Subgroups — C₅×#22234 #11944954

Order 1280.

714 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×#3131	C₂	1	1	yes	maximal, characteristic
2	C₅×#2960	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2931	C₂	1	1	yes	maximal, characteristic
4	C₅×#1994	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1962	C₂	1	1	yes	maximal, characteristic
6	C₅×#1929	C₂	1	4	yes	maximal, complemented
7	C₅×#1866	C₂	1	4	yes	maximal, complemented
8	C₅×#1848	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1744	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₅×#131	C₂²	1	2	yes	—
11	C₅×#533	C₂²	1	1	yes	characteristic
12	C₅×#532	C₂²	1	1	yes	characteristic
13	C₅×#488	C₄	1	4	yes	complemented
14	C₅×#487	C₄	1	1	yes	characteristic, complemented
15	C₅×#487	C₄	1	1	yes	characteristic, complemented
16	C₅×#486	C₄	1	1	yes	characteristic, complemented
17	C₅×#486	C₄	1	1	yes	characteristic, complemented
18	C₅×#446	—	2	1	no	—
19	C₅×#446	—	2	1	no	—
20	C₅×C₈×Q₈	—	2	1	no	—
21	C₅×C₈×Q₈	—	2	1	no	—
22	C₅×#436	—	2	1	no	—
23	C₅×#436	—	2	1	no	—
24	C₅×C₈×D₄	—	2	1	no	—
25	C₅×C₈×D₄	—	2	1	no	—
26	C₂×C₅×#108	C₂²	1	4	yes	—
27	C₅×#424	C₂²	1	2	yes	—
28	C₅×#423	C₂²	1	1	yes	characteristic
29	C₅×#423	C₂²	1	1	yes	characteristic
30	C₂×C₅×#104	C₂²	1	4	yes	—
31	C₅×#416	C₂²	1	4	yes	—
32	C₅×#408	C₂²	1	2	yes	—
33	C₅×#405	C₂²	1	2	yes	—
34	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
35	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
36	C₄³×C₅	C₂²	1	1	yes	characteristic
37	C₅×#339	C₂²	1	4	yes	—
38	C₅×#336	C₂²	1	2	yes	—
39	C₅×#336	C₂²	1	2	yes	—
40	#22234	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
41	C₂×C₅×#41	C₂³	1	2	yes	—
42	C₅×#131	—	4	4	no	—
43	C₂×C₅×M₁₆	—	2	2	no	—
44	C₂×C₅×M₁₆	C₂³	1	2	yes	—
45	C₂×C₅×M₁₆	C₂³	1	2	yes	—
46	C₂²×C₅×C₈	—	2	2	no	—
47	C₂²×C₅×C₈	C₂³	1	2	yes	—
48	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
49	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
50	C₅×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
51	C₅×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
52	C₅×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
53	C₅×#127	C₂×C₄	1	1	yes	characteristic
54	C₅×#125	C₂×C₄	1	2	yes	—
55	C₅×#124	C₂×C₄	1	2	yes	—
56	C₅×C₂²⋊Q₈	—	2	1	no	—
57	C₅×C₂²⋊Q₈	—	2	1	no	—
58	C₅×#121	—	2	1	no	—
59	C₅×#121	—	2	1	no	—
60	C₄×C₅×Q₈	—	2	1	no	—
61	C₄×C₅×Q₈	—	2	1	no	—
62	C₄×C₅×D₄	—	2	1	no	—
63	C₄×C₅×D₄	—	2	1	no	—
64	C₅×#117	C₂³	1	2	yes	—
65	C₂×C₄²×C₅	—	2	1	no	—
66	C₂×C₄²×C₅	—	2	1	no	—
67	C₂×C₄²×C₅	C₂³	1	2	yes	—
68	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
69	C₅×#108	—	4	4	no	—
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	—	2	1	no	—
74	C₅×C₄⋊C₈	—	2	1	no	—
75	C₅×C₄⋊C₈	—	2	1	no	—
76	C₅×#104	—	4	4	no	—
77	C₅×#103	C₂×C₄	1	4	yes	—
