Subgroups — C₅×#19417 #11942137

Order 1280.

608 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3230	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#3079	C₂	1	1	yes	maximal, characteristic
3	C₅×#3076	C₂	1	1	yes	maximal, characteristic
4	C₅×#2988	C₂	1	1	yes	maximal, characteristic
5	C₅×#1684	C₂	1	2	yes	maximal, complemented
6	C₅×#1683	C₂	1	2	yes	maximal, complemented
7	C₅×#1676	C₂	1	2	yes	maximal, complemented
8	C₅×#1675	C₂	1	2	yes	maximal, complemented
9	C₅×#1571	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1550	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅×#333	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#533	C₂²	1	1	yes	characteristic
13	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₄×C₅×#41	C₂²	1	1	yes	characteristic
15	C₅×#500	C₂²	1	2	yes	—
16	C₅×#487	C₂²	1	2	yes	—
17	C₅×#484	—	2	2	no	—
18	C₅×#479	—	2	1	no	—
19	C₅×#478	—	2	1	no	—
20	C₅×#477	—	2	1	no	—
21	C₅×#477	—	2	1	no	—
22	C₅×#477	C₂²	1	1	yes	characteristic
23	C₅×#477	C₂²	1	2	yes	—
24	C₅×#476	C₂²	1	1	yes	characteristic
25	C₅×#476	C₂²	1	2	yes	—
26	C₅×#475	—	2	1	no	—
27	C₅×#475	C₂²	1	1	yes	characteristic
28	C₅×#474	—	2	1	no	—
29	C₅×#474	C₂²	1	1	yes	characteristic
30	C₅×C₈×Q₈	C₂²	1	2	yes	—
31	C₅×C₈×D₄	—	2	2	no	—
32	C₅×C₈×D₄	C₂²	1	2	yes	—
33	C₅×#431	—	2	1	no	—
34	C₅×#431	C₂²	1	1	yes	characteristic
35	C₅×#428	—	2	1	no	—
36	C₅×#427	—	2	1	no	—
37	C₅×#423	C₂²	1	1	yes	characteristic
38	C₂×C₅×C₄⋊C₈	—	2	1	no	—
39	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
40	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
41	C₅×#417	—	2	1	no	—
42	C₅×#416	—	2	1	no	—
43	C₅×#335	C₂²	1	2	yes	—
44	C₅×#335	C₂²	1	2	yes	—
45	C₅×#333	C₂²	1	2	yes	—
46	C₅×#333	C₂²	1	2	yes	—
47	C₅×#333	C₂²	1	2	yes	—
48	C₅×#332	C₂²	1	2	yes	—
49	#19417	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
50	C₂×C₅×#41	D₄	1	1	yes	characteristic
51	C₂²×C₅×Q₈	—	2	1	no	—
52	C₂×C₅×M₁₆	—	2	1	no	—
53	C₂²×C₅×C₈	—	2	1	no	—
54	C₂²×C₅×C₈	—	2	1	no	—
55	C₂²×C₅×C₈	—	2	2	no	—
56	C₅×C₄⋊Q₈	—	2	1	no	—
57	C₅×C₄⋊Q₈	—	2	1	no	—
58	C₅×C₄⋊Q₈	—	2	1	no	—
59	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
60	C₅×C₄⋊Q₈	C₂³	1	2	yes	—
61	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
62	C₅×#125	—	2	1	no	—
63	C₅×C₂²⋊Q₈	—	2	1	no	—
64	C₅×C₂²⋊Q₈	—	2	1	no	—
65	C₄×C₅×Q₈	—	2	1	no	—
66	C₄×C₅×Q₈	—	2	1	no	—
