Subgroups — #10618229

Order 640.

1050 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#535	C₂	1	1	yes	maximal, characteristic, complemented
2	#66165	C₂	1	1	yes	maximal, characteristic, complemented
3	#66158	C₂	1	1	yes	maximal, characteristic, complemented
4	#66140	C₂	1	1	yes	maximal, characteristic, complemented
5	#66140	C₂	1	1	yes	maximal, characteristic, complemented
6	#66053	C₂	1	1	yes	maximal, characteristic, complemented
7	#66052	C₂	1	1	yes	maximal, characteristic, complemented
8	#66050	C₂	1	1	yes	maximal, characteristic, complemented
9	#66047	C₂	1	1	yes	maximal, characteristic, complemented
10	#66014	C₂	1	1	yes	maximal, characteristic, complemented
11	#66011	C₂	1	1	yes	maximal, characteristic, complemented
12	#66009	C₂	1	1	yes	maximal, characteristic, complemented
13	#66005	C₂	1	1	yes	maximal, characteristic, complemented
14	#65955	C₂	1	2	yes	maximal, complemented
15	#65949	C₂	1	2	yes	maximal, complemented
16	#65936	C₂	1	2	yes	maximal, complemented
17	#65935	C₂	1	2	yes	maximal, complemented
18	#65929	C₂	1	2	yes	maximal, complemented
19	#65927	C₂	1	2	yes	maximal, complemented
20	#65927	C₂	1	2	yes	maximal, complemented
21	#65921	C₂	1	2	yes	maximal, complemented
22	#65862	C₂	1	1	yes	maximal, characteristic, complemented
23	#65852	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₅×#41	C₂²	1	1	yes	characteristic
25	C₂²×C₅×D₄	C₂²	1	1	yes	characteristic
26	C₂×Q₈×D₅	C₂²	1	1	yes	characteristic, complemented
27	C₂×#711	C₂²	1	1	yes	characteristic
28	C₂×#711	C₂²	1	1	yes	characteristic
29	C₂×#711	C₂²	1	1	yes	characteristic, complemented
30	C₅×#127	C₂²	1	1	yes	characteristic
31	C₅×#127	C₂²	1	1	yes	characteristic
32	C₅×#124	C₂²	1	1	yes	characteristic
33	C₅×#124	C₂²	1	1	yes	characteristic
34	C₅×#121	C₂²	1	2	yes	—
35	C₅×#121	C₂²	1	2	yes	—
36	C₅×#120	C₂²	1	2	yes	—
37	C₅×#120	C₂²	1	2	yes	—
38	C₅×#117	C₂²	1	1	yes	characteristic
39	#4099	C₂²	1	2	yes	—
40	#4099	C₂²	1	2	yes	—
41	C₂×C₂²⋊Dic₅	C₂²	1	2	yes	—
42	C₂×C₂²⋊Dic₅	C₂²	1	2	yes	—
43	#4092	C₂²	1	1	yes	characteristic, complemented
44	Q₈×Dic₅	C₂²	1	1	yes	characteristic, complemented
45	#4090	C₂²	1	1	yes	characteristic, complemented
46	#4086	C₂²	1	2	yes	complemented
47	#4085	C₂²	1	2	yes	—
48	#4085	C₂²	1	2	yes	—
49	#4085	C₂²	1	2	yes	—
50	#4085	C₂²	1	2	yes	complemented
51	#4085	C₂²	1	2	yes	complemented
52	#4085	C₂²	1	2	yes	complemented
53	#4085	C₂²	1	2	yes	complemented
54	#4084	C₂²	1	1	yes	characteristic
55	#4084	C₂²	1	1	yes	characteristic
56	#4084	C₂²	1	2	yes	—
57	#4084	C₂²	1	2	yes	complemented
58	#4084	C₂²	1	2	yes	complemented
