Subgroups — C₅×#19421 #11942141

Order 1280.

684 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3206	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#474	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#3036	C₂	1	1	yes	maximal, characteristic
4	C₅×#2975	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1699	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×#1549	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1540	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₅×AGL(1,ℤ/8)	—	2	1	no	—
11	C₅×#532	C₂²	1	1	yes	characteristic
12	C₂×C₅×C₄⋊Q₈	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×#487	C₂²	1	2	yes	complemented
16	C₅×#474	—	2	2	no	—
17	C₅×#474	C₂²	1	4	yes	—
18	C₅×#463	—	2	2	no	—
19	C₅×#461	—	2	2	no	—
20	C₅×#461	C₂²	1	2	yes	—
21	C₅×#459	C₂²	1	2	yes	—
22	C₅×#448	—	2	2	no	—
23	C₅×#436	—	2	2	no	—
24	C₅×#436	C₂²	1	4	yes	—
25	C₅×#431	C₂²	1	1	yes	characteristic
26	C₅×#431	C₂²	1	1	yes	characteristic
27	C₂×C₅×#107	—	2	1	no	—
28	C₅×#423	C₂²	1	1	yes	characteristic
29	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
30	C₅×#417	—	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×#332	C₂²	1	2	yes	complemented
35	C₅×#332	C₂²	1	4	yes	complemented
36	C₅×#331	C₂²	1	2	yes	complemented
37	#19421	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
38	C₂×C₅×#41	—	2	1	no	—
39	C₂²×C₅×Q₈	—	2	1	no	—
40	C₂²×C₅×D₄	D₄	1	1	yes	characteristic
41	C₂³×C₄×C₅	—	2	1	no	—
42	C₅×AGL(1,ℤ/8)	—	4	4	no	—
43	C₂×C₅×SD₁₆	—	2	2	no	—
44	C₂×C₅×SD₁₆	—	2	4	no	—
45	C₂×C₅×D₈	—	2	2	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	—	2	1	no	—
50	C₅×C₄⋊Q₈	—	2	1	no	—
51	C₅×C₄⋊Q₈	—	2	1	no	—
52	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
53	C₅×C₄⋊Q₈	C₂³	1	2	yes	—
54	C₅×#127	C₂³	1	1	yes	characteristic
55	C₅×#124	—	2	1	no	—
56	C₅×#121	—	2	1	no	—
57	C₅×#121	—	2	1	no	—
58	C₄×C₅×D₄	—	2	1	no	—
59	C₄×C₅×D₄	—	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	C₂×C₅×C₄⋊C₄	—	2	1	no	—
65	C₂×C₅×C₄⋊C₄	—	2	1	no	—
66	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
67	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
68	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
69	C₅×#107	—	2	4	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×#103	—	2	4	no	—
77	C₅×#103	—	2	2	no	—
78	C₅×#102	—	2	4	no	—
79	C₅×#102	—	2	2	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	#3206	C₂×C₅	1	1	yes	characteristic, complemented
86	C₂×#474	C₂×C₅	1	1	yes	characteristic, complemented
87	#3036	C₂×C₅	1	1	yes	characteristic
88	#2975	C₂×C₅	1	1	yes	characteristic, complemented
89	#1699	C₂×C₅	1	4	yes	complemented
90	#1685	C₂×C₅	1	4	yes	complemented
91	#1571	C₂×C₅	1	1	yes	characteristic, complemented
92	#1549	C₂×C₅	1	1	yes	characteristic, complemented
93	#1540	C₂×C₅	1	1	yes	characteristic, complemented
94	C₂⁴×C₅	—	2	1	no	—
95	C₅×#41	—	4	2	no	—
96	C₅×#41	—	4	2	no	—
97	C₂×C₅×Q₈	—	2	1	no	—
98	C₂×C₅×Q₈	—	2	2	no	—
99	C₂×C₅×Q₈	—	4	1	no	—
