Subgroups — C₅×#33594 #11956314

Order 1280.

696 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3414	C₂	1	2	yes	maximal, complemented
2	C₅×#3147	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#443	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2214	C₂	1	2	yes	maximal, complemented
5	C₅×#2213	C₂	1	2	yes	maximal, complemented
6	C₅×#2212	C₂	1	4	yes	maximal, complemented
7	C₂×C₅×#364	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2148	C₂	1	2	yes	maximal, complemented
9	C₂×C₅×#135	—	2	1	no	—
10	C₂×C₅×#135	C₂²	1	1	yes	characteristic
11	C₂×C₅×#135	C₂²	1	2	yes	—
12	C₂×C₅×#131	—	2	1	no	—
13	C₅×#532	—	2	1	no	—
14	C₅×#510	—	2	2	no	—
15	C₅×#510	C₂²	1	4	yes	—
16	C₅×#509	—	2	2	no	—
17	C₅×#509	C₂²	1	4	yes	—
18	C₅×#508	—	2	4	no	—
19	C₂×C₅×M₃₂	C₂²	1	2	yes	—
20	C₅×#495	—	2	1	no	—
21	C₅×#495	C₂²	1	2	yes	complemented
22	C₅×#494	C₂²	1	1	yes	characteristic, complemented
23	C₅×#493	C₂²	1	1	yes	characteristic, complemented
24	C₅×#492	—	2	1	no	—
25	C₅×#443	—	2	1	no	—
26	C₅×#443	—	2	1	no	—
27	C₅×#443	C₂²	1	2	yes	—
28	C₅×#443	C₂²	1	2	yes	—
29	C₂×C₅×#108	C₂²	1	1	yes	characteristic
30	C₂×C₅×#104	—	2	1	no	—
31	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
32	C₅×#364	C₂²	1	2	yes	complemented
33	C₅×#364	C₂²	1	2	yes	complemented
34	C₅×#362	C₂²	1	4	yes	complemented
35	C₅×#361	C₂²	1	4	yes	complemented
36	#33594	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
37	C₂×C₅×#41	—	2	1	no	—
38	C₂×C₅×#41	—	2	2	no	—
39	C₅×#135	—	2	1	no	—
40	C₅×#135	—	2	2	no	—
41	C₅×#135	—	2	2	no	—
42	C₅×#135	—	2	1	no	—
43	C₅×#135	—	2	2	no	—
44	C₅×#135	—	2	2	no	—
45	C₅×#135	—	4	1	no	—
46	C₅×#135	—	4	1	no	—
47	C₅×#135	—	4	1	no	—
48	C₅×#135	—	4	1	no	—
49	C₅×#135	D₄	1	2	yes	complemented
50	C₅×#135	C₂³	1	2	yes	—
51	C₂×C₅×Q₁₆	—	2	1	no	—
52	C₂×C₅×Q₁₆	D₄	1	1	yes	characteristic, complemented
53	C₂×C₅×Q₁₆	C₂³	1	2	yes	—
54	C₂×C₅×SD₁₆	—	2	2	no	—
55	C₂×C₅×SD₁₆	—	2	2	no	—
56	C₂×C₅×SD₁₆	—	2	1	no	—
57	C₂×C₅×D₈	—	2	1	no	—
58	C₂×C₅×D₈	D₄	1	1	yes	characteristic, complemented
59	C₂×C₅×D₈	C₂³	1	2	yes	—
60	C₅×#131	—	2	2	no	—
61	C₅×#131	—	2	2	no	—
62	C₅×#131	—	4	1	no	—
63	C₅×#131	—	4	1	no	—
64	C₂×C₅×M₁₆	—	2	1	no	—
65	C₂×C₅×M₁₆	—	4	1	no	—
66	C₂²×C₅×C₈	—	4	1	no	—
67	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
68	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
69	C₅×C₄⋊Q₈	—	2	1	no	—
70	C₅×#127	—	2	1	no	—
71	C₅×#124	—	2	2	no	—
72	C₅×#121	—	4	2	no	—
