Subgroups — C₅×#19819 #11942539

Order 1280.

702 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3358	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#3325	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#3305	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×D₄×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1717	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1701	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1678	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1677	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1665	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1646	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1637	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1621	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1619	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1583	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#1580	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₅×SD₁₆	—	2	1	no	—
17	C₅×#555	C₂²	1	1	yes	characteristic
18	C₅×#550	C₂²	1	1	yes	characteristic, complemented
19	C₅×D₄×Q₈	C₂²	1	1	yes	characteristic
20	C₅×D₄²	C₂²	1	1	yes	characteristic
21	C₅×#493	C₂²	1	1	yes	characteristic
22	C₅×#492	C₂²	1	1	yes	characteristic
23	C₅×#487	C₂²	1	1	yes	characteristic, complemented
24	C₅×#486	—	2	1	no	—
25	C₅×#486	C₂²	1	1	yes	characteristic
26	C₅×#486	C₂²	1	1	yes	characteristic, complemented
27	C₅×#486	C₂²	1	1	yes	characteristic, complemented
28	C₅×#482	—	2	1	no	—
29	C₅×#482	—	2	1	no	—
30	C₅×#477	C₂²	1	1	yes	characteristic, complemented
31	C₅×#476	C₂²	1	1	yes	characteristic
32	C₅×#474	—	2	1	no	—
33	C₅×#474	C₂²	1	1	yes	characteristic, complemented
34	C₅×#469	—	2	1	no	—
35	C₅×#466	—	2	1	no	—
36	C₅×#465	—	2	1	no	—
37	C₅×#461	C₂²	1	1	yes	characteristic
38	C₅×#460	C₂²	1	1	yes	characteristic
39	C₅×#459	—	2	1	no	—
40	C₅×#459	C₂²	1	1	yes	characteristic
41	C₅×#459	C₂²	1	1	yes	characteristic
42	C₅×#459	C₂²	1	1	yes	characteristic
43	C₅×#450	—	2	1	no	—
44	C₅×#449	—	2	1	no	—
45	C₅×#448	—	2	1	no	—
46	C₅×#447	—	2	1	no	—
47	C₅×C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
48	C₄×C₅×SD₁₆	C₂²	1	1	yes	characteristic
49	C₄×C₅×D₈	—	2	1	no	—
50	C₄×C₅×D₈	C₂²	1	1	yes	characteristic
51	C₅×#436	C₂²	1	1	yes	characteristic
52	C₅×C₈×D₄	C₂²	1	1	yes	characteristic
53	C₅×C₈×D₄	C₂²	1	1	yes	characteristic, complemented
54	C₅×#418	—	2	1	no	—
55	C₅×#416	—	2	1	no	—
56	C₅×#334	C₂²	1	1	yes	characteristic, complemented
57	C₅×#334	C₂²	1	1	yes	characteristic, complemented
58	C₅×#333	C₂²	1	1	yes	characteristic, complemented
59	C₅×#332	C₂²	1	1	yes	characteristic, complemented
60	C₅×#331	C₂²	1	1	yes	characteristic
61	C₅×#331	C₂²	1	1	yes	characteristic, complemented
