Subgroups — #12099475

Order 1280.

772 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#65182	C₂	1	1	yes	maximal, characteristic
2	#10610908	C₂	1	1	yes	maximal, characteristic
3	#10610279	C₂	1	1	yes	maximal, characteristic
4	C₅×#1833	C₂	1	1	yes	maximal, characteristic, complemented
5	#10601491	C₂	1	1	yes	maximal, characteristic, complemented
6	#10601450	C₂	1	1	yes	maximal, characteristic, complemented
7	#10600689	C₂	1	1	yes	maximal, characteristic, complemented
8	D₅×#344	C₂	1	2	yes	maximal
9	#10599806	C₂	1	2	yes	maximal, complemented
10	D₅×H(3,ℤ/4)	C₂	1	2	yes	maximal
11	#10599492	C₂	1	2	yes	maximal, complemented
12	C₂×D₅×M₁₆	C₂²	1	2	yes	—
13	C₂×D₅×M₁₆	C₂²	1	1	yes	characteristic
14	C₂²×#676	C₂²	1	1	yes	characteristic
15	D₅×#117	C₂²	1	2	yes	—
16	D₅×#117	C₂²	1	1	yes	characteristic
17	C₂×C₅×#108	C₂²	1	1	yes	characteristic
18	C₅×#427	C₂²	1	1	yes	characteristic
19	C₅×#405	C₂²	1	1	yes	characteristic
20	C₂×#3954	C₂²	1	2	yes	—
21	#65411	C₂²	1	1	yes	characteristic
22	C₂×#3951	C₂²	1	1	yes	characteristic
23	#65395	C₂²	1	1	yes	characteristic
24	#65390	C₂²	1	1	yes	characteristic
25	#65287	C₂²	1	2	yes	—
26	#65286	C₂²	1	1	yes	characteristic
27	#65182	—	2	2	no	—
28	#65182	—	2	2	no	—
29	#65170	—	2	2	no	—
30	#65150	—	2	2	no	—
31	#64997	C₄	1	2	yes	complemented
32	#64996	C₄	1	2	yes	complemented
33	#64978	C₄	1	2	yes	complemented
34	C₄×#676	C₄	1	2	yes	complemented
35	C₅×#344	C₂²	1	2	yes	—
36	C₅×H(3,ℤ/4)	C₂²	1	2	yes	—
37	#64779	C₂²	1	2	yes	—
38	#64777	C₂²	1	2	yes	—
39	#64776	C₂²	1	2	yes	—
40	#64753	C₂²	1	2	yes	—
41	#64751	C₂²	1	2	yes	—
42	#64751	C₂²	1	2	yes	—
43	#20757	—	5	1	no	maximal, Sylow
44	C₂²×C₄×D₅	C₂³	1	1	yes	characteristic
45	C₂×C₅×M₁₆	C₂³	1	2	yes	—
46	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
47	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
48	C₅×#117	C₂³	1	2	yes	—
49	C₅×#117	C₂³	1	1	yes	characteristic
50	#4072	C₂³	1	2	yes	—
51	#4072	C₂³	1	1	yes	characteristic
52	C₂×#681	C₂³	1	2	yes	—
53	C₂×#681	C₂³	1	1	yes	characteristic
54	C₂²×#168	C₂³	1	1	yes	characteristic
55	D₅×M₁₆	—	2	2	no	—
56	D₅×M₁₆	—	2	2	no	—
57	D₅×M₁₆	—	2	2	no	—
58	D₅×M₁₆	—	2	2	no	—
59	D₅×M₁₆	—	2	2	no	—
60	D₅×M₁₆	—	2	2	no	—
61	C₂×#676	—	2	2	no	—
62	C₂×#676	C₂×C₄	1	2	yes	—
63	C₂×#676	C₂×C₄	1	1	yes	characteristic
64	C₂×#676	C₂×C₄	1	1	yes	characteristic
65	C₂×#676	C₂×C₄	1	1	yes	characteristic
66	C₂×#676	C₂×C₄	1	1	yes	characteristic
67	C₂×#676	D₄	1	2	yes	—
