	yes	complemented
102	#4027	C₂²	1	2	yes	complemented
103	D₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
104	D₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
105	D₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
106	D₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
107	D₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
108	#4025	C₂²	1	1	yes	characteristic, complemented
109	#4025	C₂²	1	2	yes	complemented
110	#4023	C₂²	1	2	yes	complemented
111	#4022	C₂²	1	2	yes	complemented
112	#4021	C₂²	1	2	yes	complemented
113	C₄×D₂₀	C₂²	1	1	yes	characteristic
114	C₄×D₂₀	C₂²	1	1	yes	characteristic
115	C₄×D₂₀	C₂²	1	1	yes	characteristic, complemented
116	C₄×D₂₀	C₂²	1	1	yes	characteristic, complemented
117	C₄×D₂₀	C₂²	1	1	yes	characteristic, complemented
118	C₄×D₂₀	C₂²	1	2	yes	complemented
119	#4018	C₂²	1	1	yes	characteristic, complemented
120	C₄²×D₅	C₂²	1	1	yes	characteristic, complemented
121	C₄²×D₅	C₂²	1	2	yes	complemented
122	C₄×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
123	#3514	—	5	1	no	maximal, Sylow
124	C₂³×D₅	C₂³	1	2	yes	—
125	C₂³×D₅	C₂³	1	2	yes	—
126	C₂×C₅×Q₈	C₂³	1	1	yes	characteristic
127	C₂×C₅×Q₈	C₂³	1	2	yes	—
128	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
129	C₂×C₅×D₄	C₂³	1	2	yes	—
130	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
131	C₂²×C₄×C₅	C₂³	1	2	yes	—
132	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
133	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
134	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
135	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
138	C₂²×Dic₅	C₂³	1	2	yes	—
139	#713	—	2	4	no	—
140	Q₈×D₅	—	4	4	no	—
141	D₄×D₅	—	2	4	no	—
142	D₄×D₅	—	4	4	no	—
143	#709	—	4	4	no	—
144	C₂×D₂₀	—	2	4	no	—
145	C₂×D₂₀	C₂³	1	1	yes	characteristic
146	C₂×D₂₀	C₂³	1	2	yes	—
147	C₂×D₂₀	C₂³	1	2	yes	—
148	C₂×D₂₀	C₂³	1	2	yes	—
149	C₂×D₂₀	C₂³	1	2	yes	—
150	C₂×D₂₀	C₂³	1	1	yes	characteristic
151	C₂×D₂₀	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	1	yes	characteristic
156	C₂×C₄×D₅	C₂³	1	2	yes	—
157	C₂×C₄×D₅	C₂³	1	2	yes	—
158	C₂×C₄×D₅	C₂³	1	2	yes	—
159	C₂×C₄×D₅	C₂³	1	2	yes	—
160	C₂×C₄×D₅	C₂³	1	2	yes	—
161	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
162	C₂×C₄×D₅	C₂³	1	2	yes	—
163	C₂×Dic₁₀	C₂³	1	2	yes	—
164	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
165	C₂×Dic₁₀	C₂³	1	2	yes	—
166	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
