Subgroups — #10618075

Order 640.

1150 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#529	C₂	1	1	yes	maximal, characteristic, complemented
2	#66038	C₂	1	4	yes	maximal, complemented
3	#66029	C₂	1	2	yes	maximal, complemented
4	#66010	C₂	1	2	yes	maximal, complemented
5	#66000	C₂	1	4	yes	maximal, complemented
6	#65963	C₂	1	2	yes	maximal, complemented
7	#65941	C₂	1	2	yes	maximal, complemented
8	#65918	C₂	1	1	yes	maximal, characteristic, complemented
9	#65911	C₂	1	1	yes	maximal, characteristic, complemented
10	#65887	C₂	1	2	yes	maximal, complemented
11	#65885	C₂	1	1	yes	maximal, characteristic, complemented
12	#65884	C₂	1	2	yes	maximal, complemented
13	D₄×D₂₀	C₂	1	1	yes	maximal, characteristic, complemented
14	#65868	C₂	1	2	yes	maximal, complemented
15	#65859	C₂	1	2	yes	maximal, complemented
16	#65811	C₂	1	1	yes	maximal, characteristic, complemented
17	#65811	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#713	C₂²	1	2	yes	complemented
19	C₂×D₄×D₅	C₂²	1	2	yes	—
20	C₂×#709	C₂²	1	2	yes	complemented
21	C₂×#709	C₂²	1	2	yes	complemented
22	C₂×#709	C₂²	1	2	yes	complemented
23	C₂²×D₂₀	C₂²	1	2	yes	—
24	C₅×#126	C₂²	1	2	yes	complemented
25	C₅×#125	C₂²	1	1	yes	characteristic, complemented
26	C₅×#124	C₂²	1	1	yes	characteristic
27	C₅×#123	C₂²	1	2	yes	complemented
28	C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
29	C₅×#121	C₂²	1	1	yes	characteristic
30	C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
31	C₄×C₅×D₄	C₂²	1	1	yes	characteristic
32	C₄×C₅×D₄	C₂²	1	2	yes	complemented
33	C₅×#117	C₂²	1	2	yes	complemented
34	C₂×C₄²×C₅	C₂²	1	1	yes	characteristic, complemented
35	#4092	C₂²	1	2	yes	complemented
36	#4086	C₂²	1	4	yes	complemented
37	#4084	C₂²	1	2	yes	—
38	#4083	C₂²	1	4	yes	complemented
39	#4076	C₂²	1	1	yes	characteristic
40	#4076	C₂²	1	2	yes	—
41	#4076	C₂²	1	1	yes	characteristic, complemented
42	#4076	C₂²	1	2	yes	complemented
43	#4076	C₂²	1	2	yes	complemented
44	#4076	C₂²	1	2	yes	complemented
45	#4070	C₂²	1	2	yes	complemented
46	#4044	C₂²	1	4	yes	complemented
47	#4044	C₂²	1	4	yes	complemented
48	#4042	C₂²	1	4	yes	complemented
49	#4041	C₂²	1	2	yes	—
50	#4041	C₂²	1	4	yes	complemented
51	#4041	C₂²	1	4	yes	complemented
52	#4041	C₂²	1	2	yes	complemented
53	#4041	C₂²	1	4	yes	complemented
54	#4040	C₂²	1	4	yes	complemented
55	#4039	C₂²	1	4	yes	complemented
56	#4038	C₂²	1	2	yes	complemented
