Subgroups — C₅×#22278 #11944998

Order 1280.

874 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#497	C₂	1	1	yes	maximal, characteristic
2	C₅×#2327	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2326	C₂	1	1	yes	maximal, characteristic
4	C₅×#1958	C₂	1	1	yes	maximal, characteristic
5	C₅×#1956	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1880	C₂	1	2	yes	maximal
7	C₅×#1878	C₂	1	2	yes	maximal, complemented
8	C₅×#1878	C₂	1	2	yes	maximal, complemented
9	C₅×#1877	C₂	1	2	yes	maximal
10	C₅×#1836	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1746	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₅×Q₁₆	C₂²	1	2	yes	—
13	C₂²×C₅×SD₁₆	C₂²	1	2	yes	—
14	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₅×#124	C₂²	1	1	yes	characteristic
16	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
18	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
19	C₅×#497	C₄	1	8	yes	complemented
20	C₂×C₅×#103	C₂²	1	2	yes	—
21	C₂×C₅×#103	C₂²	1	2	yes	—
22	C₂×C₅×#103	C₂²	1	2	yes	—
23	C₂×C₅×#102	C₂²	1	2	yes	—
24	C₂×C₅×#97	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
26	C₅×#391	C₂²	1	1	yes	characteristic
27	C₅×#391	C₂²	1	2	yes	—
28	C₅×#390	C₂²	1	1	yes	characteristic
29	C₅×#388	—	2	2	no	—
30	C₅×#387	—	2	2	no	—
31	C₅×#387	—	2	2	no	—
32	C₅×#385	—	2	2	no	—
33	C₅×#384	C₂²	1	1	yes	characteristic
34	C₅×#382	C₂²	1	1	yes	characteristic
35	C₅×#376	C₂²	1	1	yes	characteristic
36	C₅×#340	C₂²	1	2	yes	—
37	C₅×#340	C₂²	1	2	yes	—
38	C₅×#336	C₂²	1	2	yes	—
39	C₅×#336	C₂²	1	2	yes	—
40	#22278	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
41	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
42	C₂²×C₅×Q₈	C₂³	1	2	yes	—
43	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₅	—	2	1	no	—
45	C₂×C₅×Q₁₆	—	4	2	no	—
46	C₂×C₅×Q₁₆	—	4	2	no	—
47	C₂×C₅×Q₁₆	C₂×C₄	1	8	yes	complemented
48	C₂×C₅×SD₁₆	—	4	2	no	—
49	C₂×C₅×SD₁₆	—	4	2	no	—
50	C₂×C₅×SD₁₆	C₂×C₄	1	8	yes	—
51	C₂²×C₅×C₈	C₂³	1	2	yes	—
52	C₂²×C₅×C₈	C₂³	1	2	yes	—
53	C₅×C₄⋊Q₈	—	2	2	no	—
54	C₅×C₄⋊Q₈	C₂×C₄	1	4	yes	complemented
55	C₅×#124	—	2	2	no	—
56	C₅×#124	C₂×C₄	1	4	yes	—
57	C₄×C₅×Q₈	—	4	2	no	—
58	C₄×C₅×Q₈	—	4	2	no	—
59	C₄×C₅×Q₈	—	4	2	no	—
60	C₄×C₅×D₄	—	4	2	no	—
61	C₂×C₅×C₄⋊C₄	—	2	2	no	—
62	C₂×C₅×C₄⋊C₄	—	2	1	no	—
63	C₂×C₅×C₄⋊C₄	—	2	2	no	—
64	C₂×C₅×C₄⋊C₄	—	2	2	no	—
65	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
66	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
67	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
68	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
69	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
70	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