62	C₅×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
63	C₅×D₄⋊C₈	C₂²	1	1	yes	characteristic
64	C₅×D₄⋊C₈	C₂²	1	1	yes	characteristic
65	C₅×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
66	C₅×#322	C₂²	1	1	yes	characteristic, complemented
67	#19819	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
68	C₂×C₅×#41	—	2	1	no	—
69	C₂²×C₅×Q₈	—	2	1	no	—
70	C₂²×C₅×D₄	—	2	1	no	—
71	C₂²×C₅×D₄	—	2	1	no	—
72	C₂×C₅×SD₁₆	—	2	1	no	—
73	C₂×C₅×SD₁₆	—	2	1	no	—
74	C₂×C₅×SD₁₆	—	2	1	no	—
75	C₂×C₅×SD₁₆	—	2	1	no	—
76	C₂×C₅×SD₁₆	—	4	4	no	—
77	C₂×C₅×SD₁₆	D₄	1	1	yes	characteristic
78	C₂×C₅×D₈	—	2	1	no	—
79	C₂×C₅×D₈	—	2	1	no	—
80	C₂×C₅×D₈	—	2	1	no	—
81	C₂×C₅×D₈	—	4	1	no	—
82	C₂×C₅×D₈	D₄	1	1	yes	characteristic
83	C₂×C₅×M₁₆	—	2	1	no	—
84	C₂²×C₅×C₈	—	2	1	no	—
85	C₂²×C₅×C₈	—	2	1	no	—
86	C₅×C₄⋊Q₈	—	2	1	no	—
87	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
88	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
89	C₅×#127	—	2	1	no	—
90	C₅×#127	C₂³	1	1	yes	characteristic
91	C₅×#127	C₂³	1	1	yes	characteristic
92	C₅×#124	—	4	1	no	—
93	C₅×C₂²⋊Q₈	—	2	1	no	—
94	C₅×C₂²⋊Q₈	—	4	1	no	—
95	C₅×#121	—	2	1	no	—
96	C₅×#121	—	2	1	no	—
97	C₅×#121	—	2	1	no	—
98	C₅×#121	—	2	1	no	—
99	C₅×#121	—	2	1	no	—
100	C₅×#121	—	4	1	no	—
101	C₅×#120	—	4	1	no	—
102	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
103	C₄×C₅×D₄	—	2	1	no	—
104	C₄×C₅×D₄	—	2	1	no	—
105	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
106	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
107	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
108	C₅×#117	—	2	1	no	—
109	C₅×#117	—	2	1	no	—
110	C₅×#107	—	2	1	no	—
111	C₅×#107	—	2	1	no	—
112	C₅×#107	D₄	1	1	yes	characteristic
113	C₅×#106	—	2	1	no	—
114	C₅×#106	D₄	1	1	yes	characteristic
115	C₅×C₄⋊C₈	—	2	1	no	—
116	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
117	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
118	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
119	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
120	C₅×#103	—	2	1	no	—
121	C₅×#103	—	2	1	no	—
122	C₅×#103	—	4	1	no	—
123	C₅×#103	D₄	1	1	yes	characteristic
124	C₅×#102	—	2	1	no	—
125	C₅×#102	—	2	1	no	—
126	C₅×#102	—	2	1	no	—
127	C₅×#102	—	2	1	no	—
128	C₅×#102	—	2	1	no	—
129	C₅×#102	—	2	1	no	—
130	C₅×#102	—	2	1	no	—
131	C₅×#102	—	2	1	no	—
132	C₅×#102	—	2	1	no	—
133	C₅×#102	—	2	1	no	—
134	C₅×#102	—	2	1	no	—
135	C₅×#102	—	2	1	no	—
136	C₅×#102	D₄	1	1	yes	characteristic
137	C₅×#102	D₄	1	1	yes	characteristic
138	C₅×#102	D₄	1	1	yes	characteristic
139	C₅×C₂²⋊C₈	—	2	1	no	—
140	C₅×C₂²⋊C₈	—	2	1	no	—
141	C₅×C₂²⋊C₈	—	2	1	no	—
142	C₄×C₅×C₈	—	2	1	no	—
143	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
144	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