68	C₂×#676	D₄	1	2	yes	—
69	C₂×#676	Q₈	1	2	yes	—
70	C₂×#676	Q₈	1	2	yes	—
71	C₂×C₈×D₅	—	2	2	no	—
72	C₂×C₈×D₅	C₂×C₄	1	2	yes	—
73	#4038	—	2	1	no	—
74	#4038	—	2	2	no	—
75	D₅×C₄⋊C₄	—	2	1	no	—
76	D₅×C₄⋊C₄	—	2	2	no	—
77	D₅×C₂²⋊C₄	—	2	1	no	—
78	D₅×C₂²⋊C₄	—	2	2	no	—
79	#4023	—	2	1	no	—
80	#4023	—	2	2	no	—
81	#4018	—	2	2	no	—
82	#4018	C₂×C₄	1	2	yes	—
83	C₄²×D₅	—	2	2	no	—
84	C₄²×D₅	C₂×C₄	1	2	yes	—
85	C₅×#108	—	2	1	no	—
86	C₅×#108	—	2	1	no	—
87	C₅×#107	—	2	1	no	—
88	C₅×#106	—	2	1	no	—
89	C₅×#97	C₂×C₄	1	2	yes	complemented
90	C₄×C₅×C₈	C₂×C₄	1	2	yes	complemented
91	#3954	—	2	4	no	—
92	#3951	—	2	1	no	—
93	#3951	—	2	1	no	—
94	#3950	—	2	1	no	—
95	#3949	—	2	1	no	—
96	#3947	C₂×C₄	1	2	yes	complemented
97	#3947	C₂×C₄	1	2	yes	complemented
98	C₈×Dic₅	C₂×C₄	1	2	yes	complemented
99	C₈×Dic₅	C₂×C₄	1	2	yes	complemented
100	#3940	—	2	2	no	—
101	#3939	—	2	2	no	—
102	#3935	C₂×C₄	1	2	yes	complemented
103	C₄×#168	C₂×C₄	1	2	yes	complemented
104	C₂×#430	—	5	1	no	—
105	#2911	—	5	1	no	—
106	#2873	—	5	1	no	—
107	#1833	—	5	1	no	—
108	#1833	—	5	1	no	—
109	#1833	—	5	1	no	—
110	#1833	—	5	2	no	—
111	#1833	—	5	2	no	—
112	#1833	D₅	1	1	yes	characteristic, complemented
113	C₂×#344	—	5	2	no	—
114	C₂×H(3,ℤ/4)	—	5	2	no	—
115	C₂³×D₅	#41	1	1	yes	characteristic
116	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
117	C₂²×Dic₅	#41	1	1	yes	characteristic
118	C₂×C₄×D₅	—	2	2	no	—
119	C₂×C₄×D₅	—	4	2	no	—
120	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₄×D₅	C₂×D₄	1	2	yes	—
123	C₂×C₄×D₅	C₂×Q₈	1	2	yes	—
124	C₂×C₄×D₅	#41	1	2	yes	—
125	C₂×C₄×D₅	#41	1	2	yes	—
126	C₂×C₄×D₅	#41	1	1	yes	characteristic
127	C₂×C₄×D₅	#41	1	1	yes	characteristic
128	C₅×M₁₆	—	2	1	no	—
129	C₅×M₁₆	—	2	1	no	—
130	C₅×M₁₆	—	2	2	no	—
131	C₅×M₁₆	—	2	2	no	—
132	C₂×C₅×C₈	—	2	2	no	—
133	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
134	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
137	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
138	C₂×C₅×C₈	C₂×Q₈	1	1	yes	characteristic
139	C₂×C₅×C₈	C₂×Q₈	1	1	yes	characteristic
140	C₅×C₄⋊C₄	—	2	1	no	—
141	C₅×C₄⋊C₄	—	2	2	no	—
142	C₅×C₂²⋊C₄	—	2	1	no	—
143	C₅×C₂²⋊C₄	—	2	2	no	—
144	C₄²×C₅	—	2	2	no	—
145	C₄²×C₅	C₂²×C₄	1	2	yes	—
146	C₂²⋊Dic₅	—	2	1	no	—
147	C₂²⋊Dic₅	—	2	2	no	—
148	#685	—	2	2	no	—
149	#685	—	4	2	no	—
150	C₄⋊Dic₅	—	2	1	no	—
151	C₄⋊Dic₅	—	2	2	no	—
152	#683	—	2	2	no	—
153	#683	—	4	2	no	—
154	C₄×Dic₅	—	2	2	no	—
155	C₄×Dic₅	—	2	2	no	—
156	C₄×Dic₅	—	4	2	no	—
