Subgroups — C₅×#19420 #11942140

Order 1280.

714 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3208	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#3077	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#459	C₂	1	1	yes	maximal, characteristic
4	C₅×#2975	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1697	C₂	1	4	yes	maximal, complemented
6	C₅×#1685	C₂	1	4	yes	maximal, complemented
7	C₅×#1571	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1545	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1542	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₅×D₈	—	2	1	no	—
11	C₅×#533	C₂²	1	1	yes	characteristic
12	C₂×C₅×#127	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
14	C₅×#492	C₂²	1	2	yes	complemented
15	C₅×#486	C₂²	1	2	yes	complemented
16	C₅×#478	—	2	2	no	—
17	C₅×#476	C₂²	1	2	yes	complemented
18	C₅×#474	C₂²	1	2	yes	complemented
19	C₅×#460	—	2	2	no	—
20	C₅×#459	—	2	2	no	—
21	C₅×#459	C₂²	1	4	yes	—
22	C₅×#450	—	2	2	no	—
23	C₅×#436	—	2	2	no	—
24	C₅×#436	C₂²	1	4	yes	complemented
25	C₅×#431	C₂²	1	1	yes	characteristic
26	C₅×#431	C₂²	1	1	yes	characteristic
27	C₅×#428	—	2	1	no	—
28	C₅×#423	C₂²	1	1	yes	characteristic
29	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
30	C₅×#418	—	2	1	no	—
31	C₂×C₅×#102	—	2	1	no	—
32	C₅×#407	—	2	2	no	—
33	C₅×#335	C₂²	1	4	yes	complemented
34	C₅×#333	C₂²	1	2	yes	complemented
35	C₅×#332	C₂²	1	2	yes	complemented
36	C₅×#331	C₂²	1	4	yes	complemented
37	#19420	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
38	C₂²×C₅×D₄	—	2	1	no	—
39	C₂²×C₅×D₄	—	2	1	no	—
40	C₂²×C₅×D₄	—	2	1	no	—
41	C₂²×C₅×D₄	D₄	1	1	yes	characteristic
42	C₂³×C₄×C₅	—	2	1	no	—
43	C₂×C₅×SD₁₆	—	2	4	no	—
44	C₂×C₅×D₈	—	2	4	no	—
45	C₂×C₅×D₈	—	4	4	no	—
46	C₂×C₅×M₁₆	—	2	1	no	—
47	C₂×C₅×M₁₆	—	2	4	no	—
48	C₂²×C₅×C₈	—	2	1	no	—
49	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
50	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
51	C₅×#127	—	2	1	no	—
52	C₅×#127	—	2	1	no	—
53	C₅×#127	—	2	1	no	—
54	C₅×#127	C₂³	1	2	yes	—
55	C₅×#125	—	2	1	no	—
56	C₅×C₂²⋊Q₈	—	2	1	no	—
57	C₅×C₂²⋊Q₈	—	2	1	no	—
58	C₄×C₅×Q₈	—	2	1	no	—
59	C₄×C₅×Q₈	—	2	1	no	—
60	C₄×C₅×D₄	—	2	1	no	—
61	C₄×C₅×D₄	—	2	1	no	—
62	C₄×C₅×D₄	D₄	1	2	yes	—
63	C₄×C₅×D₄	C₂³	1	2	yes	—
64	C₅×#117	—	2	1	no	—
65	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
66	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
67	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
68	C₅×#107	—	2	2	no	—
69	C₅×#106	—	2	2	no	—
70	C₅×C₄⋊C₈	—	2	1	no	—
71	C₅×C₄⋊C₈	—	2	1	no	—
72	C₅×C₄⋊C₈	D₄	1	2	yes	—
73	C₅×C₄⋊C₈	C₂³	1	2	yes	—
74	C₅×C₄⋊C₈	C₂³	1	2	yes	—
75	C₅×C₄⋊C₈	C₂³	1	2	yes	—
