Subgroups — C₅×#19566 #11942286

Order 1280.

648 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3254	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#3208	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#3205	C₂	1	1	yes	maximal, characteristic
4	C₅×#2986	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1698	C₂	1	2	yes	maximal, complemented
6	C₅×#1688	C₂	1	2	yes	maximal, complemented
7	C₅×#1678	C₂	1	2	yes	maximal, complemented
8	C₅×#1668	C₂	1	2	yes	maximal, complemented
9	C₅×#1574	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1545	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1543	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#533	C₂²	1	1	yes	characteristic
13	C₅×#532	C₂²	1	1	yes	characteristic
14	C₂×C₅×#127	C₂²	1	1	yes	characteristic
15	C₅×#493	C₂²	1	2	yes	—
16	C₅×#492	—	2	1	no	—
17	C₅×#486	—	2	1	no	—
18	C₅×#486	C₂²	1	2	yes	—
19	C₅×#477	C₂²	1	2	yes	complemented
20	C₅×#474	—	2	1	no	—
21	C₅×#468	—	2	2	no	—
22	C₅×#461	—	2	1	no	—
23	C₅×#460	C₂²	1	2	yes	—
24	C₅×#460	C₂²	1	2	yes	—
25	C₅×#460	C₂²	1	2	yes	complemented
26	C₅×#459	—	2	1	no	—
27	C₅×#459	—	2	1	no	—
28	C₅×#450	—	2	2	no	—
29	C₅×#447	—	2	2	no	—
30	C₅×#446	—	2	1	no	—
31	C₅×#446	C₂²	1	2	yes	complemented
32	C₅×C₈×Q₈	—	2	1	no	—
33	C₅×C₈×Q₈	C₂²	1	2	yes	complemented
34	C₅×#433	—	2	2	no	—
35	C₅×#431	C₂²	1	1	yes	characteristic
36	C₅×#431	C₂²	1	1	yes	characteristic
37	C₅×#431	C₂²	1	1	yes	characteristic
38	C₅×#423	C₂²	1	1	yes	characteristic
39	C₅×#335	C₂²	1	2	yes	complemented
40	C₅×#334	C₂²	1	2	yes	complemented
41	C₅×#333	C₂²	1	1	yes	characteristic, complemented
42	C₅×#333	C₂²	1	1	yes	characteristic, complemented
43	C₅×#331	C₂²	1	2	yes	—
44	C₅×#331	C₂²	1	2	yes	—
45	C₅×#331	C₂²	1	1	yes	characteristic, complemented
46	C₅×#331	C₂²	1	1	yes	characteristic, complemented
47	#19566	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
48	C₂×C₅×#41	—	2	1	no	—
49	C₂²×C₅×D₄	—	2	1	no	—
50	C₂²×C₅×D₄	—	2	1	no	—
51	C₂²×C₅×D₄	—	2	1	no	—
52	C₂×C₅×SD₁₆	—	2	2	no	—
53	C₂×C₅×SD₁₆	—	2	2	no	—
54	C₂×C₅×SD₁₆	—	2	2	no	—
55	C₂×C₅×D₈	—	2	2	no	—
56	C₂×C₅×D₈	—	2	2	no	—
57	C₂×C₅×M₁₆	—	2	1	no	—
58	C₅×C₄⋊Q₈	D₄	1	1	yes	characteristic
59	C₅×C₄⋊Q₈	D₄	1	1	yes	characteristic
60	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
61	C₅×#127	—	2	1	no	—
62	C₅×#127	—	2	1	no	—
63	C₅×#127	—	2	1	no	—
64	C₅×#127	C₂³	1	2	yes	—
65	C₅×#127	C₂³	1	1	yes	characteristic
66	C₅×#125	—	2	1	no	—
67	C₅×#124	—	2	1	no	—
68	C₅×C₂²⋊Q₈	—	2	1	no	—