167	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
168	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
169	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
170	C₅×C₄⋊C₄	C₂³	1	2	yes	—
171	C₅×C₄⋊C₄	C₂³	1	2	yes	—
172	C₅×C₄⋊C₄	C₂³	1	2	yes	—
173	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
174	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
175	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
176	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
177	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
178	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
179	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
180	C₄²×C₅	C₂³	1	1	yes	characteristic
181	C₄²×C₅	C₂³	1	1	yes	characteristic
182	C₄²×C₅	C₂³	1	2	yes	—
183	C₂²⋊Dic₅	C₂³	1	2	yes	—
184	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
185	C₂²⋊Dic₅	C₂³	1	2	yes	—
186	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
187	C₂²⋊Dic₅	C₂³	1	2	yes	—
188	#685	C₂³	1	1	yes	characteristic
189	#685	C₂³	1	1	yes	characteristic
190	#685	C₂³	1	2	yes	—
191	#685	C₂³	1	2	yes	—
192	#685	C₂³	1	2	yes	—
193	#685	C₂³	1	1	yes	characteristic
194	#685	C₂³	1	2	yes	—
195	#685	C₂³	1	2	yes	—
196	#685	C₂³	1	1	yes	characteristic
197	#685	C₂³	1	2	yes	—
198	#685	C₂³	1	2	yes	—
199	#685	C₂³	1	2	yes	—
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	#683	C₂³	1	1	yes	characteristic
213	#683	C₂³	1	1	yes	characteristic
214	#683	C₂³	1	1	yes	characteristic
215	#683	C₂³	1	1	yes	characteristic
216	#683	C₂³	1	2	yes	—
217	#683	C₂³	1	2	yes	—
218	#683	C₂³	1	1	yes	characteristic
219	#683	C₂³	1	2	yes	—
220	#683	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	2	yes	—
225	C₄×Dic₅	C₂³	1	1	yes	characteristic
226	C₄×Dic₅	C₂³	1	2	yes	—
227	C₄×Dic₅	C₂³	1	2	yes	—
228	C₄×Dic₅	C₂³	1	2	yes	—
229	#559	—	5	1	no	—
230	#556	—	5	1	no	—
231	#555	—	5	1	no	—
232	#555	—	5	1	no	—
233	#551	—	5	2	no	—
234	#551	—	5	2	no	—
235	D₄×Q₈	—	5	1	no	—
236	#548	—	5	2	no	—
237	#546	—	5	1	no	—
238	#546	—	5	2	no	—
239	#546	—	5	1	no	—
240	D₄²	—	5	1	no	—
241	#542	—	5	1	no	—
242	#542	D₅	1	1	yes	characteristic, complemented
243	#538	—	5	2	no	—
244	#538	—	5	2	no	—
245	#532	—	5	1	no	—
246	#529	—	5	2	no	—
247	#529	—	5	1	no	—
248	C₂×#124	—	5	2	no	—
249	#518	—	5	1	no	—
250	#518	—	5	1	no	—
251	C₄×#41	—	5	1	no	—
252	C₂³×C₅	C₂⁴	1	1	yes	characteristic
253	C₂³×C₅	C₂⁴	1	2	yes	—
