Subgroups — #10618433

Order 640.

1150 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#542	C₂	1	1	yes	maximal, characteristic, complemented
2	#66067	C₂	1	1	yes	maximal, characteristic, complemented
3	#66059	C₂	1	1	yes	maximal, characteristic, complemented
4	#66045	C₂	1	2	yes	maximal, complemented
5	#66043	C₂	1	2	yes	maximal, complemented
6	#66012	C₂	1	2	yes	maximal, complemented
7	#66008	C₂	1	1	yes	maximal, characteristic, complemented
8	#66008	C₂	1	2	yes	maximal, complemented
9	#66002	C₂	1	1	yes	maximal, characteristic, complemented
10	#66000	C₂	1	2	yes	maximal, complemented
11	#65988	C₂	1	2	yes	maximal, complemented
12	#65978	C₂	1	2	yes	maximal, complemented
13	#65965	C₂	1	1	yes	maximal, characteristic, complemented
14	#65964	C₂	1	1	yes	maximal, characteristic, complemented
15	#65963	C₂	1	2	yes	maximal, complemented
16	#65943	C₂	1	1	yes	maximal, characteristic, complemented
17	#65933	C₂	1	1	yes	maximal, characteristic, complemented
18	#65911	C₂	1	1	yes	maximal, characteristic, complemented
19	#65902	C₂	1	1	yes	maximal, characteristic, complemented
20	#65888	C₂	1	1	yes	maximal, characteristic, complemented
21	#65887	C₂	1	1	yes	maximal, characteristic, complemented
22	#65862	C₂	1	1	yes	maximal, characteristic, complemented
23	#65859	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#713	C₂²	1	2	yes	complemented
25	C₂×#713	C₂²	1	1	yes	characteristic, complemented
26	C₂×#713	C₂²	1	1	yes	characteristic, complemented
27	C₂×#711	C₂²	1	1	yes	characteristic, complemented
28	C₂×D₄×D₅	C₂²	1	1	yes	characteristic
29	C₂×D₄×D₅	C₂²	1	2	yes	—
30	C₂×#709	C₂²	1	1	yes	characteristic, complemented
31	C₂×#709	C₂²	1	2	yes	complemented
32	C₂²×D₂₀	C₂²	1	1	yes	characteristic
33	C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
34	C₅×#126	C₂²	1	2	yes	complemented
35	C₅×#124	C₂²	1	1	yes	characteristic, complemented
36	C₅×#124	C₂²	1	2	yes	complemented
37	C₅×#123	C₂²	1	2	yes	complemented
38	C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
39	C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
40	C₅×#121	C₂²	1	1	yes	characteristic
41	C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
42	C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
43	C₅×#117	C₂²	1	1	yes	characteristic, complemented
44	#4093	C₂²	1	1	yes	characteristic
45	#4093	C₂²	1	2	yes	complemented
46	#4093	C₂²	1	2	yes	complemented
47	#4092	C₂²	1	2	yes	complemented
48	#4090	C₂²	1	1	yes	characteristic, complemented
49	#4086	C₂²	1	1	yes	characteristic
50	#4086	C₂²	1	1	yes	characteristic, complemented
51	#4086	C₂²	1	2	yes	complemented
52	#4085	C₂²	1	2	yes	complemented
53	#4083	C₂²	1	2	yes	—
54	#4076	C₂²	1	2	yes	complemented
55	#4076	C₂²	1	2	yes	complemented
56	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic
57	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic, complemented
58	C₂×#685	C₂²	1	2	yes	complemented
59	#4044	C₂²	1	2	yes	complemented
60	#4044	C₂²	1	1	yes	characteristic, complemented
61	#4044	C₂²	1	2	yes	complemented
