Subgroups — #10618405

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×#541	C₂	1	1	yes	maximal, characteristic, complemented
2	#66059	C₂	1	1	yes	maximal, characteristic, complemented
3	#66058	C₂	1	1	yes	maximal, characteristic, complemented
4	#66045	C₂	1	2	yes	maximal, complemented
5	#66039	C₂	1	2	yes	maximal, complemented
6	#66038	C₂	1	2	yes	maximal, complemented
7	#66038	C₂	1	2	yes	maximal, complemented
8	#66034	C₂	1	2	yes	maximal, complemented
9	#66032	C₂	1	1	yes	maximal, characteristic, complemented
10	#66032	C₂	1	2	yes	maximal, complemented
11	#66029	C₂	1	2	yes	maximal, complemented
12	#66026	C₂	1	2	yes	maximal, complemented
13	#66025	C₂	1	1	yes	maximal, characteristic, complemented
14	#65967	C₂	1	1	yes	maximal, characteristic, complemented
15	#65965	C₂	1	1	yes	maximal, characteristic, complemented
16	#65964	C₂	1	1	yes	maximal, characteristic, complemented
17	#65964	C₂	1	1	yes	maximal, characteristic, complemented
18	#65919	C₂	1	1	yes	maximal, characteristic, complemented
19	#65911	C₂	1	1	yes	maximal, characteristic, complemented
20	#65910	C₂	1	1	yes	maximal, characteristic, complemented
21	#65902	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	1	yes	characteristic
25	C₂×#713	C₂²	1	1	yes	characteristic
26	C₂×#713	C₂²	1	1	yes	characteristic, complemented
27	C₂×Q₈×D₅	C₂²	1	1	yes	characteristic, complemented
28	C₂×#709	C₂²	1	1	yes	characteristic
29	C₂²×D₂₀	C₂²	1	1	yes	characteristic
30	C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
31	C₅×#126	C₂²	1	2	yes	—
32	C₅×#126	C₂²	1	2	yes	—
33	C₅×#125	C₂²	1	1	yes	characteristic, complemented
34	C₅×#125	C₂²	1	2	yes	complemented
35	C₅×#125	C₂²	1	2	yes	complemented
36	C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
37	C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
38	C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
39	C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
40	C₅×#117	C₂²	1	1	yes	characteristic
41	#4093	C₂²	1	1	yes	characteristic
42	#4093	C₂²	1	1	yes	characteristic
43	#4093	C₂²	1	1	yes	characteristic, complemented
44	#4090	C₂²	1	1	yes	characteristic, complemented
45	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic
46	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic
47	#4044	C₂²	1	1	yes	characteristic, complemented
48	#4044	C₂²	1	2	yes	complemented
49	#4044	C₂²	1	2	yes	complemented
50	#4043	C₂²	1	1	yes	characteristic, complemented
51	#4043	C₂²	1	2	yes	complemented
52	#4042	C₂²	1	2	yes	complemented
53	#4042	C₂²	1	2	yes	complemented
54	#4042	C₂²	1	1	yes	characteristic, complemented
55	#4042	C₂²	1	2	yes	complemented
56	#4042	C₂²	1	2	yes	complemented
57	#4041	C₂²	1	2	yes	—
58	#4041	C₂²	1	2	yes	—
59	#4041	C₂²	1	1	yes	characteristic
60	#4041	C₂²	1	1	yes	characteristic
61	#4041	C₂²	1	2	yes	—
62	#4041	C₂²	1	2	yes	—
63	#4041	C₂²	1	2	yes	complemented