73	C₄×C₅×D₄	—	4	2	no	—
74	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
75	C₅×Q₃₂	—	2	4	no	—
76	C₅×SD₃₂	—	2	4	no	—
77	C₅×SD₃₂	—	2	4	no	—
78	C₅×D₁₆	—	2	4	no	—
79	C₅×M₃₂	—	2	2	no	—
80	C₅×M₃₂	C₂³	1	4	yes	—
81	C₂×C₅×C₁₆	—	2	2	no	—
82	C₅×#108	—	2	1	no	—
83	C₅×#108	C₂³	1	2	yes	—
84	C₅×#104	—	2	2	no	—
85	C₅×#104	—	2	2	no	—
86	C₄×C₅×C₈	D₄	1	1	yes	characteristic
87	C₄×C₅×C₈	D₄	1	1	yes	characteristic
88	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
89	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
90	#3414	C₂×C₅	1	2	yes	complemented
91	#3147	C₂×C₅	1	1	yes	characteristic, complemented
92	C₂×#443	C₂×C₅	1	1	yes	characteristic, complemented
93	#2214	C₂×C₅	1	2	yes	complemented
94	#2213	C₂×C₅	1	2	yes	complemented
95	#2212	C₂×C₅	1	4	yes	complemented
96	C₂×#364	C₂×C₅	1	1	yes	characteristic, complemented
97	#2148	C₂×C₅	1	2	yes	complemented
98	C₅×#41	—	2	2	no	—
99	C₅×#41	—	2	2	no	—
100	C₅×#41	—	4	1	no	—
101	C₅×#41	—	4	1	no	—
102	C₅×#41	—	4	2	no	—
103	C₅×#41	—	4	2	no	—
104	C₅×#41	—	4	2	no	—
105	C₅×#41	—	4	2	no	—
106	C₂×C₅×Q₈	—	2	1	no	—
107	C₂×C₅×Q₈	—	2	2	no	—
108	C₂×C₅×D₄	—	2	1	no	—
109	C₂×C₅×D₄	—	2	2	no	—
110	C₂×C₅×D₄	—	4	2	no	—
111	C₂×C₅×D₄	—	4	1	no	—
112	C₂×C₅×D₄	—	4	2	no	—
113	C₂²×C₄×C₅	—	2	1	no	—
114	C₂²×C₄×C₅	—	4	1	no	—
115	C₂²×C₄×C₅	—	4	2	no	—
116	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
117	C₅×Q₁₆	—	2	1	no	—
118	C₅×Q₁₆	—	2	2	no	—
119	C₅×Q₁₆	—	2	2	no	—
120	C₅×Q₁₆	—	4	1	no	—
121	C₅×Q₁₆	—	4	1	no	—
122	C₅×Q₁₆	C₂×D₄	1	2	yes	—
123	C₅×SD₁₆	—	2	2	no	—
124	C₅×SD₁₆	—	2	2	no	—
125	C₅×SD₁₆	—	4	2	no	—
126	C₅×SD₁₆	—	4	2	no	—
127	C₅×SD₁₆	—	4	2	no	—
128	C₅×SD₁₆	—	4	2	no	—
129	C₅×D₈	—	2	1	no	—
130	C₅×D₈	—	2	2	no	—
131	C₅×D₈	—	2	2	no	—
132	C₅×D₈	—	4	1	no	—
133	C₅×D₈	—	4	1	no	—
134	C₅×D₈	C₂×D₄	1	2	yes	—
135	C₅×M₁₆	—	2	2	no	—
136	C₅×M₁₆	—	4	1	no	—
137	C₅×M₁₆	—	4	2	no	—
138	C₅×M₁₆	—	4	2	no	—
139	C₂×C₅×C₈	—	4	1	no	—
140	C₂×C₅×C₈	—	4	2	no	—
141	C₂×C₅×C₈	—	4	2	no	—
142	C₂×C₅×C₈	D₈	1	1	yes	characteristic
143	C₂×C₅×C₈	D₈	1	1	yes	characteristic
144	C₂×C₅×C₈	D₈	1	1	yes	characteristic
145	C₂×C₅×C₈	D₈	1	1	yes	characteristic
146	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
147	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
148	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
149	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
150	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
151	C₂×C₅×C₈	#41	1	1	yes	characteristic
