Subgroups — C₅×#17876 #11940596

Order 1280.

650 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2988	C₂	1	1	yes	maximal, characteristic
2	C₅×#2983	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₅×#137	C₂	1	1	yes	maximal, characteristic
4	C₅×#1587	C₂	1	2	yes	maximal, complemented
5	C₅×#1585	C₂	1	2	yes	maximal, complemented
6	C₅×#1584	C₂	1	2	yes	maximal, complemented
7	C₅×#1582	C₂	1	2	yes	maximal, complemented
8	C₅×#1565	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1476	C₂	1	1	yes	maximal, characteristic
10	C₂×C₅×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1451	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#137	C₄	1	1	yes	characteristic
13	C₄×C₅×#41	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
15	C₅×#446	—	2	1	no	—
16	C₅×#446	—	2	1	no	—
17	C₅×#446	C₂²	1	2	yes	—
18	C₅×#446	C₂²	1	2	yes	—
19	C₅×C₈×Q₈	C₂²	1	2	yes	—
20	C₅×#441	C₄	1	2	yes	—
21	C₅×#440	C₄	1	2	yes	—
22	C₄×C₅×Q₁₆	C₂²	1	2	yes	—
23	C₄×C₅×SD₁₆	C₂²	1	2	yes	—
24	C₅×C₈×D₄	—	2	2	no	—
25	C₅×C₈×D₄	C₂²	1	2	yes	—
26	C₅×#432	—	2	2	no	—
27	C₅×#431	—	2	1	no	—
28	C₅×#431	C₂²	1	1	yes	characteristic
29	C₅×#431	C₂²	1	1	yes	characteristic
30	C₅×#428	C₄	1	1	yes	characteristic
31	C₂×C₅×C₄⋊C₈	—	2	1	no	—
32	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
33	C₅×#419	C₄	1	1	yes	characteristic
34	C₅×#417	C₄	1	1	yes	characteristic
35	C₄×C₅×M₁₆	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
37	C₅×#335	C₂²	1	2	yes	—
38	C₅×#334	C₂²	1	2	yes	—
39	C₅×Q₈⋊C₈	C₂²	1	2	yes	—
40	C₅×Q₈⋊C₈	C₂²	1	1	yes	characteristic
41	C₅×Q₈⋊C₈	C₂²	1	2	yes	—
42	C₅×Q₈⋊C₈	C₂²	1	1	yes	characteristic
43	C₅×D₄⋊C₈	C₂²	1	1	yes	characteristic
44	C₅×D₄⋊C₈	C₂²	1	1	yes	characteristic
45	C₅×#322	C₂²	1	2	yes	—
46	C₅×#322	C₂²	1	2	yes	—
47	#17876	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
48	C₂×C₅×#41	C₂×C₄	1	1	yes	characteristic
49	C₂²×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
50	C₅×#137	—	2	4	no	—
51	C₂×C₅×Q₁₆	C₂×C₄	1	2	yes	—
52	C₂×C₅×SD₁₆	C₂×C₄	1	2	yes	—
53	C₂×C₅×M₁₆	C₂×C₄	1	1	yes	characteristic
54	C₂×C₅×M₁₆	C₂×C₄	1	1	yes	characteristic
55	C₂²×C₅×C₈	—	2	1	no	—
56	C₂²×C₅×C₈	—	2	1	no	—
57	C₂²×C₅×C₈	—	2	2	no	—
58	C₄×C₅×Q₈	—	2	1	no	—
59	C₄×C₅×Q₈	—	2	1	no	—
60	C₄×C₅×Q₈	C₂×C₄	1	2	yes	—
61	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
62	C₄×C₅×Q₈	C₂³	1	2	yes	—
63	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
64	C₄×C₅×D₄	—	2	1	no	—
65	C₄×C₅×D₄	—	2	1	no	—
66	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
67	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
68	C₅×#117	—	2	1	no	—
69	C₅×#117	C₂×C₄	1	1	yes	characteristic
70	C₂×C₅×C₄⋊C₄	—	2	1	no	—
71	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄²×C₅	—	2	1	no	—
73	C₂×C₄²×C₅	—	2	1	no	—
74	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
75	C₅×#107	C₂×C₄	1	2	yes	—
76	C₅×#106	C₂×C₄	1	2	yes	—
77	C₅×C₄⋊C₈	—	2	2	no	—
78	C₅×C₄⋊C₈	—	2	2	no	—
79	C₅×C₄⋊C₈	—	2	2	no	—
80	C₅×C₄⋊C₈	—	2	1	no	—
81	C₅×C₄⋊C₈	D₄	1	1	yes	characteristic
82	C₅×C₄⋊C₈	D₄	1	1	yes	characteristic