145	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
146	#3358	C₂×C₅	1	1	yes	characteristic, complemented
147	#3325	C₂×C₅	1	1	yes	characteristic, complemented
148	#3305	C₂×C₅	1	1	yes	characteristic, complemented
149	D₄×SD₁₆	C₂×C₅	1	1	yes	characteristic, complemented
150	#1717	C₂×C₅	1	1	yes	characteristic, complemented
151	#1701	C₂×C₅	1	1	yes	characteristic, complemented
152	#1678	C₂×C₅	1	1	yes	characteristic, complemented
153	#1677	C₂×C₅	1	1	yes	characteristic, complemented
154	#1665	C₂×C₅	1	1	yes	characteristic, complemented
155	#1646	C₂×C₅	1	1	yes	characteristic, complemented
156	#1637	C₂×C₅	1	1	yes	characteristic, complemented
157	#1621	C₂×C₅	1	1	yes	characteristic, complemented
158	#1619	C₂×C₅	1	1	yes	characteristic, complemented
159	#1583	C₂×C₅	1	1	yes	characteristic, complemented
160	#1580	C₂×C₅	1	1	yes	characteristic, complemented
161	C₂⁴×C₅	—	4	1	no	—
162	C₅×#41	—	4	2	no	—
163	C₅×#41	—	8	1	no	—
164	C₂×C₅×Q₈	—	2	1	no	—
165	C₂×C₅×Q₈	—	2	1	no	—
166	C₂×C₅×Q₈	—	4	1	no	—
167	C₂×C₅×Q₈	—	4	2	no	—
168	C₂×C₅×Q₈	—	8	1	no	—
169	C₂×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
170	C₂×C₅×D₄	—	2	1	no	—
171	C₂×C₅×D₄	—	2	1	no	—
172	C₂×C₅×D₄	—	2	1	no	—
173	C₂×C₅×D₄	—	2	1	no	—
174	C₂×C₅×D₄	—	2	1	no	—
175	C₂×C₅×D₄	—	2	1	no	—
176	C₂×C₅×D₄	—	4	1	no	—
177	C₂×C₅×D₄	—	4	1	no	—
178	C₂×C₅×D₄	—	4	1	no	—
179	C₂×C₅×D₄	—	4	1	no	—
180	C₂×C₅×D₄	—	4	2	no	—
181	C₂×C₅×D₄	—	4	2	no	—
182	C₂×C₅×D₄	—	4	1	no	—
183	C₂×C₅×D₄	—	8	1	no	—
184	C₂×C₅×D₄	—	8	1	no	—
185	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
186	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
187	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
188	C₂²×C₄×C₅	—	2	1	no	—
189	C₂²×C₄×C₅	—	2	1	no	—
190	C₂²×C₄×C₅	—	2	1	no	—
191	C₂²×C₄×C₅	—	4	1	no	—
192	C₂²×C₄×C₅	—	4	1	no	—
193	C₅×SD₁₆	—	2	2	no	—
194	C₅×SD₁₆	—	4	2	no	—
195	C₅×SD₁₆	—	4	2	no	—
196	C₅×SD₁₆	—	4	2	no	—
197	C₅×SD₁₆	—	8	1	no	—
198	C₅×D₈	—	2	2	no	—
199	C₅×D₈	—	4	2	no	—
200	C₅×D₈	—	8	1	no	—
201	C₅×D₈	—	8	1	no	—
202	C₅×D₈	—	8	2	no	—
203	C₅×M₁₆	—	8	1	no	—
204	C₂×C₅×C₈	—	2	1	no	—
205	C₂×C₅×C₈	—	2	1	no	—
206	C₂×C₅×C₈	—	2	1	no	—
207	C₂×C₅×C₈	—	2	1	no	—
208	C₂×C₅×C₈	—	2	1	no	—
209	C₂×C₅×C₈	—	4	2	no	—
210	C₂×C₅×C₈	—	8	1	no	—
211	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
212	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
213	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
214	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
215	C₅×C₄⋊C₄	—	2	1	no	—
216	C₅×C₄⋊C₄	—	2	1	no	—
217	C₅×C₄⋊C₄	—	2	1	no	—
218	C₅×C₄⋊C₄	—	2	1	no	—
219	C₅×C₄⋊C₄	—	2	1	no	—
220	C₅×C₄⋊C₄	—	4	1	no	—
221	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
222	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