64	#4041	C₂²	1	2	yes	complemented
65	#4041	C₂²	1	2	yes	complemented
66	#4041	C₂²	1	1	yes	characteristic, complemented
67	#4041	C₂²	1	2	yes	complemented
68	#4041	C₂²	1	2	yes	complemented
69	#4041	C₂²	1	2	yes	complemented
70	#4041	C₂²	1	2	yes	complemented
71	#4040	C₂²	1	2	yes	—
72	#4040	C₂²	1	2	yes	—
73	#4040	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	#4040	C₂²	1	2	yes	complemented
79	#4040	C₂²	1	2	yes	complemented
80	#4040	C₂²	1	2	yes	complemented
81	#4040	C₂²	1	2	yes	complemented
82	#4039	C₂²	1	1	yes	characteristic
83	#4039	C₂²	1	1	yes	characteristic
84	#4039	C₂²	1	2	yes	complemented
85	#4039	C₂²	1	2	yes	complemented
86	#4039	C₂²	1	1	yes	characteristic, complemented
87	#4039	C₂²	1	2	yes	complemented
88	#4039	C₂²	1	2	yes	complemented
89	#4038	C₂²	1	2	yes	complemented
90	D₅×C₄⋊C₄	C₂²	1	2	yes	complemented
91	#4035	C₂²	1	1	yes	characteristic, complemented
92	#4033	C₂²	1	1	yes	characteristic, complemented
93	#4031	C₂²	1	1	yes	characteristic
94	#4031	C₂²	1	2	yes	—
95	#4030	C₂²	1	1	yes	characteristic
96	#4030	C₂²	1	2	yes	—
97	#4030	C₂²	1	2	yes	—
98	#4029	C₂²	1	1	yes	characteristic
99	#4029	C₂²	1	2	yes	—
100	#4028	C₂²	1	2	yes	—
101	#4028	C₂²	1	2	yes	—
102	#4028	C₂²	1	2	yes	—
103	#4028	C₂²	1	2	yes	—
104	D₅×C₂²⋊C₄	C₂²	1	2	yes	—
105	D₅×C₂²⋊C₄	C₂²	1	2	yes	—
106	#4025	C₂²	1	1	yes	characteristic
107	#4022	C₂²	1	2	yes	complemented
108	#4021	C₂²	1	1	yes	characteristic
109	#4021	C₂²	1	1	yes	characteristic
110	#4021	C₂²	1	2	yes	complemented
111	#4021	C₂²	1	2	yes	complemented
112	#4020	C₂²	1	1	yes	characteristic
113	#4020	C₂²	1	1	yes	characteristic
114	#4020	C₂²	1	2	yes	complemented
115	C₄×D₂₀	C₂²	1	1	yes	characteristic, complemented
116	C₄×D₂₀	C₂²	1	2	yes	complemented
117	C₄×D₂₀	C₂²	1	2	yes	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	#3562	—	5	1	no	maximal, Sylow
124	C₂³×D₅	C₂³	1	2	yes	—
125	C₂×C₅×Q₈	C₂³	1	1	yes	characteristic
126	C₂×C₅×Q₈	C₂³	1	1	yes	characteristic
127	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
128	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
129	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
130	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
131	#713	—	4	2	no	—
132	#713	—	4	2	no	—
133	#713	—	4	2	no	—
134	Q₈×D₅	—	4	2	no	—
135	#709	—	4	2	no	—
136	C₂×D₂₀	—	4	2	no	—
137	C₂×D₂₀	C₂³	1	1	yes	characteristic
138	C₂×D₂₀	C₂³	1	1	yes	characteristic
139	C₂×D₂₀	C₂³	1	1	yes	characteristic
140	C₂×D₂₀	C₂³	1	2	yes	—
141	C₂×D₂₀	C₂³	1	2	yes	—
142	C₂×D₂₀	C₂³	1	2	yes	—
143	C₂×D₂₀	C₂³	1	2	yes	—
144	C₂×D₂₀	C₂³	1	2	yes	—
145	C₂×D₂₀	C₂³	1	2	yes	—
146	C₂×D₂₀	C₂³	1	1	yes	characteristic
147	C₂×D₂₀	C₂³	1	2	yes	—
148	C₂×D₂₀	C₂³	1	2	yes	—
149	C₂×D₂₀	C₂³	1	2	yes	—
150	C₂×D₂₀	C₂³	1	2	yes	—
151	C₂×D₂₀	C₂³	1	2	yes	—
152	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
153	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
