Subgroups — C₅×#19298 #11942018

Order 1280.

586 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3160	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#3116	C₂	1	2	yes	maximal
3	C₅×#2965	C₂	1	1	yes	maximal, characteristic
4	C₅×#1696	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1695	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1694	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1693	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1692	C₂	1	2	yes	maximal, complemented
9	C₅×#1691	C₂	1	2	yes	maximal, complemented
10	C₅×#1568	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1554	C₂	1	2	yes	maximal, complemented
12	C₅×#533	C₂²	1	2	yes	—
13	C₄×C₅×#41	C₂²	1	1	yes	characteristic
14	C₅×#500	C₂²	1	1	yes	characteristic
15	C₅×#500	C₂²	1	1	yes	characteristic
16	C₅×#499	—	2	1	no	—
17	C₅×#499	—	2	1	no	—
18	C₅×#498	C₂²	1	2	yes	—
19	C₅×#485	—	2	2	no	—
20	C₅×#477	C₂²	1	2	yes	—
21	C₅×#476	C₂²	1	2	yes	—
22	C₅×#462	C₂²	1	2	yes	—
23	C₅×#461	C₂²	1	2	yes	—
24	C₅×#452	—	2	2	no	—
25	C₅×#446	C₂²	1	1	yes	characteristic
26	C₅×#446	C₂²	1	1	yes	characteristic
27	C₅×#441	—	2	2	no	—
28	C₅×#440	—	2	2	no	—
29	C₅×#436	C₂²	1	1	yes	characteristic
30	C₅×#436	C₂²	1	1	yes	characteristic
31	C₅×#435	—	2	1	no	—
32	C₅×#435	—	2	1	no	—
33	C₅×#432	C₂²	1	2	yes	—
34	C₅×#431	—	2	1	no	—
35	C₅×#431	C₂²	1	1	yes	characteristic
36	C₅×#427	—	2	1	no	—
37	C₅×#427	—	2	1	no	—
38	C₄×C₅×M₁₆	—	2	1	no	—
39	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
40	C₅×#335	C₂²	1	2	yes	—
41	C₅×#334	C₂²	1	1	yes	characteristic
42	C₅×#334	C₂²	1	1	yes	characteristic
43	C₅×#333	C₂²	1	2	yes	—
44	C₅×#333	C₂²	1	2	yes	—
45	C₅×#332	C₂²	1	2	yes	—
46	C₅×#332	C₂²	1	2	yes	—
47	#19298	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
48	C₂×C₅×#41	D₄	1	1	yes	characteristic
49	C₂×C₅×Q₁₆	—	2	2	no	—
50	C₂×C₅×SD₁₆	—	2	2	no	—
51	C₂×C₅×M₁₆	—	2	1	no	—
52	C₂×C₅×M₁₆	—	2	1	no	—
53	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
54	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
55	C₅×C₄⋊Q₈	C₂³	1	2	yes	—
56	C₅×C₄⋊Q₈	C₂³	1	2	yes	—
57	C₅×#125	—	2	2	no	—
58	C₅×C₂²⋊Q₈	—	2	2	no	—
59	C₅×C₂²⋊Q₈	—	2	2	no	—
60	C₄×C₅×Q₈	—	2	2	no	—
61	C₄×C₅×Q₈	—	2	2	no	—
62	C₄×C₅×Q₈	D₄	1	1	yes	characteristic
63	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
64	C₄×C₅×D₄	—	2	1	no	—
65	C₄×C₅×D₄	—	2	1	no	—
66	C₄×C₅×D₄	D₄	1	1	yes	characteristic
67	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
68	C₅×#117	—	2	1	no	—
69	C₅×#117	—	2	2	no	—
70	C₅×#117	D₄	1	1	yes	characteristic
71	C₂×C₄²×C₅	—	2	1	no	—
72	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
73	C₅×#107	—	2	1	no	—
74	C₅×#107	—	2	1	no	—
75	C₅×#107	—	2	1	no	—
76	C₅×#107	—	2	1	no	—
