Subgroups — C₅×#19820 #11942540

Order 1280.

676 conjugacy classes of subgroups.

The subgroup lattice has 622 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×#3330	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#3298	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#3284	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1719	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1701	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1680	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1679	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1665	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1649	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1647	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1642	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1625	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	C₂×C₅×#135	—	2	1	no	—
17	C₅×#550	C₂²	1	1	yes	characteristic
18	C₅×D₄×Q₈	C₂²	1	1	yes	characteristic
19	C₅×#547	C₂²	1	1	yes	characteristic
20	C₅×#547	C₂²	1	1	yes	characteristic
21	C₅×#500	C₂²	1	1	yes	characteristic
22	C₅×#492	C₂²	1	1	yes	characteristic
23	C₅×#487	C₂²	1	1	yes	characteristic
24	C₅×#487	C₂²	1	1	yes	characteristic
25	C₅×#486	—	2	1	no	—
26	C₅×#486	C₂²	1	1	yes	characteristic
27	C₅×#486	C₂²	1	1	yes	characteristic
28	C₅×#484	—	2	1	no	—
29	C₅×#483	—	2	1	no	—
30	C₅×#475	C₂²	1	1	yes	characteristic
31	C₅×#474	—	2	1	no	—
32	C₅×#474	C₂²	1	1	yes	characteristic
33	C₅×#474	C₂²	1	1	yes	characteristic
34	C₅×#468	—	2	1	no	—
35	C₅×#465	—	2	1	no	—
36	C₅×#465	—	2	1	no	—
37	C₅×#462	C₂²	1	1	yes	characteristic
38	C₅×#461	C₂²	1	1	yes	characteristic
39	C₅×#461	C₂²	1	1	yes	characteristic
40	C₅×#459	—	2	1	no	—
41	C₅×#459	C₂²	1	1	yes	characteristic
42	C₅×#459	C₂²	1	1	yes	characteristic
43	C₅×#452	—	2	1	no	—
44	C₅×#449	—	2	1	no	—
45	C₅×#449	—	2	1	no	—
46	C₅×#448	—	2	1	no	—
47	C₅×C₈×Q₈	C₂²	1	1	yes	characteristic
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
54	C₅×#417	—	2	1	no	—
55	C₂×C₅×#103	—	2	1	no	—
56	C₅×#334	C₂²	1	1	yes	characteristic
57	C₅×#334	C₂²	1	1	yes	characteristic
58	C₅×#332	C₂²	1	1	yes	characteristic
59	C₅×#332	C₂²	1	1	yes	characteristic
60	C₅×#332	C₂²	1	1	yes	characteristic
61	C₅×#331	C₂²	1	1	yes	characteristic
62	C₅×Q₈⋊C₈	C₂²	1	1	yes	characteristic
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
66	C₅×#322	C₂²	1	1	yes	characteristic
67	#19820	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
68	C₂×C₅×#41	—	2	1	no	—
69	C₂×C₅×#41	—	2	1	no	—
70	C₂×C₅×#41	—	2	1	no	—
71	C₂²×C₅×Q₈	—	2	1	no	—
72	C₅×#135	—	4	4	no	—
73	C₂×C₅×Q₁₆	—	2	1	no	—
