Subgroups — #10618742

Order 640.

1042 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#552	C₂	1	1	yes	maximal, characteristic, complemented
2	#66039	C₂	1	2	yes	maximal, complemented
3	D₅×#126	C₂	1	2	yes	maximal, complemented
4	#66028	C₂	1	2	yes	maximal, complemented
5	#66026	C₂	1	2	yes	maximal, complemented
6	#66025	C₂	1	1	yes	maximal, characteristic, complemented
7	#66024	C₂	1	1	yes	maximal, characteristic, complemented
8	#65993	C₂	1	2	yes	maximal, complemented
9	#65991	C₂	1	2	yes	maximal, complemented
10	#65977	C₂	1	1	yes	maximal, characteristic, complemented
11	#65965	C₂	1	1	yes	maximal, characteristic, complemented
12	#65964	C₂	1	1	yes	maximal, characteristic, complemented
13	#65959	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×#713	C₂	1	1	yes	maximal, characteristic, complemented
15	#65902	C₂	1	1	yes	maximal, characteristic, complemented
16	#65891	C₂	1	1	yes	maximal, characteristic, complemented
17	#65884	C₂	1	1	yes	maximal, characteristic, complemented
18	#65867	C₂	1	1	yes	maximal, characteristic, complemented
19	#65864	C₂	1	2	yes	maximal, complemented
20	#65862	C₂	1	2	yes	maximal, complemented
21	#65855	C₂	1	1	yes	maximal, characteristic, complemented
22	#65848	C₂	1	1	yes	maximal, characteristic, complemented
23	#65838	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#713	C₂²	1	1	yes	characteristic
25	C₂×#709	C₂²	1	1	yes	characteristic
26	C₂²×D₂₀	C₂²	1	1	yes	characteristic
27	C₅×#126	C₂²	1	2	yes	—
28	C₅×#125	C₂²	1	1	yes	characteristic, complemented
29	C₅×#125	C₂²	1	2	yes	complemented
30	C₅×#123	C₂²	1	2	yes	—
31	C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
32	C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
33	C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
34	C₄×C₅×D₄	C₂²	1	1	yes	characteristic
35	C₅×#117	C₂²	1	1	yes	characteristic
36	C₅×#117	C₂²	1	2	yes	complemented
37	C₂×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
38	#4093	C₂²	1	1	yes	characteristic
39	Q₈×Dic₅	C₂²	1	1	yes	characteristic, complemented
40	#4090	C₂²	1	1	yes	characteristic, complemented
41	#4084	C₂²	1	1	yes	characteristic
42	#4083	C₂²	1	2	yes	—
43	#4082	C₂²	1	1	yes	characteristic
44	#4076	C₂²	1	1	yes	characteristic
45	#4076	C₂²	1	2	yes	complemented
46	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic
47	C₄×C₂²⋊D₅	C₂²	1	2	yes	complemented
48	C₄×C₂²⋊D₅	C₂²	1	2	yes	complemented
49	C₄×C₂²⋊D₅	C₂²	1	2	yes	complemented
50	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic, complemented
51	#4072	C₂²	1	1	yes	characteristic
52	#4072	C₂²	1	1	yes	characteristic, complemented
53	#4070	C₂²	1	1	yes	characteristic
54	#4044	C₂²	1	2	yes	complemented
55	#4044	C₂²	1	2	yes	complemented
56	#4044	C₂²	1	2	yes	complemented
