Subgroups — C₅×#18032 #11940752

Order 1280.

566 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3104	C₂	1	1	yes	maximal, characteristic
2	C₅×#2986	C₂	1	1	yes	maximal, characteristic
3	C₅×#2984	C₂	1	1	yes	maximal, characteristic
4	C₅×#1593	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1591	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1587	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1587	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1584	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1584	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1579	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×C₈×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1572	C₂	1	1	yes	maximal, characteristic
13	C₅×#1497	C₂	1	1	yes	maximal, characteristic
14	C₅×#1479	C₂	1	1	yes	maximal, characteristic
15	C₅×#1454	C₂	1	1	yes	maximal, characteristic
16	C₅×#533	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
18	C₅×#484	C₄	1	1	yes	characteristic
19	C₅×#484	C₄	1	1	yes	characteristic
20	C₅×#477	C₄	1	1	yes	characteristic
21	C₅×#477	C₄	1	1	yes	characteristic
22	C₅×#462	C₄	1	1	yes	characteristic
23	C₅×#462	C₄	1	1	yes	characteristic
24	C₅×#451	C₄	1	1	yes	characteristic
25	C₅×#451	C₄	1	1	yes	characteristic
26	C₅×#446	—	2	1	no	—
27	C₅×#446	—	2	1	no	—
28	C₅×#446	—	2	1	no	—
29	C₅×#446	C₂²	1	1	yes	characteristic
30	C₅×#446	C₂²	1	1	yes	characteristic
31	C₅×#446	C₂²	1	1	yes	characteristic
32	C₅×#446	C₂²	1	1	yes	characteristic
33	C₅×C₈×Q₈	—	2	1	no	—
34	C₅×C₈×Q₈	C₂²	1	1	yes	characteristic
35	C₅×C₈×Q₈	C₂²	1	1	yes	characteristic
36	C₅×C₈×Q₈	C₂²	1	1	yes	characteristic
37	C₅×C₈×Q₈	C₂²	1	1	yes	characteristic
38	C₄×C₅×Q₁₆	C₂²	1	1	yes	characteristic
39	C₄×C₅×Q₁₆	C₂²	1	1	yes	characteristic
40	C₄×C₅×Q₁₆	C₂²	1	1	yes	characteristic
41	C₄×C₅×Q₁₆	C₂²	1	1	yes	characteristic
42	C₅×#433	—	2	1	no	—
43	C₅×#433	—	2	1	no	—
44	C₅×#432	—	2	1	no	—
45	C₅×#432	C₂²	1	1	yes	characteristic
46	C₅×#431	—	2	1	no	—
47	C₅×#431	C₂²	1	1	yes	characteristic
48	C₅×#431	C₂²	1	1	yes	characteristic
49	C₅×#431	C₂²	1	1	yes	characteristic
50	C₅×#431	C₂²	1	1	yes	characteristic
51	C₅×#335	C₂²	1	1	yes	characteristic
52	C₅×#335	C₂²	1	1	yes	characteristic
53	C₅×#334	C₂²	1	1	yes	characteristic
54	C₅×#334	C₂²	1	1	yes	characteristic
55	C₅×Q₈⋊C₈	C₂²	1	1	yes	characteristic
56	C₅×Q₈⋊C₈	C₂²	1	1	yes	characteristic
57	C₅×Q₈⋊C₈	C₂²	1	1	yes	characteristic
58	C₅×Q₈⋊C₈	C₂²	1	1	yes	characteristic
59	C₅×Q₈⋊C₈	C₂²	1	1	yes	characteristic
60	C₅×Q₈⋊C₈	C₂²	1	1	yes	characteristic
61	C₅×Q₈⋊C₈	C₂²	1	1	yes	characteristic
62	C₅×Q₈⋊C₈	C₂²	1	1	yes	characteristic
63	C₅×#322	C₂²	1	1	yes	characteristic
64	C₅×#322	C₂²	1	1	yes	characteristic
65	C₅×#322	C₂²	1	1	yes	characteristic
66	C₅×C₈²	C₂²	1	1	yes	characteristic
67	#18032	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
68	C₂²×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
69	C₂×C₅×Q₁₆	C₂×C₄	1	1	yes	characteristic
70	C₂×C₅×Q₁₆	C₂×C₄	1	1	yes	characteristic