223	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
224	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
225	C₅×C₂²⋊C₄	—	2	1	no	—
226	C₅×C₂²⋊C₄	—	2	1	no	—
227	C₅×C₂²⋊C₄	—	2	1	no	—
228	C₅×C₂²⋊C₄	—	4	1	no	—
229	C₅×C₂²⋊C₄	—	4	1	no	—
230	C₅×C₂²⋊C₄	—	4	1	no	—
231	C₅×C₂²⋊C₄	—	4	1	no	—
232	C₅×C₂²⋊C₄	—	4	1	no	—
233	C₄²×C₅	—	2	1	no	—
234	C₄²×C₅	—	4	1	no	—
235	C₄²×C₅	C₂⁴	1	1	yes	characteristic
236	C₂²×SD₁₆	—	2	1	no	—
237	#555	C₂²×C₅	1	1	yes	characteristic
238	#550	C₂²×C₅	1	1	yes	characteristic, complemented
239	D₄×Q₈	C₂²×C₅	1	1	yes	characteristic
240	D₄²	C₂²×C₅	1	1	yes	characteristic
241	#493	C₂²×C₅	1	1	yes	characteristic
242	#492	C₂²×C₅	1	1	yes	characteristic
243	#487	C₂²×C₅	1	1	yes	characteristic, complemented
244	#486	—	2	1	no	—
245	#486	C₂²×C₅	1	1	yes	characteristic
246	#486	C₂²×C₅	1	1	yes	characteristic, complemented
247	#486	C₂²×C₅	1	1	yes	characteristic, complemented
248	#482	—	2	1	no	—
249	#482	—	2	1	no	—
250	#477	C₂²×C₅	1	1	yes	characteristic, complemented
251	#476	C₂²×C₅	1	1	yes	characteristic
252	#474	—	2	1	no	—
253	#474	C₂²×C₅	1	1	yes	characteristic, complemented
254	#469	—	2	1	no	—
255	#466	—	2	1	no	—
256	#465	—	2	1	no	—
257	#461	C₂²×C₅	1	1	yes	characteristic
258	#460	C₂²×C₅	1	1	yes	characteristic
259	#459	—	2	1	no	—
260	#459	C₂²×C₅	1	1	yes	characteristic
261	#459	C₂²×C₅	1	1	yes	characteristic
262	#459	C₂²×C₅	1	1	yes	characteristic
263	#450	—	2	1	no	—
264	#449	—	2	1	no	—
265	#448	—	2	1	no	—
266	#447	—	2	1	no	—
267	C₈×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
268	C₄×SD₁₆	C₂²×C₅	1	1	yes	characteristic
269	C₄×D₈	—	2	1	no	—
270	C₄×D₈	C₂²×C₅	1	1	yes	characteristic
271	#436	C₂²×C₅	1	1	yes	characteristic
272	C₈×D₄	C₂²×C₅	1	1	yes	characteristic
273	C₈×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
274	#418	—	2	1	no	—
275	#416	—	2	1	no	—
276	#334	C₂²×C₅	1	1	yes	characteristic, complemented
277	#334	C₂²×C₅	1	1	yes	characteristic, complemented
278	#333	C₂²×C₅	1	1	yes	characteristic, complemented
279	#332	C₂²×C₅	1	1	yes	characteristic, complemented
280	#331	C₂²×C₅	1	1	yes	characteristic
281	#331	C₂²×C₅	1	1	yes	characteristic, complemented
282	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
283	D₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
284	D₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
285	D₄⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
286	#322	C₂²×C₅	1	1	yes	characteristic, complemented
287	C₂³×C₅	—	2	1	no	—
288	C₂³×C₅	—	2	1	no	—
289	C₂³×C₅	—	2	1	no	—
290	C₂³×C₅	—	4	1	no	—
291	C₂³×C₅	—	4	1	no	—
292	C₂³×C₅	—	8	2	no	—
293	C₂³×C₅	—	8	2	no	—
294	C₂³×C₅	—	16	1	no	—
295	C₅×Q₈	—	2	1	no	—
296	C₅×Q₈	—	4	1	no	—
297	C₅×Q₈	—	4	1	no	—
298	C₅×Q₈	—	8	2	no	—
