Subgroups — C₅×#19428 #11942148

Order 1280.

704 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3226	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#3036	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#461	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2975	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1701	C₂	1	4	yes	maximal, complemented
6	C₅×#1693	C₂	1	4	yes	maximal, complemented
7	C₅×#1570	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1546	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	C₂²×C₅×SD₁₆	—	2	1	no	—
12	C₅×#532	C₂²	1	1	yes	characteristic
13	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
15	C₅×#500	C₂²	1	2	yes	complemented
16	C₅×#486	C₂²	1	2	yes	complemented
17	C₅×#480	—	2	2	no	—
18	C₅×#474	—	2	2	no	—
19	C₅×#463	—	2	2	no	—
20	C₅×#461	—	2	2	no	—
21	C₅×#461	C₂²	1	4	yes	—
22	C₅×#461	C₂²	1	2	yes	—
23	C₅×#459	C₂²	1	2	yes	—
24	C₅×#436	—	2	2	no	—
25	C₅×#436	C₂²	1	4	yes	—
26	C₅×#431	C₂²	1	1	yes	characteristic
27	C₅×#431	C₂²	1	1	yes	characteristic
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×#103	—	2	1	no	—
32	C₅×#407	—	2	2	no	—
33	C₅×#334	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	#19428	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	4	no	—
44	C₂×C₅×SD₁₆	—	2	2	no	—
45	C₂×C₅×SD₁₆	—	4	4	no	—
46	C₂×C₅×D₈	—	2	2	no	—
47	C₂×C₅×M₁₆	—	2	1	no	—
48	C₂×C₅×M₁₆	—	2	4	no	—
49	C₂²×C₅×C₈	—	2	1	no	—
50	C₅×C₄⋊Q₈	—	2	1	no	—
51	C₅×C₄⋊Q₈	—	2	1	no	—
52	C₅×C₄⋊Q₈	—	2	1	no	—
53	C₅×C₄⋊Q₈	C₂³	1	2	yes	—
54	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
55	C₅×#127	C₂³	1	1	yes	characteristic
56	C₅×#124	—	2	1	no	—
57	C₅×#121	—	2	1	no	—
58	C₅×#121	—	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	—	2	1	no	—
63	C₄×C₅×D₄	D₄	1	2	yes	—
64	C₄×C₅×D₄	C₂³	1	2	yes	—
65	C₂×C₅×C₄⋊C₄	—	2	1	no	—
66	C₂×C₅×C₄⋊C₄	—	2	1	no	—
67	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
68	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
69	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
70	C₅×#107	—	2	4	no	—
71	C₅×C₄⋊C₈	—	2	1	no	—
72	C₅×C₄⋊C₈	—	2	1	no	—
73	C₅×C₄⋊C₈	D₄	1	2	yes	—
74	C₅×C₄⋊C₈	C₂³	1	2	yes	—
75	C₅×C₄⋊C₈	C₂³	1	2	yes	—
76	C₅×C₄⋊C₈	C₂³	1	2	yes	—
77	C₅×#103	—	2	4	no	—
78	C₅×#103	—	2	2	no	—
79	C₅×#102	—	2	4	no	—
80	C₅×#102	—	2	2	no	—
81	C₅×C₂²⋊C₈	—	2	1	no	—
82	C₅×C₂²⋊C₈	—	2	4	no	—
83	C₅×C₂²⋊C₈	D₄	1	2	yes	—
84	C₄×C₅×C₈	—	2	1	no	—
85	C₄×C₅×C₈	C₂³	1	2	yes	—
86	#3226	C₂×C₅	1	1	yes	characteristic, complemented
87	#3036	C₂×C₅	1	1	yes	characteristic