254	C₂²×D₅	—	2	4	no	—
255	C₂²×D₅	—	2	4	no	—
256	C₂²×D₅	—	4	2	no	—
257	C₂²×D₅	—	4	2	no	—
258	C₂²×D₅	—	4	2	no	—
259	C₂²×D₅	—	4	2	no	—
260	C₂²×D₅	C₂⁴	1	1	yes	characteristic
261	C₂²×D₅	C₂⁴	1	2	yes	—
262	C₂²×D₅	C₂⁴	1	1	yes	characteristic
263	C₂²×D₅	C₂⁴	1	2	yes	—
264	C₅×Q₈	—	2	2	no	—
265	C₅×Q₈	—	4	2	no	—
266	C₅×D₄	—	2	2	no	—
267	C₅×D₄	—	4	2	no	—
268	C₂×C₄×C₅	—	2	2	no	—
269	C₂×C₄×C₅	—	4	2	no	—
270	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
271	C₂×C₄×C₅	C₂⁴	1	2	yes	—
272	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
273	C₂×C₄×C₅	C₂⁴	1	2	yes	—
274	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
275	C₂×C₄×C₅	C₂⁴	1	2	yes	—
276	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
277	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
278	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
279	C₂²⋊D₅	—	2	4	no	—
280	C₂²⋊D₅	—	2	4	no	—
281	C₂²⋊D₅	—	2	2	no	—
282	C₂²⋊D₅	—	4	2	no	—
283	C₂²⋊D₅	—	4	2	no	—
284	C₂²⋊D₅	—	4	1	no	—
285	C₂×Dic₅	—	4	2	no	—
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	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
291	C₂×Dic₅	C₂⁴	1	2	yes	—
292	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
293	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
294	D₂₀	—	2	4	no	—
295	D₂₀	—	2	4	no	—
296	D₂₀	—	2	2	no	—
297	D₂₀	—	4	1	no	—
298	D₂₀	—	4	2	no	—
299	D₂₀	—	4	2	no	—
300	D₂₀	#41	1	4	yes	complemented
301	C₄×D₅	—	2	4	no	—
302	C₄×D₅	—	2	2	no	—
303	C₄×D₅	—	2	2	no	—
304	C₄×D₅	—	2	2	no	—
305	C₄×D₅	—	2	4	no	—
306	C₄×D₅	—	4	2	no	—
307	C₄×D₅	—	4	2	no	—
308	C₄×D₅	—	4	1	no	—
309	C₄×D₅	—	4	2	no	—
310	C₄×D₅	—	4	2	no	—
311	C₄×D₅	—	4	2	no	—
312	Dic₁₀	—	2	4	no	—
313	Dic₁₀	—	2	2	no	—
314	Dic₁₀	—	4	2	no	—
315	C₂×#41	—	5	1	no	—
316	C₂×#41	—	5	2	no	—
317	C₂²×Q₈	—	5	2	no	—
318	C₂²×D₄	—	5	1	no	—
319	C₂²×D₄	—	5	2	no	—
320	C₂²×D₄	—	5	1	no	—
321	C₄⋊Q₈	—	5	1	no	—
322	C₄⋊Q₈	—	5	1	no	—
323	C₄⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
324	#127	—	5	1	no	—
325	#126	—	5	1	no	—
326	#126	—	5	2	no	—
327	#126	—	5	1	no	—
328	#126	—	5	2	no	—
329	#126	—	5	2	no	—
330	#126	C₂×D₅	1	2	yes	complemented
331	#125	—	5	1	no	—
332	#124	—	5	2	no	—
333	#124	—	5	2	no	—
334	#124	—	5	1	no	—
335	#124	—	5	2	no	—
336	#124	—	5	1	no	—
337	#124	—	5	2	no	—
338	#124	—	5	2	no	—
339	#124	—	5	2	no	—
340	#124	—	5	2	no	—
341	#124	—	5	2	no	—
342	#124	C₂×D₅	1	2	yes	complemented
343	#124	C₂×D₅	1	1	yes	characteristic, complemented