57	D₅×C₄⋊C₄	C₂²	1	2	yes	complemented
58	#4031	C₂²	1	4	yes	complemented
59	#4030	C₂²	1	4	yes	complemented
60	#4030	C₂²	1	4	yes	complemented
61	#4030	C₂²	1	4	yes	complemented
62	#4029	C₂²	1	4	yes	complemented
63	#4029	C₂²	1	4	yes	complemented
64	#4028	C₂²	1	4	yes	—
65	#4028	C₂²	1	4	yes	complemented
66	#4028	C₂²	1	4	yes	complemented
67	D₅×C₂²⋊C₄	C₂²	1	4	yes	complemented
68	#4021	C₂²	1	2	yes	—
69	#4021	C₂²	1	2	yes	complemented
70	#4021	C₂²	1	2	yes	complemented
71	#4020	C₂²	1	1	yes	characteristic
72	#4020	C₂²	1	1	yes	characteristic
73	#4020	C₂²	1	2	yes	complemented
74	C₄×D₂₀	C₂²	1	1	yes	characteristic
75	C₄×D₂₀	C₂²	1	1	yes	characteristic, complemented
76	C₄×D₂₀	C₂²	1	2	yes	complemented
77	C₄×D₂₀	C₂²	1	2	yes	complemented
78	C₄×D₂₀	C₂²	1	2	yes	complemented
79	C₄×D₂₀	C₂²	1	2	yes	complemented
80	#4015	C₂²	1	1	yes	characteristic, complemented
81	#4015	C₂²	1	1	yes	characteristic, complemented
82	C₄×Dic₁₀	C₂²	1	2	yes	complemented
83	#3546	—	5	1	no	maximal, Sylow
84	C₂³×D₅	C₂³	1	4	yes	—
85	C₂×C₅×Q₈	C₂³	1	1	yes	characteristic
86	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
87	C₂×C₅×D₄	C₂³	1	2	yes	—
88	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
89	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
90	C₂²×C₄×C₅	C₂³	1	2	yes	—
91	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
92	C₂×C₂²⋊D₅	C₂³	1	4	yes	—
93	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
94	C₂×C₂²⋊D₅	C₂³	1	4	yes	—
95	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
96	C₂×C₂²⋊D₅	C₂³	1	4	yes	—
97	#713	—	4	4	no	—
98	D₄×D₅	—	4	4	no	—
99	#709	—	4	4	no	—
100	#709	—	4	4	no	—
101	#709	—	4	4	no	—
102	C₂×D₂₀	—	4	4	no	—
103	C₂×D₂₀	C₂³	1	1	yes	characteristic
104	C₂×D₂₀	C₂³	1	2	yes	—
105	C₂×D₂₀	C₂³	1	1	yes	characteristic
106	C₂×D₂₀	C₂³	1	2	yes	—
107	C₂×D₂₀	C₂³	1	4	yes	—
108	C₂×D₂₀	C₂³	1	2	yes	—
109	C₂×D₂₀	C₂³	1	4	yes	—
110	C₂×D₂₀	C₂³	1	2	yes	—
111	C₂×D₂₀	C₂³	1	2	yes	—
112	C₂×D₂₀	C₂³	1	4	yes	—
113	C₂×C₄×D₅	C₂³	1	2	yes	—
114	C₂×C₄×D₅	C₂³	1	2	yes	—
115	C₂×C₄×D₅	C₂³	1	4	yes	—
116	C₂×C₄×D₅	C₂³	1	4	yes	—
117	C₂×C₄×D₅	C₂³	1	4	yes	—
118	C₂×Dic₁₀	C₂³	1	2	yes	—
119	C₂×Dic₁₀	C₂³	1	2	yes	—
120	C₅×C₄⋊C₄	C₂³	1	2	yes	—
121	C₅×C₄⋊C₄	C₂³	1	2	yes	—
122	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
123	C₅×C₄⋊C₄	C₂³	1	2	yes	—
124	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
125	C₅×C₄⋊C₄	C₂³	1	2	yes	—
126	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