74	C₂×C₅×SD₁₆	—	2	1	no	—
75	C₂×C₅×SD₁₆	—	2	1	no	—
76	C₂×C₅×SD₁₆	—	2	1	no	—
77	C₂×C₅×SD₁₆	—	2	1	no	—
78	C₂×C₅×SD₁₆	D₄	1	1	yes	characteristic
79	C₂×C₅×D₈	—	2	1	no	—
80	C₂×C₅×D₈	—	2	1	no	—
81	C₂×C₅×D₈	D₄	1	1	yes	characteristic
82	C₂×C₅×M₁₆	—	2	1	no	—
83	C₂²×C₅×C₈	—	2	1	no	—
84	C₂²×C₅×C₈	—	2	1	no	—
85	C₅×C₄⋊Q₈	—	2	1	no	—
86	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
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×#123	—	4	1	no	—
92	C₅×#123	—	4	1	no	—
93	C₅×C₂²⋊Q₈	—	2	1	no	—
94	C₅×C₂²⋊Q₈	—	2	1	no	—
95	C₅×C₂²⋊Q₈	—	2	1	no	—
96	C₅×C₂²⋊Q₈	—	4	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	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
102	C₄×C₅×D₄	—	2	1	no	—
103	C₄×C₅×D₄	—	2	1	no	—
104	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
105	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
106	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
107	C₂×C₅×C₄⋊C₄	—	2	1	no	—
108	C₂×C₅×C₄⋊C₄	—	2	1	no	—
109	C₅×#107	—	2	1	no	—
110	C₅×#107	—	2	1	no	—
111	C₅×#107	—	4	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	—	2	1	no	—
123	C₅×#103	—	2	1	no	—
124	C₅×#103	—	2	1	no	—
125	C₅×#103	—	2	1	no	—
126	C₅×#103	—	2	1	no	—
127	C₅×#103	—	2	1	no	—
128	C₅×#103	D₄	1	1	yes	characteristic
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	—	4	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	#3330	C₂×C₅	1	1	yes	characteristic, complemented
148	#3298	C₂×C₅	1	1	yes	characteristic, complemented
149	#3284	C₂×C₅	1	1	yes	characteristic, complemented
150	#1719	C₂×C₅	1	1	yes	characteristic, complemented
151	#1701	C₂×C₅	1	1	yes	characteristic, complemented
152	#1680	C₂×C₅	1	1	yes	characteristic, complemented
153	#1679	C₂×C₅	1	1	yes	characteristic, complemented
154	#1665	C₂×C₅	1	1	yes	characteristic, complemented
155	#1649	C₂×C₅	1	1	yes	characteristic, complemented
156	#1647	C₂×C₅	1	1	yes	characteristic, complemented
157	#1642	C₂×C₅	1	1	yes	characteristic, complemented
158	#1625	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	C₅×#41	—	4	2	no	—
162	C₅×#41	—	4	2	no	—
163	C₅×#41	—	4	2	no	—
164	C₅×#41	—	8	1	no	—
165	C₅×#41	—	8	1	no	—
166	C₅×#41	—	8	1	no	—
167	C₂×C₅×Q₈	—	2	1	no	—
168	C₂×C₅×Q₈	—	2	1	no	—
169	C₂×C₅×Q₈	—	2	1	no	—
170	C₂×C₅×Q₈	—	4	1	no	—
171	C₂×C₅×Q₈	—	4	2	no	—
172	C₂×C₅×Q₈	—	8	1	no	—
173	C₂×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
174	C₂×C₅×D₄	—	2	1	no	—
175	C₂×C₅×D₄	—	2	1	no	—
176	C₂×C₅×D₄	—	2	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	1	no	—
181	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
182	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
