Subgroups — C₅×#33645 #11956365

Order 1280.

590 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3050	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#427	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2237	C₂	1	2	yes	maximal, complemented
4	C₅×#2236	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2235	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2234	C₂	1	2	yes	maximal, complemented
7	C₅×#2233	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2232	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#2158	C₂	1	2	yes	maximal, complemented
10	C₅×#2138	C₂	1	2	yes	maximal, complemented
11	C₂×C₅×C₂²⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#135	C₂²	1	1	yes	characteristic
13	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
14	C₅×#525	—	2	1	no	—
15	C₂×C₅×#117	—	2	1	no	—
16	C₂²×C₅×C₁₆	C₂²	1	2	yes	—
17	C₅×#467	C₂²	1	1	yes	characteristic
18	C₅×#467	C₂²	1	1	yes	characteristic
19	C₅×#466	C₂²	1	1	yes	characteristic
20	C₅×#466	C₂²	1	1	yes	characteristic
21	C₅×#465	—	2	1	no	—
22	C₅×#465	—	2	1	no	—
23	C₅×#427	—	2	1	no	—
24	C₅×#427	—	2	1	no	—
25	C₅×#427	C₂²	1	1	yes	characteristic
26	C₅×#427	C₂²	1	2	yes	—
27	C₅×#427	C₂²	1	2	yes	—
28	C₂×C₅×#107	C₂²	1	1	yes	characteristic
29	C₂×C₅×#107	C₂²	1	1	yes	characteristic
30	C₂×C₅×#106	—	2	1	no	—
31	C₅×#416	—	2	1	no	—
32	C₅×#367	C₂²	1	2	yes	complemented
33	C₅×#367	C₂²	1	2	yes	complemented
34	C₅×#366	C₂²	1	2	yes	complemented
35	C₅×#366	C₂²	1	2	yes	complemented
36	C₅×#358	C₂²	1	2	yes	complemented
37	C₅×#358	C₂²	1	2	yes	complemented
38	C₅×#357	C₂²	1	2	yes	complemented
39	C₅×#357	C₂²	1	2	yes	complemented
40	C₅×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
41	C₅×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
42	C₅×C₂²⋊C₁₆	C₂²	1	2	yes	—
43	#33645	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂×C₅×#41	—	2	1	no	—
45	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
46	C₅×#135	—	2	4	no	—
47	C₂×C₅×Q₁₆	C₂³	1	1	yes	characteristic
48	C₂×C₅×SD₁₆	—	2	1	no	—
49	C₂×C₅×D₈	C₂³	1	1	yes	characteristic
50	C₂²×C₅×C₈	—	2	4	no	—
51	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
52	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
53	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
54	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
55	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
56	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
57	C₅×#123	—	4	1	no	—
58	C₅×C₂²⋊Q₈	—	2	1	no	—
59	C₅×C₂²⋊Q₈	—	2	1	no	—
60	C₅×#121	—	2	1	no	—
61	C₅×#121	—	2	1	no	—
62	C₅×#120	—	4	1	no	—
63	C₄×C₅×D₄	—	4	1	no	—
64	C₄×C₅×D₄	—	4	1	no	—
65	C₅×#117	—	2	1	no	—
66	C₅×#117	—	2	2	no	—
67	C₅×#117	—	2	2	no	—
68	C₅×#117	—	4	1	no	—
69	C₅×#117	—	4	1	no	—
70	C₂×C₅×C₄⋊C₄	—	2	1	no	—
71	C₂×C₅×C₄⋊C₄	—	2	1	no	—