154	C₂×C₄×D₅	C₂³	1	2	yes	—
155	C₂×C₄×D₅	C₂³	1	2	yes	—
156	C₂×C₄×D₅	C₂³	1	2	yes	—
157	C₂×C₄×D₅	C₂³	1	2	yes	—
158	C₂×C₄×D₅	C₂³	1	2	yes	—
159	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
160	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
161	C₂×C₄×D₅	C₂³	1	2	yes	—
162	C₂×C₄×D₅	C₂³	1	2	yes	—
163	C₂×C₄×D₅	C₂³	1	2	yes	—
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×C₄⋊C₄	C₂³	1	1	yes	characteristic
170	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
171	C₅×C₄⋊C₄	C₂³	1	2	yes	—
172	C₅×C₄⋊C₄	C₂³	1	2	yes	—
173	C₅×C₄⋊C₄	C₂³	1	2	yes	—
174	C₅×C₄⋊C₄	C₂³	1	2	yes	—
175	C₅×C₄⋊C₄	C₂³	1	2	yes	—
176	C₅×C₄⋊C₄	C₂³	1	2	yes	—
177	C₅×C₄⋊C₄	C₂³	1	2	yes	—
178	C₅×C₄⋊C₄	C₂³	1	2	yes	—
179	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
180	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
181	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
182	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
183	C₄²×C₅	C₂³	1	1	yes	characteristic
184	C₄²×C₅	C₂³	1	1	yes	characteristic
185	C₄²×C₅	C₂³	1	2	yes	—
186	C₄²×C₅	C₂³	1	2	yes	—
187	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
188	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
189	#685	C₂³	1	2	yes	—
190	#685	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	2	yes	—
195	#685	C₂³	1	1	yes	characteristic
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	#685	C₂³	1	2	yes	—
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	1	yes	characteristic
212	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
213	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
214	C₄⋊Dic₅	C₂³	1	2	yes	—
215	#683	C₂³	1	1	yes	characteristic
216	#683	C₂³	1	1	yes	characteristic
217	#683	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
223	#683	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	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	D₅	1	1	yes	characteristic, complemented
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	—	5	1	no	—
249	#532	—	5	1	no	—
250	#529	—	5	1	no	—
251	#529	—	5	1	no	—
252	C₂³×C₅	C₂⁴	1	1	yes	characteristic
253	C₂²×D₅	—	4	2	no	—
254	C₂²×D₅	—	4	2	no	—
255	C₂²×D₅	—	4	2	no	—
256	C₂²×D₅	C₂⁴	1	2	yes	—
257	C₂²×D₅	C₂⁴	1	2	yes	—
258	C₂²×D₅	C₂⁴	1	1	yes	characteristic
259	C₂²×D₅	C₂⁴	1	1	yes	characteristic
260	C₂²×D₅	C₂⁴	1	2	yes	—
261	C₅×Q₈	—	2	2	no	—
262	C₅×Q₈	—	2	2	no	—
263	C₂×C₄×C₅	—	2	2	no	—
264	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
265	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
266	C₂×C₄×C₅	C₂⁴	1	2	yes	—
267	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
268	C₂×C₄×C₅	C₂⁴	1	2	yes	—
269	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
270	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
271	C₂×C₄×C₅	C₂⁴	1	2	yes	—
272	C₂×C₄×C₅	C₂⁴	1	2	yes	—
273	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
