Subgroups — C₅×#19431 #11942151

Order 1280.

604 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3231	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#3110	C₂	1	1	yes	maximal, characteristic
3	C₅×#3101	C₂	1	1	yes	maximal, characteristic
4	C₅×#2975	C₂	1	1	yes	maximal, characteristic
5	C₅×#1703	C₂	1	2	yes	maximal, complemented
6	C₅×#1699	C₂	1	2	yes	maximal, complemented
7	C₅×#1693	C₂	1	2	yes	maximal, complemented
8	C₅×#1691	C₂	1	2	yes	maximal, complemented
9	C₅×#1572	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1554	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1544	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#533	C₂²	1	1	yes	characteristic
13	C₅×#533	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
15	C₅×#500	C₂²	1	1	yes	characteristic, complemented
16	C₅×#498	C₂²	1	1	yes	characteristic, complemented
17	C₅×#487	C₂²	1	1	yes	characteristic, complemented
18	C₅×#487	C₂²	1	1	yes	characteristic, complemented
19	C₅×#485	—	2	2	no	—
20	C₅×#484	—	2	1	no	—
21	C₅×#483	—	2	1	no	—
22	C₅×#479	—	2	2	no	—
23	C₅×#476	C₂²	1	2	yes	—
24	C₅×#474	C₂²	1	2	yes	—
25	C₅×#461	C₂²	1	2	yes	—
26	C₅×#461	C₂²	1	2	yes	—
27	C₅×#450	—	2	1	no	—
28	C₅×#450	—	2	1	no	—
29	C₅×#440	—	2	2	no	—
30	C₄×C₅×SD₁₆	—	2	2	no	—
31	C₅×#436	—	2	2	no	—
32	C₅×#436	C₂²	1	2	yes	—
33	C₅×#436	C₂²	1	2	yes	—
34	C₅×#432	C₂²	1	1	yes	characteristic
35	C₅×#431	C₂²	1	1	yes	characteristic
36	C₅×#431	C₂²	1	1	yes	characteristic
37	C₅×#431	C₂²	1	1	yes	characteristic
38	C₅×#407	—	2	2	no	—
39	C₅×#335	C₂²	1	2	yes	complemented
40	C₅×#334	C₂²	1	2	yes	complemented
41	C₅×#333	C₂²	1	2	yes	complemented
42	C₅×#332	C₂²	1	2	yes	complemented
43	C₅×#332	C₂²	1	2	yes	complemented
44	C₅×#332	C₂²	1	2	yes	complemented
45	#19431	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
46	C₂²×C₅×D₄	D₄	1	1	yes	characteristic
47	C₂³×C₄×C₅	—	2	1	no	—
48	C₂×C₅×SD₁₆	—	2	2	no	—
49	C₂×C₅×SD₁₆	—	2	2	no	—
50	C₂×C₅×M₁₆	—	2	2	no	—
51	C₂×C₅×M₁₆	—	2	2	no	—
52	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
53	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
54	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
55	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
56	C₅×#125	—	2	1	no	—
57	C₅×#125	—	2	1	no	—
58	C₅×C₂²⋊Q₈	—	2	1	no	—
59	C₅×C₂²⋊Q₈	—	2	1	no	—
60	C₅×C₂²⋊Q₈	—	2	1	no	—
61	C₅×C₂²⋊Q₈	—	2	1	no	—
62	C₄×C₅×Q₈	—	2	1	no	—
63	C₄×C₅×Q₈	—	2	1	no	—
64	C₄×C₅×Q₈	—	2	1	no	—
65	C₄×C₅×Q₈	—	2	1	no	—
66	C₄×C₅×D₄	—	2	1	no	—
67	C₄×C₅×D₄	—	2	1	no	—
68	C₄×C₅×D₄	D₄	1	2	yes	—
69	C₄×C₅×D₄	C₂³	1	2	yes	—
70	C₅×#117	—	2	1	no	—
71	C₅×#117	—	2	1	no	—
72	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
73	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
74	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
