Subgroups — C₅×#17938 #11940658

Order 1280.

672 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3105	C₂	1	1	yes	maximal, characteristic
2	C₅×#2966	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#436	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1594	C₂	1	2	yes	maximal, complemented
5	C₅×#1592	C₂	1	2	yes	maximal, complemented
6	C₅×#1583	C₂	1	2	yes	maximal, complemented
7	C₅×#1581	C₂	1	2	yes	maximal, complemented
8	C₅×#1573	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1490	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1483	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1451	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₅×M₁₆	—	2	1	no	—
13	C₅×#529	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
15	C₅×#484	C₄	1	1	yes	characteristic
16	C₅×#481	C₄	1	1	yes	characteristic
17	C₅×#478	C₄	1	2	yes	—
18	C₅×#463	C₄	1	2	yes	—
19	C₅×#450	C₄	1	1	yes	characteristic
20	C₅×#447	C₄	1	1	yes	characteristic
21	C₅×#446	C₂²	1	1	yes	characteristic, complemented
22	C₅×C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
23	C₄×C₅×SD₁₆	C₂²	1	2	yes	—
24	C₄×C₅×D₈	C₂²	1	2	yes	—
25	C₅×#436	—	2	1	no	—
26	C₅×#436	—	2	1	no	—
27	C₅×#436	C₂²	1	2	yes	—
28	C₅×#436	C₂²	1	2	yes	—
29	C₅×#436	C₂²	1	1	yes	characteristic, complemented
30	C₅×#435	—	2	1	no	—
31	C₅×C₈×D₄	—	2	1	no	—
32	C₅×C₈×D₄	C₂²	1	1	yes	characteristic, complemented
33	C₅×#433	—	2	1	no	—
34	C₅×#432	C₂²	1	1	yes	characteristic
35	C₅×#431	C₂²	1	1	yes	characteristic
36	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
37	C₂×C₅×C₂²⋊C₈	—	2	1	no	—
38	C₅×#405	—	2	1	no	—
39	C₄×C₅×M₁₆	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
41	C₅×#335	C₂²	1	2	yes	complemented
42	C₅×#334	C₂²	1	2	yes	complemented
43	C₅×Q₈⋊C₈	C₂²	1	2	yes	complemented
44	C₅×D₄⋊C₈	C₂²	1	2	yes	—
45	C₅×D₄⋊C₈	C₂²	1	2	yes	—
46	C₅×D₄⋊C₈	C₂²	1	2	yes	complemented
47	C₅×#322	C₂²	1	2	yes	complemented
48	C₅×#322	C₂²	1	2	yes	complemented
49	#17938	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
50	C₂²×C₅×D₄	C₂×C₄	1	1	yes	characteristic
51	C₂³×C₄×C₅	—	2	1	no	—
52	C₂×C₅×SD₁₆	C₂×C₄	1	2	yes	—
53	C₂×C₅×D₈	C₂×C₄	1	2	yes	—
54	C₂×C₅×M₁₆	—	2	1	no	—
55	C₂×C₅×M₁₆	—	2	1	no	—
56	C₂×C₅×M₁₆	—	2	2	no	—
57	C₂×C₅×M₁₆	—	2	2	no	—
58	C₂×C₅×M₁₆	—	4	4	no	—
59	C₂²×C₅×C₈	—	2	1	no	—
60	C₂²×C₅×C₈	—	2	1	no	—
61	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
62	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
63	C₅×#126	—	2	1	no	—
64	C₅×#125	C₂×C₄	1	1	yes	characteristic
65	C₅×#124	C₂×C₄	1	1	yes	characteristic
66	C₅×#123	—	2	1	no	—
67	C₅×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
68	C₅×#121	C₂×C₄	1	1	yes	characteristic
69	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
70	C₄×C₅×D₄	—	2	1	no	—
71	C₄×C₅×D₄	—	2	1	no	—
72	C₄×C₅×D₄	—	2	1	no	—
73	C₄×C₅×D₄	C₂×C₄	1	2	yes	—
74	C₄×C₅×D₄	C₂³	1	2	yes	—