183	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
184	C₂²×C₄×C₅	—	2	1	no	—
185	C₂²×C₄×C₅	—	2	1	no	—
186	C₂²×C₄×C₅	—	2	1	no	—
187	C₂²×C₄×C₅	—	4	1	no	—
188	C₂²×C₄×C₅	—	4	1	no	—
189	C₂²×C₄×C₅	—	4	1	no	—
190	C₂²×C₄×C₅	—	4	1	no	—
191	C₅×Q₁₆	—	4	2	no	—
192	C₅×SD₁₆	—	2	2	no	—
193	C₅×SD₁₆	—	4	2	no	—
194	C₅×SD₁₆	—	8	1	no	—
195	C₅×SD₁₆	—	8	1	no	—
196	C₅×SD₁₆	—	8	1	no	—
197	C₅×D₈	—	2	2	no	—
198	C₅×D₈	—	4	2	no	—
199	C₅×D₈	—	4	2	no	—
200	C₅×M₁₆	—	8	1	no	—
201	C₂×C₅×C₈	—	2	1	no	—
202	C₂×C₅×C₈	—	2	1	no	—
203	C₂×C₅×C₈	—	2	1	no	—
204	C₂×C₅×C₈	—	2	1	no	—
205	C₂×C₅×C₈	—	2	1	no	—
206	C₂×C₅×C₈	—	4	2	no	—
207	C₂×C₅×C₈	—	8	1	no	—
208	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
209	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
210	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
211	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
212	C₅×C₄⋊C₄	—	2	1	no	—
213	C₅×C₄⋊C₄	—	2	1	no	—
214	C₅×C₄⋊C₄	—	2	1	no	—
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	—	4	1	no	—
220	C₅×C₄⋊C₄	—	4	1	no	—
221	C₅×C₄⋊C₄	—	4	1	no	—
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×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
226	C₅×C₂²⋊C₄	—	2	1	no	—
227	C₅×C₂²⋊C₄	—	2	1	no	—
228	C₅×C₂²⋊C₄	—	2	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	C₂⁴	1	1	yes	characteristic
235	C₂×#135	—	2	1	no	—
236	#550	C₂²×C₅	1	1	yes	characteristic
237	D₄×Q₈	C₂²×C₅	1	1	yes	characteristic
238	#547	C₂²×C₅	1	1	yes	characteristic
239	#547	C₂²×C₅	1	1	yes	characteristic
240	#500	C₂²×C₅	1	1	yes	characteristic
241	#492	C₂²×C₅	1	1	yes	characteristic
242	#487	C₂²×C₅	1	1	yes	characteristic
243	#487	C₂²×C₅	1	1	yes	characteristic
244	#486	—	2	1	no	—
245	#486	C₂²×C₅	1	1	yes	characteristic
246	#486	C₂²×C₅	1	1	yes	characteristic
247	#484	—	2	1	no	—
248	#483	—	2	1	no	—
249	#475	C₂²×C₅	1	1	yes	characteristic
250	#474	—	2	1	no	—
251	#474	C₂²×C₅	1	1	yes	characteristic
252	#474	C₂²×C₅	1	1	yes	characteristic
253	#468	—	2	1	no	—
254	#465	—	2	1	no	—
255	#465	—	2	1	no	—
256	#462	C₂²×C₅	1	1	yes	characteristic
257	#461	C₂²×C₅	1	1	yes	characteristic
258	#461	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	#452	—	2	1	no	—
263	#449	—	2	1	no	—
264	#449	—	2	1	no	—
265	#448	—	2	1	no	—
266	C₈×Q₈	C₂²×C₅	1	1	yes	characteristic
267	C₄×SD₁₆	C₂²×C₅	1	1	yes	characteristic
268	C₄×D₈	—	2	1	no	—
269	C₄×D₈	C₂²×C₅	1	1	yes	characteristic
270	#436	C₂²×C₅	1	1	yes	characteristic
271	C₈×D₄	C₂²×C₅	1	1	yes	characteristic
272	C₈×D₄	C₂²×C₅	1	1	yes	characteristic
273	#417	—	2	1	no	—
274	C₂×#103	—	2	1	no	—
275	#334	C₂²×C₅	1	1	yes	characteristic
276	#334	C₂²×C₅	1	1	yes	characteristic
