Subgroups — C₅×#17798 #11940518

Order 1280.

666 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2989	C₂	1	2	yes	maximal
2	C₄×C₅×#131	C₂	1	1	yes	maximal, characteristic
3	C₅×#1569	C₂	1	4	yes	maximal, complemented
4	C₅×#1568	C₂	1	2	yes	maximal, complemented
5	C₅×#1566	C₂	1	2	yes	maximal, complemented
6	C₅×#1565	C₂	1	2	yes	maximal, complemented
7	C₅×#1564	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅×#334	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅×#131	C₄	1	1	yes	characteristic
10	C₂×C₅×#131	C₄	1	1	yes	characteristic
11	C₄×C₅×#41	C₂²	1	1	yes	characteristic
12	C₅×#446	—	2	2	no	—
13	C₅×#436	—	2	2	no	—
14	C₅×#435	—	2	4	no	—
15	C₅×#432	C₂²	1	4	yes	—
16	C₅×#431	C₂²	1	2	yes	—
17	C₅×#423	C₂²	1	4	yes	—
18	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
19	C₅×#405	C₄	1	2	yes	—
20	C₅×#405	C₄	1	2	yes	—
21	C₅×#405	C₄	1	1	yes	characteristic
22	C₅×#405	C₄	1	1	yes	characteristic
23	C₄×C₅×M₁₆	C₂²	1	1	yes	characteristic
24	C₄×C₅×M₁₆	C₂²	1	2	yes	—
25	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
27	C₅×#335	C₂²	1	2	yes	—
28	C₅×#335	C₂²	1	4	yes	—
29	C₅×#334	C₂²	1	2	yes	—
30	C₅×#334	C₂²	1	2	yes	—
31	C₅×#334	C₂²	1	1	yes	characteristic
32	C₅×#334	C₂²	1	1	yes	characteristic
33	C₅×#334	C₂²	1	4	yes	—
34	#17798	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
35	C₂×C₅×#41	C₂×C₄	1	1	yes	characteristic
36	C₅×#131	—	2	4	no	—
37	C₅×#131	—	2	4	no	—
38	C₂×C₅×M₁₆	—	2	4	no	—
39	C₂×C₅×M₁₆	C₂×C₄	1	1	yes	characteristic
40	C₂×C₅×M₁₆	C₂×C₄	1	2	yes	—
41	C₂×C₅×M₁₆	C₂×C₄	1	2	yes	—
42	C₂×C₅×M₁₆	C₂×C₄	1	1	yes	characteristic
43	C₂²×C₅×C₈	—	2	2	no	—
44	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
46	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
47	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
48	C₄×C₅×Q₈	D₄	1	1	yes	characteristic
49	C₄×C₅×Q₈	Q₈	1	1	yes	characteristic
50	C₄×C₅×D₄	D₄	1	2	yes	—
51	C₄×C₅×D₄	D₄	1	1	yes	characteristic
52	C₄×C₅×D₄	Q₈	1	2	yes	—
53	C₄×C₅×D₄	Q₈	1	1	yes	characteristic
54	C₅×#117	C₂×C₄	1	2	yes	—
55	C₅×#117	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
57	C₂×C₄²×C₅	C₂³	1	2	yes	—
58	C₅×C₄⋊C₈	—	2	2	no	—
59	C₅×C₄⋊C₈	—	2	4	no	—
60	C₅×C₄⋊C₈	C₂³	1	4	yes	—
61	C₅×C₄⋊C₈	C₂³	1	2	yes	—
62	C₅×C₄⋊C₈	C₂³	1	2	yes	—
63	C₅×C₂²⋊C₈	—	2	2	no	—
64	C₅×C₂²⋊C₈	—	2	4	no	—
65	C₅×#97	—	2	4	no	—
66	C₅×#97	C₂×C₄	1	2	yes	—
67	C₅×#97	C₂×C₄	1	2	yes	—
68	C₅×#97	C₂×C₄	1	2	yes	—
69	C₄×C₅×C₈	—	2	2	no	—
70	C₄×C₅×C₈	C₂×C₄	1	2	yes	—
71	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
72	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
73	C₄×C₅×C₈	C₂×C₄	1	2	yes	—
74	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
75	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
76	C₄×C₅×C₈	C₂³	1	2	yes	—
77	#2989	C₂×C₅	1	2	yes	—
78	C₄×#131	C₂×C₅	1	1	yes	characteristic
79	#1569	C₂×C₅	1	4	yes	complemented
80	#1568	C₂×C₅	1	2	yes	complemented
81	#1566	C₂×C₅	1	2	yes	complemented
82	#1565	C₂×C₅	1	2	yes	complemented
83	#1564	C₂×C₅	1	1	yes	characteristic, complemented
84	C₂×#334	C₂×C₅	1	1	yes	characteristic, complemented
85	C₅×#41	—	2	2	no	—
86	C₅×#41	—	2	2	no	—
87	C₂×C₅×Q₈	C₄⋊C₄	1	1	yes	characteristic
88	C₂×C₅×D₄	C₄⋊C₄	1	2	yes	—
89	C₂×C₅×D₄	C₄⋊C₄	1	1	yes	characteristic
90	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