83	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
84	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
85	C₅×C₄⋊C₈	C₂³	1	2	yes	—
86	C₅×#103	C₂×C₄	1	2	yes	—
87	C₅×#103	C₂×C₄	1	2	yes	—
88	C₅×#103	C₂×C₄	1	2	yes	—
89	C₅×#102	C₂×C₄	1	2	yes	—
90	C₅×C₂²⋊C₈	—	2	1	no	—
91	C₅×C₂²⋊C₈	—	2	2	no	—
92	C₅×C₂²⋊C₈	D₄	1	2	yes	—
93	C₅×#97	—	2	2	no	—
94	C₅×#97	—	2	2	no	—
95	C₅×#97	C₂×C₄	1	2	yes	—
96	C₄×C₅×C₈	—	2	2	no	—
97	C₄×C₅×C₈	—	2	1	no	—
98	C₄×C₅×C₈	—	2	1	no	—
99	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
100	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
101	C₄×C₅×C₈	C₂³	1	2	yes	—
102	C₄×C₅×C₈	C₂³	1	2	yes	—
103	#2988	C₂×C₅	1	1	yes	characteristic
104	#2983	C₂×C₅	1	1	yes	characteristic, complemented
105	C₄×#137	C₂×C₅	1	1	yes	characteristic
106	#1587	C₂×C₅	1	2	yes	complemented
107	#1585	C₂×C₅	1	2	yes	complemented
108	#1584	C₂×C₅	1	2	yes	complemented
109	#1582	C₂×C₅	1	2	yes	complemented
110	#1565	C₂×C₅	1	1	yes	characteristic, complemented
111	#1476	C₂×C₅	1	1	yes	characteristic
112	C₂×Q₈⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
113	#1451	C₂×C₅	1	1	yes	characteristic, complemented
114	C₅×#41	—	2	2	no	—
115	C₅×#41	M₁₆	1	4	yes	—
116	C₂×C₅×Q₈	—	2	1	no	—
117	C₂×C₅×Q₈	—	2	2	no	—
118	C₂×C₅×Q₈	—	2	2	no	—
119	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
120	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₅×D₄	—	2	1	no	—
122	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
123	C₂²×C₄×C₅	—	2	1	no	—
124	C₂²×C₄×C₅	—	2	1	no	—
125	C₂²×C₄×C₅	—	2	1	no	—
126	C₂²×C₄×C₅	—	2	1	no	—
127	C₂²×C₄×C₅	—	2	1	no	—
128	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₅	#41	1	1	yes	characteristic
131	C₅×Q₁₆	—	2	4	no	—
132	C₅×SD₁₆	—	2	4	no	—
133	C₅×M₁₆	—	2	2	no	—
134	C₅×M₁₆	—	2	2	no	—
135	C₂×C₅×C₈	—	2	1	no	—
136	C₂×C₅×C₈	—	2	2	no	—
137	C₂×C₅×C₈	—	2	1	no	—
138	C₂×C₅×C₈	—	2	1	no	—
139	C₂×C₅×C₈	—	2	1	no	—
140	C₂×C₅×C₈	—	4	2	no	—
141	C₂×C₅×C₈	—	8	2	no	—
142	C₂×C₅×C₈	—	8	1	no	—
143	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
144	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
145	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
146	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
147	C₅×C₄⋊C₄	—	2	2	no	—
148	C₅×C₄⋊C₄	—	2	1	no	—
149	C₅×C₄⋊C₄	—	2	1	no	—
150	C₅×C₄⋊C₄	—	2	2	no	—
151	C₅×C₄⋊C₄	—	2	1	no	—
152	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
153	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
154	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
155	C₅×C₂²⋊C₄	—	2	1	no	—
156	C₅×C₂²⋊C₄	—	2	1	no	—
157	C₅×C₂²⋊C₄	—	2	1	no	—
158	C₄²×C₅	—	2	1	no	—
159	C₄²×C₅	—	2	1	no	—
160	C₄²×C₅	—	2	2	no	—
161	C₄²×C₅	—	2	1	no	—
162	C₄²×C₅	—	2	2	no	—
163	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
164	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
165	C₄²×C₅	#41	1	1	yes	characteristic
166	C₄²×C₅	C₂⁴	1	1	yes	characteristic
167	C₂×#137	C₄×C₅	1	1	yes	characteristic
168	C₄×#41	C₂²×C₅	1	1	yes	characteristic
