Subgroups — C₅×#19353 #11942073

Order 1280.

776 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3217	C₂	1	2	yes	maximal, complemented
2	C₂×C₅×#493	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2966	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1688	C₂	1	2	yes	maximal, complemented
5	C₅×#1687	C₂	1	2	yes	maximal, complemented
6	C₅×#1668	C₂	1	2	yes	maximal, complemented
7	C₅×#1667	C₂	1	2	yes	maximal, complemented
8	C₅×#1568	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1555	C₂	1	2	yes	maximal, complemented
10	C₂²×C₅×D₈	—	2	1	no	—
11	C₂²×C₅×D₈	—	2	1	no	—
12	C₂×C₅×#127	C₂²	1	2	yes	—
13	C₅×#529	C₂²	1	1	yes	characteristic
14	C₅×#496	—	2	2	no	—
15	C₅×#493	—	2	1	no	—
16	C₅×#493	—	2	1	no	—
17	C₅×#493	C₂²	1	2	yes	—
18	C₅×#493	C₂²	1	2	yes	—
19	C₅×#490	—	2	2	no	—
20	C₅×#460	C₂²	1	4	yes	complemented
21	C₅×#459	C₂²	1	4	yes	complemented
22	C₅×#450	—	2	2	no	—
23	C₅×#447	—	2	2	no	—
24	C₅×#446	C₂²	1	1	yes	characteristic, complemented
25	C₅×C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
26	C₅×#436	C₂²	1	1	yes	characteristic, complemented
27	C₅×#435	—	2	1	no	—
28	C₅×C₈×D₄	—	2	1	no	—
29	C₅×C₈×D₄	C₂²	1	1	yes	characteristic, complemented
30	C₅×#433	—	2	1	no	—
31	C₅×#432	C₂²	1	1	yes	characteristic
32	C₅×#432	C₂²	1	2	yes	—
33	C₅×#405	—	2	1	no	—
34	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
35	C₅×#335	C₂²	1	2	yes	complemented
36	C₅×#334	C₂²	1	2	yes	complemented
37	C₅×#331	C₂²	1	4	yes	complemented
38	C₅×#331	C₂²	1	4	yes	complemented
39	#19353	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
40	C₂²×C₅×D₄	—	2	2	no	—
41	C₂²×C₅×D₄	—	2	2	no	—
42	C₂²×C₅×D₄	—	2	2	no	—
43	C₂×C₅×SD₁₆	—	2	4	no	—
44	C₂×C₅×D₈	—	2	4	no	—
45	C₂×C₅×D₈	—	2	2	no	—
46	C₂×C₅×D₈	—	2	2	no	—
47	C₂×C₅×D₈	—	2	2	no	—
48	C₂×C₅×D₈	—	2	2	no	—
49	C₂×C₅×D₈	—	4	4	no	—
50	C₂×C₅×D₈	—	4	4	no	—
51	C₂×C₅×M₁₆	—	2	1	no	—
52	C₂²×C₅×C₈	—	2	1	no	—
53	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
54	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
55	C₅×#127	—	2	2	no	—
56	C₅×#127	—	2	2	no	—
57	C₅×#127	—	2	2	no	—
58	C₅×#127	C₂³	1	4	yes	—
59	C₅×#126	—	2	1	no	—
60	C₅×#125	D₄	1	1	yes	characteristic
61	C₅×#124	D₄	1	1	yes	characteristic
62	C₅×#123	—	2	1	no	—
63	C₅×C₂²⋊Q₈	D₄	1	1	yes	characteristic
64	C₅×#121	D₄	1	1	yes	characteristic
65	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
66	C₄×C₅×D₄	—	2	1	no	—
67	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
68	C₅×#117	—	2	1	no	—
69	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
70	C₅×C₄⋊C₈	—	2	1	no	—
71	C₅×C₄⋊C₈	—	2	1	no	—
72	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
73	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
74	C₅×C₄⋊C₈	C₂³	1	4	yes	—
75	C₅×#102	—	2	4	no	—
76	C₅×#102	—	2	4	no	—
77	C₅×C₂²⋊C₈	—	2	1	no	—
78	C₅×C₂²⋊C₈	—	2	2	no	—
