Subgroups — #10618955

Order 640.

1142 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#559	C₂	1	1	yes	maximal, characteristic, complemented
2	#66051	C₂	1	1	yes	maximal, characteristic, complemented
3	#66050	C₂	1	1	yes	maximal, characteristic, complemented
4	#66016	C₂	1	2	yes	maximal, complemented
5	#66011	C₂	1	2	yes	maximal, complemented
6	#66010	C₂	1	2	yes	maximal, complemented
7	D₅×#124	C₂	1	2	yes	maximal, complemented
8	#65992	C₂	1	4	yes	maximal, complemented
9	#65991	C₂	1	4	yes	maximal, complemented
10	#65918	C₂	1	1	yes	maximal, characteristic, complemented
11	#65914	C₂	1	1	yes	maximal, characteristic, complemented
12	Q₈×D₂₀	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×#713	C₂	1	1	yes	maximal, characteristic, complemented
14	#65897	C₂	1	2	yes	maximal, complemented
15	#65891	C₂	1	2	yes	maximal, complemented
16	#65888	C₂	1	2	yes	maximal, complemented
17	#65879	C₂	1	2	yes	maximal, complemented
18	C₂×#713	C₂²	1	1	yes	characteristic
19	C₂×Q₈×D₅	C₂²	1	2	yes	complemented
20	C₂×#711	C₂²	1	2	yes	complemented
21	C₂×D₄×D₅	C₂²	1	2	yes	—
22	C₂×D₄×D₅	C₂²	1	2	yes	—
23	C₅×#127	C₂²	1	1	yes	characteristic
24	C₅×#124	C₂²	1	2	yes	complemented
25	C₅×#124	C₂²	1	2	yes	complemented
26	C₅×#123	C₂²	1	4	yes	complemented
27	C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
28	C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
29	C₄×C₅×D₄	C₂²	1	2	yes	complemented
30	C₄×C₅×D₄	C₂²	1	2	yes	complemented
31	#4093	C₂²	1	1	yes	characteristic
32	#4092	C₂²	1	1	yes	characteristic, complemented
33	#4092	C₂²	1	2	yes	complemented
34	Q₈×Dic₅	C₂²	1	1	yes	characteristic, complemented
35	#4084	C₂²	1	2	yes	—
36	#4084	C₂²	1	2	yes	—
37	#4084	C₂²	1	2	yes	complemented
38	#4084	C₂²	1	2	yes	complemented
39	#4083	C₂²	1	4	yes	—
40	#4082	C₂²	1	2	yes	complemented
41	D₄×Dic₅	C₂²	1	2	yes	complemented
42	D₄×Dic₅	C₂²	1	2	yes	complemented
43	#4076	C₂²	1	4	yes	complemented
44	C₄×C₂²⋊D₅	C₂²	1	4	yes	complemented
45	C₂×#685	C₂²	1	4	yes	complemented
46	#4072	C₂²	1	4	yes	complemented
47	#4044	C₂²	1	2	yes	complemented
48	#4044	C₂²	1	4	yes	complemented
49	#4043	C₂²	1	2	yes	complemented
50	#4043	C₂²	1	4	yes	complemented
51	#4041	C₂²	1	1	yes	characteristic
52	#4040	C₂²	1	2	yes	complemented