274	C₂²⋊D₅	—	4	2	no	—
275	C₂²⋊D₅	—	4	1	no	—
276	C₂²⋊D₅	—	4	1	no	—
277	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
278	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
279	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
280	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
281	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
282	C₂×Dic₅	C₂⁴	1	2	yes	—
283	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
284	D₂₀	—	2	2	no	—
285	D₂₀	—	2	2	no	—
286	D₂₀	—	2	2	no	—
287	D₂₀	—	4	2	no	—
288	D₂₀	—	4	2	no	—
289	D₂₀	—	4	2	no	—
290	D₂₀	—	4	2	no	—
291	D₂₀	—	4	2	no	—
292	D₂₀	—	4	2	no	—
293	D₂₀	—	4	2	no	—
294	D₂₀	—	4	2	no	—
295	D₂₀	—	4	1	no	—
296	D₂₀	—	4	2	no	—
297	D₂₀	—	4	2	no	—
298	D₂₀	—	4	2	no	—
299	C₄×D₅	—	2	2	no	—
300	C₄×D₅	—	2	2	no	—
301	C₄×D₅	—	4	2	no	—
302	C₄×D₅	—	4	1	no	—
303	C₄×D₅	—	4	2	no	—
304	C₄×D₅	—	4	1	no	—
305	C₄×D₅	—	4	2	no	—
306	C₄×D₅	—	4	2	no	—
307	C₄×D₅	—	4	2	no	—
308	C₄×D₅	—	4	2	no	—
309	C₄×D₅	—	4	2	no	—
310	C₄×D₅	—	4	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	—	5	1	no	—
318	C₂²×Q₈	—	5	1	no	—
319	C₂²×D₄	—	5	1	no	—
320	C₄⋊Q₈	—	5	1	no	—
321	C₄⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
322	#127	—	5	1	no	—
323	#127	—	5	1	no	—
324	#127	—	5	2	no	—
325	#126	—	5	2	no	—
326	#126	—	5	1	no	—
327	#126	—	5	2	no	—
328	#126	—	5	1	no	—
329	#126	—	5	2	no	—
330	#126	C₂×D₅	1	2	yes	—
331	#126	C₂×D₅	1	2	yes	—
332	#125	—	5	1	no	—
333	#125	C₂×D₅	1	1	yes	characteristic, complemented
334	#125	C₂×D₅	1	2	yes	complemented
335	#125	C₂×D₅	1	2	yes	complemented
336	#124	—	5	1	no	—
337	#124	—	5	1	no	—
338	#124	—	5	1	no	—
339	#124	—	5	1	no	—
340	#124	—	5	2	no	—
341	#124	—	5	1	no	—
342	#124	—	5	1	no	—
343	#124	—	5	2	no	—
344	#124	—	5	2	no	—
345	#123	—	5	1	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	2	no	—
354	#123	—	5	2	no	—
355	#123	—	5	2	no	—
356	#123	—	5	1	no	—
357	#123	—	5	2	no	—
358	C₂²⋊Q₈	—	5	1	no	—
359	C₂²⋊Q₈	—	5	1	no	—
360	C₂²⋊Q₈	—	5	2	no	—
361	C₂²⋊Q₈	—	5	2	no	—
362	C₂²⋊Q₈	—	5	2	no	—
363	C₂²⋊Q₈	—	5	2	no	—
364	C₂²⋊Q₈	—	5	2	no	—
365	C₂²⋊Q₈	C₂×D₅	1	1	yes	characteristic
366	C₂²⋊Q₈	C₂×D₅	1	1	yes	characteristic
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	2	no	—
381	#121	—	5	1	no	—
382	#121	—	5	2	no	—
383	#121	—	5	2	no	—
384	#120	—	5	2	no	—
385	#120	—	5	2	no	—
386	#120	—	5	2	no	—
387	#120	—	5	2	no	—
388	C₄×Q₈	—	5	1	no	—
389	C₄×Q₈	—	5	1	no	—
390	C₄×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
391	C₄×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
392	C₄×D₄	—	5	1	no	—
393	C₄×D₄	—	5	1	no	—
394	C₄×D₄	—	5	2	no	—
395	C₄×D₄	—	5	1	no	—
396	C₄×D₄	—	5	2	no	—
397	C₄×D₄	—	5	2	no	—
398	C₄×D₄	—	5	1	no	—
399	C₄×D₄	—	5	1	no	—
400	C₄×D₄	—	5	2	no	—
401	C₄×D₄	—	5	1	no	—
402	C₄×D₄	—	5	2	no	—
403	C₄×D₄	—	5	2	no	—
404	C₄×D₄	—	5	2	no	—
405	#117	—	5	2	no	—
406	#117	—	5	1	no	—