75	C₅×#107	—	2	2	no	—
76	C₅×#107	—	2	2	no	—
77	C₅×#106	—	2	2	no	—
78	C₅×#106	—	2	2	no	—
79	C₅×C₄⋊C₈	D₄	1	2	yes	—
80	C₅×C₄⋊C₈	C₂³	1	2	yes	—
81	C₅×C₄⋊C₈	C₂³	1	2	yes	—
82	C₅×C₄⋊C₈	C₂³	1	2	yes	—
83	C₅×#103	—	2	2	no	—
84	C₅×#103	—	2	2	no	—
85	C₅×#103	—	2	2	no	—
86	C₅×#103	—	2	2	no	—
87	C₅×#102	—	2	2	no	—
88	C₅×#102	—	2	2	no	—
89	C₅×C₂²⋊C₈	—	2	1	no	—
90	C₅×C₂²⋊C₈	—	2	1	no	—
91	C₅×C₂²⋊C₈	—	2	1	no	—
92	C₅×C₂²⋊C₈	—	2	2	no	—
93	C₅×C₂²⋊C₈	—	2	2	no	—
94	C₅×C₂²⋊C₈	D₄	1	2	yes	—
95	C₅×#97	—	2	1	no	—
96	C₄×C₅×C₈	—	2	1	no	—
97	C₄×C₅×C₈	—	2	1	no	—
98	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
99	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
100	#3231	C₂×C₅	1	1	yes	characteristic, complemented
101	#3110	C₂×C₅	1	1	yes	characteristic
102	#3101	C₂×C₅	1	1	yes	characteristic
103	#2975	C₂×C₅	1	1	yes	characteristic
104	#1703	C₂×C₅	1	2	yes	complemented
105	#1699	C₂×C₅	1	2	yes	complemented
106	#1693	C₂×C₅	1	2	yes	complemented
107	#1691	C₂×C₅	1	2	yes	complemented
108	#1572	C₂×C₅	1	1	yes	characteristic, complemented
109	#1554	C₂×C₅	1	1	yes	characteristic, complemented
110	#1544	C₂×C₅	1	1	yes	characteristic, complemented
111	C₂⁴×C₅	—	2	1	no	—
112	C₂×C₅×Q₈	—	2	1	no	—
113	C₂×C₅×Q₈	—	2	1	no	—
114	C₂×C₅×Q₈	—	2	1	no	—
115	C₂×C₅×Q₈	—	2	1	no	—
116	C₂×C₅×D₄	—	2	1	no	—
117	C₂×C₅×D₄	—	4	2	no	—
118	C₂×C₅×D₄	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₅	—	2	1	no	—
120	C₂²×C₄×C₅	—	2	2	no	—
121	C₂²×C₄×C₅	—	2	2	no	—
122	C₂²×C₄×C₅	—	8	2	no	—
123	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₅	#41	1	1	yes	characteristic
126	C₅×SD₁₆	—	4	4	no	—
127	C₅×SD₁₆	—	4	4	no	—
128	C₅×M₁₆	—	8	2	no	—
129	C₅×M₁₆	—	8	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	C₂×D₄	1	2	yes	—
134	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
135	C₅×C₄⋊C₄	—	2	1	no	—
136	C₅×C₄⋊C₄	—	2	1	no	—
137	C₅×C₄⋊C₄	—	2	1	no	—
138	C₅×C₄⋊C₄	—	2	1	no	—
139	C₅×C₄⋊C₄	—	2	1	no	—
140	C₅×C₄⋊C₄	—	2	1	no	—
141	C₅×C₄⋊C₄	—	2	1	no	—
142	C₅×C₄⋊C₄	—	2	1	no	—
143	C₅×C₄⋊C₄	—	2	1	no	—
144	C₅×C₄⋊C₄	—	4	1	no	—
145	C₅×C₄⋊C₄	—	4	1	no	—
146	C₅×C₄⋊C₄	—	4	1	no	—
147	C₅×C₄⋊C₄	—	4	1	no	—
148	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
149	C₅×C₂²⋊C₄	—	2	2	no	—
150	C₅×C₂²⋊C₄	—	2	2	no	—
151	C₅×C₂²⋊C₄	—	4	1	no	—
152	C₅×C₂²⋊C₄	—	4	1	no	—
153	C₄²×C₅	—	4	1	no	—
154	C₄²×C₅	—	4	1	no	—
155	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
156	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
157	C₄²×C₅	#41	1	1	yes	characteristic
158	C₄²×C₅	C₂⁴	1	1	yes	characteristic
159	#533	C₂²×C₅	1	1	yes	characteristic
160	#533	C₂²×C₅	1	1	yes	characteristic
161	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
162	#500	C₂²×C₅	1	1	yes	characteristic, complemented