57	#4044	C₂²	1	2	yes	complemented
58	#4043	C₂²	1	1	yes	characteristic, complemented
59	#4043	C₂²	1	1	yes	characteristic, complemented
60	#4043	C₂²	1	2	yes	complemented
61	#4043	C₂²	1	2	yes	complemented
62	#4042	C₂²	1	2	yes	complemented
63	#4042	C₂²	1	2	yes	complemented
64	#4042	C₂²	1	2	yes	complemented
65	#4041	C₂²	1	1	yes	characteristic
66	#4041	C₂²	1	2	yes	—
67	#4040	C₂²	1	2	yes	—
68	#4040	C₂²	1	2	yes	—
69	#4040	C₂²	1	2	yes	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	1	yes	characteristic
75	#4039	C₂²	1	1	yes	characteristic
76	#4039	C₂²	1	1	yes	characteristic
77	#4039	C₂²	1	2	yes	complemented
78	#4039	C₂²	1	2	yes	complemented
79	#4038	C₂²	1	2	yes	complemented
80	#4038	C₂²	1	1	yes	characteristic, complemented
81	#4038	C₂²	1	2	yes	complemented
82	#4038	C₂²	1	2	yes	complemented
83	D₅×C₄⋊C₄	C₂²	1	2	yes	complemented
84	D₅×C₄⋊C₄	C₂²	1	2	yes	complemented
85	D₅×C₄⋊C₄	C₂²	1	2	yes	complemented
86	#4036	C₂²	1	1	yes	characteristic, complemented
87	#4036	C₂²	1	2	yes	complemented
88	#4036	C₂²	1	1	yes	characteristic, complemented
89	#4035	C₂²	1	2	yes	complemented
90	#4034	C₂²	1	1	yes	characteristic, complemented
91	#4033	C₂²	1	1	yes	characteristic, complemented
92	#4033	C₂²	1	1	yes	characteristic, complemented
93	#4031	C₂²	1	2	yes	—
94	#4031	C₂²	1	2	yes	complemented
95	#4030	C₂²	1	2	yes	—
96	#4030	C₂²	1	2	yes	complemented
97	#4029	C₂²	1	1	yes	characteristic
98	#4029	C₂²	1	2	yes	complemented
99	#4029	C₂²	1	1	yes	characteristic, complemented
100	#4029	C₂²	1	2	yes	complemented
101	#4028	C₂²	1	2	yes	—
102	D₅×C₂²⋊C₄	C₂²	1	2	yes	—
103	D₅×C₂²⋊C₄	C₂²	1	2	yes	—
104	D₅×C₂²⋊C₄	C₂²	1	2	yes	—
105	D₅×C₂²⋊C₄	C₂²	1	2	yes	—
106	#4025	C₂²	1	2	yes	—
107	#4025	C₂²	1	1	yes	characteristic
108	#4025	C₂²	1	2	yes	—
109	#4025	C₂²	1	2	yes	—
110	#4025	C₂²	1	1	yes	characteristic, complemented
111	#4022	C₂²	1	2	yes	complemented
112	#4022	C₂²	1	2	yes	complemented
113	#4021	C₂²	1	1	yes	characteristic
114	C₄×D₂₀	C₂²	1	2	yes	—
115	C₄×D₂₀	C₂²	1	2	yes	—
116	C₄×D₂₀	C₂²	1	1	yes	characteristic
117	C₄×D₂₀	C₂²	1	2	yes	complemented
118	#4018	C₂²	1	2	yes	complemented
119	C₄²×D₅	C₂²	1	2	yes	complemented
120	C₄²×D₅	C₂²	1	1	yes	characteristic, complemented
121	C₄×Dic₁₀	C₂²	1	2	yes	complemented
122	C₄×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
123	#3521	—	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	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
128	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
129	C₂²×C₄×C₅	C₂³	1	2	yes	—
130	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
131	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
132	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
133	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