71	C₂×C₄²×C₅	—	2	2	no	—
72	C₂×C₄²×C₅	—	2	1	no	—
73	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
74	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
76	C₅×#103	—	4	2	no	—
77	C₅×#103	—	4	2	no	—
78	C₅×#103	—	4	2	no	—
79	C₅×#102	—	4	2	no	—
80	C₅×#97	C₂×C₄	1	4	yes	complemented
81	C₄×C₅×C₈	—	2	2	no	—
82	C₅×#95	—	2	2	no	—
83	C₅×#95	—	2	2	no	—
84	C₅×#95	—	2	2	no	—
85	C₅×#95	—	2	2	no	—
86	C₅×#95	D₄	1	2	yes	—
87	C₅×#95	D₄	1	2	yes	—
88	C₂×#497	C₂×C₅	1	1	yes	characteristic
89	#2327	C₂×C₅	1	1	yes	characteristic, complemented
90	#2326	C₂×C₅	1	1	yes	characteristic
91	#1958	C₂×C₅	1	1	yes	characteristic
92	#1956	C₂×C₅	1	1	yes	characteristic, complemented
93	#1880	C₂×C₅	1	2	yes	—
94	#1878	C₂×C₅	1	2	yes	complemented
95	#1878	C₂×C₅	1	2	yes	complemented
96	#1877	C₂×C₅	1	2	yes	—
97	#1836	C₂×C₅	1	1	yes	characteristic, complemented
98	#1746	C₂×C₅	1	1	yes	characteristic, complemented
99	C₂⁴×C₅	—	2	1	no	—
100	C₂×C₅×Q₈	—	2	1	no	—
101	C₂×C₅×Q₈	—	2	2	no	—
102	C₂×C₅×Q₈	—	2	2	no	—
103	C₂×C₅×Q₈	—	2	2	no	—
104	C₂×C₅×Q₈	—	2	2	no	—
105	C₂×C₅×Q₈	—	2	2	no	—
106	C₂×C₅×Q₈	—	2	2	no	—
107	C₂×C₅×Q₈	—	2	2	no	—
108	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
109	C₂×C₅×Q₈	C₂²×C₄	1	4	yes	—
110	C₂×C₅×D₄	—	2	1	no	—
111	C₂×C₅×D₄	—	2	2	no	—
112	C₂×C₅×D₄	—	2	2	no	—
113	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
114	C₂²×C₄×C₅	—	2	1	no	—
115	C₂²×C₄×C₅	—	2	2	no	—
116	C₂²×C₄×C₅	—	2	1	no	—
117	C₂²×C₄×C₅	—	2	2	no	—
118	C₂²×C₄×C₅	—	2	1	no	—
119	C₂²×C₄×C₅	—	4	2	no	—
120	C₂²×C₄×C₅	—	8	2	no	—
121	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
122	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
126	C₅×Q₁₆	—	4	8	no	—
127	C₅×SD₁₆	—	4	8	no	—
128	C₂×C₅×C₈	—	2	2	no	—
129	C₂×C₅×C₈	—	2	2	no	—
130	C₂×C₅×C₈	—	2	2	no	—
131	C₂×C₅×C₈	—	2	2	no	—
132	C₂×C₅×C₈	—	2	2	no	—
133	C₂×C₅×C₈	C₂²×C₄	1	4	yes	—
134	C₅×C₄⋊C₄	—	2	8	no	—
135	C₅×C₄⋊C₄	—	2	2	no	—
136	C₅×C₄⋊C₄	—	2	2	no	—
137	C₅×C₄⋊C₄	—	2	2	no	—
138	C₅×C₄⋊C₄	—	2	2	no	—
139	C₅×C₄⋊C₄	—	4	4	no	—
140	C₅×C₄⋊C₄	—	4	2	no	—
141	C₅×C₄⋊C₄	—	8	2	no	—
142	C₅×C₂²⋊C₄	—	2	8	no	—
143	C₅×C₂²⋊C₄	—	4	2	no	—
144	C₅×C₂²⋊C₄	—	8	2	no	—
145	C₄²×C₅	—	2	2	no	—
146	C₄²×C₅	—	2	2	no	—
147	C₄²×C₅	—	4	2	no	—
148	C₄²×C₅	—	4	4	no	—
149	C₄²×C₅	C₂²×C₄	1	2	yes	—
150	C₄²×C₅	#41	1	2	yes	—
151	C₂²×Q₁₆	C₂²×C₅	1	2	yes	—
152	C₂²×SD₁₆	C₂²×C₅	1	2	yes	—
153	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
154	C₂×#124	C₂²×C₅	1	1	yes	characteristic
155	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
156	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
157	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
158	#497	C₄×C₅	1	8	yes	complemented