100	C₂×C₅×Q₈	—	8	2	no	—
101	C₂×C₅×D₄	—	2	1	no	—
102	C₂×C₅×D₄	—	2	2	no	—
103	C₂×C₅×D₄	—	2	2	no	—
104	C₂×C₅×D₄	—	2	1	no	—
105	C₂×C₅×D₄	—	2	1	no	—
106	C₂×C₅×D₄	—	2	1	no	—
107	C₂×C₅×D₄	—	4	1	no	—
108	C₂×C₅×D₄	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₅	—	2	1	no	—
110	C₂²×C₄×C₅	—	2	2	no	—
111	C₂²×C₄×C₅	—	2	2	no	—
112	C₂²×C₄×C₅	—	4	1	no	—
113	C₂²×C₄×C₅	—	4	1	no	—
114	C₂²×C₄×C₅	—	8	2	no	—
115	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₅	#41	1	1	yes	characteristic
118	C₅×SD₁₆	—	4	4	no	—
119	C₅×SD₁₆	—	8	4	no	—
120	C₅×D₈	—	4	4	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	2	no	—
130	C₅×C₄⋊C₄	—	2	1	no	—
131	C₅×C₄⋊C₄	—	2	2	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	C₅×C₂²⋊C₄	—	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	C₂×AGL(1,ℤ/8)	—	2	1	no	—
145	#532	C₂²×C₅	1	1	yes	characteristic
146	C₂×C₄⋊Q₈	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	#487	C₂²×C₅	1	2	yes	complemented
150	#474	—	2	2	no	—
151	#474	C₂²×C₅	1	4	yes	—
152	#463	—	2	2	no	—
153	#461	—	2	2	no	—
154	#461	C₂²×C₅	1	2	yes	—
155	#459	C₂²×C₅	1	2	yes	—
156	#448	—	2	2	no	—
157	#436	—	2	2	no	—
158	#436	C₂²×C₅	1	4	yes	—
159	#431	C₂²×C₅	1	1	yes	characteristic
160	#431	C₂²×C₅	1	1	yes	characteristic
161	C₂×#107	—	2	1	no	—
162	#423	C₂²×C₅	1	1	yes	characteristic
163	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
164	#417	—	2	1	no	—
165	C₂×#102	—	2	1	no	—
166	#407	—	2	2	no	—
167	#335	C₂²×C₅	1	4	yes	complemented
168	#332	C₂²×C₅	1	2	yes	complemented
169	#332	C₂²×C₅	1	4	yes	complemented
170	#331	C₂²×C₅	1	2	yes	complemented
171	C₂³×C₅	—	2	2	no	—
172	C₂³×C₅	—	4	2	no	—
173	C₂³×C₅	—	4	1	no	—
174	C₂³×C₅	—	8	1	no	—
175	C₂³×C₅	—	8	1	no	—
176	C₂³×C₅	#121	1	1	yes	characteristic
177	C₅×Q₈	—	4	1	no	—
178	C₅×Q₈	—	4	1	no	—
179	C₅×Q₈	—	4	4	no	—
180	C₅×Q₈	—	8	2	no	—
181	C₅×D₄	—	2	2	no	—
182	C₅×D₄	—	2	2	no	—
183	C₅×D₄	—	4	1	no	—
184	C₅×D₄	—	4	1	no	—
185	C₅×D₄	—	4	2	no	—
186	C₅×D₄	—	4	2	no	—
187	C₅×D₄	—	8	1	no	—
188	C₅×D₄	—	8	2	no	—
189	C₂×C₄×C₅	—	2	2	no	—
190	C₂×C₄×C₅	—	2	2	no	—
191	C₂×C₄×C₅	—	4	1	no	—
192	C₂×C₄×C₅	—	4	4	no	—
193	C₂×C₄×C₅	—	4	1	no	—
194	C₂×C₄×C₅	—	4	2	no	—
195	C₂×C₄×C₅	—	8	2	no	—
196	C₂×C₄×C₅	—	8	1	no	—
197	C₂×C₄×C₅	—	8	2	no	—
198	C₂×C₄×C₅	—	8	2	no	—
199	C₂×C₄×C₅	#121	1	1	yes	characteristic
200	C₂×C₄×C₅	#121	1	1	yes	characteristic
201	C₂×C₄×C₅	#121	1	1	yes	characteristic
202	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
203	C₂×C₄×C₅	#137	1	2	yes	—
204	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
205	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
206	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
207	C₅×C₈	—	2	4	no	—
208	C₅×C₈	—	4	2	no	—
209	C₅×C₈	—	4	2	no	—
210	C₅×C₈	—	4	2	no	—
211	C₂×#41	—	2	1	no	—
212	C₂²×Q₈	—	2	1	no	—
213	C₂²×D₄	C₅×D₄	1	1	yes	characteristic
214	C₂³×C₄	—	2	1	no	—
215	AGL(1,ℤ/8)	—	4	4	no	—
216	C₂×SD₁₆	—	2	2	no	—
217	C₂×SD₁₆	—	2	4	no	—
218	C₂×D₈	—	2	2	no	—
219	C₂×M₁₆	—	2	1	no	—
220	C₂×M₁₆	—	2	4	no	—
