Subgroups — C₅×#19437 #11942157

Order 1280.

612 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3207	C₂	1	1	yes	maximal, characteristic
2	C₅×#3112	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#3103	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2983	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1704	C₂	1	2	yes	maximal, complemented
6	C₅×#1698	C₂	1	2	yes	maximal, complemented
7	C₅×#1688	C₂	1	2	yes	maximal, complemented
8	C₅×#1686	C₂	1	2	yes	maximal, complemented
9	C₅×#1572	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1553	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1543	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#532	C₂²	1	1	yes	characteristic
13	C₅×#532	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
15	C₅×#493	C₂²	1	1	yes	characteristic
16	C₅×#492	C₂²	1	1	yes	characteristic
17	C₅×#487	C₂²	1	1	yes	characteristic
18	C₅×#486	C₂²	1	1	yes	characteristic
19	C₅×#481	—	2	1	no	—
20	C₅×#480	—	2	1	no	—
21	C₅×#477	C₂²	1	2	yes	—
22	C₅×#475	C₂²	1	2	yes	—
23	C₅×#463	—	2	2	no	—
24	C₅×#460	C₂²	1	2	yes	—
25	C₅×#460	C₂²	1	2	yes	—
26	C₅×#449	—	2	2	no	—
27	C₅×#448	—	2	1	no	—
28	C₅×#448	—	2	1	no	—
29	C₅×#446	—	2	2	no	—
30	C₅×#446	C₂²	1	2	yes	—
31	C₅×#446	C₂²	1	2	yes	—
32	C₅×#440	—	2	2	no	—
33	C₄×C₅×SD₁₆	—	2	2	no	—
34	C₅×#432	—	2	2	no	—
35	C₅×#432	C₂²	1	1	yes	characteristic
36	C₅×#431	C₂²	1	1	yes	characteristic
37	C₅×#431	C₂²	1	1	yes	characteristic
38	C₅×#431	C₂²	1	1	yes	characteristic
39	C₅×#335	C₂²	1	2	yes	—
40	C₅×#334	C₂²	1	2	yes	—
41	C₅×#333	C₂²	1	2	yes	—
42	C₅×#332	C₂²	1	2	yes	—
43	C₅×#331	C₂²	1	2	yes	—
44	C₅×#331	C₂²	1	2	yes	—
45	#19437	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
46	C₂×C₅×#41	—	2	1	no	—
47	C₂×C₅×#41	—	2	1	no	—
48	C₂²×C₅×Q₈	D₄	1	1	yes	characteristic
49	C₂×C₅×SD₁₆	—	2	2	no	—
50	C₂×C₅×SD₁₆	—	2	2	no	—
51	C₂×C₅×SD₁₆	—	2	2	no	—
52	C₂×C₅×D₈	—	2	2	no	—
53	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
54	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
55	C₅×#127	C₂³	1	1	yes	characteristic
56	C₅×#127	C₂³	1	1	yes	characteristic
57	C₅×#124	—	2	1	no	—
58	C₅×#124	—	2	1	no	—
59	C₅×#121	—	2	1	no	—
60	C₅×#121	—	2	1	no	—
61	C₅×#121	—	2	1	no	—
62	C₅×#121	—	2	1	no	—
63	C₄×C₅×Q₈	—	2	1	no	—
64	C₄×C₅×Q₈	—	2	1	no	—
65	C₄×C₅×Q₈	D₄	1	2	yes	—
66	C₄×C₅×Q₈	C₂³	1	2	yes	—
67	C₄×C₅×D₄	—	2	1	no	—
68	C₄×C₅×D₄	—	2	1	no	—
69	C₄×C₅×D₄	—	2	1	no	—
70	C₄×C₅×D₄	—	2	1	no	—
71	C₂×C₅×C₄⋊C₄	—	2	1	no	—
72	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
73	C₂×C₄²×C₅	—	2	1	no	—