75	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
76	C₅×#117	—	2	1	no	—
77	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
78	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
79	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
80	C₅×#107	C₂×C₄	1	2	yes	—
81	C₅×#106	C₂×C₄	1	2	yes	—
82	C₅×C₄⋊C₈	—	2	1	no	—
83	C₅×C₄⋊C₈	—	2	1	no	—
84	C₅×C₄⋊C₈	—	2	1	no	—
85	C₅×C₄⋊C₈	C₂×C₄	1	2	yes	—
86	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
87	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
88	C₅×C₄⋊C₈	C₂³	1	2	yes	—
89	C₅×#103	C₂×C₄	1	2	yes	—
90	C₅×#102	C₂×C₄	1	2	yes	—
91	C₅×#102	C₂×C₄	1	2	yes	—
92	C₅×#102	C₂×C₄	1	2	yes	—
93	C₅×C₂²⋊C₈	—	2	1	no	—
94	C₅×C₂²⋊C₈	—	2	2	no	—
95	C₅×C₂²⋊C₈	—	2	2	no	—
96	C₅×C₂²⋊C₈	—	2	1	no	—
97	C₅×C₂²⋊C₈	—	2	1	no	—
98	C₅×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
99	C₅×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
100	C₅×#97	—	2	1	no	—
101	C₅×#97	—	2	1	no	—
102	C₅×#97	—	2	1	no	—
103	C₄×C₅×C₈	—	2	1	no	—
104	C₄×C₅×C₈	D₄	1	1	yes	characteristic
105	C₄×C₅×C₈	D₄	1	1	yes	characteristic
106	C₄×C₅×C₈	C₂³	1	2	yes	—
107	C₄×C₅×C₈	C₂³	1	2	yes	—
108	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
109	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
110	#3105	C₂×C₅	1	1	yes	characteristic
111	#2966	C₂×C₅	1	1	yes	characteristic, complemented
112	C₂×#436	C₂×C₅	1	1	yes	characteristic, complemented
113	#1594	C₂×C₅	1	2	yes	complemented
114	#1592	C₂×C₅	1	2	yes	complemented
115	#1583	C₂×C₅	1	2	yes	complemented
116	#1581	C₂×C₅	1	2	yes	complemented
117	#1573	C₂×C₅	1	1	yes	characteristic, complemented
118	#1490	C₂×C₅	1	1	yes	characteristic, complemented
119	#1483	C₂×C₅	1	1	yes	characteristic, complemented
120	#1451	C₂×C₅	1	1	yes	characteristic, complemented
121	C₂⁴×C₅	—	2	1	no	—
122	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₅×D₄	—	2	1	no	—
124	C₂×C₅×D₄	—	2	1	no	—
125	C₂×C₅×D₄	—	4	2	no	—
126	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
127	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
128	C₂²×C₄×C₅	—	2	1	no	—
129	C₂²×C₄×C₅	—	2	2	no	—
130	C₂²×C₄×C₅	—	2	1	no	—
131	C₂²×C₄×C₅	—	2	2	no	—
132	C₂²×C₄×C₅	—	4	2	no	—
133	C₂²×C₄×C₅	—	4	2	no	—
134	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
135	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₅	#41	1	1	yes	characteristic
137	C₅×SD₁₆	—	4	2	no	—
138	C₅×D₈	—	4	2	no	—
139	C₅×M₁₆	—	4	2	no	—
140	C₅×M₁₆	—	4	4	no	—
141	C₅×M₁₆	—	4	2	no	—
142	C₅×M₁₆	—	4	4	no	—
143	C₂×C₅×C₈	—	2	2	no	—
144	C₂×C₅×C₈	—	2	2	no	—
145	C₂×C₅×C₈	—	2	1	no	—
146	C₂×C₅×C₈	—	2	1	no	—
147	C₂×C₅×C₈	—	2	2	no	—
148	C₂×C₅×C₈	—	4	1	no	—
149	C₂×C₅×C₈	—	4	2	no	—
150	C₂×C₅×C₈	—	4	2	no	—
151	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
152	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
153	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