88	C₂×#461	C₂×C₅	1	1	yes	characteristic, complemented
89	#2975	C₂×C₅	1	1	yes	characteristic, complemented
90	#1701	C₂×C₅	1	4	yes	complemented
91	#1693	C₂×C₅	1	4	yes	complemented
92	#1570	C₂×C₅	1	1	yes	characteristic, complemented
93	#1546	C₂×C₅	1	1	yes	characteristic, complemented
94	#1540	C₂×C₅	1	1	yes	characteristic, complemented
95	C₂⁴×C₅	—	2	1	no	—
96	C₅×#41	—	4	2	no	—
97	C₅×#41	—	4	2	no	—
98	C₂×C₅×Q₈	—	2	1	no	—
99	C₂×C₅×Q₈	—	2	2	no	—
100	C₂×C₅×Q₈	—	4	1	no	—
101	C₂×C₅×Q₈	—	4	2	no	—
102	C₂×C₅×Q₈	—	4	2	no	—
103	C₂×C₅×D₄	—	2	1	no	—
104	C₂×C₅×D₄	—	2	2	no	—
105	C₂×C₅×D₄	—	2	2	no	—
106	C₂×C₅×D₄	—	2	1	no	—
107	C₂×C₅×D₄	—	2	1	no	—
108	C₂×C₅×D₄	—	2	1	no	—
109	C₂×C₅×D₄	—	4	1	no	—
110	C₂×C₅×D₄	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₅	—	2	1	no	—
112	C₂²×C₄×C₅	—	2	2	no	—
113	C₂²×C₄×C₅	—	2	2	no	—
114	C₂²×C₄×C₅	—	4	1	no	—
115	C₂²×C₄×C₅	—	4	1	no	—
116	C₂²×C₄×C₅	—	8	2	no	—
117	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₅	#41	1	1	yes	characteristic
120	C₅×SD₁₆	—	4	8	no	—
121	C₅×SD₁₆	—	4	4	no	—
122	C₅×D₈	—	4	4	no	—
123	C₅×M₁₆	—	4	2	no	—
124	C₅×M₁₆	—	8	4	no	—
125	C₂×C₅×C₈	—	2	2	no	—
126	C₂×C₅×C₈	—	2	2	no	—
127	C₂×C₅×C₈	—	2	2	no	—
128	C₂×C₅×C₈	—	4	2	no	—
129	C₂×C₅×C₈	C₂×D₄	1	4	yes	—
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	—	2	2	no	—
134	C₅×C₄⋊C₄	—	2	1	no	—
135	C₅×C₄⋊C₄	—	4	1	no	—
136	C₅×C₄⋊C₄	—	4	1	no	—
137	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
138	C₅×C₂²⋊C₄	—	2	2	no	—
139	C₅×C₂²⋊C₄	—	2	2	no	—
140	C₅×C₂²⋊C₄	—	4	1	no	—
141	C₅×C₂²⋊C₄	—	4	1	no	—
142	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
143	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
144	C₄²×C₅	#41	1	1	yes	characteristic
145	C₄²×C₅	C₂⁴	1	1	yes	characteristic
146	C₂×AGL(1,ℤ/8)	—	2	1	no	—
147	C₂²×SD₁₆	—	2	1	no	—
148	#532	C₂²×C₅	1	1	yes	characteristic
149	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
150	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
151	#500	C₂²×C₅	1	2	yes	complemented
152	#486	C₂²×C₅	1	2	yes	complemented
153	#480	—	2	2	no	—
154	#474	—	2	2	no	—
155	#463	—	2	2	no	—
156	#461	—	2	2	no	—
157	#461	C₂²×C₅	1	2	yes	—
158	#461	C₂²×C₅	1	4	yes	—
159	#459	C₂²×C₅	1	2	yes	—
160	#436	—	2	2	no	—
161	#436	C₂²×C₅	1	4	yes	—
162	#431	C₂²×C₅	1	1	yes	characteristic
163	#431	C₂²×C₅	1	1	yes	characteristic
164	#423	C₂²×C₅	1	1	yes	characteristic
165	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
166	#417	—	2	1	no	—
167	C₂×#103	—	2	1	no	—
168	#407	—	2	2	no	—
169	#334	C₂²×C₅	1	4	yes	complemented