71	C₂×C₅×Q₁₆	C₂×C₄	1	1	yes	characteristic
72	C₂×C₅×Q₁₆	C₂×C₄	1	1	yes	characteristic
73	C₅×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
74	C₅×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
75	C₅×#125	—	2	1	no	—
76	C₅×C₂²⋊Q₈	—	2	1	no	—
77	C₅×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
78	C₅×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
79	C₄×C₅×Q₈	—	2	1	no	—
80	C₄×C₅×Q₈	—	2	1	no	—
81	C₄×C₅×Q₈	—	2	1	no	—
82	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
83	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
84	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
85	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
86	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
87	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
88	C₅×#117	—	2	1	no	—
89	C₂×C₅×C₄⋊C₄	—	2	1	no	—
90	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
91	C₂×C₄²×C₅	—	2	1	no	—
92	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
93	C₅×#107	C₂×C₄	1	1	yes	characteristic
94	C₅×#107	C₂×C₄	1	1	yes	characteristic
95	C₅×#107	C₂×C₄	1	1	yes	characteristic
96	C₅×#107	C₂×C₄	1	1	yes	characteristic
97	C₅×C₄⋊C₈	—	2	1	no	—
98	C₅×C₄⋊C₈	—	2	1	no	—
99	C₅×C₄⋊C₈	—	2	1	no	—
100	C₅×C₄⋊C₈	—	2	1	no	—
101	C₅×C₄⋊C₈	—	2	1	no	—
102	C₅×C₄⋊C₈	—	2	1	no	—
103	C₅×C₄⋊C₈	—	2	1	no	—
104	C₅×C₄⋊C₈	—	2	1	no	—
105	C₅×C₄⋊C₈	—	2	1	no	—
106	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
107	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
108	C₅×C₄⋊C₈	D₄	1	1	yes	characteristic
109	C₅×C₄⋊C₈	D₄	1	1	yes	characteristic
110	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
111	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
112	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
113	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
114	C₅×#103	C₂×C₄	1	1	yes	characteristic
115	C₅×#103	C₂×C₄	1	1	yes	characteristic
116	C₅×#103	C₂×C₄	1	1	yes	characteristic
117	C₅×#103	C₂×C₄	1	1	yes	characteristic
118	C₅×#103	C₂×C₄	1	1	yes	characteristic
119	C₅×#103	C₂×C₄	1	1	yes	characteristic
120	C₅×#103	C₂×C₄	1	1	yes	characteristic
121	C₅×#103	C₂×C₄	1	1	yes	characteristic
122	C₅×C₂²⋊C₈	—	2	1	no	—
123	C₅×C₂²⋊C₈	—	2	1	no	—
124	C₅×C₂²⋊C₈	—	2	1	no	—
125	C₅×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
126	C₅×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
127	C₅×C₂²⋊C₈	D₄	1	1	yes	characteristic
128	C₅×C₂²⋊C₈	D₄	1	1	yes	characteristic
129	C₅×#97	—	2	1	no	—
130	C₅×#97	—	2	1	no	—
131	C₅×#97	—	2	1	no	—
132	C₅×#97	—	2	1	no	—
133	C₅×#97	—	2	1	no	—
134	C₄×C₅×C₈	—	2	1	no	—
135	C₄×C₅×C₈	—	2	1	no	—
136	C₄×C₅×C₈	—	2	1	no	—
137	C₄×C₅×C₈	—	2	1	no	—
138	C₄×C₅×C₈	—	2	1	no	—
139	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
140	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
141	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
142	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
143	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