221	C₂²×C₈	—	2	1	no	—
222	C₄⋊Q₈	—	2	1	no	—
223	C₄⋊Q₈	—	2	1	no	—
224	C₄⋊Q₈	—	2	1	no	—
225	C₄⋊Q₈	C₂³×C₅	1	2	yes	—
226	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
227	#127	C₂³×C₅	1	1	yes	characteristic
228	#124	—	2	1	no	—
229	#121	—	2	1	no	—
230	#121	—	2	1	no	—
231	C₄×D₄	—	2	1	no	—
232	C₄×D₄	—	2	1	no	—
233	C₄×D₄	—	2	1	no	—
234	C₄×D₄	—	2	1	no	—
235	C₄×D₄	C₅×D₄	1	2	yes	—
236	C₄×D₄	C₂³×C₅	1	2	yes	—
237	C₂×C₄⋊C₄	—	2	1	no	—
238	C₂×C₄⋊C₄	—	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	4	no	—
243	C₄⋊C₈	—	2	1	no	—
244	C₄⋊C₈	—	2	1	no	—
245	C₄⋊C₈	C₅×D₄	1	2	yes	—
246	C₄⋊C₈	C₂³×C₅	1	2	yes	—
247	C₄⋊C₈	C₂³×C₅	1	2	yes	—
248	C₄⋊C₈	C₂³×C₅	1	2	yes	—
249	#103	—	2	4	no	—
250	#103	—	2	2	no	—
251	#102	—	2	4	no	—
252	#102	—	2	2	no	—
253	C₂²⋊C₈	—	2	1	no	—
254	C₂²⋊C₈	—	2	4	no	—
255	C₂²⋊C₈	C₅×D₄	1	2	yes	—
256	C₄×C₈	—	2	1	no	—
257	C₄×C₈	C₂³×C₅	1	2	yes	—
258	C₂²×C₅	—	2	1	no	—
259	C₂²×C₅	—	2	1	no	—
260	C₂²×C₅	—	4	2	no	—
261	C₂²×C₅	—	4	2	no	—
262	C₂²×C₅	—	4	2	no	—
263	C₂²×C₅	—	8	4	no	—
264	C₂²×C₅	—	8	1	no	—
265	C₂²×C₅	—	8	1	no	—
266	C₂²×C₅	—	8	1	no	—
267	C₂²×C₅	#468	1	2	yes	—
268	C₂²×C₅	C₂×#121	1	1	yes	characteristic
269	C₄×C₅	—	2	1	no	—
270	C₄×C₅	—	2	1	no	—
271	C₄×C₅	—	2	1	no	—
272	C₄×C₅	—	4	2	no	—
273	C₄×C₅	—	8	2	no	—
274	C₄×C₅	—	8	1	no	—
275	C₄×C₅	#468	1	2	yes	—
276	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
277	C₄×C₅	C₂×#137	1	1	yes	characteristic
278	C₄×C₅	#576	1	2	yes	—
279	C₂⁴	—	2	1	no	—
280	#41	—	4	2	no	—
281	#41	—	4	2	no	—
282	C₂×Q₈	—	2	1	no	—
283	C₂×Q₈	—	2	2	no	—
284	C₂×Q₈	—	4	1	no	—
285	C₂×Q₈	—	8	2	no	—
286	C₂×D₄	—	2	1	no	—
287	C₂×D₄	—	2	2	no	—
288	C₂×D₄	—	2	2	no	—
289	C₂×D₄	—	2	1	no	—
290	C₂×D₄	—	2	1	no	—
291	C₂×D₄	—	2	1	no	—
292	C₂×D₄	—	4	1	no	—
293	C₂×D₄	C₂×C₅×D₄	1	2	yes	—
294	C₂²×C₄	—	2	1	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	4	1	no	—
298	C₂²×C₄	—	4	1	no	—
299	C₂²×C₄	—	8	2	no	—
300	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
301	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
302	C₂²×C₄	C₅×#41	1	1	yes	characteristic
303	SD₁₆	—	4	4	no	—
304	SD₁₆	—	8	4	no	—
305	D₈	—	4	4	no	—
306	M₁₆	—	4	2	no	—
307	M₁₆	—	8	4	no	—
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	4	2	no	—
312	C₂×C₈	C₂×C₅×D₄	1	4	yes	—
313	C₄⋊C₄	—	2	1	no	—
314	C₄⋊C₄	—	2	2	no	—
315	C₄⋊C₄	—	2	1	no	—
316	C₄⋊C₄	—	2	2	no	—
317	C₄⋊C₄	—	2	1	no	—
318	C₄⋊C₄	—	4	1	no	—
319	C₄⋊C₄	—	4	1	no	—
320	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
321	C₂²⋊C₄	—	2	2	no	—
322	C₂²⋊C₄	—	2	2	no	—
323	C₂²⋊C₄	—	4	1	no	—
324	C₂²⋊C₄	—	4	1	no	—
325	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
326	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
327	C₄²	C₅×#41	1	1	yes	characteristic
328	C₄²	C₂⁴×C₅	1	1	yes	characteristic
329	C₂×C₅	—	2	2	no	—
330	C₂×C₅	—	8	2	no	—
331	C₂×C₅	—	16	1	no	—
332	C₂×C₅	#3041	1	1	yes	characteristic
333	C₂×C₅	C₂×#468	1	1	yes	characteristic
334	C₂×C₅	#3069	1	1	yes	characteristic
335	C₂³	—	2	2	no	—
336	C₂³	—	4	2	no	—