59	#4084	C₂²	1	1	yes	characteristic, complemented
60	#4082	C₂²	1	1	yes	characteristic
61	#4082	C₂²	1	1	yes	characteristic
62	#4082	C₂²	1	2	yes	—
63	#4082	C₂²	1	1	yes	characteristic, complemented
64	#4082	C₂²	1	2	yes	complemented
65	#4081	C₂²	1	2	yes	—
66	#4081	C₂²	1	2	yes	—
67	#4081	C₂²	1	2	yes	—
68	#4081	C₂²	1	2	yes	complemented
69	#4081	C₂²	1	2	yes	complemented
70	#4081	C₂²	1	2	yes	complemented
71	#4081	C₂²	1	2	yes	complemented
72	D₄×Dic₅	C₂²	1	1	yes	characteristic
73	D₄×Dic₅	C₂²	1	1	yes	characteristic
74	D₄×Dic₅	C₂²	1	2	yes	complemented
75	D₄×Dic₅	C₂²	1	2	yes	complemented
76	D₄×Dic₅	C₂²	1	2	yes	complemented
77	D₄×Dic₅	C₂²	1	1	yes	characteristic, complemented
78	D₄×Dic₅	C₂²	1	2	yes	complemented
79	#4075	C₂²	1	2	yes	complemented
80	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic
81	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic
82	C₄×C₂²⋊D₅	C₂²	1	2	yes	complemented
83	#4070	C₂²	1	1	yes	characteristic
84	#4070	C₂²	1	1	yes	characteristic
85	#4070	C₂²	1	2	yes	complemented
86	C₂×#683	C₂²	1	2	yes	complemented
87	#4044	C₂²	1	1	yes	characteristic, complemented
88	#4042	C₂²	1	1	yes	characteristic, complemented
89	#4040	C₂²	1	1	yes	characteristic, complemented
90	#4035	C₂²	1	2	yes	complemented
91	#4035	C₂²	1	2	yes	complemented
92	#4035	C₂²	1	1	yes	characteristic, complemented
93	#4031	C₂²	1	1	yes	characteristic
94	#4031	C₂²	1	2	yes	complemented
95	#4030	C₂²	1	1	yes	characteristic
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	2	yes	complemented
100	#4029	C₂²	1	2	yes	complemented
101	#4027	C₂²	1	2	yes	complemented
102	#4027	C₂²	1	2	yes	complemented
103	#4025	C₂²	1	2	yes	—
104	#4025	C₂²	1	2	yes	—
105	#4025	C₂²	1	1	yes	characteristic
106	#4025	C₂²	1	2	yes	complemented
107	#4025	C₂²	1	2	yes	complemented
108	#4025	C₂²	1	2	yes	complemented
109	#4024	C₂²	1	2	yes	complemented
110	#4024	C₂²	1	2	yes	complemented
111	#4024	C₂²	1	2	yes	complemented
112	#4024	C₂²	1	2	yes	complemented
113	#4023	C₂²	1	2	yes	complemented
114	#4023	C₂²	1	2	yes	complemented
115	C₄×D₂₀	C₂²	1	1	yes	characteristic, complemented
116	#4018	C₂²	1	1	yes	characteristic, complemented
117	C₄²×D₅	C₂²	1	1	yes	characteristic, complemented
118	#4016	C₂²	1	1	yes	characteristic, complemented
119	#4015	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	1	yes	characteristic, complemented
123	#3562	—	5	1	no	maximal, Sylow
124	C₂⁴×C₅	C₂³	1	2	yes	—
125	C₅×#41	—	4	2	no	—
126	C₂×C₅×Q₈	C₂³	1	1	yes	characteristic
127	C₂×C₅×D₄	—	4	2	no	—
128	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