77	C₅×#107	—	2	2	no	—
78	C₅×#106	—	2	2	no	—
79	C₅×#106	—	2	2	no	—
80	C₅×#106	—	2	2	no	—
81	C₅×C₄⋊C₈	—	2	1	no	—
82	C₅×C₄⋊C₈	—	2	1	no	—
83	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
84	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
85	C₅×C₄⋊C₈	C₂³	1	2	yes	—
86	C₅×C₄⋊C₈	C₂³	1	2	yes	—
87	C₅×#103	—	2	2	no	—
88	C₅×#103	—	2	2	no	—
89	C₅×#103	—	2	2	no	—
90	C₅×#102	—	2	2	no	—
91	C₅×C₂²⋊C₈	—	2	1	no	—
92	C₅×C₂²⋊C₈	—	2	2	no	—
93	C₅×C₂²⋊C₈	—	2	1	no	—
94	C₅×C₂²⋊C₈	—	2	1	no	—
95	C₅×#97	—	2	1	no	—
96	C₅×#97	—	2	1	no	—
97	C₅×#97	—	2	2	no	—
98	C₄×C₅×C₈	—	2	1	no	—
99	C₄×C₅×C₈	D₄	1	1	yes	characteristic
100	C₄×C₅×C₈	D₄	1	1	yes	characteristic
101	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
102	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
103	#3160	C₂×C₅	1	1	yes	characteristic, complemented
104	#3116	C₂×C₅	1	2	yes	—
105	#2965	C₂×C₅	1	1	yes	characteristic
106	#1696	C₂×C₅	1	1	yes	characteristic, complemented
107	#1695	C₂×C₅	1	1	yes	characteristic, complemented
108	#1694	C₂×C₅	1	1	yes	characteristic, complemented
109	#1693	C₂×C₅	1	1	yes	characteristic, complemented
110	#1692	C₂×C₅	1	2	yes	complemented
111	#1691	C₂×C₅	1	2	yes	complemented
112	#1568	C₂×C₅	1	1	yes	characteristic, complemented
113	#1554	C₂×C₅	1	2	yes	complemented
114	C₅×#41	—	4	2	no	—
115	C₂×C₅×Q₈	—	2	2	no	—
116	C₂×C₅×Q₈	—	2	2	no	—
117	C₂×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
118	C₂×C₅×D₄	—	2	1	no	—
119	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₅	—	2	1	no	—
121	C₂²×C₄×C₅	—	2	1	no	—
122	C₂²×C₄×C₅	—	2	1	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×Q₁₆	—	4	4	no	—
127	C₅×SD₁₆	—	4	4	no	—
128	C₅×M₁₆	—	4	2	no	—
129	C₅×M₁₆	—	4	2	no	—
130	C₂×C₅×C₈	—	2	2	no	—
131	C₂×C₅×C₈	—	2	2	no	—
132	C₂×C₅×C₈	—	2	1	no	—
133	C₂×C₅×C₈	—	2	1	no	—
134	C₂×C₅×C₈	—	2	2	no	—
135	C₂×C₅×C₈	—	2	2	no	—
136	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
137	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
138	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
139	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
140	C₅×C₄⋊C₄	—	2	1	no	—
141	C₅×C₄⋊C₄	—	2	1	no	—
142	C₅×C₄⋊C₄	—	2	2	no	—
143	C₅×C₄⋊C₄	—	2	2	no	—
144	C₅×C₄⋊C₄	—	2	2	no	—
145	C₅×C₄⋊C₄	—	2	2	no	—
146	C₅×C₄⋊C₄	—	4	2	no	—
147	C₅×C₄⋊C₄	—	4	2	no	—
148	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
149	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
150	C₅×C₂²⋊C₄	—	2	1	no	—
151	C₅×C₂²⋊C₄	—	2	1	no	—
152	C₅×C₂²⋊C₄	—	2	1	no	—
153	C₅×C₂²⋊C₄	—	4	2	no	—
154	C₄²×C₅	—	2	1	no	—
155	C₄²×C₅	—	2	1	no	—
156	C₄²×C₅	—	2	1	no	—
157	C₄²×C₅	—	4	2	no	—
158	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
159	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
