Subgroups — #10618386

Order 640.

1142 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#540	C₂	1	1	yes	maximal, characteristic, complemented
2	#66050	C₂	1	1	yes	maximal, characteristic, complemented
3	#66049	C₂	1	1	yes	maximal, characteristic, complemented
4	#66025	C₂	1	1	yes	maximal, characteristic, complemented
5	#66023	C₂	1	1	yes	maximal, characteristic, complemented
6	#65995	C₂	1	2	yes	maximal, complemented
7	#65993	C₂	1	2	yes	maximal, complemented
8	#65992	C₂	1	2	yes	maximal, complemented
9	#65989	C₂	1	2	yes	maximal, complemented
10	#65953	C₂	1	1	yes	maximal, characteristic, complemented
11	#65950	C₂	1	2	yes	maximal, complemented
12	#65946	C₂	1	2	yes	maximal, complemented
13	#65944	C₂	1	2	yes	maximal, complemented
14	#65940	C₂	1	1	yes	maximal, characteristic, complemented
15	D₅×#121	C₂	1	1	yes	maximal, characteristic, complemented
16	#65937	C₂	1	1	yes	maximal, characteristic, complemented
17	#65935	C₂	1	2	yes	maximal, complemented
18	#65891	C₂	1	1	yes	maximal, characteristic, complemented
19	#65882	C₂	1	1	yes	maximal, characteristic, complemented
20	#65880	C₂	1	1	yes	maximal, characteristic, complemented
21	#65879	C₂	1	1	yes	maximal, characteristic, complemented
22	#65868	C₂	1	1	yes	maximal, characteristic, complemented
23	D₅×#117	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#711	C₂²	1	1	yes	characteristic
25	C₂×#711	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×C₄×D₅	C₂²	1	1	yes	characteristic
30	C₅×#127	C₂²	1	1	yes	characteristic, complemented
31	C₅×#125	C₂²	1	1	yes	characteristic, complemented
32	C₅×#123	C₂²	1	2	yes	complemented
33	C₅×#123	C₂²	1	2	yes	complemented
34	C₅×#121	C₂²	1	1	yes	characteristic
35	C₅×#121	C₂²	1	2	yes	complemented
36	C₅×#121	C₂²	1	1	yes	characteristic, complemented
37	C₅×#121	C₂²	1	2	yes	complemented
38	C₄×C₅×D₄	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	#4086	C₂²	1	1	yes	characteristic, complemented
42	#4085	C₂²	1	2	yes	—
43	#4085	C₂²	1	2	yes	complemented
44	#4085	C₂²	1	2	yes	complemented
45	#4085	C₂²	1	2	yes	complemented
46	#4084	C₂²	1	1	yes	characteristic
47	#4084	C₂²	1	1	yes	characteristic, complemented
48	#4084	C₂²	1	2	yes	complemented
49	#4084	C₂²	1	2	yes	complemented
50	#4083	C₂²	1	2	yes	—
51	#4083	C₂²	1	2	yes	—
52	#4083	C₂²	1	2	yes	—
53	#4082	C₂²	1	1	yes	characteristic, complemented
54	#4082	C₂²	1	2	yes	complemented
55	#4082	C₂²	1	2	yes	complemented
56	#4081	C₂²	1	2	yes	complemented
57	D₄×Dic₅	C₂²	1	1	yes	characteristic, complemented
58	D₄×Dic₅	C₂²	1	1	yes	characteristic, complemented
59	D₄×Dic₅	C₂²	1	2	yes	complemented
60	D₄×Dic₅	C₂²	1	2	yes	complemented
61	#4076	C₂²	1	1	yes	characteristic
62	C₄×C₂²⋊D₅	C₂²	1	2	yes	—
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	C₂×#685	C₂²	1	2	yes	—
67	#4072	C₂²	1	1	yes	characteristic, complemented