129	C₂×C₅×D₄	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	2	yes	—
134	C₂×C₅×D₄	C₂³	1	2	yes	—
135	C₂×C₅×D₄	C₂³	1	2	yes	—
136	C₂×C₅×D₄	C₂³	1	2	yes	—
137	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
138	C₂²×C₄×C₅	C₂³	1	2	yes	—
139	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
140	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
141	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
142	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
143	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
144	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
145	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
146	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
147	C₂²×Dic₅	C₂³	1	2	yes	—
148	C₂²×Dic₅	C₂³	1	2	yes	—
149	C₂²×Dic₅	C₂³	1	2	yes	—
150	C₂²×Dic₅	C₂³	1	2	yes	—
151	C₂²×Dic₅	C₂³	1	2	yes	—
152	C₂²×Dic₅	C₂³	1	2	yes	—
153	Q₈×D₅	—	4	2	no	—
154	#711	—	4	2	no	—
155	#711	—	4	2	no	—
156	#711	—	4	2	no	—
157	C₂×D₂₀	C₂³	1	1	yes	characteristic
158	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
159	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
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×Dic₁₀	C₂³	1	1	yes	characteristic
164	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
165	C₂×Dic₁₀	C₂³	1	2	yes	—
166	C₂×Dic₁₀	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×C₂²⋊C₄	C₂³	1	1	yes	characteristic
170	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
171	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
172	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
173	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
174	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
175	C₄²×C₅	C₂³	1	1	yes	characteristic
176	C₄²×C₅	C₂³	1	1	yes	characteristic
177	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
178	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
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	2	yes	—
183	C₂²⋊Dic₅	C₂³	1	2	yes	—
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	C₂²⋊Dic₅	C₂³	1	2	yes	—
192	C₂²⋊Dic₅	C₂³	1	2	yes	—
193	#685	C₂³	1	1	yes	characteristic
194	#685	C₂³	1	1	yes	characteristic
195	#685	C₂³	1	1	yes	characteristic
196	#685	C₂³	1	1	yes	characteristic
197	#685	C₂³	1	2	yes	—
198	#685	C₂³	1	1	yes	characteristic
199	#685	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	1	yes	characteristic
203	C₄⋊Dic₅	C₂³	1	2	yes	—
204	C₄⋊Dic₅	C₂³	1	2	yes	—
205	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
206	C₄⋊Dic₅	C₂³	1	2	yes	—
207	#683	C₂³	1	1	yes	characteristic
