Subgroups — C₅×#23719 #11946439

Order 1280.

808 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₅×AGL(1,ℤ/8)	C₂	1	2	yes	maximal, complemented
2	C₂×C₅×#442	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2923	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2090	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2079	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2063	C₂	1	2	yes	maximal, complemented
7	C₅×#2051	C₂	1	2	yes	maximal, complemented
8	C₅×#2045	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#2018	C₂	1	1	yes	maximal, characteristic
10	C₅×#1778	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₅×#100	C₂	1	2	yes	maximal, complemented
12	C₂×C₅×AGL(1,ℤ/8)	C₂²	1	2	yes	—
13	C₂²×C₅×D₈	C₂²	1	1	yes	characteristic
14	C₄×C₅×#41	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
16	C₅×#442	—	2	2	no	—
17	C₅×#442	—	2	2	no	—
18	C₅×#442	—	2	2	no	—
19	C₅×#440	—	2	2	no	—
20	C₄×C₅×SD₁₆	—	2	2	no	—
21	C₄×C₅×D₈	—	2	2	no	—
22	C₅×#433	—	2	2	no	—
23	C₅×#432	—	2	2	no	—
24	C₂×C₅×#108	C₂²	1	2	yes	—
25	C₅×#428	C₂²	1	2	yes	—
26	C₂×C₅×#106	C₂²	1	1	yes	characteristic
27	C₅×#424	C₂²	1	1	yes	characteristic
28	C₅×#424	C₂²	1	1	yes	characteristic
29	C₅×#418	C₂²	1	2	yes	—
30	C₅×#417	C₂²	1	2	yes	—
31	C₂×C₅×#102	C₂²	1	2	yes	—
32	C₂×C₅×#100	C₂²	1	2	yes	—
33	C₂×C₅×#100	C₂²	1	2	yes	—
34	C₅×#408	C₂²	1	1	yes	characteristic
35	C₅×#408	C₂²	1	1	yes	characteristic
36	C₄×C₅×M₁₆	C₂²	1	2	yes	—
37	C₄×C₅×M₁₆	C₂²	1	1	yes	characteristic
38	C₂×C₅×#97	C₂²	1	1	yes	characteristic
39	C₅×#343	C₂²	1	2	yes	—
40	C₅×#343	C₂²	1	2	yes	—
41	C₅×#341	C₂²	1	1	yes	characteristic
42	C₅×#341	C₂²	1	1	yes	characteristic
43	#23719	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂×C₅×#41	C₂³	1	1	yes	characteristic
45	C₂²×C₅×D₄	C₂³	1	2	yes	—
46	C₂³×C₄×C₅	—	2	2	no	—
47	C₅×AGL(1,ℤ/8)	—	2	4	no	—
48	C₅×AGL(1,ℤ/8)	—	2	4	no	—
49	C₂×C₅×SD₁₆	—	2	2	no	—
50	C₂×C₅×D₈	—	2	2	no	—
51	C₂×C₅×D₈	—	2	4	no	—
52	C₂×C₅×D₈	—	2	2	no	—
53	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
54	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
55	C₂×C₅×M₁₆	C₂³	1	2	yes	—
56	C₂×C₅×M₁₆	C₂³	1	2	yes	—
57	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
58	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
59	C₄×C₅×Q₈	D₄	1	2	yes	—
60	C₄×C₅×D₄	—	2	2	no	—
61	C₄×C₅×D₄	—	2	2	no	—
62	C₄×C₅×D₄	—	2	2	no	—
63	C₄×C₅×D₄	—	2	2	no	—
64	C₄×C₅×D₄	—	2	2	no	—
65	C₄×C₅×D₄	D₄	1	2	yes	—
66	C₅×#117	—	2	1	no	—
67	C₅×#117	C₂³	1	1	yes	characteristic
68	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
69	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
