Subgroups — #10618887

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×#556	C₂	1	1	yes	maximal, characteristic, complemented
2	#66061	C₂	1	1	yes	maximal, characteristic, complemented
3	#66059	C₂	1	1	yes	maximal, characteristic, complemented
4	#66039	C₂	1	4	yes	maximal, complemented
5	#66038	C₂	1	4	yes	maximal, complemented
6	#66010	C₂	1	2	yes	maximal, complemented
7	D₅×#124	C₂	1	2	yes	maximal, complemented
8	#65977	C₂	1	2	yes	maximal, complemented
9	#65964	C₂	1	2	yes	maximal, complemented
10	#65919	C₂	1	1	yes	maximal, characteristic, complemented
11	#65914	C₂	1	2	yes	maximal, complemented
12	#65910	C₂	1	2	yes	maximal, complemented
13	C₄×#713	C₂	1	1	yes	maximal, characteristic, complemented
14	#65891	C₂	1	1	yes	maximal, characteristic, complemented
15	D₄×D₂₀	C₂	1	1	yes	maximal, characteristic, complemented
16	#65866	C₂	1	2	yes	maximal, complemented
17	#65855	C₂	1	2	yes	maximal, complemented
18	C₂×#713	C₂²	1	1	yes	characteristic
19	C₂×#713	C₂²	1	2	yes	complemented
20	C₂×Q₈×D₅	C₂²	1	2	yes	complemented
21	C₂×D₄×D₅	C₂²	1	2	yes	—
22	C₂²×D₂₀	C₂²	1	2	yes	—
23	C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
24	C₅×#126	C₂²	1	4	yes	complemented
25	C₅×#124	C₂²	1	2	yes	—
26	C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
27	C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
28	C₄×C₅×Q₈	C₂²	1	2	yes	complemented
29	C₄×C₅×D₄	C₂²	1	1	yes	characteristic
30	C₅×#117	C₂²	1	2	yes	complemented
31	#4093	C₂²	1	2	yes	complemented
32	#4093	C₂²	1	2	yes	complemented
33	#4092	C₂²	1	2	yes	complemented
34	Q₈×Dic₅	C₂²	1	1	yes	characteristic, complemented
35	#4084	C₂²	1	1	yes	characteristic
36	#4082	C₂²	1	1	yes	characteristic
37	#4076	C₂²	1	2	yes	—
38	C₄×C₂²⋊D₅	C₂²	1	2	yes	complemented
39	#4072	C₂²	1	2	yes	complemented
40	#4044	C₂²	1	4	yes	complemented
41	#4043	C₂²	1	1	yes	characteristic, complemented
42	#4043	C₂²	1	4	yes	complemented
43	#4042	C₂²	1	4	yes	complemented
44	#4041	C₂²	1	2	yes	—
45	#4041	C₂²	1	2	yes	complemented
46	#4041	C₂²	1	2	yes	complemented
47	#4041	C₂²	1	4	yes	complemented
48	#4040	C₂²	1	4	yes	complemented
49	#4040	C₂²	1	4	yes	complemented
50	#4039	C₂²	1	2	yes	—
51	#4039	C₂²	1	1	yes	characteristic
52	#4039	C₂²	1	2	yes	complemented
53	#4039	C₂²	1	2	yes	complemented
54	#4039	C₂²	1	2	yes	complemented
55	#4039	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	#4034	C₂²	1	2	yes	complemented