134	#713	—	2	4	no	—
135	#709	—	2	4	no	—
136	C₂×D₂₀	—	2	4	no	—
137	C₂×D₂₀	C₂³	1	2	yes	—
138	C₂×D₂₀	C₂³	1	1	yes	characteristic
139	C₂×D₂₀	C₂³	1	2	yes	—
140	C₂×D₂₀	C₂³	1	2	yes	—
141	C₂×D₂₀	C₂³	1	1	yes	characteristic
142	C₂×C₄×D₅	C₂³	1	2	yes	—
143	C₂×C₄×D₅	C₂³	1	2	yes	—
144	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
145	C₂×C₄×D₅	C₂³	1	2	yes	—
146	C₂×C₄×D₅	C₂³	1	2	yes	—
147	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
148	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
149	C₂×C₄×D₅	C₂³	1	2	yes	—
150	C₂×C₄×D₅	C₂³	1	2	yes	—
151	C₂×C₄×D₅	C₂³	1	2	yes	—
152	C₂×C₄×D₅	C₂³	1	2	yes	—
153	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
154	C₂×Dic₁₀	C₂³	1	2	yes	—
155	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
156	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
157	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
158	C₅×C₄⋊C₄	C₂³	1	2	yes	—
159	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
160	C₅×C₄⋊C₄	C₂³	1	2	yes	—
161	C₅×C₄⋊C₄	C₂³	1	2	yes	—
162	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
163	C₅×C₄⋊C₄	C₂³	1	2	yes	—
164	C₅×C₄⋊C₄	C₂³	1	2	yes	—
165	C₅×C₄⋊C₄	C₂³	1	2	yes	—
166	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
167	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
168	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
169	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
170	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
171	C₄²×C₅	C₂³	1	2	yes	—
172	C₄²×C₅	C₂³	1	2	yes	—
173	C₄²×C₅	C₂³	1	1	yes	characteristic
174	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
175	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
176	C₂²⋊Dic₅	C₂³	1	2	yes	—
177	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
178	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
179	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
180	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
181	#685	C₂³	1	2	yes	—
182	#685	C₂³	1	2	yes	—
183	#685	C₂³	1	2	yes	—
184	#685	C₂³	1	2	yes	—
185	#685	C₂³	1	2	yes	—
186	#685	C₂³	1	2	yes	—
187	#685	C₂³	1	2	yes	—
188	#685	C₂³	1	2	yes	—
189	#685	C₂³	1	2	yes	—
190	#685	C₂³	1	1	yes	characteristic
191	#685	C₂³	1	2	yes	—
192	#685	C₂³	1	2	yes	—
193	#685	C₂³	1	2	yes	—
194	#685	C₂³	1	2	yes	—
195	#685	C₂³	1	2	yes	—
196	#685	C₂³	1	1	yes	characteristic
197	C₄⋊Dic₅	C₂³	1	2	yes	—
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	1	yes	characteristic
202	C₄⋊Dic₅	C₂³	1	2	yes	—
203	C₄⋊Dic₅	C₂³	1	2	yes	—
204	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
205	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
206	#683	C₂³	1	1	yes	characteristic
207	#683	C₂³	1	1	yes	characteristic
208	#683	C₂³	1	1	yes	characteristic
209	#683	C₂³	1	2	yes	—