344	#123	—	5	1	no	—
345	#123	—	5	2	no	—
346	#123	—	5	2	no	—
347	#123	—	5	1	no	—
348	#123	—	5	2	no	—
349	#123	—	5	2	no	—
350	#123	—	5	2	no	—
351	#123	C₂×D₅	1	2	yes	complemented
352	C₂²⋊Q₈	—	5	2	no	—
353	C₂²⋊Q₈	—	5	1	no	—
354	C₂²⋊Q₈	—	5	2	no	—
355	C₂²⋊Q₈	—	5	1	no	—
356	C₂²⋊Q₈	—	5	2	no	—
357	C₂²⋊Q₈	—	5	2	no	—
358	C₂²⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
359	C₂²⋊Q₈	C₂×D₅	1	2	yes	complemented
360	#121	—	5	1	no	—
361	#121	—	5	2	no	—
362	#121	—	5	1	no	—
363	#121	—	5	2	no	—
364	#121	—	5	2	no	—
365	#121	—	5	1	no	—
366	#121	—	5	2	no	—
367	#121	—	5	1	no	—
368	#121	—	5	2	no	—
369	#121	—	5	2	no	—
370	#121	C₂×D₅	1	1	yes	characteristic
371	#120	—	5	2	no	—
372	#120	—	5	2	no	—
373	#120	—	5	2	no	—
374	#120	—	5	2	no	—
375	C₄×Q₈	—	5	1	no	—
376	C₄×Q₈	—	5	2	no	—
377	C₄×Q₈	—	5	1	no	—
378	C₄×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
379	C₄×D₄	—	5	1	no	—
380	C₄×D₄	—	5	2	no	—
381	C₄×D₄	—	5	1	no	—
382	C₄×D₄	—	5	1	no	—
383	C₄×D₄	—	5	2	no	—
384	C₄×D₄	—	5	1	no	—
385	C₄×D₄	—	5	2	no	—
386	C₄×D₄	—	5	2	no	—
387	C₄×D₄	—	5	1	no	—
388	C₄×D₄	—	5	2	no	—
389	C₄×D₄	—	5	2	no	—
390	C₄×D₄	—	5	2	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	1	no	—
396	C₄×D₄	—	5	1	no	—
397	C₄×D₄	C₂×D₅	1	1	yes	characteristic, complemented
398	#117	—	5	1	no	—
399	#117	—	5	2	no	—
400	#117	—	5	1	no	—
401	#117	—	5	1	no	—
402	#117	—	5	2	no	—
403	#117	—	5	2	no	—
404	#117	—	5	1	no	—
405	#117	C₂×D₅	1	1	yes	characteristic, complemented
406	C₂×C₂²⋊C₄	—	5	2	no	—
407	C₂×C₂²⋊C₄	—	5	2	no	—
408	C₂×C₂²⋊C₄	—	5	2	no	—
409	C₂×C₂²⋊C₄	—	5	2	no	—
410	C₂×C₂²⋊C₄	—	5	2	no	—
411	C₂×C₂²⋊C₄	—	5	2	no	—
412	C₂×C₄²	—	5	2	no	—
413	C₂×C₄²	—	5	1	no	—
414	C₂²×C₅	—	2	2	no	—
415	C₂²×C₅	—	2	1	no	—
416	C₂²×C₅	—	2	2	no	—
417	C₂²×C₅	—	2	1	no	—
418	C₂²×C₅	—	2	2	no	—
419	C₂²×C₅	—	2	1	no	—
420	C₂²×C₅	C₂⁵	1	1	yes	characteristic
421	C₂×D₅	—	2	2	no	—
422	C₂×D₅	—	2	2	no	—
423	C₂×D₅	—	2	1	no	—
424	C₂×D₅	—	2	1	no	—
425	C₂×D₅	—	2	2	no	—
426	C₂×D₅	—	2	1	no	—
427	C₂×D₅	—	2	2	no	—
428	C₂×D₅	—	2	1	no	—
429	C₂×D₅	—	2	1	no	—
430	C₂×D₅	—	2	2	no	—
431	C₂×D₅	—	2	1	no	—
432	C₂×D₅	—	8	4	no	—
433	C₂×D₅	—	8	4	no	—
434	C₂×D₅	C₂×#41	1	4	yes	—
435	C₄×C₅	—	2	2	no	—
436	C₄×C₅	—	2	1	no	—
437	C₄×C₅	—	2	1	no	—
438	C₄×C₅	—	2	2	no	—
439	C₄×C₅	—	2	2	no	—
440	C₄×C₅	—	2	1	no	—
441	C₄×C₅	—	2	1	no	—
442	C₄×C₅	—	2	1	no	—
443	C₄×C₅	C₂×#41	1	2	yes	—
444	Dic₅	—	2	1	no	—
445	Dic₅	—	2	1	no	—