69	C₅×C₂²⋊Q₈	D₄	1	2	yes	—
70	C₅×#121	—	2	1	no	—
71	C₅×#121	—	2	1	no	—
72	C₄×C₅×Q₈	—	2	1	no	—
73	C₄×C₅×Q₈	C₂³	1	2	yes	—
74	C₄×C₅×D₄	—	2	1	no	—
75	C₄×C₅×D₄	—	2	1	no	—
76	C₅×#117	—	2	1	no	—
77	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
78	C₅×#107	—	2	2	no	—
79	C₅×C₄⋊C₈	—	2	2	no	—
80	C₅×C₄⋊C₈	—	2	2	no	—
81	C₅×C₄⋊C₈	—	2	1	no	—
82	C₅×C₄⋊C₈	D₄	1	1	yes	characteristic
83	C₅×C₄⋊C₈	D₄	1	1	yes	characteristic
84	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
85	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
86	C₅×C₄⋊C₈	C₂³	1	2	yes	—
87	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
88	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
89	C₅×#103	—	2	2	no	—
90	C₅×#102	—	2	2	no	—
91	C₅×#102	—	2	2	no	—
92	C₅×#102	—	2	2	no	—
93	C₅×#102	—	2	2	no	—
94	C₅×#102	—	2	2	no	—
95	C₅×C₂²⋊C₈	—	2	1	no	—
96	C₅×C₂²⋊C₈	—	2	1	no	—
97	C₅×C₂²⋊C₈	D₄	1	2	yes	—
98	C₅×#97	—	2	2	no	—
99	C₄×C₅×C₈	—	2	2	no	—
100	C₄×C₅×C₈	—	2	1	no	—
101	C₄×C₅×C₈	—	2	1	no	—
102	C₄×C₅×C₈	C₂³	1	2	yes	—
103	#3254	C₂×C₅	1	1	yes	characteristic, complemented
104	#3208	C₂×C₅	1	1	yes	characteristic, complemented
105	#3205	C₂×C₅	1	1	yes	characteristic
106	#2986	C₂×C₅	1	1	yes	characteristic, complemented
107	#1698	C₂×C₅	1	2	yes	complemented
108	#1688	C₂×C₅	1	2	yes	complemented
109	#1678	C₂×C₅	1	2	yes	complemented
110	#1668	C₂×C₅	1	2	yes	complemented
111	#1574	C₂×C₅	1	1	yes	characteristic, complemented
112	#1545	C₂×C₅	1	1	yes	characteristic, complemented
113	#1543	C₂×C₅	1	1	yes	characteristic, complemented
114	C₂⁴×C₅	—	4	1	no	—
115	C₅×#41	—	8	2	no	—
116	C₂×C₅×Q₈	—	2	1	no	—
117	C₂×C₅×Q₈	—	2	1	no	—
118	C₂×C₅×Q₈	C₂×D₄	1	2	yes	—
119	C₂×C₅×D₄	—	2	1	no	—
120	C₂×C₅×D₄	—	2	1	no	—
121	C₂×C₅×D₄	—	2	2	no	—
122	C₂×C₅×D₄	—	2	2	no	—
123	C₂×C₅×D₄	—	2	1	no	—
124	C₂×C₅×D₄	—	2	2	no	—
125	C₂×C₅×D₄	—	4	1	no	—
126	C₂×C₅×D₄	—	4	1	no	—
127	C₂×C₅×D₄	—	4	1	no	—
128	C₂×C₅×D₄	—	4	1	no	—
129	C₂×C₅×D₄	—	8	1	no	—
130	C₂×C₅×D₄	—	8	1	no	—
131	C₂×C₅×D₄	—	8	1	no	—
132	C₂×C₅×D₄	—	8	1	no	—
133	C₂×C₅×D₄	—	8	2	no	—
134	C₂²×C₄×C₅	—	4	1	no	—
135	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₅	#41	1	1	yes	characteristic
138	C₅×SD₁₆	—	8	2	no	—
139	C₅×SD₁₆	—	8	2	no	—
140	C₅×SD₁₆	—	8	2	no	—
141	C₅×D₈	—	8	2	no	—
142	C₅×D₈	—	8	2	no	—
143	C₅×M₁₆	—	8	1	no	—
144	C₂×C₅×C₈	—	2	2	no	—
145	C₂×C₅×C₈	—	2	1	no	—
146	C₂×C₅×C₈	—	2	1	no	—
147	C₂×C₅×C₈	—	2	1	no	—
148	C₂×C₅×C₈	—	2	1	no	—
149	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