91	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
94	C₂²×C₄×C₅	C₂×Q₈	1	2	yes	—
95	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
96	C₅×M₁₆	—	2	2	no	—
97	C₅×M₁₆	—	2	4	no	—
98	C₅×M₁₆	—	2	4	no	—
99	C₅×M₁₆	—	8	4	no	—
100	C₅×M₁₆	M₁₆	1	4	yes	complemented
101	C₂×C₅×C₈	—	2	2	no	—
102	C₂×C₅×C₈	—	2	4	no	—
103	C₂×C₅×C₈	—	2	4	no	—
104	C₂×C₅×C₈	—	2	4	no	—
105	C₂×C₅×C₈	—	2	2	no	—
106	C₂×C₅×C₈	—	2	2	no	—
107	C₂×C₅×C₈	—	8	2	no	—
108	C₂×C₅×C₈	M₁₆	1	4	yes	complemented
109	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
111	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
112	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
114	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
115	C₅×C₄⋊C₄	C₄⋊C₄	1	2	yes	—
116	C₅×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
117	C₅×C₄⋊C₄	C₄⋊C₄	1	2	yes	—
118	C₅×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
119	C₅×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
120	C₅×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
121	C₅×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
122	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
123	C₄²×C₅	C₂²×C₄	1	2	yes	—
124	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
125	C₄²×C₅	C₂×D₄	1	2	yes	—
126	C₄²×C₅	C₂×Q₈	1	2	yes	—
127	C₄²×C₅	C₂×Q₈	1	1	yes	characteristic
128	C₄²×C₅	C₂⁴	1	1	yes	characteristic
129	C₂×#131	C₄×C₅	1	1	yes	characteristic
130	C₂×#131	C₄×C₅	1	1	yes	characteristic
131	C₄×#41	C₂²×C₅	1	1	yes	characteristic
132	#446	—	2	2	no	—
133	#436	—	2	2	no	—
134	#435	—	2	4	no	—
135	#432	C₂²×C₅	1	4	yes	—
136	#431	C₂²×C₅	1	2	yes	—
137	#423	C₂²×C₅	1	4	yes	—
138	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
139	#405	C₄×C₅	1	1	yes	characteristic
140	#405	C₄×C₅	1	2	yes	—
141	#405	C₄×C₅	1	2	yes	—
142	#405	C₄×C₅	1	1	yes	characteristic
143	C₄×M₁₆	C₂²×C₅	1	1	yes	characteristic
144	C₄×M₁₆	C₂²×C₅	1	2	yes	—
145	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
146	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
147	#335	C₂²×C₅	1	2	yes	—
148	#335	C₂²×C₅	1	4	yes	—
149	#334	C₂²×C₅	1	2	yes	—
150	#334	C₂²×C₅	1	2	yes	—
151	#334	C₂²×C₅	1	1	yes	characteristic
152	#334	C₂²×C₅	1	1	yes	characteristic
153	#334	C₂²×C₅	1	4	yes	—
154	C₂³×C₅	C₂×C₄⋊C₄	1	2	yes	—
155	C₂³×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
156	C₅×Q₈	—	2	2	no	—
157	C₅×D₄	—	2	4	no	—
158	C₅×D₄	—	2	2	no	—
159	C₂×C₄×C₅	—	2	2	no	—
160	C₂×C₄×C₅	—	2	2	no	—
161	C₂×C₄×C₅	—	2	2	no	—
162	C₂×C₄×C₅	—	2	4	no	—
163	C₂×C₄×C₅	—	4	1	no	—
164	C₂×C₄×C₅	—	4	2	no	—
165	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
166	C₂×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
167	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
168	C₂×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
169	C₂×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
170	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
171	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
172	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
173	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
174	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
175	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
176	C₅×C₈	—	2	1	no	—
177	C₅×C₈	—	2	1	no	—
178	C₅×C₈	—	2	2	no	—
179	C₅×C₈	—	4	2	no	—
180	C₅×C₈	—	4	4	no	—
181	C₅×C₈	—	4	2	no	—