210	#683	C₂³	1	2	yes	—
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	1	yes	characteristic
217	C₄×Dic₅	C₂³	1	2	yes	—
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	1	yes	characteristic
222	C₄×Dic₅	C₂³	1	2	yes	—
223	C₄×Dic₅	C₂³	1	1	yes	characteristic
224	C₄×Dic₅	C₂³	1	1	yes	characteristic
225	C₄×Dic₅	C₂³	1	2	yes	—
226	#556	—	5	1	no	—
227	#556	—	5	1	no	—
228	#554	—	5	1	no	—
229	#553	—	5	2	no	—
230	#553	—	5	1	no	—
231	#552	—	5	2	no	—
232	#552	D₅	1	1	yes	characteristic, complemented
233	#551	—	5	2	no	—
234	#551	—	5	2	no	—
235	#547	—	5	1	no	—
236	#546	—	5	1	no	—
237	#546	—	5	1	no	—
238	#542	—	5	1	no	—
239	#541	—	5	1	no	—
240	#539	—	5	2	no	—
241	#538	—	5	2	no	—
242	#529	—	5	1	no	—
243	#529	—	5	1	no	—
244	#529	—	5	2	no	—
245	C₂×#126	—	5	2	no	—
246	#520	—	5	1	no	—
247	#518	—	5	1	no	—
248	C₄×#41	—	5	1	no	—
249	C₂³×C₅	C₂⁴	1	1	yes	characteristic
250	C₂³×C₅	C₂⁴	1	1	yes	characteristic
251	C₂²×D₅	—	2	4	no	—
252	C₂²×D₅	—	4	2	no	—
253	C₂²×D₅	—	4	2	no	—
254	C₂²×D₅	C₂⁴	1	2	yes	—
255	C₂²×D₅	C₂⁴	1	1	yes	characteristic
256	C₂²×D₅	C₂⁴	1	2	yes	—
257	C₅×Q₈	—	2	2	no	—
258	C₅×D₄	—	4	1	no	—
259	C₂×C₄×C₅	—	2	2	no	—
260	C₂×C₄×C₅	—	2	2	no	—
261	C₂×C₄×C₅	—	4	2	no	—
262	C₂×C₄×C₅	C₂⁴	1	2	yes	—
263	C₂×C₄×C₅	C₂⁴	1	2	yes	—
264	C₂×C₄×C₅	C₂⁴	1	2	yes	—
265	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
266	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
267	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
268	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
269	C₂×C₄×C₅	C₂⁴	1	2	yes	—
270	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
271	C₂²⋊D₅	—	2	4	no	—
272	C₂²⋊D₅	—	4	1	no	—
273	C₂²⋊D₅	—	4	2	no	—
274	C₂²⋊D₅	—	4	1	no	—
275	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
276	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
277	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
278	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
279	C₂×Dic₅	C₂⁴	1	2	yes	—
280	C₂×Dic₅	C₂⁴	1	2	yes	—
281	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
282	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
283	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
284	D₂₀	—	2	4	no	—
285	D₂₀	—	2	4	no	—
286	D₂₀	—	2	2	no	—
287	D₂₀	—	4	2	no	—
288	D₂₀	#41	1	4	yes	—
289	C₄×D₅	—	2	4	no	—
290	C₄×D₅	—	2	4	no	—
291	C₄×D₅	—	2	2	no	—
292	C₄×D₅	—	4	2	no	—
293	C₄×D₅	—	4	2	no	—
294	C₄×D₅	—	4	2	no	—
295	C₄×D₅	—	4	2	no	—
296	C₄×D₅	—	4	1	no	—
297	C₄×D₅	—	4	1	no	—
298	C₄×D₅	—	4	2	no	—
299	C₄×D₅	—	4	2	no	—
300	Dic₁₀	—	2	2	no	—
301	Dic₁₀	—	4	2	no	—
302	Dic₁₀	—	4	1	no	—
303	C₂×#41	—	5	1	no	—
304	C₂×#41	—	5	1	no	—
305	C₂²×D₄	—	5	1	no	—
306	C₄⋊Q₈	—	5	1	no	—
307	C₄⋊Q₈	—	5	1	no	—
308	#126	—	5	2	no	—
309	#126	—	5	2	no	—
310	#126	—	5	2	no	—