208	#683	C₂³	1	2	yes	—
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	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	#683	C₂³	1	1	yes	characteristic
221	#683	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	2	yes	—
226	C₄×Dic₅	C₂³	1	1	yes	characteristic
227	C₄×Dic₅	C₂³	1	1	yes	characteristic
228	C₄×Dic₅	C₂³	1	2	yes	—
229	#562	—	5	2	no	—
230	#560	—	5	2	no	—
231	#559	—	5	1	no	—
232	#556	—	5	1	no	—
233	#553	—	5	2	no	—
234	#551	—	5	2	no	—
235	#550	—	5	1	no	—
236	#548	—	5	1	no	—
237	#548	—	5	1	no	—
238	#547	—	5	1	no	—
239	#546	—	5	1	no	—
240	#546	—	5	1	no	—
241	#541	—	5	1	no	—
242	#540	—	5	1	no	—
243	#540	—	5	2	no	—
244	#539	—	5	2	no	—
245	#538	—	5	2	no	—
246	#538	—	5	2	no	—
247	#536	—	5	1	no	—
248	#535	D₅	1	1	yes	characteristic, complemented
249	#532	—	5	1	no	—
250	#529	—	5	1	no	—
251	#529	—	5	1	no	—
252	C₂³×C₅	—	4	2	no	—
253	C₂³×C₅	—	4	2	no	—
254	C₂³×C₅	—	4	2	no	—
255	C₂³×C₅	C₂⁴	1	1	yes	characteristic
256	C₂³×C₅	C₂⁴	1	2	yes	—
257	C₂³×C₅	C₂⁴	1	2	yes	—
258	C₂³×C₅	C₂⁴	1	2	yes	—
259	C₂²×D₅	C₂⁴	1	1	yes	characteristic
260	C₂²×D₅	C₂⁴	1	1	yes	characteristic
261	C₅×Q₈	—	2	2	no	—
262	C₅×D₄	—	2	2	no	—
263	C₅×D₄	—	2	2	no	—
264	C₅×D₄	—	2	2	no	—
265	C₅×D₄	—	4	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	C₅×D₄	—	4	2	no	—
271	C₂×C₄×C₅	—	2	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	1	yes	characteristic
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	C₂²⋊D₅	—	4	2	no	—
281	C₂²⋊D₅	—	4	2	no	—
282	C₂²⋊D₅	—	4	2	no	—
283	C₂²⋊D₅	—	4	1	no	—
284	C₂²⋊D₅	—	4	1	no	—
285	C₂²⋊D₅	—	4	2	no	—
286	C₂²⋊D₅	—	4	2	no	—
287	C₂²⋊D₅	—	4	2	no	—
288	C₂×Dic₅	—	4	2	no	—
289	C₂×Dic₅	—	4	2	no	—
290	C₂×Dic₅	—	4	2	no	—
291	C₂×Dic₅	—	4	2	no	—
292	C₂×Dic₅	—	4	2	no	—
293	C₂×Dic₅	—	4	2	no	—
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	1	yes	characteristic
299	C₂×Dic₅	C₂⁴	1	2	yes	—
300	C₂×Dic₅	C₂⁴	1	2	yes	—
301	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
302	C₂×Dic₅	C₂⁴	1	2	yes	—
303	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
304	D₂₀	—	4	1	no	—
305	C₄×D₅	—	2	2	no	—
306	C₄×D₅	—	2	2	no	—
307	C₄×D₅	—	4	1	no	—
308	C₄×D₅	—	4	1	no	—
309	C₄×D₅	—	4	2	no	—
310	Dic₁₀	—	2	2	no	—
311	Dic₁₀	—	2	2	no	—
312	Dic₁₀	—	4	1	no	—
313	Dic₁₀	—	4	2	no	—
314	C₂×#41	—	5	1	no	—
315	C₂×#41	—	5	1	no	—
316	C₂×#41	—	5	1	no	—
317	C₂×#41	C₂×D₅	1	1	yes	characteristic
318	C₂²×Q₈	—	5	1	no	—
319	C₂²×D₄	C₂×D₅	1	1	yes	characteristic
320	C₄⋊Q₈	—	5	1	no	—
321	C₄⋊Q₈	—	5	1	no	—
322	#127	—	5	2	no	—
323	#127	C₂×D₅	1	1	yes	characteristic
324	#127	C₂×D₅	1	1	yes	characteristic
