Subgroups — #10618285

Order 640.

1134 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#537	C₂	1	1	yes	maximal, characteristic, complemented
2	#66167	C₂	1	1	yes	maximal, characteristic, complemented
3	#66165	C₂	1	1	yes	maximal, characteristic, complemented
4	#66163	C₂	1	1	yes	maximal, characteristic, complemented
5	#66162	C₂	1	1	yes	maximal, characteristic, complemented
6	#65977	C₂	1	1	yes	maximal, characteristic, complemented
7	#65972	C₂	1	2	yes	maximal, complemented
8	#65969	C₂	1	1	yes	maximal, characteristic, complemented
9	#65968	C₂	1	2	yes	maximal, complemented
10	#65967	C₂	1	1	yes	maximal, characteristic, complemented
11	D₅×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
12	#65955	C₂	1	2	yes	maximal, complemented
13	#65955	C₂	1	2	yes	maximal, complemented
14	#65947	C₂	1	2	yes	maximal, complemented
15	#65946	C₂	1	1	yes	maximal, characteristic, complemented
16	#65946	C₂	1	2	yes	maximal, complemented
17	#65945	C₂	1	1	yes	maximal, characteristic, complemented
18	#65944	C₂	1	2	yes	maximal, complemented
19	#65942	C₂	1	2	yes	maximal, complemented
20	D₅×#121	C₂	1	1	yes	maximal, characteristic, complemented
21	#65937	C₂	1	1	yes	maximal, characteristic, complemented
22	#65845	C₂	1	1	yes	maximal, characteristic, complemented
23	#65841	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₅×#41	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₅×#41	C₂²	1	1	yes	characteristic, complemented
26	C₂×Q₈×D₅	C₂²	1	1	yes	characteristic, complemented
27	C₂×#711	C₂²	1	2	yes	complemented
28	C₂×D₄×D₅	C₂²	1	1	yes	characteristic
29	C₂×D₄×D₅	C₂²	1	2	yes	—
30	C₂×#709	C₂²	1	2	yes	complemented
31	C₂×#709	C₂²	1	1	yes	characteristic, complemented
32	C₂²×C₄×D₅	C₂²	1	1	yes	characteristic
33	C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
34	C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
35	C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
36	C₅×#121	C₂²	1	1	yes	characteristic
37	C₅×#121	C₂²	1	2	yes	complemented
38	C₅×#121	C₂²	1	2	yes	complemented
39	C₅×#121	C₂²	1	1	yes	characteristic, complemented
40	C₅×#121	C₂²	1	2	yes	complemented
41	C₂×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
42	#4093	C₂²	1	1	yes	characteristic, complemented
43	#4092	C₂²	1	1	yes	characteristic
44	#4092	C₂²	1	1	yes	characteristic
45	#4092	C₂²	1	1	yes	characteristic, complemented
46	#4092	C₂²	1	2	yes	complemented
47	Q₈×Dic₅	C₂²	1	1	yes	characteristic, complemented
48	#4085	C₂²	1	2	yes	—
49	#4085	C₂²	1	2	yes	complemented
50	#4085	C₂²	1	2	yes	complemented
51	#4085	C₂²	1	2	yes	complemented
52	#4084	C₂²	1	1	yes	characteristic
53	#4084	C₂²	1	1	yes	characteristic
54	#4084	C₂²	1	1	yes	characteristic, complemented
55	#4084	C₂²	1	2	yes	complemented
56	#4084	C₂²	1	2	yes	complemented
57	#4084	C₂²	1	2	yes	complemented
58	#4083	C₂²	1	1	yes	characteristic
59	#4083	C₂²	1	1	yes	characteristic
60	#4083	C₂²	1	2	yes	—
61	#4083	C₂²	1	2	yes	—
62	#4082	C₂²	1	1	yes	characteristic, complemented