62	#4043	C₂²	1	1	yes	characteristic, complemented
63	#4042	C₂²	1	1	yes	characteristic, complemented
64	#4042	C₂²	1	2	yes	complemented
65	#4041	C₂²	1	1	yes	characteristic
66	#4041	C₂²	1	1	yes	characteristic
67	#4041	C₂²	1	1	yes	characteristic, complemented
68	#4041	C₂²	1	2	yes	complemented
69	#4041	C₂²	1	2	yes	complemented
70	#4041	C₂²	1	2	yes	complemented
71	#4041	C₂²	1	2	yes	complemented
72	#4041	C₂²	1	2	yes	complemented
73	#4041	C₂²	1	2	yes	complemented
74	#4040	C₂²	1	2	yes	complemented
75	#4040	C₂²	1	1	yes	characteristic, complemented
76	#4040	C₂²	1	2	yes	complemented
77	#4040	C₂²	1	2	yes	complemented
78	#4039	C₂²	1	1	yes	characteristic
79	#4039	C₂²	1	1	yes	characteristic, complemented
80	#4039	C₂²	1	2	yes	complemented
81	#4039	C₂²	1	1	yes	characteristic, complemented
82	D₅×C₄⋊C₄	C₂²	1	2	yes	complemented
83	#4035	C₂²	1	1	yes	characteristic, complemented
84	#4033	C₂²	1	1	yes	characteristic, complemented
85	#4032	C₂²	1	2	yes	complemented
86	#4031	C₂²	1	1	yes	characteristic
87	#4030	C₂²	1	1	yes	characteristic
88	#4030	C₂²	1	2	yes	—
89	#4030	C₂²	1	2	yes	—
90	#4030	C₂²	1	2	yes	complemented
91	#4030	C₂²	1	2	yes	complemented
92	#4030	C₂²	1	2	yes	complemented
93	#4030	C₂²	1	2	yes	complemented
94	#4030	C₂²	1	2	yes	complemented
95	#4030	C₂²	1	2	yes	complemented
96	#4030	C₂²	1	2	yes	complemented
97	#4029	C₂²	1	1	yes	characteristic, complemented
98	#4029	C₂²	1	2	yes	complemented
99	#4028	C₂²	1	2	yes	—
100	#4028	C₂²	1	2	yes	complemented
101	#4028	C₂²	1	2	yes	complemented
102	#4028	C₂²	1	2	yes	complemented
103	#4028	C₂²	1	2	yes	complemented
104	#4028	C₂²	1	2	yes	complemented
105	#4028	C₂²	1	2	yes	complemented
106	#4027	C₂²	1	2	yes	complemented
107	#4027	C₂²	1	2	yes	complemented
108	#4027	C₂²	1	2	yes	complemented
109	D₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
110	#4025	C₂²	1	1	yes	characteristic, complemented
111	#4022	C₂²	1	2	yes	complemented
112	#4021	C₂²	1	1	yes	characteristic
113	#4021	C₂²	1	1	yes	characteristic, complemented
114	#4020	C₂²	1	1	yes	characteristic
115	#4020	C₂²	1	1	yes	characteristic, complemented
116	#4020	C₂²	1	2	yes	complemented
117	C₄×D₂₀	C₂²	1	1	yes	characteristic, complemented
118	C₄×D₂₀	C₂²	1	2	yes	complemented
119	#4018	C₂²	1	1	yes	characteristic, complemented
120	#4018	C₂²	1	2	yes	complemented
121	C₄²×D₅	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
123	#3546	—	5	1	no	maximal, Sylow
124	C₂³×D₅	C₂³	1	2	yes	—
125	C₂³×D₅	C₂³	1	2	yes	—
126	C₂×C₅×Q₈	C₂³	1	1	yes	characteristic
127	C₂×C₅×Q₈	C₂³	1	2	yes	—
128	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
129	C₂×C₅×D₄	C₂³	1	2	yes	—
130	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
131	C₂²×C₄×C₅	C₂³	1	2	yes	—
132	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
133	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
134	C₂×C₂²⋊D₅	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	1	yes	characteristic
141	C₂²×Dic₅	C₂³	1	2	yes	—
142	#713	—	4	4	no	—
143	#713	—	4	2	no	—
144	#713	—	4	2	no	—
145	#711	—	4	2	no	—