160	C₄²×C₅	#41	1	1	yes	characteristic
161	C₄²×C₅	C₂⁴	1	1	yes	characteristic
162	#533	C₂²×C₅	1	2	yes	—
163	C₄×#41	C₂²×C₅	1	1	yes	characteristic
164	#500	C₂²×C₅	1	1	yes	characteristic
165	#500	C₂²×C₅	1	1	yes	characteristic
166	#499	—	2	1	no	—
167	#499	—	2	1	no	—
168	#498	C₂²×C₅	1	2	yes	—
169	#485	—	2	2	no	—
170	#477	C₂²×C₅	1	2	yes	—
171	#476	C₂²×C₅	1	2	yes	—
172	#462	C₂²×C₅	1	2	yes	—
173	#461	C₂²×C₅	1	2	yes	—
174	#452	—	2	2	no	—
175	#446	C₂²×C₅	1	1	yes	characteristic
176	#446	C₂²×C₅	1	1	yes	characteristic
177	#441	—	2	2	no	—
178	#440	—	2	2	no	—
179	#436	C₂²×C₅	1	1	yes	characteristic
180	#436	C₂²×C₅	1	1	yes	characteristic
181	#435	—	2	1	no	—
182	#435	—	2	1	no	—
183	#432	C₂²×C₅	1	2	yes	—
184	#431	—	2	1	no	—
185	#431	C₂²×C₅	1	1	yes	characteristic
186	#427	—	2	1	no	—
187	#427	—	2	1	no	—
188	C₄×M₁₆	—	2	1	no	—
189	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
190	#335	C₂²×C₅	1	2	yes	—
191	#334	C₂²×C₅	1	1	yes	characteristic
192	#334	C₂²×C₅	1	1	yes	characteristic
193	#333	C₂²×C₅	1	2	yes	—
194	#333	C₂²×C₅	1	2	yes	—
195	#332	C₂²×C₅	1	2	yes	—
196	#332	C₂²×C₅	1	2	yes	—
197	C₂³×C₅	—	2	1	no	—
198	C₂³×C₅	#121	1	1	yes	characteristic
199	C₅×Q₈	—	2	2	no	—
200	C₅×Q₈	—	4	2	no	—
201	C₅×Q₈	—	4	2	no	—
202	C₅×Q₈	—	8	2	no	—
203	C₅×D₄	—	2	2	no	—
204	C₅×D₄	—	4	2	no	—
205	C₂×C₄×C₅	—	2	1	no	—
206	C₂×C₄×C₅	—	2	1	no	—
207	C₂×C₄×C₅	—	2	2	no	—
208	C₂×C₄×C₅	—	2	1	no	—
209	C₂×C₄×C₅	—	2	1	no	—
210	C₂×C₄×C₅	—	2	1	no	—
211	C₂×C₄×C₅	—	4	1	no	—
212	C₂×C₄×C₅	—	4	2	no	—
213	C₂×C₄×C₅	—	4	2	no	—
214	C₂×C₄×C₅	—	4	1	no	—
215	C₂×C₄×C₅	—	4	1	no	—
216	C₂×C₄×C₅	—	4	2	no	—
217	C₂×C₄×C₅	—	4	2	no	—
218	C₂×C₄×C₅	#121	1	1	yes	characteristic
219	C₂×C₄×C₅	#121	1	1	yes	characteristic
220	C₂×C₄×C₅	#121	1	1	yes	characteristic
221	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
222	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
223	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
224	C₅×C₈	—	2	1	no	—
225	C₅×C₈	—	2	1	no	—
226	C₅×C₈	—	4	1	no	—
227	C₅×C₈	—	4	1	no	—
228	C₅×C₈	—	4	2	no	—
229	C₅×C₈	—	4	2	no	—
230	C₅×C₈	#137	1	2	yes	—
231	C₅×C₈	#137	1	2	yes	—
232	C₂×#41	C₅×D₄	1	1	yes	characteristic
233	C₂×Q₁₆	—	2	2	no	—
234	C₂×SD₁₆	—	2	2	no	—
235	C₂×M₁₆	—	2	1	no	—
236	C₂×M₁₆	—	2	1	no	—
237	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
238	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
239	C₄⋊Q₈	C₂³×C₅	1	2	yes	—
240	C₄⋊Q₈	C₂³×C₅	1	2	yes	—
241	#125	—	2	2	no	—
242	C₂²⋊Q₈	—	2	2	no	—
243	C₂²⋊Q₈	—	2	2	no	—
244	C₄×Q₈	—	2	2	no	—
245	C₄×Q₈	—	2	2	no	—
246	C₄×Q₈	C₅×D₄	1	1	yes	characteristic
247	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
248	C₄×D₄	—	2	1	no	—
249	C₄×D₄	—	2	1	no	—