68	#4072	C₂²	1	2	yes	complemented
69	#4070	C₂²	1	1	yes	characteristic, complemented
70	C₂×#683	C₂²	1	2	yes	complemented
71	#4044	C₂²	1	2	yes	complemented
72	#4044	C₂²	1	2	yes	complemented
73	#4043	C₂²	1	2	yes	—
74	#4043	C₂²	1	1	yes	characteristic, complemented
75	#4042	C₂²	1	2	yes	—
76	#4042	C₂²	1	2	yes	complemented
77	#4041	C₂²	1	1	yes	characteristic
78	#4040	C₂²	1	2	yes	complemented
79	#4039	C₂²	1	1	yes	characteristic, complemented
80	#4039	C₂²	1	2	yes	complemented
81	#4038	C₂²	1	1	yes	characteristic
82	#4038	C₂²	1	1	yes	characteristic
83	#4038	C₂²	1	1	yes	characteristic
84	#4038	C₂²	1	2	yes	complemented
85	D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
86	D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
87	D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, 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	#4034	C₂²	1	2	yes	complemented
92	#4033	C₂²	1	1	yes	characteristic, complemented
93	#4032	C₂²	1	2	yes	complemented
94	#4031	C₂²	1	2	yes	complemented
95	#4031	C₂²	1	2	yes	complemented
96	#4030	C₂²	1	2	yes	—
97	#4030	C₂²	1	2	yes	complemented
98	#4029	C₂²	1	2	yes	—
99	#4029	C₂²	1	2	yes	complemented
100	#4029	C₂²	1	2	yes	complemented
101	#4029	C₂²	1	2	yes	complemented
102	#4027	C₂²	1	2	yes	—
103	#4027	C₂²	1	2	yes	complemented
104	#4027	C₂²	1	2	yes	complemented
105	D₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
106	D₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
107	D₅×C₂²⋊C₄	C₂²	1	2	yes	—
108	D₅×C₂²⋊C₄	C₂²	1	2	yes	—
109	#4025	C₂²	1	2	yes	complemented
110	#4025	C₂²	1	2	yes	complemented
111	#4024	C₂²	1	2	yes	complemented
112	#4023	C₂²	1	1	yes	characteristic, complemented
113	#4023	C₂²	1	1	yes	characteristic, complemented
114	#4023	C₂²	1	2	yes	complemented
115	#4021	C₂²	1	1	yes	characteristic, complemented
116	C₄×D₂₀	C₂²	1	1	yes	characteristic, complemented
117	#4018	C₂²	1	1	yes	characteristic
118	#4018	C₂²	1	1	yes	characteristic
119	C₄²×D₅	C₂²	1	1	yes	characteristic, complemented
120	C₄²×D₅	C₂²	1	1	yes	characteristic, complemented
121	#4015	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
123	#3494	—	5	1	no	maximal, Sylow
124	C₂³×D₅	C₂³	1	1	yes	characteristic
125	C₂³×D₅	C₂³	1	2	yes	—
126	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
127	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
128	C₂×C₅×D₄	C₂³	1	2	yes	—
129	C₂×C₅×D₄	C₂³	1	2	yes	—
130	C₂×C₅×D₄	C₂³	1	2	yes	—
131	C₂×C₅×D₄	C₂³	1	2	yes	—
132	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
133	C₂²×C₄×C₅	C₂³	1	2	yes	—
134	C₂²×C₄×C₅	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	2	yes	—
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	C₂²×Dic₅	C₂³	1	1	yes	characteristic
143	C₂²×Dic₅	C₂³	1	2	yes	—
144	C₂²×Dic₅	C₂³	1	2	yes	—
145	C₂²×Dic₅	C₂³	1	2	yes	—
146	#711	—	2	4	no	—