152	C₂×C₅×C₈	#41	1	1	yes	characteristic
153	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
154	C₅×C₄⋊C₄	—	4	2	no	—
155	C₅×C₂²⋊C₄	—	4	4	no	—
156	C₄²×C₅	—	2	1	no	—
157	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
158	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
159	C₅×C₁₆	—	2	4	no	—
160	C₂×#135	—	2	1	no	—
161	C₂×#135	C₂²×C₅	1	1	yes	characteristic
162	C₂×#135	C₂²×C₅	1	2	yes	—
163	C₂×#131	—	2	1	no	—
164	#532	—	2	1	no	—
165	#510	—	2	2	no	—
166	#510	C₂²×C₅	1	4	yes	—
167	#509	—	2	2	no	—
168	#509	C₂²×C₅	1	4	yes	—
169	#508	—	2	4	no	—
170	C₂×M₃₂	C₂²×C₅	1	2	yes	—
171	#495	—	2	1	no	—
172	#495	C₂²×C₅	1	2	yes	complemented
173	#494	C₂²×C₅	1	1	yes	characteristic, complemented
174	#493	C₂²×C₅	1	1	yes	characteristic, complemented
175	#492	—	2	1	no	—
176	#443	—	2	1	no	—
177	#443	—	2	1	no	—
178	#443	C₂²×C₅	1	2	yes	—
179	#443	C₂²×C₅	1	2	yes	—
180	C₂×#108	C₂²×C₅	1	1	yes	characteristic
181	C₂×#104	—	2	1	no	—
182	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
183	#364	C₂²×C₅	1	2	yes	complemented
184	#364	C₂²×C₅	1	2	yes	complemented
185	#362	C₂²×C₅	1	4	yes	complemented
186	#361	C₂²×C₅	1	4	yes	complemented
187	C₂³×C₅	—	4	1	no	—
188	C₂³×C₅	—	4	2	no	—
189	C₂³×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
190	C₅×Q₈	—	2	2	no	—
191	C₅×Q₈	—	4	1	no	—
192	C₅×Q₈	—	4	2	no	—
193	C₅×Q₈	—	4	2	no	—
194	C₅×D₄	—	2	2	no	—
195	C₅×D₄	—	4	2	no	—
196	C₅×D₄	—	4	2	no	—
197	C₅×D₄	—	4	2	no	—
198	C₅×D₄	—	4	2	no	—
199	C₅×D₄	—	4	1	no	—
200	C₅×D₄	—	8	4	no	—
201	C₅×D₄	—	8	2	no	—
202	C₅×D₄	—	8	2	no	—
203	C₂×C₄×C₅	—	2	1	no	—
204	C₂×C₄×C₅	—	2	1	no	—
205	C₂×C₄×C₅	—	4	2	no	—
206	C₂×C₄×C₅	—	4	1	no	—
207	C₂×C₄×C₅	—	4	2	no	—
208	C₂×C₄×C₅	—	4	2	no	—
209	C₂×C₄×C₅	—	4	2	no	—
210	C₂×C₄×C₅	—	8	2	no	—
211	C₂×C₄×C₅	—	8	2	no	—
212	C₂×C₄×C₅	#121	1	1	yes	characteristic
213	C₂×C₄×C₅	#121	1	1	yes	characteristic
214	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
215	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
216	C₂×C₄×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
217	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
218	C₅×C₈	—	4	2	no	—
219	C₅×C₈	#121	1	1	yes	characteristic
220	C₅×C₈	#121	1	1	yes	characteristic
221	C₅×C₈	C₂×D₈	1	1	yes	characteristic
222	C₅×C₈	C₂×D₈	1	1	yes	characteristic
223	C₅×C₈	C₂×D₈	1	1	yes	characteristic
224	C₅×C₈	C₂×D₈	1	1	yes	characteristic
225	C₅×C₈	C₂²×D₄	1	1	yes	characteristic
