Subgroups — C₅×#17932 #11940652

Order 1280.

604 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3102	C₂	1	1	yes	maximal, characteristic
2	C₅×#2966	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2965	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1591	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1590	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1590	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1589	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1584	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1583	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1582	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1581	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1572	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1488	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1482	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#1450	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#529	C₂²	1	1	yes	characteristic
17	C₄×C₅×#41	C₂²	1	1	yes	characteristic
18	C₅×#485	C₄	1	1	yes	characteristic
19	C₅×#482	C₄	1	1	yes	characteristic
20	C₅×#479	C₄	1	1	yes	characteristic
21	C₅×#478	C₄	1	1	yes	characteristic
22	C₅×#464	C₄	1	1	yes	characteristic
23	C₅×#463	C₄	1	1	yes	characteristic
24	C₅×#452	C₄	1	1	yes	characteristic
25	C₅×#449	C₄	1	1	yes	characteristic
26	C₅×#446	C₂²	1	1	yes	characteristic
27	C₅×#446	C₂²	1	1	yes	characteristic
28	C₅×#446	C₂²	1	1	yes	characteristic
29	C₅×C₈×Q₈	C₂²	1	1	yes	characteristic
30	C₄×C₅×Q₁₆	C₂²	1	1	yes	characteristic
31	C₄×C₅×SD₁₆	C₂²	1	1	yes	characteristic
32	C₄×C₅×SD₁₆	C₂²	1	1	yes	characteristic
33	C₄×C₅×D₈	C₂²	1	1	yes	characteristic
34	C₅×#436	C₂²	1	1	yes	characteristic
35	C₅×#436	C₂²	1	1	yes	characteristic
36	C₅×#436	C₂²	1	1	yes	characteristic
37	C₅×#435	—	2	1	no	—
38	C₅×#435	—	2	1	no	—
39	C₅×#435	—	2	1	no	—
40	C₅×C₈×D₄	—	2	1	no	—
41	C₅×C₈×D₄	C₂²	1	1	yes	characteristic
42	C₅×#433	—	2	1	no	—
43	C₅×#432	C₂²	1	1	yes	characteristic
44	C₅×#431	—	2	1	no	—
45	C₅×#431	C₂²	1	1	yes	characteristic
46	C₅×#431	C₂²	1	1	yes	characteristic
47	C₅×#431	C₂²	1	1	yes	characteristic
48	C₅×#405	—	2	1	no	—
49	C₄×C₅×M₁₆	—	2	1	no	—
50	C₂×C₄×C₅×C₈	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×D₄⋊C₈	C₂²	1	1	yes	characteristic
60	C₅×D₄⋊C₈	C₂²	1	1	yes	characteristic
61	C₅×D₄⋊C₈	C₂²	1	1	yes	characteristic
62	C₅×D₄⋊C₈	C₂²	1	1	yes	characteristic
63	C₅×#322	C₂²	1	1	yes	characteristic
64	C₅×#322	C₂²	1	1	yes	characteristic
65	C₅×C₈²	C₂²	1	1	yes	characteristic
66	C₅×C₈²	C₂²	1	1	yes	characteristic
67	#17932	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
68	C₂×C₅×#41	C₂×C₄	1	1	yes	characteristic
69	C₂×C₅×Q₁₆	C₂×C₄	1	1	yes	characteristic
70	C₂×C₅×SD₁₆	C₂×C₄	1	1	yes	characteristic
71	C₂×C₅×SD₁₆	C₂×C₄	1	1	yes	characteristic
72	C₂×C₅×D₈	C₂×C₄	1	1	yes	characteristic
73	C₂×C₅×M₁₆	—	2	1	no	—
74	C₂×C₅×M₁₆	—	2	1	no	—
75	C₂×C₅×M₁₆	—	2	1	no	—
76	C₂²×C₅×C₈	—	2	1	no	—
77	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
78	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
79	C₅×#126	—	2	1	no	—
80	C₅×#125	C₂×C₄	1	1	yes	characteristic
81	C₅×#124	C₂×C₄	1	1	yes	characteristic
82	C₅×#123	—	2	1	no	—
83	C₅×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
84	C₅×#121	C₂×C₄	1	1	yes	characteristic
85	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
86	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