76	C₅×#102	—	2	2	no	—
77	C₅×#102	—	2	2	no	—
78	C₅×#102	—	2	4	no	—
79	C₅×#102	—	2	4	no	—
80	C₅×C₂²⋊C₈	—	2	1	no	—
81	C₅×C₂²⋊C₈	—	2	4	no	—
82	C₅×C₂²⋊C₈	D₄	1	2	yes	—
83	C₄×C₅×C₈	—	2	1	no	—
84	C₄×C₅×C₈	C₂³	1	2	yes	—
85	#3208	C₂×C₅	1	1	yes	characteristic, complemented
86	#3077	C₂×C₅	1	1	yes	characteristic, complemented
87	C₂×#459	C₂×C₅	1	1	yes	characteristic
88	#2975	C₂×C₅	1	1	yes	characteristic, complemented
89	#1697	C₂×C₅	1	4	yes	complemented
90	#1685	C₂×C₅	1	4	yes	complemented
91	#1571	C₂×C₅	1	1	yes	characteristic, complemented
92	#1545	C₂×C₅	1	1	yes	characteristic, complemented
93	#1542	C₂×C₅	1	1	yes	characteristic, complemented
94	C₂⁴×C₅	—	2	1	no	—
95	C₂⁴×C₅	—	4	1	no	—
96	C₂×C₅×Q₈	—	2	1	no	—
97	C₂×C₅×Q₈	—	2	1	no	—
98	C₂×C₅×D₄	—	2	1	no	—
99	C₂×C₅×D₄	—	2	2	no	—
100	C₂×C₅×D₄	—	2	2	no	—
101	C₂×C₅×D₄	—	2	2	no	—
102	C₂×C₅×D₄	—	2	2	no	—
103	C₂×C₅×D₄	—	2	2	no	—
104	C₂×C₅×D₄	—	4	1	no	—
105	C₂×C₅×D₄	—	4	1	no	—
106	C₂×C₅×D₄	—	4	1	no	—
107	C₂×C₅×D₄	—	4	2	no	—
108	C₂×C₅×D₄	—	4	2	no	—
109	C₂×C₅×D₄	—	8	2	no	—
110	C₂×C₅×D₄	—	8	2	no	—
111	C₂×C₅×D₄	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₅	—	2	1	no	—
113	C₂²×C₄×C₅	—	2	2	no	—
114	C₂²×C₄×C₅	—	2	2	no	—
115	C₂²×C₄×C₅	—	8	2	no	—
116	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₅	#41	1	1	yes	characteristic
119	C₅×SD₁₆	—	8	4	no	—
120	C₅×D₈	—	4	8	no	—
121	C₅×M₁₆	—	4	2	no	—
122	C₅×M₁₆	—	8	4	no	—
123	C₂×C₅×C₈	—	2	2	no	—
124	C₂×C₅×C₈	—	2	2	no	—
125	C₂×C₅×C₈	—	2	2	no	—
126	C₂×C₅×C₈	—	4	2	no	—
127	C₂×C₅×C₈	C₂×D₄	1	4	yes	—
128	C₅×C₄⋊C₄	—	2	1	no	—
129	C₅×C₄⋊C₄	—	2	1	no	—
130	C₅×C₄⋊C₄	—	2	1	no	—
131	C₅×C₄⋊C₄	—	2	1	no	—
132	C₅×C₄⋊C₄	—	2	1	no	—
133	C₅×C₄⋊C₄	—	4	1	no	—
134	C₅×C₄⋊C₄	—	4	1	no	—
135	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
136	C₅×C₂²⋊C₄	—	2	2	no	—
137	C₅×C₂²⋊C₄	—	2	2	no	—
138	C₅×C₂²⋊C₄	—	4	1	no	—
139	C₄²×C₅	—	4	1	no	—
140	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
141	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
142	C₄²×C₅	#41	1	1	yes	characteristic
143	C₄²×C₅	C₂⁴	1	1	yes	characteristic
144	C₂²×D₈	—	2	1	no	—
145	#533	C₂²×C₅	1	1	yes	characteristic
146	C₂×#127	C₂²×C₅	1	1	yes	characteristic
147	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
148	#492	C₂²×C₅	1	2	yes	complemented
149	#486	C₂²×C₅	1	2	yes	complemented
150	#478	—	2	2	no	—
151	#476	C₂²×C₅	1	2	yes	complemented
152	#474	C₂²×C₅	1	2	yes	complemented
153	#460	—	2	2	no	—
154	#459	—	2	2	no	—
155	#459	C₂²×C₅	1	4	yes	—
156	#450	—	2	2	no	—
157	#436	—	2	2	no	—
158	#436	C₂²×C₅	1	4	yes	complemented
159	#431	C₂²×C₅	1	1	yes	characteristic
160	#431	C₂²×C₅	1	1	yes	characteristic
161	#428	—	2	1	no	—