53	#4039	C₂²	1	1	yes	characteristic
54	#4039	C₂²	1	2	yes	complemented
55	#4038	C₂²	1	2	yes	complemented
56	#4038	C₂²	1	1	yes	characteristic, complemented
57	#4038	C₂²	1	2	yes	complemented
58	#4036	C₂²	1	1	yes	characteristic, complemented
59	#4032	C₂²	1	4	yes	complemented
60	#4031	C₂²	1	4	yes	complemented
61	#4031	C₂²	1	4	yes	complemented
62	#4031	C₂²	1	4	yes	complemented
63	#4030	C₂²	1	4	yes	complemented
64	#4029	C₂²	1	4	yes	complemented
65	#4028	C₂²	1	4	yes	complemented
66	#4027	C₂²	1	4	yes	complemented
67	D₅×C₂²⋊C₄	C₂²	1	4	yes	complemented
68	D₅×C₂²⋊C₄	C₂²	1	4	yes	complemented
69	#4025	C₂²	1	4	yes	complemented
70	#4024	C₂²	1	4	yes	complemented
71	#4021	C₂²	1	2	yes	—
72	C₄×D₂₀	C₂²	1	1	yes	characteristic
73	C₄×D₂₀	C₂²	1	1	yes	characteristic
74	C₄×D₂₀	C₂²	1	2	yes	—
75	C₄×D₂₀	C₂²	1	2	yes	complemented
76	C₄×D₂₀	C₂²	1	2	yes	complemented
77	#4018	C₂²	1	2	yes	complemented
78	C₄²×D₅	C₂²	1	1	yes	characteristic, complemented
79	C₄²×D₅	C₂²	1	2	yes	complemented
80	#4015	C₂²	1	1	yes	characteristic, complemented
81	#4015	C₂²	1	2	yes	complemented
82	C₄×Dic₁₀	C₂²	1	2	yes	complemented
83	#3514	—	5	1	no	maximal, Sylow
84	C₂³×D₅	C₂³	1	4	yes	—
85	C₂×C₅×Q₈	C₂³	1	1	yes	characteristic
86	C₂×C₅×Q₈	C₂³	1	1	yes	characteristic
87	C₂×C₅×D₄	C₂³	1	2	yes	—
88	C₂×C₅×D₄	C₂³	1	2	yes	—
89	C₂×C₅×D₄	C₂³	1	2	yes	—
90	C₂²×C₄×C₅	C₂³	1	4	yes	—
91	C₂×C₂²⋊D₅	C₂³	1	4	yes	—
92	C₂×C₂²⋊D₅	C₂³	1	4	yes	—
93	C₂×C₂²⋊D₅	C₂³	1	4	yes	—
94	C₂²×Dic₅	C₂³	1	4	yes	—
95	#713	—	2	4	no	—
96	Q₈×D₅	—	4	4	no	—
97	#711	—	4	4	no	—
98	D₄×D₅	—	2	8	no	—
99	D₄×D₅	—	4	4	no	—
100	C₂×D₂₀	C₂³	1	1	yes	characteristic
101	C₂×D₂₀	C₂³	1	2	yes	—
102	C₂×D₂₀	C₂³	1	2	yes	—
103	C₂×D₂₀	C₂³	1	1	yes	characteristic
104	C₂×C₄×D₅	C₂³	1	2	yes	—
105	C₂×C₄×D₅	C₂³	1	2	yes	—
106	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
107	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
108	C₂×C₄×D₅	C₂³	1	2	yes	—
109	C₂×C₄×D₅	C₂³	1	4	yes	—
110	C₂×C₄×D₅	C₂³	1	2	yes	—
111	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
112	C₂×Dic₁₀	C₂³	1	2	yes	—
113	C₂×Dic₁₀	C₂³	1	4	yes	—
114	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
115	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
116	C₅×C₄⋊C₄	C₂³	1	2	yes	—
117	C₅×C₄⋊C₄	C₂³	1	2	yes	—
118	C₅×C₂²⋊C₄	C₂³	1	4	yes	—