147	#711	—	4	4	no	—
148	D₄×D₅	—	2	4	no	—
149	D₄×D₅	—	4	4	no	—
150	#709	—	4	4	no	—
151	C₂×D₂₀	C₂³	1	2	yes	—
152	C₂×D₂₀	C₂³	1	1	yes	characteristic
153	C₂×C₄×D₅	—	2	4	no	—
154	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
155	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
156	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
157	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
158	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
163	C₂×C₄×D₅	C₂³	1	2	yes	—
164	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
165	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
166	C₂×Dic₁₀	C₂³	1	2	yes	—
167	C₂×Dic₁₀	C₂³	1	2	yes	—
168	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
169	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
170	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
171	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
172	C₅×C₄⋊C₄	C₂³	1	2	yes	—
173	C₅×C₄⋊C₄	C₂³	1	2	yes	—
174	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
175	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
183	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
184	C₂²⋊Dic₅	C₂³	1	2	yes	—
185	C₂²⋊Dic₅	C₂³	1	2	yes	—
186	C₂²⋊Dic₅	C₂³	1	2	yes	—
187	C₂²⋊Dic₅	C₂³	1	2	yes	—
188	C₂²⋊Dic₅	C₂³	1	2	yes	—
189	C₂²⋊Dic₅	C₂³	1	2	yes	—
190	C₂²⋊Dic₅	C₂³	1	2	yes	—
191	#685	C₂³	1	1	yes	characteristic
192	#685	C₂³	1	1	yes	characteristic
193	#685	C₂³	1	1	yes	characteristic
194	#685	C₂³	1	1	yes	characteristic
195	#685	C₂³	1	2	yes	—
196	#685	C₂³	1	2	yes	—
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	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
204	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
205	C₄⋊Dic₅	C₂³	1	2	yes	—
206	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
207	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
208	C₄⋊Dic₅	C₂³	1	2	yes	—
209	C₄⋊Dic₅	C₂³	1	2	yes	—
210	#683	C₂³	1	2	yes	—
211	#683	C₂³	1	1	yes	characteristic
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	2	yes	—
216	#683	C₂³	1	2	yes	—
217	#683	C₂³	1	2	yes	—
218	#683	C₂³	1	2	yes	—
219	#683	C₂³	1	2	yes	—
220	C₄×Dic₅	C₂³	1	2	yes	—
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	1	yes	characteristic
225	C₄×Dic₅	C₂³	1	1	yes	characteristic
226	C₄×Dic₅	C₂³	1	1	yes	characteristic
227	C₄×Dic₅	C₂³	1	2	yes	—
228	C₄×Dic₅	C₂³	1	2	yes	—
229	#555	—	5	2	no	—
230	#553	—	5	2	no	—
231	#553	—	5	2	no	—
232	#551	—	5	2	no	—
233	#551	—	5	2	no	—
234	#547	—	5	2	no	—
235	#546	—	5	2	no	—
236	#546	—	5	2	no	—
237	#544	—	5	1	no	—
238	#542	—	5	1	no	—
239	#542	—	5	1	no	—
240	#540	—	5	1	no	—
241	#540	D₅	1	1	yes	characteristic, complemented
242	#535	—	5	1	no	—
243	#532	—	5	1	no	—
244	#532	—	5	1	no	—
245	#529	—	5	1	no	—
246	#529	—	5	1	no	—
247	#525	—	5	1	no	—
248	C₂×#121	—	5	1	no	—
249	#520	—	5	1	no	—