127	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
128	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
129	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
130	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
131	C₄²×C₅	C₂³	1	1	yes	characteristic
132	C₄²×C₅	C₂³	1	1	yes	characteristic
133	C₄²×C₅	C₂³	1	1	yes	characteristic
134	C₄²×C₅	C₂³	1	1	yes	characteristic
135	C₄²×C₅	C₂³	1	2	yes	—
136	C₂²⋊Dic₅	C₂³	1	4	yes	—
137	#685	C₂³	1	2	yes	—
138	#685	C₂³	1	2	yes	—
139	#685	C₂³	1	4	yes	—
140	#685	C₂³	1	4	yes	—
141	#685	C₂³	1	2	yes	—
142	#685	C₂³	1	2	yes	—
143	#685	C₂³	1	4	yes	—
144	#685	C₂³	1	4	yes	—
145	#685	C₂³	1	4	yes	—
146	#685	C₂³	1	4	yes	—
147	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
148	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
149	C₄⋊Dic₅	C₂³	1	2	yes	—
150	C₄⋊Dic₅	C₂³	1	2	yes	—
151	C₄⋊Dic₅	C₂³	1	2	yes	—
152	#683	C₂³	1	4	yes	—
153	#683	C₂³	1	4	yes	—
154	C₄×Dic₅	C₂³	1	4	yes	—
155	#560	—	5	4	no	—
156	#556	—	5	1	no	—
157	#553	—	5	2	no	—
158	#550	—	5	1	no	—
159	#550	—	5	2	no	—
160	#547	—	5	1	no	—
161	#546	—	5	2	no	—
162	#546	—	5	2	no	—
163	D₄²	—	5	1	no	—
164	#542	—	5	2	no	—
165	#538	—	5	4	no	—
166	#537	—	5	2	no	—
167	#535	—	5	2	no	—
168	#535	—	5	2	no	—
169	#532	—	5	1	no	—
170	#532	—	5	1	no	—
171	#529	D₅	1	1	yes	characteristic, complemented
172	C₂³×C₅	C₂⁴	1	2	yes	—
173	C₂³×C₅	C₂⁴	1	1	yes	characteristic
174	C₂²×D₅	—	4	4	no	—
175	C₂²×D₅	—	4	4	no	—
176	C₂²×D₅	—	4	4	no	—
177	C₂²×D₅	C₂⁴	1	2	yes	—
178	C₂²×D₅	C₂⁴	1	4	yes	—
179	C₂²×D₅	C₂⁴	1	2	yes	—
180	C₅×Q₈	—	2	2	no	—
181	C₅×D₄	—	2	2	no	—
182	C₅×D₄	—	4	2	no	—
183	C₂×C₄×C₅	—	2	4	no	—
184	C₂×C₄×C₅	—	2	2	no	—
185	C₂×C₄×C₅	—	2	2	no	—
186	C₂×C₄×C₅	—	4	1	no	—
187	C₂×C₄×C₅	C₂⁴	1	2	yes	—
188	C₂×C₄×C₅	C₂⁴	1	2	yes	—
189	C₂×C₄×C₅	C₂⁴	1	2	yes	—
190	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
191	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
192	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
193	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
194	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
195	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
196	C₂²⋊D₅	—	4	4	no	—
197	C₂²⋊D₅	—	4	4	no	—
198	C₂²⋊D₅	—	4	2	no	—
199	C₂²⋊D₅	—	4	2	no	—
200	C₂²⋊D₅	—	4	4	no	—
201	C₂×Dic₅	C₂⁴	1	2	yes	—
202	C₂×Dic₅	C₂⁴	1	4	yes	—
203	C₂×Dic₅	C₂⁴	1	2	yes	—
204	D₂₀	—	2	2	no	—
205	D₂₀	—	2	4	no	—