311	#126	—	5	2	no	—
312	#126	—	5	1	no	—
313	#126	—	5	2	no	—
314	#126	—	5	2	no	—
315	#126	—	5	1	no	—
316	#126	—	5	2	no	—
317	#126	—	5	2	no	—
318	#126	—	5	2	no	—
319	#126	C₂×D₅	1	2	yes	—
320	#125	—	5	2	no	—
321	#125	—	5	1	no	—
322	#125	—	5	2	no	—
323	#125	—	5	1	no	—
324	#125	C₂×D₅	1	1	yes	characteristic, complemented
325	#125	C₂×D₅	1	2	yes	complemented
326	#124	—	5	1	no	—
327	#124	—	5	1	no	—
328	#124	—	5	2	no	—
329	#124	—	5	2	no	—
330	#124	—	5	1	no	—
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	1	no	—
338	#123	—	5	1	no	—
339	#123	—	5	2	no	—
340	#123	C₂×D₅	1	2	yes	—
341	C₂²⋊Q₈	—	5	1	no	—
342	C₂²⋊Q₈	—	5	1	no	—
343	C₂²⋊Q₈	—	5	1	no	—
344	C₂²⋊Q₈	—	5	2	no	—
345	C₂²⋊Q₈	—	5	2	no	—
346	C₂²⋊Q₈	—	5	2	no	—
347	C₂²⋊Q₈	—	5	2	no	—
348	C₂²⋊Q₈	—	5	2	no	—
349	C₂²⋊Q₈	C₂×D₅	1	1	yes	characteristic
350	C₂²⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
351	#121	—	5	1	no	—
352	#121	—	5	2	no	—
353	#121	—	5	1	no	—
354	#121	—	5	1	no	—
355	#121	—	5	2	no	—
356	#121	—	5	2	no	—
357	#121	—	5	2	no	—
358	#120	—	5	2	no	—
359	#120	—	5	2	no	—
360	C₄×Q₈	—	5	1	no	—
361	C₄×Q₈	—	5	1	no	—
362	C₄×Q₈	—	5	1	no	—
363	C₄×Q₈	—	5	2	no	—
364	C₄×Q₈	—	5	1	no	—
365	C₄×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
366	C₄×D₄	—	5	2	no	—
367	C₄×D₄	—	5	2	no	—
368	C₄×D₄	—	5	1	no	—
369	C₄×D₄	—	5	1	no	—
370	C₄×D₄	—	5	2	no	—
371	C₄×D₄	—	5	1	no	—
372	C₄×D₄	—	5	2	no	—
373	C₄×D₄	—	5	1	no	—
374	C₄×D₄	—	5	1	no	—
375	C₄×D₄	—	5	1	no	—
376	C₄×D₄	—	5	1	no	—
377	C₄×D₄	—	5	2	no	—
378	C₄×D₄	—	5	1	no	—
379	C₄×D₄	—	5	2	no	—
380	C₄×D₄	—	5	2	no	—
381	C₄×D₄	—	5	2	no	—
382	C₄×D₄	C₂×D₅	1	1	yes	characteristic
383	#117	—	5	1	no	—
384	#117	—	5	1	no	—
385	#117	—	5	2	no	—
386	#117	—	5	1	no	—
387	#117	—	5	2	no	—
388	#117	—	5	2	no	—
389	#117	—	5	2	no	—
390	#117	C₂×D₅	1	1	yes	characteristic
391	#117	C₂×D₅	1	2	yes	complemented
392	C₂×C₄⋊C₄	—	5	2	no	—
393	C₂×C₄⋊C₄	—	5	2	no	—
394	C₂×C₄⋊C₄	—	5	2	no	—
395	C₂×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic, complemented
396	C₂×C₂²⋊C₄	—	5	2	no	—
397	C₂×C₂²⋊C₄	—	5	2	no	—
398	C₂×C₂²⋊C₄	—	5	2	no	—
399	C₂×C₂²⋊C₄	—	5	2	no	—
400	C₂×C₄²	—	5	2	no	—
401	C₂×C₄²	—	5	1	no	—
402	C₂²×C₅	—	2	1	no	—
403	C₂²×C₅	—	2	1	no	—
404	C₂²×C₅	—	2	1	no	—
405	C₂²×C₅	—	2	1	no	—
406	C₂²×C₅	—	2	1	no	—
407	C₂²×C₅	—	2	1	no	—
408	C₂²×C₅	C₂⁵	1	1	yes	characteristic
409	C₂×D₅	—	2	2	no	—
410	C₂×D₅	—	2	2	no	—
411	C₂×D₅	—	2	1	no	—
412	C₂×D₅	—	2	2	no	—
413	C₂×D₅	—	2	1	no	—
414	C₂×D₅	—	2	2	no	—
415	C₂×D₅	—	2	1	no	—
416	C₂×D₅	—	2	2	no	—
417	C₂×D₅	—	8	4	no	—
418	C₂×D₅	C₂×#41	1	4	yes	—
419	C₄×C₅	—	2	1	no	—
420	C₄×C₅	—	2	2	no	—
421	C₄×C₅	—	2	1	no	—
422	C₄×C₅	—	2	2	no	—
423	C₄×C₅	—	2	1	no	—
424	C₄×C₅	—	2	1	no	—
425	C₄×C₅	—	2	2	no	—
426	C₄×C₅	—	2	2	no	—
427	C₄×C₅	C₂×#41	1	2	yes	—
428	Dic₅	—	2	2	no	—