79	C₅×C₂²⋊C₈	—	2	1	no	—
80	C₅×C₂²⋊C₈	—	2	1	no	—
81	C₅×#97	—	2	1	no	—
82	C₅×#97	—	2	1	no	—
83	C₅×#97	—	2	2	no	—
84	C₄×C₅×C₈	—	2	1	no	—
85	C₄×C₅×C₈	D₄	1	1	yes	characteristic
86	C₄×C₅×C₈	D₄	1	1	yes	characteristic
87	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
88	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
89	#3217	C₂×C₅	1	2	yes	complemented
90	C₂×#493	C₂×C₅	1	1	yes	characteristic, complemented
91	#2966	C₂×C₅	1	1	yes	characteristic, complemented
92	#1688	C₂×C₅	1	2	yes	complemented
93	#1687	C₂×C₅	1	2	yes	complemented
94	#1668	C₂×C₅	1	2	yes	complemented
95	#1667	C₂×C₅	1	2	yes	complemented
96	#1568	C₂×C₅	1	1	yes	characteristic, complemented
97	#1555	C₂×C₅	1	2	yes	complemented
98	C₂⁴×C₅	—	4	2	no	—
99	C₂×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
100	C₂×C₅×D₄	—	2	1	no	—
101	C₂×C₅×D₄	—	2	4	no	—
102	C₂×C₅×D₄	—	2	4	no	—
103	C₂×C₅×D₄	—	2	4	no	—
104	C₂×C₅×D₄	—	4	4	no	—
105	C₂×C₅×D₄	—	4	4	no	—
106	C₂×C₅×D₄	—	4	2	no	—
107	C₂×C₅×D₄	—	4	2	no	—
108	C₂×C₅×D₄	—	4	2	no	—
109	C₂×C₅×D₄	—	8	4	no	—
110	C₂×C₅×D₄	—	8	4	no	—
111	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₅	—	2	1	no	—
113	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₅	#41	1	1	yes	characteristic
116	C₅×SD₁₆	—	8	4	no	—
117	C₅×D₈	—	4	4	no	—
118	C₅×D₈	—	4	4	no	—
119	C₅×D₈	—	4	4	no	—
120	C₅×D₈	—	4	4	no	—
121	C₅×D₈	—	8	4	no	—
122	C₅×M₁₆	—	4	2	no	—
123	C₂×C₅×C₈	—	2	2	no	—
124	C₂×C₅×C₈	—	2	2	no	—
125	C₂×C₅×C₈	—	2	1	no	—
126	C₂×C₅×C₈	—	2	1	no	—
127	C₂×C₅×C₈	—	2	4	no	—
128	C₂×C₅×C₈	—	4	2	no	—
129	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
130	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
131	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
132	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
133	C₅×C₄⋊C₄	—	2	1	no	—
134	C₅×C₄⋊C₄	—	2	1	no	—
135	C₅×C₄⋊C₄	—	2	1	no	—
136	C₅×C₄⋊C₄	—	2	1	no	—
137	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
138	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
139	C₅×C₂²⋊C₄	—	2	1	no	—
140	C₅×C₂²⋊C₄	—	2	1	no	—
141	C₅×C₂²⋊C₄	—	2	1	no	—
142	C₅×C₂²⋊C₄	—	2	1	no	—
143	C₅×C₂²⋊C₄	—	2	1	no	—
144	C₄²×C₅	—	2	1	no	—
145	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
146	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
147	C₄²×C₅	#41	1	1	yes	characteristic
148	C₄²×C₅	C₂⁴	1	1	yes	characteristic
149	C₂²×D₈	—	2	1	no	—
150	C₂²×D₈	—	2	1	no	—
151	C₂×#127	C₂²×C₅	1	2	yes	—
152	#529	C₂²×C₅	1	1	yes	characteristic
153	#496	—	2	2	no	—
154	#493	—	2	1	no	—
155	#493	—	2	1	no	—
156	#493	C₂²×C₅	1	2	yes	—
157	#493	C₂²×C₅	1	2	yes	—
158	#490	—	2	2	no	—
159	#460	C₂²×C₅	1	4	yes	complemented
160	#459	C₂²×C₅	1	4	yes	complemented
161	#450	—	2	2	no	—
162	#447	—	2	2	no	—
163	#446	C₂²×C₅	1	1	yes	characteristic, complemented