60	#4031	C₂²	1	4	yes	complemented
61	#4031	C₂²	1	4	yes	complemented
62	#4030	C₂²	1	4	yes	complemented
63	#4029	C₂²	1	2	yes	complemented
64	#4029	C₂²	1	4	yes	complemented
65	#4028	C₂²	1	4	yes	—
66	#4028	C₂²	1	4	yes	complemented
67	D₅×C₂²⋊C₄	C₂²	1	4	yes	complemented
68	D₅×C₂²⋊C₄	C₂²	1	4	yes	complemented
69	D₅×C₂²⋊C₄	C₂²	1	4	yes	complemented
70	#4025	C₂²	1	2	yes	complemented
71	#4021	C₂²	1	4	yes	complemented
72	#4021	C₂²	1	2	yes	complemented
73	#4020	C₂²	1	1	yes	characteristic
74	C₄×D₂₀	C₂²	1	1	yes	characteristic
75	C₄×D₂₀	C₂²	1	4	yes	complemented
76	C₄×D₂₀	C₂²	1	4	yes	complemented
77	C₄×D₂₀	C₂²	1	2	yes	complemented
78	C₄×D₂₀	C₂²	1	2	yes	complemented
79	#4018	C₂²	1	4	yes	complemented
80	C₄²×D₅	C₂²	1	1	yes	characteristic, complemented
81	C₄²×D₅	C₂²	1	2	yes	complemented
82	C₄×Dic₁₀	C₂²	1	1	yes	characteristic, 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	2	yes	—
87	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
88	C₂²×C₄×C₅	C₂³	1	2	yes	—
89	C₂×C₂²⋊D₅	C₂³	1	4	yes	—
90	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
91	#713	—	2	4	no	—
92	#713	—	4	4	no	—
93	Q₈×D₅	—	4	4	no	—
94	D₄×D₅	—	4	4	no	—
95	C₂×D₂₀	—	2	8	no	—
96	C₂×D₂₀	C₂³	1	4	yes	—
97	C₂×D₂₀	C₂³	1	2	yes	—
98	C₂×D₂₀	C₂³	1	2	yes	—
99	C₂×D₂₀	C₂³	1	2	yes	—
100	C₂×D₂₀	C₂³	1	4	yes	—
101	C₂×D₂₀	C₂³	1	2	yes	—
102	C₂×D₂₀	C₂³	1	1	yes	characteristic
103	C₂×C₄×D₅	C₂³	1	2	yes	—
104	C₂×C₄×D₅	C₂³	1	2	yes	—
105	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
106	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
107	C₂×C₄×D₅	C₂³	1	4	yes	—
108	C₂×C₄×D₅	C₂³	1	4	yes	—
109	C₂×C₄×D₅	C₂³	1	2	yes	—
110	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
111	C₂×C₄×D₅	C₂³	1	4	yes	—
112	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
113	C₂×Dic₁₀	C₂³	1	4	yes	—
114	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
115	C₅×C₄⋊C₄	C₂³	1	2	yes	—
116	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
117	C₅×C₄⋊C₄	C₂³	1	4	yes	—
118	C₅×C₄⋊C₄	C₂³	1	2	yes	—
119	C₅×C₄⋊C₄	C₂³	1	2	yes	—
120	C₅×C₂²⋊C₄	C₂³	1	4	yes	—
121	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
122	C₅×C₂²⋊C₄	C₂³	1	4	yes	—
123	C₄²×C₅	C₂³	1	4	yes	—
124	C₄²×C₅	C₂³	1	1	yes	characteristic
125	C₄²×C₅	C₂³	1	2	yes	—
126	C₂²⋊Dic₅	C₂³	1	2	yes	—
127	C₂²⋊Dic₅	C₂³	1	2	yes	—
128	C₂²⋊Dic₅	C₂³	1	2	yes	—
129	#685	C₂³	1	4	yes	—
130	#685	C₂³	1	4	yes	—
131	#685	C₂³	1	2	yes	—