169	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
170	#446	—	2	1	no	—
171	#446	—	2	1	no	—
172	#446	C₂²×C₅	1	2	yes	—
173	#446	C₂²×C₅	1	2	yes	—
174	C₈×Q₈	C₂²×C₅	1	2	yes	—
175	#441	C₄×C₅	1	2	yes	—
176	#440	C₄×C₅	1	2	yes	—
177	C₄×Q₁₆	C₂²×C₅	1	2	yes	—
178	C₄×SD₁₆	C₂²×C₅	1	2	yes	—
179	C₈×D₄	—	2	2	no	—
180	C₈×D₄	C₂²×C₅	1	2	yes	—
181	#432	—	2	2	no	—
182	#431	—	2	1	no	—
183	#431	C₂²×C₅	1	1	yes	characteristic
184	#431	C₂²×C₅	1	1	yes	characteristic
185	#428	C₄×C₅	1	1	yes	characteristic
186	C₂×C₄⋊C₈	—	2	1	no	—
187	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
188	#419	C₄×C₅	1	1	yes	characteristic
189	#417	C₄×C₅	1	1	yes	characteristic
190	C₄×M₁₆	C₂²×C₅	1	1	yes	characteristic
191	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
192	#335	C₂²×C₅	1	2	yes	—
193	#334	C₂²×C₅	1	2	yes	—
194	Q₈⋊C₈	C₂²×C₅	1	2	yes	—
195	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic
196	Q₈⋊C₈	C₂²×C₅	1	2	yes	—
197	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic
198	D₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
199	D₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
200	#322	C₂²×C₅	1	2	yes	—
201	#322	C₂²×C₅	1	2	yes	—
202	C₂³×C₅	—	2	1	no	—
203	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
204	C₅×Q₈	—	2	1	no	—
205	C₅×Q₈	—	2	2	no	—
206	C₅×Q₈	—	2	2	no	—
207	C₅×Q₈	—	4	2	no	—
208	C₅×Q₈	C₂×M₁₆	1	2	yes	—
209	C₅×D₄	—	2	4	no	—
210	C₅×D₄	—	2	1	no	—
211	C₅×D₄	C₂×M₁₆	1	2	yes	—
212	C₂×C₄×C₅	—	2	1	no	—
213	C₂×C₄×C₅	—	2	1	no	—
214	C₂×C₄×C₅	—	2	1	no	—
215	C₂×C₄×C₅	—	2	4	no	—
216	C₂×C₄×C₅	—	2	1	no	—
217	C₂×C₄×C₅	—	2	1	no	—
218	C₂×C₄×C₅	—	2	2	no	—
219	C₂×C₄×C₅	—	2	2	no	—
220	C₂×C₄×C₅	—	4	1	no	—
221	C₂×C₄×C₅	—	4	2	no	—
222	C₂×C₄×C₅	—	4	1	no	—
223	C₂×C₄×C₅	—	4	1	no	—
224	C₂×C₄×C₅	—	8	1	no	—
225	C₂×C₄×C₅	—	8	1	no	—
226	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
227	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
228	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
229	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
230	C₂×C₄×C₅	#131	1	2	yes	—
231	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
232	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
233	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
234	C₅×C₈	—	2	2	no	—
235	C₅×C₈	—	2	2	no	—
236	C₅×C₈	—	2	2	no	—
237	C₅×C₈	—	2	2	no	—
238	C₅×C₈	—	2	2	no	—
239	C₅×C₈	—	4	1	no	—
240	C₅×C₈	—	4	1	no	—
241	C₅×C₈	—	4	2	no	—
242	C₅×C₈	—	4	1	no	—
243	C₂×#41	C₂×C₄×C₅	1	1	yes	characteristic
244	C₂²×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
245	#137	—	2	4	no	—
246	C₂×Q₁₆	C₂×C₄×C₅	1	2	yes	—
247	C₂×SD₁₆	C₂×C₄×C₅	1	2	yes	—
248	C₂×M₁₆	C₂×C₄×C₅	1	1	yes	characteristic
249	C₂×M₁₆	C₂×C₄×C₅	1	1	yes	characteristic
250	C₂²×C₈	—	2	1	no	—
251	C₂²×C₈	—	2	1	no	—
252	C₂²×C₈	—	2	2	no	—
253	C₄×Q₈	—	2	1	no	—
254	C₄×Q₈	—	2	1	no	—
255	C₄×Q₈	C₂×C₄×C₅	1	2	yes	—
256	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
257	C₄×Q₈	C₂³×C₅	1	2	yes	—
258	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
259	C₄×D₄	—	2	1	no	—
260	C₄×D₄	—	2	1	no	—