250	#518	—	5	1	no	—
251	C₂×#117	—	5	1	no	—
252	C₂³×C₅	C₂⁴	1	1	yes	characteristic
253	C₂³×C₅	C₂⁴	1	2	yes	—
254	C₂³×C₅	C₂⁴	1	2	yes	—
255	C₂²×D₅	—	2	2	no	—
256	C₂²×D₅	—	2	2	no	—
257	C₂²×D₅	—	2	4	no	—
258	C₂²×D₅	—	4	1	no	—
259	C₂²×D₅	—	4	2	no	—
260	C₂²×D₅	—	4	2	no	—
261	C₂²×D₅	C₂⁴	1	2	yes	—
262	C₂²×D₅	C₂⁴	1	1	yes	characteristic
263	C₂²×D₅	C₂⁴	1	1	yes	characteristic
264	C₅×D₄	—	2	2	no	—
265	C₅×D₄	—	2	2	no	—
266	C₅×D₄	—	4	2	no	—
267	C₅×D₄	—	4	2	no	—
268	C₅×D₄	—	4	2	no	—
269	C₅×D₄	—	4	2	no	—
270	C₂×C₄×C₅	—	2	2	no	—
271	C₂×C₄×C₅	—	4	2	no	—
272	C₂×C₄×C₅	—	4	2	no	—
273	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
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	2	yes	—
278	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
279	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
280	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
281	C₂²⋊D₅	—	2	4	no	—
282	C₂²⋊D₅	—	2	4	no	—
283	C₂²⋊D₅	—	2	4	no	—
284	C₂²⋊D₅	—	2	4	no	—
285	C₂²⋊D₅	—	4	2	no	—
286	C₂²⋊D₅	—	4	2	no	—
287	C₂²⋊D₅	—	4	2	no	—
288	C₂×Dic₅	—	2	2	no	—
289	C₂×Dic₅	—	2	4	no	—
290	C₂×Dic₅	—	4	2	no	—
291	C₂×Dic₅	—	4	2	no	—
292	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
293	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
294	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
295	C₂×Dic₅	C₂⁴	1	2	yes	—
296	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
297	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
298	C₂×Dic₅	C₂⁴	1	2	yes	—
299	C₂×Dic₅	C₂⁴	1	2	yes	—
300	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
301	D₂₀	—	2	4	no	—
302	D₂₀	—	2	2	no	—
303	C₄×D₅	—	2	2	no	—
304	C₄×D₅	—	2	2	no	—
305	C₄×D₅	—	2	2	no	—
306	C₄×D₅	—	2	2	no	—
307	C₄×D₅	—	2	2	no	—
308	C₄×D₅	—	4	2	no	—
309	C₄×D₅	—	4	1	no	—
310	C₄×D₅	—	4	1	no	—
311	C₄×D₅	—	4	2	no	—
312	C₄×D₅	—	4	2	no	—
313	C₄×D₅	#41	1	4	yes	complemented
314	Dic₁₀	—	2	2	no	—
315	Dic₁₀	—	4	2	no	—
316	Dic₁₀	—	4	2	no	—
317	C₂×#41	—	5	1	no	—
318	C₂×#41	—	5	2	no	—
319	C₂×#41	—	5	2	no	—
320	C₂²×D₄	—	5	1	no	—
321	C₂²×D₄	—	5	2	no	—
322	C₂³×C₄	—	5	1	no	—
323	C₄⋊Q₈	—	5	1	no	—
324	C₄⋊Q₈	—	5	2	no	—
325	C₄⋊Q₈	—	5	1	no	—
326	#127	—	5	1	no	—
327	#127	C₂×D₅	1	1	yes	characteristic, complemented
328	#126	—	5	2	no	—
329	#126	—	5	2	no	—
330	#126	—	5	2	no	—
331	#126	—	5	2	no	—
332	#125	—	5	1	no	—
333	#125	—	5	2	no	—
334	#125	C₂×D₅	1	1	yes	characteristic, complemented
335	#124	—	5	1	no	—
336	#124	—	5	2	no	—
337	#124	—	5	2	no	—
338	#124	—	5	2	no	—
339	#124	—	5	2	no	—
340	#124	—	5	1	no	—
341	#123	—	5	2	no	—
342	#123	—	5	2	no	—
343	#123	—	5	2	no	—
344	#123	—	5	2	no	—
345	#123	—	5	2	no	—
346	#123	—	5	2	no	—
347	#123	—	5	2	no	—
348	#123	C₂×D₅	1	2	yes	complemented
349	#123	C₂×D₅	1	2	yes	complemented
350	C₂²⋊Q₈	—	5	1	no	—
351	C₂²⋊Q₈	—	5	1	no	—
352	C₂²⋊Q₈	—	5	2	no	—
353	C₂²⋊Q₈	—	5	2	no	—
354	C₂²⋊Q₈	—	5	2	no	—