72	C₂×C₅×C₂²⋊C₄	—	4	1	no	—
73	C₂×C₄²×C₅	—	4	1	no	—
74	C₂×C₅×C₁₆	—	2	4	no	—
75	C₂×C₅×C₁₆	C₂³	1	2	yes	—
76	C₂×C₅×C₁₆	C₂³	1	2	yes	—
77	C₅×#107	—	2	1	no	—
78	C₅×#107	—	2	1	no	—
79	C₅×#107	C₂³	1	2	yes	—
80	C₅×#107	C₂³	1	2	yes	—
81	C₅×#107	C₂³	1	1	yes	characteristic
82	C₅×#107	C₂³	1	1	yes	characteristic
83	C₅×#106	—	2	2	no	—
84	C₅×#106	—	2	2	no	—
85	C₅×#106	—	2	1	no	—
86	C₅×#103	—	2	1	no	—
87	C₅×#103	—	2	1	no	—
88	C₅×#102	—	2	1	no	—
89	C₅×#102	—	2	1	no	—
90	#3050	C₂×C₅	1	1	yes	characteristic
91	C₂×#427	C₂×C₅	1	1	yes	characteristic, complemented
92	#2237	C₂×C₅	1	2	yes	complemented
93	#2236	C₂×C₅	1	1	yes	characteristic, complemented
94	#2235	C₂×C₅	1	1	yes	characteristic, complemented
95	#2234	C₂×C₅	1	2	yes	complemented
96	#2233	C₂×C₅	1	1	yes	characteristic, complemented
97	#2232	C₂×C₅	1	1	yes	characteristic, complemented
98	#2158	C₂×C₅	1	2	yes	complemented
99	#2138	C₂×C₅	1	2	yes	complemented
100	C₂×C₂²⋊C₁₆	C₂×C₅	1	1	yes	characteristic, complemented
101	C₂⁴×C₅	D₈	1	1	yes	characteristic
102	C₅×#41	—	4	2	no	—
103	C₅×#41	—	4	2	no	—
104	C₂×C₅×Q₈	—	2	1	no	—
105	C₂×C₅×D₄	—	2	1	no	—
106	C₂×C₅×D₄	—	4	1	no	—
107	C₂×C₅×D₄	—	4	1	no	—
108	C₂×C₅×D₄	—	4	1	no	—
109	C₂²×C₄×C₅	—	2	2	no	—
110	C₂²×C₄×C₅	—	2	2	no	—
111	C₂²×C₄×C₅	—	4	1	no	—
112	C₂²×C₄×C₅	—	4	1	no	—
113	C₂²×C₄×C₅	—	4	1	no	—
114	C₂²×C₄×C₅	D₈	1	1	yes	characteristic
115	C₂²×C₄×C₅	D₈	1	1	yes	characteristic
116	C₂²×C₄×C₅	D₈	1	1	yes	characteristic
117	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
120	C₅×Q₁₆	—	2	2	no	—
121	C₅×SD₁₆	—	4	2	no	—
122	C₅×D₈	—	2	2	no	—
123	C₂×C₅×C₈	—	2	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	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	C₂×C₅×C₈	#41	1	4	yes	—
132	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
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	—	4	1	no	—
138	C₅×C₄⋊C₄	—	4	1	no	—
139	C₅×C₄⋊C₄	—	4	1	no	—
140	C₅×C₄⋊C₄	—	4	1	no	—
141	C₅×C₂²⋊C₄	—	4	2	no	—
142	C₅×C₂²⋊C₄	—	4	2	no	—
143	C₅×C₂²⋊C₄	—	4	1	no	—
144	C₅×C₂²⋊C₄	—	4	1	no	—
145	C₅×C₂²⋊C₄	—	4	1	no	—
146	C₅×C₂²⋊C₄	—	4	1	no	—
147	C₅×C₂²⋊C₄	—	4	1	no	—
148	C₄²×C₅	—	4	2	no	—
149	C₄²×C₅	—	4	2	no	—
150	C₄²×C₅	—	4	1	no	—
151	C₅×C₁₆	—	2	2	no	—
152	C₅×C₁₆	—	2	2	no	—
153	C₂×#135	C₂²×C₅	1	1	yes	characteristic
154	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
155	#525	—	2	1	no	—
156	C₂×#117	—	2	1	no	—
157	C₂²×C₁₆	C₂²×C₅	1	2	yes	—
158	#467	C₂²×C₅	1	1	yes	characteristic
159	#467	C₂²×C₅	1	1	yes	characteristic
160	#466	C₂²×C₅	1	1	yes	characteristic
161	#466	C₂²×C₅	1	1	yes	characteristic
162	#465	—	2	1	no	—
163	#465	—	2	1	no	—
164	#427	—	2	1	no	—
165	#427	—	2	1	no	—
166	#427	C₂²×C₅	1	2	yes	—
167	#427	C₂²×C₅	1	2	yes	—
168	#427	C₂²×C₅	1	1	yes	characteristic
169	C₂×#107	C₂²×C₅	1	1	yes	characteristic
170	C₂×#107	C₂²×C₅	1	1	yes	characteristic