446	Dic₅	—	2	1	no	—
447	Dic₅	—	2	2	no	—
448	Dic₅	—	2	2	no	—
449	Dic₅	—	2	1	no	—
450	Dic₅	—	2	1	no	—
451	Dic₅	H(5,𝔽₂)	1	2	yes	—
452	C₂⁴	—	5	2	no	—
453	C₂⁴	—	5	2	no	—
454	#41	—	10	4	no	—
455	#41	—	20	4	no	—
456	C₂×Q₈	—	5	1	no	—
457	C₂×Q₈	—	5	2	no	—
458	C₂×Q₈	—	5	2	no	—
459	C₂×Q₈	—	20	4	no	—
460	C₂×Q₈	C₂²×D₅	1	1	yes	characteristic
461	C₂×Q₈	C₂²×D₅	1	2	yes	—
462	C₂×D₄	—	5	2	no	—
463	C₂×D₄	—	5	1	no	—
464	C₂×D₄	—	5	2	no	—
465	C₂×D₄	—	5	1	no	—
466	C₂×D₄	—	5	2	no	—
467	C₂×D₄	—	5	2	no	—
468	C₂×D₄	—	5	1	no	—
469	C₂×D₄	—	5	2	no	—
470	C₂×D₄	—	5	2	no	—
471	C₂×D₄	—	5	1	no	—
472	C₂×D₄	—	5	1	no	—
473	C₂×D₄	—	5	2	no	—
474	C₂×D₄	—	5	2	no	—
475	C₂×D₄	—	10	4	no	—
476	C₂×D₄	—	10	4	no	—
477	C₂×D₄	—	20	4	no	—
478	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
479	C₂×D₄	C₂²×D₅	1	2	yes	—
480	C₂²×C₄	—	5	2	no	—
481	C₂²×C₄	—	5	2	no	—
482	C₂²×C₄	—	5	1	no	—
483	C₂²×C₄	—	5	2	no	—
484	C₂²×C₄	—	5	1	no	—
485	C₂²×C₄	—	5	1	no	—
486	C₂²×C₄	—	5	2	no	—
487	C₂²×C₄	—	5	1	no	—
488	C₂²×C₄	—	5	2	no	—
489	C₂²×C₄	—	5	2	no	—
490	C₂²×C₄	—	5	2	no	—
491	C₂²×C₄	—	5	2	no	—
492	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
493	C₂²×C₄	C₂²×D₅	1	2	yes	—
494	C₄⋊C₄	—	5	1	no	—
495	C₄⋊C₄	—	5	1	no	—
496	C₄⋊C₄	—	5	1	no	—
497	C₄⋊C₄	—	5	1	no	—
498	C₄⋊C₄	—	5	1	no	—
499	C₄⋊C₄	—	5	1	no	—
500	C₄⋊C₄	—	5	2	no	—
501	C₄⋊C₄	—	5	2	no	—
502	C₄⋊C₄	—	5	1	no	—
503	C₄⋊C₄	—	5	1	no	—
504	C₄⋊C₄	—	5	2	no	—
505	C₄⋊C₄	—	5	2	no	—
506	C₄⋊C₄	—	5	1	no	—
507	C₄⋊C₄	—	5	1	no	—
508	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
509	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
510	C₄⋊C₄	C₂²×D₅	1	2	yes	—
511	C₄⋊C₄	C₂²×D₅	1	2	yes	—
512	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
513	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
514	C₄⋊C₄	C₂²×D₅	1	2	yes	—
515	C₂²⋊C₄	—	5	2	no	—
516	C₂²⋊C₄	—	5	1	no	—
517	C₂²⋊C₄	—	5	2	no	—
518	C₂²⋊C₄	—	5	2	no	—
519	C₂²⋊C₄	—	5	1	no	—
520	C₂²⋊C₄	—	5	2	no	—
521	C₂²⋊C₄	—	5	1	no	—
522	C₂²⋊C₄	—	5	2	no	—
523	C₂²⋊C₄	—	5	1	no	—
524	C₂²⋊C₄	—	5	1	no	—
525	C₂²⋊C₄	—	5	2	no	—
526	C₂²⋊C₄	—	5	2	no	—
527	C₂²⋊C₄	—	5	2	no	—
528	C₂²⋊C₄	—	5	2	no	—
529	C₂²⋊C₄	—	5	2	no	—
530	C₂²⋊C₄	—	5	2	no	—
531	C₂²⋊C₄	—	5	2	no	—
532	C₂²⋊C₄	—	5	2	no	—
533	C₂²⋊C₄	—	5	2	no	—
534	C₂²⋊C₄	—	5	2	no	—
535	C₂²⋊C₄	—	5	1	no	—
536	C₂²⋊C₄	—	5	2	no	—
537	C₂²⋊C₄	—	5	1	no	—
538	C₂²⋊C₄	—	5	1	no	—
539	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