170	#332	C₂²×C₅	1	2	yes	complemented
171	#332	C₂²×C₅	1	4	yes	complemented
172	#331	C₂²×C₅	1	2	yes	complemented
173	C₂³×C₅	—	2	2	no	—
174	C₂³×C₅	—	4	2	no	—
175	C₂³×C₅	—	4	1	no	—
176	C₂³×C₅	—	8	1	no	—
177	C₂³×C₅	—	8	1	no	—
178	C₂³×C₅	#121	1	1	yes	characteristic
179	C₅×Q₈	—	4	2	no	—
180	C₅×Q₈	—	4	1	no	—
181	C₅×Q₈	—	4	2	no	—
182	C₅×Q₈	—	4	1	no	—
183	C₅×Q₈	—	8	2	no	—
184	C₅×D₄	—	2	2	no	—
185	C₅×D₄	—	2	2	no	—
186	C₅×D₄	—	4	1	no	—
187	C₅×D₄	—	4	1	no	—
188	C₅×D₄	—	4	2	no	—
189	C₅×D₄	—	4	2	no	—
190	C₅×D₄	—	8	1	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	2	no	—
198	C₂×C₄×C₅	—	8	2	no	—
199	C₂×C₄×C₅	—	8	1	no	—
200	C₂×C₄×C₅	—	8	2	no	—
201	C₂×C₄×C₅	—	8	2	no	—
202	C₂×C₄×C₅	#121	1	1	yes	characteristic
203	C₂×C₄×C₅	#121	1	1	yes	characteristic
204	C₂×C₄×C₅	#121	1	1	yes	characteristic
205	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
206	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
207	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
208	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
209	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
210	C₅×C₈	—	2	4	no	—
211	C₅×C₈	—	4	2	no	—
212	C₅×C₈	—	4	2	no	—
213	C₅×C₈	—	4	2	no	—
214	C₂×#41	—	2	1	no	—
215	C₂²×Q₈	—	2	1	no	—
216	C₂²×D₄	C₅×D₄	1	1	yes	characteristic
217	C₂³×C₄	—	2	1	no	—
218	AGL(1,ℤ/8)	—	4	4	no	—
219	C₂×SD₁₆	—	2	4	no	—
220	C₂×SD₁₆	—	2	2	no	—
221	C₂×SD₁₆	—	4	4	no	—
222	C₂×D₈	—	2	2	no	—
223	C₂×M₁₆	—	2	1	no	—
224	C₂×M₁₆	—	2	4	no	—
225	C₂²×C₈	—	2	1	no	—
226	C₄⋊Q₈	—	2	1	no	—
227	C₄⋊Q₈	—	2	1	no	—
228	C₄⋊Q₈	—	2	1	no	—
229	C₄⋊Q₈	C₂³×C₅	1	2	yes	—
230	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
231	#127	C₂³×C₅	1	1	yes	characteristic
232	#124	—	2	1	no	—
233	#121	—	2	1	no	—
234	#121	—	2	1	no	—
235	C₄×D₄	—	2	1	no	—
236	C₄×D₄	—	2	1	no	—
237	C₄×D₄	—	2	1	no	—
238	C₄×D₄	—	2	1	no	—
239	C₄×D₄	C₅×D₄	1	2	yes	—
240	C₄×D₄	C₂³×C₅	1	2	yes	—
241	C₂×C₄⋊C₄	—	2	1	no	—
242	C₂×C₄⋊C₄	—	2	1	no	—
243	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
244	C₂×C₂²⋊C₄	—	2	1	no	—
245	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
246	#107	—	2	4	no	—
247	C₄⋊C₈	—	2	1	no	—
248	C₄⋊C₈	—	2	1	no	—
249	C₄⋊C₈	C₅×D₄	1	2	yes	—
250	C₄⋊C₈	C₂³×C₅	1	2	yes	—
251	C₄⋊C₈	C₂³×C₅	1	2	yes	—
252	C₄⋊C₈	C₂³×C₅	1	2	yes	—
253	#103	—	2	4	no	—
254	#103	—	2	2	no	—
255	#102	—	2	4	no	—
256	#102	—	2	2	no	—
257	C₂²⋊C₈	—	2	1	no	—
258	C₂²⋊C₈	—	2	4	no	—
259	C₂²⋊C₈	C₅×D₄	1	2	yes	—
260	C₄×C₈	—	2	1	no	—
261	C₄×C₈	C₂³×C₅	1	2	yes	—
262	C₂²×C₅	—	2	1	no	—
263	C₂²×C₅	—	2	1	no	—
