Subgroups — C₅×#19214 #11941934

Order 1280.

658 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3209	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#3208	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#486	C₂	1	1	yes	maximal, characteristic
4	C₅×#2960	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1702	C₂	1	4	yes	maximal, complemented
6	C₅×#1682	C₂	1	4	yes	maximal, complemented
7	C₅×#1564	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1549	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1545	C₂	1	1	yes	maximal, characteristic
10	C₅×#533	C₂²	1	1	yes	characteristic
11	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
12	C₂×C₅×#127	C₂²	1	1	yes	characteristic
13	C₅×#494	—	2	1	no	—
14	C₅×#492	—	2	1	no	—
15	C₅×#487	—	2	1	no	—
16	C₅×#486	—	2	1	no	—
17	C₅×#486	—	2	1	no	—
18	C₅×#486	—	2	1	no	—
19	C₅×#486	C₂²	1	2	yes	—
20	C₅×#486	C₂²	1	2	yes	—
21	C₅×#462	C₂²	1	4	yes	complemented
22	C₅×#460	C₂²	1	4	yes	—
23	C₅×#451	—	2	2	no	—
24	C₅×#450	—	2	2	no	—
25	C₅×#446	—	2	1	no	—
26	C₅×#446	C₂²	1	2	yes	complemented
27	C₅×C₈×Q₈	—	2	1	no	—
28	C₅×C₈×Q₈	C₂²	1	2	yes	complemented
29	C₅×#431	C₂²	1	1	yes	characteristic
30	C₅×#431	C₂²	1	1	yes	characteristic
31	C₅×#424	—	2	1	no	—
32	C₅×#423	C₂²	1	1	yes	characteristic
33	C₂×C₅×#102	—	2	1	no	—
34	C₂×C₅×#102	—	2	1	no	—
35	C₅×#405	—	2	1	no	—
36	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
37	C₅×#335	C₂²	1	2	yes	complemented
38	C₅×#334	C₂²	1	2	yes	complemented
39	C₅×#332	C₂²	1	4	yes	complemented
40	C₅×#331	C₂²	1	4	yes	—
41	#19214	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
42	C₂²×C₅×Q₈	—	2	1	no	—
43	C₂²×C₅×D₄	—	2	1	no	—
44	C₂²×C₅×D₄	—	2	1	no	—
45	C₂²×C₅×D₄	—	2	1	no	—
46	C₂×C₅×Q₁₆	—	2	4	no	—
47	C₂×C₅×SD₁₆	—	2	4	no	—
48	C₂×C₅×M₁₆	—	2	1	no	—
49	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
50	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
51	C₅×C₄⋊Q₈	—	2	1	no	—
52	C₅×C₄⋊Q₈	—	2	1	no	—
53	C₅×C₄⋊Q₈	—	2	1	no	—
54	C₅×C₄⋊Q₈	D₄	1	1	yes	characteristic
55	C₅×C₄⋊Q₈	D₄	1	1	yes	characteristic
56	C₅×C₄⋊Q₈	C₂³	1	2	yes	—
57	C₅×#127	—	2	1	no	—
58	C₅×#127	—	2	1	no	—
59	C₅×#127	—	2	1	no	—
60	C₅×#127	C₂³	1	2	yes	—
61	C₅×#125	—	2	1	no	—
62	C₅×C₂²⋊Q₈	—	2	1	no	—
63	C₅×C₂²⋊Q₈	D₄	1	2	yes	—
64	C₄×C₅×Q₈	—	2	1	no	—
65	C₄×C₅×Q₈	C₂³	1	2	yes	—
66	C₅×#117	—	2	1	no	—
67	C₂×C₅×C₄⋊C₄	—	2	1	no	—
68	C₂×C₅×C₄⋊C₄	—	2	1	no	—
69	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