540	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
541	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
542	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
543	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
544	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
545	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
546	C₄²	—	5	1	no	—
547	C₄²	—	5	2	no	—
548	C₄²	—	5	1	no	—
549	C₄²	—	5	2	no	—
550	C₄²	—	5	1	no	—
551	C₄²	—	5	2	no	—
552	C₄²	—	5	2	no	—
553	C₄²	—	5	1	no	—
554	C₄²	C₂²×D₅	1	1	yes	characteristic
555	C₄²	C₂²×D₅	1	2	yes	—
556	C₄²	C₂²×D₅	1	1	yes	characteristic
557	C₂×C₅	—	4	1	no	—
558	C₂×C₅	—	4	2	no	—
559	C₂×C₅	C₂²×#41	1	1	yes	characteristic
560	C₂×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
561	C₂×C₅	#585	1	1	yes	characteristic
562	D₅	—	2	4	no	—
563	D₅	—	4	1	no	—
564	D₅	—	4	2	no	—
565	D₅	—	4	1	no	—
566	C₂³	—	5	2	no	—
567	C₂³	—	5	1	no	—
568	C₂³	—	5	2	no	—
569	C₂³	—	5	1	no	—
570	C₂³	—	10	4	no	—
571	C₂³	—	10	4	no	—
572	C₂³	—	20	2	no	—
573	C₂³	—	20	2	no	—
574	C₂³	—	20	2	no	—
575	C₂³	—	20	2	no	—
576	C₂³	C₂³×D₅	1	1	yes	characteristic
577	C₂³	C₂³×D₅	1	2	yes	—
578	Q₈	—	2	2	no	—
579	Q₈	—	4	2	no	—
580	Q₈	—	10	2	no	—
581	Q₈	—	10	4	no	—
582	Q₈	—	20	2	no	—
583	D₄	—	2	2	no	—
584	D₄	—	4	2	no	—
585	D₄	—	5	4	no	—
586	D₄	—	10	4	no	—
587	D₄	—	10	4	no	—
588	D₄	—	10	2	no	—
589	D₄	—	10	4	no	—
590	D₄	—	10	4	no	—
591	D₄	—	10	2	no	—
592	D₄	—	20	2	no	—
593	D₄	—	20	2	no	—
594	D₄	—	20	1	no	—
595	D₄	—	20	2	no	—
596	D₄	—	20	1	no	—
597	D₄	—	20	2	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	4	2	no	—
600	C₂×C₄	—	5	1	no	—
601	C₂×C₄	—	5	1	no	—
602	C₂×C₄	—	5	2	no	—
603	C₂×C₄	—	5	1	no	—
604	C₂×C₄	—	5	1	no	—
605	C₂×C₄	—	5	1	no	—
606	C₂×C₄	—	5	1	no	—
607	C₂×C₄	—	5	2	no	—
608	C₂×C₄	—	10	4	no	—
609	C₂×C₄	—	10	2	no	—
610	C₂×C₄	—	10	4	no	—
611	C₂×C₄	—	10	2	no	—
612	C₂×C₄	—	10	2	no	—
613	C₂×C₄	—	20	2	no	—
614	C₂×C₄	—	20	2	no	—
615	C₂×C₄	—	20	2	no	—
616	C₂×C₄	—	20	2	no	—
617	C₂×C₄	—	20	1	no	—
618	C₂×C₄	—	20	2	no	—
619	C₂×C₄	—	20	2	no	—
620	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
621	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
622	C₂×C₄	C₂³×D₅	1	2	yes	—
623	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
624	C₂×C₄	C₂³×D₅	1	2	yes	—
625	C₂×C₄	C₂³×D₅	1	2	yes	—
626	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
627	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
