Subgroups — #12069340

Order 1280.

624 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10611033	C₂	1	1	yes	maximal, characteristic
2	C₈×#709	C₂	1	1	yes	maximal, characteristic
3	#10610176	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1451	C₂	1	1	yes	maximal, characteristic, complemented
5	#10601546	C₂	1	1	yes	maximal, characteristic, complemented
6	#10600649	C₂	1	1	yes	maximal, characteristic, complemented
7	#10600647	C₂	1	1	yes	maximal, characteristic
8	#10598879	C₂	1	2	yes	maximal, complemented
9	#10598877	C₂	1	2	yes	maximal, complemented
10	#10598872	C₂	1	2	yes	maximal, complemented
11	#10598869	C₂	1	2	yes	maximal, complemented
12	C₄×#709	C₂²	1	1	yes	characteristic
13	#65804	C₂²	1	1	yes	characteristic
14	C₅×#431	C₂²	1	1	yes	characteristic
15	C₄×C₅×M₁₆	C₂²	1	1	yes	characteristic
16	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
17	C₈×C₂²⋊D₅	—	2	1	no	—
18	C₈×C₂²⋊D₅	—	2	1	no	—
19	#65391	—	2	1	no	—
20	#65390	—	2	1	no	—
21	#65214	C₂²	1	1	yes	characteristic
22	#65213	C₂²	1	1	yes	characteristic
23	#65140	C₄	1	1	yes	characteristic
24	#65138	C₄	1	1	yes	characteristic
25	#65135	C₄	1	1	yes	characteristic
26	#65130	C₄	1	1	yes	characteristic
27	#65022	C₄	1	2	yes	—
28	#65012	C₄	1	2	yes	—
29	C₄×Dic₂₀	C₂²	1	2	yes	—
30	C₄×#677	C₂²	1	2	yes	—
31	C₈×D₂₀	C₂²	1	1	yes	characteristic
32	C₈×D₂₀	C₂²	1	1	yes	characteristic
33	#64974	—	2	1	no	—
34	C₄×C₈×D₅	—	2	1	no	—
35	#64968	—	2	1	no	—
36	#64968	C₂²	1	2	yes	—
37	C₈×Dic₁₀	—	2	1	no	—
38	C₈×Dic₁₀	C₂²	1	2	yes	—
39	C₈×Dic₁₀	C₂²	1	1	yes	characteristic
40	C₈×Dic₁₀	C₂²	1	1	yes	characteristic
41	C₅×#322	C₂²	1	2	yes	—
42	C₅×#322	C₂²	1	2	yes	—
43	#64679	C₂²	1	2	yes	—
44	#64678	C₂²	1	2	yes	—
45	#64677	C₂²	1	2	yes	—
46	#64676	C₂²	1	2	yes	—
47	#64676	C₂²	1	2	yes	—
48	#64676	C₂²	1	2	yes	—
49	#17916	—	5	1	no	maximal, Sylow
50	C₂×#709	C₂×C₄	1	1	yes	characteristic
51	C₂×C₅×M₁₆	—	2	1	no	—
52	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
53	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
54	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
55	C₄×C₂²⋊D₅	—	2	1	no	—
56	C₄×C₂²⋊D₅	—	2	1	no	—
57	#4072	—	2	1	no	—
58	#4072	C₂×C₄	1	1	yes	characteristic
59	#4070	—	2	1	no	—
60	#4070	C₂×C₄	1	2	yes	—
61	C₂×#681	—	2	1	no	—
62	C₂×Dic₂₀	C₂×C₄	1	2	yes	—
63	C₂×#677	C₂×C₄	1	2	yes	—