154	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
155	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
156	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
157	C₅×C₄⋊C₄	—	2	1	no	—
158	C₅×C₄⋊C₄	—	2	1	no	—
159	C₅×C₄⋊C₄	—	2	1	no	—
160	C₅×C₄⋊C₄	—	2	1	no	—
161	C₅×C₄⋊C₄	—	2	1	no	—
162	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
163	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
164	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
165	C₅×C₂²⋊C₄	—	2	1	no	—
166	C₅×C₂²⋊C₄	—	2	2	no	—
167	C₅×C₂²⋊C₄	—	2	1	no	—
168	C₅×C₂²⋊C₄	—	2	1	no	—
169	C₅×C₂²⋊C₄	—	2	1	no	—
170	C₅×C₂²⋊C₄	—	2	2	no	—
171	C₅×C₂²⋊C₄	—	2	1	no	—
172	C₄²×C₅	—	2	1	no	—
173	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
174	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
175	C₄²×C₅	#41	1	1	yes	characteristic
176	C₄²×C₅	C₂⁴	1	1	yes	characteristic
177	C₂²×M₁₆	—	2	1	no	—
178	#529	C₂²×C₅	1	1	yes	characteristic
179	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
180	#484	C₄×C₅	1	1	yes	characteristic
181	#481	C₄×C₅	1	1	yes	characteristic
182	#478	C₄×C₅	1	2	yes	—
183	#463	C₄×C₅	1	2	yes	—
184	#450	C₄×C₅	1	1	yes	characteristic
185	#447	C₄×C₅	1	1	yes	characteristic
186	#446	C₂²×C₅	1	1	yes	characteristic, complemented
187	C₈×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
188	C₄×SD₁₆	C₂²×C₅	1	2	yes	—
189	C₄×D₈	C₂²×C₅	1	2	yes	—
190	#436	—	2	1	no	—
191	#436	—	2	1	no	—
192	#436	C₂²×C₅	1	2	yes	—
193	#436	C₂²×C₅	1	2	yes	—
194	#436	C₂²×C₅	1	1	yes	characteristic, complemented
195	#435	—	2	1	no	—
196	C₈×D₄	—	2	1	no	—
197	C₈×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
198	#433	—	2	1	no	—
199	#432	C₂²×C₅	1	1	yes	characteristic
200	#431	C₂²×C₅	1	1	yes	characteristic
201	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
202	C₂×C₂²⋊C₈	—	2	1	no	—
203	#405	—	2	1	no	—
204	C₄×M₁₆	C₂²×C₅	1	1	yes	characteristic
205	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
206	#335	C₂²×C₅	1	2	yes	complemented
207	#334	C₂²×C₅	1	2	yes	complemented
208	Q₈⋊C₈	C₂²×C₅	1	2	yes	complemented
209	D₄⋊C₈	C₂²×C₅	1	2	yes	—
210	D₄⋊C₈	C₂²×C₅	1	2	yes	—
211	D₄⋊C₈	C₂²×C₅	1	2	yes	complemented
212	#322	C₂²×C₅	1	2	yes	complemented
213	#322	C₂²×C₅	1	2	yes	complemented
214	C₂³×C₅	—	2	1	no	—
215	C₂³×C₅	—	2	2	no	—
216	C₂³×C₅	—	4	2	no	—
217	C₂³×C₅	—	4	2	no	—
218	C₂³×C₅	—	4	2	no	—
219	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
220	C₅×Q₈	—	2	2	no	—
221	C₅×D₄	—	2	2	no	—
222	C₅×D₄	—	2	2	no	—
223	C₅×D₄	—	2	2	no	—
224	C₅×D₄	—	4	2	no	—
225	C₅×D₄	—	4	2	no	—
226	C₂×C₄×C₅	—	2	2	no	—
227	C₂×C₄×C₅	—	2	2	no	—
228	C₂×C₄×C₅	—	2	1	no	—
229	C₂×C₄×C₅	—	2	1	no	—
230	C₂×C₄×C₅	—	2	1	no	—
231	C₂×C₄×C₅	—	2	1	no	—
232	C₂×C₄×C₅	—	2	1	no	—
233	C₂×C₄×C₅	—	2	2	no	—
234	C₂×C₄×C₅	—	4	4	no	—
235	C₂×C₄×C₅	—	4	2	no	—
236	C₂×C₄×C₅	—	4	1	no	—
237	C₂×C₄×C₅	—	4	2	no	—
238	C₂×C₄×C₅	—	4	1	no	—
239	C₂×C₄×C₅	—	4	2	no	—