429	Dic₅	—	2	1	no	—
430	Dic₅	—	2	1	no	—
431	Dic₅	—	2	1	no	—
432	Dic₅	—	2	1	no	—
433	Dic₅	—	2	2	no	—
434	Dic₅	—	2	1	no	—
435	Dic₅	—	2	1	no	—
436	Dic₅	—	2	1	no	—
437	C₂⁴	—	5	2	no	—
438	#41	—	10	4	no	—
439	#41	—	10	4	no	—
440	C₂×Q₈	—	5	1	no	—
441	C₂×Q₈	—	5	1	no	—
442	C₂×Q₈	—	5	2	no	—
443	C₂×Q₈	C₂²×D₅	1	1	yes	characteristic
444	C₂×D₄	—	5	2	no	—
445	C₂×D₄	—	5	1	no	—
446	C₂×D₄	—	5	2	no	—
447	C₂×D₄	—	5	1	no	—
448	C₂×D₄	—	5	1	no	—
449	C₂×D₄	—	5	2	no	—
450	C₂×D₄	—	5	2	no	—
451	C₂×D₄	—	5	1	no	—
452	C₂×D₄	—	5	2	no	—
453	C₂×D₄	—	10	4	no	—
454	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
455	C₂²×C₄	—	5	2	no	—
456	C₂²×C₄	—	5	1	no	—
457	C₂²×C₄	—	5	2	no	—
458	C₂²×C₄	—	5	2	no	—
459	C₂²×C₄	—	5	2	no	—
460	C₂²×C₄	—	5	1	no	—
461	C₂²×C₄	—	5	1	no	—
462	C₂²×C₄	—	5	2	no	—
463	C₂²×C₄	—	5	2	no	—
464	C₂²×C₄	—	5	2	no	—
465	C₂²×C₄	—	5	2	no	—
466	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
467	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
468	C₂²×C₄	C₂²×D₅	1	2	yes	—
469	C₄⋊C₄	—	5	1	no	—
470	C₄⋊C₄	—	5	1	no	—
471	C₄⋊C₄	—	5	1	no	—
472	C₄⋊C₄	—	5	2	no	—
473	C₄⋊C₄	—	5	2	no	—
474	C₄⋊C₄	—	5	2	no	—
475	C₄⋊C₄	—	5	2	no	—
476	C₄⋊C₄	—	5	2	no	—
477	C₄⋊C₄	—	5	2	no	—
478	C₄⋊C₄	—	5	1	no	—
479	C₄⋊C₄	—	5	1	no	—
480	C₄⋊C₄	—	5	1	no	—
481	C₄⋊C₄	—	5	1	no	—
482	C₄⋊C₄	—	5	1	no	—
483	C₄⋊C₄	—	5	2	no	—
484	C₄⋊C₄	—	5	2	no	—
485	C₄⋊C₄	—	5	1	no	—
486	C₄⋊C₄	—	5	2	no	—
487	C₄⋊C₄	—	5	1	no	—
488	C₄⋊C₄	—	5	2	no	—
489	C₄⋊C₄	C₂²×D₅	1	2	yes	—
490	C₄⋊C₄	C₂²×D₅	1	2	yes	—
491	C₄⋊C₄	C₂²×D₅	1	2	yes	—
492	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
493	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
494	C₄⋊C₄	C₂²×D₅	1	2	yes	—
495	C₄⋊C₄	C₂²×D₅	1	2	yes	—
496	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
497	C₄⋊C₄	C₂²×D₅	1	2	yes	—
498	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
499	C₂²⋊C₄	—	5	1	no	—
500	C₂²⋊C₄	—	5	1	no	—
501	C₂²⋊C₄	—	5	1	no	—
502	C₂²⋊C₄	—	5	2	no	—
503	C₂²⋊C₄	—	5	1	no	—
504	C₂²⋊C₄	—	5	1	no	—
505	C₂²⋊C₄	—	5	1	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	2	no	—
513	C₂²⋊C₄	—	5	2	no	—
514	C₂²⋊C₄	—	5	2	no	—
515	C₂²⋊C₄	—	5	2	no	—
516	C₂²⋊C₄	—	5	2	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	C₂²×D₅	1	2	yes	—
523	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
524	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
525	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
526	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
527	C₄²	—	5	1	no	—
528	C₄²	—	5	1	no	—
529	C₄²	—	5	1	no	—
530	C₄²	—	5	2	no	—
531	C₄²	—	5	2	no	—
532	C₄²	—	5	2	no	—
533	C₄²	—	5	2	no	—
534	C₄²	—	5	1	no	—
535	C₄²	—	5	1	no	—
536	C₄²	C₂²×D₅	1	2	yes	—
537	C₄²	C₂²×D₅	1	1	yes	characteristic
538	C₄²	C₂²×D₅	1	2	yes	—
539	C₂×C₅	—	4	1	no	—
540	C₂×C₅	—	4	1	no	—
