Subgroups — C₅×#26091 #11948811

Order 1280.

714 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2571	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#2354	C₂	1	1	yes	maximal, characteristic
3	C₅×#2092	C₂	1	2	yes	maximal
4	C₅×#2065	C₂	1	2	yes	maximal
5	C₅×#1949	C₂	1	2	yes	maximal, complemented
6	C₅×#1947	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1939	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1919	C₂	1	2	yes	maximal, complemented
9	C₅×#1844	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1802	C₂	1	1	yes	maximal, characteristic
11	C₄×C₅×#102	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
13	C₂×C₅×#117	—	2	1	no	—
14	C₂×C₅×#107	C₂²	1	2	yes	—
15	C₂×C₅×#106	C₂²	1	2	yes	—
16	C₂×C₅×#106	C₂²	1	2	yes	—
17	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
19	C₂×C₅×#102	C₂²	1	1	yes	characteristic
20	C₂×C₅×#102	C₂²	1	1	yes	characteristic
21	C₂×C₅×#102	C₂²	1	2	yes	—
22	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
23	C₅×#400	—	2	2	no	—
24	C₅×#390	C₂²	1	2	yes	—
25	C₅×#389	—	2	1	no	—
26	C₅×#389	C₂²	1	2	yes	—
27	C₅×#388	—	2	2	no	—
28	C₅×#384	C₂²	1	1	yes	characteristic
29	C₅×#384	C₂²	1	1	yes	characteristic
30	C₅×#382	—	2	1	no	—
31	C₅×#382	C₂²	1	2	yes	—
32	C₅×#380	—	2	1	no	—
33	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
35	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
36	C₅×#340	C₂²	1	1	yes	characteristic
37	C₅×#340	C₂²	1	1	yes	characteristic
38	C₅×#340	C₂²	1	2	yes	—
39	C₅×#340	C₂²	1	2	yes	—
40	C₅×#336	C₂²	1	2	yes	—
41	#26091	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
42	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
43	C₂³×C₄×C₅	—	2	1	no	—
44	C₂²×C₅×C₈	C₂³	1	2	yes	—
45	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
46	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
47	C₄×C₅×D₄	—	2	2	no	—
48	C₄×C₅×D₄	Q₈	1	4	yes	—
49	C₅×#117	—	4	4	no	—
50	C₂×C₅×C₄⋊C₄	—	2	1	no	—
51	C₂×C₅×C₄⋊C₄	—	2	1	no	—
52	C₂×C₅×C₄⋊C₄	—	2	1	no	—
53	C₂×C₅×C₄⋊C₄	—	2	1	no	—
54	C₂×C₅×C₄⋊C₄	—	2	2	no	—
55	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
56	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
57	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
58	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
59	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
60	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
61	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
62	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
63	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
64	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
65	C₂×C₄²×C₅	—	2	1	no	—
66	C₂×C₄²×C₅	—	2	2	no	—
67	C₂×C₄²×C₅	C₂³	1	2	yes	—
68	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
69	C₅×#107	—	4	2	no	—
70	C₅×#106	—	2	4	no	—
71	C₅×#106	—	4	2	no	—
72	C₅×C₄⋊C₈	—	2	4	no	—