67	C₄×C₅×Q₈	D₄	1	1	yes	characteristic
68	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
69	C₄×C₅×D₄	—	2	1	no	—
70	C₄×C₅×D₄	—	2	1	no	—
71	C₄×C₅×D₄	D₄	1	1	yes	characteristic
72	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
73	C₅×#117	—	2	1	no	—
74	C₅×#117	—	2	1	no	—
75	C₅×#117	D₄	1	1	yes	characteristic
76	C₂×C₅×C₄⋊C₄	—	2	1	no	—
77	C₂×C₅×C₄⋊C₄	—	2	1	no	—
78	C₂×C₄²×C₅	—	2	1	no	—
79	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
80	C₅×#107	—	2	2	no	—
81	C₅×#107	—	2	2	no	—
82	C₅×#107	—	2	1	no	—
83	C₅×#107	—	2	1	no	—
84	C₅×#107	—	2	2	no	—
85	C₅×#106	—	2	1	no	—
86	C₅×#106	—	2	1	no	—
87	C₅×#106	—	2	2	no	—
88	C₅×C₄⋊C₈	—	2	2	no	—
89	C₅×C₄⋊C₈	—	2	1	no	—
90	C₅×C₄⋊C₈	—	2	1	no	—
91	C₅×C₄⋊C₈	—	2	1	no	—
92	C₅×C₄⋊C₈	D₄	1	1	yes	characteristic
93	C₅×C₄⋊C₈	D₄	1	1	yes	characteristic
94	C₅×C₄⋊C₈	C₂³	1	2	yes	—
95	C₅×C₄⋊C₈	C₂³	1	2	yes	—
96	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
97	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
98	C₅×#103	—	2	1	no	—
99	C₅×#103	—	2	1	no	—
100	C₅×#103	—	2	2	no	—
101	C₅×#103	—	2	2	no	—
102	C₅×#103	—	2	2	no	—
103	C₅×#102	—	2	1	no	—
104	C₅×#102	—	2	1	no	—
105	C₅×#102	—	2	2	no	—
106	C₅×C₂²⋊C₈	—	2	2	no	—
107	C₅×C₂²⋊C₈	D₄	1	2	yes	—
108	C₄×C₅×C₈	—	2	2	no	—
109	C₄×C₅×C₈	C₂³	1	2	yes	—
110	#3230	C₂×C₅	1	1	yes	characteristic, complemented
111	#3079	C₂×C₅	1	1	yes	characteristic
112	#3076	C₂×C₅	1	1	yes	characteristic
113	#2988	C₂×C₅	1	1	yes	characteristic
114	#1684	C₂×C₅	1	2	yes	complemented
115	#1683	C₂×C₅	1	2	yes	complemented
116	#1676	C₂×C₅	1	2	yes	complemented
117	#1675	C₂×C₅	1	2	yes	complemented
118	#1571	C₂×C₅	1	1	yes	characteristic, complemented
119	#1550	C₂×C₅	1	1	yes	characteristic, complemented
120	C₂×#333	C₂×C₅	1	1	yes	characteristic, complemented
121	C₅×#41	—	2	2	no	—
122	C₅×#41	Q₁₆	1	4	yes	—
123	C₂×C₅×Q₈	—	2	1	no	—
124	C₂×C₅×Q₈	—	2	1	no	—
125	C₂×C₅×Q₈	—	2	2	no	—
126	C₂×C₅×Q₈	—	4	1	no	—
127	C₂×C₅×Q₈	—	8	2	no	—
128	C₂×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
129	C₂×C₅×D₄	—	2	1	no	—
130	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₅	—	2	1	no	—
132	C₂²×C₄×C₅	—	2	1	no	—
133	C₂²×C₄×C₅	—	2	1	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×M₁₆	—	4	2	no	—
139	C₂×C₅×C₈	—	2	2	no	—
140	C₂×C₅×C₈	—	2	1	no	—
141	C₂×C₅×C₈	—	2	1	no	—
142	C₂×C₅×C₈	—	2	2	no	—
143	C₂×C₅×C₈	—	4	2	no	—
144	C₂×C₅×C₈	—	8	2	no	—