157	C₄×Dic₅	C₂²×C₄	1	2	yes	—
158	#681	—	2	1	no	—
159	#681	—	2	1	no	—
160	#681	—	2	2	no	—
161	#681	—	2	2	no	—
162	C₂×#168	—	2	2	no	—
163	C₂×#168	C₂²×C₄	1	2	yes	—
164	C₂×#168	C₂²×C₄	1	1	yes	characteristic
165	C₂×#168	C₂²×C₄	1	1	yes	characteristic
166	C₂×#168	C₂×D₄	1	2	yes	—
167	C₂×#168	C₂×Q₈	1	2	yes	—
168	#676	—	2	4	no	—
169	#676	—	4	2	no	—
170	#676	—	4	2	no	—
171	#676	C₄⋊C₄	1	2	yes	—
172	#676	C₄⋊C₄	1	2	yes	—
173	#676	C₄⋊C₄	1	2	yes	—
174	#676	C₄⋊C₄	1	2	yes	—
175	#676	C₄⋊C₄	1	2	yes	—
176	#676	C₄⋊C₄	1	2	yes	—
177	#676	C₄⋊C₄	1	2	yes	—
178	#676	C₄⋊C₄	1	2	yes	—
179	C₈×D₅	—	2	4	no	—
180	C₈×D₅	—	4	2	no	—
181	C₈×D₅	—	4	2	no	—
182	C₂²×M₁₆	—	5	1	no	—
183	C₂²×M₁₆	—	5	1	no	—
184	C₂²×M₁₆	—	5	2	no	—
185	C₂×#117	—	5	1	no	—
186	C₂×#117	—	5	2	no	—
187	#430	—	10	2	no	—
188	#430	—	10	2	no	—
189	C₂×#108	—	5	2	no	—
190	C₂×#108	—	5	1	no	—
191	C₂×#108	C₂×D₅	1	1	yes	characteristic
192	#428	—	10	2	no	—
193	#428	—	10	2	no	—
194	#427	—	5	1	no	—
195	#427	—	5	2	no	—
196	#427	C₂×D₅	1	1	yes	characteristic
197	#405	—	5	1	no	—
198	#405	—	5	1	no	—
199	#405	—	5	1	no	—
200	#405	—	5	2	no	—
201	#405	—	5	2	no	—
202	#405	C₂×D₅	1	1	yes	characteristic
203	C₄×M₁₆	—	5	2	no	—
204	C₄×M₁₆	—	5	2	no	—
205	#344	—	5	2	no	—
206	#344	—	5	2	no	—
207	#344	—	5	2	no	—
208	#344	C₂×D₅	1	2	yes	—
209	H(3,ℤ/4)	—	5	2	no	—
210	H(3,ℤ/4)	—	5	2	no	—
211	H(3,ℤ/4)	—	5	2	no	—
212	H(3,ℤ/4)	C₂×D₅	1	2	yes	—
213	C₂³×C₅	C₂×#41	1	1	yes	characteristic
214	C₂²×D₅	—	8	1	no	—
215	C₂²×D₅	#117	1	1	yes	characteristic
216	C₂²×D₅	#117	1	1	yes	characteristic
217	C₂²×D₅	#124	1	2	yes	—
218	C₂²×D₅	#125	1	2	yes	—
219	C₂×C₄×C₅	—	2	2	no	—
220	C₂×C₄×C₅	—	4	2	no	—
221	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
222	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
223	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
224	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
225	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
226	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
227	C₂×Dic₅	—	2	2	no	—
228	C₂×Dic₅	—	4	2	no	—
229	C₂×Dic₅	#117	1	1	yes	characteristic
230	C₂×Dic₅	#117	1	1	yes	characteristic
231	C₂×Dic₅	#124	1	2	yes	—
232	C₂×Dic₅	#125	1	2	yes	—
233	C₄×D₅	—	8	2	no	—
234	C₄×D₅	—	8	4	no	—
235	C₄×D₅	C₂×C₄⋊C₄	1	2	yes	—
236	C₄×D₅	C₂×C₄⋊C₄	1	2	yes	—
237	C₄×D₅	#117	1	2	yes	—
238	C₄×D₅	#117	1	2	yes	—
239	C₄×D₅	#124	1	2	yes	—
240	C₄×D₅	#124	1	2	yes	—
241	C₄×D₅	#125	1	2	yes	—
242	C₄×D₅	#125	1	2	yes	—