119	C₅×C₂²⋊C₄	C₂³	1	4	yes	—
120	C₅×C₂²⋊C₄	C₂³	1	4	yes	—
121	C₄²×C₅	C₂³	1	2	yes	—
122	C₄²×C₅	C₂³	1	2	yes	—
123	C₄²×C₅	C₂³	1	1	yes	characteristic
124	C₂²⋊Dic₅	C₂³	1	4	yes	—
125	C₂²⋊Dic₅	C₂³	1	4	yes	—
126	C₂²⋊Dic₅	C₂³	1	4	yes	—
127	#685	C₂³	1	2	yes	—
128	#685	C₂³	1	2	yes	—
129	#685	C₂³	1	4	yes	—
130	#685	C₂³	1	2	yes	—
131	#685	C₂³	1	2	yes	—
132	#685	C₂³	1	2	yes	—
133	#685	C₂³	1	2	yes	—
134	#685	C₂³	1	2	yes	—
135	#685	C₂³	1	2	yes	—
136	#685	C₂³	1	4	yes	—
137	#685	C₂³	1	4	yes	—
138	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
139	C₄⋊Dic₅	C₂³	1	2	yes	—
140	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
141	C₄⋊Dic₅	C₂³	1	4	yes	—
142	C₄⋊Dic₅	C₂³	1	2	yes	—
143	C₄⋊Dic₅	C₂³	1	2	yes	—
144	C₄⋊Dic₅	C₂³	1	2	yes	—
145	#683	C₂³	1	4	yes	—
146	#683	C₂³	1	2	yes	—
147	#683	C₂³	1	2	yes	—
148	C₄×Dic₅	C₂³	1	4	yes	—
149	C₄×Dic₅	C₂³	1	1	yes	characteristic
150	C₄×Dic₅	C₂³	1	1	yes	characteristic
151	C₄×Dic₅	C₂³	1	2	yes	—
152	C₄×Dic₅	C₂³	1	2	yes	—
153	C₄×Dic₅	C₂³	1	1	yes	characteristic
154	#559	D₅	1	1	yes	characteristic, complemented
155	#556	—	5	1	no	—
156	#555	—	5	2	no	—
157	#551	—	5	4	no	—
158	D₄×Q₈	—	5	1	no	—
159	#548	—	5	2	no	—
160	#546	—	5	2	no	—
161	#546	—	5	2	no	—
162	D₄²	—	5	1	no	—
163	#542	—	5	2	no	—
164	#538	—	5	4	no	—
165	#532	—	5	1	no	—
166	#529	—	5	1	no	—
167	#529	—	5	2	no	—
168	C₂×#124	—	5	2	no	—
169	#518	—	5	2	no	—
170	C₄×#41	—	5	1	no	—
171	C₂³×C₅	C₂⁴	1	4	yes	—
172	C₂²×D₅	—	2	8	no	—
173	C₂²×D₅	—	4	4	no	—
174	C₂²×D₅	—	4	4	no	—
175	C₂²×D₅	C₂⁴	1	2	yes	—
176	C₂²×D₅	C₂⁴	1	1	yes	characteristic
177	C₂²×D₅	C₂⁴	1	2	yes	—
178	C₅×Q₈	—	2	2	no	—
179	C₅×Q₈	—	2	2	no	—
180	C₅×D₄	—	2	4	no	—
181	C₅×D₄	—	2	4	no	—
182	C₅×D₄	—	4	2	no	—
183	C₂×C₄×C₅	—	4	4	no	—
184	C₂×C₄×C₅	C₂⁴	1	2	yes	—
185	C₂×C₄×C₅	C₂⁴	1	2	yes	—
186	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
187	C₂×C₄×C₅	C₂⁴	1	2	yes	—
188	C₂×C₄×C₅	C₂⁴	1	2	yes	—
189	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
190	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
191	C₂²⋊D₅	—	2	8	no	—
192	C₂²⋊D₅	—	4	4	no	—
193	C₂²⋊D₅	—	4	4	no	—
194	C₂×Dic₅	—	4	4	no	—
195	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
196	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
197	C₂×Dic₅	C₂⁴	1	2	yes	—