164	C₈×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
165	#436	C₂²×C₅	1	1	yes	characteristic, complemented
166	#435	—	2	1	no	—
167	C₈×D₄	—	2	1	no	—
168	C₈×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
169	#433	—	2	1	no	—
170	#432	C₂²×C₅	1	1	yes	characteristic
171	#432	C₂²×C₅	1	2	yes	—
172	#405	—	2	1	no	—
173	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
174	#335	C₂²×C₅	1	2	yes	complemented
175	#334	C₂²×C₅	1	2	yes	complemented
176	#331	C₂²×C₅	1	4	yes	complemented
177	#331	C₂²×C₅	1	4	yes	complemented
178	C₂³×C₅	—	2	1	no	—
179	C₂³×C₅	—	4	4	no	—
180	C₂³×C₅	—	8	4	no	—
181	C₂³×C₅	—	8	4	no	—
182	C₂³×C₅	—	8	4	no	—
183	C₂³×C₅	#121	1	1	yes	characteristic
184	C₅×Q₈	—	2	2	no	—
185	C₅×D₄	—	2	2	no	—
186	C₅×D₄	—	4	2	no	—
187	C₅×D₄	—	4	4	no	—
188	C₅×D₄	—	4	4	no	—
189	C₅×D₄	—	4	4	no	—
190	C₅×D₄	—	4	4	no	—
191	C₅×D₄	—	8	4	no	—
192	C₅×D₄	—	8	4	no	—
193	C₅×D₄	—	8	4	no	—
194	C₅×D₄	—	8	4	no	—
195	C₂×C₄×C₅	—	2	2	no	—
196	C₂×C₄×C₅	—	2	1	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	1	no	—
201	C₂×C₄×C₅	—	2	1	no	—
202	C₂×C₄×C₅	—	4	1	no	—
203	C₂×C₄×C₅	—	4	1	no	—
204	C₂×C₄×C₅	#121	1	1	yes	characteristic
205	C₂×C₄×C₅	#121	1	1	yes	characteristic
206	C₂×C₄×C₅	#121	1	1	yes	characteristic
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	1	no	—
211	C₅×C₈	—	2	1	no	—
212	C₅×C₈	—	4	1	no	—
213	C₅×C₈	—	4	1	no	—
214	C₅×C₈	—	4	4	no	—
215	C₅×C₈	AGL(1,ℤ/8)	1	2	yes	—
216	C₅×C₈	AGL(1,ℤ/8)	1	2	yes	—
217	C₂²×D₄	—	2	2	no	—
218	C₂²×D₄	—	2	2	no	—
219	C₂²×D₄	—	2	2	no	—
220	C₂×SD₁₆	—	2	4	no	—
221	C₂×D₈	—	2	4	no	—
222	C₂×D₈	—	2	2	no	—
223	C₂×D₈	—	2	2	no	—
224	C₂×D₈	—	2	2	no	—
225	C₂×D₈	—	2	2	no	—
226	C₂×D₈	—	4	4	no	—
227	C₂×D₈	—	4	4	no	—
228	C₂×M₁₆	—	2	1	no	—
229	C₂²×C₈	—	2	1	no	—
230	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
231	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
232	#127	—	2	2	no	—
233	#127	—	2	2	no	—
234	#127	—	2	2	no	—
235	#127	C₂³×C₅	1	4	yes	—
236	#126	—	2	1	no	—
237	#125	C₅×D₄	1	1	yes	characteristic
238	#124	C₅×D₄	1	1	yes	characteristic
239	#123	—	2	1	no	—
240	C₂²⋊Q₈	C₅×D₄	1	1	yes	characteristic
241	#121	C₅×D₄	1	1	yes	characteristic
242	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
243	C₄×D₄	—	2	1	no	—
244	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
245	#117	—	2	1	no	—
246	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
247	C₄⋊C₈	—	2	1	no	—
248	C₄⋊C₈	—	2	1	no	—
249	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
250	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
251	C₄⋊C₈	C₂³×C₅	1	4	yes	—
252	#102	—	2	4	no	—
253	#102	—	2	4	no	—
254	C₂²⋊C₈	—	2	1	no	—
255	C₂²⋊C₈	—	2	2	no	—
256	C₂²⋊C₈	—	2	1	no	—
257	C₂²⋊C₈	—	2	1	no	—
258	#97	—	2	1	no	—
259	#97	—	2	1	no	—
260	#97	—	2	2	no	—
261	C₄×C₈	—	2	1	no	—
262	C₄×C₈	C₅×D₄	1	1	yes	characteristic
263	C₄×C₈	C₅×D₄	1	1	yes	characteristic