64	C₂×C₈×D₅	—	2	1	no	—
65	C₂×C₈×D₅	—	2	1	no	—
66	C₄×D₂₀	C₂×C₄	1	1	yes	characteristic
67	C₄×D₂₀	C₂³	1	1	yes	characteristic
68	#4018	—	2	1	no	—
69	C₄²×D₅	—	2	1	no	—
70	#4016	—	2	1	no	—
71	#4015	C₂×C₄	1	1	yes	characteristic
72	#4015	C₂×C₄	1	1	yes	characteristic
73	C₄×Dic₁₀	—	2	1	no	—
74	C₄×Dic₁₀	C₂×C₄	1	1	yes	characteristic
75	C₄×Dic₁₀	C₂³	1	2	yes	—
76	C₄×Dic₁₀	C₂³	1	1	yes	characteristic
77	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
78	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
79	C₅×C₂²⋊C₈	C₂×C₄	1	2	yes	—
80	C₅×#97	—	2	1	no	—
81	C₄×C₅×C₈	D₄	1	1	yes	characteristic
82	C₄×C₅×C₈	D₄	1	1	yes	characteristic
83	C₄×C₅×C₈	C₂³	1	2	yes	—
84	C₄×C₅×C₈	C₂³	1	2	yes	—
85	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
86	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
87	C₂²⋊#168	—	2	1	no	—
88	#3953	C₂×C₄	1	2	yes	—
89	#3952	—	2	1	no	—
90	#3952	—	2	1	no	—
91	#3950	C₂×C₄	1	2	yes	—
92	#3949	C₂×C₄	1	2	yes	—
93	#3948	C₂×C₄	1	2	yes	—
94	#3948	C₂×C₄	1	2	yes	—
95	#3948	C₂×C₄	1	2	yes	—
96	#3947	—	2	2	no	—
97	#3946	—	2	2	no	—
98	#3946	—	2	2	no	—
99	#3946	—	2	1	no	—
100	#3946	—	2	1	no	—
101	C₈×Dic₅	—	2	2	no	—
102	C₈×Dic₅	—	2	1	no	—
103	C₈×Dic₅	—	2	1	no	—
104	C₄⋊#168	—	2	1	no	—
105	C₄⋊#168	C₂³	1	1	yes	characteristic
106	C₄⋊#168	C₂³	1	1	yes	characteristic
107	C₄⋊#168	C₂³	1	2	yes	—
108	C₄×#168	—	2	1	no	—
109	#3107	—	5	1	no	—
110	C₈×#41	—	5	1	no	—
111	#2960	—	5	1	no	—
112	#1584	—	5	2	no	—
113	#1582	—	5	2	no	—
114	#1579	—	5	2	no	—
115	SD₁₆⋊C₈	—	5	2	no	—
116	#1574	—	5	1	no	—
117	#1489	—	5	1	no	—
118	#1485	—	5	1	no	—
119	#1451	D₅	1	1	yes	characteristic, complemented
120	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
121	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₅	#41	1	1	yes	characteristic
123	C₂×C₂²⋊D₅	—	2	1	no	—
124	#709	—	2	2	no	—
125	#709	—	2	2	no	—
126	C₂×D₂₀	C₂²×C₄	1	1	yes	characteristic
127	C₂×C₄×D₅	—	2	1	no	—
128	C₂×C₄×D₅	—	2	1	no	—
129	C₂×C₄×D₅	—	2	1	no	—
130	C₂×Dic₁₀	—	2	1	no	—
131	C₂×Dic₁₀	C₂²×C₄	1	2	yes	—
132	C₂×Dic₁₀	C₂²×C₄	1	1	yes	characteristic
133	C₅×M₁₆	—	4	2	no	—
134	C₂×C₅×C₈	—	2	2	no	—
135	C₂×C₅×C₈	—	2	2	no	—
136	C₂×C₅×C₈	—	4	1	no	—
137	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
138	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
139	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