63	#4082	C₂²	1	2	yes	complemented
64	#4082	C₂²	1	2	yes	complemented
65	#4081	C₂²	1	1	yes	characteristic, complemented
66	#4081	C₂²	1	1	yes	characteristic, complemented
67	#4081	C₂²	1	2	yes	complemented
68	#4081	C₂²	1	2	yes	complemented
69	D₄×Dic₅	C₂²	1	1	yes	characteristic, complemented
70	#4076	C₂²	1	1	yes	characteristic
71	#4076	C₂²	1	1	yes	characteristic, complemented
72	#4075	C₂²	1	2	yes	complemented
73	#4075	C₂²	1	2	yes	complemented
74	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic
75	C₄×C₂²⋊D₅	C₂²	1	2	yes	—
76	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic
77	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic, complemented
78	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic, complemented
79	C₄×C₂²⋊D₅	C₂²	1	2	yes	complemented
80	C₂×#685	C₂²	1	2	yes	—
81	#4072	C₂²	1	1	yes	characteristic, complemented
82	C₂×C₄⋊Dic₅	C₂²	1	1	yes	characteristic, complemented
83	#4070	C₂²	1	1	yes	characteristic, complemented
84	#4070	C₂²	1	2	yes	complemented
85	#4070	C₂²	1	2	yes	complemented
86	#4070	C₂²	1	1	yes	characteristic, complemented
87	#4044	C₂²	1	2	yes	complemented
88	#4043	C₂²	1	1	yes	characteristic
89	#4043	C₂²	1	2	yes	—
90	#4043	C₂²	1	2	yes	complemented
91	#4042	C₂²	1	2	yes	—
92	#4042	C₂²	1	2	yes	—
93	#4042	C₂²	1	2	yes	complemented
94	#4042	C₂²	1	2	yes	complemented
95	#4041	C₂²	1	1	yes	characteristic
96	#4040	C₂²	1	2	yes	complemented
97	#4039	C₂²	1	1	yes	characteristic, complemented
98	#4039	C₂²	1	2	yes	complemented
99	D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
100	D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
101	D₅×C₄⋊C₄	C₂²	1	2	yes	complemented
102	#4035	C₂²	1	2	yes	complemented
103	#4035	C₂²	1	2	yes	complemented
104	#4034	C₂²	1	1	yes	characteristic, complemented
105	#4034	C₂²	1	1	yes	characteristic, complemented
106	#4033	C₂²	1	1	yes	characteristic, complemented
107	#4031	C₂²	1	2	yes	complemented
108	#4031	C₂²	1	2	yes	complemented
109	#4030	C₂²	1	2	yes	—
110	#4030	C₂²	1	2	yes	complemented
111	#4029	C₂²	1	2	yes	complemented
112	#4029	C₂²	1	2	yes	complemented
113	#4029	C₂²	1	2	yes	complemented
114	#4027	C₂²	1	2	yes	—
115	D₅×C₂²⋊C₄	C₂²	1	2	yes	—
116	D₅×C₂²⋊C₄	C₂²	1	2	yes	—
117	D₅×C₂²⋊C₄	C₂²	1	2	yes	—
118	#4025	C₂²	1	2	yes	complemented
119	#4024	C₂²	1	2	yes	complemented
120	#4024	C₂²	1	2	yes	complemented
121	#4024	C₂²	1	2	yes	complemented
122	#4024	C₂²	1	2	yes	complemented
123	#3536	—	5	1	no	maximal, Sylow
124	C₂³×D₅	C₂³	1	1	yes	characteristic
125	C₂³×D₅	C₂³	1	2	yes	—
126	C₅×#41	—	4	2	no	—
127	C₅×#41	—	4	2	no	—
128	C₂×C₅×Q₈	C₂³	1	1	yes	characteristic
129	C₂×C₅×Q₈	C₂³	1	1	yes	characteristic
130	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
131	C₂×C₅×D₄	C₂³	1	2	yes	—
132	C₂×C₅×D₄	C₂³	1	2	yes	—
133	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
134	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
135	C₂×C₅×D₄	C₂³	1	2	yes	—