206	D₂₀	—	2	2	no	—
207	D₂₀	—	2	4	no	—
208	D₂₀	—	4	4	no	—
209	D₂₀	—	4	2	no	—
210	D₂₀	—	4	2	no	—
211	D₂₀	—	4	4	no	—
212	D₂₀	—	4	2	no	—
213	D₂₀	—	4	4	no	—
214	C₄×D₅	—	2	4	no	—
215	C₄×D₅	—	2	4	no	—
216	C₄×D₅	—	4	4	no	—
217	C₄×D₅	—	4	4	no	—
218	C₄×D₅	—	4	4	no	—
219	Dic₁₀	—	2	4	no	—
220	Dic₁₀	—	4	2	no	—
221	C₂×#41	—	5	2	no	—
222	C₂×#41	—	5	2	no	—
223	C₂×#41	—	5	2	no	—
224	C₂×#41	—	5	2	no	—
225	C₂²×D₄	—	5	2	no	—
226	C₂²×D₄	—	5	2	no	—
227	C₄⋊Q₈	—	5	1	no	—
228	C₄⋊Q₈	—	5	1	no	—
229	#127	—	5	4	no	—
230	#127	—	5	1	no	—
231	#127	—	5	1	no	—
232	#127	—	5	2	no	—
233	#126	—	5	4	no	—
234	#126	—	5	4	no	—
235	#126	C₂×D₅	1	2	yes	complemented
236	#125	C₂×D₅	1	1	yes	characteristic, complemented
237	#124	—	5	4	no	—
238	#124	—	5	2	no	—
239	#124	—	5	2	no	—
240	#124	—	5	2	no	—
241	#124	C₂×D₅	1	1	yes	characteristic
242	#123	—	5	4	no	—
243	#123	—	5	4	no	—
244	#123	—	5	4	no	—
245	#123	C₂×D₅	1	2	yes	complemented
246	C₂²⋊Q₈	—	5	2	no	—
247	C₂²⋊Q₈	—	5	2	no	—
248	C₂²⋊Q₈	—	5	4	no	—
249	C₂²⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
250	#121	—	5	2	no	—
251	#121	—	5	2	no	—
252	#121	—	5	1	no	—
253	#121	—	5	1	no	—
254	#121	—	5	2	no	—
255	#121	—	5	2	no	—
256	#121	—	5	2	no	—
257	#121	—	5	4	no	—
258	#121	—	5	2	no	—
259	#121	—	5	4	no	—
260	#121	—	5	2	no	—
261	#121	—	5	4	no	—
262	#121	—	5	4	no	—
263	#121	—	5	4	no	—
264	#121	—	5	4	no	—
265	#121	C₂×D₅	1	1	yes	characteristic
266	#120	—	5	4	no	—
267	#120	—	5	4	no	—
268	#120	—	5	4	no	—
269	#120	—	5	4	no	—
270	C₄×Q₈	—	5	2	no	—
271	C₄×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
272	C₄×D₄	—	5	4	no	—
273	C₄×D₄	—	5	2	no	—
274	C₄×D₄	—	5	1	no	—
275	C₄×D₄	—	5	2	no	—
276	C₄×D₄	—	5	2	no	—
277	C₄×D₄	—	5	1	no	—
278	C₄×D₄	—	5	2	no	—
279	C₄×D₄	C₂×D₅	1	1	yes	characteristic
280	C₄×D₄	C₂×D₅	1	2	yes	complemented
281	#117	—	5	2	no	—
282	#117	C₂×D₅	1	2	yes	complemented
283	C₂×C₄⋊C₄	—	5	2	no	—
284	C₂×C₂²⋊C₄	—	5	4	no	—
285	C₂×C₄²	C₂×D₅	1	1	yes	characteristic, complemented
286	C₂²×C₅	—	2	1	no	—
287	C₂²×C₅	—	2	1	no	—
288	C₂²×C₅	—	2	2	no	—
289	C₂²×C₅	—	2	2	no	—
290	C₂²×C₅	—	2	1	no	—
291	C₂²×C₅	—	2	2	no	—
292	C₂²×C₅	C₂⁵	1	1	yes	characteristic
293	C₂×D₅	—	2	2	no	—
294	C₂×D₅	—	2	2	no	—
295	C₂×D₅	—	2	2	no	—
296	C₂×D₅	—	2	4	no	—
297	C₂×D₅	—	2	4	no	—
298	C₂×D₅	—	2	2	no	—
299	C₂×D₅	—	2	2	no	—
300	C₂×D₅	—	2	4	no	—
301	C₂×D₅	—	2	2	no	—
302	C₂×D₅	—	8	8	no	—
303	C₄×C₅	—	2	1	no	—
304	C₄×C₅	—	2	1	no	—
305	C₄×C₅	—	2	2	no	—