140	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
141	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
142	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
143	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
144	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
145	C₄²×C₅	#41	1	1	yes	characteristic
146	C₄²×C₅	C₂⁴	1	1	yes	characteristic
147	C₂²⋊Dic₅	—	2	2	no	—
148	C₂²⋊Dic₅	—	2	1	no	—
149	#685	—	2	1	no	—
150	#685	—	2	1	no	—
151	C₄⋊Dic₅	—	2	1	no	—
152	C₄⋊Dic₅	—	2	1	no	—
153	C₄⋊Dic₅	—	2	1	no	—
154	C₄⋊Dic₅	C₂²×C₄	1	1	yes	characteristic
155	C₄⋊Dic₅	C₂²×C₄	1	1	yes	characteristic
156	C₄⋊Dic₅	C₂²×C₄	1	2	yes	—
157	#683	—	2	2	no	—
158	#683	—	2	1	no	—
159	#683	—	2	2	no	—
160	#683	—	2	1	no	—
161	C₄×Dic₅	—	2	1	no	—
162	C₄×Dic₅	—	2	1	no	—
163	C₄×Dic₅	—	2	1	no	—
164	C₄×Dic₅	—	2	2	no	—
165	#681	—	4	2	no	—
166	C₂×#168	—	2	1	no	—
167	C₂×#168	—	2	1	no	—
168	C₂×#168	—	2	2	no	—
169	Dic₂₀	—	2	4	no	—
170	#677	—	2	4	no	—
171	C₈×D₅	—	4	2	no	—
172	C₈×D₅	—	4	2	no	—
173	#533	—	5	1	no	—
174	C₄×#41	—	5	1	no	—
175	#485	—	5	2	no	—
176	#475	—	5	1	no	—
177	#474	—	5	1	no	—
178	#462	—	5	1	no	—
179	#461	—	5	1	no	—
180	#452	—	5	2	no	—
181	#446	—	5	2	no	—
182	#446	—	10	1	no	—
183	C₈×Q₈	—	5	2	no	—
184	C₈×Q₈	—	5	1	no	—
185	C₈×Q₈	—	5	1	no	—
186	C₈×Q₈	—	10	1	no	—
187	C₄×Q₁₆	—	5	2	no	—
188	C₄×SD₁₆	—	5	2	no	—
189	C₈×D₄	—	5	1	no	—
190	C₈×D₄	—	5	1	no	—
191	C₈×D₄	—	10	1	no	—
192	C₈×D₄	—	10	1	no	—
193	#431	—	5	1	no	—
194	#431	—	10	1	no	—
195	#431	C₂×D₅	1	1	yes	characteristic
196	#424	—	10	1	no	—
197	#423	—	5	1	no	—
198	#405	—	10	1	no	—
199	C₄×M₁₆	C₂×D₅	1	1	yes	characteristic
200	C₂×C₄×C₈	—	10	1	no	—
201	C₂×C₄×C₈	C₂×D₅	1	1	yes	characteristic
202	#335	—	5	2	no	—
203	#334	—	5	2	no	—
204	Q₈⋊C₈	—	5	2	no	—
205	Q₈⋊C₈	—	5	2	no	—
206	Q₈⋊C₈	—	5	2	no	—
207	D₄⋊C₈	—	5	2	no	—
208	#322	C₂×D₅	1	2	yes	—
209	#322	C₂×D₅	1	2	yes	—
210	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
211	C₂²×D₅	—	2	1	no	—
212	C₂×C₄×C₅	—	2	1	no	—
213	C₂×C₄×C₅	—	2	1	no	—
214	C₂×C₄×C₅	—	2	1	no	—
215	C₂×C₄×C₅	—	2	1	no	—
216	C₂×C₄×C₅	—	2	2	no	—
217	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
218	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
219	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
220	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