87	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
88	C₄×C₅×D₄	—	2	1	no	—
89	C₄×C₅×D₄	—	2	1	no	—
90	C₄×C₅×D₄	—	2	1	no	—
91	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
92	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
93	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
94	C₅×#117	—	2	1	no	—
95	C₅×#117	—	2	1	no	—
96	C₅×#117	C₂×C₄	1	1	yes	characteristic
97	C₂×C₄²×C₅	—	2	1	no	—
98	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
99	C₅×#107	C₂×C₄	1	1	yes	characteristic
100	C₅×#107	C₂×C₄	1	1	yes	characteristic
101	C₅×#106	C₂×C₄	1	1	yes	characteristic
102	C₅×#106	C₂×C₄	1	1	yes	characteristic
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	—	2	1	no	—
107	C₅×C₄⋊C₈	—	2	1	no	—
108	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
109	C₅×C₄⋊C₈	C₂×C₄	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×#102	C₂×C₄	1	1	yes	characteristic
119	C₅×#102	C₂×C₄	1	1	yes	characteristic
120	C₅×#102	C₂×C₄	1	1	yes	characteristic
121	C₅×#102	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	—	2	1	no	—
126	C₅×C₂²⋊C₈	—	2	1	no	—
127	C₅×C₂²⋊C₈	—	2	1	no	—
128	C₅×C₂²⋊C₈	—	2	1	no	—
129	C₅×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
130	C₅×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
131	C₅×#97	—	2	1	no	—
132	C₅×#97	—	2	1	no	—
133	C₅×#97	—	2	1	no	—
134	C₅×#97	—	2	1	no	—
135	C₄×C₅×C₈	—	2	1	no	—
136	C₄×C₅×C₈	—	2	1	no	—
137	C₄×C₅×C₈	D₄	1	1	yes	characteristic
138	C₄×C₅×C₈	D₄	1	1	yes	characteristic
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	#3102	C₂×C₅	1	1	yes	characteristic
146	#2966	C₂×C₅	1	1	yes	characteristic, complemented
147	#2965	C₂×C₅	1	1	yes	characteristic, complemented
148	#1591	C₂×C₅	1	1	yes	characteristic, complemented
149	#1590	C₂×C₅	1	1	yes	characteristic, complemented
150	#1590	C₂×C₅	1	1	yes	characteristic, complemented
151	#1589	C₂×C₅	1	1	yes	characteristic, complemented
152	#1584	C₂×C₅	1	1	yes	characteristic, complemented
153	#1583	C₂×C₅	1	1	yes	characteristic, complemented
154	#1582	C₂×C₅	1	1	yes	characteristic, complemented
155	#1581	C₂×C₅	1	1	yes	characteristic, complemented
156	#1572	C₂×C₅	1	1	yes	characteristic, complemented
157	#1488	C₂×C₅	1	1	yes	characteristic, complemented
158	#1482	C₂×C₅	1	1	yes	characteristic, complemented
159	#1450	C₂×C₅	1	1	yes	characteristic, complemented
160	C₅×#41	—	4	1	no	—
161	C₅×#41	—	4	1	no	—
162	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
163	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
164	C₂×C₅×D₄	—	2	1	no	—
165	C₂×C₅×D₄	—	2	1	no	—
166	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
167	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
168	C₂²×C₄×C₅	—	2	1	no	—
169	C₂²×C₄×C₅	—	2	1	no	—
170	C₂²×C₄×C₅	—	2	1	no	—
171	C₂²×C₄×C₅	—	2	1	no	—
172	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
173	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₅	#41	1	1	yes	characteristic
175	C₅×Q₁₆	—	4	1	no	—
176	C₅×SD₁₆	—	4	1	no	—
177	C₅×SD₁₆	—	4	1	no	—
178	C₅×D₈	—	4	1	no	—
179	C₅×M₁₆	—	4	2	no	—
180	C₅×M₁₆	—	4	2	no	—
181	C₅×M₁₆	—	4	2	no	—
182	C₂×C₅×C₈	—	2	2	no	—
183	C₂×C₅×C₈	—	2	2	no	—
184	C₂×C₅×C₈	—	2	1	no	—
185	C₂×C₅×C₈	—	2	1	no	—
186	C₂×C₅×C₈	—	2	1	no	—
187	C₂×C₅×C₈	—	2	1	no	—
188	C₂×C₅×C₈	—	2	1	no	—
189	C₂×C₅×C₈	—	2	1	no	—
190	C₂×C₅×C₈	—	4	2	no	—
191	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
192	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