132	#685	C₂³	1	2	yes	—
133	#685	C₂³	1	4	yes	—
134	#685	C₂³	1	2	yes	—
135	#685	C₂³	1	4	yes	—
136	#685	C₂³	1	4	yes	—
137	#685	C₂³	1	4	yes	—
138	#685	C₂³	1	2	yes	—
139	#685	C₂³	1	4	yes	—
140	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
141	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
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	2	yes	—
146	#683	C₂³	1	2	yes	—
147	#683	C₂³	1	4	yes	—
148	C₄×Dic₅	C₂³	1	2	yes	—
149	C₄×Dic₅	C₂³	1	1	yes	characteristic
150	C₄×Dic₅	C₂³	1	2	yes	—
151	C₄×Dic₅	C₂³	1	1	yes	characteristic
152	C₄×Dic₅	C₂³	1	2	yes	—
153	C₄×Dic₅	C₂³	1	1	yes	characteristic
154	#559	—	5	1	no	—
155	#556	D₅	1	1	yes	characteristic, complemented
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	2	no	—
167	#529	—	5	1	no	—
168	C₂×#124	—	5	2	no	—
169	#518	—	5	2	no	—
170	C₄×#41	—	5	1	no	—
171	C₂³×C₅	C₂⁴	1	2	yes	—
172	C₂²×D₅	—	2	8	no	—
173	C₂²×D₅	—	4	4	no	—
174	C₂²×D₅	—	4	4	no	—
175	C₂²×D₅	C₂⁴	1	4	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	4	no	—
180	C₅×D₄	—	2	2	no	—
181	C₂×C₄×C₅	—	2	4	no	—
182	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
183	C₂×C₄×C₅	C₂⁴	1	2	yes	—
184	C₂×C₄×C₅	C₂⁴	1	2	yes	—
185	C₂×C₄×C₅	C₂⁴	1	2	yes	—
186	C₂×C₄×C₅	C₂⁴	1	4	yes	—
187	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
188	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
189	C₂²⋊D₅	—	4	4	no	—
190	C₂²⋊D₅	—	4	2	no	—
191	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
192	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
193	C₂×Dic₅	C₂⁴	1	2	yes	—
194	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
195	C₂×Dic₅	C₂⁴	1	2	yes	—
196	C₂×Dic₅	C₂⁴	1	2	yes	—
197	D₂₀	—	2	8	no	—
198	D₂₀	—	2	4	no	—
199	D₂₀	—	2	4	no	—
200	D₂₀	—	2	4	no	—
201	D₂₀	—	4	2	no	—
202	D₂₀	—	4	4	no	—
203	D₂₀	#41	1	4	yes	complemented
204	C₄×D₅	—	2	4	no	—
205	C₄×D₅	—	2	2	no	—
206	C₄×D₅	—	2	4	no	—
207	C₄×D₅	—	2	2	no	—
208	C₄×D₅	—	4	2	no	—
209	C₄×D₅	—	4	1	no	—
210	C₄×D₅	—	4	4	no	—
211	C₄×D₅	—	4	4	no	—
212	C₄×D₅	—	4	4	no	—
213	Dic₁₀	—	2	2	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	2	no	—
221	C₄⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
222	#127	—	5	1	no	—
223	#126	—	5	4	no	—
224	#126	—	5	2	no	—
225	#126	C₂×D₅	1	4	yes	complemented
226	#125	—	5	1	no	—
227	#124	—	5	2	no	—
228	#124	—	5	2	no	—
229	#124	—	5	1	no	—
230	#124	—	5	4	no	—
231	#124	—	5	4	no	—
232	#124	—	5	2	no	—