198	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
199	C₂×Dic₅	C₂⁴	1	2	yes	—
200	C₂×Dic₅	C₂⁴	1	4	yes	—
201	D₂₀	—	2	4	no	—
202	D₂₀	—	2	2	no	—
203	D₂₀	—	4	2	no	—
204	D₂₀	#41	1	4	yes	complemented
205	C₄×D₅	—	2	4	no	—
206	C₄×D₅	—	2	4	no	—
207	C₄×D₅	—	2	2	no	—
208	C₄×D₅	—	2	4	no	—
209	C₄×D₅	—	2	2	no	—
210	C₄×D₅	—	4	2	no	—
211	C₄×D₅	—	4	1	no	—
212	C₄×D₅	—	4	4	no	—
213	Dic₁₀	—	2	4	no	—
214	Dic₁₀	—	4	4	no	—
215	C₂×#41	—	5	1	no	—
216	C₂×#41	—	5	2	no	—
217	C₂²×Q₈	—	5	2	no	—
218	C₂²×D₄	—	5	2	no	—
219	C₂²×D₄	—	5	2	no	—
220	C₄⋊Q₈	—	5	1	no	—
221	C₄⋊Q₈	—	5	2	no	—
222	#127	C₂×D₅	1	1	yes	characteristic
223	#126	—	5	2	no	—
224	#126	—	5	4	no	—
225	#126	—	5	4	no	—
226	#125	—	5	1	no	—
227	#124	—	5	1	no	—
228	#124	—	5	2	no	—
229	#124	—	5	4	no	—
230	#124	—	5	4	no	—
231	#124	—	5	4	no	—
232	#124	—	5	2	no	—
233	#124	C₂×D₅	1	2	yes	complemented
234	#124	C₂×D₅	1	2	yes	complemented
235	#123	—	5	2	no	—
236	#123	—	5	4	no	—
237	#123	—	5	4	no	—
238	#123	C₂×D₅	1	4	yes	complemented
239	C₂²⋊Q₈	—	5	1	no	—
240	C₂²⋊Q₈	—	5	2	no	—
241	C₂²⋊Q₈	—	5	2	no	—
242	C₂²⋊Q₈	—	5	4	no	—
243	C₂²⋊Q₈	—	5	4	no	—
244	#121	—	5	2	no	—
245	#121	—	5	2	no	—
246	#121	—	5	2	no	—
247	#121	—	5	2	no	—
248	#121	—	5	4	no	—
249	#121	—	5	1	no	—
250	#121	—	5	4	no	—
251	#120	—	5	4	no	—
252	#120	—	5	4	no	—
253	C₄×Q₈	—	5	1	no	—
254	C₄×Q₈	—	5	2	no	—
255	C₄×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
256	C₄×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
257	C₄×D₄	—	5	2	no	—
258	C₄×D₄	—	5	2	no	—
259	C₄×D₄	—	5	4	no	—
260	C₄×D₄	—	5	1	no	—
261	C₄×D₄	—	5	2	no	—
262	C₄×D₄	—	5	4	no	—
263	C₄×D₄	—	5	1	no	—
264	C₄×D₄	—	5	2	no	—
265	C₄×D₄	—	5	2	no	—
266	C₄×D₄	—	5	1	no	—
267	C₄×D₄	—	5	2	no	—
268	C₄×D₄	C₂×D₅	1	2	yes	complemented
269	C₄×D₄	C₂×D₅	1	2	yes	complemented
270	#117	—	5	4	no	—
271	#117	—	5	2	no	—
272	#117	—	5	1	no	—
273	#117	—	5	2	no	—
274	#117	—	5	2	no	—
275	C₂×C₂²⋊C₄	—	5	4	no	—
276	C₂×C₂²⋊C₄	—	5	4	no	—
277	C₂×C₂²⋊C₄	—	5	4	no	—
278	C₂×C₄²	—	5	2	no	—
279	C₂×C₄²	—	5	1	no	—
280	C₂²×C₅	—	2	4	no	—
281	C₂²×C₅	—	2	4	no	—
282	C₂²×C₅	—	2	4	no	—
283	C₂²×C₅	C₂⁵	1	1	yes	characteristic
284	C₂×D₅	—	2	2	no	—
285	C₂×D₅	—	2	2	no	—
286	C₂×D₅	—	2	1	no	—
287	C₂×D₅	—	2	2	no	—
288	C₂×D₅	—	2	1	no	—
289	C₂×D₅	—	2	2	no	—
290	C₂×D₅	—	2	1	no	—