163	#498	C₂²×C₅	1	1	yes	characteristic, complemented
164	#487	C₂²×C₅	1	1	yes	characteristic, complemented
165	#487	C₂²×C₅	1	1	yes	characteristic, complemented
166	#485	—	2	2	no	—
167	#484	—	2	1	no	—
168	#483	—	2	1	no	—
169	#479	—	2	2	no	—
170	#476	C₂²×C₅	1	2	yes	—
171	#474	C₂²×C₅	1	2	yes	—
172	#461	C₂²×C₅	1	2	yes	—
173	#461	C₂²×C₅	1	2	yes	—
174	#450	—	2	1	no	—
175	#450	—	2	1	no	—
176	#440	—	2	2	no	—
177	C₄×SD₁₆	—	2	2	no	—
178	#436	—	2	2	no	—
179	#436	C₂²×C₅	1	2	yes	—
180	#436	C₂²×C₅	1	2	yes	—
181	#432	C₂²×C₅	1	1	yes	characteristic
182	#431	C₂²×C₅	1	1	yes	characteristic
183	#431	C₂²×C₅	1	1	yes	characteristic
184	#431	C₂²×C₅	1	1	yes	characteristic
185	#407	—	2	2	no	—
186	#335	C₂²×C₅	1	2	yes	complemented
187	#334	C₂²×C₅	1	2	yes	complemented
188	#333	C₂²×C₅	1	2	yes	complemented
189	#332	C₂²×C₅	1	2	yes	complemented
190	#332	C₂²×C₅	1	2	yes	complemented
191	#332	C₂²×C₅	1	2	yes	complemented
192	C₂³×C₅	—	2	2	no	—
193	C₂³×C₅	—	4	2	no	—
194	C₂³×C₅	—	8	1	no	—
195	C₂³×C₅	—	8	1	no	—
196	C₂³×C₅	#121	1	1	yes	characteristic
197	C₅×Q₈	—	4	2	no	—
198	C₅×Q₈	—	4	2	no	—
199	C₅×Q₈	—	4	2	no	—
200	C₅×Q₈	—	8	1	no	—
201	C₅×D₄	—	2	2	no	—
202	C₅×D₄	—	2	2	no	—
203	C₅×D₄	—	4	2	no	—
204	C₂×C₄×C₅	—	2	2	no	—
205	C₂×C₄×C₅	—	2	2	no	—
206	C₂×C₄×C₅	—	2	2	no	—
207	C₂×C₄×C₅	—	4	1	no	—
208	C₂×C₄×C₅	—	4	2	no	—
209	C₂×C₄×C₅	—	4	2	no	—
210	C₂×C₄×C₅	—	4	1	no	—
211	C₂×C₄×C₅	—	4	1	no	—
212	C₂×C₄×C₅	—	4	1	no	—
213	C₂×C₄×C₅	—	4	1	no	—
214	C₂×C₄×C₅	—	8	2	no	—
215	C₂×C₄×C₅	—	8	1	no	—
216	C₂×C₄×C₅	#121	1	1	yes	characteristic
217	C₂×C₄×C₅	#121	1	1	yes	characteristic
218	C₂×C₄×C₅	#121	1	1	yes	characteristic
219	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
220	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
221	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
222	C₅×C₈	—	2	2	no	—
223	C₅×C₈	—	2	2	no	—
224	C₅×C₈	—	4	2	no	—
225	C₅×C₈	—	4	2	no	—
226	C₅×C₈	—	4	2	no	—
227	C₂²×D₄	C₅×D₄	1	1	yes	characteristic
228	C₂³×C₄	—	2	1	no	—
229	C₂×SD₁₆	—	2	2	no	—
230	C₂×SD₁₆	—	2	2	no	—
231	C₂×M₁₆	—	2	2	no	—
232	C₂×M₁₆	—	2	2	no	—
233	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
234	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
235	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
236	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
237	#125	—	2	1	no	—
238	#125	—	2	1	no	—
239	C₂²⋊Q₈	—	2	1	no	—
240	C₂²⋊Q₈	—	2	1	no	—
241	C₂²⋊Q₈	—	2	1	no	—
242	C₂²⋊Q₈	—	2	1	no	—
243	C₄×Q₈	—	2	1	no	—
244	C₄×Q₈	—	2	1	no	—
245	C₄×Q₈	—	2	1	no	—
246	C₄×Q₈	—	2	1	no	—
247	C₄×D₄	—	2	1	no	—
248	C₄×D₄	—	2	1	no	—
249	C₄×D₄	C₅×D₄	1	2	yes	—
250	C₄×D₄	C₂³×C₅	1	2	yes	—
251	#117	—	2	1	no	—
252	#117	—	2	1	no	—
253	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
254	C₂×C₂²⋊C₄	—	2	1	no	—
255	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