150	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
151	C₅×C₄⋊C₄	—	2	1	no	—
152	C₅×C₄⋊C₄	—	2	1	no	—
153	C₅×C₄⋊C₄	—	2	1	no	—
154	C₅×C₄⋊C₄	—	2	2	no	—
155	C₅×C₄⋊C₄	—	2	2	no	—
156	C₅×C₄⋊C₄	—	2	1	no	—
157	C₅×C₄⋊C₄	—	2	1	no	—
158	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
159	C₅×C₂²⋊C₄	—	2	2	no	—
160	C₅×C₂²⋊C₄	—	4	1	no	—
161	C₅×C₂²⋊C₄	—	4	1	no	—
162	C₄²×C₅	—	2	2	no	—
163	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
164	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
165	C₄²×C₅	#41	1	1	yes	characteristic
166	C₄²×C₅	C₂⁴	1	1	yes	characteristic
167	#533	C₂²×C₅	1	1	yes	characteristic
168	#532	C₂²×C₅	1	1	yes	characteristic
169	C₂×#127	C₂²×C₅	1	1	yes	characteristic
170	#493	C₂²×C₅	1	2	yes	—
171	#492	—	2	1	no	—
172	#486	—	2	1	no	—
173	#486	C₂²×C₅	1	2	yes	—
174	#477	C₂²×C₅	1	2	yes	complemented
175	#474	—	2	1	no	—
176	#468	—	2	2	no	—
177	#461	—	2	1	no	—
178	#460	C₂²×C₅	1	2	yes	—
179	#460	C₂²×C₅	1	2	yes	—
180	#460	C₂²×C₅	1	2	yes	complemented
181	#459	—	2	1	no	—
182	#459	—	2	1	no	—
183	#450	—	2	2	no	—
184	#447	—	2	2	no	—
185	#446	—	2	1	no	—
186	#446	C₂²×C₅	1	2	yes	complemented
187	C₈×Q₈	—	2	1	no	—
188	C₈×Q₈	C₂²×C₅	1	2	yes	complemented
189	#433	—	2	2	no	—
190	#431	C₂²×C₅	1	1	yes	characteristic
191	#431	C₂²×C₅	1	1	yes	characteristic
192	#431	C₂²×C₅	1	1	yes	characteristic
193	#423	C₂²×C₅	1	1	yes	characteristic
194	#335	C₂²×C₅	1	2	yes	complemented
195	#334	C₂²×C₅	1	2	yes	complemented
196	#333	C₂²×C₅	1	1	yes	characteristic, complemented
197	#333	C₂²×C₅	1	1	yes	characteristic, complemented
198	#331	C₂²×C₅	1	2	yes	—
199	#331	C₂²×C₅	1	2	yes	—
200	#331	C₂²×C₅	1	1	yes	characteristic, complemented
201	#331	C₂²×C₅	1	1	yes	characteristic, complemented
202	C₂³×C₅	—	4	1	no	—
203	C₂³×C₅	—	4	2	no	—
204	C₂³×C₅	—	8	2	no	—
205	C₂³×C₅	—	8	2	no	—
206	C₂³×C₅	—	8	2	no	—
207	C₂³×C₅	#121	1	1	yes	characteristic
208	C₅×Q₈	—	2	2	no	—
209	C₅×Q₈	—	2	2	no	—
210	C₅×Q₈	—	4	2	no	—
211	C₅×Q₈	—	8	1	no	—
212	C₅×D₄	—	4	1	no	—
213	C₅×D₄	—	4	2	no	—
214	C₅×D₄	—	4	1	no	—
215	C₅×D₄	—	4	1	no	—
216	C₅×D₄	—	4	2	no	—
217	C₅×D₄	—	4	2	no	—
218	C₅×D₄	—	4	2	no	—
219	C₅×D₄	—	4	1	no	—
220	C₅×D₄	—	8	2	no	—
221	C₅×D₄	—	8	1	no	—
222	C₅×D₄	—	8	2	no	—
223	C₅×D₄	—	8	2	no	—
224	C₅×D₄	—	8	2	no	—
225	C₅×D₄	—	8	2	no	—
226	C₂×C₄×C₅	—	2	1	no	—
227	C₂×C₄×C₅	—	2	1	no	—
228	C₂×C₄×C₅	—	2	1	no	—
229	C₂×C₄×C₅	—	2	1	no	—
230	C₂×C₄×C₅	—	2	2	no	—
231	C₂×C₄×C₅	—	2	2	no	—
232	C₂×C₄×C₅	—	2	2	no	—
233	C₂×C₄×C₅	—	4	1	no	—
234	C₂×C₄×C₅	—	8	2	no	—