264	C₂²×C₅	—	4	2	no	—
265	C₂²×C₅	—	4	2	no	—
266	C₂²×C₅	—	4	2	no	—
267	C₂²×C₅	—	8	4	no	—
268	C₂²×C₅	—	8	1	no	—
269	C₂²×C₅	—	8	1	no	—
270	C₂²×C₅	—	8	1	no	—
271	C₂²×C₅	#469	1	2	yes	—
272	C₂²×C₅	C₂×#121	1	1	yes	characteristic
273	C₄×C₅	—	2	1	no	—
274	C₄×C₅	—	2	1	no	—
275	C₄×C₅	—	2	1	no	—
276	C₄×C₅	—	4	2	no	—
277	C₄×C₅	—	8	1	no	—
278	C₄×C₅	—	8	2	no	—
279	C₄×C₅	#469	1	2	yes	—
280	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
281	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
282	C₄×C₅	#577	1	2	yes	—
283	C₂⁴	—	2	1	no	—
284	#41	—	4	2	no	—
285	#41	—	4	2	no	—
286	C₂×Q₈	—	2	1	no	—
287	C₂×Q₈	—	2	2	no	—
288	C₂×Q₈	—	4	1	no	—
289	C₂×Q₈	—	4	2	no	—
290	C₂×Q₈	—	4	2	no	—
291	C₂×D₄	—	2	1	no	—
292	C₂×D₄	—	2	2	no	—
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	—	2	1	no	—
295	C₂×D₄	—	2	1	no	—
296	C₂×D₄	—	2	1	no	—
297	C₂×D₄	—	4	1	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	—	4	1	no	—
303	C₂²×C₄	—	4	1	no	—
304	C₂²×C₄	—	8	2	no	—
305	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
306	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
307	C₂²×C₄	C₅×#41	1	1	yes	characteristic
308	SD₁₆	—	4	8	no	—
309	SD₁₆	—	4	4	no	—
310	D₈	—	4	4	no	—
311	M₁₆	—	4	2	no	—
312	M₁₆	—	8	4	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	4	2	no	—
317	C₂×C₈	C₂×C₅×D₄	1	4	yes	—
318	C₄⋊C₄	—	2	1	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	—	2	1	no	—
321	C₄⋊C₄	—	2	2	no	—
322	C₄⋊C₄	—	2	1	no	—
323	C₄⋊C₄	—	4	1	no	—
324	C₄⋊C₄	—	4	1	no	—
325	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
326	C₂²⋊C₄	—	2	2	no	—
327	C₂²⋊C₄	—	2	2	no	—
328	C₂²⋊C₄	—	4	1	no	—
329	C₂²⋊C₄	—	4	1	no	—
330	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
331	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
332	C₄²	C₅×#41	1	1	yes	characteristic
333	C₄²	C₂⁴×C₅	1	1	yes	characteristic
334	C₂×C₅	—	2	2	no	—
335	C₂×C₅	—	8	2	no	—
336	C₂×C₅	—	16	1	no	—
337	C₂×C₅	#3042	1	1	yes	characteristic
338	C₂×C₅	C₂×#469	1	1	yes	characteristic
339	C₂×C₅	#3069	1	1	yes	characteristic
340	C₂³	—	2	2	no	—
341	C₂³	—	4	2	no	—
342	C₂³	—	4	1	no	—
343	C₂³	—	8	1	no	—
344	C₂³	—	8	1	no	—
345	C₂³	C₅×#121	1	1	yes	characteristic
346	Q₈	—	4	2	no	—
347	Q₈	—	4	1	no	—
348	Q₈	—	4	2	no	—
349	Q₈	—	4	1	no	—
350	Q₈	—	8	2	no	—
351	D₄	—	2	2	no	—
352	D₄	—	2	2	no	—
353	D₄	—	4	2	no	—
354	D₄	—	4	1	no	—
355	D₄	—	4	1	no	—
356	D₄	—	4	2	no	—
357	D₄	—	8	1	no	—
358	D₄	—	8	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	4	1	no	—
362	C₂×C₄	—	4	4	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	8	2	no	—