541	C₂×C₅	C₂²×#41	1	1	yes	characteristic
542	C₂×C₅	#585	1	1	yes	characteristic
543	C₂×C₅	#585	1	1	yes	characteristic
544	D₅	—	2	4	no	—
545	D₅	—	4	1	no	—
546	D₅	—	4	2	no	—
547	C₂³	—	5	2	no	—
548	C₂³	—	5	2	no	—
549	C₂³	—	5	1	no	—
550	C₂³	—	10	4	no	—
551	C₂³	—	20	2	no	—
552	C₂³	—	20	2	no	—
553	C₂³	C₂³×D₅	1	1	yes	characteristic
554	C₂³	C₂³×D₅	1	1	yes	characteristic
555	Q₈	—	2	2	no	—
556	Q₈	—	10	2	no	—
557	Q₈	—	20	1	no	—
558	Q₈	—	20	2	no	—
559	D₄	—	4	1	no	—
560	D₄	—	5	4	no	—
561	D₄	—	10	4	no	—
562	D₄	—	10	4	no	—
563	D₄	—	10	4	no	—
564	D₄	—	10	2	no	—
565	D₄	—	20	2	no	—
566	D₄	—	20	1	no	—
567	D₄	—	20	2	no	—
568	D₄	—	20	1	no	—
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	4	2	no	—
572	C₂×C₄	—	5	1	no	—
573	C₂×C₄	—	5	1	no	—
574	C₂×C₄	—	5	1	no	—
575	C₂×C₄	—	5	1	no	—
576	C₂×C₄	—	5	2	no	—
577	C₂×C₄	—	5	2	no	—
578	C₂×C₄	—	5	1	no	—
579	C₂×C₄	—	5	1	no	—
580	C₂×C₄	—	5	1	no	—
581	C₂×C₄	—	10	4	no	—
582	C₂×C₄	—	10	4	no	—
583	C₂×C₄	—	10	2	no	—
584	C₂×C₄	—	20	2	no	—
585	C₂×C₄	—	20	2	no	—
586	C₂×C₄	—	20	2	no	—
587	C₂×C₄	—	20	1	no	—
588	C₂×C₄	—	20	1	no	—
589	C₂×C₄	—	20	2	no	—
590	C₂×C₄	—	20	2	no	—
591	C₂×C₄	—	20	2	no	—
592	C₂×C₄	C₂³×D₅	1	2	yes	—
593	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
594	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
595	C₂×C₄	C₂³×D₅	1	2	yes	—
596	C₂×C₄	C₂³×D₅	1	2	yes	—
597	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
598	C₂×C₄	C₂³×D₅	1	2	yes	—
599	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
600	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
601	C₅	#3521	1	1	yes	characteristic, complemented, Sylow
602	C₂²	—	2	1	no	—
603	C₂²	—	2	1	no	—
604	C₂²	—	2	1	no	—
605	C₂²	—	2	1	no	—
606	C₂²	—	2	1	no	—
607	C₂²	—	2	1	no	—
608	C₂²	—	5	4	no	—
609	C₂²	—	10	2	no	—
610	C₂²	—	10	2	no	—
611	C₂²	—	10	1	no	—
612	C₂²	—	10	2	no	—
613	C₂²	—	10	1	no	—
614	C₂²	—	10	2	no	—
615	C₂²	—	10	1	no	—
616	C₂²	—	10	2	no	—
617	C₂²	—	40	4	no	—
618	C₂²	C₂⁴×D₅	1	1	yes	characteristic
619	C₄	—	2	1	no	—
620	C₄	—	2	1	no	—
621	C₄	—	2	2	no	—
622	C₄	—	2	2	no	—
623	C₄	—	2	2	no	—
624	C₄	—	2	1	no	—
625	C₄	—	2	1	no	—
626	C₄	—	2	2	no	—
627	C₄	—	10	1	no	—
628	C₄	—	10	2	no	—
629	C₄	—	10	1	no	—
630	C₄	—	10	1	no	—
631	C₄	—	10	1	no	—
632	C₄	—	10	1	no	—
633	C₄	—	10	1	no	—
634	C₄	—	10	2	no	—
635	C₄	—	10	1	no	—
636	C₄	D₅×#41	1	2	yes	—
637	C₂	—	4	1	no	—
638	C₂	—	4	1	no	—
639	C₂	—	10	4	no	—
640	C₂	—	20	2	no	—
641	C₂	—	20	1	no	—
642	C₂	C₂×D₅×#41	1	1	yes	characteristic
643	C₂	#66283	1	1	yes	characteristic
644	C₂	#66287	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅
commutator, socle, cosocle	C₂²×C₅	C₂⁵
Fitting	C₅×#552	C₂
hypercenter	#552	D₅
hypocenter	C₅	#3521
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ #552

Complements