221	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
222	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
223	C₂²⋊D₅	—	2	4	no	—
224	C₂×Dic₅	—	2	1	no	—
225	C₂×Dic₅	—	2	1	no	—
226	C₂×Dic₅	—	2	1	no	—
227	C₂×Dic₅	—	2	2	no	—
228	C₂×Dic₅	—	2	2	no	—
229	D₂₀	—	2	1	no	—
230	D₂₀	#131	1	2	yes	—
231	C₄×D₅	—	2	4	no	—
232	C₄×D₅	—	4	1	no	—
233	C₄×D₅	—	4	1	no	—
234	C₄×D₅	—	4	2	no	—
235	Dic₁₀	—	2	1	no	—
236	Dic₁₀	—	2	2	no	—
237	Dic₁₀	—	2	2	no	—
238	Dic₁₀	—	4	2	no	—
239	Dic₁₀	#131	1	2	yes	—
240	C₅×C₈	—	2	2	no	—
241	C₅×C₈	—	2	2	no	—
242	C₅×C₈	—	2	1	no	—
243	C₅×C₈	—	2	1	no	—
244	C₅×C₈	—	2	1	no	—
245	C₅×C₈	—	4	2	no	—
246	C₅×C₈	#137	1	2	yes	—
247	#168	—	4	1	no	—
248	#168	—	4	1	no	—
249	#168	—	4	2	no	—
250	C₂×#41	—	5	1	no	—
251	C₂×Q₁₆	—	5	2	no	—
252	C₂×SD₁₆	—	5	2	no	—
253	C₂×M₁₆	—	2	1	no	—
254	C₂×M₁₆	—	10	1	no	—
255	C₂²×C₈	—	10	1	no	—
256	C₂²×C₈	—	10	1	no	—
257	C₂²×C₈	D₂₀	1	1	yes	characteristic
258	C₂²×C₈	D₂₀	1	1	yes	characteristic
259	C₄⋊Q₈	—	5	1	no	—
260	C₄⋊Q₈	—	5	1	no	—
261	#125	—	10	1	no	—
262	C₂²⋊Q₈	—	5	2	no	—
263	C₂²⋊Q₈	—	10	1	no	—
264	C₄×Q₈	—	5	1	no	—
265	C₄×Q₈	—	5	1	no	—
266	C₄×Q₈	—	5	2	no	—
267	C₄×Q₈	—	10	1	no	—
268	C₄×D₄	—	5	1	no	—
269	C₄×D₄	—	5	1	no	—
270	C₄×D₄	—	10	1	no	—
271	C₄×D₄	—	10	1	no	—
272	#117	—	5	1	no	—
273	#117	—	10	1	no	—
274	#117	—	10	1	no	—
275	C₂×C₄²	—	10	1	no	—
276	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
277	#107	—	5	2	no	—
278	#106	—	5	2	no	—
279	C₄⋊C₈	—	5	2	no	—
280	C₄⋊C₈	—	5	1	no	—
281	C₄⋊C₈	—	5	1	no	—
282	C₄⋊C₈	—	10	2	no	—
283	C₄⋊C₈	—	10	2	no	—
284	C₄⋊C₈	—	10	1	no	—
285	C₄⋊C₈	—	10	1	no	—
286	C₄⋊C₈	—	10	1	no	—
287	C₄⋊C₈	C₄×D₅	1	1	yes	characteristic
288	C₄⋊C₈	C₄×D₅	1	1	yes	characteristic
289	#103	—	5	2	no	—
290	#103	—	5	2	no	—
291	#103	—	5	2	no	—
292	#102	—	5	2	no	—
293	C₂²⋊C₈	—	10	1	no	—
294	C₂²⋊C₈	—	10	1	no	—
295	C₂²⋊C₈	—	10	1	no	—
296	C₂²⋊C₈	C₄×D₅	1	2	yes	—
297	#97	—	2	1	no	—
298	#97	—	10	2	no	—
299	C₄×C₈	—	10	1	no	—
300	C₄×C₈	—	10	1	no	—
301	C₄×C₈	—	10	2	no	—
302	C₄×C₈	—	10	1	no	—
303	C₄×C₈	D₂₀	1	1	yes	characteristic
304	C₄×C₈	D₂₀	1	1	yes	characteristic
305	C₄×C₈	C₂²×D₅	1	2	yes	—
306	C₄×C₈	C₂²×D₅	1	2	yes	—
307	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
308	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
309	C₂²×C₅	—	2	1	no	—
310	C₂²×C₅	—	2	1	no	—