78	C₅×#103	C₂×C₄	1	4	yes	—
79	C₅×#102	C₂×C₄	1	4	yes	—
80	C₅×#102	C₂×C₄	1	4	yes	—
81	C₅×C₂²⋊C₈	—	2	2	no	—
82	C₅×C₂²⋊C₈	—	2	2	no	—
83	C₅×#97	—	2	2	no	—
84	C₄×C₅×C₈	—	2	2	no	—
85	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
86	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
87	C₄×C₅×C₈	C₂×C₄	1	2	yes	—
88	C₄×C₅×C₈	D₄	1	1	yes	characteristic
89	C₄×C₅×C₈	D₄	1	1	yes	characteristic
90	C₄×C₅×C₈	D₄	1	1	yes	characteristic
91	C₄×C₅×C₈	D₄	1	1	yes	characteristic
92	#3131	C₂×C₅	1	1	yes	characteristic
93	#2960	C₂×C₅	1	1	yes	characteristic, complemented
94	#2931	C₂×C₅	1	1	yes	characteristic
95	#1994	C₂×C₅	1	1	yes	characteristic, complemented
96	#1962	C₂×C₅	1	1	yes	characteristic
97	#1929	C₂×C₅	1	4	yes	complemented
98	#1866	C₂×C₅	1	4	yes	complemented
99	#1848	C₂×C₅	1	1	yes	characteristic, complemented
100	#1744	C₂×C₅	1	1	yes	characteristic, complemented
101	C₅×#41	—	2	4	no	—
102	C₅×#41	—	2	4	no	—
103	C₂×C₅×Q₈	—	2	1	no	—
104	C₂×C₅×Q₈	—	2	1	no	—
105	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
106	C₂×C₅×D₄	—	2	2	no	—
107	C₂×C₅×D₄	—	2	1	no	—
108	C₂×C₅×D₄	—	2	1	no	—
109	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
110	C₂²×C₄×C₅	—	2	2	no	—
111	C₂²×C₄×C₅	—	2	2	no	—
112	C₂²×C₄×C₅	#41	1	1	yes	characteristic
113	C₂²×C₄×C₅	#41	1	1	yes	characteristic
114	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
115	C₅×M₁₆	—	2	4	no	—
116	C₅×M₁₆	—	2	4	no	—
117	C₅×M₁₆	—	4	4	no	—
118	C₂×C₅×C₈	—	2	2	no	—
119	C₂×C₅×C₈	—	2	2	no	—
120	C₂×C₅×C₈	—	2	2	no	—
121	C₂×C₅×C₈	—	2	2	no	—
122	C₂×C₅×C₈	—	2	2	no	—
123	C₂×C₅×C₈	—	2	2	no	—
124	C₂×C₅×C₈	—	4	4	no	—
125	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
126	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
127	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
128	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
129	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
130	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
131	C₅×C₄⋊C₄	—	2	1	no	—
132	C₅×C₄⋊C₄	—	2	1	no	—
133	C₅×C₄⋊C₄	—	2	2	no	—
134	C₅×C₄⋊C₄	—	2	2	no	—
135	C₅×C₄⋊C₄	—	2	1	no	—
136	C₅×C₄⋊C₄	—	2	1	no	—
137	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
138	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
139	C₅×C₂²⋊C₄	—	2	2	no	—
140	C₅×C₂²⋊C₄	—	2	2	no	—
141	C₅×C₂²⋊C₄	—	2	2	no	—
142	C₄²×C₅	—	2	4	no	—
143	C₄²×C₅	—	2	2	no	—
144	C₄²×C₅	—	2	2	no	—
145	C₄²×C₅	—	2	2	no	—
146	C₄²×C₅	—	4	2	no	—
147	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
148	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
149	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
150	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
151	C₂×#131	C₂²×C₅	1	2	yes	—
152	#533	C₂²×C₅	1	1	yes	characteristic
153	#532	C₂²×C₅	1	1	yes	characteristic