146	D₄×D₅	—	4	2	no	—
147	D₄×D₅	—	4	4	no	—
148	#709	—	4	4	no	—
149	#709	—	4	2	no	—
150	C₂×D₂₀	—	4	2	no	—
151	C₂×D₂₀	C₂³	1	1	yes	characteristic
152	C₂×D₂₀	C₂³	1	1	yes	characteristic
153	C₂×D₂₀	C₂³	1	1	yes	characteristic
154	C₂×D₂₀	C₂³	1	2	yes	—
155	C₂×D₂₀	C₂³	1	2	yes	—
156	C₂×D₂₀	C₂³	1	2	yes	—
157	C₂×D₂₀	C₂³	1	2	yes	—
158	C₂×D₂₀	C₂³	1	2	yes	—
159	C₂×D₂₀	C₂³	1	2	yes	—
160	C₂×D₂₀	C₂³	1	2	yes	—
161	C₂×D₂₀	C₂³	1	2	yes	—
162	C₂×D₂₀	C₂³	1	1	yes	characteristic
163	C₂×D₂₀	C₂³	1	2	yes	—
164	C₂×D₂₀	C₂³	1	2	yes	—
165	C₂×C₄×D₅	C₂³	1	2	yes	—
166	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
167	C₂×C₄×D₅	C₂³	1	2	yes	—
168	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
169	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
170	C₂×C₄×D₅	C₂³	1	2	yes	—
171	C₂×C₄×D₅	C₂³	1	2	yes	—
172	C₂×C₄×D₅	C₂³	1	2	yes	—
173	C₂×C₄×D₅	C₂³	1	2	yes	—
174	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
175	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
176	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
177	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
178	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
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×C₄⋊C₄	C₂³	1	2	yes	—
183	C₅×C₄⋊C₄	C₂³	1	2	yes	—
184	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
185	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
186	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
187	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
188	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
189	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
190	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
191	C₄²×C₅	C₂³	1	1	yes	characteristic
192	C₄²×C₅	C₂³	1	1	yes	characteristic
193	C₄²×C₅	C₂³	1	2	yes	—
194	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
195	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
196	#685	C₂³	1	2	yes	—
197	#685	C₂³	1	1	yes	characteristic
198	#685	C₂³	1	2	yes	—
199	#685	C₂³	1	1	yes	characteristic
200	#685	C₂³	1	2	yes	—
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	2	yes	—
209	#685	C₂³	1	2	yes	—
210	#685	C₂³	1	1	yes	characteristic
211	#685	C₂³	1	2	yes	—
212	#685	C₂³	1	2	yes	—
213	#685	C₂³	1	2	yes	—
214	#685	C₂³	1	1	yes	characteristic
215	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
216	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
217	C₄⋊Dic₅	C₂³	1	2	yes	—
218	#683	C₂³	1	1	yes	characteristic
219	#683	C₂³	1	1	yes	characteristic
220	#683	C₂³	1	1	yes	characteristic
221	#683	C₂³	1	2	yes	—
222	#683	C₂³	1	1	yes	characteristic
223	#683	C₂³	1	2	yes	—
224	#683	C₂³	1	2	yes	—
225	#683	C₂³	1	1	yes	characteristic
226	#683	C₂³	1	1	yes	characteristic
227	C₄×Dic₅	C₂³	1	1	yes	characteristic
228	C₄×Dic₅	C₂³	1	1	yes	characteristic
229	C₄×Dic₅	C₂³	1	1	yes	characteristic
230	C₄×Dic₅	C₂³	1	1	yes	characteristic
231	C₄×Dic₅	C₂³	1	2	yes	—
232	#560	—	5	2	no	—
233	#560	—	5	2	no	—
234	#556	—	5	1	no	—
235	#553	—	5	2	no	—
236	#550	—	5	1	no	—
237	#550	—	5	1	no	—