256	#107	—	2	2	no	—
257	#107	—	2	2	no	—
258	#106	—	2	2	no	—
259	#106	—	2	2	no	—
260	C₄⋊C₈	C₅×D₄	1	2	yes	—
261	C₄⋊C₈	C₂³×C₅	1	2	yes	—
262	C₄⋊C₈	C₂³×C₅	1	2	yes	—
263	C₄⋊C₈	C₂³×C₅	1	2	yes	—
264	#103	—	2	2	no	—
265	#103	—	2	2	no	—
266	#103	—	2	2	no	—
267	#103	—	2	2	no	—
268	#102	—	2	2	no	—
269	#102	—	2	2	no	—
270	C₂²⋊C₈	—	2	1	no	—
271	C₂²⋊C₈	—	2	1	no	—
272	C₂²⋊C₈	—	2	1	no	—
273	C₂²⋊C₈	—	2	2	no	—
274	C₂²⋊C₈	—	2	2	no	—
275	C₂²⋊C₈	C₅×D₄	1	2	yes	—
276	#97	—	2	1	no	—
277	C₄×C₈	—	2	1	no	—
278	C₄×C₈	—	2	1	no	—
279	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
280	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
281	C₂²×C₅	—	2	1	no	—
282	C₂²×C₅	—	2	1	no	—
283	C₂²×C₅	—	2	1	no	—
284	C₂²×C₅	—	4	2	no	—
285	C₂²×C₅	—	4	2	no	—
286	C₂²×C₅	—	4	2	no	—
287	C₂²×C₅	—	8	4	no	—
288	C₂²×C₅	C₂×#121	1	1	yes	characteristic
289	C₄×C₅	—	2	1	no	—
290	C₄×C₅	—	2	1	no	—
291	C₄×C₅	—	2	1	no	—
292	C₄×C₅	—	2	1	no	—
293	C₄×C₅	—	4	2	no	—
294	C₄×C₅	—	8	1	no	—
295	C₄×C₅	—	8	1	no	—
296	C₄×C₅	—	8	1	no	—
297	C₄×C₅	—	8	1	no	—
298	C₄×C₅	#575	1	2	yes	—
299	C₄×C₅	#577	1	2	yes	—
300	C₂⁴	—	2	1	no	—
301	C₂×Q₈	—	2	1	no	—
302	C₂×Q₈	—	2	1	no	—
303	C₂×Q₈	—	2	1	no	—
304	C₂×Q₈	—	2	1	no	—
305	C₂×D₄	—	2	1	no	—
306	C₂×D₄	—	4	2	no	—
307	C₂×D₄	C₂×C₅×D₄	1	2	yes	—
308	C₂²×C₄	—	2	1	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	8	2	no	—
312	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
313	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
314	C₂²×C₄	C₅×#41	1	1	yes	characteristic
315	SD₁₆	—	4	4	no	—
316	SD₁₆	—	4	4	no	—
317	M₁₆	—	8	2	no	—
318	M₁₆	—	8	2	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
323	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
324	C₄⋊C₄	—	2	1	no	—
325	C₄⋊C₄	—	2	1	no	—
326	C₄⋊C₄	—	2	1	no	—
327	C₄⋊C₄	—	2	1	no	—
328	C₄⋊C₄	—	2	1	no	—
329	C₄⋊C₄	—	2	1	no	—
330	C₄⋊C₄	—	2	1	no	—
331	C₄⋊C₄	—	2	1	no	—
332	C₄⋊C₄	—	2	1	no	—
333	C₄⋊C₄	—	4	1	no	—
334	C₄⋊C₄	—	4	1	no	—
335	C₄⋊C₄	—	4	1	no	—
336	C₄⋊C₄	—	4	1	no	—
337	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
338	C₂²⋊C₄	—	2	2	no	—
339	C₂²⋊C₄	—	2	2	no	—
340	C₂²⋊C₄	—	4	1	no	—
341	C₂²⋊C₄	—	4	1	no	—
342	C₄²	—	4	1	no	—
343	C₄²	—	4	1	no	—
344	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
345	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
346	C₄²	C₅×#41	1	1	yes	characteristic
347	C₄²	C₂⁴×C₅	1	1	yes	characteristic
348	C₂×C₅	—	4	1	no	—
349	C₂×C₅	—	8	2	no	—
350	C₂×C₅	#3042	1	1	yes	characteristic
351	C₂×C₅	#3054	1	1	yes	characteristic
352	C₂×C₅	#3069	1	1	yes	characteristic
353	C₂³	—	2	2	no	—
354	C₂³	—	4	2	no	—
355	C₂³	—	8	1	no	—
356	C₂³	—	8	1	no	—
357	C₂³	C₅×#121	1	1	yes	characteristic
358	Q₈	—	4	2	no	—
359	Q₈	—	4	2	no	—
360	Q₈	—	4	2	no	—
361	Q₈	—	8	1	no	—