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

N	H ≅ G/N	type
1. C₅×#552	C₂	semidirect
2. #66039	C₂	semidirect
3. D₅×#126	C₂	semidirect
4. #66028	C₂	semidirect
5. #66026	C₂	semidirect
6. #66025	C₂	semidirect
7. #66024	C₂	semidirect
8. #65993	C₂	semidirect
9. #65991	C₂	semidirect
10. #65977	C₂	semidirect
11. #65965	C₂	semidirect
12. #65964	C₂	semidirect
13. #65959	C₂	semidirect
14. C₄×#713	C₂	semidirect
15. #65902	C₂	semidirect
16. #65891	C₂	semidirect
17. #65884	C₂	semidirect
18. #65867	C₂	semidirect
19. #65864	C₂	semidirect
20. #65862	C₂	semidirect
21. #65855	C₂	semidirect
22. #65848	C₂	semidirect
23. #65838	C₂	semidirect
28. C₅×#125	C₂²	semidirect
29. C₅×#125	C₂²	semidirect
32. C₅×C₂²⋊Q₈	C₂²	semidirect
33. C₄×C₅×Q₈	C₂²	semidirect
36. C₅×#117	C₂²	semidirect
37. C₂×C₅×C₄⋊C₄	C₂²	semidirect
39. Q₈×Dic₅	C₂²	semidirect
40. #4090	C₂²	semidirect
45. #4076	C₂²	semidirect
47. C₄×C₂²⋊D₅	C₂²	semidirect
48. C₄×C₂²⋊D₅	C₂²	semidirect
49. C₄×C₂²⋊D₅	C₂²	semidirect
50. C₄×C₂²⋊D₅	C₂²	semidirect
52. #4072	C₂²	semidirect
54. #4044	C₂²	semidirect
55. #4044	C₂²	semidirect
56. #4044	C₂²	semidirect
57. #4044	C₂²	semidirect
58. #4043	C₂²	semidirect
59. #4043	C₂²	semidirect
60. #4043	C₂²	semidirect
61. #4043	C₂²	semidirect
62. #4042	C₂²	semidirect
63. #4042	C₂²	semidirect
64. #4042	C₂²	semidirect
69. #4040	C₂²	semidirect
70. #4040	C₂²	semidirect
71. #4040	C₂²	semidirect
77. #4039	C₂²	semidirect
78. #4039	C₂²	semidirect
79. #4038	C₂²	semidirect
80. #4038	C₂²	semidirect
81. #4038	C₂²	semidirect
82. #4038	C₂²	semidirect
83. D₅×C₄⋊C₄	C₂²	semidirect
84. D₅×C₄⋊C₄	C₂²	semidirect
85. D₅×C₄⋊C₄	C₂²	semidirect
86. #4036	C₂²	semidirect
87. #4036	C₂²	semidirect
88. #4036	C₂²	semidirect
89. #4035	C₂²	semidirect
90. #4034	C₂²	semidirect
91. #4033	C₂²	semidirect
92. #4033	C₂²	semidirect
94. #4031	C₂²	semidirect
96. #4030	C₂²	semidirect
98. #4029	C₂²	semidirect
99. #4029	C₂²	semidirect
100. #4029	C₂²	semidirect
110. #4025	C₂²	semidirect
111. #4022	C₂²	semidirect
112. #4022	C₂²	semidirect
117. C₄×D₂₀	C₂²	semidirect
118. #4018	C₂²	semidirect
119. C₄²×D₅	C₂²	semidirect
120. C₄²×D₅	C₂²	semidirect
121. C₄×Dic₁₀	C₂²	semidirect
122. C₄×Dic₁₀	C₂²	semidirect
232. #552	D₅	semidirect
324. #125	C₂×D₅	semidirect
325. #125	C₂×D₅	semidirect
350. C₂²⋊Q₈	C₂×D₅	semidirect
365. C₄×Q₈	C₂×D₅	semidirect
391. #117	C₂×D₅	semidirect
395. C₂×C₄⋊C₄	C₂×D₅	semidirect
601. C₅	#3521	semidirect

Maximal subgroups

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

subgroup	index
C₅×#552	2
#66039	2
D₅×#126	2
#66028	2
#66026	2
#66025	2
#66024	2
#65993	2
#65991	2
#65977	2
#65965	2
#65964	2
#65959	2
C₄×#713	2
#65902	2
#65891	2
#65884	2
#65867	2
#65864	2
#65862	2
#65855	2
#65848	2
#65838	2
#3521	5