240	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
241	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
242	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
243	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
244	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
245	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
246	C₅×C₈	—	2	2	no	—
247	C₅×C₈	—	2	2	no	—
248	C₅×C₈	—	2	1	no	—
249	C₅×C₈	—	2	1	no	—
250	C₅×C₈	—	2	1	no	—
251	C₅×C₈	—	4	2	no	—
252	C₅×C₈	—	4	1	no	—
253	C₅×C₈	—	4	2	no	—
254	C₅×C₈	—	4	1	no	—
255	C₅×C₈	AGL(1,ℤ/8)	1	2	yes	—
256	C₂²×D₄	C₂×C₄×C₅	1	1	yes	characteristic
257	C₂³×C₄	—	2	1	no	—
258	C₂×SD₁₆	C₂×C₄×C₅	1	2	yes	—
259	C₂×D₈	C₂×C₄×C₅	1	2	yes	—
260	C₂×M₁₆	—	2	1	no	—
261	C₂×M₁₆	—	2	2	no	—
262	C₂×M₁₆	—	2	2	no	—
263	C₂×M₁₆	—	2	1	no	—
264	C₂×M₁₆	—	4	4	no	—
265	C₂²×C₈	—	2	1	no	—
266	C₂²×C₈	—	2	1	no	—
267	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
268	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
269	#126	—	2	1	no	—
270	#125	C₂×C₄×C₅	1	1	yes	characteristic
271	#124	C₂×C₄×C₅	1	1	yes	characteristic
272	#123	—	2	1	no	—
273	C₂²⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
274	#121	C₂×C₄×C₅	1	1	yes	characteristic
275	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
276	C₄×D₄	—	2	1	no	—
277	C₄×D₄	—	2	1	no	—
278	C₄×D₄	—	2	1	no	—
279	C₄×D₄	C₂×C₄×C₅	1	2	yes	—
280	C₄×D₄	C₂³×C₅	1	2	yes	—
281	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
282	#117	—	2	1	no	—
283	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
284	C₂×C₂²⋊C₄	—	2	1	no	—
285	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
286	#107	C₂×C₄×C₅	1	2	yes	—
287	#106	C₂×C₄×C₅	1	2	yes	—
288	C₄⋊C₈	—	2	1	no	—
289	C₄⋊C₈	—	2	1	no	—
290	C₄⋊C₈	—	2	1	no	—
291	C₄⋊C₈	C₂×C₄×C₅	1	2	yes	—
292	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
293	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
294	C₄⋊C₈	C₂³×C₅	1	2	yes	—
295	#103	C₂×C₄×C₅	1	2	yes	—
296	#102	C₂×C₄×C₅	1	2	yes	—
297	#102	C₂×C₄×C₅	1	2	yes	—
298	#102	C₂×C₄×C₅	1	2	yes	—
299	C₂²⋊C₈	—	2	1	no	—
300	C₂²⋊C₈	—	2	2	no	—
301	C₂²⋊C₈	—	2	2	no	—
302	C₂²⋊C₈	—	2	1	no	—
303	C₂²⋊C₈	—	2	1	no	—
304	C₂²⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
305	C₂²⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
306	#97	—	2	1	no	—
307	#97	—	2	1	no	—
308	#97	—	2	1	no	—
309	C₄×C₈	—	2	1	no	—
310	C₄×C₈	C₅×D₄	1	1	yes	characteristic
311	C₄×C₈	C₅×D₄	1	1	yes	characteristic
312	C₄×C₈	C₂³×C₅	1	2	yes	—
313	C₄×C₈	C₂³×C₅	1	2	yes	—
314	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
315	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
316	C₂²×C₅	—	2	1	no	—
317	C₂²×C₅	—	2	1	no	—
318	C₂²×C₅	—	4	2	no	—
319	C₂²×C₅	—	4	1	no	—
320	C₂²×C₅	—	4	2	no	—
321	C₂²×C₅	—	4	1	no	—
322	C₂²×C₅	—	4	1	no	—
323	C₂²×C₅	—	4	2	no	—
324	C₂²×C₅	—	8	4	no	—
325	C₂²×C₅	#444	1	2	yes	—