238	#550	—	5	1	no	—
239	#547	—	5	1	no	—
240	#546	—	5	2	no	—
241	#546	—	5	1	no	—
242	#546	—	5	1	no	—
243	D₄²	—	5	1	no	—
244	#542	—	5	1	no	—
245	#542	D₅	1	1	yes	characteristic, complemented
246	#538	—	5	2	no	—
247	#538	—	5	2	no	—
248	#537	—	5	2	no	—
249	#535	—	5	1	no	—
250	#535	—	5	2	no	—
251	#535	—	5	1	no	—
252	#532	—	5	1	no	—
253	#532	—	5	1	no	—
254	#529	—	5	1	no	—
255	C₂³×C₅	C₂⁴	1	1	yes	characteristic
256	C₂³×C₅	C₂⁴	1	2	yes	—
257	C₂²×D₅	—	4	2	no	—
258	C₂²×D₅	—	4	2	no	—
259	C₂²×D₅	—	4	2	no	—
260	C₂²×D₅	—	4	2	no	—
261	C₂²×D₅	—	4	2	no	—
262	C₂²×D₅	—	4	2	no	—
263	C₂²×D₅	C₂⁴	1	2	yes	—
264	C₂²×D₅	C₂⁴	1	1	yes	characteristic
265	C₂²×D₅	C₂⁴	1	2	yes	—
266	C₂²×D₅	C₂⁴	1	1	yes	characteristic
267	C₂²×D₅	C₂⁴	1	2	yes	—
268	C₅×Q₈	—	2	2	no	—
269	C₅×Q₈	—	4	2	no	—
270	C₅×D₄	—	2	2	no	—
271	C₅×D₄	—	4	2	no	—
272	C₂×C₄×C₅	—	2	2	no	—
273	C₂×C₄×C₅	—	4	2	no	—
274	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
275	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
276	C₂×C₄×C₅	C₂⁴	1	2	yes	—
277	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
278	C₂×C₄×C₅	C₂⁴	1	2	yes	—
279	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
280	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
281	C₂×C₄×C₅	C₂⁴	1	2	yes	—
282	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
283	C₂²⋊D₅	—	2	4	no	—
284	C₂²⋊D₅	—	2	2	no	—
285	C₂²⋊D₅	—	4	2	no	—
286	C₂²⋊D₅	—	4	2	no	—
287	C₂²⋊D₅	—	4	2	no	—
288	C₂²⋊D₅	—	4	2	no	—
289	C₂²⋊D₅	—	4	2	no	—
290	C₂²⋊D₅	—	4	1	no	—
291	C₂²⋊D₅	—	4	2	no	—
292	C₂×Dic₅	—	4	2	no	—
293	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
294	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
295	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
296	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
297	C₂×Dic₅	C₂⁴	1	2	yes	—
298	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
299	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
300	D₂₀	—	2	2	no	—
301	D₂₀	—	2	2	no	—
302	D₂₀	—	2	2	no	—
303	D₂₀	—	4	2	no	—
304	D₂₀	—	4	2	no	—
305	D₂₀	—	4	1	no	—
306	D₂₀	—	4	2	no	—
307	D₂₀	—	4	2	no	—
308	D₂₀	—	4	2	no	—
309	D₂₀	—	4	2	no	—
310	D₂₀	—	4	2	no	—
311	D₂₀	—	4	2	no	—
312	D₂₀	—	4	2	no	—
313	D₂₀	—	4	2	no	—
314	C₄×D₅	—	2	2	no	—
315	C₄×D₅	—	2	2	no	—
316	C₄×D₅	—	2	4	no	—
317	C₄×D₅	—	2	4	no	—
318	C₄×D₅	—	2	2	no	—
319	C₄×D₅	—	4	1	no	—
320	C₄×D₅	—	4	2	no	—
321	C₄×D₅	—	4	2	no	—
322	C₄×D₅	—	4	2	no	—
323	C₄×D₅	—	4	2	no	—
324	Dic₁₀	—	2	2	no	—
325	Dic₁₀	—	2	2	no	—
326	C₂×#41	—	5	2	no	—
327	C₂×#41	—	5	1	no	—
328	C₂×#41	—	5	1	no	—
329	C₂×#41	—	5	1	no	—
330	C₂×#41	—	5	1	no	—
331	C₂×#41	—	5	2	no	—
332	C₂²×D₄	—	5	2	no	—
333	C₂²×D₄	—	5	1	no	—
334	C₂²×D₄	—	5	1	no	—
335	C₄⋊Q₈	—	5	1	no	—
336	C₄⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
337	#127	—	5	1	no	—
338	#127	—	5	1	no	—
339	#127	—	5	2	no	—
340	#127	—	5	1	no	—
341	#127	—	5	1	no	—
342	#127	—	5	2	no	—
343	#126	—	5	1	no	—
344	#126	—	5	2	no	—
345	#126	—	5	2	no	—
346	#126	—	5	1	no	—
347	#126	—	5	2	no	—
348	#126	C₂×D₅	1	2	yes	complemented
349	#125	—	5	1	no	—
350	#124	—	5	2	no	—