193	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
194	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
195	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
196	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
197	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
198	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
204	C₅×C₄⋊C₄	—	2	1	no	—
205	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
206	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
207	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
208	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
209	C₅×C₂²⋊C₄	—	2	1	no	—
210	C₅×C₂²⋊C₄	—	2	1	no	—
211	C₅×C₂²⋊C₄	—	2	1	no	—
212	C₅×C₂²⋊C₄	—	2	1	no	—
213	C₅×C₂²⋊C₄	—	2	1	no	—
214	C₅×C₂²⋊C₄	—	2	1	no	—
215	C₅×C₂²⋊C₄	—	2	1	no	—
216	C₅×C₂²⋊C₄	—	2	1	no	—
217	C₄²×C₅	—	2	1	no	—
218	C₄²×C₅	—	2	1	no	—
219	C₄²×C₅	—	2	1	no	—
220	C₄²×C₅	—	2	1	no	—
221	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
222	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
223	C₄²×C₅	#41	1	1	yes	characteristic
224	C₄²×C₅	C₂⁴	1	1	yes	characteristic
225	#529	C₂²×C₅	1	1	yes	characteristic
226	C₄×#41	C₂²×C₅	1	1	yes	characteristic
227	#485	C₄×C₅	1	1	yes	characteristic
228	#482	C₄×C₅	1	1	yes	characteristic
229	#479	C₄×C₅	1	1	yes	characteristic
230	#478	C₄×C₅	1	1	yes	characteristic
231	#464	C₄×C₅	1	1	yes	characteristic
232	#463	C₄×C₅	1	1	yes	characteristic
233	#452	C₄×C₅	1	1	yes	characteristic
234	#449	C₄×C₅	1	1	yes	characteristic
235	#446	C₂²×C₅	1	1	yes	characteristic
236	#446	C₂²×C₅	1	1	yes	characteristic
237	#446	C₂²×C₅	1	1	yes	characteristic
238	C₈×Q₈	C₂²×C₅	1	1	yes	characteristic
239	C₄×Q₁₆	C₂²×C₅	1	1	yes	characteristic
240	C₄×SD₁₆	C₂²×C₅	1	1	yes	characteristic
241	C₄×SD₁₆	C₂²×C₅	1	1	yes	characteristic
242	C₄×D₈	C₂²×C₅	1	1	yes	characteristic
243	#436	C₂²×C₅	1	1	yes	characteristic
244	#436	C₂²×C₅	1	1	yes	characteristic
245	#436	C₂²×C₅	1	1	yes	characteristic
246	#435	—	2	1	no	—
247	#435	—	2	1	no	—
248	#435	—	2	1	no	—
249	C₈×D₄	—	2	1	no	—
250	C₈×D₄	C₂²×C₅	1	1	yes	characteristic
251	#433	—	2	1	no	—
252	#432	C₂²×C₅	1	1	yes	characteristic
253	#431	—	2	1	no	—
254	#431	C₂²×C₅	1	1	yes	characteristic
255	#431	C₂²×C₅	1	1	yes	characteristic
256	#431	C₂²×C₅	1	1	yes	characteristic
257	#405	—	2	1	no	—
258	C₄×M₁₆	—	2	1	no	—
259	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
260	#335	C₂²×C₅	1	1	yes	characteristic
261	#335	C₂²×C₅	1	1	yes	characteristic
262	#334	C₂²×C₅	1	1	yes	characteristic
263	#334	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	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic
267	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic
268	D₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
269	D₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
270	D₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
271	D₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
272	#322	C₂²×C₅	1	1	yes	characteristic
273	#322	C₂²×C₅	1	1	yes	characteristic
274	C₈²	C₂²×C₅	1	1	yes	characteristic
275	C₈²	C₂²×C₅	1	1	yes	characteristic
276	C₂³×C₅	—	2	1	no	—
277	C₂³×C₅	—	2	1	no	—
278	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
279	C₅×Q₈	—	2	1	no	—
280	C₅×Q₈	—	2	1	no	—
281	C₅×Q₈	—	2	1	no	—
282	C₅×Q₈	—	2	1	no	—
283	C₅×D₄	—	2	1	no	—
284	C₅×D₄	—	2	1	no	—
285	C₅×D₄	—	2	1	no	—
286	C₅×D₄	—	2	1	no	—
287	C₅×D₄	—	4	2	no	—