70	C₅×C₄⋊C₈	—	2	2	no	—
71	C₅×C₄⋊C₈	—	2	2	no	—
72	C₅×C₄⋊C₈	—	2	1	no	—
73	C₅×C₄⋊C₈	C₂³	1	2	yes	—
74	C₅×C₄⋊C₈	C₂³	1	2	yes	—
75	C₅×C₄⋊C₈	C₂³	1	2	yes	—
76	C₅×#103	—	2	4	no	—
77	C₅×#102	—	2	2	no	—
78	C₅×#102	—	2	2	no	—
79	C₅×#102	—	2	2	no	—
80	C₅×#102	—	2	2	no	—
81	C₅×#102	—	2	4	no	—
82	C₅×C₂²⋊C₈	—	2	1	no	—
83	C₅×C₂²⋊C₈	—	2	1	no	—
84	C₅×#97	—	2	2	no	—
85	C₄×C₅×C₈	—	2	2	no	—
86	C₄×C₅×C₈	—	2	1	no	—
87	C₄×C₅×C₈	—	2	1	no	—
88	C₄×C₅×C₈	D₄	1	1	yes	characteristic
89	C₄×C₅×C₈	D₄	1	1	yes	characteristic
90	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
91	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
92	#3209	C₂×C₅	1	1	yes	characteristic, complemented
93	#3208	C₂×C₅	1	1	yes	characteristic
94	C₂×#486	C₂×C₅	1	1	yes	characteristic
95	#2960	C₂×C₅	1	1	yes	characteristic, complemented
96	#1702	C₂×C₅	1	4	yes	complemented
97	#1682	C₂×C₅	1	4	yes	complemented
98	#1564	C₂×C₅	1	1	yes	characteristic, complemented
99	#1549	C₂×C₅	1	1	yes	characteristic, complemented
100	#1545	C₂×C₅	1	1	yes	characteristic
101	C₂⁴×C₅	—	4	1	no	—
102	C₂×C₅×Q₈	—	2	1	no	—
103	C₂×C₅×Q₈	—	2	2	no	—
104	C₂×C₅×Q₈	—	4	1	no	—
105	C₂×C₅×Q₈	—	8	2	no	—
106	C₂×C₅×Q₈	C₂×D₄	1	2	yes	—
107	C₂×C₅×D₄	—	2	2	no	—
108	C₂×C₅×D₄	—	2	2	no	—
109	C₂×C₅×D₄	—	2	2	no	—
110	C₂×C₅×D₄	—	4	1	no	—
111	C₂×C₅×D₄	—	4	1	no	—
112	C₂×C₅×D₄	—	4	1	no	—
113	C₂×C₅×D₄	—	4	2	no	—
114	C₂×C₅×D₄	—	4	2	no	—
115	C₂×C₅×D₄	—	8	2	no	—
116	C₂×C₅×D₄	—	8	2	no	—
117	C₂²×C₄×C₅	—	4	1	no	—
118	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₅	#41	1	1	yes	characteristic
121	C₅×Q₁₆	—	8	4	no	—
122	C₅×SD₁₆	—	8	4	no	—
123	C₅×M₁₆	—	4	2	no	—
124	C₂×C₅×C₈	—	2	2	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	—	2	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	2	no	—
137	C₅×C₄⋊C₄	—	2	2	no	—
138	C₅×C₄⋊C₄	—	2	2	no	—
139	C₅×C₄⋊C₄	—	2	2	no	—
140	C₅×C₄⋊C₄	—	4	1	no	—
141	C₅×C₄⋊C₄	—	4	1	no	—
142	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
143	C₅×C₂²⋊C₄	—	2	2	no	—
144	C₄²×C₅	—	2	2	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	#533	C₂²×C₅	1	1	yes	characteristic
150	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
151	C₂×#127	C₂²×C₅	1	1	yes	characteristic
152	#494	—	2	1	no	—
153	#492	—	2	1	no	—
154	#487	—	2	1	no	—
155	#486	—	2	1	no	—
156	#486	—	2	1	no	—
157	#486	—	2	1	no	—
158	#486	C₂²×C₅	1	2	yes	—
159	#486	C₂²×C₅	1	2	yes	—
160	#462	C₂²×C₅	1	4	yes	complemented
161	#460	C₂²×C₅	1	4	yes	—