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	—	5	2	no	—
331	#126	—	5	2	no	—
332	#125	—	5	1	no	—
333	#125	—	5	2	no	—
334	#125	—	5	2	no	—
335	#125	—	5	1	no	—
336	#124	—	5	1	no	—
337	#124	—	5	1	no	—
338	#124	—	5	1	no	—
339	#124	—	5	2	no	—
340	#124	—	5	2	no	—
341	#124	—	5	1	no	—
342	#124	—	5	2	no	—
343	#124	C₂×D₅	1	1	yes	characteristic
344	#124	C₂×D₅	1	1	yes	characteristic
345	#123	—	5	2	no	—
346	#123	—	5	2	no	—
347	#123	—	5	2	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	1	no	—
354	#123	—	5	1	no	—
355	#123	—	5	2	no	—
356	#123	—	5	2	no	—
357	#123	—	5	2	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	1	no	—
363	C₂²⋊Q₈	—	5	2	no	—
364	C₂²⋊Q₈	—	5	2	no	—
365	C₂²⋊Q₈	—	5	2	no	—
366	C₂²⋊Q₈	—	5	2	no	—
367	#121	—	5	1	no	—
368	#121	—	5	2	no	—
369	#121	—	5	2	no	—
370	#121	—	5	2	no	—
371	#121	—	5	2	no	—
372	#121	—	5	2	no	—
373	#121	—	5	2	no	—
374	#121	—	5	2	no	—
375	#121	—	5	1	no	—
376	#121	—	5	2	no	—
377	#121	—	5	2	no	—
378	#121	—	5	1	no	—
379	#121	—	5	2	no	—
380	#121	—	5	1	no	—
381	#121	—	5	2	no	—
382	#121	C₂×D₅	1	2	yes	—
383	#121	C₂×D₅	1	2	yes	—
384	#120	—	5	2	no	—
385	#120	—	5	2	no	—
386	#120	C₂×D₅	1	2	yes	—
387	#120	C₂×D₅	1	2	yes	—
388	C₄×Q₈	—	5	1	no	—
389	C₄×Q₈	—	5	1	no	—
390	C₄×Q₈	—	5	1	no	—
391	C₄×Q₈	—	5	1	no	—
392	C₄×D₄	—	5	1	no	—
393	C₄×D₄	—	5	2	no	—
394	C₄×D₄	—	5	2	no	—
395	C₄×D₄	—	5	2	no	—
396	C₄×D₄	—	5	2	no	—
397	C₄×D₄	—	5	1	no	—
398	C₄×D₄	—	5	1	no	—
399	C₄×D₄	—	5	1	no	—
400	C₄×D₄	—	5	1	no	—
401	C₄×D₄	—	5	2	no	—
402	C₄×D₄	—	5	2	no	—
403	C₄×D₄	—	5	2	no	—
404	C₄×D₄	—	5	1	no	—
405	#117	—	5	2	no	—
406	#117	—	5	2	no	—
407	#117	—	5	1	no	—
408	#117	C₂×D₅	1	1	yes	characteristic
409	C₂×C₄⋊C₄	—	5	2	no	—
410	C₂×C₂²⋊C₄	—	5	2	no	—
411	C₂×C₂²⋊C₄	—	5	2	no	—
412	C₂×C₄²	—	5	1	no	—
413	C₂²×C₅	—	2	2	no	—
414	C₂²×C₅	—	2	2	no	—
415	C₂²×C₅	—	2	2	no	—
416	C₂²×C₅	—	2	1	no	—
417	C₂²×C₅	—	2	2	no	—
418	C₂²×C₅	—	2	2	no	—
419	C₂²×C₅	—	2	2	no	—
420	C₂²×C₅	—	2	2	no	—
421	C₂²×C₅	—	2	2	no	—
422	C₂²×C₅	—	2	2	no	—
423	C₂²×C₅	—	2	1	no	—
424	C₂²×C₅	—	2	1	no	—
425	C₂²×C₅	—	8	4	no	—
426	C₂²×C₅	C₂⁵	1	1	yes	characteristic
427	C₂×D₅	—	2	1	no	—
428	C₂×D₅	—	2	1	no	—
429	C₂×D₅	—	2	1	no	—
430	C₂×D₅	—	2	1	no	—
431	C₂×D₅	—	2	1	no	—
432	C₂×D₅	—	2	1	no	—
433	C₄×C₅	—	2	2	no	—
434	C₄×C₅	—	2	1	no	—
435	C₄×C₅	—	2	1	no	—
436	C₄×C₅	—	2	1	no	—
437	C₄×C₅	—	2	1	no	—
438	C₄×C₅	—	2	1	no	—
439	C₄×C₅	H(5,𝔽₂)	1	2	yes	—
440	Dic₅	—	2	2	no	—
441	Dic₅	—	2	2	no	—
442	Dic₅	—	2	1	no	—
443	Dic₅	—	2	1	no	—
444	Dic₅	—	2	1	no	—
445	Dic₅	—	2	1	no	—
446	Dic₅	—	2	1	no	—
447	Dic₅	—	2	2	no	—
448	Dic₅	—	2	1	no	—
449	Dic₅	—	2	2	no	—