407	#117	—	5	2	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	1	no	—
414	C₂²×C₅	—	2	1	no	—
415	C₂²×C₅	—	2	1	no	—
416	C₂²×C₅	C₂⁵	1	1	yes	characteristic
417	C₂×D₅	—	2	1	no	—
418	C₂×D₅	—	2	1	no	—
419	C₂×D₅	—	2	2	no	—
420	C₂×D₅	—	2	2	no	—
421	C₂×D₅	—	2	2	no	—
422	C₂×D₅	—	2	1	no	—
423	C₂×D₅	—	2	2	no	—
424	C₂×D₅	—	2	1	no	—
425	C₂×D₅	—	2	2	no	—
426	C₂×D₅	—	2	2	no	—
427	C₂×D₅	—	2	1	no	—
428	C₂×D₅	—	2	2	no	—
429	C₂×D₅	—	2	1	no	—
430	C₂×D₅	—	2	2	no	—
431	C₂×D₅	—	2	2	no	—
432	C₂×D₅	—	8	4	no	—
433	C₄×C₅	—	2	2	no	—
434	C₄×C₅	—	2	1	no	—
435	C₄×C₅	—	2	2	no	—
436	C₄×C₅	—	2	1	no	—
437	C₄×C₅	—	2	2	no	—
438	C₄×C₅	—	2	2	no	—
439	C₄×C₅	—	2	1	no	—
440	C₄×C₅	—	2	1	no	—
441	C₄×C₅	—	2	1	no	—
442	C₄×C₅	H(5,𝔽₂)	1	2	yes	—
443	Dic₅	—	2	2	no	—
444	Dic₅	—	2	1	no	—
445	Dic₅	—	2	1	no	—
446	Dic₅	—	2	1	no	—
447	Dic₅	—	2	1	no	—
448	Dic₅	—	2	1	no	—
449	Dic₅	—	2	1	no	—
450	C₂⁴	—	5	2	no	—
451	#41	—	20	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	2	no	—
458	C₂×Q₈	—	20	2	no	—
459	C₂×Q₈	C₂²×D₅	1	1	yes	characteristic
460	C₂×Q₈	C₂²×D₅	1	1	yes	characteristic
461	C₂×D₄	—	5	1	no	—
462	C₂×D₄	—	5	1	no	—
463	C₂×D₄	—	5	2	no	—
464	C₂×D₄	—	5	1	no	—
465	C₂×D₄	—	5	1	no	—
466	C₂×D₄	—	5	1	no	—
467	C₂×D₄	—	5	2	no	—
468	C₂×D₄	—	5	2	no	—
469	C₂×D₄	—	5	2	no	—
470	C₂×D₄	—	5	2	no	—
471	C₂×D₄	—	5	2	no	—
472	C₂×D₄	—	5	2	no	—
473	C₂×D₄	—	5	2	no	—
474	C₂×D₄	—	5	1	no	—
475	C₂×D₄	—	5	2	no	—
476	C₂×D₄	—	5	2	no	—
477	C₂×D₄	—	5	2	no	—
478	C₂×D₄	—	5	2	no	—
479	C₂×D₄	—	20	2	no	—
480	C₂²×C₄	—	5	1	no	—
481	C₂²×C₄	—	5	1	no	—
482	C₂²×C₄	—	5	1	no	—
483	C₂²×C₄	—	5	1	no	—
484	C₂²×C₄	—	5	2	no	—
485	C₂²×C₄	—	5	2	no	—
486	C₂²×C₄	—	5	2	no	—
487	C₂²×C₄	—	5	2	no	—
488	C₂²×C₄	—	5	2	no	—
489	C₂²×C₄	—	5	2	no	—
490	C₂²×C₄	—	5	2	no	—
491	C₂²×C₄	—	5	2	no	—
492	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
493	C₄⋊C₄	—	5	1	no	—
494	C₄⋊C₄	—	5	2	no	—
495	C₄⋊C₄	—	5	2	no	—
496	C₄⋊C₄	—	5	1	no	—
497	C₄⋊C₄	—	5	1	no	—
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	2	no	—
504	C₄⋊C₄	—	5	1	no	—
505	C₄⋊C₄	C₂²×D₅	1	2	yes	—
506	C₄⋊C₄	C₂²×D₅	1	2	yes	—
507	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
508	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
509	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
510	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
511	C₄⋊C₄	C₂²×D₅	1	2	yes	—
512	C₄⋊C₄	C₂²×D₅	1	2	yes	—
513	C₄⋊C₄	C₂²×D₅	1	2	yes	—
514	C₄⋊C₄	C₂²×D₅	1	2	yes	—
515	C₄⋊C₄	C₂²×D₅	1	2	yes	—
516	C₄⋊C₄	C₂²×D₅	1	2	yes	—
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	1	no	—
526	C₂²⋊C₄	—	5	1	no	—
527	C₂²⋊C₄	—	5	1	no	—
528	C₂²⋊C₄	—	5	1	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	2	no	—
534	C₂²⋊C₄	—	5	2	no	—
535	C₂²⋊C₄	—	5	2	no	—
536	C₂²⋊C₄	—	5	1	no	—
537	C₂²⋊C₄	—	5	2	no	—
538	C₂²⋊C₄	—	5	2	no	—
539	C₂²⋊C₄	—	5	2	no	—
540	C₂²⋊C₄	—	5	1	no	—
541	C₂²⋊C₄	—	5	2	no	—
542	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