162	#451	—	2	2	no	—
163	#450	—	2	2	no	—
164	#446	—	2	1	no	—
165	#446	C₂²×C₅	1	2	yes	complemented
166	C₈×Q₈	—	2	1	no	—
167	C₈×Q₈	C₂²×C₅	1	2	yes	complemented
168	#431	C₂²×C₅	1	1	yes	characteristic
169	#431	C₂²×C₅	1	1	yes	characteristic
170	#424	—	2	1	no	—
171	#423	C₂²×C₅	1	1	yes	characteristic
172	C₂×#102	—	2	1	no	—
173	C₂×#102	—	2	1	no	—
174	#405	—	2	1	no	—
175	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
176	#335	C₂²×C₅	1	2	yes	complemented
177	#334	C₂²×C₅	1	2	yes	complemented
178	#332	C₂²×C₅	1	4	yes	complemented
179	#331	C₂²×C₅	1	4	yes	—
180	C₂³×C₅	—	4	2	no	—
181	C₂³×C₅	—	8	2	no	—
182	C₂³×C₅	—	8	2	no	—
183	C₂³×C₅	—	8	2	no	—
184	C₂³×C₅	#121	1	1	yes	characteristic
185	C₅×Q₈	—	2	4	no	—
186	C₅×Q₈	—	4	2	no	—
187	C₅×Q₈	—	4	4	no	—
188	C₅×Q₈	—	8	2	no	—
189	C₅×D₄	—	4	2	no	—
190	C₅×D₄	—	4	2	no	—
191	C₅×D₄	—	4	4	no	—
192	C₅×D₄	—	8	2	no	—
193	C₅×D₄	—	8	2	no	—
194	C₅×D₄	—	8	2	no	—
195	C₅×D₄	—	8	2	no	—
196	C₂×C₄×C₅	—	2	2	no	—
197	C₂×C₄×C₅	—	2	2	no	—
198	C₂×C₄×C₅	—	2	2	no	—
199	C₂×C₄×C₅	—	2	2	no	—
200	C₂×C₄×C₅	—	4	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	#135	1	2	yes	—
206	C₂×C₄×C₅	#137	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	1	no	—
211	C₅×C₈	—	2	1	no	—
212	C₅×C₈	—	2	1	no	—
213	C₅×C₈	—	2	1	no	—
214	C₅×C₈	—	4	2	no	—
215	C₅×C₈	—	4	2	no	—
216	C₅×C₈	—	4	2	no	—
217	C₂²×Q₈	—	2	1	no	—
218	C₂²×D₄	—	2	1	no	—
219	C₂²×D₄	—	2	1	no	—
220	C₂²×D₄	—	2	1	no	—
221	C₂×Q₁₆	—	2	4	no	—
222	C₂×SD₁₆	—	2	4	no	—
223	C₂×M₁₆	—	2	1	no	—
224	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
225	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
226	C₄⋊Q₈	—	2	1	no	—
227	C₄⋊Q₈	—	2	1	no	—
228	C₄⋊Q₈	—	2	1	no	—
229	C₄⋊Q₈	C₅×D₄	1	1	yes	characteristic
230	C₄⋊Q₈	C₅×D₄	1	1	yes	characteristic
231	C₄⋊Q₈	C₂³×C₅	1	2	yes	—
232	#127	—	2	1	no	—
233	#127	—	2	1	no	—
234	#127	—	2	1	no	—
235	#127	C₂³×C₅	1	2	yes	—
236	#125	—	2	1	no	—
237	C₂²⋊Q₈	—	2	1	no	—
238	C₂²⋊Q₈	C₅×D₄	1	2	yes	—
239	C₄×Q₈	—	2	1	no	—
240	C₄×Q₈	C₂³×C₅	1	2	yes	—
241	#117	—	2	1	no	—
242	C₂×C₄⋊C₄	—	2	1	no	—
243	C₂×C₄⋊C₄	—	2	1	no	—
244	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
245	C₄⋊C₈	—	2	2	no	—
246	C₄⋊C₈	—	2	2	no	—
247	C₄⋊C₈	—	2	1	no	—
248	C₄⋊C₈	C₂³×C₅	1	2	yes	—
249	C₄⋊C₈	C₂³×C₅	1	2	yes	—
250	C₄⋊C₈	C₂³×C₅	1	2	yes	—
251	#103	—	2	4	no	—
252	#102	—	2	2	no	—
253	#102	—	2	2	no	—
254	#102	—	2	2	no	—
255	#102	—	2	2	no	—
256	#102	—	2	4	no	—
257	C₂²⋊C₈	—	2	1	no	—
