Subgroups — #10617857

Order 640.

1160 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#121	C₂	1	1	yes	maximal, characteristic, complemented
2	#66140	C₂	1	1	yes	maximal, characteristic, complemented
3	#66139	C₂	1	2	yes	maximal, complemented
4	#66138	C₂	1	2	yes	maximal, complemented
5	D₄×C₂²⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
6	#66125	C₂	1	1	yes	maximal, characteristic, complemented
7	#66125	C₂	1	1	yes	maximal, characteristic, complemented
8	#65955	C₂	1	2	yes	maximal, complemented
9	#65954	C₂	1	2	yes	maximal, complemented
10	#65953	C₂	1	1	yes	maximal, characteristic, complemented
11	#65950	C₂	1	1	yes	maximal, characteristic, complemented
12	#65949	C₂	1	2	yes	maximal, complemented
13	#65948	C₂	1	1	yes	maximal, characteristic, complemented
14	#65947	C₂	1	2	yes	maximal, complemented
15	#65946	C₂	1	1	yes	maximal, characteristic, complemented
16	#65942	C₂	1	1	yes	maximal, characteristic, complemented
17	#65941	C₂	1	1	yes	maximal, characteristic, complemented
18	#65937	C₂	1	1	yes	maximal, characteristic, complemented
19	#65933	C₂	1	1	yes	maximal, characteristic, complemented
20	#65847	C₂	1	1	yes	maximal, characteristic, complemented
21	#65841	C₂	1	1	yes	maximal, characteristic, complemented
22	#65829	C₂	1	2	yes	maximal, complemented
23	#65824	C₂	1	2	yes	maximal, complemented
24	C₂²×C₅×D₄	C₂²	1	1	yes	characteristic
25	C₂²×C₅×D₄	C₂²	1	2	yes	complemented
26	C₂³×C₄×C₅	C₂²	1	1	yes	characteristic, complemented
27	C₂²×C₂²⋊D₅	C₂²	1	2	yes	—
28	C₂×#711	C₂²	1	1	yes	characteristic, complemented
29	C₂×D₄×D₅	C₂²	1	1	yes	characteristic, complemented
30	C₂×#709	C₂²	1	2	yes	complemented
31	C₂×#709	C₂²	1	1	yes	characteristic, complemented
32	C₂×#709	C₂²	1	1	yes	characteristic, complemented
33	C₅×#121	C₂²	1	1	yes	characteristic
34	C₅×#121	C₂²	1	1	yes	characteristic
35	C₅×#121	C₂²	1	1	yes	characteristic, complemented
36	C₅×#121	C₂²	1	1	yes	characteristic, complemented
37	C₅×#121	C₂²	1	2	yes	complemented
38	C₅×#121	C₂²	1	2	yes	complemented
39	C₂×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
41	#4099	C₂²	1	2	yes	—
42	#4099	C₂²	1	1	yes	characteristic
43	#4099	C₂²	1	2	yes	complemented
44	#4099	C₂²	1	2	yes	complemented
45	#4099	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₂²⋊Dic₅	C₂²	1	2	yes	complemented
47	#4086	C₂²	1	1	yes	characteristic, complemented
48	#4086	C₂²	1	2	yes	complemented
49	#4086	C₂²	1	2	yes	complemented
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	#4085	C₂²	1	2	yes	complemented
55	#4085	C₂²	1	2	yes	complemented
56	#4084	C₂²	1	1	yes	characteristic, complemented
57	#4084	C₂²	1	2	yes	complemented
58	#4084	C₂²	1	2	yes	complemented
59	#4084	C₂²	1	2	yes	complemented
60	#4084	C₂²	1	2	yes	complemented
61	#4084	C₂²	1	1	yes	characteristic, complemented
62	#4083	C₂²	1	2	yes	complemented
63	#4083	C₂²	1	2	yes	complemented
64	#4083	C₂²	1	2	yes	complemented
65	#4082	C₂²	1	2	yes	complemented
66	#4082	C₂²	1	2	yes	complemented
67	#4082	C₂²	1	1	yes	characteristic, complemented
68	#4081	C₂²	1	2	yes	complemented
69	#4081	C₂²	1	2	yes	complemented
70	#4081	C₂²	1	2	yes	complemented