277	#332	C₂²×C₅	1	1	yes	characteristic
278	#332	C₂²×C₅	1	1	yes	characteristic
279	#332	C₂²×C₅	1	1	yes	characteristic
280	#331	C₂²×C₅	1	1	yes	characteristic
281	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic
282	D₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
283	D₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
284	D₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
285	#322	C₂²×C₅	1	1	yes	characteristic
286	C₂³×C₅	—	2	1	no	—
287	C₂³×C₅	—	2	1	no	—
288	C₂³×C₅	—	2	1	no	—
289	C₂³×C₅	—	4	1	no	—
290	C₅×Q₈	—	2	1	no	—
291	C₅×Q₈	—	4	1	no	—
292	C₅×Q₈	—	4	1	no	—
293	C₅×Q₈	—	4	1	no	—
294	C₅×Q₈	—	4	1	no	—
295	C₅×Q₈	—	4	1	no	—
296	C₅×Q₈	—	4	1	no	—
297	C₅×Q₈	—	8	2	no	—
298	C₅×Q₈	AGL(1,ℤ/8)	1	2	yes	—
299	C₅×D₄	—	2	1	no	—
300	C₅×D₄	—	2	1	no	—
301	C₅×D₄	—	2	1	no	—
302	C₅×D₄	—	2	1	no	—
303	C₅×D₄	—	2	1	no	—
304	C₅×D₄	—	4	1	no	—
305	C₅×D₄	—	4	1	no	—
306	C₅×D₄	—	4	1	no	—
307	C₅×D₄	—	4	1	no	—
308	C₅×D₄	—	8	2	no	—
309	C₅×D₄	—	8	1	no	—
310	C₅×D₄	—	8	2	no	—
311	C₅×D₄	—	8	2	no	—
312	C₅×D₄	—	16	1	no	—
313	C₅×D₄	#135	1	2	yes	complemented
314	C₂×C₄×C₅	—	2	1	no	—
315	C₂×C₄×C₅	—	2	1	no	—
316	C₂×C₄×C₅	—	2	1	no	—
317	C₂×C₄×C₅	—	2	1	no	—
318	C₂×C₄×C₅	—	2	1	no	—
319	C₂×C₄×C₅	—	4	1	no	—
320	C₂×C₄×C₅	—	4	1	no	—
321	C₂×C₄×C₅	—	4	1	no	—
322	C₂×C₄×C₅	—	4	1	no	—
323	C₂×C₄×C₅	—	4	1	no	—
324	C₂×C₄×C₅	—	4	1	no	—
325	C₂×C₄×C₅	—	4	1	no	—
326	C₂×C₄×C₅	—	4	1	no	—
327	C₂×C₄×C₅	—	4	1	no	—
328	C₂×C₄×C₅	—	8	2	no	—
329	C₂×C₄×C₅	—	8	2	no	—
330	C₂×C₄×C₅	—	8	2	no	—
331	C₂×C₄×C₅	—	8	2	no	—
332	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
333	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
334	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
335	C₅×C₈	—	2	1	no	—
336	C₅×C₈	—	2	1	no	—
337	C₅×C₈	—	2	1	no	—
338	C₅×C₈	—	2	1	no	—
339	C₅×C₈	—	4	1	no	—
340	C₅×C₈	—	4	1	no	—
341	C₅×C₈	—	4	1	no	—
342	C₅×C₈	—	4	1	no	—
343	C₅×C₈	—	4	1	no	—
344	C₂×#41	—	2	1	no	—
345	C₂×#41	—	2	1	no	—
346	C₂×#41	—	2	1	no	—
347	C₂²×Q₈	—	2	1	no	—
348	#135	—	4	4	no	—
349	C₂×Q₁₆	—	2	1	no	—
350	C₂×SD₁₆	—	2	1	no	—
351	C₂×SD₁₆	—	2	1	no	—
352	C₂×SD₁₆	—	2	1	no	—
353	C₂×SD₁₆	—	2	1	no	—
354	C₂×SD₁₆	C₅×D₄	1	1	yes	characteristic
355	C₂×D₈	—	2	1	no	—
356	C₂×D₈	—	2	1	no	—
357	C₂×D₈	C₅×D₄	1	1	yes	characteristic
358	C₂×M₁₆	—	2	1	no	—
359	C₂²×C₈	—	2	1	no	—
360	C₂²×C₈	—	2	1	no	—
361	C₄⋊Q₈	—	2	1	no	—
362	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
363	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
364	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
365	#127	—	2	1	no	—
366	#127	C₂³×C₅	1	1	yes	characteristic
367	#123	—	4	1	no	—