182	C₅×C₈	C₂×M₁₆	1	2	yes	—
183	C₅×C₈	C₂×M₁₆	1	4	yes	—
184	C₅×C₈	C₂×M₁₆	1	2	yes	—
185	C₂×#41	C₂×C₄×C₅	1	1	yes	characteristic
186	#131	—	2	4	no	—
187	#131	—	2	4	no	—
188	C₂×M₁₆	—	2	4	no	—
189	C₂×M₁₆	C₂×C₄×C₅	1	1	yes	characteristic
190	C₂×M₁₆	C₂×C₄×C₅	1	2	yes	—
191	C₂×M₁₆	C₂×C₄×C₅	1	2	yes	—
192	C₂×M₁₆	C₂×C₄×C₅	1	1	yes	characteristic
193	C₂²×C₈	—	2	2	no	—
194	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
195	C₂²×C₈	C₂×C₄×C₅	1	2	yes	—
196	C₂²×C₈	C₂×C₄×C₅	1	2	yes	—
197	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
198	C₄×Q₈	C₅×D₄	1	1	yes	characteristic
199	C₄×Q₈	C₅×Q₈	1	1	yes	characteristic
200	C₄×D₄	C₅×D₄	1	2	yes	—
201	C₄×D₄	C₅×D₄	1	1	yes	characteristic
202	C₄×D₄	C₅×Q₈	1	2	yes	—
203	C₄×D₄	C₅×Q₈	1	1	yes	characteristic
204	#117	C₂×C₄×C₅	1	2	yes	—
205	#117	C₂×C₄×C₅	1	1	yes	characteristic
206	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
207	C₂×C₄²	C₂³×C₅	1	2	yes	—
208	C₄⋊C₈	—	2	2	no	—
209	C₄⋊C₈	—	2	4	no	—
210	C₄⋊C₈	C₂³×C₅	1	4	yes	—
211	C₄⋊C₈	C₂³×C₅	1	2	yes	—
212	C₄⋊C₈	C₂³×C₅	1	2	yes	—
213	C₂²⋊C₈	—	2	2	no	—
214	C₂²⋊C₈	—	2	4	no	—
215	#97	—	2	4	no	—
216	#97	C₂×C₄×C₅	1	2	yes	—
217	#97	C₂×C₄×C₅	1	2	yes	—
218	#97	C₂×C₄×C₅	1	2	yes	—
219	C₄×C₈	—	2	2	no	—
220	C₄×C₈	C₂×C₄×C₅	1	2	yes	—
221	C₄×C₈	C₂×C₄×C₅	1	1	yes	characteristic
222	C₄×C₈	C₂×C₄×C₅	1	1	yes	characteristic
223	C₄×C₈	C₂×C₄×C₅	1	2	yes	—
224	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
225	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
226	C₄×C₈	C₂³×C₅	1	2	yes	—
227	C₂²×C₅	—	2	1	no	—
228	C₂²×C₅	—	2	1	no	—
229	C₂²×C₅	—	2	2	no	—
230	C₂²×C₅	—	2	2	no	—
231	C₂²×C₅	—	2	2	no	—
232	C₂²×C₅	#423	1	2	yes	—
233	C₂²×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
234	C₄×C₅	—	2	2	no	—
235	C₄×C₅	—	2	1	no	—
236	C₄×C₅	—	2	2	no	—
237	C₄×C₅	—	2	1	no	—
238	C₄×C₅	—	2	1	no	—
239	C₄×C₅	—	2	2	no	—
240	C₄×C₅	#423	1	2	yes	—
241	C₄×C₅	C₂²×M₁₆	1	1	yes	characteristic
242	C₄×C₅	C₂²×M₁₆	1	1	yes	characteristic
243	C₄×C₅	#577	1	2	yes	—
244	#41	—	2	2	no	—
245	#41	—	2	2	no	—
246	C₂×Q₈	C₅×C₄⋊C₄	1	1	yes	characteristic
247	C₂×D₄	C₅×C₄⋊C₄	1	2	yes	—
248	C₂×D₄	C₅×C₄⋊C₄	1	1	yes	characteristic
249	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
250	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
251	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
252	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
253	C₂²×C₄	C₂×C₅×Q₈	1	2	yes	—
254	C₂²×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
255	M₁₆	—	2	2	no	—
256	M₁₆	—	2	4	no	—
257	M₁₆	—	2	4	no	—
258	M₁₆	—	8	4	no	—
259	M₁₆	C₅×M₁₆	1	4	yes	complemented
260	C₂×C₈	—	2	2	no	—
261	C₂×C₈	—	2	4	no	—
262	C₂×C₈	—	2	4	no	—
263	C₂×C₈	—	2	2	no	—
264	C₂×C₈	—	2	2	no	—
265	C₂×C₈	—	2	4	no	—
266	C₂×C₈	—	8	2	no	—
267	C₂×C₈	C₅×M₁₆	1	4	yes	complemented
268	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
269	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
270	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
271	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
272	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
273	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
274	C₄⋊C₄	C₅×C₄⋊C₄	1	2	yes	—
275	C₄⋊C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
276	C₄⋊C₄	C₅×C₄⋊C₄	1	2	yes	—
277	C₄⋊C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