71	D₄×Dic₅	C₂²	1	1	yes	characteristic, complemented
72	D₄×Dic₅	C₂²	1	1	yes	characteristic, complemented
73	#4076	C₂²	1	1	yes	characteristic
74	#4076	C₂²	1	1	yes	characteristic
75	#4076	C₂²	1	1	yes	characteristic, complemented
76	#4076	C₂²	1	1	yes	characteristic, complemented
77	#4075	C₂²	1	2	yes	—
78	#4075	C₂²	1	2	yes	complemented
79	#4075	C₂²	1	1	yes	characteristic, complemented
80	#4075	C₂²	1	1	yes	characteristic, complemented
81	#4075	C₂²	1	2	yes	complemented
82	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic
83	C₄×C₂²⋊D₅	C₂²	1	2	yes	complemented
84	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic, complemented
85	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic, complemented
86	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic, complemented
87	C₄×C₂²⋊D₅	C₂²	1	2	yes	complemented
88	#4072	C₂²	1	2	yes	complemented
89	#4072	C₂²	1	1	yes	characteristic, complemented
90	#4072	C₂²	1	1	yes	characteristic, complemented
91	#4070	C₂²	1	1	yes	characteristic, complemented
92	#4070	C₂²	1	1	yes	characteristic, complemented
93	#4070	C₂²	1	1	yes	characteristic, complemented
94	#4070	C₂²	1	1	yes	characteristic, complemented
95	#4044	C₂²	1	2	yes	complemented
96	#4043	C₂²	1	1	yes	characteristic, complemented
97	#4042	C₂²	1	2	yes	complemented
98	#4041	C₂²	1	1	yes	characteristic, complemented
99	#4040	C₂²	1	2	yes	complemented
100	#4039	C₂²	1	1	yes	characteristic, complemented
101	#4038	C₂²	1	1	yes	characteristic, complemented
102	D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
103	#4036	C₂²	1	1	yes	characteristic, complemented
104	#4035	C₂²	1	2	yes	complemented
105	#4034	C₂²	1	1	yes	characteristic, complemented
106	#4033	C₂²	1	1	yes	characteristic, complemented
107	#4032	C₂²	1	2	yes	complemented
108	#4031	C₂²	1	2	yes	complemented
109	#4031	C₂²	1	2	yes	complemented
110	#4030	C₂²	1	2	yes	complemented
111	#4030	C₂²	1	2	yes	complemented
112	#4029	C₂²	1	2	yes	complemented
113	#4029	C₂²	1	2	yes	complemented
114	#4028	C₂²	1	2	yes	complemented
115	#4027	C₂²	1	2	yes	complemented
116	#4027	C₂²	1	2	yes	complemented
117	D₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
118	#4025	C₂²	1	2	yes	complemented
119	#4025	C₂²	1	2	yes	complemented
120	#4024	C₂²	1	2	yes	complemented
121	#4024	C₂²	1	2	yes	complemented
122	#4023	C₂²	1	2	yes	complemented
123	#3542	—	5	1	no	maximal, Sylow
124	C₂⁴×C₅	C₂³	1	2	yes	—
125	C₂⁴×C₅	C₂³	1	1	yes	characteristic
126	C₂³×D₅	C₂³	1	2	yes	—
127	C₂×C₅×D₄	—	4	2	no	—
128	C₂×C₅×D₄	—	4	4	no	—
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	C₂²×C₄×C₅	—	4	2	no	—
137	C₂²×C₄×C₅	C₂³	1	2	yes	—
138	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
139	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
140	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
141	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
142	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
143	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
144	C₂×C₂²⋊D₅	—	4	4	no	—
145	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
146	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