250	C₄×D₄	C₅×D₄	1	1	yes	characteristic
251	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
252	#117	—	2	1	no	—
253	#117	—	2	2	no	—
254	#117	C₅×D₄	1	1	yes	characteristic
255	C₂×C₄²	—	2	1	no	—
256	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
257	#107	—	2	1	no	—
258	#107	—	2	1	no	—
259	#107	—	2	1	no	—
260	#107	—	2	1	no	—
261	#107	—	2	2	no	—
262	#106	—	2	2	no	—
263	#106	—	2	2	no	—
264	#106	—	2	2	no	—
265	C₄⋊C₈	—	2	1	no	—
266	C₄⋊C₈	—	2	1	no	—
267	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
268	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
269	C₄⋊C₈	C₂³×C₅	1	2	yes	—
270	C₄⋊C₈	C₂³×C₅	1	2	yes	—
271	#103	—	2	2	no	—
272	#103	—	2	2	no	—
273	#103	—	2	2	no	—
274	#102	—	2	2	no	—
275	C₂²⋊C₈	—	2	1	no	—
276	C₂²⋊C₈	—	2	2	no	—
277	C₂²⋊C₈	—	2	1	no	—
278	C₂²⋊C₈	—	2	1	no	—
279	#97	—	2	1	no	—
280	#97	—	2	1	no	—
281	#97	—	2	2	no	—
282	C₄×C₈	—	2	1	no	—
283	C₄×C₈	C₅×D₄	1	1	yes	characteristic
284	C₄×C₈	C₅×D₄	1	1	yes	characteristic
285	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
286	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
287	C₂²×C₅	—	2	1	no	—
288	C₂²×C₅	—	2	1	no	—
289	C₂²×C₅	—	2	1	no	—
290	C₂²×C₅	—	4	1	no	—
291	C₂²×C₅	—	4	1	no	—
292	C₂²×C₅	—	4	1	no	—
293	C₂²×C₅	C₂×#121	1	1	yes	characteristic
294	C₄×C₅	—	2	1	no	—
295	C₄×C₅	—	2	1	no	—
296	C₄×C₅	—	2	1	no	—
297	C₄×C₅	—	2	1	no	—
298	C₄×C₅	—	4	1	no	—
299	C₄×C₅	—	4	1	no	—
300	C₄×C₅	—	4	1	no	—
301	C₄×C₅	—	8	2	no	—
302	C₄×C₅	—	8	2	no	—
303	C₄×C₅	C₂×#137	1	1	yes	characteristic
304	C₄×C₅	C₂×#137	1	1	yes	characteristic
305	C₄×C₅	#575	1	2	yes	—
306	#41	—	4	2	no	—
307	C₂×Q₈	—	2	2	no	—
308	C₂×Q₈	—	2	2	no	—
309	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
310	C₂×D₄	—	2	1	no	—
311	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
312	C₂²×C₄	—	2	1	no	—
313	C₂²×C₄	—	2	1	no	—
314	C₂²×C₄	—	2	1	no	—
315	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
316	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
317	C₂²×C₄	C₅×#41	1	1	yes	characteristic
318	Q₁₆	—	4	4	no	—
319	SD₁₆	—	4	4	no	—
320	M₁₆	—	4	2	no	—
321	M₁₆	—	4	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	—	2	2	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
329	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
330	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
331	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
332	C₄⋊C₄	—	2	1	no	—
333	C₄⋊C₄	—	2	1	no	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	2	2	no	—
338	C₄⋊C₄	—	4	2	no	—
339	C₄⋊C₄	—	4	2	no	—
340	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
341	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
342	C₂²⋊C₄	—	2	1	no	—
343	C₂²⋊C₄	—	2	1	no	—
344	C₂²⋊C₄	—	2	1	no	—