278	C₂²⋊C₄	C₅×C₄⋊C₄	1	2	yes	—
279	C₂²⋊C₄	C₅×C₄⋊C₄	1	2	yes	—
280	C₂²⋊C₄	C₅×C₄⋊C₄	1	2	yes	—
281	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
282	C₄²	C₂²×C₄×C₅	1	2	yes	—
283	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
284	C₄²	C₂×C₅×D₄	1	2	yes	—
285	C₄²	C₂×C₅×Q₈	1	2	yes	—
286	C₄²	C₂×C₅×Q₈	1	1	yes	characteristic
287	C₄²	C₂⁴×C₅	1	1	yes	characteristic
288	C₂×C₅	—	2	2	no	—
289	C₂×C₅	—	4	2	no	—
290	C₂×C₅	C₂×#423	1	1	yes	characteristic
291	C₂×C₅	#2912	1	1	yes	characteristic
292	C₂×C₅	#2916	1	1	yes	characteristic
293	C₂³	C₂×C₅×C₄⋊C₄	1	2	yes	—
294	C₂³	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
295	Q₈	—	2	2	no	—
296	D₄	—	2	4	no	—
297	D₄	—	2	2	no	—
298	C₂×C₄	—	2	2	no	—
299	C₂×C₄	—	2	2	no	—
300	C₂×C₄	—	2	2	no	—
301	C₂×C₄	—	2	4	no	—
302	C₂×C₄	—	4	1	no	—
303	C₂×C₄	—	4	2	no	—
304	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
305	C₂×C₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
306	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
307	C₂×C₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
308	C₂×C₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
309	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
310	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
311	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
312	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
313	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
314	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
315	C₈	—	2	1	no	—
316	C₈	—	2	1	no	—
317	C₈	—	2	2	no	—
318	C₈	—	4	4	no	—
319	C₈	—	4	2	no	—
320	C₈	—	4	2	no	—
321	C₈	C₂×C₅×M₁₆	1	2	yes	—
322	C₈	C₂×C₅×M₁₆	1	4	yes	—
323	C₈	C₂×C₅×M₁₆	1	2	yes	—
324	C₅	#17798	1	1	yes	characteristic, direct product factor, Sylow
325	C₂²	—	2	1	no	—
326	C₂²	—	2	1	no	—
327	C₂²	—	2	2	no	—
328	C₂²	—	2	2	no	—
329	C₂²	—	2	2	no	—
330	C₂²	C₅×#423	1	2	yes	—
331	C₂²	C₂²×C₅×C₄⋊C₄	1	1	yes	characteristic
332	C₄	—	2	2	no	—
333	C₄	—	2	1	no	—
334	C₄	—	2	2	no	—
335	C₄	—	2	1	no	—
336	C₄	—	2	1	no	—
337	C₄	—	2	2	no	—
338	C₄	C₅×#423	1	2	yes	—
339	C₄	C₂²×C₅×M₁₆	1	1	yes	characteristic
340	C₄	C₂²×C₅×M₁₆	1	1	yes	characteristic
341	C₄	C₅×#577	1	2	yes	—
342	C₂	—	2	2	no	—
343	C₂	—	4	2	no	—
344	C₂	C₂×C₅×#423	1	1	yes	characteristic
345	C₂	C₅×#2912	1	1	yes	characteristic
346	C₂	C₅×#2916	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₄²	C₂⁴×C₅
socle	C₂²×C₅	C₂²×C₄⋊C₄
prime radical	C₂×C₅×#41	C₂×C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₄×C₅×#41 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
3. C₅×#1569	C₂	semidirect
4. C₅×#1568	C₂	semidirect
5. C₅×#1566	C₂	semidirect
6. C₅×#1565	C₂	semidirect
7. C₅×#1564	C₂	semidirect
8. C₂×C₅×#334	C₂	semidirect
34. #17798	C₅	direct (N × H)
79. #1569	C₂×C₅	semidirect
80. #1568	C₂×C₅	semidirect
81. #1566	C₂×C₅	semidirect
82. #1565	C₂×C₅	semidirect
83. #1564	C₂×C₅	semidirect
84. C₂×#334	C₂×C₅	semidirect
100. C₅×M₁₆	M₁₆	semidirect
108. C₂×C₅×C₈	M₁₆	semidirect
259. M₁₆	C₅×M₁₆	semidirect
267. C₂×C₈	C₅×M₁₆	semidirect
324. C₅	#17798	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×#2989	2
C₄×C₅×#131	2
C₅×#1569	2
C₅×#1568	2
C₅×#1566	2
C₅×#1565	2
C₅×#1564	2
C₂×C₅×#334	2
#17798	5

Subgroups — C5×#17798 #11940518

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#17798 #11940518