136	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
137	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
138	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
139	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
140	C₂²×C₄×C₅	C₂³	1	2	yes	—
141	C₂²×C₄×C₅	C₂³	1	2	yes	—
142	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
143	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
144	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
145	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
146	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
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	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
151	C₂²×Dic₅	C₂³	1	1	yes	characteristic
152	C₂²×Dic₅	C₂³	1	2	yes	—
153	C₂²×Dic₅	C₂³	1	2	yes	—
154	Q₈×D₅	—	4	2	no	—
155	#711	—	4	4	no	—
156	D₄×D₅	—	4	2	no	—
157	D₄×D₅	—	4	4	no	—
158	#709	—	4	2	no	—
159	#709	—	4	4	no	—
160	C₂×D₂₀	C₂³	1	2	yes	—
161	C₂×D₂₀	C₂³	1	1	yes	characteristic
162	C₂×C₄×D₅	—	4	2	no	—
163	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
164	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
165	C₂×C₄×D₅	C₂³	1	2	yes	—
166	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
167	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
168	C₂×C₄×D₅	C₂³	1	2	yes	—
169	C₂×C₄×D₅	C₂³	1	2	yes	—
170	C₂×C₄×D₅	C₂³	1	2	yes	—
171	C₂×C₄×D₅	C₂³	1	2	yes	—
172	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
173	C₂×Dic₁₀	C₂³	1	2	yes	—
174	C₂×Dic₁₀	C₂³	1	2	yes	—
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	2	yes	—
179	C₅×C₄⋊C₄	C₂³	1	2	yes	—
180	C₅×C₄⋊C₄	C₂³	1	2	yes	—
181	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
182	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
183	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
184	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
185	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
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	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
192	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
193	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
194	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
195	C₂²⋊Dic₅	C₂³	1	2	yes	—
196	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
197	#685	C₂³	1	2	yes	—
198	#685	C₂³	1	1	yes	characteristic
199	#685	C₂³	1	2	yes	—
200	#685	C₂³	1	2	yes	—
201	#685	C₂³	1	2	yes	—
202	#685	C₂³	1	1	yes	characteristic
203	#685	C₂³	1	2	yes	—
204	#685	C₂³	1	2	yes	—
205	#685	C₂³	1	2	yes	—
206	#685	C₂³	1	1	yes	characteristic
207	#685	C₂³	1	2	yes	—
208	#685	C₂³	1	1	yes	characteristic
209	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
210	C₄⋊Dic₅	C₂³	1	2	yes	—
211	C₄⋊Dic₅	C₂³	1	2	yes	—
212	C₄⋊Dic₅	C₂³	1	2	yes	—
213	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
214	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
215	C₄⋊Dic₅	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	2	yes	—
221	#683	C₂³	1	2	yes	—