144	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
145	#3104	C₂×C₅	1	1	yes	characteristic
146	#2986	C₂×C₅	1	1	yes	characteristic
147	#2984	C₂×C₅	1	1	yes	characteristic
148	#1593	C₂×C₅	1	1	yes	characteristic, complemented
149	#1591	C₂×C₅	1	1	yes	characteristic, complemented
150	#1587	C₂×C₅	1	1	yes	characteristic, complemented
151	#1587	C₂×C₅	1	1	yes	characteristic, complemented
152	#1584	C₂×C₅	1	1	yes	characteristic, complemented
153	#1584	C₂×C₅	1	1	yes	characteristic, complemented
154	#1579	C₂×C₅	1	1	yes	characteristic, complemented
155	C₈×Q₁₆	C₂×C₅	1	1	yes	characteristic, complemented
156	#1572	C₂×C₅	1	1	yes	characteristic
157	#1497	C₂×C₅	1	1	yes	characteristic
158	#1479	C₂×C₅	1	1	yes	characteristic
159	#1454	C₂×C₅	1	1	yes	characteristic
160	C₂×C₅×Q₈	—	2	1	no	—
161	C₂×C₅×Q₈	—	2	1	no	—
162	C₂×C₅×Q₈	—	2	2	no	—
163	C₂×C₅×Q₈	—	4	1	no	—
164	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
165	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
166	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
167	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
168	C₂²×C₄×C₅	—	2	1	no	—
169	C₂²×C₄×C₅	—	2	1	no	—
170	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
171	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₅	#41	1	1	yes	characteristic
173	C₅×Q₁₆	—	2	2	no	—
174	C₅×Q₁₆	—	2	2	no	—
175	C₅×Q₁₆	—	4	1	no	—
176	C₅×Q₁₆	—	4	1	no	—
177	C₂×C₅×C₈	—	2	1	no	—
178	C₂×C₅×C₈	—	2	1	no	—
179	C₂×C₅×C₈	—	2	1	no	—
180	C₂×C₅×C₈	—	2	1	no	—
181	C₂×C₅×C₈	—	2	1	no	—
182	C₂×C₅×C₈	—	2	1	no	—
183	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
184	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
185	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
186	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
187	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
188	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
189	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
190	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
191	C₅×C₄⋊C₄	—	2	1	no	—
192	C₅×C₄⋊C₄	—	2	1	no	—
193	C₅×C₄⋊C₄	—	2	1	no	—
194	C₅×C₄⋊C₄	—	2	1	no	—
195	C₅×C₄⋊C₄	—	2	1	no	—
196	C₅×C₄⋊C₄	—	2	1	no	—
197	C₅×C₄⋊C₄	—	2	1	no	—
198	C₅×C₄⋊C₄	—	2	1	no	—
199	C₅×C₄⋊C₄	—	2	1	no	—
200	C₅×C₄⋊C₄	—	2	1	no	—
201	C₅×C₄⋊C₄	—	2	1	no	—
202	C₅×C₄⋊C₄	—	2	1	no	—
203	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
204	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
205	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
206	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
207	C₅×C₂²⋊C₄	—	2	1	no	—
208	C₅×C₂²⋊C₄	—	2	1	no	—
209	C₄²×C₅	—	2	1	no	—
210	C₄²×C₅	—	2	1	no	—
211	C₄²×C₅	—	2	1	no	—
212	C₄²×C₅	—	2	1	no	—
213	C₄²×C₅	—	2	1	no	—
214	C₄²×C₅	—	2	1	no	—
215	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
216	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
217	C₄²×C₅	#41	1	1	yes	characteristic
218	C₄²×C₅	C₂⁴	1	1	yes	characteristic
219	#533	C₂²×C₅	1	1	yes	characteristic