243	C₅×C₈	—	2	2	no	—
244	C₅×C₈	—	4	2	no	—
245	C₅×C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
246	C₅×C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
247	C₅×C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
248	C₅×C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
249	#168	—	2	2	no	—
250	#168	—	4	2	no	—
251	#168	C₂×C₄⋊C₄	1	2	yes	—
252	#168	C₂×C₄⋊C₄	1	2	yes	—
253	C₂³×C₄	—	5	1	no	—
254	C₂×M₁₆	—	5	1	no	—
255	C₂×M₁₆	—	5	1	no	—
256	C₂×M₁₆	—	5	1	no	—
257	C₂×M₁₆	—	5	1	no	—
258	C₂×M₁₆	—	5	1	no	—
259	C₂×M₁₆	—	5	2	no	—
260	C₂×M₁₆	—	5	2	no	—
261	C₂×M₁₆	—	5	2	no	—
262	C₂×M₁₆	—	5	2	no	—
263	C₂×M₁₆	—	5	2	no	—
264	C₂×M₁₆	—	5	2	no	—
265	C₂×M₁₆	—	10	2	no	—
266	C₂×M₁₆	—	10	2	no	—
267	C₂×M₁₆	—	10	2	no	—
268	C₂×M₁₆	—	10	2	no	—
269	C₂×M₁₆	—	10	2	no	—
270	C₂×M₁₆	—	10	2	no	—
271	C₂×M₁₆	—	10	2	no	—
272	C₂×M₁₆	C₂²×D₅	1	2	yes	—
273	C₂×M₁₆	C₂²×D₅	1	1	yes	characteristic
274	C₂²×C₈	—	5	1	no	—
275	C₂²×C₈	—	5	2	no	—
276	C₂²×C₈	—	10	2	no	—
277	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
278	#117	—	5	1	no	—
279	#117	—	5	2	no	—
280	#117	—	5	2	no	—
281	#117	—	10	2	no	—
282	#117	—	10	1	no	—
283	#117	—	10	1	no	—
284	#117	—	10	2	no	—
285	#117	—	10	2	no	—
286	#117	C₂²×D₅	1	2	yes	—
287	#117	C₂²×D₅	1	1	yes	characteristic
288	C₂×C₄⋊C₄	—	10	1	no	—
289	C₂×C₄⋊C₄	—	10	2	no	—
290	C₂×C₂²⋊C₄	—	10	1	no	—
291	C₂×C₂²⋊C₄	—	10	2	no	—
292	C₂×C₄²	—	5	2	no	—
293	C₂×C₄²	—	10	2	no	—
294	#108	—	2	1	no	—
295	#108	—	2	1	no	—
296	#108	—	10	4	no	—
297	#108	—	10	1	no	—
298	#108	—	10	1	no	—
299	#107	—	2	1	no	—
300	#107	—	10	2	no	—
301	#107	—	10	1	no	—
302	#106	—	2	1	no	—
303	#106	—	10	2	no	—
304	#106	—	10	1	no	—
305	#97	—	5	2	no	—
306	#97	—	5	2	no	—
307	#97	—	5	2	no	—
308	#97	C₄×D₅	1	2	yes	complemented
309	C₄×C₈	—	5	2	no	—
310	C₄×C₈	—	5	2	no	—
311	C₄×C₈	—	5	2	no	—
312	C₄×C₈	C₄×D₅	1	2	yes	complemented
313	C₂²×C₅	—	4	1	no	—
314	C₂²×C₅	C₂×#117	1	1	yes	characteristic
315	C₂²×C₅	C₂×#124	1	1	yes	characteristic
316	C₂²×C₅	C₂×#125	1	1	yes	characteristic
317	C₂×D₅	—	4	1	no	—
318	C₂×D₅	—	4	2	no	—
319	C₂×D₅	—	4	1	no	—
320	C₂×D₅	—	4	2	no	—
321	C₂×D₅	#382	1	2	yes	—
322	C₂×D₅	#382	1	2	yes	—
323	C₄×C₅	—	4	2	no	—
324	C₄×C₅	—	8	2	no	—
325	C₄×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
326	C₄×C₅	C₂×#117	1	1	yes	characteristic
327	C₄×C₅	C₂×#124	1	1	yes	characteristic
328	C₄×C₅	C₂×#125	1	1	yes	characteristic
329	Dic₅	—	4	2	no	—
330	Dic₅	—	8	2	no	—
331	Dic₅	#382	1	2	yes	—