222	#683	C₂³	1	2	yes	—
223	#683	C₂³	1	2	yes	—
224	#683	C₂³	1	1	yes	characteristic
225	#683	C₂³	1	1	yes	characteristic
226	#683	C₂³	1	2	yes	—
227	#683	C₂³	1	1	yes	characteristic
228	C₄×Dic₅	C₂³	1	2	yes	—
229	C₄×Dic₅	C₂³	1	2	yes	—
230	C₄×Dic₅	C₂³	1	1	yes	characteristic
231	C₄×Dic₅	C₂³	1	1	yes	characteristic
232	#562	—	5	2	no	—
233	#562	—	5	2	no	—
234	#554	—	5	1	no	—
235	#554	—	5	1	no	—
236	#548	—	5	1	no	—
237	#548	—	5	1	no	—
238	#547	—	5	1	no	—
239	#547	—	5	1	no	—
240	#546	—	5	1	no	—
241	#546	—	5	2	no	—
242	#546	—	5	2	no	—
243	#546	—	5	1	no	—
244	#543	—	5	2	no	—
245	#542	—	5	1	no	—
246	#542	—	5	1	no	—
247	#539	—	5	2	no	—
248	#538	—	5	2	no	—
249	#537	—	5	1	no	—
250	#537	—	5	2	no	—
251	#537	D₅	1	1	yes	characteristic, complemented
252	#525	—	5	1	no	—
253	C₂×C₂²⋊Q₈	—	5	1	no	—
254	C₂×#121	—	5	1	no	—
255	C₂³×C₅	C₂⁴	1	2	yes	—
256	C₂³×C₅	C₂⁴	1	1	yes	characteristic
257	C₂³×C₅	C₂⁴	1	1	yes	characteristic
258	C₂³×C₅	C₂⁴	1	1	yes	characteristic
259	C₂²×D₅	—	2	2	no	—
260	C₂²×D₅	—	2	2	no	—
261	C₂²×D₅	—	2	4	no	—
262	C₂²×D₅	—	4	1	no	—
263	C₂²×D₅	—	4	2	no	—
264	C₂²×D₅	—	4	2	no	—
265	C₂²×D₅	C₂⁴	1	2	yes	—
266	C₂²×D₅	C₂⁴	1	1	yes	characteristic
267	C₂²×D₅	C₂⁴	1	1	yes	characteristic
268	C₅×Q₈	—	2	2	no	—
269	C₅×Q₈	—	4	1	no	—
270	C₅×D₄	—	2	2	no	—
271	C₅×D₄	—	4	2	no	—
272	C₅×D₄	—	4	2	no	—
273	C₅×D₄	—	4	2	no	—
274	C₅×D₄	—	4	1	no	—
275	C₅×D₄	—	4	1	no	—
276	C₅×D₄	—	4	1	no	—
277	C₂×C₄×C₅	—	2	2	no	—
278	C₂×C₄×C₅	—	2	2	no	—
279	C₂×C₄×C₅	—	2	2	no	—
280	C₂×C₄×C₅	—	4	2	no	—
281	C₂×C₄×C₅	—	4	2	no	—
282	C₂×C₄×C₅	C₂⁴	1	2	yes	—
283	C₂×C₄×C₅	C₂⁴	1	2	yes	—
284	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
285	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
286	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
287	C₂×C₄×C₅	C₂⁴	1	2	yes	—
288	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
289	C₂²⋊D₅	—	2	2	no	—
290	C₂²⋊D₅	—	2	4	no	—
291	C₂²⋊D₅	—	2	2	no	—
292	C₂²⋊D₅	—	2	2	no	—
293	C₂²⋊D₅	—	2	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	C₂×Dic₅	—	4	1	no	—
299	C₂×Dic₅	—	4	2	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	2	yes	—
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	1	yes	characteristic
308	C₂×Dic₅	C₂⁴	1	2	yes	—
309	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
310	D₂₀	—	2	4	no	—
311	D₂₀	—	2	2	no	—
312	C₄×D₅	—	2	4	no	—
313	C₄×D₅	—	2	2	no	—
314	C₄×D₅	—	2	2	no	—
315	C₄×D₅	—	4	1	no	—
316	C₄×D₅	—	4	1	no	—
317	C₄×D₅	—	4	2	no	—
318	C₄×D₅	—	4	2	no	—
319	C₄×D₅	—	4	2	no	—
320	C₄×D₅	—	4	2	no	—
321	Dic₁₀	—	2	2	no	—
322	Dic₁₀	—	4	2	no	—
323	Dic₁₀	—	4	2	no	—
324	Dic₁₀	—	4	2	no	—
325	C₂×#41	—	5	2	no	—
326	C₂×#41	—	5	2	no	—
327	C₂×#41	—	5	1	no	—
328	C₂×#41	C₂×D₅	1	1	yes	characteristic, complemented
329	C₂×#41	C₂×D₅	1	1	yes	characteristic, complemented
330	C₂²×Q₈	—	5	1	no	—
331	C₂²×D₄	—	5	1	no	—
332	C₂²×D₄	—	5	2	no	—
333	C₂³×C₄	—	5	1	no	—
334	C₄⋊Q₈	—	5	1	no	—
335	C₄⋊Q₈	—	5	1	no	—
336	#126	—	5	2	no	—
337	#126	—	5	2	no	—
338	#125	—	5	2	no	—