73	C₅×C₄⋊C₈	—	2	2	no	—
74	C₅×#102	—	2	2	no	—
75	C₅×#102	—	2	2	no	—
76	C₅×#102	—	4	2	no	—
77	C₄×C₅×C₈	—	2	2	no	—
78	C₅×#95	—	2	2	no	—
79	C₅×#95	—	2	1	no	—
80	C₅×#95	—	2	2	no	—
81	C₅×#95	—	2	2	no	—
82	C₅×#95	—	2	2	no	—
83	C₅×#95	D₄	1	2	yes	—
84	#2571	C₂×C₅	1	1	yes	characteristic, complemented
85	#2354	C₂×C₅	1	1	yes	characteristic
86	#2092	C₂×C₅	1	2	yes	—
87	#2065	C₂×C₅	1	2	yes	—
88	#1949	C₂×C₅	1	2	yes	complemented
89	#1947	C₂×C₅	1	1	yes	characteristic, complemented
90	#1939	C₂×C₅	1	1	yes	characteristic, complemented
91	#1919	C₂×C₅	1	2	yes	complemented
92	#1844	C₂×C₅	1	1	yes	characteristic, complemented
93	#1802	C₂×C₅	1	1	yes	characteristic
94	C₄×#102	C₂×C₅	1	1	yes	characteristic
95	C₂⁴×C₅	—	2	1	no	—
96	C₂×C₅×D₄	—	2	1	no	—
97	C₂×C₅×D₄	—	2	1	no	—
98	C₂×C₅×D₄	—	2	1	no	—
99	C₂×C₅×D₄	—	2	1	no	—
100	C₂×C₅×D₄	—	2	1	no	—
101	C₂×C₅×D₄	C₂×Q₈	1	2	yes	—
102	C₂²×C₄×C₅	—	2	1	no	—
103	C₂²×C₄×C₅	—	2	4	no	—
104	C₂²×C₄×C₅	—	2	2	no	—
105	C₂²×C₄×C₅	—	2	1	no	—
106	C₂²×C₄×C₅	—	2	1	no	—
107	C₂²×C₄×C₅	—	2	2	no	—
108	C₂²×C₄×C₅	—	4	2	no	—
109	C₂²×C₄×C₅	—	4	2	no	—
110	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
115	C₂×C₅×C₈	—	2	1	no	—
116	C₂×C₅×C₈	—	2	1	no	—
117	C₂×C₅×C₈	—	2	1	no	—
118	C₂×C₅×C₈	—	2	1	no	—
119	C₂×C₅×C₈	—	2	2	no	—
120	C₂×C₅×C₈	—	2	2	no	—
121	C₂×C₅×C₈	—	2	2	no	—
122	C₂×C₅×C₈	#41	1	2	yes	—
123	C₂×C₅×C₈	#41	1	2	yes	—
124	C₅×C₄⋊C₄	—	2	2	no	—
125	C₅×C₄⋊C₄	—	2	2	no	—
126	C₅×C₄⋊C₄	—	2	1	no	—
127	C₅×C₄⋊C₄	—	2	1	no	—
128	C₅×C₄⋊C₄	—	2	1	no	—
129	C₅×C₄⋊C₄	—	2	2	no	—
130	C₅×C₄⋊C₄	—	2	2	no	—
131	C₅×C₄⋊C₄	—	2	2	no	—
132	C₅×C₄⋊C₄	—	2	2	no	—
133	C₅×C₄⋊C₄	—	2	1	no	—
134	C₅×C₄⋊C₄	—	2	1	no	—
135	C₅×C₄⋊C₄	—	4	2	no	—
136	C₅×C₄⋊C₄	—	4	2	no	—
137	C₅×C₄⋊C₄	—	8	1	no	—
138	C₅×C₄⋊C₄	—	8	1	no	—
139	C₅×C₄⋊C₄	—	8	2	no	—
140	C₅×C₄⋊C₄	C₂×Q₈	1	2	yes	—
141	C₅×C₂²⋊C₄	—	2	4	no	—
142	C₅×C₂²⋊C₄	—	4	4	no	—
143	C₅×C₂²⋊C₄	—	8	2	no	—
144	C₄²×C₅	—	2	2	no	—
145	C₄²×C₅	—	2	2	no	—
146	C₄²×C₅	—	4	4	no	—
147	C₄²×C₅	—	4	2	no	—
148	C₄²×C₅	C₂×Q₈	1	2	yes	—
149	C₄²×C₅	#41	1	2	yes	—
150	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
151	C₂×#117	—	2	1	no	—
152	C₂×#107	C₂²×C₅	1	2	yes	—
153	C₂×#106	C₂²×C₅	1	2	yes	—
154	C₂×#106	C₂²×C₅	1	2	yes	—
155	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
156	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
157	C₂×#102	C₂²×C₅	1	1	yes	characteristic
158	C₂×#102	C₂²×C₅	1	1	yes	characteristic
159	C₂×#102	C₂²×C₅	1	2	yes	—
160	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
161	#400	—	2	2	no	—
162	#390	C₂²×C₅	1	2	yes	—
163	#389	—	2	1	no	—
164	#389	C₂²×C₅	1	2	yes	—
165	#388	—	2	2	no	—
166	#384	C₂²×C₅	1	1	yes	characteristic
167	#384	C₂²×C₅	1	1	yes	characteristic
168	#382	—	2	1	no	—
169	#382	C₂²×C₅	1	2	yes	—
170	#380	—	2	1	no	—
171	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