332	Dic₅	#382	1	2	yes	—
333	C₂⁴	—	5	1	no	—
334	C₂²×C₄	—	5	1	no	—
335	C₂²×C₄	—	5	1	no	—
336	C₂²×C₄	—	5	1	no	—
337	C₂²×C₄	—	5	2	no	—
338	C₂²×C₄	—	5	2	no	—
339	C₂²×C₄	—	5	2	no	—
340	C₂²×C₄	—	5	1	no	—
341	C₂²×C₄	—	5	1	no	—
342	C₂²×C₄	—	5	2	no	—
343	C₂²×C₄	—	10	2	no	—
344	C₂²×C₄	—	20	2	no	—
345	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
346	M₁₆	—	2	1	no	—
347	M₁₆	—	2	1	no	—
348	M₁₆	—	2	2	no	—
349	M₁₆	—	2	2	no	—
350	M₁₆	—	5	2	no	—
351	M₁₆	—	5	2	no	—
352	M₁₆	—	5	2	no	—
353	M₁₆	—	5	2	no	—
354	M₁₆	—	5	2	no	—
355	M₁₆	—	5	2	no	—
356	M₁₆	—	5	2	no	—
357	M₁₆	—	5	2	no	—
358	M₁₆	—	10	4	no	—
359	M₁₆	—	10	1	no	—
360	M₁₆	—	10	1	no	—
361	M₁₆	—	10	2	no	—
362	M₁₆	—	10	2	no	—
363	M₁₆	—	20	2	no	—
364	M₁₆	—	20	2	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	5	1	no	—
367	C₂×C₈	—	5	1	no	—
368	C₂×C₈	—	5	2	no	—
369	C₂×C₈	—	5	2	no	—
370	C₂×C₈	—	5	2	no	—
371	C₂×C₈	—	10	4	no	—
372	C₂×C₈	—	10	2	no	—
373	C₂×C₈	—	20	2	no	—
374	C₂×C₈	—	20	2	no	—
375	C₂×C₈	C₂×C₄×D₅	1	2	yes	—
376	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
377	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
378	C₂×C₈	D₄×D₅	1	1	yes	characteristic
379	C₂×C₈	D₄×D₅	1	1	yes	characteristic
380	C₂×C₈	Q₈×D₅	1	1	yes	characteristic
381	C₂×C₈	Q₈×D₅	1	1	yes	characteristic
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	—	10	2	no	—
385	C₄⋊C₄	—	10	1	no	—
386	C₄⋊C₄	—	10	2	no	—
387	C₄⋊C₄	—	20	2	no	—
388	C₂²⋊C₄	—	2	1	no	—
389	C₂²⋊C₄	—	2	2	no	—
390	C₂²⋊C₄	—	10	2	no	—
391	C₂²⋊C₄	—	10	1	no	—
392	C₂²⋊C₄	—	10	2	no	—
393	C₂²⋊C₄	—	20	2	no	—
394	C₄²	—	2	2	no	—
395	C₄²	—	5	2	no	—
396	C₄²	—	10	2	no	—
397	C₄²	—	10	2	no	—
398	C₄²	—	20	2	no	—
399	C₄²	C₂×C₄×D₅	1	2	yes	—
400	C₂×C₅	—	2	1	no	—
401	C₂×C₅	—	2	1	no	—
402	C₂×C₅	—	2	1	no	—
403	C₂×C₅	C₂×#382	1	1	yes	characteristic
404	D₅	—	2	2	no	—
405	D₅	—	2	2	no	—
406	C₂³	—	5	1	no	—
407	C₂³	—	5	1	no	—
408	C₂³	—	5	2	no	—
409	C₂³	—	5	2	no	—
410	C₂³	—	40	1	no	—
411	C₂³	D₅×#41	1	1	yes	characteristic
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	5	1	no	—
415	C₂×C₄	—	5	1	no	—
416	C₂×C₄	—	5	2	no	—
417	C₂×C₄	—	5	2	no	—
418	C₂×C₄	—	5	2	no	—
419	C₂×C₄	—	5	2	no	—
420	C₂×C₄	—	5	2	no	—
421	C₂×C₄	—	5	2	no	—
422	C₂×C₄	—	5	2	no	—
423	C₂×C₄	—	5	2	no	—
424	C₂×C₄	—	5	2	no	—
425	C₂×C₄	—	5	2	no	—
426	C₂×C₄	—	10	2	no	—
427	C₂×C₄	—	20	2	no	—
428	C₂×C₄	—	40	2	no	—
429	C₂×C₄	—	40	4	no	—
430	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
431	C₂×C₄	C₂×D₄×D₅	1	1	yes	characteristic