264	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
265	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
266	C₂²×C₅	—	2	1	no	—
267	C₂²×C₅	—	2	1	no	—
268	C₂²×C₅	—	4	1	no	—
269	C₂²×C₅	—	4	1	no	—
270	C₂²×C₅	—	4	1	no	—
271	C₂²×C₅	—	8	4	no	—
272	C₂²×C₅	—	8	4	no	—
273	C₂²×C₅	—	8	4	no	—
274	C₂²×C₅	—	16	8	no	—
275	C₂²×C₅	#472	1	2	yes	—
276	C₂²×C₅	C₂×#121	1	1	yes	characteristic
277	C₄×C₅	—	2	1	no	—
278	C₄×C₅	—	2	1	no	—
279	C₄×C₅	—	2	1	no	—
280	C₄×C₅	—	2	1	no	—
281	C₄×C₅	—	4	1	no	—
282	C₄×C₅	—	4	1	no	—
283	C₄×C₅	—	4	1	no	—
284	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
285	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
286	C₄×C₅	#576	1	2	yes	—
287	C₂⁴	—	4	2	no	—
288	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
289	C₂×D₄	—	2	1	no	—
290	C₂×D₄	—	2	4	no	—
291	C₂×D₄	—	2	4	no	—
292	C₂×D₄	—	2	4	no	—
293	C₂×D₄	—	4	4	no	—
294	C₂×D₄	—	4	4	no	—
295	C₂×D₄	—	4	2	no	—
296	C₂×D₄	—	4	2	no	—
297	C₂×D₄	—	4	2	no	—
298	C₂×D₄	—	8	4	no	—
299	C₂×D₄	—	8	4	no	—
300	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
301	C₂²×C₄	—	2	1	no	—
302	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
303	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
304	C₂²×C₄	C₅×#41	1	1	yes	characteristic
305	SD₁₆	—	8	4	no	—
306	D₈	—	4	4	no	—
307	D₈	—	4	4	no	—
308	D₈	—	4	4	no	—
309	D₈	—	4	4	no	—
310	D₈	—	8	4	no	—
311	M₁₆	—	4	2	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	2	1	no	—
315	C₂×C₈	—	2	1	no	—
316	C₂×C₈	—	2	4	no	—
317	C₂×C₈	—	4	2	no	—
318	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
319	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
320	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
321	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
322	C₄⋊C₄	—	2	1	no	—
323	C₄⋊C₄	—	2	1	no	—
324	C₄⋊C₄	—	2	1	no	—
325	C₄⋊C₄	—	2	1	no	—
326	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
327	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
328	C₂²⋊C₄	—	2	1	no	—
329	C₂²⋊C₄	—	2	1	no	—
330	C₂²⋊C₄	—	2	1	no	—
331	C₂²⋊C₄	—	2	1	no	—
332	C₂²⋊C₄	—	2	1	no	—
333	C₄²	—	2	1	no	—
334	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
335	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
336	C₄²	C₅×#41	1	1	yes	characteristic
337	C₄²	C₂⁴×C₅	1	1	yes	characteristic
338	C₂×C₅	—	2	2	no	—
339	C₂×C₅	—	8	1	no	—
340	C₂×C₅	—	16	4	no	—
341	C₂×C₅	#3038	1	1	yes	characteristic
342	C₂×C₅	#3058	1	1	yes	characteristic
343	C₂×C₅	C₂×#472	1	1	yes	characteristic
344	C₂³	—	2	1	no	—
345	C₂³	—	4	4	no	—
346	C₂³	—	8	4	no	—
347	C₂³	—	8	4	no	—
348	C₂³	—	8	4	no	—
349	C₂³	C₅×#121	1	1	yes	characteristic
350	Q₈	—	2	2	no	—
351	D₄	—	2	2	no	—
352	D₄	—	4	2	no	—
353	D₄	—	4	4	no	—
354	D₄	—	4	4	no	—
355	D₄	—	4	4	no	—
356	D₄	—	4	4	no	—
357	D₄	—	8	4	no	—
358	D₄	—	8	4	no	—
359	D₄	—	8	4	no	—