337	C₂³	—	4	1	no	—
338	C₂³	—	8	1	no	—
339	C₂³	—	8	1	no	—
340	C₂³	C₅×#121	1	1	yes	characteristic
341	Q₈	—	4	1	no	—
342	Q₈	—	4	1	no	—
343	Q₈	—	4	4	no	—
344	Q₈	—	8	2	no	—
345	D₄	—	2	2	no	—
346	D₄	—	2	2	no	—
347	D₄	—	4	2	no	—
348	D₄	—	4	1	no	—
349	D₄	—	4	1	no	—
350	D₄	—	4	2	no	—
351	D₄	—	8	1	no	—
352	D₄	—	8	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	4	1	no	—
356	C₂×C₄	—	4	4	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	8	2	no	—
360	C₂×C₄	—	8	1	no	—
361	C₂×C₄	—	8	2	no	—
362	C₂×C₄	—	8	2	no	—
363	C₂×C₄	C₅×#121	1	1	yes	characteristic
364	C₂×C₄	C₅×#121	1	1	yes	characteristic
365	C₂×C₄	C₅×#121	1	1	yes	characteristic
366	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
367	C₂×C₄	C₅×#137	1	2	yes	—
368	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
369	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
370	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
371	C₈	—	2	4	no	—
372	C₈	—	4	2	no	—
373	C₈	—	4	2	no	—
374	C₈	—	4	2	no	—
375	C₅	#19421	1	1	yes	characteristic, direct product factor, Sylow
376	C₂²	—	2	1	no	—
377	C₂²	—	2	1	no	—
378	C₂²	—	4	2	no	—
379	C₂²	—	4	2	no	—
380	C₂²	—	4	2	no	—
381	C₂²	—	8	4	no	—
382	C₂²	—	8	1	no	—
383	C₂²	—	8	1	no	—
384	C₂²	—	8	1	no	—
385	C₂²	C₅×#468	1	2	yes	—
386	C₂²	C₂×C₅×#121	1	1	yes	characteristic
387	C₄	—	2	1	no	—
388	C₄	—	2	1	no	—
389	C₄	—	2	1	no	—
390	C₄	—	4	2	no	—
391	C₄	—	8	2	no	—
392	C₄	—	8	1	no	—
393	C₄	C₅×#468	1	2	yes	—
394	C₄	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
395	C₄	C₂×C₅×#137	1	1	yes	characteristic
396	C₄	C₅×#576	1	2	yes	—
397	C₂	—	2	2	no	—
398	C₂	—	8	2	no	—
399	C₂	—	16	1	no	—
400	C₂	C₅×#3041	1	1	yes	characteristic
401	C₂	C₂×C₅×#468	1	1	yes	characteristic
402	C₂	C₅×#3069	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₅
prime radical	C₅×#3036	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×#3206	C₂	semidirect
2. C₂×C₅×#474	C₂	semidirect
4. C₅×#2975	C₂	semidirect
5. C₅×#1699	C₂	semidirect
6. C₅×#1685	C₂	semidirect
7. C₅×#1571	C₂	semidirect
8. C₅×#1549	C₂	semidirect
9. C₅×#1540	C₂	semidirect
14. C₅×#492	C₂²	semidirect
15. C₅×#487	C₂²	semidirect
33. C₅×#335	C₂²	semidirect
34. C₅×#332	C₂²	semidirect
35. C₅×#332	C₂²	semidirect
36. C₅×#331	C₂²	semidirect
37. #19421	C₅	direct (N × H)
85. #3206	C₂×C₅	semidirect
86. C₂×#474	C₂×C₅	semidirect
88. #2975	C₂×C₅	semidirect
89. #1699	C₂×C₅	semidirect
90. #1685	C₂×C₅	semidirect
91. #1571	C₂×C₅	semidirect
92. #1549	C₂×C₅	semidirect
93. #1540	C₂×C₅	semidirect
148. #492	C₂²×C₅	semidirect
149. #487	C₂²×C₅	semidirect
167. #335	C₂²×C₅	semidirect
168. #332	C₂²×C₅	semidirect
169. #332	C₂²×C₅	semidirect
170. #331	C₂²×C₅	semidirect
375. C₅	#19421	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×#3206	2
C₂×C₅×#474	2
C₅×#3036	2
C₅×#2975	2
C₅×#1699	2
C₅×#1685	2
C₅×#1571	2
C₅×#1549	2
C₅×#1540	2
#19421	5

Subgroups — C5×#19421 #11942141

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#19421 #11942141