226	C₅×C₈	C₂×#41	1	1	yes	characteristic
227	C₂×#41	—	2	1	no	—
228	C₂×#41	—	2	2	no	—
229	#135	—	2	1	no	—
230	#135	—	2	2	no	—
231	#135	—	2	2	no	—
232	#135	—	2	1	no	—
233	#135	—	2	2	no	—
234	#135	—	2	2	no	—
235	#135	—	4	1	no	—
236	#135	—	4	1	no	—
237	#135	—	4	1	no	—
238	#135	—	4	1	no	—
239	#135	C₅×D₄	1	2	yes	complemented
240	#135	C₂³×C₅	1	2	yes	—
241	C₂×Q₁₆	—	2	1	no	—
242	C₂×Q₁₆	C₅×D₄	1	1	yes	characteristic, complemented
243	C₂×Q₁₆	C₂³×C₅	1	2	yes	—
244	C₂×SD₁₆	—	2	2	no	—
245	C₂×SD₁₆	—	2	2	no	—
246	C₂×SD₁₆	—	2	1	no	—
247	C₂×D₈	—	2	1	no	—
248	C₂×D₈	C₅×D₄	1	1	yes	characteristic, complemented
249	C₂×D₈	C₂³×C₅	1	2	yes	—
250	#131	—	2	2	no	—
251	#131	—	2	2	no	—
252	#131	—	4	1	no	—
253	#131	—	4	1	no	—
254	C₂×M₁₆	—	2	1	no	—
255	C₂×M₁₆	—	4	1	no	—
256	C₂²×C₈	—	4	1	no	—
257	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
258	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
259	C₄⋊Q₈	—	2	1	no	—
260	#127	—	2	1	no	—
261	#124	—	2	2	no	—
262	#121	—	4	2	no	—
263	C₄×D₄	—	4	2	no	—
264	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
265	Q₃₂	—	2	4	no	—
266	SD₃₂	—	2	4	no	—
267	SD₃₂	—	2	4	no	—
268	D₁₆	—	2	4	no	—
269	M₃₂	—	2	2	no	—
270	M₃₂	C₂³×C₅	1	4	yes	—
271	C₂×C₁₆	—	2	2	no	—
272	#108	—	2	1	no	—
273	#108	C₂³×C₅	1	2	yes	—
274	#104	—	2	2	no	—
275	#104	—	2	2	no	—
276	C₄×C₈	C₅×D₄	1	1	yes	characteristic
277	C₄×C₈	C₅×D₄	1	1	yes	characteristic
278	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
279	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
280	C₂²×C₅	—	4	1	no	—
281	C₂²×C₅	—	4	2	no	—
282	C₂²×C₅	—	8	2	no	—
283	C₂²×C₅	—	8	4	no	—
284	C₂²×C₅	—	8	2	no	—
285	C₂²×C₅	#459	1	1	yes	characteristic
286	C₂²×C₅	#459	1	1	yes	characteristic
287	C₂²×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
288	C₄×C₅	—	2	2	no	—
289	C₄×C₅	—	4	1	no	—
290	C₄×C₅	—	4	2	no	—
291	C₄×C₅	—	8	2	no	—
292	C₄×C₅	#459	1	1	yes	characteristic
293	C₄×C₅	#459	1	1	yes	characteristic
294	C₄×C₅	C₂×#121	1	1	yes	characteristic
295	C₄×C₅	C₂²×D₈	1	1	yes	characteristic
296	#41	—	2	2	no	—
297	#41	—	2	2	no	—
298	#41	—	4	1	no	—
299	#41	—	4	1	no	—
300	#41	—	4	2	no	—
301	#41	—	4	2	no	—
302	#41	—	4	2	no	—
303	#41	—	4	2	no	—
304	C₂×Q₈	—	2	1	no	—
305	C₂×Q₈	—	2	2	no	—
306	C₂×D₄	—	2	1	no	—
307	C₂×D₄	—	2	2	no	—
308	C₂×D₄	—	4	2	no	—
309	C₂×D₄	—	4	1	no	—
310	C₂×D₄	—	4	2	no	—
311	C₂²×C₄	—	2	1	no	—
312	C₂²×C₄	—	4	1	no	—
313	C₂²×C₄	—	4	2	no	—
314	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