147	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
148	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
149	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
150	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
151	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
152	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
153	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
154	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
155	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
156	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
157	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
158	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
159	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
160	C₂²×Dic₅	C₂³	1	2	yes	—
161	C₂²×Dic₅	C₂³	1	2	yes	—
162	C₂²×Dic₅	C₂³	1	2	yes	—
163	#711	—	4	2	no	—
164	D₄×D₅	—	4	2	no	—
165	#709	—	4	2	no	—
166	#709	—	4	2	no	—
167	#709	—	4	4	no	—
168	C₂×D₂₀	C₂³	1	1	yes	characteristic
169	C₂×D₂₀	C₂³	1	1	yes	characteristic
170	C₂×D₂₀	C₂³	1	2	yes	—
171	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
172	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
173	C₂×C₄×D₅	C₂³	1	2	yes	—
174	C₂×C₄×D₅	C₂³	1	2	yes	—
175	C₂×C₄×D₅	C₂³	1	2	yes	—
176	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
177	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
178	C₂×Dic₁₀	C₂³	1	2	yes	—
179	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
180	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
181	C₅×C₄⋊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	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
186	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
191	C₂²⋊Dic₅	C₂³	1	2	yes	—
192	C₂²⋊Dic₅	C₂³	1	2	yes	—
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	2	yes	—
197	C₂²⋊Dic₅	C₂³	1	2	yes	—
198	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
199	C₂²⋊Dic₅	C₂³	1	2	yes	—
200	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
201	#685	C₂³	1	1	yes	characteristic
202	#685	C₂³	1	2	yes	—
203	#685	C₂³	1	1	yes	characteristic
204	#685	C₂³	1	2	yes	—
205	#685	C₂³	1	2	yes	—
206	#685	C₂³	1	2	yes	—
207	#685	C₂³	1	2	yes	—
208	#685	C₂³	1	1	yes	characteristic
209	#685	C₂³	1	2	yes	—
210	#685	C₂³	1	1	yes	characteristic
211	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
212	C₄⋊Dic₅	C₂³	1	2	yes	—
213	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
214	C₄⋊Dic₅	C₂³	1	2	yes	—
215	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
216	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
217	#683	C₂³	1	1	yes	characteristic
218	#683	C₂³	1	2	yes	—
219	#683	C₂³	1	2	yes	—
220	#683	C₂³	1	2	yes	—
221	#683	C₂³	1	2	yes	—
222	#683	C₂³	1	1	yes	characteristic
223	#683	C₂³	1	2	yes	—
224	#683	C₂³	1	1	yes	characteristic
225	#683	C₂³	1	2	yes	—
226	#683	C₂³	1	1	yes	characteristic
227	C₄×Dic₅	C₂³	1	2	yes	—
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	#560	—	5	2	no	—
234	#555	—	5	1	no	—
235	#553	—	5	1	no	—
236	#552	—	5	1	no	—
237	#551	—	5	2	no	—
238	#550	—	5	1	no	—
239	#547	—	5	1	no	—
240	#546	—	5	1	no	—
241	#546	—	5	1	no	—