145	C₂×C₅×C₈	—	8	1	no	—
146	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
147	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
148	C₅×C₄⋊C₄	—	2	1	no	—
149	C₅×C₄⋊C₄	—	2	1	no	—
150	C₅×C₄⋊C₄	—	2	2	no	—
151	C₅×C₄⋊C₄	—	2	2	no	—
152	C₅×C₄⋊C₄	—	2	1	no	—
153	C₅×C₄⋊C₄	—	2	1	no	—
154	C₅×C₄⋊C₄	—	2	1	no	—
155	C₅×C₄⋊C₄	—	2	1	no	—
156	C₅×C₄⋊C₄	—	4	1	no	—
157	C₅×C₄⋊C₄	—	4	1	no	—
158	C₅×C₄⋊C₄	—	4	1	no	—
159	C₅×C₄⋊C₄	—	4	1	no	—
160	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
161	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
162	C₅×C₂²⋊C₄	—	2	1	no	—
163	C₅×C₂²⋊C₄	—	2	1	no	—
164	C₅×C₂²⋊C₄	—	2	1	no	—
165	C₅×C₂²⋊C₄	—	4	1	no	—
166	C₄²×C₅	—	2	1	no	—
167	C₄²×C₅	—	2	1	no	—
168	C₄²×C₅	—	2	1	no	—
169	C₄²×C₅	—	4	1	no	—
170	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
171	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
172	C₄²×C₅	#41	1	1	yes	characteristic
173	C₄²×C₅	C₂⁴	1	1	yes	characteristic
174	#533	C₂²×C₅	1	1	yes	characteristic
175	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
176	C₄×#41	C₂²×C₅	1	1	yes	characteristic
177	#500	C₂²×C₅	1	2	yes	—
178	#487	C₂²×C₅	1	2	yes	—
179	#484	—	2	2	no	—
180	#479	—	2	1	no	—
181	#478	—	2	1	no	—
182	#477	—	2	1	no	—
183	#477	—	2	1	no	—
184	#477	C₂²×C₅	1	1	yes	characteristic
185	#477	C₂²×C₅	1	2	yes	—
186	#476	C₂²×C₅	1	1	yes	characteristic
187	#476	C₂²×C₅	1	2	yes	—
188	#475	—	2	1	no	—
189	#475	C₂²×C₅	1	1	yes	characteristic
190	#474	—	2	1	no	—
191	#474	C₂²×C₅	1	1	yes	characteristic
192	C₈×Q₈	C₂²×C₅	1	2	yes	—
193	C₈×D₄	—	2	2	no	—
194	C₈×D₄	C₂²×C₅	1	2	yes	—
195	#431	—	2	1	no	—
196	#431	C₂²×C₅	1	1	yes	characteristic
197	#428	—	2	1	no	—
198	#427	—	2	1	no	—
199	#423	C₂²×C₅	1	1	yes	characteristic
200	C₂×C₄⋊C₈	—	2	1	no	—
201	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
202	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
203	#417	—	2	1	no	—
204	#416	—	2	1	no	—
205	#335	C₂²×C₅	1	2	yes	—
206	#335	C₂²×C₅	1	2	yes	—
207	#333	C₂²×C₅	1	2	yes	—
208	#333	C₂²×C₅	1	2	yes	—
209	#333	C₂²×C₅	1	2	yes	—
210	#332	C₂²×C₅	1	2	yes	—
211	C₂³×C₅	—	2	1	no	—
212	C₂³×C₅	#121	1	1	yes	characteristic
213	C₅×Q₈	—	2	1	no	—
214	C₅×Q₈	—	4	1	no	—
215	C₅×Q₈	—	4	1	no	—
216	C₅×Q₈	—	8	1	no	—
217	C₅×Q₈	—	8	2	no	—
218	C₅×Q₈	—	8	2	no	—
219	C₅×Q₈	C₂×Q₁₆	1	2	yes	—
220	C₅×D₄	—	2	4	no	—
221	C₅×D₄	—	2	1	no	—