306	C₄×C₅	—	2	2	no	—
307	C₄×C₅	—	2	1	no	—
308	C₄×C₅	—	2	1	no	—
309	C₄×C₅	—	2	2	no	—
310	C₄×C₅	H(5,𝔽₂)	1	2	yes	—
311	C₄×C₅	H(5,𝔽₂)	1	2	yes	—
312	Dic₅	—	2	4	no	—
313	Dic₅	—	2	2	no	—
314	Dic₅	—	2	2	no	—
315	C₂⁴	—	5	4	no	—
316	#41	—	20	4	no	—
317	#41	—	20	4	no	—
318	#41	—	20	4	no	—
319	#41	—	20	4	no	—
320	C₂×Q₈	—	5	2	no	—
321	C₂×Q₈	—	5	2	no	—
322	C₂×Q₈	C₂²×D₅	1	1	yes	characteristic
323	C₂×D₄	—	5	2	no	—
324	C₂×D₄	—	5	4	no	—
325	C₂×D₄	—	5	4	no	—
326	C₂×D₄	—	5	4	no	—
327	C₂×D₄	—	5	2	no	—
328	C₂×D₄	—	5	2	no	—
329	C₂×D₄	—	5	1	no	—
330	C₂×D₄	—	5	2	no	—
331	C₂×D₄	—	5	1	no	—
332	C₂×D₄	—	5	2	no	—
333	C₂×D₄	—	5	2	no	—
334	C₂×D₄	—	5	4	no	—
335	C₂×D₄	—	5	2	no	—
336	C₂×D₄	—	5	4	no	—
337	C₂×D₄	—	5	4	no	—
338	C₂×D₄	—	20	4	no	—
339	C₂×D₄	—	20	4	no	—
340	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
341	C₂×D₄	C₂²×D₅	1	2	yes	—
342	C₂²×C₄	—	5	2	no	—
343	C₂²×C₄	—	5	2	no	—
344	C₂²×C₄	—	5	4	no	—
345	C₂²×C₄	—	5	4	no	—
346	C₂²×C₄	—	5	4	no	—
347	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
348	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
349	C₂²×C₄	C₂²×D₅	1	2	yes	—
350	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
351	C₄⋊C₄	—	5	2	no	—
352	C₄⋊C₄	—	5	4	no	—
353	C₄⋊C₄	—	5	1	no	—
354	C₄⋊C₄	—	5	1	no	—
355	C₄⋊C₄	—	5	2	no	—
356	C₄⋊C₄	—	5	2	no	—
357	C₄⋊C₄	—	5	4	no	—
358	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
359	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
360	C₄⋊C₄	C₂²×D₅	1	2	yes	—
361	C₄⋊C₄	C₂²×D₅	1	2	yes	—
362	C₄⋊C₄	C₂²×D₅	1	2	yes	—
363	C₄⋊C₄	C₂²×D₅	1	2	yes	—
364	C₂²⋊C₄	—	5	4	no	—
365	C₂²⋊C₄	—	5	2	no	—
366	C₂²⋊C₄	—	5	4	no	—
367	C₂²⋊C₄	—	5	4	no	—
368	C₂²⋊C₄	—	5	2	no	—
369	C₂²⋊C₄	—	5	2	no	—
370	C₂²⋊C₄	—	5	4	no	—
371	C₂²⋊C₄	—	5	4	no	—
372	C₂²⋊C₄	—	5	4	no	—
373	C₂²⋊C₄	—	5	4	no	—
374	C₂²⋊C₄	—	5	2	no	—
375	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
376	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
377	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
378	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
379	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
380	C₄²	—	5	4	no	—
381	C₄²	C₂²×D₅	1	1	yes	characteristic
382	C₄²	C₂²×D₅	1	1	yes	characteristic
383	C₄²	C₂²×D₅	1	1	yes	characteristic
384	C₄²	C₂²×D₅	1	1	yes	characteristic
385	C₄²	C₂²×D₅	1	2	yes	—
386	C₂×C₅	—	4	2	no	—
387	C₂×C₅	—	4	1	no	—
388	C₂×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