362	D₄	—	2	2	no	—
363	D₄	—	2	2	no	—
364	D₄	—	4	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	4	1	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	1	no	—
372	C₂×C₄	—	4	1	no	—
373	C₂×C₄	—	4	1	no	—
374	C₂×C₄	—	4	1	no	—
375	C₂×C₄	—	8	2	no	—
376	C₂×C₄	—	8	1	no	—
377	C₂×C₄	C₅×#121	1	1	yes	characteristic
378	C₂×C₄	C₅×#121	1	1	yes	characteristic
379	C₂×C₄	C₅×#121	1	1	yes	characteristic
380	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
381	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
382	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
383	C₈	—	2	2	no	—
384	C₈	—	2	2	no	—
385	C₈	—	4	2	no	—
386	C₈	—	4	2	no	—
387	C₈	—	4	2	no	—
388	C₅	#19431	1	1	yes	characteristic, direct product factor, Sylow
389	C₂²	—	2	1	no	—
390	C₂²	—	2	1	no	—
391	C₂²	—	2	1	no	—
392	C₂²	—	4	2	no	—
393	C₂²	—	4	2	no	—
394	C₂²	—	4	2	no	—
395	C₂²	—	8	4	no	—
396	C₂²	C₂×C₅×#121	1	1	yes	characteristic
397	C₄	—	2	1	no	—
398	C₄	—	2	1	no	—
399	C₄	—	2	1	no	—
400	C₄	—	2	1	no	—
401	C₄	—	4	2	no	—
402	C₄	—	8	1	no	—
403	C₄	—	8	1	no	—
404	C₄	—	8	1	no	—
405	C₄	—	8	1	no	—
406	C₄	C₅×#575	1	2	yes	—
407	C₄	C₅×#577	1	2	yes	—
408	C₂	—	4	1	no	—
409	C₂	—	8	2	no	—
410	C₂	C₅×#3042	1	1	yes	characteristic
411	C₂	C₅×#3054	1	1	yes	characteristic
412	C₂	C₅×#3069	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₅
prime radical	C₂²×C₅×D₄	D₄
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×#3231	C₂	semidirect
5. C₅×#1703	C₂	semidirect
6. C₅×#1699	C₂	semidirect
7. C₅×#1693	C₂	semidirect
8. C₅×#1691	C₂	semidirect
9. C₅×#1572	C₂	semidirect
10. C₅×#1554	C₂	semidirect
11. C₅×#1544	C₂	semidirect
15. C₅×#500	C₂²	semidirect
16. C₅×#498	C₂²	semidirect
17. C₅×#487	C₂²	semidirect
18. C₅×#487	C₂²	semidirect
39. C₅×#335	C₂²	semidirect
40. C₅×#334	C₂²	semidirect
41. C₅×#333	C₂²	semidirect
42. C₅×#332	C₂²	semidirect
43. C₅×#332	C₂²	semidirect
44. C₅×#332	C₂²	semidirect
45. #19431	C₅	direct (N × H)
100. #3231	C₂×C₅	semidirect
104. #1703	C₂×C₅	semidirect
105. #1699	C₂×C₅	semidirect
106. #1693	C₂×C₅	semidirect
107. #1691	C₂×C₅	semidirect
108. #1572	C₂×C₅	semidirect
109. #1554	C₂×C₅	semidirect
110. #1544	C₂×C₅	semidirect
162. #500	C₂²×C₅	semidirect
163. #498	C₂²×C₅	semidirect
164. #487	C₂²×C₅	semidirect
165. #487	C₂²×C₅	semidirect
186. #335	C₂²×C₅	semidirect
187. #334	C₂²×C₅	semidirect
188. #333	C₂²×C₅	semidirect
189. #332	C₂²×C₅	semidirect
190. #332	C₂²×C₅	semidirect
191. #332	C₂²×C₅	semidirect
388. C₅	#19431	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×#3231	2
C₅×#3110	2
C₅×#3101	2
C₅×#2975	2
C₅×#1703	2
C₅×#1699	2
C₅×#1693	2
C₅×#1691	2
C₅×#1572	2
C₅×#1554	2
C₅×#1544	2
#19431	5

Subgroups — C5×#19431 #11942151

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#19431 #11942151