355	C₂²⋊Q₈	—	5	2	no	—
356	#121	—	5	1	no	—
357	#121	—	5	2	no	—
358	#121	—	5	1	no	—
359	#121	—	5	2	no	—
360	#121	—	5	2	no	—
361	#121	—	5	2	no	—
362	#121	—	5	2	no	—
363	#121	—	5	2	no	—
364	#121	—	5	1	no	—
365	#121	—	5	1	no	—
366	#121	—	5	2	no	—
367	#121	—	5	2	no	—
368	#121	C₂×D₅	1	1	yes	characteristic
369	#121	C₂×D₅	1	1	yes	characteristic, complemented
370	#121	C₂×D₅	1	2	yes	complemented
371	#121	C₂×D₅	1	2	yes	complemented
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	1	no	—
377	C₄×D₄	—	5	1	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	—	5	2	no	—
383	C₄×D₄	—	5	2	no	—
384	C₄×D₄	—	5	2	no	—
385	C₄×D₄	—	5	1	no	—
386	C₄×D₄	—	5	2	no	—
387	C₄×D₄	—	5	2	no	—
388	C₄×D₄	—	5	2	no	—
389	C₄×D₄	—	5	2	no	—
390	C₄×D₄	—	5	1	no	—
391	C₄×D₄	C₂×D₅	1	1	yes	characteristic, complemented
392	C₄×D₄	C₂×D₅	1	1	yes	characteristic, complemented
393	#117	—	5	1	no	—
394	#117	—	5	2	no	—
395	#117	—	5	1	no	—
396	#117	—	5	1	no	—
397	#117	—	5	1	no	—
398	#117	—	5	2	no	—
399	#117	—	5	1	no	—
400	#117	—	5	1	no	—
401	#117	—	5	2	no	—
402	#117	—	5	1	no	—
403	#117	—	5	1	no	—
404	#117	C₂×D₅	1	1	yes	characteristic, complemented
405	C₂×C₄⋊C₄	—	5	2	no	—
406	C₂×C₄⋊C₄	—	5	1	no	—
407	C₂×C₄⋊C₄	—	5	1	no	—
408	C₂×C₄⋊C₄	—	5	1	no	—
409	C₂×C₂²⋊C₄	—	5	2	no	—
410	C₂×C₂²⋊C₄	—	5	1	no	—
411	C₂×C₂²⋊C₄	—	5	1	no	—
412	C₂×C₂²⋊C₄	—	5	2	no	—
413	C₂×C₂²⋊C₄	—	5	2	no	—
414	C₂×C₄²	—	5	1	no	—
415	C₂×C₄²	—	5	1	no	—
416	C₂²×C₅	—	2	2	no	—
417	C₂²×C₅	—	2	1	no	—
418	C₂²×C₅	—	2	2	no	—
419	C₂²×C₅	—	2	2	no	—
420	C₂²×C₅	—	2	2	no	—
421	C₂²×C₅	—	2	1	no	—
422	C₂²×C₅	—	2	2	no	—
423	C₂²×C₅	—	2	2	no	—
424	C₂²×C₅	—	2	1	no	—
425	C₂²×C₅	C₂⁵	1	1	yes	characteristic
426	C₂×D₅	—	2	1	no	—
427	C₂×D₅	—	2	1	no	—
428	C₂×D₅	—	2	1	no	—
429	C₂×D₅	—	2	1	no	—
430	C₂×D₅	—	2	2	no	—
431	C₂×D₅	—	2	2	no	—
432	C₂×D₅	—	2	2	no	—
433	C₂×D₅	—	4	4	no	—
434	C₂×D₅	—	8	4	no	—
435	C₂×D₅	C₂×#41	1	2	yes	—
436	C₂×D₅	H(5,𝔽₂)	1	2	yes	—
437	C₄×C₅	—	2	1	no	—
438	C₄×C₅	—	2	1	no	—
439	C₄×C₅	—	2	2	no	—
440	C₄×C₅	—	2	1	no	—
441	C₄×C₅	—	2	1	no	—
442	C₄×C₅	—	2	2	no	—
443	C₄×C₅	—	2	1	no	—
444	C₄×C₅	C₂×#41	1	2	yes	—
445	Dic₅	—	2	2	no	—
446	Dic₅	—	2	1	no	—
447	Dic₅	—	2	1	no	—
448	Dic₅	—	2	2	no	—
449	Dic₅	—	2	2	no	—
450	Dic₅	—	2	1	no	—
451	Dic₅	—	2	1	no	—
452	Dic₅	—	2	1	no	—
453	Dic₅	C₂×#41	1	2	yes	—
454	C₂⁴	—	5	1	no	—
455	C₂⁴	—	5	2	no	—
456	#41	—	10	4	no	—
457	#41	—	20	4	no	—
458	#41	—	20	4	no	—
459	C₂×Q₈	—	5	1	no	—
460	C₂×Q₈	—	5	2	no	—
461	C₂×Q₈	—	5	2	no	—
462	C₂×D₄	—	5	2	no	—
463	C₂×D₄	—	5	2	no	—
464	C₂×D₄	—	5	2	no	—
465	C₂×D₄	—	5	2	no	—
466	C₂×D₄	—	5	2	no	—
467	C₂×D₄	—	5	2	no	—
468	C₂×D₄	—	5	2	no	—
469	C₂×D₄	—	5	1	no	—
470	C₂×D₄	—	5	2	no	—
471	C₂×D₄	—	10	4	no	—
472	C₂×D₄	—	20	4	no	—
473	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
474	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
475	C₂×D₄	C₂²×D₅	1	2	yes	—