368	#123	—	4	1	no	—
369	C₂²⋊Q₈	—	2	1	no	—
370	C₂²⋊Q₈	—	2	1	no	—
371	C₂²⋊Q₈	—	2	1	no	—
372	C₂²⋊Q₈	—	4	1	no	—
373	#121	—	2	1	no	—
374	#121	—	2	1	no	—
375	#121	—	2	1	no	—
376	#121	—	4	1	no	—
377	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
378	C₄×D₄	—	2	1	no	—
379	C₄×D₄	—	2	1	no	—
380	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
381	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
382	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
383	C₂×C₄⋊C₄	—	2	1	no	—
384	C₂×C₄⋊C₄	—	2	1	no	—
385	#107	—	2	1	no	—
386	#107	—	2	1	no	—
387	#107	—	4	1	no	—
388	#107	C₅×D₄	1	1	yes	characteristic
389	#106	—	2	1	no	—
390	#106	C₅×D₄	1	1	yes	characteristic
391	C₄⋊C₈	—	2	1	no	—
392	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
393	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
394	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
395	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
396	#103	—	2	1	no	—
397	#103	—	2	1	no	—
398	#103	—	2	1	no	—
399	#103	—	2	1	no	—
400	#103	—	2	1	no	—
401	#103	—	2	1	no	—
402	#103	—	2	1	no	—
403	#103	—	2	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	—	4	1	no	—
412	#102	C₅×D₄	1	1	yes	characteristic
413	#102	C₅×D₄	1	1	yes	characteristic
414	#102	C₅×D₄	1	1	yes	characteristic
415	C₂²⋊C₈	—	2	1	no	—
416	C₂²⋊C₈	—	2	1	no	—
417	C₂²⋊C₈	—	2	1	no	—
418	C₄×C₈	—	2	1	no	—
419	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
420	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
421	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
422	C₂²×C₅	—	2	2	no	—
423	C₂²×C₅	—	4	1	no	—
424	C₂²×C₅	—	4	1	no	—
425	C₂²×C₅	—	4	1	no	—
426	C₂²×C₅	—	4	1	no	—
427	C₂²×C₅	—	4	1	no	—
428	C₂²×C₅	—	4	1	no	—
429	C₂²×C₅	—	4	1	no	—
430	C₂²×C₅	—	4	1	no	—
431	C₂²×C₅	—	8	1	no	—
432	C₂²×C₅	—	8	1	no	—
433	C₂²×C₅	—	8	1	no	—
434	C₂²×C₅	D₄²	1	1	yes	characteristic
435	C₄×C₅	—	2	2	no	—
436	C₄×C₅	—	2	1	no	—
437	C₄×C₅	—	4	1	no	—
438	C₄×C₅	—	4	1	no	—
439	C₄×C₅	—	4	1	no	—
440	C₄×C₅	—	4	1	no	—
441	C₄×C₅	—	8	1	no	—
442	C₄×C₅	—	8	1	no	—
443	C₄×C₅	—	8	1	no	—
444	C₄×C₅	C₂×#135	1	1	yes	characteristic
445	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
446	C₄×C₅	#576	1	1	yes	characteristic
447	C₄×C₅	#577	1	1	yes	characteristic
448	#41	—	4	2	no	—
449	#41	—	4	2	no	—
450	#41	—	4	2	no	—
451	#41	—	8	1	no	—
452	#41	—	8	1	no	—
453	#41	—	8	1	no	—
454	C₂×Q₈	—	2	1	no	—
455	C₂×Q₈	—	2	1	no	—
456	C₂×Q₈	—	2	1	no	—
457	C₂×Q₈	—	4	1	no	—
458	C₂×Q₈	—	4	2	no	—
459	C₂×Q₈	—	8	1	no	—
460	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
461	C₂×D₄	—	2	1	no	—
462	C₂×D₄	—	2	1	no	—
463	C₂×D₄	—	2	1	no	—
464	C₂×D₄	—	4	1	no	—