339	#125	—	5	2	no	—
340	#124	—	5	1	no	—
341	#124	—	5	2	no	—
342	#124	—	5	1	no	—
343	#124	—	5	2	no	—
344	#124	—	5	2	no	—
345	#124	—	5	2	no	—
346	#123	—	5	1	no	—
347	#123	—	5	1	no	—
348	#123	—	5	2	no	—
349	#123	—	5	2	no	—
350	#123	—	5	2	no	—
351	#123	—	5	2	no	—
352	#123	—	5	2	no	—
353	#123	—	5	2	no	—
354	#123	—	5	2	no	—
355	#123	—	5	2	no	—
356	C₂²⋊Q₈	—	5	1	no	—
357	C₂²⋊Q₈	—	5	1	no	—
358	C₂²⋊Q₈	—	5	1	no	—
359	C₂²⋊Q₈	—	5	2	no	—
360	C₂²⋊Q₈	—	5	1	no	—
361	C₂²⋊Q₈	—	5	1	no	—
362	C₂²⋊Q₈	—	5	2	no	—
363	C₂²⋊Q₈	—	5	2	no	—
364	C₂²⋊Q₈	—	5	2	no	—
365	C₂²⋊Q₈	—	5	1	no	—
366	C₂²⋊Q₈	—	5	2	no	—
367	C₂²⋊Q₈	—	5	2	no	—
368	C₂²⋊Q₈	—	5	2	no	—
369	C₂²⋊Q₈	—	5	2	no	—
370	C₂²⋊Q₈	—	5	2	no	—
371	C₂²⋊Q₈	—	5	2	no	—
372	C₂²⋊Q₈	—	5	2	no	—
373	C₂²⋊Q₈	—	5	2	no	—
374	C₂²⋊Q₈	—	5	2	no	—
375	C₂²⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
376	C₂²⋊Q₈	C₂×D₅	1	2	yes	complemented
377	C₂²⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
378	#121	—	5	1	no	—
379	#121	—	5	2	no	—
380	#121	—	5	1	no	—
381	#121	—	5	1	no	—
382	#121	—	5	2	no	—
383	#121	—	5	2	no	—
384	#121	—	5	2	no	—
385	#121	—	5	2	no	—
386	#121	—	5	2	no	—
387	#121	—	5	2	no	—
388	#121	—	5	1	no	—
389	#121	—	5	1	no	—
390	#121	—	5	1	no	—
391	#121	—	5	2	no	—
392	#121	—	5	2	no	—
393	#121	C₂×D₅	1	1	yes	characteristic
394	#121	C₂×D₅	1	2	yes	complemented
395	#121	C₂×D₅	1	1	yes	characteristic, complemented
396	#121	C₂×D₅	1	2	yes	complemented
397	#121	C₂×D₅	1	2	yes	complemented
398	#120	—	5	1	no	—
399	#120	—	5	1	no	—
400	#120	—	5	2	no	—
401	#120	—	5	2	no	—
402	C₄×Q₈	—	5	1	no	—
403	C₄×Q₈	—	5	1	no	—
404	C₄×D₄	—	5	1	no	—
405	C₄×D₄	—	5	1	no	—
406	C₄×D₄	—	5	1	no	—
407	C₄×D₄	—	5	1	no	—
408	C₄×D₄	—	5	1	no	—
409	C₄×D₄	—	5	2	no	—
410	C₄×D₄	—	5	2	no	—
411	C₄×D₄	—	5	2	no	—
412	C₄×D₄	—	5	1	no	—
413	C₄×D₄	—	5	2	no	—
414	#117	—	5	1	no	—
415	C₂×C₄⋊C₄	—	5	1	no	—
416	C₂×C₄⋊C₄	—	5	1	no	—
417	C₂×C₄⋊C₄	—	5	2	no	—
418	C₂×C₄⋊C₄	—	5	1	no	—
419	C₂×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic, complemented
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	—	5	2	no	—
424	C₂²×C₅	—	2	1	no	—
425	C₂²×C₅	—	2	2	no	—
426	C₂²×C₅	—	2	1	no	—
427	C₂²×C₅	—	2	1	no	—
428	C₂²×C₅	—	2	1	no	—
429	C₂²×C₅	—	2	1	no	—
430	C₂²×C₅	—	2	2	no	—
431	C₂²×C₅	—	2	1	no	—
432	C₂²×C₅	—	2	1	no	—
433	C₂²×C₅	—	2	1	no	—
434	C₂²×C₅	—	2	1	no	—
435	C₂²×C₅	—	2	2	no	—
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	1	no	—
441	C₂×D₅	—	2	2	no	—
442	C₂×D₅	—	2	2	no	—
443	C₂×D₅	—	2	2	no	—
444	C₂×D₅	—	4	4	no	—
445	C₂×D₅	—	8	4	no	—
446	C₂×D₅	H(5,𝔽₂)	1	2	yes	—
447	C₂×D₅	2₋¹⁺⁴	1	2	yes	—
448	C₄×C₅	—	2	2	no	—
449	C₄×C₅	—	2	2	no	—
450	C₄×C₅	—	2	2	no	—
451	C₄×C₅	—	2	1	no	—
452	C₄×C₅	—	2	1	no	—
453	C₄×C₅	—	2	1	no	—
454	C₄×C₅	H(5,𝔽₂)	1	2	yes	—
455	Dic₅	—	2	2	no	—
456	Dic₅	—	2	1	no	—
457	Dic₅	—	2	1	no	—
458	Dic₅	—	2	1	no	—
459	Dic₅	—	2	2	no	—
460	Dic₅	—	2	2	no	—
461	Dic₅	—	2	1	no	—
462	Dic₅	—	2	1	no	—
463	Dic₅	—	2	1	no	—
464	C₂⁴	—	5	1	no	—
465	C₂⁴	—	5	2	no	—
466	#41	—	4	2	no	—