242	#546	—	5	2	no	—
243	D₄²	—	5	1	no	—
244	#542	—	5	1	no	—
245	#540	—	5	2	no	—
246	#540	—	5	1	no	—
247	#538	—	5	2	no	—
248	#537	—	5	1	no	—
249	#535	—	5	2	no	—
250	#535	—	5	1	no	—
251	#534	—	5	2	no	—
252	#525	—	5	1	no	—
253	#525	—	5	1	no	—
254	C₂×#121	D₅	1	1	yes	characteristic, complemented
255	C₂³×C₅	—	2	2	no	—
256	C₂³×C₅	—	2	4	no	—
257	C₂³×C₅	—	4	1	no	—
258	C₂³×C₅	—	4	1	no	—
259	C₂³×C₅	—	4	2	no	—
260	C₂³×C₅	—	4	2	no	—
261	C₂³×C₅	C₂⁴	1	2	yes	—
262	C₂³×C₅	C₂⁴	1	1	yes	characteristic
263	C₂³×C₅	C₂⁴	1	1	yes	characteristic
264	C₂³×C₅	C₂⁴	1	2	yes	—
265	C₂³×C₅	C₂⁴	1	1	yes	characteristic
266	C₂²×D₅	—	4	2	no	—
267	C₂²×D₅	—	4	2	no	—
268	C₂²×D₅	—	4	2	no	—
269	C₂²×D₅	C₂⁴	1	1	yes	characteristic
270	C₂²×D₅	C₂⁴	1	2	yes	—
271	C₂²×D₅	C₂⁴	1	1	yes	characteristic
272	C₅×D₄	—	2	2	no	—
273	C₅×D₄	—	2	2	no	—
274	C₅×D₄	—	4	2	no	—
275	C₅×D₄	—	4	2	no	—
276	C₅×D₄	—	4	2	no	—
277	C₅×D₄	—	4	2	no	—
278	C₅×D₄	—	4	2	no	—
279	C₂×C₄×C₅	—	2	4	no	—
280	C₂×C₄×C₅	—	2	2	no	—
281	C₂×C₄×C₅	—	2	2	no	—
282	C₂×C₄×C₅	—	2	2	no	—
283	C₂×C₄×C₅	—	4	1	no	—
284	C₂×C₄×C₅	—	4	1	no	—
285	C₂×C₄×C₅	—	4	1	no	—
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	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
290	C₂×C₄×C₅	C₂⁴	1	2	yes	—
291	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
292	C₂²⋊D₅	—	2	2	no	—
293	C₂²⋊D₅	—	2	4	no	—
294	C₂²⋊D₅	—	2	2	no	—
295	C₂²⋊D₅	—	4	2	no	—
296	C₂²⋊D₅	—	4	1	no	—
297	C₂²⋊D₅	—	4	1	no	—
298	C₂²⋊D₅	—	4	2	no	—
299	C₂²⋊D₅	—	4	2	no	—
300	C₂²⋊D₅	—	4	2	no	—
301	C₂²⋊D₅	—	4	2	no	—
302	C₂²⋊D₅	—	4	1	no	—
303	C₂²⋊D₅	—	4	2	no	—
304	C₂²⋊D₅	—	4	2	no	—
305	C₂²⋊D₅	—	4	1	no	—
306	C₂²⋊D₅	—	4	2	no	—
307	C₂×Dic₅	—	4	2	no	—
308	C₂×Dic₅	—	4	2	no	—
309	C₂×Dic₅	—	4	2	no	—
310	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
311	C₂×Dic₅	C₂⁴	1	2	yes	—
312	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
313	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
314	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
315	C₂×Dic₅	C₂⁴	1	2	yes	—
316	C₂×Dic₅	C₂⁴	1	2	yes	—
317	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
318	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
319	D₂₀	—	2	2	no	—
320	D₂₀	—	4	1	no	—
321	D₂₀	—	4	2	no	—
322	C₄×D₅	—	2	2	no	—
323	C₄×D₅	—	2	2	no	—
324	C₄×D₅	—	4	2	no	—
325	C₄×D₅	—	4	2	no	—
326	C₄×D₅	—	4	2	no	—
327	Dic₁₀	—	2	2	no	—
328	Dic₁₀	—	4	2	no	—
329	Dic₁₀	—	4	1	no	—
330	C₂×#41	—	5	1	no	—
331	C₂×#41	—	5	1	no	—
332	C₂×#41	—	5	1	no	—
333	C₂×#41	—	5	2	no	—
334	C₂²×D₄	—	5	2	no	—
335	C₂²×D₄	—	5	1	no	—
336	C₂²×D₄	C₂×D₅	1	1	yes	characteristic
337	C₂²×D₄	C₂×D₅	1	2	yes	complemented
338	C₂³×C₄	C₂×D₅	1	1	yes	characteristic, complemented
339	C₄⋊Q₈	—	5	1	no	—
340	#127	—	5	2	no	—
341	#127	—	5	2	no	—
342	#127	—	5	1	no	—
343	#126	—	5	2	no	—
344	#126	—	5	2	no	—
345	#126	—	5	2	no	—
346	#125	—	5	1	no	—
347	#125	—	5	2	no	—
348	#124	—	5	2	no	—
349	#124	—	5	2	no	—
350	#124	—	5	1	no	—
351	#124	—	5	2	no	—
352	#124	—	5	2	no	—
353	#123	—	5	2	no	—
354	#123	—	5	2	no	—
355	#123	—	5	2	no	—
356	#123	—	5	1	no	—
357	#123	—	5	1	no	—
358	#123	—	5	2	no	—
359	#123	—	5	2	no	—
360	#123	—	5	2	no	—
361	#123	—	5	2	no	—
362	#123	—	5	2	no	—