299	C₅×Q₈	—	8	1	no	—
300	C₅×Q₈	AGL(1,ℤ/8)	1	2	yes	—
301	C₅×D₄	—	2	1	no	—
302	C₅×D₄	—	2	1	no	—
303	C₅×D₄	—	2	1	no	—
304	C₅×D₄	—	2	1	no	—
305	C₅×D₄	—	2	1	no	—
306	C₅×D₄	—	4	1	no	—
307	C₅×D₄	—	4	1	no	—
308	C₅×D₄	—	4	1	no	—
309	C₅×D₄	—	4	1	no	—
310	C₅×D₄	—	4	1	no	—
311	C₅×D₄	—	4	1	no	—
312	C₅×D₄	—	4	1	no	—
313	C₅×D₄	—	4	1	no	—
314	C₅×D₄	—	8	2	no	—
315	C₅×D₄	—	8	1	no	—
316	C₅×D₄	—	8	1	no	—
317	C₅×D₄	—	8	2	no	—
318	C₅×D₄	—	8	2	no	—
319	C₅×D₄	—	16	1	no	—
320	C₅×D₄	—	16	1	no	—
321	C₅×D₄	#135	1	2	yes	—
322	C₂×C₄×C₅	—	2	1	no	—
323	C₂×C₄×C₅	—	2	1	no	—
324	C₂×C₄×C₅	—	2	1	no	—
325	C₂×C₄×C₅	—	2	1	no	—
326	C₂×C₄×C₅	—	2	1	no	—
327	C₂×C₄×C₅	—	4	1	no	—
328	C₂×C₄×C₅	—	4	1	no	—
329	C₂×C₄×C₅	—	4	1	no	—
330	C₂×C₄×C₅	—	4	1	no	—
331	C₂×C₄×C₅	—	4	1	no	—
332	C₂×C₄×C₅	—	4	1	no	—
333	C₂×C₄×C₅	—	4	1	no	—
334	C₂×C₄×C₅	—	4	1	no	—
335	C₂×C₄×C₅	—	8	2	no	—
336	C₂×C₄×C₅	—	8	2	no	—
337	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
338	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
339	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
340	C₅×C₈	—	2	1	no	—
341	C₅×C₈	—	2	1	no	—
342	C₅×C₈	—	2	1	no	—
343	C₅×C₈	—	2	1	no	—
344	C₅×C₈	—	4	1	no	—
345	C₅×C₈	—	4	1	no	—
346	C₅×C₈	—	4	1	no	—
347	C₅×C₈	—	4	1	no	—
348	C₅×C₈	—	4	1	no	—
349	C₂×#41	—	2	1	no	—
350	C₂²×Q₈	—	2	1	no	—
351	C₂²×D₄	—	2	1	no	—
352	C₂²×D₄	—	2	1	no	—
353	C₂×SD₁₆	—	2	1	no	—
354	C₂×SD₁₆	—	2	1	no	—
355	C₂×SD₁₆	—	2	1	no	—
356	C₂×SD₁₆	—	2	1	no	—
357	C₂×SD₁₆	—	4	4	no	—
358	C₂×SD₁₆	C₅×D₄	1	1	yes	characteristic
359	C₂×D₈	—	2	1	no	—
360	C₂×D₈	—	2	1	no	—
361	C₂×D₈	—	2	1	no	—
362	C₂×D₈	—	4	1	no	—
363	C₂×D₈	C₅×D₄	1	1	yes	characteristic
364	C₂×M₁₆	—	2	1	no	—
365	C₂²×C₈	—	2	1	no	—
366	C₂²×C₈	—	2	1	no	—
367	C₄⋊Q₈	—	2	1	no	—
368	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
369	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
370	#127	—	2	1	no	—
371	#127	C₂³×C₅	1	1	yes	characteristic
372	#127	C₂³×C₅	1	1	yes	characteristic
373	#124	—	4	1	no	—
374	C₂²⋊Q₈	—	2	1	no	—
375	C₂²⋊Q₈	—	4	1	no	—
376	#121	—	2	1	no	—
377	#121	—	2	1	no	—
378	#121	—	2	1	no	—
379	#121	—	2	1	no	—
380	#121	—	2	1	no	—
381	#121	—	4	1	no	—
382	#120	—	4	1	no	—
383	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
384	C₄×D₄	—	2	1	no	—
385	C₄×D₄	—	2	1	no	—
386	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
387	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
388	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
389	#117	—	2	1	no	—
390	#117	—	2	1	no	—
391	#107	—	2	1	no	—
392	#107	—	2	1	no	—
393	#107	C₅×D₄	1	1	yes	characteristic
394	#106	—	2	1	no	—
395	#106	C₅×D₄	1	1	yes	characteristic
396	C₄⋊C₈	—	2	1	no	—
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	#103	—	2	1	no	—
402	#103	—	2	1	no	—
403	#103	—	4	1	no	—