70	C₂×C₄²×C₅	—	2	1	no	—
71	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
72	C₅×#108	—	2	4	no	—
73	C₅×#107	—	2	2	no	—
74	C₅×#106	—	2	2	no	—
75	C₅×#106	—	2	2	no	—
76	C₅×C₄⋊C₈	—	2	2	no	—
77	C₅×C₄⋊C₈	—	2	2	no	—
78	C₅×#103	—	2	2	no	—
79	C₅×#102	—	2	2	no	—
80	C₅×#102	—	2	4	no	—
81	C₅×#102	—	2	2	no	—
82	C₅×#102	—	2	2	no	—
83	C₅×#100	—	2	4	no	—
84	C₅×#100	—	2	4	no	—
85	C₅×C₂²⋊C₈	—	2	2	no	—
86	C₅×C₂²⋊C₈	—	2	2	no	—
87	C₅×#97	—	2	1	no	—
88	C₅×#97	—	2	2	no	—
89	C₅×#97	D₄	1	2	yes	—
90	C₅×#97	D₄	1	2	yes	—
91	C₄×C₅×C₈	—	2	1	no	—
92	C₄×C₅×C₈	—	2	2	no	—
93	C₄×AGL(1,ℤ/8)	C₂×C₅	1	2	yes	complemented
94	C₂×#442	C₂×C₅	1	1	yes	characteristic, complemented
95	#2923	C₂×C₅	1	1	yes	characteristic, complemented
96	#2090	C₂×C₅	1	1	yes	characteristic, complemented
97	#2079	C₂×C₅	1	1	yes	characteristic, complemented
98	#2063	C₂×C₅	1	2	yes	complemented
99	#2051	C₂×C₅	1	2	yes	complemented
100	#2045	C₂×C₅	1	1	yes	characteristic, complemented
101	#2018	C₂×C₅	1	1	yes	characteristic
102	#1778	C₂×C₅	1	1	yes	characteristic, complemented
103	C₄×#100	C₂×C₅	1	2	yes	complemented
104	C₂⁴×C₅	—	2	2	no	—
105	C₅×#41	—	2	2	no	—
106	C₅×#41	—	2	2	no	—
107	C₂×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
108	C₂×C₅×D₄	—	2	1	no	—
109	C₂×C₅×D₄	—	2	2	no	—
110	C₂×C₅×D₄	—	2	2	no	—
111	C₂×C₅×D₄	—	2	2	no	—
112	C₂×C₅×D₄	—	2	2	no	—
113	C₂×C₅×D₄	—	2	2	no	—
114	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
115	C₂×C₅×D₄	#41	1	4	yes	—
116	C₂²×C₄×C₅	—	2	1	no	—
117	C₂²×C₄×C₅	—	2	2	no	—
118	C₂²×C₄×C₅	—	2	2	no	—
119	C₂²×C₄×C₅	—	4	2	no	—
120	C₂²×C₄×C₅	—	4	2	no	—
121	C₂²×C₄×C₅	—	8	4	no	—
122	C₂²×C₄×C₅	#41	1	2	yes	—
123	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
124	C₅×SD₁₆	—	2	8	no	—
125	C₅×D₈	—	2	8	no	—
126	C₅×D₈	—	2	8	no	—
127	C₅×M₁₆	—	2	2	no	—
128	C₅×M₁₆	—	2	2	no	—
129	C₅×M₁₆	—	2	2	no	—
130	C₅×M₁₆	—	2	2	no	—
131	C₅×M₁₆	—	2	2	no	—
132	C₅×M₁₆	#41	1	4	yes	—
133	C₂×C₅×C₈	—	2	2	no	—
134	C₂×C₅×C₈	—	2	2	no	—
135	C₂×C₅×C₈	—	2	2	no	—
136	C₂×C₅×C₈	—	2	1	no	—
137	C₂×C₅×C₈	—	2	1	no	—
138	C₂×C₅×C₈	—	2	2	no	—
139	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
140	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
141	C₅×C₄⋊C₄	—	2	2	no	—
142	C₅×C₄⋊C₄	—	2	2	no	—
143	C₅×C₄⋊C₄	—	2	2	no	—
144	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
145	C₅×C₂²⋊C₄	—	2	1	no	—
146	C₅×C₂²⋊C₄	—	2	2	no	—
147	C₅×C₂²⋊C₄	—	4	2	no	—
148	C₅×C₂²⋊C₄	—	4	2	no	—
149	C₄²×C₅	—	2	2	no	—
150	C₄²×C₅	—	2	1	no	—
151	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
152	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
153	C₄²×C₅	C₂×D₄	1	2	yes	—