233	#124	—	5	4	no	—
234	#124	C₂×D₅	1	2	yes	—
235	#123	—	5	4	no	—
236	#123	—	5	4	no	—
237	#123	—	5	2	no	—
238	#123	—	5	4	no	—
239	C₂²⋊Q₈	—	5	2	no	—
240	C₂²⋊Q₈	—	5	1	no	—
241	C₂²⋊Q₈	—	5	4	no	—
242	C₂²⋊Q₈	—	5	4	no	—
243	C₂²⋊Q₈	C₂×D₅	1	2	yes	complemented
244	#121	—	5	1	no	—
245	#121	—	5	2	no	—
246	#121	—	5	2	no	—
247	#121	—	5	2	no	—
248	#121	—	5	2	no	—
249	#121	—	5	4	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	1	no	—
255	C₄×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
256	C₄×Q₈	C₂×D₅	1	2	yes	complemented
257	C₄×D₄	—	5	2	no	—
258	C₄×D₄	—	5	1	no	—
259	C₄×D₄	—	5	2	no	—
260	C₄×D₄	—	5	2	no	—
261	C₄×D₄	—	5	2	no	—
262	C₄×D₄	—	5	2	no	—
263	C₄×D₄	—	5	2	no	—
264	C₄×D₄	—	5	1	no	—
265	C₄×D₄	—	5	2	no	—
266	C₄×D₄	—	5	4	no	—
267	C₄×D₄	—	5	4	no	—
268	C₄×D₄	—	5	2	no	—
269	C₄×D₄	C₂×D₅	1	1	yes	characteristic
270	#117	—	5	2	no	—
271	#117	—	5	2	no	—
272	#117	—	5	1	no	—
273	#117	—	5	4	no	—
274	#117	C₂×D₅	1	2	yes	complemented
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	2	no	—
281	C₂²×C₅	—	2	2	no	—
282	C₂²×C₅	—	2	2	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	4	no	—
288	C₂×D₅	—	2	1	no	—
289	C₂×D₅	—	2	4	no	—
290	C₂×D₅	—	2	4	no	—
291	C₂×D₅	—	2	1	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	4	no	—
297	C₄×C₅	—	2	2	no	—
298	C₄×C₅	—	2	1	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	2	no	—
304	Dic₅	—	2	1	no	—
305	Dic₅	—	2	1	no	—
306	Dic₅	—	2	2	no	—
307	C₂⁴	—	5	4	no	—
308	#41	—	10	4	no	—
309	#41	—	20	4	no	—
310	C₂×Q₈	—	5	1	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	2	yes	—
315	C₂×D₄	—	5	2	no	—
316	C₂×D₄	—	5	4	no	—
317	C₂×D₄	—	5	1	no	—
318	C₂×D₄	—	5	2	no	—
319	C₂×D₄	—	5	4	no	—
320	C₂×D₄	—	5	2	no	—
321	C₂×D₄	—	5	2	no	—
322	C₂×D₄	—	5	2	no	—
323	C₂×D₄	—	5	4	no	—
324	C₂×D₄	—	10	8	no	—
325	C₂×D₄	—	20	4	no	—
326	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
327	C₂²×C₄	—	5	2	no	—
328	C₂²×C₄	—	5	1	no	—
329	C₂²×C₄	—	5	2	no	—
330	C₂²×C₄	—	5	1	no	—
331	C₂²×C₄	—	5	2	no	—
332	C₂²×C₄	—	5	1	no	—
333	C₂²×C₄	—	5	4	no	—
334	C₂²×C₄	—	5	4	no	—
335	C₂²×C₄	—	5	4	no	—
336	C₂²×C₄	C₂²×D₅	1	2	yes	—
337	C₄⋊C₄	—	5	2	no	—
338	C₄⋊C₄	—	5	2	no	—
339	C₄⋊C₄	—	5	2	no	—
340	C₄⋊C₄	—	5	1	no	—
341	C₄⋊C₄	—	5	2	no	—
342	C₄⋊C₄	—	5	4	no	—
343	C₄⋊C₄	—	5	1	no	—
344	C₄⋊C₄	—	5	2	no	—
345	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
346	C₄⋊C₄	C₂²×D₅	1	2	yes	—
347	C₄⋊C₄	C₂²×D₅	1	2	yes	—