222	C₅×D₄	C₂×Q₁₆	1	2	yes	—
223	C₂×C₄×C₅	—	2	1	no	—
224	C₂×C₄×C₅	—	2	1	no	—
225	C₂×C₄×C₅	—	2	1	no	—
226	C₂×C₄×C₅	—	2	4	no	—
227	C₂×C₄×C₅	—	2	1	no	—
228	C₂×C₄×C₅	—	2	1	no	—
229	C₂×C₄×C₅	—	4	1	no	—
230	C₂×C₄×C₅	—	4	1	no	—
231	C₂×C₄×C₅	—	4	1	no	—
232	C₂×C₄×C₅	—	4	1	no	—
233	C₂×C₄×C₅	—	4	1	no	—
234	C₂×C₄×C₅	—	4	2	no	—
235	C₂×C₄×C₅	—	8	1	no	—
236	C₂×C₄×C₅	—	8	2	no	—
237	C₂×C₄×C₅	#121	1	1	yes	characteristic
238	C₂×C₄×C₅	#121	1	1	yes	characteristic
239	C₂×C₄×C₅	#121	1	1	yes	characteristic
240	C₂×C₄×C₅	C₂×Q₁₆	1	2	yes	—
241	C₂×C₄×C₅	#135	1	2	yes	—
242	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
243	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
244	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
245	C₅×C₈	—	2	2	no	—
246	C₅×C₈	—	2	2	no	—
247	C₅×C₈	—	4	1	no	—
248	C₅×C₈	—	4	1	no	—
249	C₅×C₈	—	4	2	no	—
250	C₅×C₈	—	4	2	no	—
251	C₂×#41	C₅×D₄	1	1	yes	characteristic
252	C₂²×Q₈	—	2	1	no	—
253	C₂×M₁₆	—	2	1	no	—
254	C₂²×C₈	—	2	1	no	—
255	C₂²×C₈	—	2	1	no	—
256	C₂²×C₈	—	2	2	no	—
257	C₄⋊Q₈	—	2	1	no	—
258	C₄⋊Q₈	—	2	1	no	—
259	C₄⋊Q₈	—	2	1	no	—
260	C₄⋊Q₈	C₂³×C₅	1	2	yes	—
261	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
262	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
263	#125	—	2	1	no	—
264	C₂²⋊Q₈	—	2	1	no	—
265	C₂²⋊Q₈	—	2	1	no	—
266	C₄×Q₈	—	2	1	no	—
267	C₄×Q₈	—	2	1	no	—
268	C₄×Q₈	C₅×D₄	1	1	yes	characteristic
269	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
270	C₄×D₄	—	2	1	no	—
271	C₄×D₄	—	2	1	no	—
272	C₄×D₄	C₅×D₄	1	1	yes	characteristic
273	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
274	#117	—	2	1	no	—
275	#117	—	2	1	no	—
276	#117	C₅×D₄	1	1	yes	characteristic
277	C₂×C₄⋊C₄	—	2	1	no	—
278	C₂×C₄⋊C₄	—	2	1	no	—
279	C₂×C₄²	—	2	1	no	—
280	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
281	#107	—	2	2	no	—
282	#107	—	2	2	no	—
283	#107	—	2	1	no	—
284	#107	—	2	1	no	—
285	#107	—	2	2	no	—
286	#106	—	2	1	no	—
287	#106	—	2	1	no	—
288	#106	—	2	2	no	—
289	C₄⋊C₈	—	2	2	no	—
290	C₄⋊C₈	—	2	1	no	—
291	C₄⋊C₈	—	2	1	no	—
292	C₄⋊C₈	—	2	1	no	—
293	C₄⋊C₈	C₅×D₄	1	1	yes	characteristic
294	C₄⋊C₈	C₅×D₄	1	1	yes	characteristic
295	C₄⋊C₈	C₂³×C₅	1	2	yes	—
296	C₄⋊C₈	C₂³×C₅	1	2	yes	—
297	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
298	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
299	#103	—	2	1	no	—
300	#103	—	2	1	no	—
301	#103	—	2	2	no	—