154	C₂×AGL(1,ℤ/8)	C₂²×C₅	1	2	yes	—
155	C₂²×D₈	C₂²×C₅	1	1	yes	characteristic
156	C₄×#41	C₂²×C₅	1	1	yes	characteristic
157	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
158	#442	—	2	2	no	—
159	#442	—	2	2	no	—
160	#442	—	2	2	no	—
161	#440	—	2	2	no	—
162	C₄×SD₁₆	—	2	2	no	—
163	C₄×D₈	—	2	2	no	—
164	#433	—	2	2	no	—
165	#432	—	2	2	no	—
166	C₂×#108	C₂²×C₅	1	2	yes	—
167	#428	C₂²×C₅	1	2	yes	—
168	C₂×#106	C₂²×C₅	1	1	yes	characteristic
169	#424	C₂²×C₅	1	1	yes	characteristic
170	#424	C₂²×C₅	1	1	yes	characteristic
171	#418	C₂²×C₅	1	2	yes	—
172	#417	C₂²×C₅	1	2	yes	—
173	C₂×#102	C₂²×C₅	1	2	yes	—
174	C₂×#100	C₂²×C₅	1	2	yes	—
175	C₂×#100	C₂²×C₅	1	2	yes	—
176	#408	C₂²×C₅	1	1	yes	characteristic
177	#408	C₂²×C₅	1	1	yes	characteristic
178	C₄×M₁₆	C₂²×C₅	1	1	yes	characteristic
179	C₄×M₁₆	C₂²×C₅	1	2	yes	—
180	C₂×#97	C₂²×C₅	1	1	yes	characteristic
181	#343	C₂²×C₅	1	2	yes	—
182	#343	C₂²×C₅	1	2	yes	—
183	#341	C₂²×C₅	1	1	yes	characteristic
184	#341	C₂²×C₅	1	1	yes	characteristic
185	C₂³×C₅	—	2	1	no	—
186	C₂³×C₅	—	2	4	no	—
187	C₂³×C₅	—	4	2	no	—
188	C₂³×C₅	—	4	2	no	—
189	C₂³×C₅	—	8	2	no	—
190	C₂³×C₅	—	8	2	no	—
191	C₂³×C₅	C₂×#41	1	1	yes	characteristic
192	C₅×Q₈	—	2	2	no	—
193	C₅×D₄	—	2	4	no	—
194	C₅×D₄	—	2	2	no	—
195	C₅×D₄	—	2	4	no	—
196	C₅×D₄	—	4	2	no	—
197	C₅×D₄	—	4	2	no	—
198	C₅×D₄	—	4	2	no	—
199	C₂×C₄×C₅	—	2	2	no	—
200	C₂×C₄×C₅	—	2	1	no	—
201	C₂×C₄×C₅	—	4	2	no	—
202	C₂×C₄×C₅	—	4	1	no	—
203	C₂×C₄×C₅	—	4	1	no	—
204	C₂×C₄×C₅	—	4	2	no	—
205	C₂×C₄×C₅	—	8	2	no	—
206	C₂×C₄×C₅	—	8	4	no	—
207	C₂×C₄×C₅	—	8	4	no	—
208	C₂×C₄×C₅	—	8	2	no	—
209	C₂×C₄×C₅	#121	1	2	yes	—
210	C₂×C₄×C₅	#121	1	2	yes	—
211	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
212	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
213	C₂×C₄×C₅	C₂×#41	1	2	yes	—
214	C₂×C₄×C₅	C₂×#41	1	2	yes	—
215	C₅×C₈	—	2	2	no	—
216	C₅×C₈	—	2	4	no	—
217	C₅×C₈	—	2	2	no	—
218	C₅×C₈	—	4	1	no	—
219	C₅×C₈	—	4	2	no	—
220	C₅×C₈	—	4	1	no	—
221	C₂×#41	C₂³×C₅	1	1	yes	characteristic
222	C₂²×D₄	C₂³×C₅	1	2	yes	—
223	C₂³×C₄	—	2	2	no	—
224	AGL(1,ℤ/8)	—	2	4	no	—
225	AGL(1,ℤ/8)	—	2	4	no	—
226	C₂×SD₁₆	—	2	2	no	—
227	C₂×D₈	—	2	2	no	—
228	C₂×D₈	—	2	4	no	—
229	C₂×D₈	—	2	2	no	—
230	C₂×M₁₆	C₂³×C₅	1	2	yes	—
231	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
232	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
233	C₂×M₁₆	C₂³×C₅	1	2	yes	—
234	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
235	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
236	C₄×Q₈	C₅×D₄	1	2	yes	—
237	C₄×D₄	—	2	2	no	—
238	C₄×D₄	—	2	2	no	—
239	C₄×D₄	—	2	2	no	—
240	C₄×D₄	—	2	2	no	—
241	C₄×D₄	—	2	2	no	—