450	C₂⁴	C₂²×D₅	1	2	yes	—
451	#41	—	4	2	no	—
452	#41	—	20	2	no	—
453	#41	—	20	2	no	—
454	#41	—	20	2	no	—
455	C₂×Q₈	—	5	1	no	—
456	C₂×Q₈	—	5	1	no	—
457	C₂×Q₈	—	5	1	no	—
458	C₂×Q₈	—	5	2	no	—
459	C₂×Q₈	—	20	2	no	—
460	C₂×Q₈	C₂²×D₅	1	1	yes	characteristic
461	C₂×D₄	—	4	2	no	—
462	C₂×D₄	—	5	1	no	—
463	C₂×D₄	—	5	1	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	2	no	—
470	C₂×D₄	—	5	1	no	—
471	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
472	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
473	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
474	C₂×D₄	C₂²×D₅	1	2	yes	—
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	C₂×D₄	C₂²×D₅	1	2	yes	—
480	C₂²×C₄	—	5	2	no	—
481	C₂²×C₄	—	5	2	no	—
482	C₂²×C₄	—	5	2	no	—
483	C₂²×C₄	—	5	2	no	—
484	C₂²×C₄	—	5	2	no	—
485	C₂²×C₄	—	5	2	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	2	no	—
491	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
492	C₂²×C₄	C₂²×D₅	1	2	yes	—
493	C₄⋊C₄	—	5	1	no	—
494	C₄⋊C₄	—	5	2	no	—
495	C₄⋊C₄	—	5	2	no	—
496	C₄⋊C₄	—	5	2	no	—
497	C₄⋊C₄	—	5	1	no	—
498	C₄⋊C₄	—	5	2	no	—
499	C₄⋊C₄	—	5	1	no	—
500	C₄⋊C₄	—	5	1	no	—
501	C₄⋊C₄	—	5	2	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	2	no	—
510	C₄⋊C₄	—	5	1	no	—
511	C₄⋊C₄	—	5	2	no	—
512	C₄⋊C₄	—	5	2	no	—
513	C₄⋊C₄	—	5	2	no	—
514	C₄⋊C₄	—	5	1	no	—
515	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
516	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
517	C₂²⋊C₄	—	5	1	no	—
518	C₂²⋊C₄	—	5	1	no	—
519	C₂²⋊C₄	—	5	2	no	—
520	C₂²⋊C₄	—	5	2	no	—
521	C₂²⋊C₄	—	5	2	no	—
522	C₂²⋊C₄	—	5	2	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	2	no	—
531	C₂²⋊C₄	—	5	2	no	—
532	C₂²⋊C₄	—	5	2	no	—
533	C₂²⋊C₄	—	5	1	no	—
534	C₂²⋊C₄	—	5	1	no	—
535	C₂²⋊C₄	—	5	1	no	—
536	C₂²⋊C₄	—	5	1	no	—
537	C₂²⋊C₄	—	5	1	no	—
538	C₂²⋊C₄	—	5	2	no	—
539	C₂²⋊C₄	—	5	1	no	—
540	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
541	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
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	C₄²	—	5	1	no	—
547	C₄²	—	5	1	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	C₂²×D₅	1	1	yes	characteristic
554	C₄²	C₂²×D₅	1	1	yes	characteristic
555	C₂×C₅	—	4	2	no	—
556	C₂×C₅	—	4	2	no	—
557	C₂×C₅	—	4	2	no	—
558	C₂×C₅	—	4	1	no	—
559	C₂×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
560	C₂×C₅	#585	1	1	yes	characteristic
561	C₂×C₅	#585	1	1	yes	characteristic
562	D₅	—	4	1	no	—
563	D₅	—	4	1	no	—
564	C₂³	—	4	2	no	—
565	C₂³	—	4	2	no	—
566	C₂³	—	4	2	no	—
567	C₂³	—	5	1	no	—
568	C₂³	—	5	1	no	—
569	C₂³	C₂³×D₅	1	1	yes	characteristic