154	#488	C₄×C₅	1	4	yes	complemented
155	#487	C₄×C₅	1	1	yes	characteristic, complemented
156	#487	C₄×C₅	1	1	yes	characteristic, complemented
157	#486	C₄×C₅	1	1	yes	characteristic, complemented
158	#486	C₄×C₅	1	1	yes	characteristic, complemented
159	#446	—	2	1	no	—
160	#446	—	2	1	no	—
161	C₈×Q₈	—	2	1	no	—
162	C₈×Q₈	—	2	1	no	—
163	#436	—	2	1	no	—
164	#436	—	2	1	no	—
165	C₈×D₄	—	2	1	no	—
166	C₈×D₄	—	2	1	no	—
167	C₂×#108	C₂²×C₅	1	4	yes	—
168	#424	C₂²×C₅	1	2	yes	—
169	#423	C₂²×C₅	1	1	yes	characteristic
170	#423	C₂²×C₅	1	1	yes	characteristic
171	C₂×#104	C₂²×C₅	1	4	yes	—
172	#416	C₂²×C₅	1	4	yes	—
173	#408	C₂²×C₅	1	2	yes	—
174	#405	C₂²×C₅	1	2	yes	—
175	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
176	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
177	C₄³	C₂²×C₅	1	1	yes	characteristic
178	#339	C₂²×C₅	1	4	yes	—
179	#336	C₂²×C₅	1	2	yes	—
180	#336	C₂²×C₅	1	2	yes	—
181	C₂³×C₅	—	2	2	no	—
182	C₂³×C₅	C₂×#41	1	1	yes	characteristic
183	C₅×Q₈	—	2	4	no	—
184	C₅×Q₈	—	4	2	no	—
185	C₅×Q₈	—	4	2	no	—
186	C₅×D₄	—	2	4	no	—
187	C₅×D₄	—	4	4	no	—
188	C₅×D₄	—	4	2	no	—
189	C₅×D₄	—	4	2	no	—
190	C₂×C₄×C₅	—	2	2	no	—
191	C₂×C₄×C₅	—	2	2	no	—
192	C₂×C₄×C₅	—	2	4	no	—
193	C₂×C₄×C₅	—	2	2	no	—
194	C₂×C₄×C₅	—	2	2	no	—
195	C₂×C₄×C₅	—	2	2	no	—
196	C₂×C₄×C₅	—	4	2	no	—
197	C₂×C₄×C₅	—	4	2	no	—
198	C₂×C₄×C₅	—	4	2	no	—
199	C₂×C₄×C₅	—	4	2	no	—
200	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
201	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
202	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
203	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
204	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
205	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
206	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
207	C₂×C₄×C₅	2₋¹⁺⁴	1	2	yes	—
208	C₅×C₈	—	2	2	no	—
209	C₅×C₈	—	2	2	no	—
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	C₂×#41	C₂³×C₅	1	2	yes	—
217	#131	—	4	4	no	—
218	C₂×M₁₆	—	2	2	no	—
219	C₂×M₁₆	C₂³×C₅	1	2	yes	—
220	C₂×M₁₆	C₂³×C₅	1	2	yes	—
221	C₂²×C₈	—	2	2	no	—
222	C₂²×C₈	C₂³×C₅	1	2	yes	—
223	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
224	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
225	C₄⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
226	C₄⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
227	C₄⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
228	#127	C₂×C₄×C₅	1	1	yes	characteristic
229	#125	C₂×C₄×C₅	1	2	yes	—
230	#124	C₂×C₄×C₅	1	2	yes	—
231	C₂²⋊Q₈	—	2	1	no	—
232	C₂²⋊Q₈	—	2	1	no	—
233	#121	—	2	1	no	—
234	#121	—	2	1	no	—
235	C₄×Q₈	—	2	1	no	—
236	C₄×Q₈	—	2	1	no	—
237	C₄×D₄	—	2	1	no	—
238	C₄×D₄	—	2	1	no	—
239	#117	C₂³×C₅	1	2	yes	—
240	C₂×C₄²	—	2	1	no	—
241	C₂×C₄²	—	2	1	no	—