242	C₄×D₄	C₅×D₄	1	2	yes	—
243	#117	—	2	1	no	—
244	#117	C₂³×C₅	1	1	yes	characteristic
245	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
246	C₂×C₂²⋊C₄	—	2	2	no	—
247	C₂×C₄²	—	2	1	no	—
248	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
249	#108	—	2	4	no	—
250	#107	—	2	2	no	—
251	#106	—	2	2	no	—
252	#106	—	2	2	no	—
253	C₄⋊C₈	—	2	2	no	—
254	C₄⋊C₈	—	2	2	no	—
255	#103	—	2	2	no	—
256	#102	—	2	2	no	—
257	#102	—	2	4	no	—
258	#102	—	2	2	no	—
259	#102	—	2	2	no	—
260	#100	—	2	4	no	—
261	#100	—	2	4	no	—
262	C₂²⋊C₈	—	2	2	no	—
263	C₂²⋊C₈	—	2	2	no	—
264	#97	—	2	1	no	—
265	#97	—	2	2	no	—
266	#97	C₅×D₄	1	2	yes	—
267	#97	C₅×D₄	1	2	yes	—
268	C₄×C₈	—	2	1	no	—
269	C₄×C₈	—	2	2	no	—
270	C₂²×C₅	—	2	2	no	—
271	C₂²×C₅	—	4	1	no	—
272	C₂²×C₅	—	4	4	no	—
273	C₂²×C₅	—	4	2	no	—
274	C₂²×C₅	—	8	4	no	—
275	C₂²×C₅	—	8	4	no	—
276	C₂²×C₅	—	8	2	no	—
277	C₂²×C₅	—	8	2	no	—
278	C₂²×C₅	C₂×#121	1	1	yes	characteristic
279	C₂²×C₅	#529	1	2	yes	—
280	C₄×C₅	—	2	2	no	—
281	C₄×C₅	—	2	2	no	—
282	C₄×C₅	—	4	1	no	—
283	C₄×C₅	—	4	2	no	—
284	C₄×C₅	—	8	2	no	—
285	C₄×C₅	#525	1	1	yes	characteristic
286	C₄×C₅	#525	1	2	yes	—
287	C₄×C₅	#532	1	1	yes	characteristic
288	C₂⁴	—	2	2	no	—
289	#41	—	2	2	no	—
290	#41	—	2	2	no	—
291	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
292	C₂×D₄	—	2	1	no	—
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	—	2	2	no	—
295	C₂×D₄	—	2	2	no	—
296	C₂×D₄	—	2	2	no	—
297	C₂×D₄	—	2	2	no	—
298	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
299	C₂×D₄	C₅×#41	1	4	yes	—
300	C₂²×C₄	—	2	1	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	4	2	no	—
304	C₂²×C₄	—	4	2	no	—
305	C₂²×C₄	—	8	4	no	—
306	C₂²×C₄	C₅×#41	1	2	yes	—
307	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
308	SD₁₆	—	2	8	no	—
309	D₈	—	2	8	no	—
310	D₈	—	2	8	no	—
311	M₁₆	—	2	2	no	—
312	M₁₆	—	2	2	no	—
313	M₁₆	—	2	2	no	—
314	M₁₆	—	2	2	no	—
315	M₁₆	—	2	2	no	—
316	M₁₆	C₅×#41	1	4	yes	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	2	1	no	—
321	C₂×C₈	—	2	1	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
324	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
325	C₄⋊C₄	—	2	2	no	—
326	C₄⋊C₄	—	2	2	no	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
329	C₂²⋊C₄	—	2	1	no	—
330	C₂²⋊C₄	—	2	2	no	—
331	C₂²⋊C₄	—	4	2	no	—
332	C₂²⋊C₄	—	4	2	no	—
333	C₄²	—	2	2	no	—
334	C₄²	—	2	1	no	—
335	C₄²	C₂×C₅×D₄	1	2	yes	—
336	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
337	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
338	C₂×C₅	—	2	2	no	—
339	C₂×C₅	—	8	1	no	—
340	C₂×C₅	—	8	4	no	—
341	C₂×C₅	#2392	1	1	yes	characteristic
342	C₂×C₅	#3068	1	2	yes	—