363	#123	—	5	2	no	—
364	#123	—	5	2	no	—
365	C₂²⋊Q₈	—	5	1	no	—
366	C₂²⋊Q₈	—	5	1	no	—
367	C₂²⋊Q₈	—	5	1	no	—
368	C₂²⋊Q₈	—	5	1	no	—
369	C₂²⋊Q₈	—	5	1	no	—
370	C₂²⋊Q₈	—	5	2	no	—
371	C₂²⋊Q₈	—	5	2	no	—
372	C₂²⋊Q₈	—	5	2	no	—
373	#121	—	5	2	no	—
374	#121	—	5	2	no	—
375	#121	—	5	2	no	—
376	#121	—	5	2	no	—
377	#121	—	5	2	no	—
378	#121	—	5	2	no	—
379	#121	—	5	1	no	—
380	#121	—	5	2	no	—
381	#121	—	5	2	no	—
382	#121	—	5	1	no	—
383	#121	—	5	2	no	—
384	#121	—	5	2	no	—
385	#121	—	5	1	no	—
386	#121	—	5	1	no	—
387	#121	—	5	1	no	—
388	#121	—	5	1	no	—
389	#121	—	5	1	no	—
390	#121	—	5	2	no	—
391	#121	—	5	2	no	—
392	#121	C₂×D₅	1	1	yes	characteristic
393	#121	C₂×D₅	1	1	yes	characteristic
394	#121	C₂×D₅	1	1	yes	characteristic, complemented
395	#121	C₂×D₅	1	2	yes	complemented
396	#121	C₂×D₅	1	1	yes	characteristic, complemented
397	#121	C₂×D₅	1	2	yes	complemented
398	#120	—	5	1	no	—
399	#120	—	5	2	no	—
400	#120	—	5	2	no	—
401	#120	—	5	1	no	—
402	#120	—	5	2	no	—
403	#120	—	5	2	no	—
404	#120	—	5	2	no	—
405	#120	—	5	2	no	—
406	#120	—	5	2	no	—
407	C₄×Q₈	—	5	1	no	—
408	C₄×D₄	—	5	1	no	—
409	C₄×D₄	—	5	1	no	—
410	C₄×D₄	—	5	2	no	—
411	C₄×D₄	—	5	1	no	—
412	C₄×D₄	—	5	1	no	—
413	C₄×D₄	—	5	2	no	—
414	C₄×D₄	—	5	1	no	—
415	C₄×D₄	—	5	1	no	—
416	C₄×D₄	—	5	1	no	—
417	C₄×D₄	—	5	2	no	—
418	C₄×D₄	—	5	2	no	—
419	#117	—	5	1	no	—
420	#117	—	5	1	no	—
421	#117	—	5	2	no	—
422	#117	—	5	1	no	—
423	#117	—	5	2	no	—
424	C₂×C₄⋊C₄	—	5	1	no	—
425	C₂×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic, complemented
426	C₂×C₂²⋊C₄	—	5	2	no	—
427	C₂×C₂²⋊C₄	—	5	2	no	—
428	C₂×C₂²⋊C₄	C₂×D₅	1	2	yes	complemented
429	C₂²×C₅	—	2	1	no	—
430	C₂²×C₅	—	2	1	no	—
431	C₂²×C₅	—	2	2	no	—
432	C₂²×C₅	—	2	2	no	—
433	C₂²×C₅	—	2	1	no	—
434	C₂²×C₅	—	2	1	no	—
435	C₂²×C₅	—	2	2	no	—
436	C₂²×C₅	—	2	2	no	—
437	C₂²×C₅	—	2	1	no	—
438	C₂²×C₅	—	2	1	no	—
439	C₂²×C₅	—	2	2	no	—
440	C₂²×C₅	—	2	1	no	—
441	C₂²×C₅	—	2	1	no	—
442	C₂²×C₅	—	2	2	no	—
443	C₂²×C₅	—	4	4	no	—
444	C₂²×C₅	—	8	4	no	—
445	C₂²×C₅	H(5,𝔽₂)	1	2	yes	—
446	C₂²×C₅	C₂⁵	1	1	yes	characteristic
447	C₂×D₅	—	2	1	no	—
448	C₂×D₅	—	2	1	no	—
449	C₂×D₅	—	2	1	no	—
450	C₂×D₅	—	2	2	no	—
451	C₂×D₅	—	2	2	no	—
452	C₂×D₅	—	2	1	no	—
453	C₂×D₅	—	2	1	no	—
454	C₂×D₅	—	2	2	no	—
455	C₂×D₅	—	2	1	no	—
456	C₂×D₅	—	8	4	no	—
457	C₄×C₅	—	2	1	no	—
458	C₄×C₅	—	2	2	no	—
459	C₄×C₅	—	2	1	no	—
460	C₄×C₅	—	2	2	no	—
461	C₄×C₅	—	2	1	no	—
462	C₄×C₅	H(5,𝔽₂)	1	2	yes	—
463	Dic₅	—	2	2	no	—
464	Dic₅	—	2	1	no	—
465	Dic₅	—	2	1	no	—
466	Dic₅	—	2	1	no	—
467	Dic₅	—	2	2	no	—
468	Dic₅	—	2	1	no	—
469	Dic₅	—	2	1	no	—
470	Dic₅	—	2	2	no	—
471	Dic₅	—	2	1	no	—
472	C₂⁴	—	5	2	no	—
473	C₂⁴	C₂²×D₅	1	2	yes	—
474	C₂⁴	C₂²×D₅	1	1	yes	characteristic
475	#41	—	20	2	no	—
476	#41	—	20	4	no	—
477	#41	—	20	2	no	—
478	#41	—	20	2	no	—
479	C₂×Q₈	—	5	1	no	—
480	C₂×Q₈	—	5	1	no	—
481	C₂×Q₈	—	5	2	no	—
482	C₂×D₄	—	4	2	no	—
483	C₂×D₄	—	4	4	no	—
484	C₂×D₄	—	5	1	no	—
485	C₂×D₄	—	5	2	no	—
486	C₂×D₄	—	5	1	no	—
487	C₂×D₄	—	5	1	no	—
488	C₂×D₄	—	5	2	no	—
489	C₂×D₄	—	5	2	no	—
490	C₂×D₄	—	5	2	no	—
491	C₂×D₄	—	5	1	no	—
492	C₂×D₄	—	5	1	no	—
493	C₂×D₄	—	5	2	no	—
494	C₂×D₄	—	5	2	no	—
495	C₂×D₄	—	5	2	no	—
496	C₂×D₄	—	5	2	no	—