235	C₂×C₄×C₅	#121	1	1	yes	characteristic
236	C₂×C₄×C₅	#121	1	1	yes	characteristic
237	C₂×C₄×C₅	#121	1	1	yes	characteristic
238	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
239	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
240	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
241	C₅×C₈	—	2	2	no	—
242	C₅×C₈	—	2	2	no	—
243	C₅×C₈	—	4	2	no	—
244	C₅×C₈	—	4	1	no	—
245	C₅×C₈	—	4	1	no	—
246	C₅×C₈	—	4	1	no	—
247	C₅×C₈	—	4	1	no	—
248	C₂×#41	—	2	1	no	—
249	C₂²×D₄	—	2	1	no	—
250	C₂²×D₄	—	2	1	no	—
251	C₂²×D₄	—	2	1	no	—
252	C₂×SD₁₆	—	2	2	no	—
253	C₂×SD₁₆	—	2	2	no	—
254	C₂×SD₁₆	—	2	2	no	—
255	C₂×D₈	—	2	2	no	—
256	C₂×D₈	—	2	2	no	—
257	C₂×M₁₆	—	2	1	no	—
258	C₄⋊Q₈	C₅×D₄	1	1	yes	characteristic
259	C₄⋊Q₈	C₅×D₄	1	1	yes	characteristic
260	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
261	#127	—	2	1	no	—
262	#127	—	2	1	no	—
263	#127	—	2	1	no	—
264	#127	C₂³×C₅	1	2	yes	—
265	#127	C₂³×C₅	1	1	yes	characteristic
266	#125	—	2	1	no	—
267	#124	—	2	1	no	—
268	C₂²⋊Q₈	—	2	1	no	—
269	C₂²⋊Q₈	C₅×D₄	1	2	yes	—
270	#121	—	2	1	no	—
271	#121	—	2	1	no	—
272	C₄×Q₈	—	2	1	no	—
273	C₄×Q₈	C₂³×C₅	1	2	yes	—
274	C₄×D₄	—	2	1	no	—
275	C₄×D₄	—	2	1	no	—
276	#117	—	2	1	no	—
277	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
278	#107	—	2	2	no	—
279	C₄⋊C₈	—	2	2	no	—
280	C₄⋊C₈	—	2	2	no	—
281	C₄⋊C₈	—	2	1	no	—
282	C₄⋊C₈	C₅×D₄	1	1	yes	characteristic
283	C₄⋊C₈	C₅×D₄	1	1	yes	characteristic
284	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
285	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
286	C₄⋊C₈	C₂³×C₅	1	2	yes	—
287	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
288	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
289	#103	—	2	2	no	—
290	#102	—	2	2	no	—
291	#102	—	2	2	no	—
292	#102	—	2	2	no	—
293	#102	—	2	2	no	—
294	#102	—	2	2	no	—
295	C₂²⋊C₈	—	2	1	no	—
296	C₂²⋊C₈	—	2	1	no	—
297	C₂²⋊C₈	C₅×D₄	1	2	yes	—
298	#97	—	2	2	no	—
299	C₄×C₈	—	2	2	no	—
300	C₄×C₈	—	2	1	no	—
301	C₄×C₈	—	2	1	no	—
302	C₄×C₈	C₂³×C₅	1	2	yes	—
303	C₂²×C₅	—	2	1	no	—
304	C₂²×C₅	—	2	1	no	—
305	C₂²×C₅	—	2	1	no	—
306	C₂²×C₅	—	8	2	no	—
307	C₂²×C₅	—	8	1	no	—
308	C₂²×C₅	—	8	2	no	—
309	C₂²×C₅	—	8	1	no	—
310	C₂²×C₅	—	8	1	no	—
311	C₂²×C₅	—	8	2	no	—
312	C₂²×C₅	—	16	4	no	—
313	C₂²×C₅	C₂×#121	1	1	yes	characteristic
314	C₄×C₅	—	2	1	no	—
315	C₄×C₅	—	2	1	no	—
316	C₄×C₅	—	2	1	no	—
317	C₄×C₅	—	4	2	no	—
318	C₄×C₅	—	4	2	no	—
319	C₄×C₅	—	8	1	no	—
320	C₄×C₅	#472	1	2	yes	—
321	C₄×C₅	#576	1	1	yes	characteristic