404	#103	C₅×D₄	1	1	yes	characteristic
405	#102	—	2	1	no	—
406	#102	—	2	1	no	—
407	#102	—	2	1	no	—
408	#102	—	2	1	no	—
409	#102	—	2	1	no	—
410	#102	—	2	1	no	—
411	#102	—	2	1	no	—
412	#102	—	2	1	no	—
413	#102	—	2	1	no	—
414	#102	—	2	1	no	—
415	#102	—	2	1	no	—
416	#102	—	2	1	no	—
417	#102	C₅×D₄	1	1	yes	characteristic
418	#102	C₅×D₄	1	1	yes	characteristic
419	#102	C₅×D₄	1	1	yes	characteristic
420	C₂²⋊C₈	—	2	1	no	—
421	C₂²⋊C₈	—	2	1	no	—
422	C₂²⋊C₈	—	2	1	no	—
423	C₄×C₈	—	2	1	no	—
424	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
425	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
426	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
427	C₂²×C₅	—	2	2	no	—
428	C₂²×C₅	—	4	1	no	—
429	C₂²×C₅	—	4	1	no	—
430	C₂²×C₅	—	4	1	no	—
431	C₂²×C₅	—	4	1	no	—
432	C₂²×C₅	—	4	1	no	—
433	C₂²×C₅	—	4	1	no	—
434	C₂²×C₅	—	4	1	no	—
435	C₂²×C₅	—	4	1	no	—
436	C₂²×C₅	—	8	1	no	—
437	C₂²×C₅	—	8	1	no	—
438	C₂²×C₅	—	8	1	no	—
439	C₂²×C₅	—	8	1	no	—
440	C₂²×C₅	—	8	1	no	—
441	C₂²×C₅	—	8	1	no	—
442	C₂²×C₅	—	16	4	no	—
443	C₂²×C₅	D₄²	1	1	yes	characteristic
444	C₄×C₅	—	2	2	no	—
445	C₄×C₅	—	2	1	no	—
446	C₄×C₅	—	4	1	no	—
447	C₄×C₅	—	4	1	no	—
448	C₄×C₅	—	4	1	no	—
449	C₄×C₅	—	4	1	no	—
450	C₄×C₅	—	8	1	no	—
451	C₄×C₅	—	8	1	no	—
452	C₄×C₅	C₂×#135	1	1	yes	characteristic
453	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
454	C₄×C₅	#576	1	1	yes	characteristic
455	C₄×C₅	#577	1	1	yes	characteristic
456	C₂⁴	—	4	1	no	—
457	#41	—	4	2	no	—
458	#41	—	8	1	no	—
459	C₂×Q₈	—	2	1	no	—
460	C₂×Q₈	—	2	1	no	—
461	C₂×Q₈	—	4	1	no	—
462	C₂×Q₈	—	4	2	no	—
463	C₂×Q₈	—	8	1	no	—
464	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
465	C₂×D₄	—	2	1	no	—
466	C₂×D₄	—	2	1	no	—
467	C₂×D₄	—	2	1	no	—
468	C₂×D₄	—	2	1	no	—
469	C₂×D₄	—	2	1	no	—
470	C₂×D₄	—	2	1	no	—
471	C₂×D₄	—	4	1	no	—
472	C₂×D₄	—	4	1	no	—
473	C₂×D₄	—	4	1	no	—
474	C₂×D₄	—	4	1	no	—
475	C₂×D₄	—	4	2	no	—
476	C₂×D₄	—	4	2	no	—
477	C₂×D₄	—	4	1	no	—
478	C₂×D₄	—	8	1	no	—
479	C₂×D₄	—	8	1	no	—
480	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
481	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
482	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
483	C₂²×C₄	—	2	1	no	—
484	C₂²×C₄	—	2	1	no	—
485	C₂²×C₄	—	2	1	no	—
486	C₂²×C₄	—	4	1	no	—
487	C₂²×C₄	—	4	1	no	—
488	SD₁₆	—	2	2	no	—
489	SD₁₆	—	4	2	no	—
490	SD₁₆	—	4	2	no	—
491	SD₁₆	—	4	2	no	—
492	SD₁₆	—	8	1	no	—
493	D₈	—	2	2	no	—
494	D₈	—	4	2	no	—
495	D₈	—	8	1	no	—
496	D₈	—	8	1	no	—
497	D₈	—	8	2	no	—
498	M₁₆	—	8	1	no	—
499	C₂×C₈	—	2	1	no	—
500	C₂×C₈	—	2	1	no	—
501	C₂×C₈	—	2	1	no	—
502	C₂×C₈	—	2	1	no	—
503	C₂×C₈	—	2	1	no	—
504	C₂×C₈	—	4	2	no	—
505	C₂×C₈	—	8	1	no	—
506	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
507	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