171	C₂×#106	—	2	1	no	—
172	#416	—	2	1	no	—
173	#367	C₂²×C₅	1	2	yes	complemented
174	#367	C₂²×C₅	1	2	yes	complemented
175	#366	C₂²×C₅	1	2	yes	complemented
176	#366	C₂²×C₅	1	2	yes	complemented
177	#358	C₂²×C₅	1	2	yes	complemented
178	#358	C₂²×C₅	1	2	yes	complemented
179	#357	C₂²×C₅	1	2	yes	complemented
180	#357	C₂²×C₅	1	2	yes	complemented
181	C₂²⋊C₁₆	C₂²×C₅	1	1	yes	characteristic
182	C₂²⋊C₁₆	C₂²×C₅	1	1	yes	characteristic
183	C₂²⋊C₁₆	C₂²×C₅	1	2	yes	—
184	C₂³×C₅	—	2	2	no	—
185	C₂³×C₅	—	2	2	no	—
186	C₂³×C₅	—	4	1	no	—
187	C₂³×C₅	—	4	1	no	—
188	C₂³×C₅	C₂×D₈	1	1	yes	characteristic
189	C₂³×C₅	C₂×D₈	1	1	yes	characteristic
190	C₂³×C₅	C₂×D₈	1	1	yes	characteristic
191	C₅×Q₈	—	4	1	no	—
192	C₅×Q₈	—	4	1	no	—
193	C₅×D₄	—	4	1	no	—
194	C₅×D₄	—	4	1	no	—
195	C₅×D₄	—	8	2	no	—
196	C₅×D₄	—	8	2	no	—
197	C₅×D₄	—	8	2	no	—
198	C₂×C₄×C₅	—	2	2	no	—
199	C₂×C₄×C₅	—	2	1	no	—
200	C₂×C₄×C₅	—	2	1	no	—
201	C₂×C₄×C₅	—	2	1	no	—
202	C₂×C₄×C₅	—	2	1	no	—
203	C₂×C₄×C₅	—	2	2	no	—
204	C₂×C₄×C₅	—	2	2	no	—
205	C₂×C₄×C₅	—	4	2	no	—
206	C₂×C₄×C₅	—	4	2	no	—
207	C₂×C₄×C₅	—	4	1	no	—
208	C₂×C₄×C₅	—	4	1	no	—
209	C₂×C₄×C₅	—	4	1	no	—
210	C₂×C₄×C₅	—	8	2	no	—
211	C₂×C₄×C₅	—	8	2	no	—
212	C₂×C₄×C₅	—	8	2	no	—
213	C₂×C₄×C₅	#123	1	2	yes	—
214	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
215	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
216	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
217	C₂×C₄×C₅	#137	1	2	yes	—
218	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
219	C₅×C₈	—	2	1	no	—
220	C₅×C₈	—	2	1	no	—
221	C₅×C₈	#123	1	2	yes	—
222	C₅×C₈	C₂×#41	1	2	yes	—
223	C₂×#41	—	2	1	no	—
224	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
225	#135	—	2	4	no	—
226	C₂×Q₁₆	C₂³×C₅	1	1	yes	characteristic
227	C₂×SD₁₆	—	2	1	no	—
228	C₂×D₈	C₂³×C₅	1	1	yes	characteristic
229	C₂²×C₈	—	2	4	no	—
230	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
231	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
232	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
233	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
234	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
235	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
236	#123	—	4	1	no	—
237	C₂²⋊Q₈	—	2	1	no	—
238	C₂²⋊Q₈	—	2	1	no	—
239	#121	—	2	1	no	—
240	#121	—	2	1	no	—
241	#120	—	4	1	no	—
242	C₄×D₄	—	4	1	no	—
243	C₄×D₄	—	4	1	no	—
244	#117	—	2	2	no	—
245	#117	—	2	2	no	—
246	#117	—	2	1	no	—
247	#117	—	4	1	no	—
248	#117	—	4	1	no	—
249	C₂×C₄⋊C₄	—	2	1	no	—
250	C₂×C₄⋊C₄	—	2	1	no	—
251	C₂×C₂²⋊C₄	—	4	1	no	—
252	C₂×C₄²	—	4	1	no	—
253	C₂×C₁₆	—	2	4	no	—
254	C₂×C₁₆	C₂³×C₅	1	2	yes	—
255	C₂×C₁₆	C₂³×C₅	1	2	yes	—
256	#107	—	2	1	no	—
257	#107	—	2	1	no	—
258	#107	C₂³×C₅	1	2	yes	—
259	#107	C₂³×C₅	1	2	yes	—
260	#107	C₂³×C₅	1	1	yes	characteristic