465	C₂×D₄	—	4	1	no	—
466	C₂×D₄	—	4	1	no	—
467	C₂×D₄	—	4	1	no	—
468	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
469	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
470	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
471	C₂²×C₄	—	2	1	no	—
472	C₂²×C₄	—	2	1	no	—
473	C₂²×C₄	—	2	1	no	—
474	C₂²×C₄	—	4	1	no	—
475	C₂²×C₄	—	4	1	no	—
476	C₂²×C₄	—	4	1	no	—
477	C₂²×C₄	—	4	1	no	—
478	Q₁₆	—	4	2	no	—
479	SD₁₆	—	2	2	no	—
480	SD₁₆	—	4	2	no	—
481	SD₁₆	—	8	1	no	—
482	SD₁₆	—	8	1	no	—
483	SD₁₆	—	8	1	no	—
484	D₈	—	2	2	no	—
485	D₈	—	4	2	no	—
486	D₈	—	4	2	no	—
487	M₁₆	—	8	1	no	—
488	C₂×C₈	—	2	1	no	—
489	C₂×C₈	—	2	1	no	—
490	C₂×C₈	—	2	1	no	—
491	C₂×C₈	—	2	1	no	—
492	C₂×C₈	—	2	1	no	—
493	C₂×C₈	—	4	2	no	—
494	C₂×C₈	—	8	1	no	—
495	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
496	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
497	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
498	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
499	C₄⋊C₄	—	2	1	no	—
500	C₄⋊C₄	—	2	1	no	—
501	C₄⋊C₄	—	2	1	no	—
502	C₄⋊C₄	—	2	1	no	—
503	C₄⋊C₄	—	2	1	no	—
504	C₄⋊C₄	—	2	1	no	—
505	C₄⋊C₄	—	2	1	no	—
506	C₄⋊C₄	—	4	1	no	—
507	C₄⋊C₄	—	4	1	no	—
508	C₄⋊C₄	—	4	1	no	—
509	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
510	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
511	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
512	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
513	C₂²⋊C₄	—	2	1	no	—
514	C₂²⋊C₄	—	2	1	no	—
515	C₂²⋊C₄	—	2	1	no	—
516	C₂²⋊C₄	—	4	1	no	—
517	C₂²⋊C₄	—	4	1	no	—
518	C₂²⋊C₄	—	4	1	no	—
519	C₂²⋊C₄	—	4	1	no	—
520	C₄²	—	2	1	no	—
521	C₄²	C₂⁴×C₅	1	1	yes	characteristic
522	C₂×C₅	—	4	2	no	—
523	C₂×C₅	—	8	1	no	—
524	C₂×C₅	—	8	1	no	—
525	C₂×C₅	—	16	1	no	—
526	C₂×C₅	#3264	1	1	yes	characteristic
527	C₂×C₅	#3282	1	1	yes	characteristic
528	C₂×C₅	#3289	1	1	yes	characteristic
529	C₂³	—	2	1	no	—
530	C₂³	—	2	1	no	—
531	C₂³	—	2	1	no	—
532	C₂³	—	4	1	no	—
533	Q₈	—	2	1	no	—
534	Q₈	—	4	1	no	—
535	Q₈	—	4	1	no	—
536	Q₈	—	4	1	no	—
537	Q₈	—	4	1	no	—
538	Q₈	—	4	1	no	—
539	Q₈	—	4	1	no	—
540	Q₈	—	8	2	no	—
541	Q₈	C₅×AGL(1,ℤ/8)	1	2	yes	—
542	D₄	—	2	1	no	—
543	D₄	—	2	1	no	—
544	D₄	—	2	1	no	—
545	D₄	—	2	1	no	—
546	D₄	—	2	1	no	—
547	D₄	—	4	1	no	—
548	D₄	—	4	1	no	—
549	D₄	—	4	1	no	—
550	D₄	—	4	1	no	—
551	D₄	—	8	2	no	—
552	D₄	—	8	1	no	—
553	D₄	—	8	2	no	—
554	D₄	—	8	2	no	—
555	D₄	—	16	1	no	—
556	D₄	C₅×#135	1	2	yes	complemented
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	4	1	no	—
563	C₂×C₄	—	4	1	no	—
564	C₂×C₄	—	4	1	no	—
565	C₂×C₄	—	4	1	no	—
566	C₂×C₄	—	4	1	no	—
567	C₂×C₄	—	4	1	no	—
568	C₂×C₄	—	4	1	no	—