497	C₂×D₄	—	5	1	no	—
498	C₂×D₄	—	5	2	no	—
499	C₂×D₄	—	5	1	no	—
500	C₂×D₄	—	5	1	no	—
501	C₂×D₄	—	5	2	no	—
502	C₂×D₄	—	20	2	no	—
503	C₂×D₄	—	20	4	no	—
504	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
505	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
506	C₂×D₄	C₂²×D₅	1	2	yes	—
507	C₂×D₄	C₂²×D₅	1	2	yes	—
508	C₂×D₄	C₂²×D₅	1	2	yes	—
509	C₂×D₄	C₂²×D₅	1	2	yes	—
510	C₂×D₄	C₂²×D₅	1	2	yes	—
511	C₂²×C₄	—	4	2	no	—
512	C₂²×C₄	—	5	2	no	—
513	C₂²×C₄	—	5	2	no	—
514	C₂²×C₄	—	5	2	no	—
515	C₂²×C₄	—	5	1	no	—
516	C₂²×C₄	—	5	1	no	—
517	C₂²×C₄	—	5	2	no	—
518	C₂²×C₄	—	5	2	no	—
519	C₂²×C₄	—	5	2	no	—
520	C₂²×C₄	C₂²×D₅	1	2	yes	—
521	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
522	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
523	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
524	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
525	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
526	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
527	C₄⋊C₄	—	5	1	no	—
528	C₄⋊C₄	—	5	2	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	1	no	—
534	C₄⋊C₄	—	5	1	no	—
535	C₄⋊C₄	—	5	2	no	—
536	C₄⋊C₄	—	5	1	no	—
537	C₄⋊C₄	—	5	1	no	—
538	C₄⋊C₄	—	5	2	no	—
539	C₄⋊C₄	—	5	2	no	—
540	C₄⋊C₄	—	5	2	no	—
541	C₄⋊C₄	—	5	1	no	—
542	C₄⋊C₄	—	5	2	no	—
543	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
544	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
545	C₄⋊C₄	C₂²×D₅	1	2	yes	—
546	C₂²⋊C₄	—	5	1	no	—
547	C₂²⋊C₄	—	5	2	no	—
548	C₂²⋊C₄	—	5	2	no	—
549	C₂²⋊C₄	—	5	2	no	—
550	C₂²⋊C₄	—	5	2	no	—
551	C₂²⋊C₄	—	5	1	no	—
552	C₂²⋊C₄	—	5	2	no	—
553	C₂²⋊C₄	—	5	1	no	—
554	C₂²⋊C₄	—	5	2	no	—
555	C₂²⋊C₄	—	5	1	no	—
556	C₂²⋊C₄	—	5	2	no	—
557	C₂²⋊C₄	—	5	1	no	—
558	C₂²⋊C₄	—	5	2	no	—
559	C₂²⋊C₄	—	5	1	no	—
560	C₂²⋊C₄	—	5	2	no	—
561	C₂²⋊C₄	—	5	1	no	—
562	C₂²⋊C₄	—	5	2	no	—
563	C₂²⋊C₄	—	5	2	no	—
564	C₂²⋊C₄	—	5	1	no	—
565	C₂²⋊C₄	—	5	1	no	—
566	C₂²⋊C₄	—	5	2	no	—
567	C₂²⋊C₄	—	5	2	no	—
568	C₂²⋊C₄	—	5	2	no	—
569	C₂²⋊C₄	—	5	2	no	—
570	C₂²⋊C₄	—	5	1	no	—
571	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
572	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
573	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
574	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
575	C₄²	—	5	2	no	—
576	C₄²	—	5	2	no	—
577	C₄²	—	5	1	no	—
578	C₄²	—	5	1	no	—
579	C₄²	—	5	2	no	—
580	C₂×C₅	—	2	2	no	—
581	C₂×C₅	—	4	2	no	—
582	C₂×C₅	—	4	1	no	—
583	C₂×C₅	—	4	1	no	—
584	C₂×C₅	—	4	2	no	—
585	C₂×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
586	C₂×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
587	C₂×C₅	#585	1	1	yes	characteristic
588	D₅	—	4	1	no	—
589	D₅	—	4	2	no	—
590	D₅	—	4	1	no	—
591	C₂³	—	2	2	no	—
592	C₂³	—	2	4	no	—
593	C₂³	—	4	1	no	—
594	C₂³	—	4	1	no	—
595	C₂³	—	4	2	no	—
596	C₂³	—	4	2	no	—
597	C₂³	—	5	1	no	—
598	C₂³	—	5	2	no	—
599	C₂³	—	5	1	no	—
600	C₂³	—	20	2	no	—
601	C₂³	—	20	2	no	—
602	C₂³	—	20	2	no	—
603	C₂³	C₂³×D₅	1	2	yes	—
604	C₂³	C₂³×D₅	1	1	yes	characteristic
605	C₂³	C₂³×D₅	1	1	yes	characteristic
606	C₂³	C₂³×D₅	1	2	yes	—
607	C₂³	C₂³×D₅	1	1	yes	characteristic
608	Q₈	—	10	2	no	—
609	Q₈	—	20	1	no	—
610	Q₈	—	20	2	no	—
611	D₄	—	2	2	no	—