220	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
221	#484	C₄×C₅	1	1	yes	characteristic
222	#484	C₄×C₅	1	1	yes	characteristic
223	#477	C₄×C₅	1	1	yes	characteristic
224	#477	C₄×C₅	1	1	yes	characteristic
225	#462	C₄×C₅	1	1	yes	characteristic
226	#462	C₄×C₅	1	1	yes	characteristic
227	#451	C₄×C₅	1	1	yes	characteristic
228	#451	C₄×C₅	1	1	yes	characteristic
229	#446	—	2	1	no	—
230	#446	—	2	1	no	—
231	#446	—	2	1	no	—
232	#446	C₂²×C₅	1	1	yes	characteristic
233	#446	C₂²×C₅	1	1	yes	characteristic
234	#446	C₂²×C₅	1	1	yes	characteristic
235	#446	C₂²×C₅	1	1	yes	characteristic
236	C₈×Q₈	—	2	1	no	—
237	C₈×Q₈	C₂²×C₅	1	1	yes	characteristic
238	C₈×Q₈	C₂²×C₅	1	1	yes	characteristic
239	C₈×Q₈	C₂²×C₅	1	1	yes	characteristic
240	C₈×Q₈	C₂²×C₅	1	1	yes	characteristic
241	C₄×Q₁₆	C₂²×C₅	1	1	yes	characteristic
242	C₄×Q₁₆	C₂²×C₅	1	1	yes	characteristic
243	C₄×Q₁₆	C₂²×C₅	1	1	yes	characteristic
244	C₄×Q₁₆	C₂²×C₅	1	1	yes	characteristic
245	#433	—	2	1	no	—
246	#433	—	2	1	no	—
247	#432	—	2	1	no	—
248	#432	C₂²×C₅	1	1	yes	characteristic
249	#431	—	2	1	no	—
250	#431	C₂²×C₅	1	1	yes	characteristic
251	#431	C₂²×C₅	1	1	yes	characteristic
252	#431	C₂²×C₅	1	1	yes	characteristic
253	#431	C₂²×C₅	1	1	yes	characteristic
254	#335	C₂²×C₅	1	1	yes	characteristic
255	#335	C₂²×C₅	1	1	yes	characteristic
256	#334	C₂²×C₅	1	1	yes	characteristic
257	#334	C₂²×C₅	1	1	yes	characteristic
258	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic
259	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic
260	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic
261	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic
262	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic
263	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic
264	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic
265	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic
266	#322	C₂²×C₅	1	1	yes	characteristic
267	#322	C₂²×C₅	1	1	yes	characteristic
268	#322	C₂²×C₅	1	1	yes	characteristic
269	C₈²	C₂²×C₅	1	1	yes	characteristic
270	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
271	C₅×Q₈	—	2	1	no	—
272	C₅×Q₈	—	2	1	no	—
273	C₅×Q₈	—	2	1	no	—
274	C₅×Q₈	—	2	1	no	—
275	C₅×Q₈	—	2	1	no	—
276	C₅×Q₈	—	2	1	no	—
277	C₅×Q₈	—	2	1	no	—
278	C₅×Q₈	—	4	2	no	—
279	C₅×Q₈	—	4	2	no	—
280	C₅×Q₈	#131	1	2	yes	—
281	C₂×C₄×C₅	—	2	1	no	—
282	C₂×C₄×C₅	—	2	1	no	—
283	C₂×C₄×C₅	—	2	1	no	—
284	C₂×C₄×C₅	—	2	1	no	—
285	C₂×C₄×C₅	—	2	1	no	—
286	C₂×C₄×C₅	—	2	1	no	—
287	C₂×C₄×C₅	—	2	1	no	—
288	C₂×C₄×C₅	—	2	1	no	—
289	C₂×C₄×C₅	—	2	1	no	—
290	C₂×C₄×C₅	—	2	1	no	—
291	C₂×C₄×C₅	—	2	1	no	—
292	C₂×C₄×C₅	—	2	1	no	—
293	C₂×C₄×C₅	—	4	1	no	—
294	C₂×C₄×C₅	—	4	2	no	—
295	C₂×C₄×C₅	—	4	2	no	—
296	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
297	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
298	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
299	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
300	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