242	C₂×C₄²	C₂³×C₅	1	2	yes	—
243	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
244	#108	—	4	4	no	—
245	C₄⋊C₈	—	2	2	no	—
246	C₄⋊C₈	—	2	2	no	—
247	C₄⋊C₈	—	2	1	no	—
248	C₄⋊C₈	—	2	1	no	—
249	C₄⋊C₈	—	2	1	no	—
250	C₄⋊C₈	—	2	1	no	—
251	#104	—	4	4	no	—
252	#103	C₂×C₄×C₅	1	4	yes	—
253	#103	C₂×C₄×C₅	1	4	yes	—
254	#102	C₂×C₄×C₅	1	4	yes	—
255	#102	C₂×C₄×C₅	1	4	yes	—
256	C₂²⋊C₈	—	2	2	no	—
257	C₂²⋊C₈	—	2	2	no	—
258	#97	—	2	2	no	—
259	C₄×C₈	—	2	2	no	—
260	C₄×C₈	C₂×C₄×C₅	1	1	yes	characteristic
261	C₄×C₈	C₂×C₄×C₅	1	1	yes	characteristic
262	C₄×C₈	C₂×C₄×C₅	1	2	yes	—
263	C₄×C₈	C₅×D₄	1	1	yes	characteristic
264	C₄×C₈	C₅×D₄	1	1	yes	characteristic
265	C₄×C₈	C₅×D₄	1	1	yes	characteristic
266	C₄×C₈	C₅×D₄	1	1	yes	characteristic
267	C₂²×C₅	—	2	1	no	—
268	C₂²×C₅	—	2	1	no	—
269	C₂²×C₅	—	4	2	no	—
270	C₂²×C₅	—	4	2	no	—
271	C₂²×C₅	—	4	2	no	—
272	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
273	C₂²×C₅	#542	1	2	yes	—
274	C₄×C₅	—	2	1	no	—
275	C₄×C₅	—	2	1	no	—
276	C₄×C₅	—	4	4	no	—
277	C₄×C₅	—	4	2	no	—
278	C₄×C₅	—	4	2	no	—
279	C₄×C₅	—	4	2	no	—
280	C₄×C₅	#443	1	2	yes	—
281	C₄×C₅	#444	1	2	yes	—
282	C₄×C₅	#520	1	2	yes	—
283	C₄×C₅	#535	1	1	yes	characteristic
284	C₄×C₅	#536	1	1	yes	characteristic
285	#41	—	2	4	no	—
286	#41	—	2	4	no	—
287	C₂×Q₈	—	2	1	no	—
288	C₂×Q₈	—	2	1	no	—
289	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	—	2	1	no	—
292	C₂×D₄	—	2	1	no	—
293	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	C₅×#41	1	1	yes	characteristic
297	C₂²×C₄	C₅×#41	1	1	yes	characteristic
298	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
299	M₁₆	—	2	4	no	—
300	M₁₆	—	2	4	no	—
301	M₁₆	—	4	4	no	—
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	2	2	no	—
308	C₂×C₈	—	4	4	no	—
309	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
310	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
311	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
312	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
313	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
314	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
315	C₄⋊C₄	—	2	1	no	—
316	C₄⋊C₄	—	2	1	no	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	2	1	no	—
320	C₄⋊C₄	—	2	1	no	—
321	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
322	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
323	C₂²⋊C₄	—	2	2	no	—
324	C₂²⋊C₄	—	2	2	no	—
325	C₂²⋊C₄	—	2	2	no	—
326	C₄²	—	2	4	no	—
327	C₄²	—	2	2	no	—
328	C₄²	—	2	2	no	—
329	C₄²	—	2	2	no	—
330	C₄²	—	4	2	no	—
331	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
332	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
333	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
334	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
335	C₂×C₅	—	2	2	no	—
