Subgroups — C₅×#19893 #11942613

Order 1280.

684 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3385	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#3362	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#3295	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#3274	C₂	1	1	yes	maximal, characteristic
5	C₅×#1706	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1695	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1688	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1678	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1677	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1631	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1629	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1623	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1622	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1590	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×C₈×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₅×AGL(1,ℤ/8)	—	2	1	no	—
17	C₅×Q₈²	C₂²	1	1	yes	characteristic, complemented
18	C₅×#554	C₂²	1	1	yes	characteristic
19	C₅×#550	C₂²	1	1	yes	characteristic
20	C₅×D₄²	C₂²	1	1	yes	characteristic
21	C₅×#501	—	2	1	no	—
22	C₅×#500	C₂²	1	1	yes	characteristic, complemented
23	C₅×#493	C₂²	1	1	yes	characteristic
24	C₅×#492	C₂²	1	1	yes	characteristic
25	C₅×#492	C₂²	1	1	yes	characteristic, complemented
26	C₅×#486	—	2	1	no	—
27	C₅×#486	C₂²	1	1	yes	characteristic
28	C₅×#486	C₂²	1	1	yes	characteristic, complemented
29	C₅×#481	—	2	1	no	—
30	C₅×#479	—	2	1	no	—
31	C₅×#477	C₂²	1	1	yes	characteristic, complemented
32	C₅×#476	—	2	1	no	—
33	C₅×#476	C₂²	1	1	yes	characteristic
34	C₅×#476	C₂²	1	1	yes	characteristic
35	C₅×#476	C₂²	1	1	yes	characteristic
36	C₅×#474	—	2	1	no	—
37	C₅×#469	—	2	1	no	—
38	C₅×#465	—	2	1	no	—
39	C₅×#460	—	2	1	no	—
40	C₅×#460	C₂²	1	1	yes	characteristic
41	C₅×#460	C₂²	1	1	yes	characteristic
42	C₅×#460	C₂²	1	1	yes	characteristic, complemented
43	C₅×#459	C₂²	1	1	yes	characteristic
44	C₅×#450	—	2	1	no	—
45	C₅×#449	—	2	1	no	—
46	C₅×#447	—	2	1	no	—
47	C₅×#446	C₂²	1	1	yes	characteristic, complemented
48	C₅×C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
49	C₅×#440	—	2	1	no	—
50	C₄×C₅×SD₁₆	—	2	1	no	—
51	C₄×C₅×SD₁₆	C₂²	1	1	yes	characteristic
52	C₄×C₅×SD₁₆	C₂²	1	1	yes	characteristic
53	C₅×#436	C₂²	1	1	yes	characteristic
54	C₅×C₈×D₄	C₂²	1	1	yes	characteristic
55	C₂×C₅×#102	—	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×#333	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×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
64	C₅×D₄⋊C₈	C₂²	1	1	yes	characteristic
65	C₅×D₄⋊C₈	C₂²	1	1	yes	characteristic
66	C₅×C₈²	C₂²	1	1	yes	characteristic, complemented
67	#19893	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
68	C₂×C₅×#41	—	2	1	no	—
69	C₂²×C₅×D₄	—	2	1	no	—
70	C₂²×C₅×D₄	—	2	1	no	—
71	C₅×AGL(1,ℤ/8)	—	4	4	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	—	4	1	no	—
76	C₂×C₅×SD₁₆	—	4	1	no	—
77	C₂×C₅×SD₁₆	D₄	1	1	yes	characteristic
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	—	2	1	no	—