301	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
302	C₅×C₈	—	2	1	no	—
303	C₅×C₈	—	2	1	no	—
304	C₅×C₈	—	2	1	no	—
305	C₅×C₈	—	2	1	no	—
306	C₅×C₈	—	2	1	no	—
307	C₅×C₈	—	2	1	no	—
308	C₅×C₈	—	2	1	no	—
309	C₅×C₈	—	2	1	no	—
310	C₅×C₈	—	4	1	no	—
311	C₅×C₈	—	4	1	no	—
312	C₅×C₈	—	4	1	no	—
313	C₅×C₈	—	4	1	no	—
314	C₅×C₈	—	4	1	no	—
315	C₅×C₈	—	4	1	no	—
316	C₂²×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
317	C₂×Q₁₆	C₂×C₄×C₅	1	1	yes	characteristic
318	C₂×Q₁₆	C₂×C₄×C₅	1	1	yes	characteristic
319	C₂×Q₁₆	C₂×C₄×C₅	1	1	yes	characteristic
320	C₂×Q₁₆	C₂×C₄×C₅	1	1	yes	characteristic
321	C₄⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
322	C₄⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
323	#125	—	2	1	no	—
324	C₂²⋊Q₈	—	2	1	no	—
325	C₂²⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
326	C₂²⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
327	C₄×Q₈	—	2	1	no	—
328	C₄×Q₈	—	2	1	no	—
329	C₄×Q₈	—	2	1	no	—
330	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
331	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
332	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
333	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
334	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
335	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
336	#117	—	2	1	no	—
337	C₂×C₄⋊C₄	—	2	1	no	—
338	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
339	C₂×C₄²	—	2	1	no	—
340	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
341	#107	C₂×C₄×C₅	1	1	yes	characteristic
342	#107	C₂×C₄×C₅	1	1	yes	characteristic
343	#107	C₂×C₄×C₅	1	1	yes	characteristic
344	#107	C₂×C₄×C₅	1	1	yes	characteristic
345	C₄⋊C₈	—	2	1	no	—
346	C₄⋊C₈	—	2	1	no	—
347	C₄⋊C₈	—	2	1	no	—
348	C₄⋊C₈	—	2	1	no	—
349	C₄⋊C₈	—	2	1	no	—
350	C₄⋊C₈	—	2	1	no	—
351	C₄⋊C₈	—	2	1	no	—
352	C₄⋊C₈	—	2	1	no	—
353	C₄⋊C₈	—	2	1	no	—
354	C₄⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
355	C₄⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
356	C₄⋊C₈	C₅×D₄	1	1	yes	characteristic
357	C₄⋊C₈	C₅×D₄	1	1	yes	characteristic
358	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
359	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
360	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
361	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
362	#103	C₂×C₄×C₅	1	1	yes	characteristic
363	#103	C₂×C₄×C₅	1	1	yes	characteristic
364	#103	C₂×C₄×C₅	1	1	yes	characteristic
365	#103	C₂×C₄×C₅	1	1	yes	characteristic
366	#103	C₂×C₄×C₅	1	1	yes	characteristic
367	#103	C₂×C₄×C₅	1	1	yes	characteristic
368	#103	C₂×C₄×C₅	1	1	yes	characteristic
369	#103	C₂×C₄×C₅	1	1	yes	characteristic
370	C₂²⋊C₈	—	2	1	no	—
371	C₂²⋊C₈	—	2	1	no	—
372	C₂²⋊C₈	—	2	1	no	—
373	C₂²⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
374	C₂²⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
375	C₂²⋊C₈	C₅×D₄	1	1	yes	characteristic
376	C₂²⋊C₈	C₅×D₄	1	1	yes	characteristic
377	#97	—	2	1	no	—