172	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
173	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
174	#340	C₂²×C₅	1	2	yes	—
175	#340	C₂²×C₅	1	2	yes	—
176	#340	C₂²×C₅	1	1	yes	characteristic
177	#340	C₂²×C₅	1	1	yes	characteristic
178	#336	C₂²×C₅	1	2	yes	—
179	C₂³×C₅	—	2	2	no	—
180	C₂³×C₅	—	4	1	no	—
181	C₂³×C₅	—	4	1	no	—
182	C₂³×C₅	—	4	1	no	—
183	C₂³×C₅	—	4	1	no	—
184	C₂³×C₅	—	4	1	no	—
185	C₂³×C₅	—	4	1	no	—
186	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
187	C₅×D₄	—	2	2	no	—
188	C₅×D₄	—	2	2	no	—
189	C₅×D₄	—	4	1	no	—
190	C₅×D₄	—	4	1	no	—
191	C₂×C₄×C₅	—	2	1	no	—
192	C₂×C₄×C₅	—	2	1	no	—
193	C₂×C₄×C₅	—	2	2	no	—
194	C₂×C₄×C₅	—	2	2	no	—
195	C₂×C₄×C₅	—	2	2	no	—
196	C₂×C₄×C₅	—	2	2	no	—
197	C₂×C₄×C₅	—	2	2	no	—
198	C₂×C₄×C₅	—	2	2	no	—
199	C₂×C₄×C₅	—	2	2	no	—
200	C₂×C₄×C₅	—	4	1	no	—
201	C₂×C₄×C₅	—	4	1	no	—
202	C₂×C₄×C₅	—	4	8	no	—
203	C₂×C₄×C₅	—	4	1	no	—
204	C₂×C₄×C₅	—	4	2	no	—
205	C₂×C₄×C₅	—	4	1	no	—
206	C₂×C₄×C₅	—	4	2	no	—
207	C₂×C₄×C₅	—	4	2	no	—
208	C₂×C₄×C₅	—	4	2	no	—
209	C₂×C₄×C₅	—	4	1	no	—
210	C₂×C₄×C₅	—	4	1	no	—
211	C₂×C₄×C₅	—	4	2	no	—
212	C₂×C₄×C₅	—	4	1	no	—
213	C₂×C₄×C₅	—	4	2	no	—
214	C₂×C₄×C₅	—	4	1	no	—
215	C₂×C₄×C₅	C₂²⋊Q₈	1	2	yes	—
216	C₂×C₄×C₅	C₂²⋊Q₈	1	2	yes	—
217	C₂×C₄×C₅	#135	1	2	yes	—
218	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
219	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
220	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
221	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
222	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
223	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
224	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
225	C₅×C₈	—	2	2	no	—
226	C₅×C₈	—	2	2	no	—
227	C₅×C₈	—	4	2	no	—
228	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
229	C₂³×C₄	—	2	1	no	—
230	C₂²×C₈	C₂³×C₅	1	2	yes	—
231	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
232	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
233	C₄×D₄	—	2	2	no	—
234	C₄×D₄	C₅×Q₈	1	4	yes	—
235	#117	—	4	4	no	—
236	C₂×C₄⋊C₄	—	2	1	no	—
237	C₂×C₄⋊C₄	—	2	1	no	—
238	C₂×C₄⋊C₄	—	2	1	no	—
239	C₂×C₄⋊C₄	—	2	1	no	—
240	C₂×C₄⋊C₄	—	2	2	no	—
241	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
242	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
243	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
244	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
245	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
246	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
247	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
248	C₂×C₂²⋊C₄	—	2	1	no	—
249	C₂×C₂²⋊C₄	—	2	2	no	—
250	C₂×C₂²⋊C₄	—	2	2	no	—
251	C₂×C₄²	—	2	2	no	—
252	C₂×C₄²	—	2	1	no	—
253	C₂×C₄²	C₂³×C₅	1	2	yes	—
254	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
255	#107	—	4	2	no	—
256	#106	—	2	4	no	—
257	#106	—	4	2	no	—