315	Q₁₆	—	2	1	no	—
316	Q₁₆	—	2	2	no	—
317	Q₁₆	—	2	2	no	—
318	Q₁₆	—	4	1	no	—
319	Q₁₆	—	4	1	no	—
320	Q₁₆	C₂×C₅×D₄	1	2	yes	—
321	SD₁₆	—	2	2	no	—
322	SD₁₆	—	2	2	no	—
323	SD₁₆	—	4	2	no	—
324	SD₁₆	—	4	2	no	—
325	SD₁₆	—	4	2	no	—
326	SD₁₆	—	4	2	no	—
327	D₈	—	2	1	no	—
328	D₈	—	2	2	no	—
329	D₈	—	2	2	no	—
330	D₈	—	4	1	no	—
331	D₈	—	4	1	no	—
332	D₈	C₂×C₅×D₄	1	2	yes	—
333	M₁₆	—	2	2	no	—
334	M₁₆	—	4	1	no	—
335	M₁₆	—	4	2	no	—
336	M₁₆	—	4	2	no	—
337	C₂×C₈	—	4	1	no	—
338	C₂×C₈	—	4	2	no	—
339	C₂×C₈	—	4	2	no	—
340	C₂×C₈	C₅×D₈	1	1	yes	characteristic
341	C₂×C₈	C₅×D₈	1	1	yes	characteristic
342	C₂×C₈	C₅×D₈	1	1	yes	characteristic
343	C₂×C₈	C₅×D₈	1	1	yes	characteristic
344	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
345	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
346	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
347	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
348	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
349	C₂×C₈	C₅×#41	1	1	yes	characteristic
350	C₂×C₈	C₅×#41	1	1	yes	characteristic
351	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
352	C₄⋊C₄	—	4	2	no	—
353	C₂²⋊C₄	—	4	4	no	—
354	C₄²	—	2	1	no	—
355	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
356	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
357	C₁₆	—	2	4	no	—
358	C₂×C₅	—	2	1	no	—
359	C₂×C₅	—	2	1	no	—
360	C₂×C₅	—	2	1	no	—
361	C₂×C₅	—	8	2	no	—
362	C₂×C₅	—	16	2	no	—
363	C₂×C₅	C₂×#459	1	1	yes	characteristic
364	C₂³	—	4	1	no	—
365	C₂³	—	4	2	no	—
366	C₂³	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
367	Q₈	—	2	2	no	—
368	Q₈	—	4	1	no	—
369	Q₈	—	4	2	no	—
370	Q₈	—	4	2	no	—
371	D₄	—	2	2	no	—
372	D₄	—	4	2	no	—
373	D₄	—	4	2	no	—
374	D₄	—	4	1	no	—
375	D₄	—	4	2	no	—
376	D₄	—	4	2	no	—
377	D₄	—	8	4	no	—
378	D₄	—	8	2	no	—
379	D₄	—	8	2	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	1	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	8	2	no	—
388	C₂×C₄	—	8	2	no	—
389	C₂×C₄	C₅×#121	1	1	yes	characteristic
390	C₂×C₄	C₅×#121	1	1	yes	characteristic
391	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
392	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
393	C₂×C₄	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
394	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
395	C₈	—	4	2	no	—
396	C₈	C₅×#121	1	1	yes	characteristic
397	C₈	C₅×#121	1	1	yes	characteristic
398	C₈	C₂×C₅×D₈	1	1	yes	characteristic