467	#41	—	4	2	no	—
468	#41	—	20	2	no	—
469	#41	—	20	4	no	—
470	#41	—	20	4	no	—
471	C₂×Q₈	—	5	1	no	—
472	C₂×Q₈	—	5	2	no	—
473	C₂×Q₈	—	5	2	no	—
474	C₂×Q₈	—	5	2	no	—
475	C₂×Q₈	—	20	2	no	—
476	C₂×Q₈	C₂²×D₅	1	1	yes	characteristic
477	C₂×Q₈	C₂²×D₅	1	1	yes	characteristic
478	C₂×D₄	—	5	1	no	—
479	C₂×D₄	—	5	1	no	—
480	C₂×D₄	—	5	1	no	—
481	C₂×D₄	—	5	1	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	2	no	—
488	C₂×D₄	—	5	1	no	—
489	C₂×D₄	—	20	2	no	—
490	C₂×D₄	—	20	4	no	—
491	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
492	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
493	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
494	C₂×D₄	C₂²×D₅	1	2	yes	—
495	C₂×D₄	C₂²×D₅	1	2	yes	—
496	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
497	C₂×D₄	C₂²×D₅	1	2	yes	—
498	C₂²×C₄	—	5	2	no	—
499	C₂²×C₄	—	5	2	no	—
500	C₂²×C₄	—	5	1	no	—
501	C₂²×C₄	—	5	2	no	—
502	C₂²×C₄	—	5	1	no	—
503	C₂²×C₄	—	5	1	no	—
504	C₂²×C₄	—	5	1	no	—
505	C₂²×C₄	—	5	2	no	—
506	C₂²×C₄	—	5	2	no	—
507	C₂²×C₄	—	5	2	no	—
508	C₂²×C₄	—	5	2	no	—
509	C₂²×C₄	—	5	1	no	—
510	C₂²×C₄	—	20	2	no	—
511	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
512	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
513	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
514	C₂²×C₄	C₂²×D₅	1	2	yes	—
515	C₂²×C₄	C₂²×D₅	1	2	yes	—
516	C₄⋊C₄	—	5	1	no	—
517	C₄⋊C₄	—	5	1	no	—
518	C₄⋊C₄	—	5	2	no	—
519	C₄⋊C₄	—	5	2	no	—
520	C₄⋊C₄	—	5	2	no	—
521	C₄⋊C₄	—	5	2	no	—
522	C₄⋊C₄	—	5	2	no	—
523	C₄⋊C₄	—	5	2	no	—
524	C₄⋊C₄	—	5	1	no	—
525	C₄⋊C₄	—	5	1	no	—
526	C₄⋊C₄	—	5	2	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	2	no	—
534	C₄⋊C₄	—	5	2	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	2	yes	—
538	C₄⋊C₄	C₂²×D₅	1	2	yes	—
539	C₄⋊C₄	C₂²×D₅	1	2	yes	—
540	C₂²⋊C₄	—	5	2	no	—
541	C₂²⋊C₄	—	5	2	no	—
542	C₂²⋊C₄	—	5	2	no	—
543	C₂²⋊C₄	—	5	1	no	—
544	C₂²⋊C₄	—	5	1	no	—
545	C₂²⋊C₄	—	5	2	no	—
546	C₂²⋊C₄	—	5	2	no	—
547	C₂²⋊C₄	—	5	1	no	—
548	C₂²⋊C₄	—	5	1	no	—
549	C₂²⋊C₄	—	5	2	no	—
550	C₂²⋊C₄	—	5	1	no	—
551	C₂²⋊C₄	—	5	1	no	—
552	C₂²⋊C₄	—	5	1	no	—
553	C₂²⋊C₄	—	5	1	no	—
554	C₂²⋊C₄	—	5	2	no	—
555	C₂²⋊C₄	—	5	2	no	—
556	C₂²⋊C₄	—	5	2	no	—
557	C₂²⋊C₄	—	5	2	no	—
558	C₂²⋊C₄	—	5	2	no	—
559	C₂²⋊C₄	—	5	2	no	—
560	C₂²⋊C₄	—	5	1	no	—
561	C₂²⋊C₄	—	5	1	no	—
562	C₂²⋊C₄	—	5	2	no	—
563	C₂²⋊C₄	—	5	2	no	—
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	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
568	C₄²	—	5	1	no	—
569	C₄²	—	5	1	no	—
570	C₄²	—	5	2	no	—
571	C₄²	—	5	2	no	—
572	C₂×C₅	—	4	1	no	—
573	C₂×C₅	—	4	2	no	—
574	C₂×C₅	—	4	1	no	—
575	C₂×C₅	—	4	1	no	—
576	C₂×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
577	C₂×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
578	C₂×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
579	D₅	—	2	2	no	—
580	D₅	—	2	2	no	—
581	D₅	—	4	2	no	—
582	C₂³	—	5	1	no	—
583	C₂³	—	5	1	no	—
584	C₂³	—	5	2	no	—
585	C₂³	—	10	2	no	—
586	C₂³	—	10	2	no	—
587	C₂³	—	10	4	no	—