159	C₂×#103	C₂²×C₅	1	2	yes	—
160	C₂×#103	C₂²×C₅	1	2	yes	—
161	C₂×#103	C₂²×C₅	1	2	yes	—
162	C₂×#102	C₂²×C₅	1	2	yes	—
163	C₂×#97	C₂²×C₅	1	1	yes	characteristic
164	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
165	#391	C₂²×C₅	1	1	yes	characteristic
166	#391	C₂²×C₅	1	2	yes	—
167	#390	C₂²×C₅	1	1	yes	characteristic
168	#388	—	2	2	no	—
169	#387	—	2	2	no	—
170	#387	—	2	2	no	—
171	#385	—	2	2	no	—
172	#384	C₂²×C₅	1	1	yes	characteristic
173	#382	C₂²×C₅	1	1	yes	characteristic
174	#376	C₂²×C₅	1	1	yes	characteristic
175	#340	C₂²×C₅	1	2	yes	—
176	#340	C₂²×C₅	1	2	yes	—
177	#336	C₂²×C₅	1	2	yes	—
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	2	no	—
183	C₂³×C₅	—	4	2	no	—
184	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
185	C₅×Q₈	—	2	4	no	—
186	C₅×Q₈	—	2	4	no	—
187	C₅×Q₈	—	2	4	no	—
188	C₅×Q₈	—	4	2	no	—
189	C₅×Q₈	—	4	2	no	—
190	C₅×Q₈	—	4	2	no	—
191	C₅×D₄	—	2	4	no	—
192	C₅×D₄	—	4	2	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	4	no	—
197	C₂×C₄×C₅	—	2	1	no	—
198	C₂×C₄×C₅	—	2	2	no	—
199	C₂×C₄×C₅	—	2	1	no	—
200	C₂×C₄×C₅	—	2	2	no	—
201	C₂×C₄×C₅	—	2	2	no	—
202	C₂×C₄×C₅	—	2	2	no	—
203	C₂×C₄×C₅	—	2	2	no	—
204	C₂×C₄×C₅	—	4	1	no	—
205	C₂×C₄×C₅	—	4	2	no	—
206	C₂×C₄×C₅	—	4	2	no	—
207	C₂×C₄×C₅	—	4	1	no	—
208	C₂×C₄×C₅	—	4	1	no	—
209	C₂×C₄×C₅	—	4	2	no	—
210	C₂×C₄×C₅	—	4	1	no	—
211	C₂×C₄×C₅	—	4	2	no	—
212	C₂×C₄×C₅	—	4	2	no	—
213	C₂×C₄×C₅	—	4	2	no	—
214	C₂×C₄×C₅	—	4	2	no	—
215	C₂×C₄×C₅	—	8	4	no	—
216	C₂×C₄×C₅	C₄×D₄	1	4	yes	—
217	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
218	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
219	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
220	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
221	C₅×C₈	—	2	4	no	—
222	C₅×C₈	—	4	2	no	—
223	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
224	C₂²×Q₈	C₂³×C₅	1	2	yes	—
225	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
226	C₂³×C₄	—	2	1	no	—
227	C₂×Q₁₆	—	4	2	no	—
228	C₂×Q₁₆	—	4	2	no	—
229	C₂×Q₁₆	C₂×C₄×C₅	1	8	yes	complemented
230	C₂×SD₁₆	—	4	2	no	—
231	C₂×SD₁₆	—	4	2	no	—
232	C₂×SD₁₆	C₂×C₄×C₅	1	8	yes	—
233	C₂²×C₈	C₂³×C₅	1	2	yes	—
234	C₂²×C₈	C₂³×C₅	1	2	yes	—
235	C₄⋊Q₈	—	2	2	no	—
236	C₄⋊Q₈	C₂×C₄×C₅	1	4	yes	complemented
237	#124	—	2	2	no	—
238	#124	C₂×C₄×C₅	1	4	yes	—
239	C₄×Q₈	—	4	2	no	—
240	C₄×Q₈	—	4	2	no	—
241	C₄×Q₈	—	4	2	no	—
242	C₄×D₄	—	4	2	no	—
243	C₂×C₄⋊C₄	—	2	2	no	—
244	C₂×C₄⋊C₄	—	2	1	no	—
245	C₂×C₄⋊C₄	—	2	2	no	—
246	C₂×C₄⋊C₄	—	2	2	no	—
247	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
248	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
249	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
250	C₂×C₂²⋊C₄	—	2	2	no	—