348	C₄⋊C₄	C₂²×D₅	1	2	yes	—
349	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
350	C₄⋊C₄	C₂²×D₅	1	4	yes	—
351	C₂²⋊C₄	—	5	2	no	—
352	C₂²⋊C₄	—	5	2	no	—
353	C₂²⋊C₄	—	5	2	no	—
354	C₂²⋊C₄	—	5	2	no	—
355	C₂²⋊C₄	—	5	4	no	—
356	C₂²⋊C₄	—	5	4	no	—
357	C₂²⋊C₄	—	5	4	no	—
358	C₂²⋊C₄	—	5	4	no	—
359	C₂²⋊C₄	—	5	4	no	—
360	C₂²⋊C₄	—	5	2	no	—
361	C₂²⋊C₄	—	5	2	no	—
362	C₂²⋊C₄	—	5	4	no	—
363	C₂²⋊C₄	—	5	4	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	2	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	2	no	—
374	C₄²	C₂²×D₅	1	2	yes	—
375	C₄²	C₂²×D₅	1	1	yes	characteristic
376	C₄²	C₂²×D₅	1	4	yes	—
377	C₂×C₅	—	4	2	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	4	no	—
384	C₂³	—	5	2	no	—
385	C₂³	—	5	4	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	2	yes	—
391	Q₈	—	2	2	no	—
392	Q₈	—	2	4	no	—
393	Q₈	—	10	2	no	—
394	Q₈	—	20	4	no	—
395	D₄	—	2	2	no	—
396	D₄	—	5	4	no	—
397	D₄	—	10	8	no	—
398	D₄	—	10	4	no	—
399	D₄	—	10	4	no	—
400	D₄	—	10	4	no	—
401	D₄	—	20	4	no	—
402	D₄	—	20	2	no	—
403	D₄	—	20	4	no	—
404	D₄	—	20	2	no	—
405	C₂×C₄	—	2	4	no	—
406	C₂×C₄	—	5	1	no	—
407	C₂×C₄	—	5	1	no	—
408	C₂×C₄	—	5	1	no	—
409	C₂×C₄	—	5	2	no	—
410	C₂×C₄	—	5	2	no	—
411	C₂×C₄	—	5	2	no	—
412	C₂×C₄	—	10	4	no	—
413	C₂×C₄	—	10	2	no	—
414	C₂×C₄	—	10	4	no	—
415	C₂×C₄	—	10	2	no	—
416	C₂×C₄	—	20	4	no	—
417	C₂×C₄	—	20	4	no	—
418	C₂×C₄	—	20	2	no	—
419	C₂×C₄	—	20	4	no	—
420	C₂×C₄	—	20	1	no	—
421	C₂×C₄	C₂³×D₅	1	2	yes	—
422	C₂×C₄	C₂³×D₅	1	2	yes	—
423	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
424	C₂×C₄	C₂³×D₅	1	2	yes	—
425	C₂×C₄	C₂³×D₅	1	4	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	2	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	2	2	no	—
432	C₂²	—	5	4	no	—
433	C₂²	—	10	2	no	—
434	C₂²	—	10	2	no	—
435	C₂²	—	10	1	no	—
436	C₂²	—	10	4	no	—
437	C₂²	—	10	1	no	—
438	C₂²	—	10	4	no	—
439	C₂²	—	10	1	no	—
440	C₂²	—	10	4	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	4	no	—
446	C₄	—	2	2	no	—
447	C₄	—	2	1	no	—
448	C₄	—	10	1	no	—
449	C₄	—	10	1	no	—
450	C₄	—	10	2	no	—
451	C₄	—	10	2	no	—
452	C₄	—	10	1	no	—
453	C₄	—	10	2	no	—
454	C₄	D₅×#41	1	2	yes	—
455	C₄	#4149	1	2	yes	—
456	C₂	—	4	2	no	—
457	C₂	—	10	4	no	—
458	C₂	—	20	4	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	#66287	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅
commutator, socle, cosocle	C₂²×C₅	C₂⁵
Fitting	C₅×#556	C₂
hypercenter	#556	D₅