612	D₄	—	2	2	no	—
613	D₄	—	4	2	no	—
614	D₄	—	4	2	no	—
615	D₄	—	4	2	no	—
616	D₄	—	4	2	no	—
617	D₄	—	4	2	no	—
618	D₄	—	10	2	no	—
619	D₄	—	10	4	no	—
620	D₄	—	10	2	no	—
621	D₄	—	10	2	no	—
622	D₄	—	20	1	no	—
623	D₄	—	20	2	no	—
624	D₄	—	20	2	no	—
625	D₄	—	20	2	no	—
626	D₄	—	20	2	no	—
627	D₄	—	20	1	no	—
628	D₄	—	20	1	no	—
629	D₄	—	20	2	no	—
630	D₄	—	20	2	no	—
631	D₄	—	20	1	no	—
632	D₄	—	20	2	no	—
633	D₄	—	20	2	no	—
634	D₄	—	20	2	no	—
635	D₄	—	20	1	no	—
636	C₂×C₄	—	2	4	no	—
637	C₂×C₄	—	2	2	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	2	2	no	—
640	C₂×C₄	—	4	1	no	—
641	C₂×C₄	—	4	1	no	—
642	C₂×C₄	—	4	1	no	—
643	C₂×C₄	—	5	1	no	—
644	C₂×C₄	—	5	2	no	—
645	C₂×C₄	—	5	1	no	—
646	C₂×C₄	—	5	1	no	—
647	C₂×C₄	—	5	1	no	—
648	C₂×C₄	—	5	2	no	—
649	C₂×C₄	—	5	2	no	—
650	C₂×C₄	—	5	1	no	—
651	C₂×C₄	—	5	1	no	—
652	C₂×C₄	—	10	2	no	—
653	C₂×C₄	—	10	2	no	—
654	C₂×C₄	—	20	2	no	—
655	C₂×C₄	—	20	2	no	—
656	C₂×C₄	—	20	2	no	—
657	C₂×C₄	—	20	2	no	—
658	C₂×C₄	—	20	2	no	—
659	C₂×C₄	—	20	2	no	—
660	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
661	C₂×C₄	C₂³×D₅	1	2	yes	—
662	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
663	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
664	C₂×C₄	C₂³×D₅	1	2	yes	—
665	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
666	C₅	#3542	1	1	yes	characteristic, complemented, Sylow
667	C₂²	—	2	1	no	—
668	C₂²	—	2	1	no	—
669	C₂²	—	2	1	no	—
670	C₂²	—	2	1	no	—
671	C₂²	—	2	2	no	—
672	C₂²	—	2	2	no	—
673	C₂²	—	2	2	no	—
674	C₂²	—	2	1	no	—
675	C₂²	—	2	1	no	—
676	C₂²	—	2	2	no	—
677	C₂²	—	2	2	no	—
678	C₂²	—	2	1	no	—
679	C₂²	—	2	1	no	—
680	C₂²	—	2	2	no	—
681	C₂²	—	4	4	no	—
682	C₂²	—	8	4	no	—
683	C₂²	—	10	1	no	—
684	C₂²	—	10	1	no	—
685	C₂²	—	10	1	no	—
686	C₂²	—	10	2	no	—
687	C₂²	—	10	2	no	—
688	C₂²	—	10	1	no	—
689	C₂²	—	10	1	no	—
690	C₂²	—	10	2	no	—
691	C₂²	—	10	1	no	—
692	C₂²	—	40	4	no	—
693	C₂²	#4144	1	2	yes	—
694	C₂²	C₂⁴×D₅	1	1	yes	characteristic
695	C₄	—	2	1	no	—
696	C₄	—	2	1	no	—
697	C₄	—	2	1	no	—
698	C₄	—	2	2	no	—
699	C₄	—	2	2	no	—
700	C₄	—	10	1	no	—
701	C₄	—	10	1	no	—
702	C₄	—	10	1	no	—
703	C₄	—	10	2	no	—
704	C₄	—	10	1	no	—
705	C₄	—	10	2	no	—
706	C₄	—	10	1	no	—
707	C₄	—	10	2	no	—
708	C₄	—	10	1	no	—
709	C₄	#4144	1	2	yes	—
710	C₂	—	2	2	no	—
711	C₂	—	4	1	no	—
712	C₂	—	4	1	no	—
713	C₂	—	4	2	no	—
714	C₂	—	4	2	no	—
715	C₂	—	20	1	no	—
716	C₂	—	20	2	no	—
717	C₂	—	20	1	no	—
718	C₂	C₂×#4144	1	1	yes	characteristic
719	C₂	C₂×#4144	1	1	yes	characteristic
720	C₂	#66283	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅
commutator, socle, cosocle	C₂²×C₅	C₂⁵
Fitting	C₂×C₅×#121	C₂
hypercenter	C₂×#121	D₅
hypocenter	C₅	#3542
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ C₂×#121

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#121	C₂	semidirect
2. #66140	C₂	semidirect
3. #66139	C₂	semidirect
4. #66138	C₂	semidirect
5. D₄×C₂²⋊D₅	C₂	semidirect
6. #66125	C₂	semidirect
7. #66125	C₂	semidirect
8. #65955	C₂	semidirect
9. #65954	C₂	semidirect
10. #65953	C₂	semidirect
11. #65950	C₂	semidirect
12. #65949	C₂	semidirect
13. #65948	C₂	semidirect
14. #65947	C₂	semidirect
15. #65946	C₂	semidirect