311	C₂²×C₅	—	2	1	no	—
312	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
313	C₂×D₅	—	2	2	no	—
314	C₂×D₅	—	4	1	no	—
315	C₂×D₅	—	4	1	no	—
316	C₄×C₅	—	2	1	no	—
317	C₄×C₅	—	2	1	no	—
318	C₄×C₅	—	2	1	no	—
319	C₄×C₅	#444	1	2	yes	—
320	C₄×C₅	C₂×#131	1	1	yes	characteristic
321	C₄×C₅	C₂×#131	1	1	yes	characteristic
322	C₄×C₅	C₂×#137	1	1	yes	characteristic
323	C₄×C₅	#575	1	1	yes	characteristic
324	Dic₅	—	2	2	no	—
325	Dic₅	—	4	2	no	—
326	Dic₅	—	4	1	no	—
327	Dic₅	—	4	2	no	—
328	Dic₅	—	4	1	no	—
329	#41	—	10	2	no	—
330	#41	—	10	2	no	—
331	C₂×Q₈	—	5	1	no	—
332	C₂×Q₈	—	5	2	no	—
333	C₂×Q₈	—	10	1	no	—
334	C₂×D₄	—	5	1	no	—
335	C₂×D₄	—	10	1	no	—
336	C₂²×C₄	—	10	1	no	—
337	C₂²×C₄	—	10	1	no	—
338	C₂²×C₄	—	10	1	no	—
339	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
340	C₂²×C₄	C₂×D₂₀	1	1	yes	characteristic
341	C₂²×C₄	#709	1	1	yes	characteristic
342	Q₁₆	—	10	4	no	—
343	SD₁₆	—	10	4	no	—
344	M₁₆	—	4	2	no	—
345	M₁₆	—	20	2	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	4	1	no	—
349	C₂×C₈	—	10	1	no	—
350	C₂×C₈	—	10	1	no	—
351	C₂×C₈	—	10	2	no	—
352	C₂×C₈	—	20	2	no	—
353	C₂×C₈	—	20	2	no	—
354	C₂×C₈	C₂×C₄×D₅	1	2	yes	—
355	C₂×C₈	C₂×C₄×D₅	1	2	yes	—
356	C₂×C₈	C₂×D₂₀	1	1	yes	characteristic
357	C₂×C₈	C₂×D₂₀	1	1	yes	characteristic
358	C₂×C₈	C₂×D₂₀	1	1	yes	characteristic
359	C₂×C₈	C₂×D₂₀	1	1	yes	characteristic
360	C₄⋊C₄	—	5	2	no	—
361	C₄⋊C₄	—	5	1	no	—
362	C₄⋊C₄	—	5	1	no	—
363	C₄⋊C₄	—	10	1	no	—
364	C₄⋊C₄	—	10	2	no	—
365	C₄⋊C₄	—	10	1	no	—
366	C₄⋊C₄	—	10	1	no	—
367	C₄⋊C₄	—	10	1	no	—
368	C₄⋊C₄	—	10	2	no	—
369	C₄⋊C₄	—	10	1	no	—
370	C₂²⋊C₄	—	10	1	no	—
371	C₂²⋊C₄	—	10	2	no	—
372	C₂²⋊C₄	—	10	1	no	—
373	C₂²⋊C₄	—	10	1	no	—
374	C₄²	—	10	1	no	—
375	C₄²	—	10	2	no	—
376	C₄²	—	10	1	no	—
377	C₄²	—	10	1	no	—
378	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
379	C₄²	C₂×D₂₀	1	1	yes	characteristic
380	C₄²	#709	1	1	yes	characteristic
381	C₄²	C₂³×D₅	1	1	yes	characteristic
382	C₂×C₅	—	4	1	no	—
383	C₂×C₅	#2929	1	1	yes	characteristic
384	C₂×C₅	C₄×#137	1	1	yes	characteristic
385	C₂×C₅	C₂×#444	1	1	yes	characteristic
386	D₅	—	4	2	no	—
387	C₂³	—	10	1	no	—
388	C₂³	C₄×D₂₀	1	1	yes	characteristic
389	Q₈	—	5	2	no	—
390	Q₈	—	10	1	no	—
391	Q₈	—	10	2	no	—
392	Q₈	—	10	2	no	—
393	Q₈	—	20	2	no	—
394	D₄	—	5	2	no	—
395	D₄	—	10	4	no	—