288	C₅×D₄	—	4	2	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	—	2	1	no	—
294	C₂×C₄×C₅	—	2	1	no	—
295	C₂×C₄×C₅	—	2	1	no	—
296	C₂×C₄×C₅	—	2	1	no	—
297	C₂×C₄×C₅	—	2	1	no	—
298	C₂×C₄×C₅	—	2	1	no	—
299	C₂×C₄×C₅	—	4	1	no	—
300	C₂×C₄×C₅	—	4	2	no	—
301	C₂×C₄×C₅	—	4	2	no	—
302	C₂×C₄×C₅	—	4	1	no	—
303	C₂×C₄×C₅	—	4	1	no	—
304	C₂×C₄×C₅	—	4	1	no	—
305	C₂×C₄×C₅	—	4	1	no	—
306	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
307	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
308	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
309	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
310	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
311	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
312	C₅×C₈	—	2	1	no	—
313	C₅×C₈	—	2	1	no	—
314	C₅×C₈	—	2	1	no	—
315	C₅×C₈	—	2	1	no	—
316	C₅×C₈	—	2	1	no	—
317	C₅×C₈	—	2	1	no	—
318	C₅×C₈	—	4	1	no	—
319	C₅×C₈	—	4	1	no	—
320	C₅×C₈	—	4	1	no	—
321	C₅×C₈	—	4	1	no	—
322	C₅×C₈	—	4	1	no	—
323	C₅×C₈	—	4	1	no	—
324	C₅×C₈	#135	1	2	yes	—
325	C₅×C₈	#135	1	2	yes	—
326	C₂×#41	C₂×C₄×C₅	1	1	yes	characteristic
327	C₂×Q₁₆	C₂×C₄×C₅	1	1	yes	characteristic
328	C₂×SD₁₆	C₂×C₄×C₅	1	1	yes	characteristic
329	C₂×SD₁₆	C₂×C₄×C₅	1	1	yes	characteristic
330	C₂×D₈	C₂×C₄×C₅	1	1	yes	characteristic
331	C₂×M₁₆	—	2	1	no	—
332	C₂×M₁₆	—	2	1	no	—
333	C₂×M₁₆	—	2	1	no	—
334	C₂²×C₈	—	2	1	no	—
335	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
336	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
337	#126	—	2	1	no	—
338	#125	C₂×C₄×C₅	1	1	yes	characteristic
339	#124	C₂×C₄×C₅	1	1	yes	characteristic
340	#123	—	2	1	no	—
341	C₂²⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
342	#121	C₂×C₄×C₅	1	1	yes	characteristic
343	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
344	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
345	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
346	C₄×D₄	—	2	1	no	—
347	C₄×D₄	—	2	1	no	—
348	C₄×D₄	—	2	1	no	—
349	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
350	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
351	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
352	#117	—	2	1	no	—
353	#117	—	2	1	no	—
354	#117	C₂×C₄×C₅	1	1	yes	characteristic
355	C₂×C₄²	—	2	1	no	—
356	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
357	#107	C₂×C₄×C₅	1	1	yes	characteristic
358	#107	C₂×C₄×C₅	1	1	yes	characteristic
359	#106	C₂×C₄×C₅	1	1	yes	characteristic
360	#106	C₂×C₄×C₅	1	1	yes	characteristic
361	C₄⋊C₈	—	2	1	no	—
362	C₄⋊C₈	—	2	1	no	—
363	C₄⋊C₈	—	2	1	no	—
364	C₄⋊C₈	—	2	1	no	—
365	C₄⋊C₈	—	2	1	no	—
366	C₄⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
367	C₄⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
368	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
369	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
370	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
371	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
372	#103	C₂×C₄×C₅	1	1	yes	characteristic
373	#103	C₂×C₄×C₅	1	1	yes	characteristic
374	#103	C₂×C₄×C₅	1	1	yes	characteristic
375	#103	C₂×C₄×C₅	1	1	yes	characteristic
376	#102	C₂×C₄×C₅	1	1	yes	characteristic
377	#102	C₂×C₄×C₅	1	1	yes	characteristic
378	#102	C₂×C₄×C₅	1	1	yes	characteristic
379	#102	C₂×C₄×C₅	1	1	yes	characteristic
380	C₂²⋊C₈	—	2	1	no	—
381	C₂²⋊C₈	—	2	1	no	—
382	C₂²⋊C₈	—	2	1	no	—
383	C₂²⋊C₈	—	2	1	no	—
384	C₂²⋊C₈	—	2	1	no	—
385	C₂²⋊C₈	—	2	1	no	—
386	C₂²⋊C₈	—	2	1	no	—