322	C₄×C₅	#577	1	1	yes	characteristic
323	C₄×C₅	#577	1	1	yes	characteristic
324	C₄×C₅	#577	1	1	yes	characteristic
325	C₂⁴	—	4	1	no	—
326	#41	—	8	2	no	—
327	C₂×Q₈	—	2	1	no	—
328	C₂×Q₈	—	2	1	no	—
329	C₂×Q₈	C₂×C₅×D₄	1	2	yes	—
330	C₂×D₄	—	2	1	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	2	2	no	—
333	C₂×D₄	—	2	1	no	—
334	C₂×D₄	—	2	1	no	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	—	4	1	no	—
337	C₂×D₄	—	4	1	no	—
338	C₂×D₄	—	4	1	no	—
339	C₂×D₄	—	4	1	no	—
340	C₂×D₄	—	8	1	no	—
341	C₂×D₄	—	8	1	no	—
342	C₂×D₄	—	8	1	no	—
343	C₂×D₄	—	8	1	no	—
344	C₂×D₄	—	8	2	no	—
345	C₂²×C₄	—	4	1	no	—
346	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
347	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
348	C₂²×C₄	C₅×#41	1	1	yes	characteristic
349	SD₁₆	—	8	2	no	—
350	SD₁₆	—	8	2	no	—
351	SD₁₆	—	8	2	no	—
352	D₈	—	8	2	no	—
353	D₈	—	8	2	no	—
354	M₁₆	—	8	1	no	—
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	—	2	1	no	—
357	C₂×C₈	—	2	1	no	—
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	—	2	2	no	—
360	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
361	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
370	C₂²⋊C₄	—	2	2	no	—
371	C₂²⋊C₄	—	4	1	no	—
372	C₂²⋊C₄	—	4	1	no	—
373	C₄²	—	2	2	no	—
374	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
375	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
376	C₄²	C₅×#41	1	1	yes	characteristic
377	C₄²	C₂⁴×C₅	1	1	yes	characteristic
378	C₂×C₅	—	4	1	no	—
379	C₂×C₅	—	16	1	no	—
380	C₂×C₅	—	16	2	no	—
381	C₂×C₅	#3043	1	1	yes	characteristic
382	C₂×C₅	#3062	1	1	yes	characteristic
383	C₂×C₅	C₂×#472	1	1	yes	characteristic
384	C₂³	—	4	1	no	—
385	C₂³	—	4	2	no	—
386	C₂³	—	8	2	no	—
387	C₂³	—	8	2	no	—
388	C₂³	—	8	2	no	—
389	C₂³	C₅×#121	1	1	yes	characteristic
390	Q₈	—	2	2	no	—
391	Q₈	—	2	2	no	—
392	Q₈	—	4	2	no	—
393	Q₈	—	8	1	no	—
394	D₄	—	4	1	no	—
395	D₄	—	4	2	no	—
396	D₄	—	4	1	no	—
397	D₄	—	4	1	no	—
398	D₄	—	4	2	no	—
399	D₄	—	4	2	no	—
400	D₄	—	4	2	no	—
401	D₄	—	4	1	no	—
402	D₄	—	8	2	no	—
403	D₄	—	8	1	no	—
404	D₄	—	8	2	no	—
405	D₄	—	8	2	no	—
406	D₄	—	8	2	no	—
407	D₄	—	8	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	8	2	no	—
417	C₂×C₄	C₅×#121	1	1	yes	characteristic
418	C₂×C₄	C₅×#121	1	1	yes	characteristic
419	C₂×C₄	C₅×#121	1	1	yes	characteristic
420	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
421	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
422	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