588	C₂³	—	20	1	no	—
589	C₂³	—	20	2	no	—
590	C₂³	—	20	2	no	—
591	C₂³	C₂³×D₅	1	1	yes	characteristic
592	C₂³	C₂³×D₅	1	2	yes	—
593	C₂³	C₂³×D₅	1	1	yes	characteristic
594	C₂³	C₂³×D₅	1	1	yes	characteristic
595	Q₈	—	2	2	no	—
596	Q₈	—	4	1	no	—
597	Q₈	—	10	2	no	—
598	Q₈	—	20	2	no	—
599	Q₈	—	20	2	no	—
600	Q₈	—	20	2	no	—
601	D₄	—	2	2	no	—
602	D₄	—	4	2	no	—
603	D₄	—	4	1	no	—
604	D₄	—	4	1	no	—
605	D₄	—	4	1	no	—
606	D₄	—	4	2	no	—
607	D₄	—	4	2	no	—
608	D₄	—	10	4	no	—
609	D₄	—	10	4	no	—
610	D₄	—	10	2	no	—
611	D₄	—	10	2	no	—
612	D₄	—	10	2	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	C₂×C₄	—	2	2	no	—
620	C₂×C₄	—	2	2	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	4	2	no	—
623	C₂×C₄	—	4	2	no	—
624	C₂×C₄	—	5	1	no	—
625	C₂×C₄	—	5	1	no	—
626	C₂×C₄	—	5	2	no	—
627	C₂×C₄	—	5	1	no	—
628	C₂×C₄	—	5	1	no	—
629	C₂×C₄	—	5	2	no	—
630	C₂×C₄	—	5	1	no	—
631	C₂×C₄	—	5	2	no	—
632	C₂×C₄	—	5	1	no	—
633	C₂×C₄	—	10	4	no	—
634	C₂×C₄	—	10	2	no	—
635	C₂×C₄	—	10	2	no	—
636	C₂×C₄	—	20	1	no	—
637	C₂×C₄	—	20	1	no	—
638	C₂×C₄	—	20	2	no	—
639	C₂×C₄	—	20	2	no	—
640	C₂×C₄	—	20	2	no	—
641	C₂×C₄	—	20	2	no	—
642	C₂×C₄	—	20	1	no	—
643	C₂×C₄	—	20	2	no	—
644	C₂×C₄	—	20	2	no	—
645	C₂×C₄	C₂³×D₅	1	2	yes	—
646	C₂×C₄	C₂³×D₅	1	2	yes	—
647	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
648	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
649	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
650	C₂×C₄	C₂³×D₅	1	2	yes	—
651	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
652	C₅	#3536	1	1	yes	characteristic, complemented, Sylow
653	C₂²	—	2	1	no	—
654	C₂²	—	2	1	no	—
655	C₂²	—	2	1	no	—
656	C₂²	—	2	2	no	—
657	C₂²	—	2	1	no	—
658	C₂²	—	2	1	no	—
659	C₂²	—	2	2	no	—
660	C₂²	—	2	1	no	—
661	C₂²	—	2	1	no	—
662	C₂²	—	2	1	no	—
663	C₂²	—	2	1	no	—
664	C₂²	—	2	2	no	—
665	C₂²	—	5	2	no	—
666	C₂²	—	5	2	no	—
667	C₂²	—	10	1	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	—	20	4	no	—
675	C₂²	—	40	4	no	—
676	C₂²	C₂⁴×D₅	1	1	yes	characteristic
677	C₄	—	2	1	no	—
678	C₄	—	2	1	no	—
679	C₄	—	2	1	no	—
680	C₄	—	2	2	no	—
681	C₄	—	2	2	no	—
682	C₄	—	2	2	no	—
683	C₄	—	10	1	no	—
684	C₄	—	10	1	no	—
685	C₄	—	10	2	no	—
686	C₄	—	10	2	no	—
687	C₄	—	10	2	no	—
688	C₄	—	10	1	no	—
689	C₄	—	10	1	no	—
690	C₄	—	10	1	no	—
691	C₄	—	10	1	no	—
692	C₄	#4144	1	2	yes	—
693	C₂	—	4	1	no	—
694	C₂	—	4	2	no	—
695	C₂	—	4	1	no	—
696	C₂	—	4	1	no	—
697	C₂	—	10	2	no	—
698	C₂	—	10	2	no	—
699	C₂	—	20	2	no	—
700	C₂	C₂×#4144	1	1	yes	characteristic
701	C₂	D₅×H(5,𝔽₂)	1	1	yes	characteristic
702	C₂	D₅×2₋¹⁺⁴	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅
commutator, socle, cosocle	C₂²×C₅	C₂⁵
Fitting	C₅×#537	C₂
hypercenter	#537	D₅
hypocenter	C₅	#3536
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ #537

Complements

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

N	H ≅ G/N	type
1. C₅×#537	C₂	semidirect
2. #66167	C₂	semidirect
3. #66165	C₂	semidirect
4. #66163	C₂	semidirect
5. #66162	C₂	semidirect
6. #65977	C₂	semidirect