74	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
75	C₅×#107	—	2	2	no	—
76	C₅×#106	—	2	2	no	—
77	C₅×C₄⋊C₈	—	2	2	no	—
78	C₅×C₄⋊C₈	—	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×#102	—	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	D₄	1	2	yes	—
93	C₅×#97	—	2	2	no	—
94	C₅×#97	—	2	2	no	—
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	#3207	C₂×C₅	1	1	yes	characteristic
101	#3112	C₂×C₅	1	1	yes	characteristic, complemented
102	#3103	C₂×C₅	1	1	yes	characteristic, complemented
103	#2983	C₂×C₅	1	1	yes	characteristic, complemented
104	#1704	C₂×C₅	1	2	yes	complemented
105	#1698	C₂×C₅	1	2	yes	complemented
106	#1688	C₂×C₅	1	2	yes	complemented
107	#1686	C₂×C₅	1	2	yes	complemented
108	#1572	C₂×C₅	1	1	yes	characteristic, complemented
109	#1553	C₂×C₅	1	1	yes	characteristic, complemented
110	#1543	C₂×C₅	1	1	yes	characteristic, complemented
111	C₅×#41	—	8	2	no	—
112	C₅×#41	—	8	2	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×Q₈	—	4	2	no	—
117	C₂×C₅×Q₈	C₂×D₄	1	2	yes	—
118	C₂×C₅×D₄	—	2	1	no	—
119	C₂×C₅×D₄	—	2	1	no	—
120	C₂×C₅×D₄	—	2	1	no	—
121	C₂×C₅×D₄	—	2	1	no	—
122	C₂×C₅×D₄	—	2	1	no	—
123	C₂×C₅×D₄	—	2	1	no	—
124	C₂×C₅×D₄	—	4	1	no	—
125	C₂×C₅×D₄	—	4	1	no	—
126	C₂²×C₄×C₅	—	2	1	no	—
127	C₂²×C₄×C₅	—	2	1	no	—
128	C₂²×C₄×C₅	—	4	1	no	—
129	C₂²×C₄×C₅	—	4	1	no	—
130	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₅	#41	1	1	yes	characteristic
133	C₅×SD₁₆	—	4	4	no	—
134	C₅×SD₁₆	—	4	4	no	—
135	C₅×SD₁₆	—	8	2	no	—
136	C₅×D₈	—	8	2	no	—
137	C₂×C₅×C₈	—	2	2	no	—
138	C₂×C₅×C₈	—	2	2	no	—
139	C₂×C₅×C₈	—	2	2	no	—
140	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
141	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
142	C₅×C₄⋊C₄	—	2	2	no	—
143	C₅×C₄⋊C₄	—	2	1	no	—
144	C₅×C₄⋊C₄	—	2	2	no	—
145	C₅×C₄⋊C₄	—	2	1	no	—
146	C₅×C₄⋊C₄	—	2	1	no	—
147	C₅×C₄⋊C₄	—	2	1	no	—
148	C₅×C₄⋊C₄	—	2	1	no	—
149	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
150	C₅×C₂²⋊C₄	—	4	1	no	—
151	C₅×C₂²⋊C₄	—	4	1	no	—
152	C₅×C₂²⋊C₄	—	4	1	no	—
153	C₅×C₂²⋊C₄	—	4	1	no	—
154	C₄²×C₅	—	2	2	no	—
155	C₄²×C₅	—	2	2	no	—
156	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
157	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
158	C₄²×C₅	#41	1	1	yes	characteristic
159	C₄²×C₅	C₂⁴	1	1	yes	characteristic
160	#532	C₂²×C₅	1	1	yes	characteristic
161	#532	C₂²×C₅	1	1	yes	characteristic
162	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
163	#493	C₂²×C₅	1	1	yes	characteristic
164	#492	C₂²×C₅	1	1	yes	characteristic
165	#487	C₂²×C₅	1	1	yes	characteristic
166	#486	C₂²×C₅	1	1	yes	characteristic