423	C₈	—	2	2	no	—
424	C₈	—	2	2	no	—
425	C₈	—	4	2	no	—
426	C₈	—	4	1	no	—
427	C₈	—	4	1	no	—
428	C₈	—	4	1	no	—
429	C₈	—	4	1	no	—
430	C₅	#19566	1	1	yes	characteristic, direct product factor, Sylow
431	C₂²	—	2	1	no	—
432	C₂²	—	2	1	no	—
433	C₂²	—	2	1	no	—
434	C₂²	—	8	2	no	—
435	C₂²	—	8	1	no	—
436	C₂²	—	8	2	no	—
437	C₂²	—	8	1	no	—
438	C₂²	—	8	1	no	—
439	C₂²	—	8	2	no	—
440	C₂²	—	16	4	no	—
441	C₂²	C₂×C₅×#121	1	1	yes	characteristic
442	C₄	—	2	1	no	—
443	C₄	—	2	1	no	—
444	C₄	—	2	1	no	—
445	C₄	—	4	2	no	—
446	C₄	—	4	2	no	—
447	C₄	—	8	1	no	—
448	C₄	C₅×#472	1	2	yes	—
449	C₄	C₅×#576	1	1	yes	characteristic
450	C₄	C₅×#577	1	1	yes	characteristic
451	C₄	C₅×#577	1	1	yes	characteristic
452	C₄	C₅×#577	1	1	yes	characteristic
453	C₂	—	4	1	no	—
454	C₂	—	16	2	no	—
455	C₂	—	16	1	no	—
456	C₂	C₅×#3043	1	1	yes	characteristic
457	C₂	C₅×#3062	1	1	yes	characteristic
458	C₂	C₂×C₅×#472	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₅
prime radical	C₅×#3205	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×#3254	C₂	semidirect
2. C₅×#3208	C₂	semidirect
4. C₅×#2986	C₂	semidirect
5. C₅×#1698	C₂	semidirect
6. C₅×#1688	C₂	semidirect
7. C₅×#1678	C₂	semidirect
8. C₅×#1668	C₂	semidirect
9. C₅×#1574	C₂	semidirect
10. C₅×#1545	C₂	semidirect
11. C₅×#1543	C₂	semidirect
19. C₅×#477	C₂²	semidirect
25. C₅×#460	C₂²	semidirect
31. C₅×#446	C₂²	semidirect
33. C₅×C₈×Q₈	C₂²	semidirect
39. C₅×#335	C₂²	semidirect
40. C₅×#334	C₂²	semidirect
41. C₅×#333	C₂²	semidirect
42. C₅×#333	C₂²	semidirect
45. C₅×#331	C₂²	semidirect
46. C₅×#331	C₂²	semidirect
47. #19566	C₅	direct (N × H)
103. #3254	C₂×C₅	semidirect
104. #3208	C₂×C₅	semidirect
106. #2986	C₂×C₅	semidirect
107. #1698	C₂×C₅	semidirect
108. #1688	C₂×C₅	semidirect
109. #1678	C₂×C₅	semidirect
110. #1668	C₂×C₅	semidirect
111. #1574	C₂×C₅	semidirect
112. #1545	C₂×C₅	semidirect
113. #1543	C₂×C₅	semidirect
174. #477	C₂²×C₅	semidirect
180. #460	C₂²×C₅	semidirect
186. #446	C₂²×C₅	semidirect
188. C₈×Q₈	C₂²×C₅	semidirect
194. #335	C₂²×C₅	semidirect
195. #334	C₂²×C₅	semidirect
196. #333	C₂²×C₅	semidirect
197. #333	C₂²×C₅	semidirect
200. #331	C₂²×C₅	semidirect
201. #331	C₂²×C₅	semidirect
430. C₅	#19566	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×#3254	2
C₅×#3208	2
C₅×#3205	2
C₅×#2986	2
C₅×#1698	2
C₅×#1688	2
C₅×#1678	2
C₅×#1668	2
C₅×#1574	2
C₅×#1545	2
C₅×#1543	2
#19566	5

Subgroups — C5×#19566 #11942286

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#19566 #11942286