82	C₂×C₅×M₁₆	—	2	1	no	—
83	C₂²×C₅×C₈	—	2	1	no	—
84	C₅×C₄⋊Q₈	—	2	1	no	—
85	C₅×C₄⋊Q₈	—	2	1	no	—
86	C₅×C₄⋊Q₈	—	4	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×#125	—	2	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	—	4	1	no	—
99	C₅×#120	—	4	1	no	—
100	C₄×C₅×Q₈	—	2	1	no	—
101	C₄×C₅×Q₈	—	2	1	no	—
102	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
103	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
104	C₄×C₅×D₄	—	2	1	no	—
105	C₄×C₅×D₄	—	2	1	no	—
106	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
107	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
108	C₂×C₅×C₄⋊C₄	—	2	1	no	—
109	C₅×#107	—	2	1	no	—
110	C₅×#107	—	2	1	no	—
111	C₅×#107	—	2	1	no	—
112	C₅×#106	—	2	1	no	—
113	C₅×#106	—	2	1	no	—
114	C₅×#106	—	2	1	no	—
115	C₅×#106	D₄	1	1	yes	characteristic
116	C₅×#106	D₄	1	1	yes	characteristic
117	C₅×C₄⋊C₈	—	2	1	no	—
118	C₅×C₄⋊C₈	—	2	1	no	—
119	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
120	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
121	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
122	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
123	C₅×#103	—	2	1	no	—
124	C₅×#103	D₄	1	1	yes	characteristic
125	C₅×#103	D₄	1	1	yes	characteristic
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	—	2	1	no	—
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×#97	—	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	#3385	C₂×C₅	1	1	yes	characteristic, complemented
147	#3362	C₂×C₅	1	1	yes	characteristic, complemented
148	#3295	C₂×C₅	1	1	yes	characteristic, complemented
149	#3274	C₂×C₅	1	1	yes	characteristic
150	#1706	C₂×C₅	1	1	yes	characteristic, complemented
151	#1695	C₂×C₅	1	1	yes	characteristic, complemented
152	#1688	C₂×C₅	1	1	yes	characteristic, complemented
153	#1678	C₂×C₅	1	1	yes	characteristic, complemented
154	#1677	C₂×C₅	1	1	yes	characteristic, complemented
155	#1631	C₂×C₅	1	1	yes	characteristic, complemented
156	#1629	C₂×C₅	1	1	yes	characteristic, complemented
157	#1623	C₂×C₅	1	1	yes	characteristic, complemented
158	#1622	C₂×C₅	1	1	yes	characteristic, complemented
159	#1590	C₂×C₅	1	1	yes	characteristic, complemented
160	C₈×SD₁₆	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	C₂×D₄	1	1	yes	characteristic
168	C₂×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
169	C₂×C₅×D₄	—	2	1	no	—
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	—	4	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	2	no	—
180	C₂×C₅×D₄	—	4	2	no	—
181	C₂×C₅×D₄	—	8	1	no	—
182	C₂×C₅×D₄	—	8	1	no	—
183	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
184	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
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	C₅×SD₁₆	—	4	1	no	—
190	C₅×SD₁₆	—	4	2	no	—
191	C₅×SD₁₆	—	4	2	no	—
192	C₅×SD₁₆	—	8	2	no	—
193	C₅×SD₁₆	—	8	2	no	—
194	C₅×SD₁₆	—	8	1	no	—
195	C₅×SD₁₆	SD₁₆	1	4	yes	complemented
196	C₅×D₈	—	4	2	no	—
197	C₅×D₈	—	4	2	no	—
198	C₅×D₈	—	8	1	no	—
199	C₅×M₁₆	—	4	2	no	—
200	C₂×C₅×C₈	—	2	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	—	8	1	no	—