508	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
509	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
510	C₄⋊C₄	—	2	1	no	—
511	C₄⋊C₄	—	2	1	no	—
512	C₄⋊C₄	—	2	1	no	—
513	C₄⋊C₄	—	2	1	no	—
514	C₄⋊C₄	—	2	1	no	—
515	C₄⋊C₄	—	4	1	no	—
516	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
517	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
518	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
519	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
520	C₂²⋊C₄	—	2	1	no	—
521	C₂²⋊C₄	—	2	1	no	—
522	C₂²⋊C₄	—	2	1	no	—
523	C₂²⋊C₄	—	4	1	no	—
524	C₂²⋊C₄	—	4	1	no	—
525	C₂²⋊C₄	—	4	1	no	—
526	C₂²⋊C₄	—	4	1	no	—
527	C₂²⋊C₄	—	4	1	no	—
528	C₄²	—	2	1	no	—
529	C₄²	—	4	1	no	—
530	C₄²	C₂⁴×C₅	1	1	yes	characteristic
531	C₂×C₅	—	4	2	no	—
532	C₂×C₅	—	8	1	no	—
533	C₂×C₅	—	8	1	no	—
534	C₂×C₅	—	16	1	no	—
535	C₂×C₅	—	16	1	no	—
536	C₂×C₅	#3264	1	1	yes	characteristic
537	C₂×C₅	#3282	1	1	yes	characteristic
538	C₂×C₅	#3288	1	1	yes	characteristic
539	C₂³	—	2	1	no	—
540	C₂³	—	2	1	no	—
541	C₂³	—	2	1	no	—
542	C₂³	—	4	1	no	—
543	C₂³	—	4	1	no	—
544	C₂³	—	8	2	no	—
545	C₂³	—	8	2	no	—
546	C₂³	—	16	1	no	—
547	Q₈	—	2	1	no	—
548	Q₈	—	4	1	no	—
549	Q₈	—	4	1	no	—
550	Q₈	—	8	2	no	—
551	Q₈	—	8	1	no	—
552	Q₈	C₅×AGL(1,ℤ/8)	1	2	yes	—
553	D₄	—	2	1	no	—
554	D₄	—	2	1	no	—
555	D₄	—	2	1	no	—
556	D₄	—	2	1	no	—
557	D₄	—	2	1	no	—
558	D₄	—	4	1	no	—
559	D₄	—	4	1	no	—
560	D₄	—	4	1	no	—
561	D₄	—	4	1	no	—
562	D₄	—	4	1	no	—
563	D₄	—	4	1	no	—
564	D₄	—	4	1	no	—
565	D₄	—	4	1	no	—
566	D₄	—	8	2	no	—
567	D₄	—	8	1	no	—
568	D₄	—	8	1	no	—
569	D₄	—	8	2	no	—
570	D₄	—	8	2	no	—
571	D₄	—	16	1	no	—
572	D₄	—	16	1	no	—
573	D₄	C₅×#135	1	2	yes	—
574	C₂×C₄	—	2	1	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	4	1	no	—
580	C₂×C₄	—	4	1	no	—
581	C₂×C₄	—	4	1	no	—
582	C₂×C₄	—	4	1	no	—
583	C₂×C₄	—	4	1	no	—
584	C₂×C₄	—	4	1	no	—
585	C₂×C₄	—	4	1	no	—
586	C₂×C₄	—	4	1	no	—
587	C₂×C₄	—	8	2	no	—
588	C₂×C₄	—	8	2	no	—
589	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
590	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
591	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
592	C₈	—	2	1	no	—
593	C₈	—	2	1	no	—
594	C₈	—	2	1	no	—
595	C₈	—	2	1	no	—
596	C₈	—	4	1	no	—
597	C₈	—	4	1	no	—
598	C₈	—	4	1	no	—
599	C₈	—	4	1	no	—
600	C₈	—	4	1	no	—
601	C₅	#19819	1	1	yes	characteristic, direct product factor, Sylow
602	C₂²	—	2	2	no	—
603	C₂²	—	4	1	no	—
604	C₂²	—	4	1	no	—
605	C₂²	—	4	1	no	—
606	C₂²	—	4	1	no	—
607	C₂²	—	4	1	no	—
608	C₂²	—	4	1	no	—
609	C₂²	—	4	1	no	—
610	C₂²	—	4	1	no	—
611	C₂²	—	8	1	no	—
612	C₂²	—	8	1	no	—
613	C₂²	—	8	1	no	—
614	C₂²	—	8	1	no	—
615	C₂²	—	8	1	no	—
616	C₂²	—	8	1	no	—
617	C₂²	—	16	4	no	—
618	C₂²	C₅×D₄²	1	1	yes	characteristic
619	C₄	—	2	2	no	—
620	C₄	—	2	1	no	—