378	#97	—	2	1	no	—
379	#97	—	2	1	no	—
380	#97	—	2	1	no	—
381	#97	—	2	1	no	—
382	C₄×C₈	—	2	1	no	—
383	C₄×C₈	—	2	1	no	—
384	C₄×C₈	—	2	1	no	—
385	C₄×C₈	—	2	1	no	—
386	C₄×C₈	—	2	1	no	—
387	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
388	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
389	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
390	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
391	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
392	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
393	C₂²×C₅	—	2	1	no	—
394	C₂²×C₅	—	2	1	no	—
395	C₂²×C₅	—	2	1	no	—
396	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
397	C₄×C₅	—	2	1	no	—
398	C₄×C₅	—	2	2	no	—
399	C₄×C₅	—	2	1	no	—
400	C₄×C₅	—	2	1	no	—
401	C₄×C₅	—	2	1	no	—
402	C₄×C₅	—	4	1	no	—
403	C₄×C₅	—	4	1	no	—
404	C₄×C₅	—	4	1	no	—
405	C₄×C₅	—	4	1	no	—
406	C₄×C₅	—	4	1	no	—
407	C₄×C₅	—	4	1	no	—
408	C₄×C₅	—	4	1	no	—
409	C₄×C₅	C₂×#131	1	1	yes	characteristic
410	C₄×C₅	#568	1	1	yes	characteristic
411	C₄×C₅	#578	1	1	yes	characteristic
412	C₄×C₅	#578	1	1	yes	characteristic
413	C₂×Q₈	—	2	1	no	—
414	C₂×Q₈	—	2	1	no	—
415	C₂×Q₈	—	2	2	no	—
416	C₂×Q₈	—	4	1	no	—
417	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
418	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
419	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
420	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
421	C₂²×C₄	—	2	1	no	—
422	C₂²×C₄	—	2	1	no	—
423	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
424	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
425	C₂²×C₄	C₅×#41	1	1	yes	characteristic
426	Q₁₆	—	2	2	no	—
427	Q₁₆	—	2	2	no	—
428	Q₁₆	—	4	1	no	—
429	Q₁₆	—	4	1	no	—
430	C₂×C₈	—	2	1	no	—
431	C₂×C₈	—	2	1	no	—
432	C₂×C₈	—	2	1	no	—
433	C₂×C₈	—	2	1	no	—
434	C₂×C₈	—	2	1	no	—
435	C₂×C₈	—	2	1	no	—
436	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
437	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
438	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
439	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
440	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
441	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
442	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
443	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
444	C₄⋊C₄	—	2	1	no	—
445	C₄⋊C₄	—	2	1	no	—
446	C₄⋊C₄	—	2	1	no	—
447	C₄⋊C₄	—	2	1	no	—
448	C₄⋊C₄	—	2	1	no	—
449	C₄⋊C₄	—	2	1	no	—
450	C₄⋊C₄	—	2	1	no	—
451	C₄⋊C₄	—	2	1	no	—
452	C₄⋊C₄	—	2	1	no	—
453	C₄⋊C₄	—	2	1	no	—
454	C₄⋊C₄	—	2	1	no	—
455	C₄⋊C₄	—	2	1	no	—
456	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
457	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
458	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
459	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
460	C₂²⋊C₄	—	2	1	no	—
461	C₂²⋊C₄	—	2	1	no	—
462	C₄²	—	2	1	no	—
463	C₄²	—	2	1	no	—
464	C₄²	—	2	1	no	—
465	C₄²	—	2	1	no	—
466	C₄²	—	2	1	no	—
467	C₄²	—	2	1	no	—