258	C₂²⋊C₈	—	2	1	no	—
259	#97	—	2	2	no	—
260	C₄×C₈	—	2	2	no	—
261	C₄×C₈	—	2	1	no	—
262	C₄×C₈	—	2	1	no	—
263	C₄×C₈	C₅×D₄	1	1	yes	characteristic
264	C₄×C₈	C₅×D₄	1	1	yes	characteristic
265	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
266	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
267	C₂²×C₅	—	2	1	no	—
268	C₂²×C₅	—	2	1	no	—
269	C₂²×C₅	—	8	2	no	—
270	C₂²×C₅	—	8	2	no	—
271	C₂²×C₅	—	8	2	no	—
272	C₂²×C₅	—	16	4	no	—
273	C₂²×C₅	#464	1	2	yes	—
274	C₂²×C₅	C₂×#121	1	1	yes	characteristic
275	C₄×C₅	—	2	1	no	—
276	C₄×C₅	—	2	1	no	—
277	C₄×C₅	—	4	2	no	—
278	C₄×C₅	—	4	2	no	—
279	C₄×C₅	—	8	2	no	—
280	C₄×C₅	#464	1	2	yes	—
281	C₄×C₅	#471	1	2	yes	—
282	C₄×C₅	C₂×#135	1	1	yes	characteristic
283	C₄×C₅	C₂×#137	1	1	yes	characteristic
284	C₄×C₅	#576	1	2	yes	—
285	C₂⁴	—	4	1	no	—
286	C₂×Q₈	—	2	1	no	—
287	C₂×Q₈	—	2	2	no	—
288	C₂×Q₈	—	4	1	no	—
289	C₂×Q₈	—	8	2	no	—
290	C₂×Q₈	C₂×C₅×D₄	1	2	yes	—
291	C₂×D₄	—	2	2	no	—
292	C₂×D₄	—	2	2	no	—
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	—	4	1	no	—
295	C₂×D₄	—	4	1	no	—
296	C₂×D₄	—	4	1	no	—
297	C₂×D₄	—	4	2	no	—
298	C₂×D₄	—	4	2	no	—
299	C₂×D₄	—	8	2	no	—
300	C₂×D₄	—	8	2	no	—
301	C₂²×C₄	—	4	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	Q₁₆	—	8	4	no	—
306	SD₁₆	—	8	4	no	—
307	M₁₆	—	4	2	no	—
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
314	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
315	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
316	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
317	C₄⋊C₄	—	2	1	no	—
318	C₄⋊C₄	—	2	1	no	—
319	C₄⋊C₄	—	2	1	no	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	2	2	no	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	4	1	no	—
325	C₄⋊C₄	—	4	1	no	—
326	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
327	C₂²⋊C₄	—	2	2	no	—
328	C₄²	—	2	2	no	—
329	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
330	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
331	C₄²	C₅×#41	1	1	yes	characteristic
332	C₄²	C₂⁴×C₅	1	1	yes	characteristic
333	C₂×C₅	—	2	2	no	—
334	C₂×C₅	—	16	2	no	—
335	C₂×C₅	C₂×#464	1	1	yes	characteristic
336	C₂×C₅	#3058	1	1	yes	characteristic
337	C₂×C₅	C₂×#471	1	1	yes	characteristic
338	C₂³	—	4	2	no	—
339	C₂³	—	8	2	no	—
340	C₂³	—	8	2	no	—
341	C₂³	—	8	2	no	—
342	C₂³	C₅×#121	1	1	yes	characteristic
343	Q₈	—	2	4	no	—
344	Q₈	—	4	2	no	—
345	Q₈	—	4	4	no	—
346	Q₈	—	8	2	no	—
347	D₄	—	4	2	no	—