351	#124	—	5	2	no	—
352	#124	—	5	1	no	—
353	#124	—	5	1	no	—
354	#124	—	5	1	no	—
355	#124	—	5	1	no	—
356	#124	C₂×D₅	1	1	yes	characteristic, complemented
357	#124	C₂×D₅	1	2	yes	complemented
358	#123	—	5	1	no	—
359	#123	—	5	2	no	—
360	#123	—	5	2	no	—
361	#123	—	5	2	no	—
362	#123	—	5	1	no	—
363	#123	—	5	2	no	—
364	#123	—	5	2	no	—
365	#123	C₂×D₅	1	2	yes	complemented
366	C₂²⋊Q₈	—	5	2	no	—
367	C₂²⋊Q₈	—	5	1	no	—
368	C₂²⋊Q₈	—	5	2	no	—
369	C₂²⋊Q₈	—	5	1	no	—
370	C₂²⋊Q₈	C₂×D₅	1	2	yes	complemented
371	C₂²⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
372	#121	—	5	2	no	—
373	#121	—	5	2	no	—
374	#121	—	5	2	no	—
375	#121	—	5	1	no	—
376	#121	—	5	1	no	—
377	#121	—	5	2	no	—
378	#121	—	5	2	no	—
379	#121	—	5	2	no	—
380	#121	—	5	2	no	—
381	#121	—	5	2	no	—
382	#121	—	5	2	no	—
383	#121	—	5	1	no	—
384	#121	—	5	1	no	—
385	#121	—	5	2	no	—
386	#121	—	5	2	no	—
387	#121	—	5	2	no	—
388	#121	—	5	2	no	—
389	#121	—	5	2	no	—
390	#121	—	5	2	no	—
391	#121	—	5	2	no	—
392	#121	—	5	2	no	—
393	#121	—	5	2	no	—
394	#121	C₂×D₅	1	1	yes	characteristic
395	#120	—	5	2	no	—
396	#120	—	5	2	no	—
397	#120	—	5	2	no	—
398	#120	—	5	2	no	—
399	#120	—	5	2	no	—
400	#120	—	5	2	no	—
401	#120	—	5	2	no	—
402	#120	—	5	2	no	—
403	C₄×Q₈	—	5	1	no	—
404	C₄×Q₈	—	5	1	no	—
405	C₄×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
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	1	no	—
411	C₄×D₄	—	5	1	no	—
412	C₄×D₄	—	5	2	no	—
413	C₄×D₄	—	5	2	no	—
414	C₄×D₄	—	5	2	no	—
415	C₄×D₄	—	5	1	no	—
416	C₄×D₄	—	5	2	no	—
417	C₄×D₄	C₂×D₅	1	1	yes	characteristic, complemented
418	#117	—	5	1	no	—
419	#117	—	5	2	no	—
420	#117	C₂×D₅	1	1	yes	characteristic, complemented
421	C₂×C₄⋊C₄	—	5	2	no	—
422	C₂×C₂²⋊C₄	—	5	2	no	—
423	C₂×C₂²⋊C₄	—	5	2	no	—
424	C₂×C₄²	—	5	1	no	—
425	C₂²×C₅	—	2	2	no	—
426	C₂²×C₅	—	2	2	no	—
427	C₂²×C₅	—	2	1	no	—
428	C₂²×C₅	—	2	1	no	—
429	C₂²×C₅	—	2	2	no	—
430	C₂²×C₅	—	2	1	no	—
431	C₂²×C₅	C₂⁵	1	1	yes	characteristic
432	C₂×D₅	—	2	1	no	—
433	C₂×D₅	—	2	2	no	—
434	C₂×D₅	—	2	1	no	—
435	C₂×D₅	—	2	1	no	—
436	C₂×D₅	—	2	2	no	—
437	C₂×D₅	—	2	2	no	—
438	C₂×D₅	—	2	2	no	—
439	C₂×D₅	—	2	2	no	—
440	C₂×D₅	—	2	2	no	—
441	C₂×D₅	—	2	1	no	—
442	C₂×D₅	—	2	1	no	—
443	C₂×D₅	—	2	2	no	—
444	C₂×D₅	—	2	2	no	—
445	C₂×D₅	—	2	2	no	—
446	C₂×D₅	—	2	1	no	—
447	C₂×D₅	—	8	4	no	—
448	C₂×D₅	—	8	4	no	—
449	C₄×C₅	—	2	1	no	—
450	C₄×C₅	—	2	2	no	—
451	C₄×C₅	—	2	2	no	—
452	C₄×C₅	—	2	1	no	—
453	C₄×C₅	—	2	1	no	—
454	C₄×C₅	—	2	2	no	—
455	C₄×C₅	—	2	1	no	—
456	C₄×C₅	—	2	1	no	—
457	C₄×C₅	H(5,𝔽₂)	1	2	yes	—
458	Dic₅	—	2	1	no	—
459	Dic₅	—	2	2	no	—
460	Dic₅	—	2	1	no	—
461	Dic₅	—	2	1	no	—
462	Dic₅	—	2	1	no	—
463	Dic₅	—	2	1	no	—
464	Dic₅	H(5,𝔽₂)	1	2	yes	—
465	C₂⁴	—	5	2	no	—
466	C₂⁴	—	5	2	no	—
467	#41	—	20	2	no	—
468	#41	—	20	4	no	—
469	#41	—	20	4	no	—
470	#41	—	20	2	no	—
471	#41	—	20	2	no	—
472	#41	—	20	2	no	—
473	C₂×Q₈	—	5	1	no	—
474	C₂×Q₈	—	5	1	no	—
475	C₂×Q₈	C₂²×D₅	1	1	yes	characteristic
476	C₂×Q₈	C₂²×D₅	1	2	yes	—
477	C₂×D₄	—	5	1	no	—
478	C₂×D₄	—	5	2	no	—
479	C₂×D₄	—	5	2	no	—
480	C₂×D₄	—	5	1	no	—