628	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
629	C₅	#3514	1	1	yes	characteristic, complemented, Sylow
630	C₂²	—	2	1	no	—
631	C₂²	—	2	2	no	—
632	C₂²	—	2	2	no	—
633	C₂²	—	2	1	no	—
634	C₂²	—	2	2	no	—
635	C₂²	—	2	1	no	—
636	C₂²	—	5	4	no	—
637	C₂²	—	10	2	no	—
638	C₂²	—	10	2	no	—
639	C₂²	—	10	1	no	—
640	C₂²	—	10	1	no	—
641	C₂²	—	10	2	no	—
642	C₂²	—	10	1	no	—
643	C₂²	—	10	2	no	—
644	C₂²	—	10	1	no	—
645	C₂²	—	10	1	no	—
646	C₂²	—	10	2	no	—
647	C₂²	—	10	1	no	—
648	C₂²	—	40	4	no	—
649	C₂²	—	40	4	no	—
650	C₂²	C₂⁴×D₅	1	1	yes	characteristic
651	C₄	—	2	1	no	—
652	C₄	—	2	2	no	—
653	C₄	—	2	1	no	—
654	C₄	—	2	2	no	—
655	C₄	—	2	2	no	—
656	C₄	—	2	1	no	—
657	C₄	—	2	1	no	—
658	C₄	—	2	1	no	—
659	C₄	—	5	2	no	—
660	C₄	—	10	1	no	—
661	C₄	—	10	1	no	—
662	C₄	—	10	2	no	—
663	C₄	—	10	1	no	—
664	C₄	—	10	2	no	—
665	C₄	—	10	1	no	—
666	C₄	—	10	1	no	—
667	C₄	D₅×#41	1	2	yes	—
668	C₂	—	4	1	no	—
669	C₂	—	4	2	no	—
670	C₂	—	10	4	no	—
671	C₂	—	20	1	no	—
672	C₂	—	20	2	no	—
673	C₂	—	20	1	no	—
674	C₂	C₂×D₅×#41	1	1	yes	characteristic
675	C₂	D₅×H(5,𝔽₂)	1	1	yes	characteristic
676	C₂	#66287	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅
commutator, socle, cosocle	C₂²×C₅	C₂⁵
Fitting	C₅×#542	C₂
hypercenter	#542	D₅
hypocenter	C₅	#3514
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ #542

Complements

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

N	H ≅ G/N	type
1. C₅×#542	C₂	semidirect
2. #66068	C₂	semidirect
3. #66061	C₂	semidirect
4. #66040	C₂	semidirect
5. #66038	C₂	semidirect
6. #66015	C₂	semidirect
7. #66012	C₂	semidirect
8. #66010	C₂	semidirect
9. D₅×#124	C₂	semidirect
10. #65993	C₂	semidirect
11. #65988	C₂	semidirect
12. #65975	C₂	semidirect
13. #65971	C₂	semidirect
14. #65967	C₂	semidirect
15. #65964	C₂	semidirect
16. #65950	C₂	semidirect
17. #65943	C₂	semidirect
18. #65916	C₂	semidirect
19. C₄×#713	C₂	semidirect
20. #65882	C₂	semidirect
21. #65879	C₂	semidirect
22. #65862	C₂	semidirect
23. #65855	C₂	semidirect
25. C₂×Q₈×D₅	C₂²	semidirect
28. C₂×#709	C₂²	semidirect
30. C₅×C₄⋊Q₈	C₂²	semidirect
31. C₅×#126	C₂²	semidirect
32. C₅×#124	C₂²	semidirect
33. C₅×#124	C₂²	semidirect
34. C₅×#123	C₂²	semidirect
35. C₅×C₂²⋊Q₈	C₂²	semidirect
36. C₅×C₂²⋊Q₈	C₂²	semidirect
38. C₄×C₅×Q₈	C₂²	semidirect
39. C₄×C₅×D₄	C₂²	semidirect
40. C₅×#117	C₂²	semidirect
41. #4093	C₂²	semidirect
42. #4093	C₂²	semidirect
43. #4093	C₂²	semidirect
44. #4092	C₂²	semidirect