389	C₂×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
390	C₂×C₅	#585	1	1	yes	characteristic
391	D₅	—	4	2	no	—
392	D₅	—	4	4	no	—
393	D₅	—	4	2	no	—
394	C₂³	—	5	2	no	—
395	C₂³	—	5	4	no	—
396	C₂³	—	5	2	no	—
397	C₂³	—	20	4	no	—
398	C₂³	—	20	4	no	—
399	C₂³	—	20	4	no	—
400	C₂³	C₂³×D₅	1	2	yes	—
401	C₂³	C₂³×D₅	1	1	yes	characteristic
402	Q₈	—	2	2	no	—
403	Q₈	—	10	4	no	—
404	Q₈	—	20	2	no	—
405	D₄	—	2	2	no	—
406	D₄	—	4	2	no	—
407	D₄	—	10	2	no	—
408	D₄	—	10	4	no	—
409	D₄	—	10	4	no	—
410	D₄	—	10	2	no	—
411	D₄	—	20	4	no	—
412	D₄	—	20	2	no	—
413	D₄	—	20	4	no	—
414	D₄	—	20	2	no	—
415	D₄	—	20	2	no	—
416	D₄	—	20	4	no	—
417	D₄	—	20	4	no	—
418	D₄	—	20	2	no	—
419	D₄	—	20	2	no	—
420	D₄	—	20	4	no	—
421	D₄	—	20	4	no	—
422	C₂×C₄	—	2	4	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	5	2	no	—
427	C₂×C₄	—	5	4	no	—
428	C₂×C₄	—	5	2	no	—
429	C₂×C₄	—	10	4	no	—
430	C₂×C₄	—	10	4	no	—
431	C₂×C₄	—	20	4	no	—
432	C₂×C₄	—	20	4	no	—
433	C₂×C₄	—	20	4	no	—
434	C₂×C₄	C₂³×D₅	1	2	yes	—
435	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
436	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
437	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
438	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
439	C₂×C₄	C₂³×D₅	1	2	yes	—
440	C₂×C₄	C₂³×D₅	1	2	yes	—
441	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
442	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
443	C₅	#3546	1	1	yes	characteristic, complemented, Sylow
444	C₂²	—	2	1	no	—
445	C₂²	—	2	1	no	—
446	C₂²	—	2	2	no	—
447	C₂²	—	2	2	no	—
448	C₂²	—	2	1	no	—
449	C₂²	—	2	2	no	—
450	C₂²	—	10	2	no	—
451	C₂²	—	10	2	no	—
452	C₂²	—	10	2	no	—
453	C₂²	—	10	4	no	—
454	C₂²	—	10	4	no	—
455	C₂²	—	10	2	no	—
456	C₂²	—	10	2	no	—
457	C₂²	—	10	4	no	—
458	C₂²	—	10	2	no	—
459	C₂²	—	40	8	no	—
460	C₂²	C₂⁴×D₅	1	1	yes	characteristic
461	C₄	—	2	1	no	—
462	C₄	—	2	2	no	—
463	C₄	—	2	1	no	—
464	C₄	—	2	2	no	—
465	C₄	—	2	1	no	—
466	C₄	—	2	1	no	—
467	C₄	—	2	2	no	—
468	C₄	—	10	2	no	—
469	C₄	—	10	2	no	—
470	C₄	—	10	4	no	—
471	C₄	#4149	1	2	yes	—
472	C₄	#4149	1	2	yes	—
473	C₂	—	4	2	no	—
474	C₂	—	4	1	no	—
475	C₂	—	20	2	no	—
476	C₂	—	20	4	no	—
477	C₂	—	20	2	no	—
478	C₂	C₂×#4149	1	1	yes	characteristic
479	C₂	C₂×#4149	1	1	yes	characteristic
480	C₂	#66283	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅
commutator, socle, cosocle	C₂²×C₅	C₂⁵
Fitting	C₅×#529	C₂
hypercenter	#529	D₅
hypocenter	C₅	#3546