570	C₂³	C₂³×D₅	1	2	yes	—
571	C₂³	C₂³×D₅	1	2	yes	—
572	C₂³	C₂³×D₅	1	2	yes	—
573	Q₈	—	2	2	no	—
574	Q₈	—	10	2	no	—
575	Q₈	—	10	2	no	—
576	Q₈	—	20	2	no	—
577	Q₈	—	20	1	no	—
578	D₄	—	2	2	no	—
579	D₄	—	2	2	no	—
580	D₄	—	2	2	no	—
581	D₄	—	4	2	no	—
582	D₄	—	4	2	no	—
583	D₄	—	4	2	no	—
584	D₄	—	4	2	no	—
585	D₄	—	4	2	no	—
586	D₄	—	4	2	no	—
587	D₄	—	20	1	no	—
588	D₄	—	20	2	no	—
589	D₄	—	20	2	no	—
590	D₄	—	20	2	no	—
591	D₄	—	20	2	no	—
592	D₄	—	20	1	no	—
593	D₄	—	20	2	no	—
594	D₄	—	20	2	no	—
595	D₄	—	20	1	no	—
596	C₂×C₄	—	2	2	no	—
597	C₂×C₄	—	4	2	no	—
598	C₂×C₄	—	5	1	no	—
599	C₂×C₄	—	5	1	no	—
600	C₂×C₄	—	5	2	no	—
601	C₂×C₄	—	5	1	no	—
602	C₂×C₄	—	5	1	no	—
603	C₂×C₄	—	5	1	no	—
604	C₂×C₄	—	5	2	no	—
605	C₂×C₄	—	5	2	no	—
606	C₂×C₄	—	5	2	no	—
607	C₂×C₄	—	5	1	no	—
608	C₂×C₄	—	10	2	no	—
609	C₂×C₄	—	10	2	no	—
610	C₂×C₄	—	20	2	no	—
611	C₂×C₄	—	20	1	no	—
612	C₂×C₄	—	20	1	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	2	no	—
618	C₂×C₄	—	20	2	no	—
619	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
620	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
621	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
622	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
623	C₂×C₄	C₂³×D₅	1	2	yes	—
624	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
625	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
626	C₅	#3562	1	1	yes	characteristic, complemented, Sylow
627	C₂²	—	2	1	no	—
628	C₂²	—	2	2	no	—
629	C₂²	—	2	2	no	—
630	C₂²	—	2	2	no	—
631	C₂²	—	2	2	no	—
632	C₂²	—	2	2	no	—
633	C₂²	—	2	2	no	—
634	C₂²	—	2	2	no	—
635	C₂²	—	2	2	no	—
636	C₂²	—	2	2	no	—
637	C₂²	—	2	1	no	—
638	C₂²	—	2	1	no	—
639	C₂²	—	8	4	no	—
640	C₂²	—	10	1	no	—
641	C₂²	—	10	1	no	—
642	C₂²	—	10	1	no	—
643	C₂²	—	10	1	no	—
644	C₂²	—	10	1	no	—
645	C₂²	—	10	1	no	—
646	C₂²	C₂⁴×D₅	1	1	yes	characteristic
647	C₄	—	2	1	no	—
648	C₄	—	2	2	no	—
649	C₄	—	2	1	no	—
650	C₄	—	2	1	no	—
651	C₄	—	2	1	no	—
652	C₄	—	2	1	no	—
653	C₄	—	10	1	no	—
654	C₄	—	10	1	no	—
655	C₄	—	10	2	no	—
656	C₄	—	10	2	no	—
657	C₄	—	10	1	no	—
658	C₄	—	10	1	no	—
659	C₄	—	10	2	no	—
660	C₄	—	10	1	no	—
661	C₄	—	10	2	no	—
662	C₄	—	10	1	no	—
663	C₄	#4144	1	2	yes	—
664	C₂	—	4	1	no	—
665	C₂	—	4	2	no	—
666	C₂	—	4	2	no	—
667	C₂	—	4	2	no	—
668	C₂	—	20	1	no	—
669	C₂	—	20	1	no	—
670	C₂	C₂×#4144	1	1	yes	characteristic
671	C₂	#66285	1	1	yes	characteristic
672	C₂	#66285	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅
commutator, socle, cosocle	C₂²×C₅	C₂⁵
Fitting	C₅×#535	C₂
hypercenter	#535	D₅
hypocenter	C₅	#3562
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ #535