569	C₂×C₄	—	4	1	no	—
570	C₂×C₄	—	4	1	no	—
571	C₂×C₄	—	8	2	no	—
572	C₂×C₄	—	8	2	no	—
573	C₂×C₄	—	8	2	no	—
574	C₂×C₄	—	8	2	no	—
575	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
576	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
577	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
578	C₈	—	2	1	no	—
579	C₈	—	2	1	no	—
580	C₈	—	2	1	no	—
581	C₈	—	2	1	no	—
582	C₈	—	4	1	no	—
583	C₈	—	4	1	no	—
584	C₈	—	4	1	no	—
585	C₈	—	4	1	no	—
586	C₈	—	4	1	no	—
587	C₅	#19820	1	1	yes	characteristic, direct product factor, Sylow
588	C₂²	—	2	2	no	—
589	C₂²	—	4	1	no	—
590	C₂²	—	4	1	no	—
591	C₂²	—	4	1	no	—
592	C₂²	—	4	1	no	—
593	C₂²	—	4	1	no	—
594	C₂²	—	4	1	no	—
595	C₂²	—	4	1	no	—
596	C₂²	—	4	1	no	—
597	C₂²	—	8	1	no	—
598	C₂²	—	8	1	no	—
599	C₂²	—	8	1	no	—
600	C₂²	C₅×D₄²	1	1	yes	characteristic
601	C₄	—	2	2	no	—
602	C₄	—	2	1	no	—
603	C₄	—	4	1	no	—
604	C₄	—	4	1	no	—
605	C₄	—	4	1	no	—
606	C₄	—	4	1	no	—
607	C₄	—	8	1	no	—
608	C₄	—	8	1	no	—
609	C₄	—	8	1	no	—
610	C₄	C₂×C₅×#135	1	1	yes	characteristic
611	C₄	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
612	C₄	C₅×#576	1	1	yes	characteristic
613	C₄	C₅×#577	1	1	yes	characteristic
614	C₂	—	4	2	no	—
615	C₂	—	8	1	no	—
616	C₂	—	8	1	no	—
617	C₂	—	16	1	no	—
618	C₂	C₅×#3264	1	1	yes	characteristic
619	C₂	C₅×#3282	1	1	yes	characteristic
620	C₂	C₅×#3289	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×#3330	C₂	semidirect
3. C₅×#3298	C₂	semidirect
4. C₅×#3284	C₂	semidirect
5. C₅×#1719	C₂	semidirect
6. C₅×#1701	C₂	semidirect
7. C₅×#1680	C₂	semidirect
8. C₅×#1679	C₂	semidirect
9. C₅×#1665	C₂	semidirect
10. C₅×#1649	C₂	semidirect
11. C₅×#1647	C₂	semidirect
12. C₅×#1642	C₂	semidirect
13. C₅×#1625	C₂	semidirect
14. C₅×#1583	C₂	semidirect
15. C₅×#1580	C₂	semidirect
67. #19820	C₅	direct (N × H)
146. #3358	C₂×C₅	semidirect
147. #3330	C₂×C₅	semidirect
148. #3298	C₂×C₅	semidirect
149. #3284	C₂×C₅	semidirect
150. #1719	C₂×C₅	semidirect
151. #1701	C₂×C₅	semidirect
152. #1680	C₂×C₅	semidirect
153. #1679	C₂×C₅	semidirect
154. #1665	C₂×C₅	semidirect
155. #1649	C₂×C₅	semidirect
156. #1647	C₂×C₅	semidirect
157. #1642	C₂×C₅	semidirect
158. #1625	C₂×C₅	semidirect
159. #1583	C₂×C₅	semidirect
160. #1580	C₂×C₅	semidirect
313. C₅×D₄	#135	semidirect
556. D₄	C₅×#135	semidirect
587. C₅	#19820	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×#3330	2
C₅×#3298	2
C₅×#3284	2
C₅×#1719	2
C₅×#1701	2
C₅×#1680	2
C₅×#1679	2
C₅×#1665	2
C₅×#1649	2
C₅×#1647	2
C₅×#1642	2
C₅×#1625	2
C₅×#1583	2
C₅×#1580	2
#19820	5

Subgroups — C5×#19820 #11942540

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#19820 #11942540