261	#107	C₂³×C₅	1	1	yes	characteristic
262	#106	—	2	2	no	—
263	#106	—	2	2	no	—
264	#106	—	2	1	no	—
265	#103	—	2	1	no	—
266	#103	—	2	1	no	—
267	#102	—	2	1	no	—
268	#102	—	2	1	no	—
269	C₂²×C₅	—	2	1	no	—
270	C₂²×C₅	—	2	1	no	—
271	C₂²×C₅	—	2	1	no	—
272	C₂²×C₅	—	2	1	no	—
273	C₂²×C₅	—	2	1	no	—
274	C₂²×C₅	—	2	1	no	—
275	C₂²×C₅	—	2	1	no	—
276	C₂²×C₅	—	4	4	no	—
277	C₂²×C₅	—	8	1	no	—
278	C₂²×C₅	—	8	1	no	—
279	C₂²×C₅	—	8	1	no	—
280	C₂²×C₅	#480	1	2	yes	—
281	C₂²×C₅	#508	1	2	yes	—
282	C₂²×C₅	C₂²×D₈	1	1	yes	characteristic
283	C₄×C₅	—	2	1	no	—
284	C₄×C₅	—	2	1	no	—
285	C₄×C₅	—	8	1	no	—
286	C₄×C₅	—	8	2	no	—
287	C₄×C₅	—	8	1	no	—
288	C₄×C₅	—	8	2	no	—
289	C₄×C₅	—	8	1	no	—
290	C₄×C₅	#480	1	2	yes	—
291	C₄×C₅	C₂×#123	1	1	yes	characteristic
292	C₄×C₅	C₂×#137	1	1	yes	characteristic
293	C₂⁴	C₅×D₈	1	1	yes	characteristic
294	#41	—	4	2	no	—
295	#41	—	4	2	no	—
296	C₂×Q₈	—	2	1	no	—
297	C₂×D₄	—	2	1	no	—
298	C₂×D₄	—	4	1	no	—
299	C₂×D₄	—	4	1	no	—
300	C₂×D₄	—	4	1	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	4	1	no	—
304	C₂²×C₄	—	4	1	no	—
305	C₂²×C₄	—	4	1	no	—
306	C₂²×C₄	C₅×D₈	1	1	yes	characteristic
307	C₂²×C₄	C₅×D₈	1	1	yes	characteristic
308	C₂²×C₄	C₅×D₈	1	1	yes	characteristic
309	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
310	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
311	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
312	Q₁₆	—	2	2	no	—
313	SD₁₆	—	4	2	no	—
314	D₈	—	2	2	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
321	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
322	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
323	C₂×C₈	C₅×#41	1	4	yes	—
324	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
325	C₄⋊C₄	—	2	1	no	—
326	C₄⋊C₄	—	2	1	no	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	2	2	no	—
329	C₄⋊C₄	—	4	1	no	—
330	C₄⋊C₄	—	4	1	no	—
331	C₄⋊C₄	—	4	1	no	—
332	C₄⋊C₄	—	4	1	no	—
333	C₂²⋊C₄	—	4	2	no	—
334	C₂²⋊C₄	—	4	2	no	—
335	C₂²⋊C₄	—	4	1	no	—
336	C₂²⋊C₄	—	4	1	no	—
337	C₂²⋊C₄	—	4	1	no	—
338	C₂²⋊C₄	—	4	1	no	—
339	C₂²⋊C₄	—	4	1	no	—
340	C₄²	—	4	2	no	—
341	C₄²	—	4	2	no	—
342	C₄²	—	4	1	no	—
343	C₁₆	—	2	2	no	—
344	C₁₆	—	2	2	no	—
345	C₂×C₅	—	2	2	no	—
346	C₂×C₅	—	2	2	no	—
347	C₂×C₅	—	4	1	no	—
348	C₂×C₅	—	16	1	no	—
349	C₂×C₅	C₂×#480	1	1	yes	characteristic
350	C₂×C₅	C₂×#508	1	1	yes	characteristic
351	C₂×C₅	#3414	1	1	yes	characteristic
352	C₂³	—	2	2	no	—
353	C₂³	—	2	2	no	—
354	C₂³	—	4	1	no	—
355	C₂³	—	4	1	no	—
356	C₂³	C₂×C₅×D₈	1	1	yes	characteristic
357	C₂³	C₂×C₅×D₈	1	1	yes	characteristic
358	C₂³	C₂×C₅×D₈	1	1	yes	characteristic
359	Q₈	—	4	1	no	—
360	Q₈	—	4	1	no	—
361	D₄	—	4	1	no	—
362	D₄	—	4	1	no	—
363	D₄	—	8	2	no	—
364	D₄	—	8	2	no	—
365	D₄	—	8	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	1	no	—
376	C₂×C₄	—	4	1	no	—
377	C₂×C₄	—	4	1	no	—
378	C₂×C₄	—	8	2	no	—