291	C₂×D₅	—	2	2	no	—
292	C₂×D₅	—	8	8	no	—
293	C₂×D₅	C₂×#41	1	4	yes	—
294	C₄×C₅	—	2	2	no	—
295	C₄×C₅	—	2	2	no	—
296	C₄×C₅	—	2	2	no	—
297	C₄×C₅	—	2	1	no	—
298	C₄×C₅	—	2	2	no	—
299	C₄×C₅	C₂×#41	1	2	yes	—
300	C₄×C₅	H(5,𝔽₂)	1	2	yes	—
301	Dic₅	—	2	1	no	—
302	Dic₅	—	2	2	no	—
303	Dic₅	—	2	4	no	—
304	Dic₅	—	2	2	no	—
305	Dic₅	—	2	1	no	—
306	Dic₅	—	2	1	no	—
307	C₂⁴	—	5	4	no	—
308	#41	—	10	4	no	—
309	#41	—	20	4	no	—
310	C₂×Q₈	—	5	2	no	—
311	C₂×Q₈	—	5	4	no	—
312	C₂×Q₈	—	20	4	no	—
313	C₂×Q₈	C₂²×D₅	1	1	yes	characteristic
314	C₂×Q₈	C₂²×D₅	1	1	yes	characteristic
315	C₂×D₄	—	5	4	no	—
316	C₂×D₄	—	5	4	no	—
317	C₂×D₄	—	5	4	no	—
318	C₂×D₄	—	5	1	no	—
319	C₂×D₄	—	5	2	no	—
320	C₂×D₄	—	5	1	no	—
321	C₂×D₄	—	5	2	no	—
322	C₂×D₄	—	10	8	no	—
323	C₂×D₄	—	20	4	no	—
324	C₂×D₄	C₂²×D₅	1	2	yes	—
325	C₂×D₄	C₂²×D₅	1	2	yes	—
326	C₂×D₄	C₂²×D₅	1	2	yes	—
327	C₂²×C₄	—	5	4	no	—
328	C₂²×C₄	—	5	2	no	—
329	C₂²×C₄	—	5	1	no	—
330	C₂²×C₄	—	5	2	no	—
331	C₂²×C₄	—	5	1	no	—
332	C₂²×C₄	—	5	2	no	—
333	C₂²×C₄	—	5	2	no	—
334	C₂²×C₄	—	5	1	no	—
335	C₂²×C₄	—	5	4	no	—
336	C₂²×C₄	C₂²×D₅	1	4	yes	—
337	C₄⋊C₄	—	5	2	no	—
338	C₄⋊C₄	—	5	2	no	—
339	C₄⋊C₄	—	5	2	no	—
340	C₄⋊C₄	—	5	2	no	—
341	C₄⋊C₄	—	5	1	no	—
342	C₄⋊C₄	—	5	2	no	—
343	C₄⋊C₄	—	5	4	no	—
344	C₄⋊C₄	—	5	1	no	—
345	C₄⋊C₄	—	5	2	no	—
346	C₄⋊C₄	—	5	4	no	—
347	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
348	C₄⋊C₄	C₂²×D₅	1	2	yes	—
349	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
350	C₄⋊C₄	C₂²×D₅	1	2	yes	—
351	C₂²⋊C₄	—	5	4	no	—
352	C₂²⋊C₄	—	5	4	no	—
353	C₂²⋊C₄	—	5	4	no	—
354	C₂²⋊C₄	—	5	2	no	—
355	C₂²⋊C₄	—	5	2	no	—
356	C₂²⋊C₄	—	5	4	no	—
357	C₂²⋊C₄	—	5	2	no	—
358	C₂²⋊C₄	—	5	2	no	—
359	C₂²⋊C₄	—	5	4	no	—
360	C₂²⋊C₄	—	5	4	no	—
361	C₂²⋊C₄	—	5	2	no	—
362	C₂²⋊C₄	—	5	2	no	—
363	C₂²⋊C₄	—	5	2	no	—
364	C₂²⋊C₄	—	5	2	no	—
365	C₂²⋊C₄	C₂²×D₅	1	4	yes	—
366	C₂²⋊C₄	C₂²×D₅	1	4	yes	—
367	C₂²⋊C₄	C₂²×D₅	1	4	yes	—
368	C₄²	—	5	1	no	—
369	C₄²	—	5	2	no	—
370	C₄²	—	5	1	no	—
371	C₄²	—	5	1	no	—
372	C₄²	—	5	2	no	—
373	C₄²	—	5	4	no	—
374	C₄²	C₂²×D₅	1	1	yes	characteristic
375	C₄²	C₂²×D₅	1	2	yes	—
376	C₄²	C₂²×D₅	1	2	yes	—
377	C₂×C₅	—	4	4	no	—
378	C₂×C₅	C₂²×#41	1	1	yes	characteristic
379	C₂×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
380	C₂×C₅	#585	1	1	yes	characteristic
381	D₅	—	2	4	no	—