326	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
327	C₄×C₅	—	2	1	no	—
328	C₄×C₅	—	2	1	no	—
329	C₄×C₅	—	2	1	no	—
330	C₄×C₅	—	2	1	no	—
331	C₄×C₅	—	4	1	no	—
332	C₄×C₅	—	4	1	no	—
333	C₄×C₅	—	4	2	no	—
334	C₄×C₅	—	4	1	no	—
335	C₄×C₅	#568	1	2	yes	—
336	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
337	C₄×C₅	#575	1	1	yes	characteristic
338	C₂⁴	—	2	1	no	—
339	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
340	C₂×D₄	—	2	1	no	—
341	C₂×D₄	—	2	1	no	—
342	C₂×D₄	—	4	2	no	—
343	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
344	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
345	C₂²×C₄	—	2	1	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	4	2	no	—
350	C₂²×C₄	—	4	2	no	—
351	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
352	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
353	C₂²×C₄	C₅×#41	1	1	yes	characteristic
354	SD₁₆	—	4	2	no	—
355	D₈	—	4	2	no	—
356	M₁₆	—	4	4	no	—
357	M₁₆	—	4	2	no	—
358	M₁₆	—	4	2	no	—
359	M₁₆	—	4	4	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	2	1	no	—
362	C₂×C₈	—	2	1	no	—
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	—	4	1	no	—
366	C₂×C₈	—	4	2	no	—
367	C₂×C₈	—	4	2	no	—
368	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
369	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
370	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
371	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
372	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
373	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
374	C₄⋊C₄	—	2	1	no	—
375	C₄⋊C₄	—	2	1	no	—
376	C₄⋊C₄	—	2	1	no	—
377	C₄⋊C₄	—	2	1	no	—
378	C₄⋊C₄	—	2	1	no	—
379	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
380	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
381	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
382	C₂²⋊C₄	—	2	1	no	—
383	C₂²⋊C₄	—	2	2	no	—
384	C₂²⋊C₄	—	2	1	no	—
385	C₂²⋊C₄	—	2	1	no	—
386	C₂²⋊C₄	—	2	1	no	—
387	C₂²⋊C₄	—	2	2	no	—
388	C₂²⋊C₄	—	2	1	no	—
389	C₄²	—	2	1	no	—
390	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
391	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
392	C₄²	C₅×#41	1	1	yes	characteristic
393	C₄²	C₂⁴×C₅	1	1	yes	characteristic
394	C₂×C₅	—	2	2	no	—
395	C₂×C₅	—	8	1	no	—
396	C₂×C₅	—	8	2	no	—
397	C₂×C₅	#2930	1	1	yes	characteristic
398	C₂×C₅	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
399	C₂×C₅	C₂×#444	1	1	yes	characteristic
400	C₂³	—	2	1	no	—
401	C₂³	—	2	2	no	—
402	C₂³	—	4	2	no	—
403	C₂³	—	4	2	no	—
404	C₂³	—	4	2	no	—
405	C₂³	C₄×C₅×D₄	1	1	yes	characteristic
406	Q₈	—	2	2	no	—
407	D₄	—	2	2	no	—
408	D₄	—	2	2	no	—
409	D₄	—	2	2	no	—
410	D₄	—	4	2	no	—
411	D₄	—	4	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	4	4	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	4	1	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	1	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