396	D₄	—	10	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	10	4	no	—
403	C₂×C₄	—	10	1	no	—
404	C₂×C₄	—	10	1	no	—
405	C₂×C₄	—	10	1	no	—
406	C₂×C₄	—	10	2	no	—
407	C₂×C₄	—	10	2	no	—
408	C₂×C₄	—	20	1	no	—
409	C₂×C₄	—	20	1	no	—
410	C₂×C₄	—	20	2	no	—
411	C₂×C₄	C₄×D₂₀	1	1	yes	characteristic
412	C₂×C₄	C₄×D₂₀	1	1	yes	characteristic
413	C₂×C₄	C₄×D₂₀	1	1	yes	characteristic
414	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
415	C₂×C₄	C₂²×D₂₀	1	1	yes	characteristic
416	C₂×C₄	C₂×#709	1	1	yes	characteristic
417	C₈	—	2	1	no	—
418	C₈	—	2	1	no	—
419	C₈	—	2	1	no	—
420	C₈	—	2	2	no	—
421	C₈	—	2	2	no	—
422	C₈	—	4	2	no	—
423	C₈	—	20	1	no	—
424	C₈	—	20	1	no	—
425	C₈	—	20	2	no	—
426	C₈	#4055	1	2	yes	—
427	C₅	#17916	1	1	yes	characteristic, complemented, Sylow
428	C₂²	—	2	1	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	2	1	no	—
431	C₂²	—	10	2	no	—
432	C₂²	—	20	1	no	—
433	C₂²	—	20	1	no	—
434	C₂²	C₂×C₄×D₂₀	1	1	yes	characteristic
435	C₄	—	2	1	no	—
436	C₄	—	2	1	no	—
437	C₄	—	2	1	no	—
438	C₄	—	10	2	no	—
439	C₄	—	20	1	no	—
440	C₄	—	20	2	no	—
441	C₄	—	20	1	no	—
442	C₄	—	20	2	no	—
443	C₄	#65006	1	2	yes	—
444	C₄	C₂×#4055	1	1	yes	characteristic
445	C₄	#66082	1	1	yes	characteristic
446	C₄	D₅×#131	1	1	yes	characteristic
447	C₄	D₅×#131	1	1	yes	characteristic
448	C₂	—	4	1	no	—
449	C₂	—	20	2	no	—
450	C₂	C₂×#65006	1	1	yes	characteristic
451	C₂	C₄×#4055	1	1	yes	characteristic
452	C₂	#10610284	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₂₀
commutator	C₂×C₄×C₅	C₂³×C₄
Frattini	C₄²	C₂³×D₅
Fitting	C₅×#1451	C₂
socle	C₂²×C₅	C₂×C₄×D₄
prime radical	C₂×#709	C₂×C₄
cosocle	C₄²×C₅	C₂⁴
hypercenter	#1451	D₅
hypocenter	C₅	#17916
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×C₈ ◁ #1451

Complements

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

N	H ≅ G/N	type
3. #10610176	C₂	semidirect
4. C₅×#1451	C₂	semidirect
5. #10601546	C₂	semidirect
6. #10600649	C₂	semidirect
8. #10598879	C₂	semidirect
9. #10598877	C₂	semidirect
10. #10598872	C₂	semidirect
11. #10598869	C₂	semidirect
119. #1451	D₅	semidirect
427. C₅	#17916	semidirect

Maximal subgroups

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

subgroup	index
#10611033	2
C₈×#709	2
#10610176	2
C₅×#1451	2
#10601546	2
#10600649	2
#10600647	2
#10598879	2
#10598877	2
#10598872	2
#10598869	2
#17916	5