468	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
469	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
470	C₄²	C₅×#41	1	1	yes	characteristic
471	C₄²	C₂⁴×C₅	1	1	yes	characteristic
472	C₂×C₅	—	4	1	no	—
473	C₂×C₅	#2933	1	1	yes	characteristic
474	C₂×C₅	#2950	1	1	yes	characteristic
475	C₂×C₅	#2955	1	1	yes	characteristic
476	C₂³	C₄×C₅×D₄	1	1	yes	characteristic
477	Q₈	—	2	1	no	—
478	Q₈	—	2	1	no	—
479	Q₈	—	2	1	no	—
480	Q₈	—	2	1	no	—
481	Q₈	—	2	1	no	—
482	Q₈	—	2	1	no	—
483	Q₈	—	2	1	no	—
484	Q₈	—	4	2	no	—
485	Q₈	—	4	2	no	—
486	Q₈	C₅×#131	1	2	yes	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	2	1	no	—
489	C₂×C₄	—	2	1	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	4	1	no	—
500	C₂×C₄	—	4	2	no	—
501	C₂×C₄	—	4	2	no	—
502	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
503	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
504	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
505	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
506	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
507	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
508	C₈	—	2	1	no	—
509	C₈	—	2	1	no	—
510	C₈	—	2	1	no	—
511	C₈	—	2	1	no	—
512	C₈	—	2	1	no	—
513	C₈	—	2	1	no	—
514	C₈	—	2	1	no	—
515	C₈	—	2	1	no	—
516	C₈	—	4	1	no	—
517	C₈	—	4	1	no	—
518	C₈	—	4	1	no	—
519	C₈	—	4	1	no	—
520	C₈	—	4	1	no	—
521	C₈	—	4	1	no	—
522	C₅	#18032	1	1	yes	characteristic, direct product factor, Sylow
523	C₂²	—	2	1	no	—
524	C₂²	—	2	1	no	—
525	C₂²	—	2	1	no	—
526	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
527	C₄	—	2	1	no	—
528	C₄	—	2	2	no	—
529	C₄	—	2	1	no	—
530	C₄	—	2	1	no	—
531	C₄	—	2	1	no	—
532	C₄	—	4	1	no	—
533	C₄	—	4	1	no	—
534	C₄	—	4	1	no	—
535	C₄	—	4	1	no	—
536	C₄	—	4	1	no	—
537	C₄	—	4	1	no	—
538	C₄	—	4	1	no	—
539	C₄	C₂×C₅×#131	1	1	yes	characteristic
540	C₄	C₅×#568	1	1	yes	characteristic
541	C₄	C₅×#578	1	1	yes	characteristic
542	C₄	C₅×#578	1	1	yes	characteristic
543	C₂	—	4	1	no	—
544	C₂	C₅×#2933	1	1	yes	characteristic
545	C₂	C₅×#2950	1	1	yes	characteristic
546	C₂	C₅×#2955	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	C₂³×C₅	C₄×D₄
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
4. C₅×#1593	C₂	semidirect
5. C₅×#1591	C₂	semidirect
6. C₅×#1587	C₂	semidirect
7. C₅×#1587	C₂	semidirect
8. C₅×#1584	C₂	semidirect
9. C₅×#1584	C₂	semidirect
10. C₅×#1579	C₂	semidirect
11. C₅×C₈×Q₁₆	C₂	semidirect
67. #18032	C₅	direct (N × H)
148. #1593	C₂×C₅	semidirect
149. #1591	C₂×C₅	semidirect
150. #1587	C₂×C₅	semidirect
151. #1587	C₂×C₅	semidirect
152. #1584	C₂×C₅	semidirect
153. #1584	C₂×C₅	semidirect
154. #1579	C₂×C₅	semidirect
155. C₈×Q₁₆	C₂×C₅	semidirect
522. C₅	#18032	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×#3104	2
C₅×#2986	2
C₅×#2984	2
C₅×#1593	2
C₅×#1591	2
C₅×#1587	2
C₅×#1584	2
C₅×#1579	2
C₅×C₈×Q₁₆	2
C₅×#1572	2
C₅×#1497	2
C₅×#1479	2
C₅×#1454	2
#18032	5

Subgroups — C5×#18032 #11940752

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#18032 #11940752