7. #65972	C₂	semidirect
8. #65969	C₂	semidirect
9. #65968	C₂	semidirect
10. #65967	C₂	semidirect
11. D₅×C₂²⋊Q₈	C₂	semidirect
12. #65955	C₂	semidirect
13. #65955	C₂	semidirect
14. #65947	C₂	semidirect
15. #65946	C₂	semidirect
16. #65946	C₂	semidirect
17. #65945	C₂	semidirect
18. #65944	C₂	semidirect
19. #65942	C₂	semidirect
20. D₅×#121	C₂	semidirect
21. #65937	C₂	semidirect
22. #65845	C₂	semidirect
23. #65841	C₂	semidirect
24. C₂×C₅×#41	C₂²	semidirect
25. C₂×C₅×#41	C₂²	semidirect
26. C₂×Q₈×D₅	C₂²	semidirect
27. C₂×#711	C₂²	semidirect
30. C₂×#709	C₂²	semidirect
31. C₂×#709	C₂²	semidirect
33. C₅×C₂²⋊Q₈	C₂²	semidirect
34. C₅×C₂²⋊Q₈	C₂²	semidirect
35. C₅×C₂²⋊Q₈	C₂²	semidirect
37. C₅×#121	C₂²	semidirect
38. C₅×#121	C₂²	semidirect
39. C₅×#121	C₂²	semidirect
40. C₅×#121	C₂²	semidirect
41. C₂×C₅×C₄⋊C₄	C₂²	semidirect
42. #4093	C₂²	semidirect
45. #4092	C₂²	semidirect
46. #4092	C₂²	semidirect
47. Q₈×Dic₅	C₂²	semidirect
49. #4085	C₂²	semidirect
50. #4085	C₂²	semidirect
51. #4085	C₂²	semidirect
54. #4084	C₂²	semidirect
55. #4084	C₂²	semidirect
56. #4084	C₂²	semidirect
57. #4084	C₂²	semidirect
62. #4082	C₂²	semidirect
63. #4082	C₂²	semidirect
64. #4082	C₂²	semidirect
65. #4081	C₂²	semidirect
66. #4081	C₂²	semidirect
67. #4081	C₂²	semidirect
68. #4081	C₂²	semidirect
69. D₄×Dic₅	C₂²	semidirect
71. #4076	C₂²	semidirect
72. #4075	C₂²	semidirect
73. #4075	C₂²	semidirect
77. C₄×C₂²⋊D₅	C₂²	semidirect
78. C₄×C₂²⋊D₅	C₂²	semidirect
79. C₄×C₂²⋊D₅	C₂²	semidirect
81. #4072	C₂²	semidirect
82. C₂×C₄⋊Dic₅	C₂²	semidirect
83. #4070	C₂²	semidirect
84. #4070	C₂²	semidirect
85. #4070	C₂²	semidirect
86. #4070	C₂²	semidirect
87. #4044	C₂²	semidirect
90. #4043	C₂²	semidirect
93. #4042	C₂²	semidirect
94. #4042	C₂²	semidirect
96. #4040	C₂²	semidirect
97. #4039	C₂²	semidirect
98. #4039	C₂²	semidirect
100. D₅×C₄⋊C₄	C₂²	semidirect
101. D₅×C₄⋊C₄	C₂²	semidirect
102. #4035	C₂²	semidirect
103. #4035	C₂²	semidirect
104. #4034	C₂²	semidirect
105. #4034	C₂²	semidirect
106. #4033	C₂²	semidirect
107. #4031	C₂²	semidirect
108. #4031	C₂²	semidirect
110. #4030	C₂²	semidirect
111. #4029	C₂²	semidirect
112. #4029	C₂²	semidirect
113. #4029	C₂²	semidirect
118. #4025	C₂²	semidirect
119. #4024	C₂²	semidirect
120. #4024	C₂²	semidirect
121. #4024	C₂²	semidirect
122. #4024	C₂²	semidirect
251. #537	D₅	semidirect
328. C₂×#41	C₂×D₅	semidirect
329. C₂×#41	C₂×D₅	semidirect
375. C₂²⋊Q₈	C₂×D₅	semidirect
376. C₂²⋊Q₈	C₂×D₅	semidirect
377. C₂²⋊Q₈	C₂×D₅	semidirect
394. #121	C₂×D₅	semidirect
395. #121	C₂×D₅	semidirect
396. #121	C₂×D₅	semidirect
397. #121	C₂×D₅	semidirect
419. C₂×C₄⋊C₄	C₂×D₅	semidirect
652. C₅	#3536	semidirect

Maximal subgroups

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

subgroup	index
C₅×#537	2
#66167	2
#66165	2
#66163	2
#66162	2
#65977	2
#65972	2
#65969	2
#65968	2
#65967	2
D₅×C₂²⋊Q₈	2
#65955	2
#65947	2
#65946	2
#65945	2
#65944	2
#65942	2
D₅×#121	2
#65937	2
#65845	2
#65841	2
#3536	5