476	C₂×D₄	C₂²×D₅	1	2	yes	—
477	C₂×D₄	C₂²×D₅	1	2	yes	—
478	C₂×D₄	C₂²×D₅	1	2	yes	—
479	C₂²×C₄	—	5	1	no	—
480	C₂²×C₄	—	5	2	no	—
481	C₂²×C₄	—	5	1	no	—
482	C₂²×C₄	—	5	2	no	—
483	C₂²×C₄	—	5	2	no	—
484	C₂²×C₄	—	5	1	no	—
485	C₂²×C₄	—	5	1	no	—
486	C₂²×C₄	—	5	1	no	—
487	C₂²×C₄	—	5	1	no	—
488	C₂²×C₄	—	5	1	no	—
489	C₂²×C₄	—	5	1	no	—
490	C₂²×C₄	—	5	1	no	—
491	C₂²×C₄	—	5	2	no	—
492	C₂²×C₄	—	5	2	no	—
493	C₂²×C₄	—	5	2	no	—
494	C₂²×C₄	—	10	4	no	—
495	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
496	C₂²×C₄	C₂²×D₅	1	2	yes	—
497	C₂²×C₄	C₂²×D₅	1	2	yes	—
498	C₄⋊C₄	—	5	1	no	—
499	C₄⋊C₄	—	5	2	no	—
500	C₄⋊C₄	—	5	1	no	—
501	C₄⋊C₄	—	5	1	no	—
502	C₄⋊C₄	—	5	1	no	—
503	C₄⋊C₄	—	5	1	no	—
504	C₄⋊C₄	—	5	1	no	—
505	C₄⋊C₄	—	5	1	no	—
506	C₄⋊C₄	—	5	2	no	—
507	C₄⋊C₄	—	5	2	no	—
508	C₄⋊C₄	—	5	2	no	—
509	C₄⋊C₄	—	5	1	no	—
510	C₄⋊C₄	—	5	2	no	—
511	C₄⋊C₄	—	5	2	no	—
512	C₄⋊C₄	—	5	2	no	—
513	C₄⋊C₄	—	5	2	no	—
514	C₄⋊C₄	—	5	2	no	—
515	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
516	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
517	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
518	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
519	C₄⋊C₄	C₂²×D₅	1	2	yes	—
520	C₄⋊C₄	C₂²×D₅	1	2	yes	—
521	C₂²⋊C₄	—	5	1	no	—
522	C₂²⋊C₄	—	5	1	no	—
523	C₂²⋊C₄	—	5	2	no	—
524	C₂²⋊C₄	—	5	2	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	1	no	—
531	C₂²⋊C₄	—	5	1	no	—
532	C₂²⋊C₄	—	5	2	no	—
533	C₂²⋊C₄	—	5	1	no	—
534	C₂²⋊C₄	—	5	1	no	—
535	C₂²⋊C₄	—	5	2	no	—
536	C₂²⋊C₄	—	5	2	no	—
537	C₂²⋊C₄	—	5	2	no	—
538	C₂²⋊C₄	—	5	2	no	—
539	C₂²⋊C₄	—	5	2	no	—
540	C₂²⋊C₄	—	5	2	no	—
541	C₂²⋊C₄	—	5	2	no	—
542	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
543	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
544	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
545	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
546	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
547	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
548	C₄²	—	5	1	no	—
549	C₄²	—	5	1	no	—
550	C₄²	—	5	1	no	—
551	C₄²	—	5	1	no	—
552	C₄²	—	5	1	no	—
553	C₄²	—	5	1	no	—
554	C₄²	—	5	2	no	—
555	C₄²	—	5	2	no	—
556	C₄²	—	5	2	no	—
557	C₄²	C₂²×D₅	1	1	yes	characteristic
558	C₄²	C₂²×D₅	1	1	yes	characteristic
559	C₂×C₅	—	4	1	no	—
560	C₂×C₅	—	4	2	no	—
561	C₂×C₅	—	4	2	no	—
562	C₂×C₅	C₂²×#41	1	1	yes	characteristic
563	C₂×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
564	C₂×C₅	#585	1	1	yes	characteristic
565	D₅	—	2	2	no	—
566	D₅	—	2	2	no	—
567	D₅	—	4	2	no	—
568	C₂³	—	5	1	no	—
569	C₂³	—	5	1	no	—
570	C₂³	—	5	2	no	—
571	C₂³	—	10	2	no	—
572	C₂³	—	10	2	no	—
573	C₂³	—	10	4	no	—
574	C₂³	—	20	1	no	—
575	C₂³	—	20	2	no	—
576	C₂³	—	20	2	no	—
577	C₂³	C₂³×D₅	1	1	yes	characteristic
578	C₂³	C₂³×D₅	1	2	yes	—
579	C₂³	C₂³×D₅	1	2	yes	—
580	Q₈	—	10	2	no	—
581	Q₈	—	20	2	no	—
582	Q₈	—	20	2	no	—