Complements

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

N	H ≅ G/N	type
1. C₅×#535	C₂	semidirect
2. #66165	C₂	semidirect
3. #66158	C₂	semidirect
4. #66140	C₂	semidirect
5. #66140	C₂	semidirect
6. #66053	C₂	semidirect
7. #66052	C₂	semidirect
8. #66050	C₂	semidirect
9. #66047	C₂	semidirect
10. #66014	C₂	semidirect
11. #66011	C₂	semidirect
12. #66009	C₂	semidirect
13. #66005	C₂	semidirect
14. #65955	C₂	semidirect
15. #65949	C₂	semidirect
16. #65936	C₂	semidirect
17. #65935	C₂	semidirect
18. #65929	C₂	semidirect
19. #65927	C₂	semidirect
20. #65927	C₂	semidirect
21. #65921	C₂	semidirect
22. #65862	C₂	semidirect
23. #65852	C₂	semidirect
26. C₂×Q₈×D₅	C₂²	semidirect
29. C₂×#711	C₂²	semidirect
43. #4092	C₂²	semidirect
44. Q₈×Dic₅	C₂²	semidirect
45. #4090	C₂²	semidirect
46. #4086	C₂²	semidirect
50. #4085	C₂²	semidirect
51. #4085	C₂²	semidirect
52. #4085	C₂²	semidirect
53. #4085	C₂²	semidirect
57. #4084	C₂²	semidirect
58. #4084	C₂²	semidirect
59. #4084	C₂²	semidirect
63. #4082	C₂²	semidirect
64. #4082	C₂²	semidirect
68. #4081	C₂²	semidirect
69. #4081	C₂²	semidirect
70. #4081	C₂²	semidirect
71. #4081	C₂²	semidirect
74. D₄×Dic₅	C₂²	semidirect
75. D₄×Dic₅	C₂²	semidirect
76. D₄×Dic₅	C₂²	semidirect
77. D₄×Dic₅	C₂²	semidirect
78. D₄×Dic₅	C₂²	semidirect
79. #4075	C₂²	semidirect
82. C₄×C₂²⋊D₅	C₂²	semidirect
85. #4070	C₂²	semidirect
86. C₂×#683	C₂²	semidirect
87. #4044	C₂²	semidirect
88. #4042	C₂²	semidirect
89. #4040	C₂²	semidirect
90. #4035	C₂²	semidirect
91. #4035	C₂²	semidirect
92. #4035	C₂²	semidirect
94. #4031	C₂²	semidirect
96. #4030	C₂²	semidirect
98. #4029	C₂²	semidirect
99. #4029	C₂²	semidirect
100. #4029	C₂²	semidirect
101. #4027	C₂²	semidirect
102. #4027	C₂²	semidirect
106. #4025	C₂²	semidirect
107. #4025	C₂²	semidirect
108. #4025	C₂²	semidirect
109. #4024	C₂²	semidirect
110. #4024	C₂²	semidirect
111. #4024	C₂²	semidirect
112. #4024	C₂²	semidirect
113. #4023	C₂²	semidirect
114. #4023	C₂²	semidirect
115. C₄×D₂₀	C₂²	semidirect
116. #4018	C₂²	semidirect
117. C₄²×D₅	C₂²	semidirect
118. #4016	C₂²	semidirect
119. #4015	C₂²	semidirect
120. C₄×Dic₁₀	C₂²	semidirect
121. C₄×Dic₁₀	C₂²	semidirect
122. C₄×Dic₁₀	C₂²	semidirect
248. #535	D₅	semidirect
626. C₅	#3562	semidirect

Maximal subgroups

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

subgroup	index
C₅×#535	2
#66165	2
#66158	2
#66140	2
#66053	2
#66052	2
#66050	2
#66047	2
#66014	2
#66011	2
#66009	2
#66005	2
#65955	2
#65949	2
#65936	2
#65935	2
#65929	2
#65927	2
#65921	2
#65862	2
#65852	2
#3562	5