382	D₅	—	4	1	no	—
383	D₅	—	4	2	no	—
384	C₂³	—	5	2	no	—
385	C₂³	—	5	2	no	—
386	C₂³	—	5	1	no	—
387	C₂³	—	10	8	no	—
388	C₂³	—	20	4	no	—
389	C₂³	—	20	4	no	—
390	C₂³	C₂³×D₅	1	4	yes	—
391	Q₈	—	2	2	no	—
392	Q₈	—	2	2	no	—
393	Q₈	—	10	4	no	—
394	Q₈	—	20	4	no	—
395	D₄	—	2	4	no	—
396	D₄	—	2	4	no	—
397	D₄	—	4	2	no	—
398	D₄	—	5	4	no	—
399	D₄	—	10	4	no	—
400	D₄	—	10	8	no	—
401	D₄	—	10	2	no	—
402	D₄	—	20	2	no	—
403	D₄	—	20	4	no	—
404	D₄	—	20	4	no	—
405	C₂×C₄	—	4	4	no	—
406	C₂×C₄	—	5	1	no	—
407	C₂×C₄	—	5	1	no	—
408	C₂×C₄	—	5	2	no	—
409	C₂×C₄	—	5	1	no	—
410	C₂×C₄	—	5	2	no	—
411	C₂×C₄	—	5	4	no	—
412	C₂×C₄	—	10	4	no	—
413	C₂×C₄	—	10	4	no	—
414	C₂×C₄	—	10	2	no	—
415	C₂×C₄	—	10	4	no	—
416	C₂×C₄	—	10	2	no	—
417	C₂×C₄	—	20	4	no	—
418	C₂×C₄	—	20	2	no	—
419	C₂×C₄	—	20	1	no	—
420	C₂×C₄	—	20	4	no	—
421	C₂×C₄	C₂³×D₅	1	2	yes	—
422	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
423	C₂×C₄	C₂³×D₅	1	2	yes	—
424	C₂×C₄	C₂³×D₅	1	2	yes	—
425	C₂×C₄	C₂³×D₅	1	2	yes	—
426	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
427	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
428	C₅	#3514	1	1	yes	characteristic, complemented, Sylow
429	C₂²	—	2	4	no	—
430	C₂²	—	2	4	no	—
431	C₂²	—	2	4	no	—
432	C₂²	—	5	4	no	—
433	C₂²	—	10	2	no	—
434	C₂²	—	10	2	no	—
435	C₂²	—	10	1	no	—
436	C₂²	—	10	2	no	—
437	C₂²	—	10	1	no	—
438	C₂²	—	10	2	no	—
439	C₂²	—	10	1	no	—
440	C₂²	—	10	2	no	—
441	C₂²	—	40	8	no	—
442	C₂²	C₂⁴×D₅	1	1	yes	characteristic
443	C₄	—	2	2	no	—
444	C₄	—	2	2	no	—
445	C₄	—	2	2	no	—
446	C₄	—	2	2	no	—
447	C₄	—	2	1	no	—
448	C₄	—	10	1	no	—
449	C₄	—	10	2	no	—
450	C₄	—	10	1	no	—
451	C₄	—	10	2	no	—
452	C₄	—	10	4	no	—
453	C₄	—	10	1	no	—
454	C₄	D₅×#41	1	2	yes	—
455	C₄	#4149	1	2	yes	—
456	C₂	—	4	4	no	—
457	C₂	—	10	4	no	—
458	C₂	—	20	2	no	—
459	C₂	—	20	1	no	—
460	C₂	C₂×D₅×#41	1	1	yes	characteristic
461	C₂	C₂×#4149	1	1	yes	characteristic
462	C₂	#66285	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅
commutator, socle, cosocle	C₂²×C₅	C₂⁵
Fitting	C₅×#559	C₂
hypercenter	#559	D₅
hypocenter	C₅	#3514
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ #559

Complements

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

N	H ≅ G/N	type
1. C₅×#559	C₂	semidirect
2. #66051	C₂	semidirect
3. #66050	C₂	semidirect