261	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
262	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
263	#117	—	2	1	no	—
264	#117	C₂×C₄×C₅	1	1	yes	characteristic
265	C₂×C₄⋊C₄	—	2	1	no	—
266	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
267	C₂×C₄²	—	2	1	no	—
268	C₂×C₄²	—	2	1	no	—
269	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
270	#107	C₂×C₄×C₅	1	2	yes	—
271	#106	C₂×C₄×C₅	1	2	yes	—
272	C₄⋊C₈	—	2	2	no	—
273	C₄⋊C₈	—	2	2	no	—
274	C₄⋊C₈	—	2	2	no	—
275	C₄⋊C₈	—	2	1	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	C₄⋊C₈	C₂³×C₅	1	2	yes	—
281	#103	C₂×C₄×C₅	1	2	yes	—
282	#103	C₂×C₄×C₅	1	2	yes	—
283	#103	C₂×C₄×C₅	1	2	yes	—
284	#102	C₂×C₄×C₅	1	2	yes	—
285	C₂²⋊C₈	—	2	1	no	—
286	C₂²⋊C₈	—	2	2	no	—
287	C₂²⋊C₈	C₅×D₄	1	2	yes	—
288	#97	—	2	2	no	—
289	#97	—	2	2	no	—
290	#97	C₂×C₄×C₅	1	2	yes	—
291	C₄×C₈	—	2	2	no	—
292	C₄×C₈	—	2	1	no	—
293	C₄×C₈	—	2	1	no	—
294	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
295	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
296	C₄×C₈	C₂³×C₅	1	2	yes	—
297	C₄×C₈	C₂³×C₅	1	2	yes	—
298	C₂²×C₅	—	2	1	no	—
299	C₂²×C₅	—	2	1	no	—
300	C₂²×C₅	—	2	2	no	—
301	C₂²×C₅	—	4	1	no	—
302	C₂²×C₅	—	4	1	no	—
303	C₂²×C₅	#435	1	2	yes	—
304	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
305	C₄×C₅	—	2	2	no	—
306	C₄×C₅	—	2	1	no	—
307	C₄×C₅	—	2	1	no	—
308	C₄×C₅	—	2	1	no	—
309	C₄×C₅	—	4	2	no	—
310	C₄×C₅	—	4	1	no	—
311	C₄×C₅	—	4	1	no	—
312	C₄×C₅	—	4	2	no	—
313	C₄×C₅	#435	1	2	yes	—
314	C₄×C₅	C₂²×M₁₆	1	1	yes	characteristic
315	C₄×C₅	C₂×#131	1	1	yes	characteristic
316	C₄×C₅	#577	1	1	yes	characteristic
317	C₄×C₅	#578	1	1	yes	characteristic
318	#41	—	2	2	no	—
319	#41	C₅×M₁₆	1	4	yes	—
320	C₂×Q₈	—	2	1	no	—
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
324	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
325	C₂×D₄	—	2	1	no	—
326	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
333	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
334	C₂²×C₄	C₅×#41	1	1	yes	characteristic
335	Q₁₆	—	2	4	no	—
336	SD₁₆	—	2	4	no	—
337	M₁₆	—	2	2	no	—
338	M₁₆	—	2	2	no	—
339	C₂×C₈	—	2	1	no	—
340	C₂×C₈	—	2	1	no	—
341	C₂×C₈	—	2	1	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	2	1	no	—
344	C₂×C₈	—	4	2	no	—
345	C₂×C₈	—	8	2	no	—
346	C₂×C₈	—	8	1	no	—
347	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
348	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
349	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
350	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	—	2	1	no	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	2	1	no	—
356	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
357	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
358	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
359	C₂²⋊C₄	—	2	1	no	—
360	C₂²⋊C₄	—	2	1	no	—
361	C₂²⋊C₄	—	2	1	no	—
362	C₄²	—	2	1	no	—
363	C₄²	—	2	1	no	—
364	C₄²	—	2	2	no	—
365	C₄²	—	2	1	no	—
366	C₄²	—	2	2	no	—
367	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