162	#423	C₂²×C₅	1	1	yes	characteristic
163	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
164	#418	—	2	1	no	—
165	C₂×#102	—	2	1	no	—
166	#407	—	2	2	no	—
167	#335	C₂²×C₅	1	4	yes	complemented
168	#333	C₂²×C₅	1	2	yes	complemented
169	#332	C₂²×C₅	1	2	yes	complemented
170	#331	C₂²×C₅	1	4	yes	complemented
171	C₂³×C₅	—	2	2	no	—
172	C₂³×C₅	—	4	2	no	—
173	C₂³×C₅	—	4	2	no	—
174	C₂³×C₅	—	8	1	no	—
175	C₂³×C₅	—	8	1	no	—
176	C₂³×C₅	—	8	2	no	—
177	C₂³×C₅	—	8	2	no	—
178	C₂³×C₅	—	8	2	no	—
179	C₂³×C₅	#121	1	1	yes	characteristic
180	C₅×Q₈	—	4	2	no	—
181	C₅×Q₈	—	8	1	no	—
182	C₅×D₄	—	2	2	no	—
183	C₅×D₄	—	2	2	no	—
184	C₅×D₄	—	4	2	no	—
185	C₅×D₄	—	4	2	no	—
186	C₅×D₄	—	4	4	no	—
187	C₅×D₄	—	4	2	no	—
188	C₅×D₄	—	8	2	no	—
189	C₅×D₄	—	8	2	no	—
190	C₅×D₄	—	8	2	no	—
191	C₅×D₄	—	8	2	no	—
192	C₂×C₄×C₅	—	2	2	no	—
193	C₂×C₄×C₅	—	2	2	no	—
194	C₂×C₄×C₅	—	4	1	no	—
195	C₂×C₄×C₅	—	4	4	no	—
196	C₂×C₄×C₅	—	4	1	no	—
197	C₂×C₄×C₅	—	4	1	no	—
198	C₂×C₄×C₅	—	8	2	no	—
199	C₂×C₄×C₅	—	8	1	no	—
200	C₂×C₄×C₅	#121	1	1	yes	characteristic
201	C₂×C₄×C₅	#121	1	1	yes	characteristic
202	C₂×C₄×C₅	#121	1	1	yes	characteristic
203	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
204	C₂×C₄×C₅	#137	1	2	yes	—
205	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
206	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
207	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
208	C₅×C₈	—	2	4	no	—
209	C₅×C₈	—	4	2	no	—
210	C₅×C₈	—	4	2	no	—
211	C₅×C₈	—	4	2	no	—
212	C₂²×D₄	—	2	1	no	—
213	C₂²×D₄	—	2	1	no	—
214	C₂²×D₄	—	2	1	no	—
215	C₂²×D₄	C₅×D₄	1	1	yes	characteristic
216	C₂³×C₄	—	2	1	no	—
217	C₂×SD₁₆	—	2	4	no	—
218	C₂×D₈	—	2	4	no	—
219	C₂×D₈	—	4	4	no	—
220	C₂×M₁₆	—	2	1	no	—
221	C₂×M₁₆	—	2	4	no	—
222	C₂²×C₈	—	2	1	no	—
223	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
224	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
225	#127	—	2	1	no	—
226	#127	—	2	1	no	—
227	#127	—	2	1	no	—
228	#127	C₂³×C₅	1	2	yes	—
229	#125	—	2	1	no	—
230	C₂²⋊Q₈	—	2	1	no	—
231	C₂²⋊Q₈	—	2	1	no	—
232	C₄×Q₈	—	2	1	no	—
233	C₄×Q₈	—	2	1	no	—
234	C₄×D₄	—	2	1	no	—
235	C₄×D₄	—	2	1	no	—
236	C₄×D₄	C₅×D₄	1	2	yes	—
237	C₄×D₄	C₂³×C₅	1	2	yes	—
238	#117	—	2	1	no	—
239	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
240	C₂×C₂²⋊C₄	—	2	1	no	—
241	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
242	#107	—	2	2	no	—
243	#106	—	2	2	no	—
244	C₄⋊C₈	—	2	1	no	—
245	C₄⋊C₈	—	2	1	no	—
246	C₄⋊C₈	C₅×D₄	1	2	yes	—
247	C₄⋊C₈	C₂³×C₅	1	2	yes	—
248	C₄⋊C₈	C₂³×C₅	1	2	yes	—
249	C₄⋊C₈	C₂³×C₅	1	2	yes	—
250	#102	—	2	2	no	—
251	#102	—	2	2	no	—
252	#102	—	2	4	no	—
253	#102	—	2	4	no	—
254	C₂²⋊C₈	—	2	1	no	—
255	C₂²⋊C₈	—	2	4	no	—
256	C₂²⋊C₈	C₅×D₄	1	2	yes	—