481	C₂×D₄	—	5	2	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	1	no	—
487	C₂×D₄	—	5	1	no	—
488	C₂×D₄	—	5	1	no	—
489	C₂×D₄	—	5	2	no	—
490	C₂×D₄	—	5	1	no	—
491	C₂×D₄	—	5	2	no	—
492	C₂×D₄	—	5	2	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	2	no	—
498	C₂×D₄	—	5	2	no	—
499	C₂×D₄	—	5	2	no	—
500	C₂×D₄	—	20	2	no	—
501	C₂×D₄	—	20	2	no	—
502	C₂×D₄	—	20	4	no	—
503	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
504	C₂×D₄	C₂²×D₅	1	2	yes	—
505	C₂²×C₄	—	5	2	no	—
506	C₂²×C₄	—	5	1	no	—
507	C₂²×C₄	—	5	1	no	—
508	C₂²×C₄	—	5	2	no	—
509	C₂²×C₄	—	5	2	no	—
510	C₂²×C₄	—	5	1	no	—
511	C₂²×C₄	—	5	1	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	C₂²×D₅	1	1	yes	characteristic
517	C₂²×C₄	C₂²×D₅	1	2	yes	—
518	C₄⋊C₄	—	5	1	no	—
519	C₄⋊C₄	—	5	2	no	—
520	C₄⋊C₄	—	5	2	no	—
521	C₄⋊C₄	—	5	1	no	—
522	C₄⋊C₄	—	5	1	no	—
523	C₄⋊C₄	—	5	1	no	—
524	C₄⋊C₄	—	5	1	no	—
525	C₄⋊C₄	—	5	1	no	—
526	C₄⋊C₄	—	5	2	no	—
527	C₄⋊C₄	—	5	2	no	—
528	C₄⋊C₄	—	5	1	no	—
529	C₄⋊C₄	—	5	1	no	—
530	C₄⋊C₄	C₂²×D₅	1	2	yes	—
531	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
532	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
533	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
534	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
535	C₄⋊C₄	C₂²×D₅	1	2	yes	—
536	C₄⋊C₄	C₂²×D₅	1	2	yes	—
537	C₂²⋊C₄	—	5	1	no	—
538	C₂²⋊C₄	—	5	1	no	—
539	C₂²⋊C₄	—	5	1	no	—
540	C₂²⋊C₄	—	5	2	no	—
541	C₂²⋊C₄	—	5	2	no	—
542	C₂²⋊C₄	—	5	2	no	—
543	C₂²⋊C₄	—	5	2	no	—
544	C₂²⋊C₄	—	5	2	no	—
545	C₂²⋊C₄	—	5	2	no	—
546	C₂²⋊C₄	—	5	1	no	—
547	C₂²⋊C₄	—	5	1	no	—
548	C₂²⋊C₄	—	5	2	no	—
549	C₂²⋊C₄	—	5	2	no	—
550	C₂²⋊C₄	—	5	1	no	—
551	C₂²⋊C₄	—	5	2	no	—
552	C₂²⋊C₄	—	5	2	no	—
553	C₂²⋊C₄	—	5	2	no	—
554	C₂²⋊C₄	—	5	2	no	—
555	C₂²⋊C₄	—	5	1	no	—
556	C₂²⋊C₄	—	5	1	no	—
557	C₂²⋊C₄	—	5	2	no	—
558	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
559	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
560	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
561	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
562	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
563	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
564	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
565	C₄²	—	5	1	no	—
566	C₄²	—	5	1	no	—
567	C₄²	—	5	1	no	—
568	C₄²	—	5	1	no	—
569	C₄²	—	5	2	no	—
570	C₄²	C₂²×D₅	1	1	yes	characteristic
571	C₄²	C₂²×D₅	1	2	yes	—
572	C₄²	C₂²×D₅	1	1	yes	characteristic
573	C₂×C₅	—	4	1	no	—
574	C₂×C₅	—	4	2	no	—
575	C₂×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
576	C₂×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
577	C₂×C₅	#585	1	1	yes	characteristic
578	D₅	—	4	1	no	—
579	D₅	—	4	2	no	—
580	D₅	—	4	2	no	—
581	D₅	—	4	2	no	—
582	D₅	—	4	1	no	—
583	C₂³	—	5	1	no	—
584	C₂³	—	5	2	no	—
585	C₂³	—	5	2	no	—
586	C₂³	—	5	1	no	—
587	C₂³	—	5	2	no	—
588	C₂³	—	20	2	no	—
589	C₂³	—	20	2	no	—
590	C₂³	—	20	2	no	—
591	C₂³	—	20	2	no	—
592	C₂³	—	20	2	no	—
593	C₂³	—	20	2	no	—
594	C₂³	C₂³×D₅	1	1	yes	characteristic
595	C₂³	C₂³×D₅	1	2	yes	—
596	Q₈	—	2	2	no	—
597	Q₈	—	4	2	no	—
598	Q₈	—	10	2	no	—