583	D₄	—	2	2	no	—
584	D₄	—	2	2	no	—
585	D₄	—	4	2	no	—
586	D₄	—	4	2	no	—
587	D₄	—	4	2	no	—
588	D₄	—	4	2	no	—
589	D₄	—	10	4	no	—
590	D₄	—	10	4	no	—
591	D₄	—	10	4	no	—
592	D₄	—	10	4	no	—
593	D₄	—	10	4	no	—
594	D₄	—	10	2	no	—
595	D₄	—	20	2	no	—
596	D₄	—	20	2	no	—
597	D₄	—	20	2	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	4	2	no	—
600	C₂×C₄	—	4	2	no	—
601	C₂×C₄	—	5	1	no	—
602	C₂×C₄	—	5	4	no	—
603	C₂×C₄	—	5	1	no	—
604	C₂×C₄	—	5	1	no	—
605	C₂×C₄	—	5	2	no	—
606	C₂×C₄	—	5	1	no	—
607	C₂×C₄	—	5	1	no	—
608	C₂×C₄	—	5	1	no	—
609	C₂×C₄	—	5	2	no	—
610	C₂×C₄	—	5	2	no	—
611	C₂×C₄	—	10	2	no	—
612	C₂×C₄	—	10	2	no	—
613	C₂×C₄	—	10	2	no	—
614	C₂×C₄	—	10	2	no	—
615	C₂×C₄	—	10	2	no	—
616	C₂×C₄	—	10	4	no	—
617	C₂×C₄	—	10	2	no	—
618	C₂×C₄	—	20	2	no	—
619	C₂×C₄	—	20	2	no	—
620	C₂×C₄	—	20	1	no	—
621	C₂×C₄	—	20	2	no	—
622	C₂×C₄	—	20	1	no	—
623	C₂×C₄	—	20	2	no	—
624	C₂×C₄	—	20	2	no	—
625	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
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	C₂×C₄	C₂³×D₅	1	2	yes	—
630	C₂×C₄	C₂³×D₅	1	2	yes	—
631	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
632	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
633	C₅	#3494	1	1	yes	characteristic, complemented, Sylow
634	C₂²	—	2	1	no	—
635	C₂²	—	2	2	no	—
636	C₂²	—	2	2	no	—
637	C₂²	—	2	2	no	—
638	C₂²	—	2	2	no	—
639	C₂²	—	2	1	no	—
640	C₂²	—	2	2	no	—
641	C₂²	—	2	2	no	—
642	C₂²	—	2	1	no	—
643	C₂²	—	5	2	no	—
644	C₂²	—	5	2	no	—
645	C₂²	—	10	1	no	—
646	C₂²	—	10	1	no	—
647	C₂²	—	10	1	no	—
648	C₂²	—	10	1	no	—
649	C₂²	—	10	2	no	—
650	C₂²	—	10	2	no	—
651	C₂²	—	10	2	no	—
652	C₂²	—	20	4	no	—
653	C₂²	—	40	4	no	—
654	C₂²	C₂⁴×D₅	1	1	yes	characteristic
655	C₄	—	2	1	no	—
656	C₄	—	2	1	no	—
657	C₄	—	2	2	no	—
658	C₄	—	2	1	no	—
659	C₄	—	2	1	no	—
660	C₄	—	2	2	no	—
661	C₄	—	2	1	no	—
662	C₄	—	5	2	no	—
663	C₄	—	10	1	no	—
664	C₄	—	10	2	no	—
665	C₄	—	10	1	no	—
666	C₄	—	10	1	no	—
667	C₄	—	10	2	no	—
668	C₄	—	10	2	no	—
669	C₄	—	10	1	no	—
670	C₄	—	10	1	no	—
671	C₄	D₅×#41	1	2	yes	—
672	C₂	—	4	1	no	—
673	C₂	—	4	2	no	—
674	C₂	—	4	2	no	—
675	C₂	—	10	2	no	—
676	C₂	—	10	2	no	—
677	C₂	—	20	2	no	—
678	C₂	C₂×D₅×#41	1	1	yes	characteristic
679	C₂	D₅×H(5,𝔽₂)	1	1	yes	characteristic
680	C₂	#66285	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅
commutator, socle, cosocle	C₂²×C₅	C₂⁵
Fitting	C₅×#540	C₂
hypercenter	#540	D₅
hypocenter	C₅	#3494
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ #540

Complements

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

N	H ≅ G/N	type
1. C₅×#540	C₂	semidirect
2. #66050	C₂	semidirect
3. #66049	C₂	semidirect
4. #66025	C₂	semidirect
5. #66023	C₂	semidirect
6. #65995	C₂	semidirect
7. #65993	C₂	semidirect
8. #65992	C₂	semidirect
9. #65989	C₂	semidirect
10. #65953	C₂	semidirect
11. #65950	C₂	semidirect
12. #65946	C₂	semidirect