hypocenter	C₅	#3514
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ #556

Complements

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

N	H ≅ G/N	type
1. C₅×#556	C₂	semidirect
2. #66061	C₂	semidirect
3. #66059	C₂	semidirect
4. #66039	C₂	semidirect
5. #66038	C₂	semidirect
6. #66010	C₂	semidirect
7. D₅×#124	C₂	semidirect
8. #65977	C₂	semidirect
9. #65964	C₂	semidirect
10. #65919	C₂	semidirect
11. #65914	C₂	semidirect
12. #65910	C₂	semidirect
13. C₄×#713	C₂	semidirect
14. #65891	C₂	semidirect
15. D₄×D₂₀	C₂	semidirect
16. #65866	C₂	semidirect
17. #65855	C₂	semidirect
19. C₂×#713	C₂²	semidirect
20. C₂×Q₈×D₅	C₂²	semidirect
23. C₅×C₄⋊Q₈	C₂²	semidirect
24. C₅×#126	C₂²	semidirect
26. C₅×C₂²⋊Q₈	C₂²	semidirect
27. C₄×C₅×Q₈	C₂²	semidirect
28. C₄×C₅×Q₈	C₂²	semidirect
30. C₅×#117	C₂²	semidirect
31. #4093	C₂²	semidirect
32. #4093	C₂²	semidirect
33. #4092	C₂²	semidirect
34. Q₈×Dic₅	C₂²	semidirect
38. C₄×C₂²⋊D₅	C₂²	semidirect
39. #4072	C₂²	semidirect
40. #4044	C₂²	semidirect
41. #4043	C₂²	semidirect
42. #4043	C₂²	semidirect
43. #4042	C₂²	semidirect
45. #4041	C₂²	semidirect
46. #4041	C₂²	semidirect
47. #4041	C₂²	semidirect
48. #4040	C₂²	semidirect
49. #4040	C₂²	semidirect
52. #4039	C₂²	semidirect
53. #4039	C₂²	semidirect
54. #4039	C₂²	semidirect
55. #4039	C₂²	semidirect
56. #4038	C₂²	semidirect
57. #4038	C₂²	semidirect
58. #4036	C₂²	semidirect
59. #4034	C₂²	semidirect
60. #4031	C₂²	semidirect
61. #4031	C₂²	semidirect
62. #4030	C₂²	semidirect
63. #4029	C₂²	semidirect
64. #4029	C₂²	semidirect
66. #4028	C₂²	semidirect
67. D₅×C₂²⋊C₄	C₂²	semidirect
68. D₅×C₂²⋊C₄	C₂²	semidirect
69. D₅×C₂²⋊C₄	C₂²	semidirect
70. #4025	C₂²	semidirect
71. #4021	C₂²	semidirect
72. #4021	C₂²	semidirect
75. C₄×D₂₀	C₂²	semidirect
76. C₄×D₂₀	C₂²	semidirect
77. C₄×D₂₀	C₂²	semidirect
78. C₄×D₂₀	C₂²	semidirect
79. #4018	C₂²	semidirect
80. C₄²×D₅	C₂²	semidirect
81. C₄²×D₅	C₂²	semidirect
82. C₄×Dic₁₀	C₂²	semidirect
155. #556	D₅	semidirect
203. D₂₀	#41	semidirect
221. C₄⋊Q₈	C₂×D₅	semidirect
225. #126	C₂×D₅	semidirect
243. C₂²⋊Q₈	C₂×D₅	semidirect
255. C₄×Q₈	C₂×D₅	semidirect
256. C₄×Q₈	C₂×D₅	semidirect
274. #117	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×#556	2
#66061	2
#66059	2
#66039	2
#66038	2
#66010	2
D₅×#124	2
#65977	2
#65964	2
#65919	2
#65914	2
#65910	2
C₄×#713	2
#65891	2
D₄×D₂₀	2
#65866	2
#65855	2
#3514	5