387	C₂²⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
388	C₂²⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
389	#97	—	2	1	no	—
390	#97	—	2	1	no	—
391	#97	—	2	1	no	—
392	#97	—	2	1	no	—
393	C₄×C₈	—	2	1	no	—
394	C₄×C₈	—	2	1	no	—
395	C₄×C₈	C₅×D₄	1	1	yes	characteristic
396	C₄×C₈	C₅×D₄	1	1	yes	characteristic
397	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
398	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
399	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
400	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
401	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
402	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
403	C₂²×C₅	—	2	1	no	—
404	C₂²×C₅	—	2	1	no	—
405	C₂²×C₅	—	2	1	no	—
406	C₂²×C₅	—	4	1	no	—
407	C₂²×C₅	—	4	1	no	—
408	C₂²×C₅	—	4	1	no	—
409	C₂²×C₅	—	4	1	no	—
410	C₂²×C₅	—	4	1	no	—
411	C₂²×C₅	—	4	1	no	—
412	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
413	C₄×C₅	—	2	1	no	—
414	C₄×C₅	—	2	1	no	—
415	C₄×C₅	—	2	1	no	—
416	C₄×C₅	—	2	1	no	—
417	C₄×C₅	—	4	1	no	—
418	C₄×C₅	—	4	1	no	—
419	C₄×C₅	—	4	1	no	—
420	C₄×C₅	—	4	1	no	—
421	C₄×C₅	—	4	1	no	—
422	C₄×C₅	—	4	1	no	—
423	C₄×C₅	#568	1	1	yes	characteristic
424	C₄×C₅	#568	1	1	yes	characteristic
425	C₄×C₅	C₂×#135	1	1	yes	characteristic
426	C₄×C₅	C₂×#135	1	1	yes	characteristic
427	#41	—	4	1	no	—
428	#41	—	4	1	no	—
429	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
430	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
431	C₂×D₄	—	2	1	no	—
432	C₂×D₄	—	2	1	no	—
433	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
434	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
435	C₂²×C₄	—	2	1	no	—
436	C₂²×C₄	—	2	1	no	—
437	C₂²×C₄	—	2	1	no	—
438	C₂²×C₄	—	2	1	no	—
439	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
440	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
441	C₂²×C₄	C₅×#41	1	1	yes	characteristic
442	Q₁₆	—	4	1	no	—
443	SD₁₆	—	4	1	no	—
444	SD₁₆	—	4	1	no	—
445	D₈	—	4	1	no	—
446	M₁₆	—	4	2	no	—
447	M₁₆	—	4	2	no	—
448	M₁₆	—	4	2	no	—
449	C₂×C₈	—	2	2	no	—
450	C₂×C₈	—	2	2	no	—
451	C₂×C₈	—	2	1	no	—
452	C₂×C₈	—	2	1	no	—
453	C₂×C₈	—	2	1	no	—
454	C₂×C₈	—	2	1	no	—
455	C₂×C₈	—	2	1	no	—
456	C₂×C₈	—	2	1	no	—
457	C₂×C₈	—	4	2	no	—
458	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
459	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
460	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
461	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
462	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
463	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
464	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
465	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
466	C₄⋊C₄	—	2	1	no	—
467	C₄⋊C₄	—	2	1	no	—
468	C₄⋊C₄	—	2	1	no	—
469	C₄⋊C₄	—	2	1	no	—
470	C₄⋊C₄	—	2	1	no	—
471	C₄⋊C₄	—	2	1	no	—
472	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
473	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
474	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
475	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
476	C₂²⋊C₄	—	2	1	no	—
477	C₂²⋊C₄	—	2	1	no	—
478	C₂²⋊C₄	—	2	1	no	—
479	C₂²⋊C₄	—	2	1	no	—
480	C₂²⋊C₄	—	2	1	no	—
481	C₂²⋊C₄	—	2	1	no	—
482	C₂²⋊C₄	—	2	1	no	—
483	C₂²⋊C₄	—	2	1	no	—
484	C₄²	—	2	1	no	—
485	C₄²	—	2	1	no	—
486	C₄²	—	2	1	no	—
487	C₄²	—	2	1	no	—
488	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
489	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