599	Q₈	—	10	2	no	—
600	D₄	—	2	2	no	—
601	D₄	—	4	2	no	—
602	D₄	—	10	2	no	—
603	D₄	—	10	4	no	—
604	D₄	—	10	2	no	—
605	D₄	—	10	2	no	—
606	D₄	—	10	2	no	—
607	D₄	—	20	2	no	—
608	D₄	—	20	2	no	—
609	D₄	—	20	2	no	—
610	D₄	—	20	2	no	—
611	D₄	—	20	2	no	—
612	D₄	—	20	2	no	—
613	D₄	—	20	2	no	—
614	D₄	—	20	2	no	—
615	D₄	—	20	2	no	—
616	D₄	—	20	1	no	—
617	D₄	—	20	2	no	—
618	D₄	—	20	2	no	—
619	D₄	—	20	2	no	—
620	D₄	—	20	2	no	—
621	D₄	—	20	2	no	—
622	D₄	—	20	2	no	—
623	D₄	—	20	2	no	—
624	D₄	—	20	1	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	4	2	no	—
627	C₂×C₄	—	5	1	no	—
628	C₂×C₄	—	5	1	no	—
629	C₂×C₄	—	5	1	no	—
630	C₂×C₄	—	5	1	no	—
631	C₂×C₄	—	5	2	no	—
632	C₂×C₄	—	5	1	no	—
633	C₂×C₄	—	5	1	no	—
634	C₂×C₄	—	10	4	no	—
635	C₂×C₄	—	10	4	no	—
636	C₂×C₄	—	10	2	no	—
637	C₂×C₄	—	10	2	no	—
638	C₂×C₄	—	10	2	no	—
639	C₂×C₄	—	20	2	no	—
640	C₂×C₄	—	20	2	no	—
641	C₂×C₄	—	20	2	no	—
642	C₂×C₄	—	20	2	no	—
643	C₂×C₄	—	20	1	no	—
644	C₂×C₄	—	20	2	no	—
645	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
646	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
647	C₂×C₄	C₂³×D₅	1	2	yes	—
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	2	yes	—
652	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
653	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
654	C₅	#3546	1	1	yes	characteristic, complemented, Sylow
655	C₂²	—	2	1	no	—
656	C₂²	—	2	2	no	—
657	C₂²	—	2	2	no	—
658	C₂²	—	2	1	no	—
659	C₂²	—	2	2	no	—
660	C₂²	—	2	1	no	—
661	C₂²	—	10	1	no	—
662	C₂²	—	10	1	no	—
663	C₂²	—	10	2	no	—
664	C₂²	—	10	2	no	—
665	C₂²	—	10	2	no	—
666	C₂²	—	10	1	no	—
667	C₂²	—	10	2	no	—
668	C₂²	—	10	2	no	—
669	C₂²	—	10	2	no	—
670	C₂²	—	10	1	no	—
671	C₂²	—	10	1	no	—
672	C₂²	—	10	2	no	—
673	C₂²	—	10	2	no	—
674	C₂²	—	10	1	no	—
675	C₂²	—	10	2	no	—
676	C₂²	—	40	4	no	—
677	C₂²	—	40	4	no	—
678	C₂²	C₂⁴×D₅	1	1	yes	characteristic
679	C₄	—	2	1	no	—
680	C₄	—	2	2	no	—
681	C₄	—	2	1	no	—
682	C₄	—	2	2	no	—
683	C₄	—	2	2	no	—
684	C₄	—	2	1	no	—
685	C₄	—	2	1	no	—
686	C₄	—	2	1	no	—
687	C₄	—	5	2	no	—
688	C₄	—	10	1	no	—
689	C₄	—	10	1	no	—
690	C₄	—	10	2	no	—
691	C₄	—	10	1	no	—
692	C₄	—	10	1	no	—
693	C₄	—	10	1	no	—
694	C₄	#4149	1	2	yes	—
695	C₂	—	4	1	no	—
696	C₂	—	4	2	no	—
697	C₂	—	20	1	no	—
698	C₂	—	20	2	no	—
699	C₂	—	20	2	no	—
700	C₂	—	20	1	no	—
701	C₂	—	20	2	no	—
702	C₂	C₂×#4149	1	1	yes	characteristic
703	C₂	D₅×H(5,𝔽₂)	1	1	yes	characteristic
704	C₂	#66287	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅
commutator, socle, cosocle	C₂²×C₅	C₂⁵
Fitting	C₅×#542	C₂
hypercenter	#542	D₅
hypocenter	C₅	#3546
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ #542

Complements

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

N	H ≅ G/N	type
1. C₅×#542	C₂	semidirect
2. #66067	C₂	semidirect
3. #66059	C₂	semidirect
4. #66045	C₂	semidirect
5. #66043	C₂	semidirect
6. #66012	C₂	semidirect
7. #66008	C₂	semidirect
8. #66008	C₂	semidirect
9. #66002	C₂	semidirect
10. #66000	C₂	semidirect
11. #65988	C₂	semidirect
12. #65978	C₂	semidirect
13. #65965	C₂	semidirect
14. #65964	C₂	semidirect