348	D₄	—	4	2	no	—
349	D₄	—	4	4	no	—
350	D₄	—	8	2	no	—
351	D₄	—	8	2	no	—
352	D₄	—	8	2	no	—
353	D₄	—	8	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	8	2	no	—
360	C₂×C₄	C₅×#121	1	1	yes	characteristic
361	C₂×C₄	C₅×#121	1	1	yes	characteristic
362	C₂×C₄	C₅×#121	1	1	yes	characteristic
363	C₂×C₄	C₅×#135	1	2	yes	—
364	C₂×C₄	C₅×#137	1	2	yes	—
365	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
366	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
367	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
368	C₈	—	2	1	no	—
369	C₈	—	2	1	no	—
370	C₈	—	2	1	no	—
371	C₈	—	2	1	no	—
372	C₈	—	4	2	no	—
373	C₈	—	4	2	no	—
374	C₈	—	4	2	no	—
375	C₅	#19214	1	1	yes	characteristic, direct product factor, Sylow
376	C₂²	—	2	1	no	—
377	C₂²	—	2	1	no	—
378	C₂²	—	8	2	no	—
379	C₂²	—	8	2	no	—
380	C₂²	—	8	2	no	—
381	C₂²	—	16	4	no	—
382	C₂²	C₅×#464	1	2	yes	—
383	C₂²	C₂×C₅×#121	1	1	yes	characteristic
384	C₄	—	2	1	no	—
385	C₄	—	2	1	no	—
386	C₄	—	4	2	no	—
387	C₄	—	4	2	no	—
388	C₄	—	8	2	no	—
389	C₄	C₅×#464	1	2	yes	—
390	C₄	C₅×#471	1	2	yes	—
391	C₄	C₂×C₅×#135	1	1	yes	characteristic
392	C₄	C₂×C₅×#137	1	1	yes	characteristic
393	C₄	C₅×#576	1	2	yes	—
394	C₂	—	2	2	no	—
395	C₂	—	16	2	no	—
396	C₂	C₂×C₅×#464	1	1	yes	characteristic
397	C₂	C₅×#3058	1	1	yes	characteristic
398	C₂	C₂×C₅×#471	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₅
prime radical	C₂×C₅×#127	C₂²
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×#3209	C₂	semidirect
4. C₅×#2960	C₂	semidirect
5. C₅×#1702	C₂	semidirect
6. C₅×#1682	C₂	semidirect
7. C₅×#1564	C₂	semidirect
8. C₅×#1549	C₂	semidirect
21. C₅×#462	C₂²	semidirect
26. C₅×#446	C₂²	semidirect
28. C₅×C₈×Q₈	C₂²	semidirect
37. C₅×#335	C₂²	semidirect
38. C₅×#334	C₂²	semidirect
39. C₅×#332	C₂²	semidirect
41. #19214	C₅	direct (N × H)
92. #3209	C₂×C₅	semidirect
95. #2960	C₂×C₅	semidirect
96. #1702	C₂×C₅	semidirect
97. #1682	C₂×C₅	semidirect
98. #1564	C₂×C₅	semidirect
99. #1549	C₂×C₅	semidirect
160. #462	C₂²×C₅	semidirect
165. #446	C₂²×C₅	semidirect
167. C₈×Q₈	C₂²×C₅	semidirect
176. #335	C₂²×C₅	semidirect
177. #334	C₂²×C₅	semidirect
178. #332	C₂²×C₅	semidirect
375. C₅	#19214	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×#3209	2
C₅×#3208	2
C₂×C₅×#486	2
C₅×#2960	2
C₅×#1702	2
C₅×#1682	2
C₅×#1564	2
C₅×#1549	2
C₅×#1545	2
#19214	5

Subgroups — C5×#19214 #11941934

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#19214 #11941934