16. #65942	C₂	semidirect
17. #65941	C₂	semidirect
18. #65937	C₂	semidirect
19. #65933	C₂	semidirect
20. #65847	C₂	semidirect
21. #65841	C₂	semidirect
22. #65829	C₂	semidirect
23. #65824	C₂	semidirect
25. C₂²×C₅×D₄	C₂²	semidirect
26. C₂³×C₄×C₅	C₂²	semidirect
28. C₂×#711	C₂²	semidirect
29. C₂×D₄×D₅	C₂²	semidirect
30. C₂×#709	C₂²	semidirect
31. C₂×#709	C₂²	semidirect
32. C₂×#709	C₂²	semidirect
35. C₅×#121	C₂²	semidirect
36. C₅×#121	C₂²	semidirect
37. C₅×#121	C₂²	semidirect
38. C₅×#121	C₂²	semidirect
39. C₂×C₅×C₄⋊C₄	C₂²	semidirect
40. C₂×C₅×C₂²⋊C₄	C₂²	semidirect
43. #4099	C₂²	semidirect
44. #4099	C₂²	semidirect
45. #4099	C₂²	semidirect
46. C₂×C₂²⋊Dic₅	C₂²	semidirect
47. #4086	C₂²	semidirect
48. #4086	C₂²	semidirect
49. #4086	C₂²	semidirect
50. #4085	C₂²	semidirect
51. #4085	C₂²	semidirect
52. #4085	C₂²	semidirect
53. #4085	C₂²	semidirect
54. #4085	C₂²	semidirect
55. #4085	C₂²	semidirect
56. #4084	C₂²	semidirect
57. #4084	C₂²	semidirect
58. #4084	C₂²	semidirect
59. #4084	C₂²	semidirect
60. #4084	C₂²	semidirect
61. #4084	C₂²	semidirect
62. #4083	C₂²	semidirect
63. #4083	C₂²	semidirect
64. #4083	C₂²	semidirect
65. #4082	C₂²	semidirect
66. #4082	C₂²	semidirect
67. #4082	C₂²	semidirect
68. #4081	C₂²	semidirect
69. #4081	C₂²	semidirect
70. #4081	C₂²	semidirect
71. D₄×Dic₅	C₂²	semidirect
72. D₄×Dic₅	C₂²	semidirect
75. #4076	C₂²	semidirect
76. #4076	C₂²	semidirect
78. #4075	C₂²	semidirect
79. #4075	C₂²	semidirect
80. #4075	C₂²	semidirect
81. #4075	C₂²	semidirect
83. C₄×C₂²⋊D₅	C₂²	semidirect
84. C₄×C₂²⋊D₅	C₂²	semidirect
85. C₄×C₂²⋊D₅	C₂²	semidirect
86. C₄×C₂²⋊D₅	C₂²	semidirect
87. C₄×C₂²⋊D₅	C₂²	semidirect
88. #4072	C₂²	semidirect
89. #4072	C₂²	semidirect
90. #4072	C₂²	semidirect
91. #4070	C₂²	semidirect
92. #4070	C₂²	semidirect
93. #4070	C₂²	semidirect
94. #4070	C₂²	semidirect
95. #4044	C₂²	semidirect
96. #4043	C₂²	semidirect
97. #4042	C₂²	semidirect
98. #4041	C₂²	semidirect
99. #4040	C₂²	semidirect
100. #4039	C₂²	semidirect
101. #4038	C₂²	semidirect
102. D₅×C₄⋊C₄	C₂²	semidirect
103. #4036	C₂²	semidirect
104. #4035	C₂²	semidirect
105. #4034	C₂²	semidirect
106. #4033	C₂²	semidirect
107. #4032	C₂²	semidirect
108. #4031	C₂²	semidirect
109. #4031	C₂²	semidirect
110. #4030	C₂²	semidirect
111. #4030	C₂²	semidirect
112. #4029	C₂²	semidirect
113. #4029	C₂²	semidirect
114. #4028	C₂²	semidirect
115. #4027	C₂²	semidirect
116. #4027	C₂²	semidirect
117. D₅×C₂²⋊C₄	C₂²	semidirect
118. #4025	C₂²	semidirect
119. #4025	C₂²	semidirect
120. #4024	C₂²	semidirect
121. #4024	C₂²	semidirect
122. #4023	C₂²	semidirect
254. C₂×#121	D₅	semidirect
337. C₂²×D₄	C₂×D₅	semidirect
338. C₂³×C₄	C₂×D₅	semidirect
394. #121	C₂×D₅	semidirect
395. #121	C₂×D₅	semidirect
396. #121	C₂×D₅	semidirect
397. #121	C₂×D₅	semidirect
425. C₂×C₄⋊C₄	C₂×D₅	semidirect
428. C₂×C₂²⋊C₄	C₂×D₅	semidirect
666. C₅	#3542	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#121	2
#66140	2
#66139	2
#66138	2
D₄×C₂²⋊D₅	2
#66125	2
#65955	2
#65954	2
#65953	2
#65950	2
#65949	2
#65948	2
#65947	2
#65946	2
#65942	2
#65941	2
#65937	2
#65933	2
#65847	2
#65841	2
#65829	2
#65824	2
#3542	5