15. #65963	C₂	semidirect
16. #65943	C₂	semidirect
17. #65933	C₂	semidirect
18. #65911	C₂	semidirect
19. #65902	C₂	semidirect
20. #65888	C₂	semidirect
21. #65887	C₂	semidirect
22. #65862	C₂	semidirect
23. #65859	C₂	semidirect
24. C₂×#713	C₂²	semidirect
25. C₂×#713	C₂²	semidirect
26. C₂×#713	C₂²	semidirect
27. C₂×#711	C₂²	semidirect
30. C₂×#709	C₂²	semidirect
31. C₂×#709	C₂²	semidirect
33. C₅×C₄⋊Q₈	C₂²	semidirect
34. C₅×#126	C₂²	semidirect
35. C₅×#124	C₂²	semidirect
36. C₅×#124	C₂²	semidirect
37. C₅×#123	C₂²	semidirect
38. C₅×C₂²⋊Q₈	C₂²	semidirect
39. C₅×C₂²⋊Q₈	C₂²	semidirect
41. C₄×C₅×Q₈	C₂²	semidirect
42. C₄×C₅×D₄	C₂²	semidirect
43. C₅×#117	C₂²	semidirect
45. #4093	C₂²	semidirect
46. #4093	C₂²	semidirect
47. #4092	C₂²	semidirect
48. #4090	C₂²	semidirect
50. #4086	C₂²	semidirect
51. #4086	C₂²	semidirect
52. #4085	C₂²	semidirect
54. #4076	C₂²	semidirect
55. #4076	C₂²	semidirect
57. C₄×C₂²⋊D₅	C₂²	semidirect
58. C₂×#685	C₂²	semidirect
59. #4044	C₂²	semidirect
60. #4044	C₂²	semidirect
61. #4044	C₂²	semidirect
62. #4043	C₂²	semidirect
63. #4042	C₂²	semidirect
64. #4042	C₂²	semidirect
67. #4041	C₂²	semidirect
68. #4041	C₂²	semidirect
69. #4041	C₂²	semidirect
70. #4041	C₂²	semidirect
71. #4041	C₂²	semidirect
72. #4041	C₂²	semidirect
73. #4041	C₂²	semidirect
74. #4040	C₂²	semidirect
75. #4040	C₂²	semidirect
76. #4040	C₂²	semidirect
77. #4040	C₂²	semidirect
79. #4039	C₂²	semidirect
80. #4039	C₂²	semidirect
81. #4039	C₂²	semidirect
82. D₅×C₄⋊C₄	C₂²	semidirect
83. #4035	C₂²	semidirect
84. #4033	C₂²	semidirect
85. #4032	C₂²	semidirect
90. #4030	C₂²	semidirect
91. #4030	C₂²	semidirect
92. #4030	C₂²	semidirect
93. #4030	C₂²	semidirect
94. #4030	C₂²	semidirect
95. #4030	C₂²	semidirect
96. #4030	C₂²	semidirect
97. #4029	C₂²	semidirect
98. #4029	C₂²	semidirect
100. #4028	C₂²	semidirect
101. #4028	C₂²	semidirect
102. #4028	C₂²	semidirect
103. #4028	C₂²	semidirect
104. #4028	C₂²	semidirect
105. #4028	C₂²	semidirect
106. #4027	C₂²	semidirect
107. #4027	C₂²	semidirect
108. #4027	C₂²	semidirect
109. D₅×C₂²⋊C₄	C₂²	semidirect
110. #4025	C₂²	semidirect
111. #4022	C₂²	semidirect
113. #4021	C₂²	semidirect
115. #4020	C₂²	semidirect
116. #4020	C₂²	semidirect
117. C₄×D₂₀	C₂²	semidirect
118. C₄×D₂₀	C₂²	semidirect
119. #4018	C₂²	semidirect
120. #4018	C₂²	semidirect
121. C₄²×D₅	C₂²	semidirect
122. C₄×Dic₁₀	C₂²	semidirect
245. #542	D₅	semidirect
336. C₄⋊Q₈	C₂×D₅	semidirect
348. #126	C₂×D₅	semidirect
356. #124	C₂×D₅	semidirect
357. #124	C₂×D₅	semidirect
365. #123	C₂×D₅	semidirect
370. C₂²⋊Q₈	C₂×D₅	semidirect
371. C₂²⋊Q₈	C₂×D₅	semidirect
405. C₄×Q₈	C₂×D₅	semidirect
417. C₄×D₄	C₂×D₅	semidirect
420. #117	C₂×D₅	semidirect
654. C₅	#3546	semidirect

Maximal subgroups

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

subgroup	index
C₅×#542	2
#66067	2
#66059	2
#66045	2
#66043	2
#66012	2
#66008	2
#66002	2
#66000	2
#65988	2
#65978	2
#65965	2
#65964	2
#65963	2
#65943	2
#65933	2
#65911	2
#65902	2
#65888	2
#65887	2
#65862	2
#65859	2
#3546	5