167	#481	—	2	1	no	—
168	#480	—	2	1	no	—
169	#477	C₂²×C₅	1	2	yes	—
170	#475	C₂²×C₅	1	2	yes	—
171	#463	—	2	2	no	—
172	#460	C₂²×C₅	1	2	yes	—
173	#460	C₂²×C₅	1	2	yes	—
174	#449	—	2	2	no	—
175	#448	—	2	1	no	—
176	#448	—	2	1	no	—
177	#446	—	2	2	no	—
178	#446	C₂²×C₅	1	2	yes	—
179	#446	C₂²×C₅	1	2	yes	—
180	#440	—	2	2	no	—
181	C₄×SD₁₆	—	2	2	no	—
182	#432	—	2	2	no	—
183	#432	C₂²×C₅	1	1	yes	characteristic
184	#431	C₂²×C₅	1	1	yes	characteristic
185	#431	C₂²×C₅	1	1	yes	characteristic
186	#431	C₂²×C₅	1	1	yes	characteristic
187	#335	C₂²×C₅	1	2	yes	—
188	#334	C₂²×C₅	1	2	yes	—
189	#333	C₂²×C₅	1	2	yes	—
190	#332	C₂²×C₅	1	2	yes	—
191	#331	C₂²×C₅	1	2	yes	—
192	#331	C₂²×C₅	1	2	yes	—
193	C₂³×C₅	—	4	1	no	—
194	C₂³×C₅	—	4	1	no	—
195	C₂³×C₅	#121	1	1	yes	characteristic
196	C₅×Q₈	—	2	2	no	—
197	C₅×Q₈	—	2	2	no	—
198	C₅×Q₈	—	4	2	no	—
199	C₅×Q₈	—	4	2	no	—
200	C₅×Q₈	—	8	1	no	—
201	C₅×D₄	—	4	2	no	—
202	C₅×D₄	—	4	2	no	—
203	C₅×D₄	—	4	2	no	—
204	C₅×D₄	—	4	2	no	—
205	C₅×D₄	—	8	1	no	—
206	C₅×D₄	—	8	1	no	—
207	C₅×D₄	—	8	2	no	—
208	C₅×D₄	—	8	2	no	—
209	C₂×C₄×C₅	—	2	2	no	—
210	C₂×C₄×C₅	—	2	2	no	—
211	C₂×C₄×C₅	—	2	2	no	—
212	C₂×C₄×C₅	—	2	2	no	—
213	C₂×C₄×C₅	—	4	1	no	—
214	C₂×C₄×C₅	—	4	2	no	—
215	C₂×C₄×C₅	—	4	1	no	—
216	C₂×C₄×C₅	—	4	1	no	—
217	C₂×C₄×C₅	—	8	2	no	—
218	C₂×C₄×C₅	—	8	2	no	—
219	C₂×C₄×C₅	—	8	1	no	—
220	C₂×C₄×C₅	#121	1	1	yes	characteristic
221	C₂×C₄×C₅	#121	1	1	yes	characteristic
222	C₂×C₄×C₅	#121	1	1	yes	characteristic
223	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
224	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
225	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
226	C₅×C₈	—	2	2	no	—
227	C₅×C₈	—	2	2	no	—
228	C₅×C₈	—	4	2	no	—
229	C₅×C₈	—	4	2	no	—
230	C₅×C₈	—	4	2	no	—
231	C₂×#41	—	2	1	no	—
232	C₂×#41	—	2	1	no	—
233	C₂²×Q₈	C₅×D₄	1	1	yes	characteristic
234	C₂×SD₁₆	—	2	2	no	—
235	C₂×SD₁₆	—	2	2	no	—
236	C₂×SD₁₆	—	2	2	no	—
237	C₂×D₈	—	2	2	no	—
238	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
239	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
240	#127	C₂³×C₅	1	1	yes	characteristic
241	#127	C₂³×C₅	1	1	yes	characteristic
242	#124	—	2	1	no	—
243	#124	—	2	1	no	—
244	#121	—	2	1	no	—
245	#121	—	2	1	no	—
246	#121	—	2	1	no	—
247	#121	—	2	1	no	—
248	C₄×Q₈	—	2	1	no	—
249	C₄×Q₈	—	2	1	no	—
250	C₄×Q₈	C₅×D₄	1	2	yes	—
251	C₄×Q₈	C₂³×C₅	1	2	yes	—
252	C₄×D₄	—	2	1	no	—
253	C₄×D₄	—	2	1	no	—
254	C₄×D₄	—	2	1	no	—
255	C₄×D₄	—	2	1	no	—
256	C₂×C₄⋊C₄	—	2	1	no	—
257	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
258	C₂×C₄²	—	2	1	no	—