360	D₄	—	8	4	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	4	1	no	—
369	C₂×C₄	—	4	1	no	—
370	C₂×C₄	C₅×#121	1	1	yes	characteristic
371	C₂×C₄	C₅×#121	1	1	yes	characteristic
372	C₂×C₄	C₅×#121	1	1	yes	characteristic
373	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
374	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
375	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
376	C₈	—	2	1	no	—
377	C₈	—	2	1	no	—
378	C₈	—	4	1	no	—
379	C₈	—	4	1	no	—
380	C₈	—	4	4	no	—
381	C₈	C₅×AGL(1,ℤ/8)	1	2	yes	—
382	C₈	C₅×AGL(1,ℤ/8)	1	2	yes	—
383	C₅	#19353	1	1	yes	characteristic, direct product factor, Sylow
384	C₂²	—	2	1	no	—
385	C₂²	—	2	1	no	—
386	C₂²	—	4	1	no	—
387	C₂²	—	4	1	no	—
388	C₂²	—	4	1	no	—
389	C₂²	—	8	4	no	—
390	C₂²	—	8	4	no	—
391	C₂²	—	8	4	no	—
392	C₂²	—	16	8	no	—
393	C₂²	C₅×#472	1	2	yes	—
394	C₂²	C₂×C₅×#121	1	1	yes	characteristic
395	C₄	—	2	1	no	—
396	C₄	—	2	1	no	—
397	C₄	—	2	1	no	—
398	C₄	—	2	1	no	—
399	C₄	—	4	1	no	—
400	C₄	—	4	1	no	—
401	C₄	—	4	1	no	—
402	C₄	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
403	C₄	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
404	C₄	C₅×#576	1	2	yes	—
405	C₂	—	2	2	no	—
406	C₂	—	8	1	no	—
407	C₂	—	16	4	no	—
408	C₂	C₅×#3038	1	1	yes	characteristic
409	C₂	C₅×#3058	1	1	yes	characteristic
410	C₂	C₂×C₅×#472	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₅
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×#3217	C₂	semidirect
2. C₂×C₅×#493	C₂	semidirect
3. C₅×#2966	C₂	semidirect
4. C₅×#1688	C₂	semidirect
5. C₅×#1687	C₂	semidirect
6. C₅×#1668	C₂	semidirect
7. C₅×#1667	C₂	semidirect
8. C₅×#1568	C₂	semidirect
9. C₅×#1555	C₂	semidirect
20. C₅×#460	C₂²	semidirect
21. C₅×#459	C₂²	semidirect
24. C₅×#446	C₂²	semidirect
25. C₅×C₈×Q₈	C₂²	semidirect
26. C₅×#436	C₂²	semidirect
29. C₅×C₈×D₄	C₂²	semidirect
35. C₅×#335	C₂²	semidirect
36. C₅×#334	C₂²	semidirect
37. C₅×#331	C₂²	semidirect
38. C₅×#331	C₂²	semidirect
39. #19353	C₅	direct (N × H)
89. #3217	C₂×C₅	semidirect
90. C₂×#493	C₂×C₅	semidirect
91. #2966	C₂×C₅	semidirect
92. #1688	C₂×C₅	semidirect
93. #1687	C₂×C₅	semidirect
94. #1668	C₂×C₅	semidirect
95. #1667	C₂×C₅	semidirect
96. #1568	C₂×C₅	semidirect
97. #1555	C₂×C₅	semidirect
159. #460	C₂²×C₅	semidirect
160. #459	C₂²×C₅	semidirect
163. #446	C₂²×C₅	semidirect
164. C₈×Q₈	C₂²×C₅	semidirect
165. #436	C₂²×C₅	semidirect
168. C₈×D₄	C₂²×C₅	semidirect
174. #335	C₂²×C₅	semidirect
175. #334	C₂²×C₅	semidirect
176. #331	C₂²×C₅	semidirect
177. #331	C₂²×C₅	semidirect
383. C₅	#19353	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×#3217	2
C₂×C₅×#493	2
C₅×#2966	2
C₅×#1688	2
C₅×#1687	2
C₅×#1668	2
C₅×#1667	2
C₅×#1568	2
C₅×#1555	2
#19353	5

Subgroups — C5×#19353 #11942073

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#19353 #11942073