336	C₂×C₅	—	8	2	no	—
337	C₂×C₅	#2326	1	1	yes	characteristic
338	C₂×C₅	C₂×#443	1	1	yes	characteristic
339	C₂×C₅	C₂×#444	1	1	yes	characteristic
340	C₂³	—	2	2	no	—
341	C₂³	C₂×C₅×#41	1	1	yes	characteristic
342	Q₈	—	2	4	no	—
343	Q₈	—	4	2	no	—
344	Q₈	—	4	2	no	—
345	D₄	—	2	4	no	—
346	D₄	—	4	4	no	—
347	D₄	—	4	2	no	—
348	D₄	—	4	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	4	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
360	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
361	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
362	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
363	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
364	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
365	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
366	C₂×C₄	C₅×2₋¹⁺⁴	1	2	yes	—
367	C₈	—	2	2	no	—
368	C₈	—	2	2	no	—
369	C₈	—	2	1	no	—
370	C₈	—	2	1	no	—
371	C₈	—	2	1	no	—
372	C₈	—	2	1	no	—
373	C₈	—	4	2	no	—
374	C₈	—	4	2	no	—
375	C₅	#22234	1	1	yes	characteristic, direct product factor, Sylow
376	C₂²	—	2	1	no	—
377	C₂²	—	2	1	no	—
378	C₂²	—	4	2	no	—
379	C₂²	—	4	2	no	—
380	C₂²	—	4	2	no	—
381	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
382	C₂²	C₅×#542	1	2	yes	—
383	C₄	—	2	1	no	—
384	C₄	—	2	1	no	—
385	C₄	—	4	4	no	—
386	C₄	—	4	2	no	—
387	C₄	—	4	2	no	—
388	C₄	—	4	2	no	—
389	C₄	C₅×#443	1	2	yes	—
390	C₄	C₅×#444	1	2	yes	—
391	C₄	C₅×#520	1	2	yes	—
392	C₄	C₅×#535	1	1	yes	characteristic
393	C₄	C₅×#536	1	1	yes	characteristic
394	C₂	—	2	2	no	—
395	C₂	—	8	2	no	—
396	C₂	C₅×#2326	1	1	yes	characteristic
397	C₂	C₂×C₅×#443	1	1	yes	characteristic
398	C₂	C₂×C₅×#444	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
socle	C₂²×C₅	C₂×C₄×D₄
prime radical	C₅×#532	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂×C₄×C₅×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×#2960	C₂	semidirect
4. C₅×#1994	C₂	semidirect
6. C₅×#1929	C₂	semidirect
7. C₅×#1866	C₂	semidirect
8. C₅×#1848	C₂	semidirect
9. C₅×#1744	C₂	semidirect
13. C₅×#488	C₄	semidirect
14. C₅×#487	C₄	semidirect
15. C₅×#487	C₄	semidirect
16. C₅×#486	C₄	semidirect
17. C₅×#486	C₄	semidirect
40. #22234	C₅	direct (N × H)
93. #2960	C₂×C₅	semidirect
95. #1994	C₂×C₅	semidirect
97. #1929	C₂×C₅	semidirect
98. #1866	C₂×C₅	semidirect
99. #1848	C₂×C₅	semidirect
100. #1744	C₂×C₅	semidirect
154. #488	C₄×C₅	semidirect
155. #487	C₄×C₅	semidirect
156. #487	C₄×C₅	semidirect
157. #486	C₄×C₅	semidirect
158. #486	C₄×C₅	semidirect
375. C₅	#22234	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×#3131	2
C₅×#2960	2
C₅×#2931	2
C₅×#1994	2
C₅×#1962	2
C₅×#1929	2
C₅×#1866	2
C₅×#1848	2
C₅×#1744	2
#22234	5

Subgroups — C5×#22234 #11944954

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22234 #11944954