621	C₄	—	4	1	no	—
622	C₄	—	4	1	no	—
623	C₄	—	4	1	no	—
624	C₄	—	4	1	no	—
625	C₄	—	8	1	no	—
626	C₄	—	8	1	no	—
627	C₄	C₂×C₅×#135	1	1	yes	characteristic
628	C₄	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
629	C₄	C₅×#576	1	1	yes	characteristic
630	C₄	C₅×#577	1	1	yes	characteristic
631	C₂	—	4	2	no	—
632	C₂	—	8	1	no	—
633	C₂	—	8	1	no	—
634	C₂	—	16	1	no	—
635	C₂	—	16	1	no	—
636	C₂	C₅×#3264	1	1	yes	characteristic
637	C₂	C₅×#3282	1	1	yes	characteristic
638	C₂	C₅×#3288	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₅
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×#3358	C₂	semidirect
2. C₅×#3325	C₂	semidirect
3. C₅×#3305	C₂	semidirect
4. C₅×D₄×SD₁₆	C₂	semidirect
5. C₅×#1717	C₂	semidirect
6. C₅×#1701	C₂	semidirect
7. C₅×#1678	C₂	semidirect
8. C₅×#1677	C₂	semidirect
9. C₅×#1665	C₂	semidirect
10. C₅×#1646	C₂	semidirect
11. C₅×#1637	C₂	semidirect
12. C₅×#1621	C₂	semidirect
13. C₅×#1619	C₂	semidirect
14. C₅×#1583	C₂	semidirect
15. C₅×#1580	C₂	semidirect
18. C₅×#550	C₂²	semidirect
23. C₅×#487	C₂²	semidirect
26. C₅×#486	C₂²	semidirect
27. C₅×#486	C₂²	semidirect
30. C₅×#477	C₂²	semidirect
33. C₅×#474	C₂²	semidirect
47. C₅×C₈×Q₈	C₂²	semidirect
53. C₅×C₈×D₄	C₂²	semidirect
56. C₅×#334	C₂²	semidirect
57. C₅×#334	C₂²	semidirect
58. C₅×#333	C₂²	semidirect
59. C₅×#332	C₂²	semidirect
61. C₅×#331	C₂²	semidirect
62. C₅×Q₈⋊C₈	C₂²	semidirect
65. C₅×D₄⋊C₈	C₂²	semidirect
66. C₅×#322	C₂²	semidirect
67. #19819	C₅	direct (N × H)
146. #3358	C₂×C₅	semidirect
147. #3325	C₂×C₅	semidirect
148. #3305	C₂×C₅	semidirect
149. D₄×SD₁₆	C₂×C₅	semidirect
150. #1717	C₂×C₅	semidirect
151. #1701	C₂×C₅	semidirect
152. #1678	C₂×C₅	semidirect
153. #1677	C₂×C₅	semidirect
154. #1665	C₂×C₅	semidirect
155. #1646	C₂×C₅	semidirect
156. #1637	C₂×C₅	semidirect
157. #1621	C₂×C₅	semidirect
158. #1619	C₂×C₅	semidirect
159. #1583	C₂×C₅	semidirect
160. #1580	C₂×C₅	semidirect
238. #550	C₂²×C₅	semidirect
243. #487	C₂²×C₅	semidirect
246. #486	C₂²×C₅	semidirect
247. #486	C₂²×C₅	semidirect
250. #477	C₂²×C₅	semidirect
253. #474	C₂²×C₅	semidirect
267. C₈×Q₈	C₂²×C₅	semidirect
273. C₈×D₄	C₂²×C₅	semidirect
276. #334	C₂²×C₅	semidirect
277. #334	C₂²×C₅	semidirect
278. #333	C₂²×C₅	semidirect
279. #332	C₂²×C₅	semidirect
281. #331	C₂²×C₅	semidirect
282. Q₈⋊C₈	C₂²×C₅	semidirect
285. D₄⋊C₈	C₂²×C₅	semidirect
286. #322	C₂²×C₅	semidirect
601. C₅	#19819	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×#3358	2
C₅×#3325	2
C₅×#3305	2
C₅×D₄×SD₁₆	2
C₅×#1717	2
C₅×#1701	2
C₅×#1678	2
C₅×#1677	2
C₅×#1665	2
C₅×#1646	2
C₅×#1637	2
C₅×#1621	2
C₅×#1619	2
C₅×#1583	2
C₅×#1580	2
#19819	5

Subgroups — C5×#19819 #11942539

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#19819 #11942539