490	C₄²	C₅×#41	1	1	yes	characteristic
491	C₄²	C₂⁴×C₅	1	1	yes	characteristic
492	C₂×C₅	—	4	1	no	—
493	C₂×C₅	—	8	1	no	—
494	C₂×C₅	—	8	1	no	—
495	C₂×C₅	#2930	1	1	yes	characteristic
496	C₂×C₅	C₄×#135	1	1	yes	characteristic
497	C₂×C₅	#2955	1	1	yes	characteristic
498	C₂³	—	2	1	no	—
499	C₂³	—	2	1	no	—
500	C₂³	C₄×C₅×D₄	1	1	yes	characteristic
501	Q₈	—	2	1	no	—
502	Q₈	—	2	1	no	—
503	Q₈	—	2	1	no	—
504	Q₈	—	2	1	no	—
505	D₄	—	2	1	no	—
506	D₄	—	2	1	no	—
507	D₄	—	2	1	no	—
508	D₄	—	2	1	no	—
509	D₄	—	4	2	no	—
510	D₄	—	4	2	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	2	no	—
523	C₂×C₄	—	4	2	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	4	1	no	—
528	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
529	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
530	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
531	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
532	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
533	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
534	C₈	—	2	1	no	—
535	C₈	—	2	1	no	—
536	C₈	—	2	1	no	—
537	C₈	—	2	1	no	—
538	C₈	—	2	1	no	—
539	C₈	—	2	1	no	—
540	C₈	—	4	1	no	—
541	C₈	—	4	1	no	—
542	C₈	—	4	1	no	—
543	C₈	—	4	1	no	—
544	C₈	—	4	1	no	—
545	C₈	—	4	1	no	—
546	C₈	C₅×#135	1	2	yes	—
547	C₈	C₅×#135	1	2	yes	—
548	C₅	#17932	1	1	yes	characteristic, direct product factor, Sylow
549	C₂²	—	2	1	no	—
550	C₂²	—	2	1	no	—
551	C₂²	—	2	1	no	—
552	C₂²	—	4	1	no	—
553	C₂²	—	4	1	no	—
554	C₂²	—	4	1	no	—
555	C₂²	—	4	1	no	—
556	C₂²	—	4	1	no	—
557	C₂²	—	4	1	no	—
558	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
559	C₄	—	2	1	no	—
560	C₄	—	2	1	no	—
561	C₄	—	2	1	no	—
562	C₄	—	2	1	no	—
563	C₄	—	4	1	no	—
564	C₄	—	4	1	no	—
565	C₄	—	4	1	no	—
566	C₄	—	4	1	no	—
567	C₄	—	4	1	no	—
568	C₄	—	4	1	no	—
569	C₄	C₅×#568	1	1	yes	characteristic
570	C₄	C₅×#568	1	1	yes	characteristic
571	C₄	C₂×C₅×#135	1	1	yes	characteristic
572	C₄	C₂×C₅×#135	1	1	yes	characteristic
573	C₂	—	4	1	no	—
574	C₂	—	8	1	no	—
575	C₂	—	8	1	no	—
576	C₂	C₅×#2930	1	1	yes	characteristic
577	C₂	C₄×C₅×#135	1	1	yes	characteristic
578	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	C₅×#449	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂×C₄×C₅×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×#2966	C₂	semidirect
3. C₅×#2965	C₂	semidirect
4. C₅×#1591	C₂	semidirect
5. C₅×#1590	C₂	semidirect
6. C₅×#1590	C₂	semidirect
7. C₅×#1589	C₂	semidirect
8. C₅×#1584	C₂	semidirect
9. C₅×#1583	C₂	semidirect
10. C₅×#1582	C₂	semidirect
11. C₅×#1581	C₂	semidirect
12. C₅×#1572	C₂	semidirect
13. C₅×#1488	C₂	semidirect
14. C₅×#1482	C₂	semidirect
15. C₅×#1450	C₂	semidirect
67. #17932	C₅	direct (N × H)
146. #2966	C₂×C₅	semidirect
147. #2965	C₂×C₅	semidirect
148. #1591	C₂×C₅	semidirect
149. #1590	C₂×C₅	semidirect
150. #1590	C₂×C₅	semidirect
151. #1589	C₂×C₅	semidirect
152. #1584	C₂×C₅	semidirect
153. #1583	C₂×C₅	semidirect
154. #1582	C₂×C₅	semidirect
155. #1581	C₂×C₅	semidirect
156. #1572	C₂×C₅	semidirect
157. #1488	C₂×C₅	semidirect
158. #1482	C₂×C₅	semidirect
159. #1450	C₂×C₅	semidirect
548. C₅	#17932	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×#3102	2
C₅×#2966	2
C₅×#2965	2
C₅×#1591	2
C₅×#1590	2
C₅×#1589	2
C₅×#1584	2
C₅×#1583	2
C₅×#1582	2
C₅×#1581	2
C₅×#1572	2
C₅×#1488	2
C₅×#1482	2
C₅×#1450	2
#17932	5

Subgroups — C5×#17932 #11940652

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#17932 #11940652