432	C₂×C₄	C₂×Q₈×D₅	1	1	yes	characteristic
433	C₂×C₄	D₅×#41	1	1	yes	characteristic
434	C₂×C₄	D₅×#41	1	1	yes	characteristic
435	C₂×C₄	D₅×#41	1	1	yes	characteristic
436	C₈	—	2	2	no	—
437	C₈	—	4	2	no	—
438	C₈	—	5	2	no	—
439	C₈	—	5	2	no	—
440	C₈	—	10	2	no	—
441	C₈	—	20	2	no	—
442	C₈	D₅×C₄⋊C₄	1	1	yes	characteristic
443	C₈	D₅×C₄⋊C₄	1	1	yes	characteristic
444	C₈	D₅×C₄⋊C₄	1	1	yes	characteristic
445	C₈	D₅×C₄⋊C₄	1	1	yes	characteristic
446	C₅	#20757	1	1	yes	characteristic, complemented, Sylow
447	C₂²	—	4	1	no	—
448	C₂²	—	5	2	no	—
449	C₂²	—	5	2	no	—
450	C₂²	—	20	1	no	—
451	C₂²	—	20	2	no	—
452	C₂²	—	20	1	no	—
453	C₂²	—	20	2	no	—
454	C₂²	D₅×#117	1	1	yes	characteristic
455	C₂²	D₅×#124	1	1	yes	characteristic
456	C₂²	D₅×#125	1	1	yes	characteristic
457	C₄	—	4	2	no	—
458	C₄	—	5	2	no	—
459	C₄	—	5	2	no	—
460	C₄	—	8	2	no	—
461	C₄	—	20	2	no	—
462	C₄	—	40	2	no	—
463	C₄	C₂×D₅×C₄⋊C₄	1	1	yes	characteristic
464	C₄	D₅×#117	1	1	yes	characteristic
465	C₄	D₅×#124	1	1	yes	characteristic
466	C₄	D₅×#125	1	1	yes	characteristic
467	C₂	—	2	1	no	—
468	C₂	—	2	1	no	—
469	C₂	—	2	1	no	—
470	C₂	—	10	2	no	—
471	C₂	—	10	2	no	—
472	C₂	D₅×#382	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₅×#117
commutator	C₂×C₄×C₅	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₅
Fitting	C₅×#1833	C₂
socle	C₂×C₅	C₂×#382
prime radical	C₂³×D₅	#41
cosocle	C₂²×C₄×C₅	C₂⁴
hypercenter	#1833	D₅
hypocenter	C₅	#20757
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₄ ◁ #117 ◁ #1833

Complements

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

N	H ≅ G/N	type
4. C₅×#1833	C₂	semidirect
5. #10601491	C₂	semidirect
6. #10601450	C₂	semidirect
7. #10600689	C₂	semidirect
9. #10599806	C₂	semidirect
11. #10599492	C₂	semidirect
31. #64997	C₄	semidirect
32. #64996	C₄	semidirect
33. #64978	C₄	semidirect
34. C₄×#676	C₄	semidirect
89. C₅×#97	C₂×C₄	semidirect
90. C₄×C₅×C₈	C₂×C₄	semidirect
96. #3947	C₂×C₄	semidirect
97. #3947	C₂×C₄	semidirect
98. C₈×Dic₅	C₂×C₄	semidirect
99. C₈×Dic₅	C₂×C₄	semidirect
102. #3935	C₂×C₄	semidirect
103. C₄×#168	C₂×C₄	semidirect
112. #1833	D₅	semidirect
308. #97	C₄×D₅	semidirect
312. C₄×C₈	C₄×D₅	semidirect
446. C₅	#20757	semidirect

Maximal subgroups

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

subgroup	index
C₂×#65182	2
#10610908	2
#10610279	2
C₅×#1833	2
#10601491	2
#10601450	2
#10600689	2
D₅×#344	2
#10599806	2
D₅×H(3,ℤ/4)	2
#10599492	2
#20757	5