259	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
260	#107	—	2	2	no	—
261	#106	—	2	2	no	—
262	C₄⋊C₈	—	2	2	no	—
263	C₄⋊C₈	—	2	2	no	—
264	C₄⋊C₈	C₅×D₄	1	2	yes	—
265	C₄⋊C₈	C₂³×C₅	1	2	yes	—
266	C₄⋊C₈	C₂³×C₅	1	2	yes	—
267	C₄⋊C₈	C₂³×C₅	1	2	yes	—
268	#103	—	2	2	no	—
269	#103	—	2	2	no	—
270	#103	—	2	2	no	—
271	#102	—	2	2	no	—
272	#102	—	2	2	no	—
273	#102	—	2	2	no	—
274	C₂²⋊C₈	—	2	1	no	—
275	C₂²⋊C₈	—	2	1	no	—
276	C₂²⋊C₈	—	2	1	no	—
277	C₂²⋊C₈	C₅×D₄	1	2	yes	—
278	#97	—	2	2	no	—
279	#97	—	2	2	no	—
280	#97	—	2	1	no	—
281	C₄×C₈	—	2	1	no	—
282	C₄×C₈	—	2	1	no	—
283	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
284	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
285	C₂²×C₅	—	2	1	no	—
286	C₂²×C₅	—	2	1	no	—
287	C₂²×C₅	—	2	1	no	—
288	C₂²×C₅	—	8	1	no	—
289	C₂²×C₅	—	8	1	no	—
290	C₂²×C₅	—	8	1	no	—
291	C₂²×C₅	—	8	1	no	—
292	C₂²×C₅	—	8	1	no	—
293	C₂²×C₅	—	8	1	no	—
294	C₂²×C₅	C₂×#121	1	1	yes	characteristic
295	C₄×C₅	—	2	1	no	—
296	C₄×C₅	—	2	1	no	—
297	C₄×C₅	—	2	1	no	—
298	C₄×C₅	—	2	1	no	—
299	C₄×C₅	—	4	2	no	—
300	C₄×C₅	—	4	2	no	—
301	C₄×C₅	—	8	1	no	—
302	C₄×C₅	—	8	1	no	—
303	C₄×C₅	#575	1	2	yes	—
304	C₄×C₅	#577	1	2	yes	—
305	#41	—	8	2	no	—
306	#41	—	8	2	no	—
307	C₂×Q₈	—	2	1	no	—
308	C₂×Q₈	—	2	1	no	—
309	C₂×Q₈	—	2	1	no	—
310	C₂×Q₈	—	4	2	no	—
311	C₂×Q₈	C₂×C₅×D₄	1	2	yes	—
312	C₂×D₄	—	2	1	no	—
313	C₂×D₄	—	2	1	no	—
314	C₂×D₄	—	2	1	no	—
315	C₂×D₄	—	2	1	no	—
316	C₂×D₄	—	2	1	no	—
317	C₂×D₄	—	2	1	no	—
318	C₂×D₄	—	4	1	no	—
319	C₂×D₄	—	4	1	no	—
320	C₂²×C₄	—	2	1	no	—
321	C₂²×C₄	—	2	1	no	—
322	C₂²×C₄	—	4	1	no	—
323	C₂²×C₄	—	4	1	no	—
324	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
325	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
326	C₂²×C₄	C₅×#41	1	1	yes	characteristic
327	SD₁₆	—	4	4	no	—
328	SD₁₆	—	4	4	no	—
329	SD₁₆	—	8	2	no	—
330	D₈	—	8	2	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
335	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	2	1	no	—
338	C₄⋊C₄	—	2	2	no	—
339	C₄⋊C₄	—	2	1	no	—
340	C₄⋊C₄	—	2	1	no	—
341	C₄⋊C₄	—	2	1	no	—
342	C₄⋊C₄	—	2	1	no	—
343	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
344	C₂²⋊C₄	—	4	1	no	—
345	C₂²⋊C₄	—	4	1	no	—
346	C₂²⋊C₄	—	4	1	no	—
347	C₂²⋊C₄	—	4	1	no	—
348	C₄²	—	2	2	no	—
349	C₄²	—	2	2	no	—
350	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
351	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
352	C₄²	C₅×#41	1	1	yes	characteristic
353	C₄²	C₂⁴×C₅	1	1	yes	characteristic
354	C₂×C₅	—	4	1	no	—
355	C₂×C₅	—	16	1	no	—
356	C₂×C₅	—	16	1	no	—
357	C₂×C₅	#3043	1	1	yes	characteristic
358	C₂×C₅	#3054	1	1	yes	characteristic