258	C₄⋊C₈	—	2	4	no	—
259	C₄⋊C₈	—	2	2	no	—
260	#102	—	2	2	no	—
261	#102	—	2	2	no	—
262	#102	—	4	2	no	—
263	C₄×C₈	—	2	2	no	—
264	#95	—	2	2	no	—
265	#95	—	2	1	no	—
266	#95	—	2	2	no	—
267	#95	—	2	2	no	—
268	#95	—	2	2	no	—
269	#95	C₅×D₄	1	2	yes	—
270	C₂²×C₅	—	4	2	no	—
271	C₂²×C₅	—	4	2	no	—
272	C₂²×C₅	—	4	2	no	—
273	C₂²×C₅	—	8	1	no	—
274	C₂²×C₅	—	8	1	no	—
275	C₂²×C₅	—	8	1	no	—
276	C₂²×C₅	—	8	1	no	—
277	C₂²×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
278	C₂²×C₅	#547	1	1	yes	characteristic
279	C₂²×C₅	#550	1	1	yes	characteristic
280	C₂²×C₅	C₂×#135	1	1	yes	characteristic
281	C₂²×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
282	C₂²×C₅	#577	1	1	yes	characteristic
283	C₂²×C₅	#577	1	1	yes	characteristic
284	C₄×C₅	—	2	2	no	—
285	C₄×C₅	—	4	2	no	—
286	C₄×C₅	—	4	2	no	—
287	C₄×C₅	—	4	2	no	—
288	C₄×C₅	—	8	1	no	—
289	C₄×C₅	—	8	2	no	—
290	C₄×C₅	—	8	2	no	—
291	C₄×C₅	—	8	1	no	—
292	C₄×C₅	#478	1	4	yes	—
293	C₄×C₅	#533	1	1	yes	characteristic
294	C₄×C₅	#544	1	1	yes	characteristic
295	C₄×C₅	#552	1	1	yes	characteristic
296	C₄×C₅	#553	1	1	yes	characteristic
297	C₂⁴	—	2	1	no	—
298	C₂×D₄	—	2	1	no	—
299	C₂×D₄	—	2	1	no	—
300	C₂×D₄	—	2	1	no	—
301	C₂×D₄	—	2	1	no	—
302	C₂×D₄	—	2	1	no	—
303	C₂×D₄	C₂×C₅×Q₈	1	2	yes	—
304	C₂²×C₄	—	2	1	no	—
305	C₂²×C₄	—	2	4	no	—
306	C₂²×C₄	—	2	1	no	—
307	C₂²×C₄	—	2	1	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	4	2	no	—
311	C₂²×C₄	—	4	2	no	—
312	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
313	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
314	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
315	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
316	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
317	C₂×C₈	—	2	1	no	—
318	C₂×C₈	—	2	1	no	—
319	C₂×C₈	—	2	1	no	—
320	C₂×C₈	—	2	1	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	C₅×#41	1	2	yes	—
325	C₂×C₈	C₅×#41	1	2	yes	—
326	C₄⋊C₄	—	2	2	no	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	2	1	no	—
329	C₄⋊C₄	—	2	1	no	—
330	C₄⋊C₄	—	2	1	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	2	1	no	—
336	C₄⋊C₄	—	2	1	no	—
337	C₄⋊C₄	—	4	2	no	—
338	C₄⋊C₄	—	4	2	no	—
339	C₄⋊C₄	—	8	1	no	—
340	C₄⋊C₄	—	8	1	no	—
341	C₄⋊C₄	—	8	2	no	—
342	C₄⋊C₄	C₂×C₅×Q₈	1	2	yes	—
343	C₂²⋊C₄	—	2	4	no	—
344	C₂²⋊C₄	—	4	4	no	—
345	C₂²⋊C₄	—	8	2	no	—
346	C₄²	—	2	2	no	—
347	C₄²	—	2	2	no	—
348	C₄²	—	4	4	no	—
349	C₄²	—	4	2	no	—
350	C₄²	C₂×C₅×Q₈	1	2	yes	—
351	C₄²	C₅×#41	1	2	yes	—
352	C₂×C₅	—	8	2	no	—
353	C₂×C₅	#2441	1	1	yes	characteristic
354	C₂×C₅	C₂×#478	1	1	yes	characteristic
355	C₂×C₅	#3084	1	1	yes	characteristic
356	C₂×C₅	#3340	1	1	yes	characteristic
357	C₂×C₅	#3354	1	1	yes	characteristic
358	C₂×C₅	#3394	1	1	yes	characteristic
359	C₂×C₅	#3397	1	1	yes	characteristic
360	C₂³	—	2	2	no	—
361	C₂³	—	4	1	no	—
362	C₂³	—	4	1	no	—
363	C₂³	—	4	1	no	—
364	C₂³	—	4	1	no	—