345	C₂²⋊C₄	—	4	2	no	—
346	C₄²	—	2	1	no	—
347	C₄²	—	2	1	no	—
348	C₄²	—	2	1	no	—
349	C₄²	—	4	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	—	8	1	no	—
356	C₂×C₅	#3039	1	1	yes	characteristic
357	C₂×C₅	#3054	1	1	yes	characteristic
358	C₂×C₅	#3067	1	1	yes	characteristic
359	C₂³	—	2	1	no	—
360	C₂³	C₅×#121	1	1	yes	characteristic
361	Q₈	—	2	2	no	—
362	Q₈	—	4	2	no	—
363	Q₈	—	4	2	no	—
364	Q₈	—	8	2	no	—
365	D₄	—	2	2	no	—
366	D₄	—	4	2	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	4	1	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	1	no	—
377	C₂×C₄	—	4	1	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	C₅×#121	1	1	yes	characteristic
381	C₂×C₄	C₅×#121	1	1	yes	characteristic
382	C₂×C₄	C₅×#121	1	1	yes	characteristic
383	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
384	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
385	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
386	C₈	—	2	1	no	—
387	C₈	—	2	1	no	—
388	C₈	—	4	1	no	—
389	C₈	—	4	1	no	—
390	C₈	—	4	2	no	—
391	C₈	—	4	2	no	—
392	C₈	C₅×#137	1	2	yes	—
393	C₈	C₅×#137	1	2	yes	—
394	C₅	#19298	1	1	yes	characteristic, direct product factor, Sylow
395	C₂²	—	2	1	no	—
396	C₂²	—	2	1	no	—
397	C₂²	—	2	1	no	—
398	C₂²	—	4	1	no	—
399	C₂²	—	4	1	no	—
400	C₂²	—	4	1	no	—
401	C₂²	C₂×C₅×#121	1	1	yes	characteristic
402	C₄	—	2	1	no	—
403	C₄	—	2	1	no	—
404	C₄	—	2	1	no	—
405	C₄	—	2	1	no	—
406	C₄	—	4	1	no	—
407	C₄	—	4	1	no	—
408	C₄	—	4	1	no	—
409	C₄	—	8	2	no	—
410	C₄	—	8	2	no	—
411	C₄	C₂×C₅×#137	1	1	yes	characteristic
412	C₄	C₂×C₅×#137	1	1	yes	characteristic
413	C₄	C₅×#575	1	2	yes	—
414	C₂	—	4	1	no	—
415	C₂	—	8	1	no	—
416	C₂	C₅×#3039	1	1	yes	characteristic
417	C₂	C₅×#3054	1	1	yes	characteristic
418	C₂	C₅×#3067	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₅
prime radical	C₂×C₅×#41	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×#3160	C₂	semidirect
4. C₅×#1696	C₂	semidirect
5. C₅×#1695	C₂	semidirect
6. C₅×#1694	C₂	semidirect
7. C₅×#1693	C₂	semidirect
8. C₅×#1692	C₂	semidirect
9. C₅×#1691	C₂	semidirect
10. C₅×#1568	C₂	semidirect
11. C₅×#1554	C₂	semidirect
47. #19298	C₅	direct (N × H)
103. #3160	C₂×C₅	semidirect
106. #1696	C₂×C₅	semidirect
107. #1695	C₂×C₅	semidirect
108. #1694	C₂×C₅	semidirect
109. #1693	C₂×C₅	semidirect
110. #1692	C₂×C₅	semidirect
111. #1691	C₂×C₅	semidirect
112. #1568	C₂×C₅	semidirect
113. #1554	C₂×C₅	semidirect
394. C₅	#19298	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×#3160	2
C₅×#3116	2
C₅×#2965	2
C₅×#1696	2
C₅×#1695	2
C₅×#1694	2
C₅×#1693	2
C₅×#1692	2
C₅×#1691	2
C₅×#1568	2
C₅×#1554	2
#19298	5

Subgroups — C5×#19298 #11942018

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#19298 #11942018