399	C₈	C₂×C₅×D₈	1	1	yes	characteristic
400	C₈	C₂×C₅×D₈	1	1	yes	characteristic
401	C₈	C₂×C₅×D₈	1	1	yes	characteristic
402	C₈	C₂²×C₅×D₄	1	1	yes	characteristic
403	C₈	C₂×C₅×#41	1	1	yes	characteristic
404	C₅	#33594	1	1	yes	characteristic, direct product factor, Sylow
405	C₂²	—	4	1	no	—
406	C₂²	—	4	2	no	—
407	C₂²	—	8	2	no	—
408	C₂²	—	8	4	no	—
409	C₂²	—	8	2	no	—
410	C₂²	C₅×#459	1	1	yes	characteristic
411	C₂²	C₅×#459	1	1	yes	characteristic
412	C₂²	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
413	C₄	—	2	2	no	—
414	C₄	—	4	1	no	—
415	C₄	—	4	2	no	—
416	C₄	—	8	2	no	—
417	C₄	C₅×#459	1	1	yes	characteristic
418	C₄	C₅×#459	1	1	yes	characteristic
419	C₄	C₂×C₅×#121	1	1	yes	characteristic
420	C₄	C₂²×C₅×D₈	1	1	yes	characteristic
421	C₂	—	2	1	no	—
422	C₂	—	2	1	no	—
423	C₂	—	2	1	no	—
424	C₂	—	8	2	no	—
425	C₂	—	16	2	no	—
426	C₂	C₂×C₅×#459	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₅	#459
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₅
socle	C₂×C₅	C₂×#459
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₅ ◁ C₂²×C₄×C₅ ◁ C₂×C₄×C₅×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×#3414	C₂	semidirect
2. C₅×#3147	C₂	semidirect
3. C₂×C₅×#443	C₂	semidirect
4. C₅×#2214	C₂	semidirect
5. C₅×#2213	C₂	semidirect
6. C₅×#2212	C₂	semidirect
7. C₂×C₅×#364	C₂	semidirect
8. C₅×#2148	C₂	semidirect
21. C₅×#495	C₂²	semidirect
22. C₅×#494	C₂²	semidirect
23. C₅×#493	C₂²	semidirect
32. C₅×#364	C₂²	semidirect
33. C₅×#364	C₂²	semidirect
34. C₅×#362	C₂²	semidirect
35. C₅×#361	C₂²	semidirect
36. #33594	C₅	direct (N × H)
49. C₅×#135	D₄	semidirect
52. C₂×C₅×Q₁₆	D₄	semidirect
58. C₂×C₅×D₈	D₄	semidirect
90. #3414	C₂×C₅	semidirect
91. #3147	C₂×C₅	semidirect
92. C₂×#443	C₂×C₅	semidirect
93. #2214	C₂×C₅	semidirect
94. #2213	C₂×C₅	semidirect
95. #2212	C₂×C₅	semidirect
96. C₂×#364	C₂×C₅	semidirect
97. #2148	C₂×C₅	semidirect
172. #495	C₂²×C₅	semidirect
173. #494	C₂²×C₅	semidirect
174. #493	C₂²×C₅	semidirect
183. #364	C₂²×C₅	semidirect
184. #364	C₂²×C₅	semidirect
185. #362	C₂²×C₅	semidirect
186. #361	C₂²×C₅	semidirect
239. #135	C₅×D₄	semidirect
242. C₂×Q₁₆	C₅×D₄	semidirect
248. C₂×D₈	C₅×D₄	semidirect
404. C₅	#33594	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×#3414	2
C₅×#3147	2
C₂×C₅×#443	2
C₅×#2214	2
C₅×#2213	2
C₅×#2212	2
C₂×C₅×#364	2
C₅×#2148	2
#33594	5

Subgroups — C5×#33594 #11956314

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#33594 #11956314