359	C₂×C₅	#3068	1	1	yes	characteristic
360	C₂³	—	4	1	no	—
361	C₂³	—	4	1	no	—
362	C₂³	C₅×#121	1	1	yes	characteristic
363	Q₈	—	2	2	no	—
364	Q₈	—	2	2	no	—
365	Q₈	—	4	2	no	—
366	Q₈	—	4	2	no	—
367	Q₈	—	8	1	no	—
368	D₄	—	4	2	no	—
369	D₄	—	4	2	no	—
370	D₄	—	4	2	no	—
371	D₄	—	4	2	no	—
372	D₄	—	8	1	no	—
373	D₄	—	8	1	no	—
374	D₄	—	8	2	no	—
375	D₄	—	8	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	4	1	no	—
384	C₂×C₄	—	8	2	no	—
385	C₂×C₄	—	8	2	no	—
386	C₂×C₄	—	8	1	no	—
387	C₂×C₄	C₅×#121	1	1	yes	characteristic
388	C₂×C₄	C₅×#121	1	1	yes	characteristic
389	C₂×C₄	C₅×#121	1	1	yes	characteristic
390	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
391	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
392	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
393	C₈	—	2	2	no	—
394	C₈	—	2	2	no	—
395	C₈	—	4	2	no	—
396	C₈	—	4	2	no	—
397	C₈	—	4	2	no	—
398	C₅	#19437	1	1	yes	characteristic, direct product factor, Sylow
399	C₂²	—	2	1	no	—
400	C₂²	—	2	1	no	—
401	C₂²	—	2	1	no	—
402	C₂²	—	8	1	no	—
403	C₂²	—	8	1	no	—
404	C₂²	—	8	1	no	—
405	C₂²	—	8	1	no	—
406	C₂²	—	8	1	no	—
407	C₂²	—	8	1	no	—
408	C₂²	C₂×C₅×#121	1	1	yes	characteristic
409	C₄	—	2	1	no	—
410	C₄	—	2	1	no	—
411	C₄	—	2	1	no	—
412	C₄	—	2	1	no	—
413	C₄	—	4	2	no	—
414	C₄	—	4	2	no	—
415	C₄	—	8	1	no	—
416	C₄	—	8	1	no	—
417	C₄	C₅×#575	1	2	yes	—
418	C₄	C₅×#577	1	2	yes	—
419	C₂	—	4	1	no	—
420	C₂	—	16	1	no	—
421	C₂	—	16	1	no	—
422	C₂	C₅×#3043	1	1	yes	characteristic
423	C₂	C₅×#3054	1	1	yes	characteristic
424	C₂	C₅×#3068	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₅
prime radical	C₅×#3207	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
2. C₅×#3112	C₂	semidirect
3. C₅×#3103	C₂	semidirect
4. C₅×#2983	C₂	semidirect
5. C₅×#1704	C₂	semidirect
6. C₅×#1698	C₂	semidirect
7. C₅×#1688	C₂	semidirect
8. C₅×#1686	C₂	semidirect
9. C₅×#1572	C₂	semidirect
10. C₅×#1553	C₂	semidirect
11. C₅×#1543	C₂	semidirect
45. #19437	C₅	direct (N × H)
101. #3112	C₂×C₅	semidirect
102. #3103	C₂×C₅	semidirect
103. #2983	C₂×C₅	semidirect
104. #1704	C₂×C₅	semidirect
105. #1698	C₂×C₅	semidirect
106. #1688	C₂×C₅	semidirect
107. #1686	C₂×C₅	semidirect
108. #1572	C₂×C₅	semidirect
109. #1553	C₂×C₅	semidirect
110. #1543	C₂×C₅	semidirect
398. C₅	#19437	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×#3207	2
C₅×#3112	2
C₅×#3103	2
C₅×#2983	2
C₅×#1704	2
C₅×#1698	2
C₅×#1688	2
C₅×#1686	2
C₅×#1572	2
C₅×#1553	2
C₅×#1543	2
#19437	5

Subgroups — C5×#19437 #11942157

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#19437 #11942157