302	#103	—	2	2	no	—
303	#103	—	2	2	no	—
304	#102	—	2	1	no	—
305	#102	—	2	1	no	—
306	#102	—	2	2	no	—
307	C₂²⋊C₈	—	2	2	no	—
308	C₂²⋊C₈	C₅×D₄	1	2	yes	—
309	C₄×C₈	—	2	2	no	—
310	C₄×C₈	C₂³×C₅	1	2	yes	—
311	C₂²×C₅	—	2	1	no	—
312	C₂²×C₅	—	2	1	no	—
313	C₂²×C₅	—	2	2	no	—
314	C₂²×C₅	—	4	1	no	—
315	C₂²×C₅	—	4	1	no	—
316	C₂²×C₅	#467	1	2	yes	—
317	C₂²×C₅	C₂×#121	1	1	yes	characteristic
318	C₄×C₅	—	2	1	no	—
319	C₄×C₅	—	2	2	no	—
320	C₄×C₅	—	2	1	no	—
321	C₄×C₅	—	2	1	no	—
322	C₄×C₅	—	4	1	no	—
323	C₄×C₅	—	4	1	no	—
324	C₄×C₅	—	8	1	no	—
325	C₄×C₅	—	8	2	no	—
326	C₄×C₅	—	8	1	no	—
327	C₄×C₅	#467	1	2	yes	—
328	C₄×C₅	C₂²×Q₁₆	1	1	yes	characteristic
329	C₄×C₅	C₂×#135	1	1	yes	characteristic
330	C₄×C₅	#577	1	1	yes	characteristic
331	C₄×C₅	#578	1	1	yes	characteristic
332	#41	—	2	2	no	—
333	#41	C₅×Q₁₆	1	4	yes	—
334	C₂×Q₈	—	2	1	no	—
335	C₂×Q₈	—	2	1	no	—
336	C₂×Q₈	—	2	2	no	—
337	C₂×Q₈	—	4	1	no	—
338	C₂×Q₈	—	8	2	no	—
339	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
340	C₂×D₄	—	2	1	no	—
341	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	1	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	M₁₆	—	4	2	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	4	2	no	—
355	C₂×C₈	—	8	2	no	—
356	C₂×C₈	—	8	1	no	—
357	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
358	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	2	1	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	—	2	1	no	—
367	C₄⋊C₄	—	4	1	no	—
368	C₄⋊C₄	—	4	1	no	—
369	C₄⋊C₄	—	4	1	no	—
370	C₄⋊C₄	—	4	1	no	—
371	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
372	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
373	C₂²⋊C₄	—	2	1	no	—
374	C₂²⋊C₄	—	2	1	no	—
375	C₂²⋊C₄	—	2	1	no	—
376	C₂²⋊C₄	—	4	1	no	—
377	C₄²	—	2	1	no	—
378	C₄²	—	2	1	no	—
379	C₄²	—	2	1	no	—
380	C₄²	—	4	1	no	—
381	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
382	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
383	C₄²	C₅×#41	1	1	yes	characteristic
384	C₄²	C₂⁴×C₅	1	1	yes	characteristic
385	C₂×C₅	—	2	2	no	—
386	C₂×C₅	—	4	2	no	—
387	C₂×C₅	#3046	1	1	yes	characteristic
388	C₂×C₅	C₂×#467	1	1	yes	characteristic
389	C₂×C₅	#3068	1	1	yes	characteristic
390	C₂³	—	2	1	no	—
391	C₂³	C₅×#121	1	1	yes	characteristic
392	Q₈	—	2	1	no	—
393	Q₈	—	4	1	no	—
394	Q₈	—	4	1	no	—
395	Q₈	—	8	2	no	—
396	Q₈	—	8	1	no	—
397	Q₈	—	8	2	no	—