251	C₂×C₂²⋊C₄	—	2	1	no	—
252	C₂×C₂²⋊C₄	—	2	2	no	—
253	C₂×C₄²	—	2	2	no	—
254	C₂×C₄²	—	2	1	no	—
255	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
256	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
257	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
258	#103	—	4	2	no	—
259	#103	—	4	2	no	—
260	#103	—	4	2	no	—
261	#102	—	4	2	no	—
262	#97	C₂×C₄×C₅	1	4	yes	complemented
263	C₄×C₈	—	2	2	no	—
264	#95	—	2	2	no	—
265	#95	—	2	2	no	—
266	#95	—	2	2	no	—
267	#95	—	2	2	no	—
268	#95	C₅×D₄	1	2	yes	—
269	#95	C₅×D₄	1	2	yes	—
270	C₂²×C₅	—	4	2	no	—
271	C₂²×C₅	—	4	4	no	—
272	C₂²×C₅	—	8	1	no	—
273	C₂²×C₅	—	8	1	no	—
274	C₂²×C₅	—	8	2	no	—
275	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
276	C₂²×C₅	#535	1	1	yes	characteristic
277	C₂²×C₅	#535	1	1	yes	characteristic
278	C₂²×C₅	#577	1	2	yes	—
279	C₂²×C₅	#578	1	2	yes	—
280	C₄×C₅	—	2	4	no	—
281	C₄×C₅	—	4	2	no	—
282	C₄×C₅	—	4	4	no	—
283	C₄×C₅	—	4	1	no	—
284	C₄×C₅	—	4	1	no	—
285	C₄×C₅	—	4	2	no	—
286	C₄×C₅	—	8	1	no	—
287	C₄×C₅	—	8	1	no	—
288	C₄×C₅	—	8	2	no	—
289	C₄×C₅	#518	1	2	yes	—
290	C₄×C₅	#540	1	2	yes	—
291	C₂⁴	—	2	1	no	—
292	C₂×Q₈	—	2	1	no	—
293	C₂×Q₈	—	2	2	no	—
294	C₂×Q₈	—	2	2	no	—
295	C₂×Q₈	—	2	2	no	—
296	C₂×Q₈	—	2	2	no	—
297	C₂×Q₈	—	2	2	no	—
298	C₂×Q₈	—	2	2	no	—
299	C₂×Q₈	—	2	2	no	—
300	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
301	C₂×Q₈	C₂²×C₄×C₅	1	4	yes	—
302	C₂×D₄	—	2	1	no	—
303	C₂×D₄	—	2	2	no	—
304	C₂×D₄	—	2	2	no	—
305	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
306	C₂²×C₄	—	2	1	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	2	1	no	—
311	C₂²×C₄	—	4	2	no	—
312	C₂²×C₄	—	8	2	no	—
313	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
314	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
315	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
316	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
317	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
318	Q₁₆	—	4	8	no	—
319	SD₁₆	—	4	8	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	C₂²×C₄×C₅	1	4	yes	—
326	C₄⋊C₄	—	2	8	no	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	2	2	no	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	4	4	no	—
332	C₄⋊C₄	—	4	2	no	—
333	C₄⋊C₄	—	8	2	no	—
334	C₂²⋊C₄	—	2	8	no	—
335	C₂²⋊C₄	—	4	2	no	—
336	C₂²⋊C₄	—	8	2	no	—
337	C₄²	—	2	2	no	—
338	C₄²	—	2	2	no	—
339	C₄²	—	4	2	no	—
340	C₄²	—	4	4	no	—
341	C₄²	C₂²×C₄×C₅	1	2	yes	—
342	C₄²	C₅×#41	1	2	yes	—
343	C₂×C₅	—	8	2	no	—
344	C₂×C₅	#2328	1	1	yes	characteristic
345	C₂×C₅	#2947	1	2	yes	—
346	C₂×C₅	#3222	1	1	yes	characteristic
347	C₂×C₅	#3223	1	1	yes	characteristic
348	C₂×C₅	#3225	1	2	yes	—
349	C₂³	—	2	2	no	—
350	C₂³	—	4	1	no	—