368	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
369	C₄²	C₅×#41	1	1	yes	characteristic
370	C₄²	C₂⁴×C₅	1	1	yes	characteristic
371	C₂×C₅	—	2	2	no	—
372	C₂×C₅	—	4	2	no	—
373	C₂×C₅	C₂×#435	1	1	yes	characteristic
374	C₂×C₅	#2947	1	1	yes	characteristic
375	C₂×C₅	#2956	1	1	yes	characteristic
376	C₂³	—	2	1	no	—
377	C₂³	C₄×C₅×D₄	1	1	yes	characteristic
378	Q₈	—	2	1	no	—
379	Q₈	—	2	2	no	—
380	Q₈	—	2	2	no	—
381	Q₈	—	4	2	no	—
382	Q₈	C₂×C₅×M₁₆	1	2	yes	—
383	D₄	—	2	4	no	—
384	D₄	—	2	1	no	—
385	D₄	C₂×C₅×M₁₆	1	2	yes	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	4	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	8	1	no	—
399	C₂×C₄	—	8	1	no	—
400	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
401	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
402	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
403	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
404	C₂×C₄	C₅×#131	1	2	yes	—
405	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
406	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
407	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
408	C₈	—	2	2	no	—
409	C₈	—	2	2	no	—
410	C₈	—	2	2	no	—
411	C₈	—	2	2	no	—
412	C₈	—	2	2	no	—
413	C₈	—	4	1	no	—
414	C₈	—	4	2	no	—
415	C₈	—	4	1	no	—
416	C₈	—	4	1	no	—
417	C₅	#17876	1	1	yes	characteristic, direct product factor, Sylow
418	C₂²	—	2	1	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	2	2	no	—
421	C₂²	—	4	1	no	—
422	C₂²	—	4	1	no	—
423	C₂²	C₅×#435	1	2	yes	—
424	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
425	C₄	—	2	2	no	—
426	C₄	—	2	1	no	—
427	C₄	—	2	1	no	—
428	C₄	—	2	1	no	—
429	C₄	—	4	2	no	—
430	C₄	—	4	1	no	—
431	C₄	—	4	1	no	—
432	C₄	—	4	2	no	—
433	C₄	C₅×#435	1	2	yes	—
434	C₄	C₂²×C₅×M₁₆	1	1	yes	characteristic
435	C₄	C₂×C₅×#131	1	1	yes	characteristic
436	C₄	C₅×#577	1	1	yes	characteristic
437	C₄	C₅×#578	1	1	yes	characteristic
438	C₂	—	2	2	no	—
439	C₂	—	4	2	no	—
440	C₂	C₂×C₅×#435	1	1	yes	characteristic
441	C₂	C₅×#2947	1	1	yes	characteristic
442	C₂	C₅×#2956	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	C₂×C₄×D₄
prime radical	C₂×C₅×#41	C₂×C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₅×#431 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×#2983	C₂	semidirect
4. C₅×#1587	C₂	semidirect
5. C₅×#1585	C₂	semidirect
6. C₅×#1584	C₂	semidirect
7. C₅×#1582	C₂	semidirect
8. C₅×#1565	C₂	semidirect
10. C₂×C₅×Q₈⋊C₈	C₂	semidirect
11. C₅×#1451	C₂	semidirect
47. #17876	C₅	direct (N × H)
104. #2983	C₂×C₅	semidirect
106. #1587	C₂×C₅	semidirect
107. #1585	C₂×C₅	semidirect
108. #1584	C₂×C₅	semidirect
109. #1582	C₂×C₅	semidirect
110. #1565	C₂×C₅	semidirect
112. C₂×Q₈⋊C₈	C₂×C₅	semidirect
113. #1451	C₂×C₅	semidirect
417. C₅	#17876	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×#2988	2
C₅×#2983	2
C₄×C₅×#137	2
C₅×#1587	2
C₅×#1585	2
C₅×#1584	2
C₅×#1582	2
C₅×#1565	2
C₅×#1476	2
C₂×C₅×Q₈⋊C₈	2
C₅×#1451	2
#17876	5

Subgroups — C5×#17876 #11940596

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#17876 #11940596