45. #4092	C₂²	semidirect
46. Q₈×Dic₅	C₂²	semidirect
48. #4085	C₂²	semidirect
49. #4084	C₂²	semidirect
51. #4082	C₂²	semidirect
52. D₄×Dic₅	C₂²	semidirect
54. C₄×C₂²⋊D₅	C₂²	semidirect
55. C₄×C₂²⋊D₅	C₂²	semidirect
56. C₄×C₂²⋊D₅	C₂²	semidirect
57. C₂×#685	C₂²	semidirect
58. #4072	C₂²	semidirect
59. #4044	C₂²	semidirect
60. #4044	C₂²	semidirect
61. #4042	C₂²	semidirect
62. #4042	C₂²	semidirect
63. #4042	C₂²	semidirect
64. #4042	C₂²	semidirect
66. #4041	C₂²	semidirect
67. #4041	C₂²	semidirect
68. #4041	C₂²	semidirect
69. #4040	C₂²	semidirect
70. #4040	C₂²	semidirect
71. #4040	C₂²	semidirect
74. #4039	C₂²	semidirect
75. #4039	C₂²	semidirect
76. #4039	C₂²	semidirect
77. #4038	C₂²	semidirect
78. #4038	C₂²	semidirect
79. #4038	C₂²	semidirect
80. #4038	C₂²	semidirect
81. #4035	C₂²	semidirect
82. #4034	C₂²	semidirect
83. #4034	C₂²	semidirect
84. #4033	C₂²	semidirect
85. #4032	C₂²	semidirect
88. #4031	C₂²	semidirect
89. #4031	C₂²	semidirect
90. #4031	C₂²	semidirect
93. #4030	C₂²	semidirect
94. #4030	C₂²	semidirect
95. #4029	C₂²	semidirect
96. #4029	C₂²	semidirect
97. #4029	C₂²	semidirect
99. #4028	C₂²	semidirect
100. #4028	C₂²	semidirect
101. #4027	C₂²	semidirect
102. #4027	C₂²	semidirect
103. D₅×C₂²⋊C₄	C₂²	semidirect
104. D₅×C₂²⋊C₄	C₂²	semidirect
105. D₅×C₂²⋊C₄	C₂²	semidirect
106. D₅×C₂²⋊C₄	C₂²	semidirect
107. D₅×C₂²⋊C₄	C₂²	semidirect
108. #4025	C₂²	semidirect
109. #4025	C₂²	semidirect
110. #4023	C₂²	semidirect
111. #4022	C₂²	semidirect
112. #4021	C₂²	semidirect
115. C₄×D₂₀	C₂²	semidirect
116. C₄×D₂₀	C₂²	semidirect
117. C₄×D₂₀	C₂²	semidirect
118. C₄×D₂₀	C₂²	semidirect
119. #4018	C₂²	semidirect
120. C₄²×D₅	C₂²	semidirect
121. C₄²×D₅	C₂²	semidirect
122. C₄×Dic₁₀	C₂²	semidirect
242. #542	D₅	semidirect
300. D₂₀	#41	semidirect
323. C₄⋊Q₈	C₂×D₅	semidirect
330. #126	C₂×D₅	semidirect
342. #124	C₂×D₅	semidirect
343. #124	C₂×D₅	semidirect
351. #123	C₂×D₅	semidirect
358. C₂²⋊Q₈	C₂×D₅	semidirect
359. C₂²⋊Q₈	C₂×D₅	semidirect
378. C₄×Q₈	C₂×D₅	semidirect
397. C₄×D₄	C₂×D₅	semidirect
405. #117	C₂×D₅	semidirect
629. C₅	#3514	semidirect

Maximal subgroups

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

subgroup	index
C₅×#542	2
#66068	2
#66061	2
#66040	2
#66038	2
#66015	2
#66012	2
#66010	2
D₅×#124	2
#65993	2
#65988	2
#65975	2
#65971	2
#65967	2
#65964	2
#65950	2
#65943	2
#65916	2
C₄×#713	2
#65882	2
#65879	2
#65862	2
#65855	2
#3514	5