427	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
428	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
429	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
430	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
431	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
432	C₈	—	2	2	no	—
433	C₈	—	2	2	no	—
434	C₈	—	2	1	no	—
435	C₈	—	2	1	no	—
436	C₈	—	2	1	no	—
437	C₈	—	4	2	no	—
438	C₈	—	4	2	no	—
439	C₈	—	4	1	no	—
440	C₈	—	4	1	no	—
441	C₈	C₅×AGL(1,ℤ/8)	1	2	yes	—
442	C₅	#17938	1	1	yes	characteristic, direct product factor, Sylow
443	C₂²	—	2	1	no	—
444	C₂²	—	2	1	no	—
445	C₂²	—	4	2	no	—
446	C₂²	—	4	1	no	—
447	C₂²	—	4	2	no	—
448	C₂²	—	4	1	no	—
449	C₂²	—	4	1	no	—
450	C₂²	—	4	2	no	—
451	C₂²	—	8	4	no	—
452	C₂²	C₅×#444	1	2	yes	—
453	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
454	C₄	—	2	1	no	—
455	C₄	—	2	1	no	—
456	C₄	—	2	1	no	—
457	C₄	—	2	1	no	—
458	C₄	—	4	1	no	—
459	C₄	—	4	2	no	—
460	C₄	—	4	1	no	—
461	C₄	—	4	1	no	—
462	C₄	C₅×#568	1	2	yes	—
463	C₄	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
464	C₄	C₅×#575	1	1	yes	characteristic
465	C₂	—	2	2	no	—
466	C₂	—	8	2	no	—
467	C₂	—	8	1	no	—
468	C₂	C₅×#2930	1	1	yes	characteristic
469	C₂	C₄×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
470	C₂	C₂×C₅×#444	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×#447	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. C₂×C₅×#436	C₂	semidirect
4. C₅×#1594	C₂	semidirect
5. C₅×#1592	C₂	semidirect
6. C₅×#1583	C₂	semidirect
7. C₅×#1581	C₂	semidirect
8. C₅×#1573	C₂	semidirect
9. C₅×#1490	C₂	semidirect
10. C₅×#1483	C₂	semidirect
11. C₅×#1451	C₂	semidirect
21. C₅×#446	C₂²	semidirect
22. C₅×C₈×Q₈	C₂²	semidirect
29. C₅×#436	C₂²	semidirect
32. C₅×C₈×D₄	C₂²	semidirect
41. C₅×#335	C₂²	semidirect
42. C₅×#334	C₂²	semidirect
43. C₅×Q₈⋊C₈	C₂²	semidirect
46. C₅×D₄⋊C₈	C₂²	semidirect
47. C₅×#322	C₂²	semidirect
48. C₅×#322	C₂²	semidirect
49. #17938	C₅	direct (N × H)
111. #2966	C₂×C₅	semidirect
112. C₂×#436	C₂×C₅	semidirect
113. #1594	C₂×C₅	semidirect
114. #1592	C₂×C₅	semidirect
115. #1583	C₂×C₅	semidirect
116. #1581	C₂×C₅	semidirect
117. #1573	C₂×C₅	semidirect
118. #1490	C₂×C₅	semidirect
119. #1483	C₂×C₅	semidirect
120. #1451	C₂×C₅	semidirect
186. #446	C₂²×C₅	semidirect
187. C₈×Q₈	C₂²×C₅	semidirect
194. #436	C₂²×C₅	semidirect
197. C₈×D₄	C₂²×C₅	semidirect
206. #335	C₂²×C₅	semidirect
207. #334	C₂²×C₅	semidirect
208. Q₈⋊C₈	C₂²×C₅	semidirect
211. D₄⋊C₈	C₂²×C₅	semidirect
212. #322	C₂²×C₅	semidirect
213. #322	C₂²×C₅	semidirect
442. C₅	#17938	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×#3105	2
C₅×#2966	2
C₂×C₅×#436	2
C₅×#1594	2
C₅×#1592	2
C₅×#1583	2
C₅×#1581	2
C₅×#1573	2
C₅×#1490	2
C₅×#1483	2
C₅×#1451	2
#17938	5

Subgroups — C5×#17938 #11940658

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#17938 #11940658