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ #529

Complements

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

N	H ≅ G/N	type
1. C₅×#529	C₂	semidirect
2. #66038	C₂	semidirect
3. #66029	C₂	semidirect
4. #66010	C₂	semidirect
5. #66000	C₂	semidirect
6. #65963	C₂	semidirect
7. #65941	C₂	semidirect
8. #65918	C₂	semidirect
9. #65911	C₂	semidirect
10. #65887	C₂	semidirect
11. #65885	C₂	semidirect
12. #65884	C₂	semidirect
13. D₄×D₂₀	C₂	semidirect
14. #65868	C₂	semidirect
15. #65859	C₂	semidirect
16. #65811	C₂	semidirect
17. #65811	C₂	semidirect
18. C₂×#713	C₂²	semidirect
20. C₂×#709	C₂²	semidirect
21. C₂×#709	C₂²	semidirect
22. C₂×#709	C₂²	semidirect
24. C₅×#126	C₂²	semidirect
25. C₅×#125	C₂²	semidirect
27. C₅×#123	C₂²	semidirect
28. C₅×C₂²⋊Q₈	C₂²	semidirect
30. C₄×C₅×Q₈	C₂²	semidirect
32. C₄×C₅×D₄	C₂²	semidirect
33. C₅×#117	C₂²	semidirect
34. C₂×C₄²×C₅	C₂²	semidirect
35. #4092	C₂²	semidirect
36. #4086	C₂²	semidirect
38. #4083	C₂²	semidirect
41. #4076	C₂²	semidirect
42. #4076	C₂²	semidirect
43. #4076	C₂²	semidirect
44. #4076	C₂²	semidirect
45. #4070	C₂²	semidirect
46. #4044	C₂²	semidirect
47. #4044	C₂²	semidirect
48. #4042	C₂²	semidirect
50. #4041	C₂²	semidirect
51. #4041	C₂²	semidirect
52. #4041	C₂²	semidirect
53. #4041	C₂²	semidirect
54. #4040	C₂²	semidirect
55. #4039	C₂²	semidirect
56. #4038	C₂²	semidirect
57. D₅×C₄⋊C₄	C₂²	semidirect
58. #4031	C₂²	semidirect
59. #4030	C₂²	semidirect
60. #4030	C₂²	semidirect
61. #4030	C₂²	semidirect
62. #4029	C₂²	semidirect
63. #4029	C₂²	semidirect
65. #4028	C₂²	semidirect
66. #4028	C₂²	semidirect
67. D₅×C₂²⋊C₄	C₂²	semidirect
69. #4021	C₂²	semidirect
70. #4021	C₂²	semidirect
73. #4020	C₂²	semidirect
75. C₄×D₂₀	C₂²	semidirect
76. C₄×D₂₀	C₂²	semidirect
77. C₄×D₂₀	C₂²	semidirect
78. C₄×D₂₀	C₂²	semidirect
79. C₄×D₂₀	C₂²	semidirect
80. #4015	C₂²	semidirect
81. #4015	C₂²	semidirect
82. C₄×Dic₁₀	C₂²	semidirect
171. #529	D₅	semidirect
235. #126	C₂×D₅	semidirect
236. #125	C₂×D₅	semidirect
245. #123	C₂×D₅	semidirect
249. C₂²⋊Q₈	C₂×D₅	semidirect
271. C₄×Q₈	C₂×D₅	semidirect
280. C₄×D₄	C₂×D₅	semidirect
282. #117	C₂×D₅	semidirect
285. C₂×C₄²	C₂×D₅	semidirect
443. 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×#529	2
#66038	2
#66029	2
#66010	2
#66000	2
#65963	2
#65941	2
#65918	2
#65911	2
#65887	2
#65885	2
#65884	2
D₄×D₂₀	2
#65868	2
#65859	2
#65811	2
#3546	5