543	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
544	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
545	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
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	C₂²×D₅	1	1	yes	characteristic
552	C₄²	C₂²×D₅	1	2	yes	—
553	C₄²	C₂²×D₅	1	1	yes	characteristic
554	C₄²	C₂²×D₅	1	2	yes	—
555	C₂×C₅	—	4	1	no	—
556	C₂×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
557	C₂×C₅	#585	1	1	yes	characteristic
558	C₂×C₅	#585	1	1	yes	characteristic
559	D₅	—	4	1	no	—
560	D₅	—	4	1	no	—
561	D₅	—	4	2	no	—
562	D₅	—	4	2	no	—
563	D₅	—	4	2	no	—
564	C₂³	—	5	2	no	—
565	C₂³	—	5	2	no	—
566	C₂³	—	5	1	no	—
567	C₂³	—	5	1	no	—
568	C₂³	—	5	2	no	—
569	C₂³	—	20	2	no	—
570	C₂³	—	20	2	no	—
571	C₂³	—	20	2	no	—
572	C₂³	C₂³×D₅	1	1	yes	characteristic
573	Q₈	—	2	2	no	—
574	Q₈	—	2	2	no	—
575	Q₈	—	10	2	no	—
576	Q₈	—	20	2	no	—
577	Q₈	—	20	1	no	—
578	D₄	—	10	2	no	—
579	D₄	—	10	2	no	—
580	D₄	—	10	2	no	—
581	D₄	—	20	2	no	—
582	D₄	—	20	2	no	—
583	D₄	—	20	2	no	—
584	D₄	—	20	2	no	—
585	D₄	—	20	2	no	—
586	D₄	—	20	2	no	—
587	D₄	—	20	2	no	—
588	D₄	—	20	2	no	—
589	D₄	—	20	2	no	—
590	D₄	—	20	2	no	—
591	D₄	—	20	1	no	—
592	D₄	—	20	2	no	—
593	D₄	—	20	2	no	—
594	D₄	—	20	1	no	—
595	D₄	—	20	1	no	—
596	C₂×C₄	—	2	2	no	—
597	C₂×C₄	—	5	1	no	—
598	C₂×C₄	—	5	1	no	—
599	C₂×C₄	—	5	1	no	—
600	C₂×C₄	—	5	1	no	—
601	C₂×C₄	—	5	1	no	—
602	C₂×C₄	—	5	2	no	—
603	C₂×C₄	—	5	1	no	—
604	C₂×C₄	—	10	2	no	—
605	C₂×C₄	—	10	2	no	—
606	C₂×C₄	—	20	2	no	—
607	C₂×C₄	—	20	2	no	—
608	C₂×C₄	—	20	2	no	—
609	C₂×C₄	—	20	2	no	—
610	C₂×C₄	—	20	2	no	—
611	C₂×C₄	—	20	2	no	—
612	C₂×C₄	—	20	2	no	—
613	C₂×C₄	—	20	1	no	—
614	C₂×C₄	—	20	2	no	—
615	C₂×C₄	—	20	1	no	—
616	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
617	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
618	C₂×C₄	C₂³×D₅	1	2	yes	—
619	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
620	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
621	C₂×C₄	C₂³×D₅	1	2	yes	—
622	C₂×C₄	C₂³×D₅	1	2	yes	—
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	1	no	—
629	C₂²	—	2	1	no	—
630	C₂²	—	10	1	no	—
631	C₂²	—	10	1	no	—
632	C₂²	—	10	2	no	—
633	C₂²	—	10	2	no	—
634	C₂²	—	10	2	no	—
635	C₂²	—	10	1	no	—
636	C₂²	—	10	2	no	—
637	C₂²	—	10	1	no	—
638	C₂²	—	10	2	no	—
639	C₂²	—	10	2	no	—
640	C₂²	—	10	1	no	—
641	C₂²	—	10	2	no	—
642	C₂²	—	10	1	no	—
643	C₂²	—	10	2	no	—
644	C₂²	—	10	2	no	—
645	C₂²	—	40	4	no	—
646	C₂²	C₂⁴×D₅	1	1	yes	characteristic
647	C₄	—	2	1	no	—
648	C₄	—	2	2	no	—
649	C₄	—	2	2	no	—
650	C₄	—	2	2	no	—
651	C₄	—	2	1	no	—
652	C₄	—	2	2	no	—
653	C₄	—	2	1	no	—
654	C₄	—	2	1	no	—
655	C₄	—	2	1	no	—
656	C₄	—	10	1	no	—
657	C₄	—	10	1	no	—
658	C₄	—	10	2	no	—
659	C₄	—	10	1	no	—
660	C₄	—	10	1	no	—
661	C₄	—	10	1	no	—
662	C₄	—	10	1	no	—
663	C₄	#4149	1	2	yes	—
664	C₂	—	4	1	no	—
665	C₂	—	20	2	no	—
666	C₂	—	20	2	no	—