366	C₂×C₄	—	8	1	no	—
367	C₂×C₄	—	8	2	no	—
368	C₂×C₄	—	8	2	no	—
369	C₂×C₄	C₅×#121	1	1	yes	characteristic
370	C₂×C₄	C₅×#121	1	1	yes	characteristic
371	C₂×C₄	C₅×#121	1	1	yes	characteristic
372	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
373	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
374	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
375	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
376	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
377	C₈	—	2	4	no	—
378	C₈	—	4	2	no	—
379	C₈	—	4	2	no	—
380	C₈	—	4	2	no	—
381	C₅	#19428	1	1	yes	characteristic, direct product factor, Sylow
382	C₂²	—	2	1	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	4	2	no	—
385	C₂²	—	4	2	no	—
386	C₂²	—	4	2	no	—
387	C₂²	—	8	4	no	—
388	C₂²	—	8	1	no	—
389	C₂²	—	8	1	no	—
390	C₂²	—	8	1	no	—
391	C₂²	C₅×#469	1	2	yes	—
392	C₂²	C₂×C₅×#121	1	1	yes	characteristic
393	C₄	—	2	1	no	—
394	C₄	—	2	1	no	—
395	C₄	—	2	1	no	—
396	C₄	—	4	2	no	—
397	C₄	—	8	1	no	—
398	C₄	—	8	2	no	—
399	C₄	C₅×#469	1	2	yes	—
400	C₄	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
401	C₄	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
402	C₄	C₅×#577	1	2	yes	—
403	C₂	—	2	2	no	—
404	C₂	—	8	2	no	—
405	C₂	—	16	1	no	—
406	C₂	C₅×#3042	1	1	yes	characteristic
407	C₂	C₂×C₅×#469	1	1	yes	characteristic
408	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×#3226	C₂	semidirect
3. C₂×C₅×#461	C₂	semidirect
4. C₅×#2975	C₂	semidirect
5. C₅×#1701	C₂	semidirect
6. C₅×#1693	C₂	semidirect
7. C₅×#1570	C₂	semidirect
8. C₅×#1546	C₂	semidirect
9. C₅×#1540	C₂	semidirect
15. C₅×#500	C₂²	semidirect
16. C₅×#486	C₂²	semidirect
33. C₅×#334	C₂²	semidirect
34. C₅×#332	C₂²	semidirect
35. C₅×#332	C₂²	semidirect
36. C₅×#331	C₂²	semidirect
37. #19428	C₅	direct (N × H)
86. #3226	C₂×C₅	semidirect
88. C₂×#461	C₂×C₅	semidirect
89. #2975	C₂×C₅	semidirect
90. #1701	C₂×C₅	semidirect
91. #1693	C₂×C₅	semidirect
92. #1570	C₂×C₅	semidirect
93. #1546	C₂×C₅	semidirect
94. #1540	C₂×C₅	semidirect
151. #500	C₂²×C₅	semidirect
152. #486	C₂²×C₅	semidirect
169. #334	C₂²×C₅	semidirect
170. #332	C₂²×C₅	semidirect
171. #332	C₂²×C₅	semidirect
172. #331	C₂²×C₅	semidirect
381. C₅	#19428	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×#3226	2
C₅×#3036	2
C₂×C₅×#461	2
C₅×#2975	2
C₅×#1701	2
C₅×#1693	2
C₅×#1570	2
C₅×#1546	2
C₅×#1540	2
#19428	5

Subgroups — C5×#19428 #11942148

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#19428 #11942148