343	C₂³	—	2	1	no	—
344	C₂³	—	2	4	no	—
345	C₂³	—	4	2	no	—
346	C₂³	—	4	2	no	—
347	C₂³	—	8	2	no	—
348	C₂³	—	8	2	no	—
349	C₂³	C₂×C₅×#41	1	1	yes	characteristic
350	Q₈	—	2	2	no	—
351	D₄	—	2	4	no	—
352	D₄	—	2	2	no	—
353	D₄	—	2	4	no	—
354	D₄	—	4	2	no	—
355	D₄	—	4	2	no	—
356	D₄	—	4	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	4	1	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	8	2	no	—
364	C₂×C₄	—	8	4	no	—
365	C₂×C₄	—	8	4	no	—
366	C₂×C₄	—	8	2	no	—
367	C₂×C₄	C₅×#121	1	2	yes	—
368	C₂×C₄	C₅×#121	1	2	yes	—
369	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
370	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
371	C₂×C₄	C₂×C₅×#41	1	2	yes	—
372	C₂×C₄	C₂×C₅×#41	1	2	yes	—
373	C₈	—	2	2	no	—
374	C₈	—	2	4	no	—
375	C₈	—	2	2	no	—
376	C₈	—	4	1	no	—
377	C₈	—	4	2	no	—
378	C₈	—	4	1	no	—
379	C₅	#23719	1	1	yes	characteristic, direct product factor, Sylow
380	C₂²	—	2	2	no	—
381	C₂²	—	4	2	no	—
382	C₂²	—	4	1	no	—
383	C₂²	—	4	4	no	—
384	C₂²	—	8	4	no	—
385	C₂²	—	8	4	no	—
386	C₂²	—	8	2	no	—
387	C₂²	—	8	2	no	—
388	C₂²	C₂×C₅×#121	1	1	yes	characteristic
389	C₂²	C₅×#529	1	2	yes	—
390	C₄	—	2	2	no	—
391	C₄	—	2	2	no	—
392	C₄	—	4	2	no	—
393	C₄	—	4	1	no	—
394	C₄	—	8	2	no	—
395	C₄	C₅×#525	1	1	yes	characteristic
396	C₄	C₅×#525	1	2	yes	—
397	C₄	C₅×#532	1	1	yes	characteristic
398	C₂	—	2	2	no	—
399	C₂	—	8	1	no	—
400	C₂	—	8	4	no	—
401	C₂	C₅×#2392	1	1	yes	characteristic
402	C₂	C₅×#3068	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₅	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
prime radical	C₅×#2018	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ 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. C₄×C₅×AGL(1,ℤ/8)	C₂	semidirect
2. C₂×C₅×#442	C₂	semidirect
3. C₅×#2923	C₂	semidirect
4. C₅×#2090	C₂	semidirect
5. C₅×#2079	C₂	semidirect
6. C₅×#2063	C₂	semidirect
7. C₅×#2051	C₂	semidirect
8. C₅×#2045	C₂	semidirect
10. C₅×#1778	C₂	semidirect
11. C₄×C₅×#100	C₂	semidirect
43. #23719	C₅	direct (N × H)
93. C₄×AGL(1,ℤ/8)	C₂×C₅	semidirect
94. C₂×#442	C₂×C₅	semidirect
95. #2923	C₂×C₅	semidirect
96. #2090	C₂×C₅	semidirect
97. #2079	C₂×C₅	semidirect
98. #2063	C₂×C₅	semidirect
99. #2051	C₂×C₅	semidirect
100. #2045	C₂×C₅	semidirect
102. #1778	C₂×C₅	semidirect
103. C₄×#100	C₂×C₅	semidirect
379. C₅	#23719	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₄×C₅×AGL(1,ℤ/8)	2
C₂×C₅×#442	2
C₅×#2923	2
C₅×#2090	2
C₅×#2079	2
C₅×#2063	2
C₅×#2051	2
C₅×#2045	2
C₅×#2018	2
C₅×#1778	2
C₄×C₅×#100	2
#23719	5

Subgroups — C5×#23719 #11946439

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#23719 #11946439