667	C₂	—	20	1	no	—
668	C₂	—	20	1	no	—
669	C₂	—	20	2	no	—
670	C₂	C₂×#4149	1	1	yes	characteristic
671	C₂	#66287	1	1	yes	characteristic
672	C₂	#66287	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅
commutator, socle, cosocle	C₂²×C₅	C₂⁵
Fitting	C₅×#541	C₂
hypercenter	#541	D₅
hypocenter	C₅	#3562
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ #541

Complements

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

N	H ≅ G/N	type
1. C₅×#541	C₂	semidirect
2. #66059	C₂	semidirect
3. #66058	C₂	semidirect
4. #66045	C₂	semidirect
5. #66039	C₂	semidirect
6. #66038	C₂	semidirect
7. #66038	C₂	semidirect
8. #66034	C₂	semidirect
9. #66032	C₂	semidirect
10. #66032	C₂	semidirect
11. #66029	C₂	semidirect
12. #66026	C₂	semidirect
13. #66025	C₂	semidirect
14. #65967	C₂	semidirect
15. #65965	C₂	semidirect
16. #65964	C₂	semidirect
17. #65964	C₂	semidirect
18. #65919	C₂	semidirect
19. #65911	C₂	semidirect
20. #65910	C₂	semidirect
21. #65902	C₂	semidirect
22. #65862	C₂	semidirect
23. #65859	C₂	semidirect
26. C₂×#713	C₂²	semidirect
27. C₂×Q₈×D₅	C₂²	semidirect
30. C₅×C₄⋊Q₈	C₂²	semidirect
33. C₅×#125	C₂²	semidirect
34. C₅×#125	C₂²	semidirect
35. C₅×#125	C₂²	semidirect
38. C₄×C₅×Q₈	C₂²	semidirect
39. C₄×C₅×Q₈	C₂²	semidirect
43. #4093	C₂²	semidirect
44. #4090	C₂²	semidirect
47. #4044	C₂²	semidirect
48. #4044	C₂²	semidirect
49. #4044	C₂²	semidirect
50. #4043	C₂²	semidirect
51. #4043	C₂²	semidirect
52. #4042	C₂²	semidirect
53. #4042	C₂²	semidirect
54. #4042	C₂²	semidirect
55. #4042	C₂²	semidirect
56. #4042	C₂²	semidirect
63. #4041	C₂²	semidirect
64. #4041	C₂²	semidirect
65. #4041	C₂²	semidirect
66. #4041	C₂²	semidirect
67. #4041	C₂²	semidirect
68. #4041	C₂²	semidirect
69. #4041	C₂²	semidirect
70. #4041	C₂²	semidirect
73. #4040	C₂²	semidirect
74. #4040	C₂²	semidirect
75. #4040	C₂²	semidirect
76. #4040	C₂²	semidirect
77. #4040	C₂²	semidirect
78. #4040	C₂²	semidirect
79. #4040	C₂²	semidirect
80. #4040	C₂²	semidirect
81. #4040	C₂²	semidirect
84. #4039	C₂²	semidirect
85. #4039	C₂²	semidirect
86. #4039	C₂²	semidirect
87. #4039	C₂²	semidirect
88. #4039	C₂²	semidirect
89. #4038	C₂²	semidirect
90. D₅×C₄⋊C₄	C₂²	semidirect
91. #4035	C₂²	semidirect
92. #4033	C₂²	semidirect
107. #4022	C₂²	semidirect
110. #4021	C₂²	semidirect
111. #4021	C₂²	semidirect
114. #4020	C₂²	semidirect
115. C₄×D₂₀	C₂²	semidirect
116. C₄×D₂₀	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
241. #541	D₅	semidirect
321. C₄⋊Q₈	C₂×D₅	semidirect
333. #125	C₂×D₅	semidirect
334. #125	C₂×D₅	semidirect
335. #125	C₂×D₅	semidirect
390. C₄×Q₈	C₂×D₅	semidirect
391. C₄×Q₈	C₂×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×#541	2
#66059	2
#66058	2
#66045	2
#66039	2
#66038	2
#66034	2
#66032	2
#66029	2
#66026	2
#66025	2
#65967	2
#65965	2
#65964	2
#65919	2
#65911	2
#65910	2
#65902	2
#65862	2
#65859	2
#3562	5