365	C₂³	—	4	1	no	—
366	C₂³	—	4	1	no	—
367	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
368	D₄	—	2	2	no	—
369	D₄	—	2	2	no	—
370	D₄	—	4	1	no	—
371	D₄	—	4	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	4	8	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	C₅×C₂²⋊Q₈	1	2	yes	—
397	C₂×C₄	C₅×C₂²⋊Q₈	1	2	yes	—
398	C₂×C₄	C₅×#135	1	2	yes	—
399	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
400	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
401	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
402	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
403	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
404	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
405	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
406	C₈	—	2	2	no	—
407	C₈	—	2	2	no	—
408	C₈	—	4	2	no	—
409	C₅	#26091	1	1	yes	characteristic, direct product factor, Sylow
410	C₂²	—	4	2	no	—
411	C₂²	—	4	2	no	—
412	C₂²	—	4	2	no	—
413	C₂²	—	8	1	no	—
414	C₂²	—	8	1	no	—
415	C₂²	—	8	1	no	—
416	C₂²	—	8	1	no	—
417	C₂²	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
418	C₂²	C₅×#547	1	1	yes	characteristic
419	C₂²	C₅×#550	1	1	yes	characteristic
420	C₂²	C₂×C₅×#135	1	1	yes	characteristic
421	C₂²	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
422	C₂²	C₅×#577	1	1	yes	characteristic
423	C₂²	C₅×#577	1	1	yes	characteristic
424	C₄	—	2	2	no	—
425	C₄	—	4	2	no	—
426	C₄	—	4	2	no	—
427	C₄	—	4	2	no	—
428	C₄	—	8	1	no	—
429	C₄	—	8	2	no	—
430	C₄	—	8	2	no	—
431	C₄	—	8	1	no	—
432	C₄	C₅×#478	1	4	yes	—
433	C₄	C₅×#533	1	1	yes	characteristic
434	C₄	C₅×#544	1	1	yes	characteristic
435	C₄	C₅×#552	1	1	yes	characteristic
436	C₄	C₅×#553	1	1	yes	characteristic
437	C₂	—	8	2	no	—
438	C₂	C₅×#2441	1	1	yes	characteristic
439	C₂	C₂×C₅×#478	1	1	yes	characteristic
440	C₂	C₅×#3084	1	1	yes	characteristic
441	C₂	C₅×#3340	1	1	yes	characteristic
442	C₂	C₅×#3354	1	1	yes	characteristic
443	C₂	C₅×#3394	1	1	yes	characteristic
444	C₂	C₅×#3397	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
prime radical	C₂²×C₅×D₄	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₄×C₅×C₄⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×#2571	C₂	semidirect
5. C₅×#1949	C₂	semidirect
6. C₅×#1947	C₂	semidirect
7. C₅×#1939	C₂	semidirect
8. C₅×#1919	C₂	semidirect
9. C₅×#1844	C₂	semidirect
41. #26091	C₅	direct (N × H)
84. #2571	C₂×C₅	semidirect
88. #1949	C₂×C₅	semidirect
89. #1947	C₂×C₅	semidirect
90. #1939	C₂×C₅	semidirect
91. #1919	C₂×C₅	semidirect
92. #1844	C₂×C₅	semidirect
409. C₅	#26091	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×#2571	2
C₅×#2354	2
C₅×#2092	2
C₅×#2065	2
C₅×#1949	2
C₅×#1947	2
C₅×#1939	2
C₅×#1919	2
C₅×#1844	2
C₅×#1802	2
C₄×C₅×#102	2
#26091	5

Subgroups — C5×#26091 #11948811

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#26091 #11948811