13. #65944	C₂	semidirect
14. #65940	C₂	semidirect
15. D₅×#121	C₂	semidirect
16. #65937	C₂	semidirect
17. #65935	C₂	semidirect
18. #65891	C₂	semidirect
19. #65882	C₂	semidirect
20. #65880	C₂	semidirect
21. #65879	C₂	semidirect
22. #65868	C₂	semidirect
23. D₅×#117	C₂	semidirect
25. C₂×#711	C₂²	semidirect
28. C₂×#709	C₂²	semidirect
30. C₅×#127	C₂²	semidirect
31. C₅×#125	C₂²	semidirect
32. C₅×#123	C₂²	semidirect
33. C₅×#123	C₂²	semidirect
35. C₅×#121	C₂²	semidirect
36. C₅×#121	C₂²	semidirect
37. C₅×#121	C₂²	semidirect
38. C₄×C₅×D₄	C₂²	semidirect
39. C₄×C₅×D₄	C₂²	semidirect
40. C₅×#117	C₂²	semidirect
41. #4086	C₂²	semidirect
43. #4085	C₂²	semidirect
44. #4085	C₂²	semidirect
45. #4085	C₂²	semidirect
47. #4084	C₂²	semidirect
48. #4084	C₂²	semidirect
49. #4084	C₂²	semidirect
53. #4082	C₂²	semidirect
54. #4082	C₂²	semidirect
55. #4082	C₂²	semidirect
56. #4081	C₂²	semidirect
57. D₄×Dic₅	C₂²	semidirect
58. D₄×Dic₅	C₂²	semidirect
59. D₄×Dic₅	C₂²	semidirect
60. D₄×Dic₅	C₂²	semidirect
63. C₄×C₂²⋊D₅	C₂²	semidirect
64. C₄×C₂²⋊D₅	C₂²	semidirect
65. C₄×C₂²⋊D₅	C₂²	semidirect
67. #4072	C₂²	semidirect
68. #4072	C₂²	semidirect
69. #4070	C₂²	semidirect
70. C₂×#683	C₂²	semidirect
71. #4044	C₂²	semidirect
72. #4044	C₂²	semidirect
74. #4043	C₂²	semidirect
76. #4042	C₂²	semidirect
78. #4040	C₂²	semidirect
79. #4039	C₂²	semidirect
80. #4039	C₂²	semidirect
84. #4038	C₂²	semidirect
86. D₅×C₄⋊C₄	C₂²	semidirect
87. D₅×C₄⋊C₄	C₂²	semidirect
88. #4036	C₂²	semidirect
89. #4035	C₂²	semidirect
90. #4034	C₂²	semidirect
91. #4034	C₂²	semidirect
92. #4033	C₂²	semidirect
93. #4032	C₂²	semidirect
94. #4031	C₂²	semidirect
95. #4031	C₂²	semidirect
97. #4030	C₂²	semidirect
99. #4029	C₂²	semidirect
100. #4029	C₂²	semidirect
101. #4029	C₂²	semidirect
103. #4027	C₂²	semidirect
104. #4027	C₂²	semidirect
109. #4025	C₂²	semidirect
110. #4025	C₂²	semidirect
111. #4024	C₂²	semidirect
112. #4023	C₂²	semidirect
113. #4023	C₂²	semidirect
114. #4023	C₂²	semidirect
115. #4021	C₂²	semidirect
116. C₄×D₂₀	C₂²	semidirect
119. C₄²×D₅	C₂²	semidirect
120. C₄²×D₅	C₂²	semidirect
121. #4015	C₂²	semidirect
122. C₄×Dic₁₀	C₂²	semidirect
241. #540	D₅	semidirect
313. C₄×D₅	#41	semidirect
327. #127	C₂×D₅	semidirect
334. #125	C₂×D₅	semidirect
348. #123	C₂×D₅	semidirect
349. #123	C₂×D₅	semidirect
369. #121	C₂×D₅	semidirect
370. #121	C₂×D₅	semidirect
371. #121	C₂×D₅	semidirect
391. C₄×D₄	C₂×D₅	semidirect
392. C₄×D₄	C₂×D₅	semidirect
404. #117	C₂×D₅	semidirect
633. C₅	#3494	semidirect

Maximal subgroups

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

subgroup	index
C₅×#540	2
#66050	2
#66049	2
#66025	2
#66023	2
#65995	2
#65993	2
#65992	2
#65989	2
#65953	2
#65950	2
#65946	2
#65944	2
#65940	2
D₅×#121	2
#65937	2
#65935	2
#65891	2
#65882	2
#65880	2
#65879	2
#65868	2
D₅×#117	2
#3494	5