257	C₄×C₈	—	2	1	no	—
258	C₄×C₈	C₂³×C₅	1	2	yes	—
259	C₂²×C₅	—	2	1	no	—
260	C₂²×C₅	—	2	1	no	—
261	C₂²×C₅	—	4	2	no	—
262	C₂²×C₅	—	4	2	no	—
263	C₂²×C₅	—	4	2	no	—
264	C₂²×C₅	—	8	4	no	—
265	C₂²×C₅	—	8	2	no	—
266	C₂²×C₅	—	8	2	no	—
267	C₂²×C₅	—	8	2	no	—
268	C₂²×C₅	—	16	4	no	—
269	C₂²×C₅	#468	1	2	yes	—
270	C₂²×C₅	C₂×#121	1	1	yes	characteristic
271	C₄×C₅	—	2	1	no	—
272	C₄×C₅	—	2	1	no	—
273	C₄×C₅	—	2	1	no	—
274	C₄×C₅	—	4	2	no	—
275	C₄×C₅	—	8	1	no	—
276	C₄×C₅	—	8	1	no	—
277	C₄×C₅	#468	1	2	yes	—
278	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
279	C₄×C₅	C₂×#137	1	1	yes	characteristic
280	C₄×C₅	#576	1	2	yes	—
281	C₂⁴	—	2	1	no	—
282	C₂⁴	—	4	1	no	—
283	C₂×Q₈	—	2	1	no	—
284	C₂×Q₈	—	2	1	no	—
285	C₂×D₄	—	2	1	no	—
286	C₂×D₄	—	2	2	no	—
287	C₂×D₄	—	2	2	no	—
288	C₂×D₄	—	2	2	no	—
289	C₂×D₄	—	2	2	no	—
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	—	4	1	no	—
292	C₂×D₄	—	4	1	no	—
293	C₂×D₄	—	4	1	no	—
294	C₂×D₄	—	4	2	no	—
295	C₂×D₄	—	4	2	no	—
296	C₂×D₄	—	8	2	no	—
297	C₂×D₄	—	8	2	no	—
298	C₂×D₄	C₂×C₅×D₄	1	2	yes	—
299	C₂²×C₄	—	2	1	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	8	2	no	—
303	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
304	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
305	C₂²×C₄	C₅×#41	1	1	yes	characteristic
306	SD₁₆	—	8	4	no	—
307	D₈	—	4	8	no	—
308	M₁₆	—	4	2	no	—
309	M₁₆	—	8	4	no	—
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	4	2	no	—
314	C₂×C₈	C₂×C₅×D₄	1	4	yes	—
315	C₄⋊C₄	—	2	1	no	—
316	C₄⋊C₄	—	2	1	no	—
317	C₄⋊C₄	—	2	1	no	—
318	C₄⋊C₄	—	2	1	no	—
319	C₄⋊C₄	—	2	1	no	—
320	C₄⋊C₄	—	4	1	no	—
321	C₄⋊C₄	—	4	1	no	—
322	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
323	C₂²⋊C₄	—	2	2	no	—
324	C₂²⋊C₄	—	2	2	no	—
325	C₂²⋊C₄	—	4	1	no	—
326	C₄²	—	4	1	no	—
327	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
328	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
329	C₄²	C₅×#41	1	1	yes	characteristic
330	C₄²	C₂⁴×C₅	1	1	yes	characteristic
331	C₂×C₅	—	2	2	no	—
332	C₂×C₅	—	8	2	no	—
333	C₂×C₅	—	16	2	no	—
334	C₂×C₅	#3041	1	1	yes	characteristic
335	C₂×C₅	C₂×#468	1	1	yes	characteristic
336	C₂×C₅	#3068	1	1	yes	characteristic
337	C₂³	—	2	2	no	—
338	C₂³	—	4	2	no	—
339	C₂³	—	4	2	no	—
340	C₂³	—	8	1	no	—
341	C₂³	—	8	1	no	—
342	C₂³	—	8	2	no	—
343	C₂³	—	8	2	no	—
344	C₂³	—	8	2	no	—
345	C₂³	C₅×#121	1	1	yes	characteristic
346	Q₈	—	4	2	no	—
347	Q₈	—	8	1	no	—
348	D₄	—	2	2	no	—
349	D₄	—	2	2	no	—
350	D₄	—	4	2	no	—
351	D₄	—	4	2	no	—
352	D₄	—	4	2	no	—
353	D₄	—	4	4	no	—
354	D₄	—	8	2	no	—
355	D₄	—	8	2	no	—
356	D₄	—	8	2	no	—
357	D₄	—	8	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	4	4	no	—