4. #66016	C₂	semidirect
5. #66011	C₂	semidirect
6. #66010	C₂	semidirect
7. D₅×#124	C₂	semidirect
8. #65992	C₂	semidirect
9. #65991	C₂	semidirect
10. #65918	C₂	semidirect
11. #65914	C₂	semidirect
12. Q₈×D₂₀	C₂	semidirect
13. C₄×#713	C₂	semidirect
14. #65897	C₂	semidirect
15. #65891	C₂	semidirect
16. #65888	C₂	semidirect
17. #65879	C₂	semidirect
19. C₂×Q₈×D₅	C₂²	semidirect
20. C₂×#711	C₂²	semidirect
24. C₅×#124	C₂²	semidirect
25. C₅×#124	C₂²	semidirect
26. C₅×#123	C₂²	semidirect
27. C₄×C₅×Q₈	C₂²	semidirect
28. C₄×C₅×Q₈	C₂²	semidirect
29. C₄×C₅×D₄	C₂²	semidirect
30. C₄×C₅×D₄	C₂²	semidirect
32. #4092	C₂²	semidirect
33. #4092	C₂²	semidirect
34. Q₈×Dic₅	C₂²	semidirect
37. #4084	C₂²	semidirect
38. #4084	C₂²	semidirect
40. #4082	C₂²	semidirect
41. D₄×Dic₅	C₂²	semidirect
42. D₄×Dic₅	C₂²	semidirect
43. #4076	C₂²	semidirect
44. C₄×C₂²⋊D₅	C₂²	semidirect
45. C₂×#685	C₂²	semidirect
46. #4072	C₂²	semidirect
47. #4044	C₂²	semidirect
48. #4044	C₂²	semidirect
49. #4043	C₂²	semidirect
50. #4043	C₂²	semidirect
52. #4040	C₂²	semidirect
54. #4039	C₂²	semidirect
55. #4038	C₂²	semidirect
56. #4038	C₂²	semidirect
57. #4038	C₂²	semidirect
58. #4036	C₂²	semidirect
59. #4032	C₂²	semidirect
60. #4031	C₂²	semidirect
61. #4031	C₂²	semidirect
62. #4031	C₂²	semidirect
63. #4030	C₂²	semidirect
64. #4029	C₂²	semidirect
65. #4028	C₂²	semidirect
66. #4027	C₂²	semidirect
67. D₅×C₂²⋊C₄	C₂²	semidirect
68. D₅×C₂²⋊C₄	C₂²	semidirect
69. #4025	C₂²	semidirect
70. #4024	C₂²	semidirect
75. C₄×D₂₀	C₂²	semidirect
76. C₄×D₂₀	C₂²	semidirect
77. #4018	C₂²	semidirect
78. C₄²×D₅	C₂²	semidirect
79. C₄²×D₅	C₂²	semidirect
80. #4015	C₂²	semidirect
81. #4015	C₂²	semidirect
82. C₄×Dic₁₀	C₂²	semidirect
154. #559	D₅	semidirect
204. D₂₀	#41	semidirect
233. #124	C₂×D₅	semidirect
234. #124	C₂×D₅	semidirect
238. #123	C₂×D₅	semidirect
255. C₄×Q₈	C₂×D₅	semidirect
256. C₄×Q₈	C₂×D₅	semidirect
268. C₄×D₄	C₂×D₅	semidirect
269. C₄×D₄	C₂×D₅	semidirect
428. C₅	#3514	semidirect

Maximal subgroups

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

subgroup	index
C₅×#559	2
#66051	2
#66050	2
#66016	2
#66011	2
#66010	2
D₅×#124	2
#65992	2
#65991	2
#65918	2
#65914	2
Q₈×D₂₀	2
C₄×#713	2
#65897	2
#65891	2
#65888	2
#65879	2
#3514	5