351	C₂³	—	4	1	no	—
352	C₂³	—	4	2	no	—
353	C₂³	—	4	2	no	—
354	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
355	Q₈	—	2	4	no	—
356	Q₈	—	2	4	no	—
357	Q₈	—	2	4	no	—
358	Q₈	—	4	2	no	—
359	Q₈	—	4	2	no	—
360	Q₈	—	4	2	no	—
361	D₄	—	2	4	no	—
362	D₄	—	4	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	4	1	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	1	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	8	4	no	—
386	C₂×C₄	C₄×C₅×D₄	1	4	yes	—
387	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
388	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
389	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
390	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
391	C₈	—	2	4	no	—
392	C₈	—	4	2	no	—
393	C₅	#22278	1	1	yes	characteristic, direct product factor, Sylow
394	C₂²	—	4	2	no	—
395	C₂²	—	4	4	no	—
396	C₂²	—	8	1	no	—
397	C₂²	—	8	1	no	—
398	C₂²	—	8	2	no	—
399	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
400	C₂²	C₅×#535	1	1	yes	characteristic
401	C₂²	C₅×#535	1	1	yes	characteristic
402	C₂²	C₅×#577	1	2	yes	—
403	C₂²	C₅×#578	1	2	yes	—
404	C₄	—	2	4	no	—
405	C₄	—	4	2	no	—
406	C₄	—	4	4	no	—
407	C₄	—	4	1	no	—
408	C₄	—	4	1	no	—
409	C₄	—	4	2	no	—
410	C₄	—	8	1	no	—
411	C₄	—	8	1	no	—
412	C₄	—	8	2	no	—
413	C₄	C₅×#518	1	2	yes	—
414	C₄	C₅×#540	1	2	yes	—
415	C₂	—	8	2	no	—
416	C₂	C₅×#2328	1	1	yes	characteristic
417	C₂	C₅×#2947	1	2	yes	—
418	C₂	C₅×#3222	1	1	yes	characteristic
419	C₂	C₅×#3223	1	1	yes	characteristic
420	C₂	C₅×#3225	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₅	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
prime radical	C₂²×C₅×D₄	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₅×#376 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×#2327	C₂	semidirect
5. C₅×#1956	C₂	semidirect
7. C₅×#1878	C₂	semidirect
8. C₅×#1878	C₂	semidirect
10. C₅×#1836	C₂	semidirect
11. C₅×#1746	C₂	semidirect
19. C₅×#497	C₄	semidirect
40. #22278	C₅	direct (N × H)
47. C₂×C₅×Q₁₆	C₂×C₄	semidirect
54. C₅×C₄⋊Q₈	C₂×C₄	semidirect
80. C₅×#97	C₂×C₄	semidirect
89. #2327	C₂×C₅	semidirect
92. #1956	C₂×C₅	semidirect
94. #1878	C₂×C₅	semidirect
95. #1878	C₂×C₅	semidirect
97. #1836	C₂×C₅	semidirect
98. #1746	C₂×C₅	semidirect
158. #497	C₄×C₅	semidirect
229. C₂×Q₁₆	C₂×C₄×C₅	semidirect
236. C₄⋊Q₈	C₂×C₄×C₅	semidirect
262. #97	C₂×C₄×C₅	semidirect
393. C₅	#22278	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×#497	2
C₅×#2327	2
C₅×#2326	2
C₅×#1958	2
C₅×#1956	2
C₅×#1880	2
C₅×#1878	2
C₅×#1877	2
C₅×#1836	2
C₅×#1746	2
#22278	5

Subgroups — C5×#22278 #11944998

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22278 #11944998