379	C₂×C₄	—	8	2	no	—
380	C₂×C₄	—	8	2	no	—
381	C₂×C₄	C₅×#123	1	2	yes	—
382	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
383	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
384	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
385	C₂×C₄	C₅×#137	1	2	yes	—
386	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
387	C₈	—	2	1	no	—
388	C₈	—	2	1	no	—
389	C₈	C₅×#123	1	2	yes	—
390	C₈	C₂×C₅×#41	1	2	yes	—
391	C₅	#33645	1	1	yes	characteristic, direct product factor, Sylow
392	C₂²	—	2	1	no	—
393	C₂²	—	2	1	no	—
394	C₂²	—	2	1	no	—
395	C₂²	—	2	1	no	—
396	C₂²	—	2	1	no	—
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	4	4	no	—
400	C₂²	—	8	1	no	—
401	C₂²	—	8	1	no	—
402	C₂²	—	8	1	no	—
403	C₂²	C₅×#480	1	2	yes	—
404	C₂²	C₅×#508	1	2	yes	—
405	C₂²	C₂²×C₅×D₈	1	1	yes	characteristic
406	C₄	—	2	1	no	—
407	C₄	—	2	1	no	—
408	C₄	—	8	1	no	—
409	C₄	—	8	2	no	—
410	C₄	—	8	1	no	—
411	C₄	—	8	2	no	—
412	C₄	—	8	1	no	—
413	C₄	C₅×#480	1	2	yes	—
414	C₄	C₂×C₅×#123	1	1	yes	characteristic
415	C₄	C₂×C₅×#137	1	1	yes	characteristic
416	C₂	—	2	2	no	—
417	C₂	—	2	2	no	—
418	C₂	—	4	1	no	—
419	C₂	—	16	1	no	—
420	C₂	C₂×C₅×#480	1	1	yes	characteristic
421	C₂	C₂×C₅×#508	1	1	yes	characteristic
422	C₂	C₅×#3414	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₅
socle	C₂²×C₅	C₂²×D₈
prime radical	C₅×#3050	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂³×C₄×C₅ ◁ C₂³×C₅×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#427	C₂	semidirect
3. C₅×#2237	C₂	semidirect
4. C₅×#2236	C₂	semidirect
5. C₅×#2235	C₂	semidirect
6. C₅×#2234	C₂	semidirect
7. C₅×#2233	C₂	semidirect
8. C₅×#2232	C₂	semidirect
9. C₅×#2158	C₂	semidirect
10. C₅×#2138	C₂	semidirect
11. C₂×C₅×C₂²⋊C₁₆	C₂	semidirect
32. C₅×#367	C₂²	semidirect
33. C₅×#367	C₂²	semidirect
34. C₅×#366	C₂²	semidirect
35. C₅×#366	C₂²	semidirect
36. C₅×#358	C₂²	semidirect
37. C₅×#358	C₂²	semidirect
38. C₅×#357	C₂²	semidirect
39. C₅×#357	C₂²	semidirect
43. #33645	C₅	direct (N × H)
91. C₂×#427	C₂×C₅	semidirect
92. #2237	C₂×C₅	semidirect
93. #2236	C₂×C₅	semidirect
94. #2235	C₂×C₅	semidirect
95. #2234	C₂×C₅	semidirect
96. #2233	C₂×C₅	semidirect
97. #2232	C₂×C₅	semidirect
98. #2158	C₂×C₅	semidirect
99. #2138	C₂×C₅	semidirect
100. C₂×C₂²⋊C₁₆	C₂×C₅	semidirect
173. #367	C₂²×C₅	semidirect
174. #367	C₂²×C₅	semidirect
175. #366	C₂²×C₅	semidirect
176. #366	C₂²×C₅	semidirect
177. #358	C₂²×C₅	semidirect
178. #358	C₂²×C₅	semidirect
179. #357	C₂²×C₅	semidirect
180. #357	C₂²×C₅	semidirect
391. C₅	#33645	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×#3050	2
C₂×C₅×#427	2
C₅×#2237	2
C₅×#2236	2
C₅×#2235	2
C₅×#2234	2
C₅×#2233	2
C₅×#2232	2
C₅×#2158	2
C₅×#2138	2
C₂×C₅×C₂²⋊C₁₆	2
#33645	5

Subgroups — C5×#33645 #11956365

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#33645 #11956365