398	Q₈	C₂×C₅×Q₁₆	1	2	yes	—
399	D₄	—	2	4	no	—
400	D₄	—	2	1	no	—
401	D₄	C₂×C₅×Q₁₆	1	2	yes	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	4	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	8	1	no	—
415	C₂×C₄	—	8	2	no	—
416	C₂×C₄	C₅×#121	1	1	yes	characteristic
417	C₂×C₄	C₅×#121	1	1	yes	characteristic
418	C₂×C₄	C₅×#121	1	1	yes	characteristic
419	C₂×C₄	C₂×C₅×Q₁₆	1	2	yes	—
420	C₂×C₄	C₅×#135	1	2	yes	—
421	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
422	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
423	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
424	C₈	—	2	2	no	—
425	C₈	—	2	2	no	—
426	C₈	—	4	1	no	—
427	C₈	—	4	1	no	—
428	C₈	—	4	2	no	—
429	C₈	—	4	2	no	—
430	C₅	#19417	1	1	yes	characteristic, direct product factor, Sylow
431	C₂²	—	2	1	no	—
432	C₂²	—	2	1	no	—
433	C₂²	—	2	2	no	—
434	C₂²	—	4	1	no	—
435	C₂²	—	4	1	no	—
436	C₂²	C₅×#467	1	2	yes	—
437	C₂²	C₂×C₅×#121	1	1	yes	characteristic
438	C₄	—	2	1	no	—
439	C₄	—	2	2	no	—
440	C₄	—	2	1	no	—
441	C₄	—	2	1	no	—
442	C₄	—	4	1	no	—
443	C₄	—	4	1	no	—
444	C₄	—	8	1	no	—
445	C₄	—	8	2	no	—
446	C₄	—	8	1	no	—
447	C₄	C₅×#467	1	2	yes	—
448	C₄	C₂²×C₅×Q₁₆	1	1	yes	characteristic
449	C₄	C₂×C₅×#135	1	1	yes	characteristic
450	C₄	C₅×#577	1	1	yes	characteristic
451	C₄	C₅×#578	1	1	yes	characteristic
452	C₂	—	2	2	no	—
453	C₂	—	4	2	no	—
454	C₂	C₅×#3046	1	1	yes	characteristic
455	C₂	C₂×C₅×#467	1	1	yes	characteristic
456	C₂	C₅×#3068	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₅
prime radical	C₂×C₅×#41	D₄
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×#3230	C₂	semidirect
5. C₅×#1684	C₂	semidirect
6. C₅×#1683	C₂	semidirect
7. C₅×#1676	C₂	semidirect
8. C₅×#1675	C₂	semidirect
9. C₅×#1571	C₂	semidirect
10. C₅×#1550	C₂	semidirect
11. C₂×C₅×#333	C₂	semidirect
49. #19417	C₅	direct (N × H)
110. #3230	C₂×C₅	semidirect
114. #1684	C₂×C₅	semidirect
115. #1683	C₂×C₅	semidirect
116. #1676	C₂×C₅	semidirect
117. #1675	C₂×C₅	semidirect
118. #1571	C₂×C₅	semidirect
119. #1550	C₂×C₅	semidirect
120. C₂×#333	C₂×C₅	semidirect
430. C₅	#19417	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×#3230	2
C₅×#3079	2
C₅×#3076	2
C₅×#2988	2
C₅×#1684	2
C₅×#1683	2
C₅×#1676	2
C₅×#1675	2
C₅×#1571	2
C₅×#1550	2
C₂×C₅×#333	2
#19417	5

Subgroups — C5×#19417 #11942137

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#19417 #11942137