362	C₂×C₄	—	4	1	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	—	8	2	no	—
365	C₂×C₄	—	8	1	no	—
366	C₂×C₄	C₅×#121	1	1	yes	characteristic
367	C₂×C₄	C₅×#121	1	1	yes	characteristic
368	C₂×C₄	C₅×#121	1	1	yes	characteristic
369	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
370	C₂×C₄	C₅×#137	1	2	yes	—
371	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
372	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
373	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
374	C₈	—	2	4	no	—
375	C₈	—	4	2	no	—
376	C₈	—	4	2	no	—
377	C₈	—	4	2	no	—
378	C₅	#19420	1	1	yes	characteristic, direct product factor, Sylow
379	C₂²	—	2	1	no	—
380	C₂²	—	2	1	no	—
381	C₂²	—	4	2	no	—
382	C₂²	—	4	2	no	—
383	C₂²	—	4	2	no	—
384	C₂²	—	8	4	no	—
385	C₂²	—	8	2	no	—
386	C₂²	—	8	2	no	—
387	C₂²	—	8	2	no	—
388	C₂²	—	16	4	no	—
389	C₂²	C₅×#468	1	2	yes	—
390	C₂²	C₂×C₅×#121	1	1	yes	characteristic
391	C₄	—	2	1	no	—
392	C₄	—	2	1	no	—
393	C₄	—	2	1	no	—
394	C₄	—	4	2	no	—
395	C₄	—	8	1	no	—
396	C₄	—	8	1	no	—
397	C₄	C₅×#468	1	2	yes	—
398	C₄	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
399	C₄	C₂×C₅×#137	1	1	yes	characteristic
400	C₄	C₅×#576	1	2	yes	—
401	C₂	—	2	2	no	—
402	C₂	—	8	2	no	—
403	C₂	—	16	2	no	—
404	C₂	C₅×#3041	1	1	yes	characteristic
405	C₂	C₂×C₅×#468	1	1	yes	characteristic
406	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×#459	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×#3208	C₂	semidirect
2. C₅×#3077	C₂	semidirect
4. C₅×#2975	C₂	semidirect
5. C₅×#1697	C₂	semidirect
6. C₅×#1685	C₂	semidirect
7. C₅×#1571	C₂	semidirect
8. C₅×#1545	C₂	semidirect
9. C₅×#1542	C₂	semidirect
14. C₅×#492	C₂²	semidirect
15. C₅×#486	C₂²	semidirect
17. C₅×#476	C₂²	semidirect
18. C₅×#474	C₂²	semidirect
24. C₅×#436	C₂²	semidirect
33. C₅×#335	C₂²	semidirect
34. C₅×#333	C₂²	semidirect
35. C₅×#332	C₂²	semidirect
36. C₅×#331	C₂²	semidirect
37. #19420	C₅	direct (N × H)
85. #3208	C₂×C₅	semidirect
86. #3077	C₂×C₅	semidirect
88. #2975	C₂×C₅	semidirect
89. #1697	C₂×C₅	semidirect
90. #1685	C₂×C₅	semidirect
91. #1571	C₂×C₅	semidirect
92. #1545	C₂×C₅	semidirect
93. #1542	C₂×C₅	semidirect
148. #492	C₂²×C₅	semidirect
149. #486	C₂²×C₅	semidirect
151. #476	C₂²×C₅	semidirect
152. #474	C₂²×C₅	semidirect
158. #436	C₂²×C₅	semidirect
167. #335	C₂²×C₅	semidirect
168. #333	C₂²×C₅	semidirect
169. #332	C₂²×C₅	semidirect
170. #331	C₂²×C₅	semidirect
378. C₅	#19420	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×#3208	2
C₅×#3077	2
C₂×C₅×#459	2
C₅×#2975	2
C₅×#1697	2
C₅×#1685	2
C₅×#1571	2
C₅×#1545	2
C₅×#1542	2
#19420	5

Subgroups — C5×#19420 #11942140

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#19420 #11942140