206	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
207	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
208	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
209	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
210	C₅×C₄⋊C₄	—	2	1	no	—
211	C₅×C₄⋊C₄	—	2	1	no	—
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	—	4	1	no	—
217	C₅×C₄⋊C₄	—	4	1	no	—
218	C₅×C₄⋊C₄	—	4	1	no	—
219	C₅×C₄⋊C₄	—	4	1	no	—
220	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
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×C₂²⋊C₄	—	2	1	no	—
225	C₅×C₂²⋊C₄	—	2	1	no	—
226	C₅×C₂²⋊C₄	—	4	1	no	—
227	C₅×C₂²⋊C₄	—	4	1	no	—
228	C₅×C₂²⋊C₄	—	4	1	no	—
229	C₄²×C₅	—	2	1	no	—
230	C₄²×C₅	—	2	1	no	—
231	C₄²×C₅	—	4	1	no	—
232	C₄²×C₅	C₂⁴	1	1	yes	characteristic
233	C₂×AGL(1,ℤ/8)	—	2	1	no	—
234	Q₈²	C₂²×C₅	1	1	yes	characteristic, complemented
235	#554	C₂²×C₅	1	1	yes	characteristic
236	#550	C₂²×C₅	1	1	yes	characteristic
237	D₄²	C₂²×C₅	1	1	yes	characteristic
238	#501	—	2	1	no	—
239	#500	C₂²×C₅	1	1	yes	characteristic, complemented
240	#493	C₂²×C₅	1	1	yes	characteristic
241	#492	C₂²×C₅	1	1	yes	characteristic
242	#492	C₂²×C₅	1	1	yes	characteristic, complemented
243	#486	—	2	1	no	—
244	#486	C₂²×C₅	1	1	yes	characteristic
245	#486	C₂²×C₅	1	1	yes	characteristic, complemented
246	#481	—	2	1	no	—
247	#479	—	2	1	no	—
248	#477	C₂²×C₅	1	1	yes	characteristic, complemented
249	#476	—	2	1	no	—
250	#476	C₂²×C₅	1	1	yes	characteristic
251	#476	C₂²×C₅	1	1	yes	characteristic
252	#476	C₂²×C₅	1	1	yes	characteristic
253	#474	—	2	1	no	—
254	#469	—	2	1	no	—
255	#465	—	2	1	no	—
256	#460	—	2	1	no	—
257	#460	C₂²×C₅	1	1	yes	characteristic
258	#460	C₂²×C₅	1	1	yes	characteristic
259	#460	C₂²×C₅	1	1	yes	characteristic, complemented
260	#459	C₂²×C₅	1	1	yes	characteristic
261	#450	—	2	1	no	—
262	#449	—	2	1	no	—
263	#447	—	2	1	no	—
264	#446	C₂²×C₅	1	1	yes	characteristic, complemented
265	C₈×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
266	#440	—	2	1	no	—
267	C₄×SD₁₆	—	2	1	no	—
268	C₄×SD₁₆	C₂²×C₅	1	1	yes	characteristic
269	C₄×SD₁₆	C₂²×C₅	1	1	yes	characteristic
270	#436	C₂²×C₅	1	1	yes	characteristic
271	C₈×D₄	C₂²×C₅	1	1	yes	characteristic
272	C₂×#102	—	2	1	no	—
273	#334	C₂²×C₅	1	1	yes	characteristic, complemented
274	#334	C₂²×C₅	1	1	yes	characteristic, complemented
275	#333	C₂²×C₅	1	1	yes	characteristic, complemented
276	#333	C₂²×C₅	1	1	yes	characteristic, complemented
277	#331	C₂²×C₅	1	1	yes	characteristic
278	#331	C₂²×C₅	1	1	yes	characteristic, complemented
279	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
280	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
281	D₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
282	D₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
283	C₈²	C₂²×C₅	1	1	yes	characteristic, complemented
284	C₂³×C₅	—	2	1	no	—
285	C₂³×C₅	—	2	1	no	—
286	C₂³×C₅	—	4	1	no	—
287	C₂³×C₅	—	4	1	no	—
288	C₂³×C₅	—	8	2	no	—
289	C₂³×C₅	—	8	2	no	—
290	C₂³×C₅	—	16	1	no	—
291	C₅×Q₈	—	2	1	no	—
292	C₅×Q₈	—	2	1	no	—
293	C₅×Q₈	—	2	1	no	—
294	C₅×Q₈	—	8	1	no	—
295	C₅×Q₈	—	8	1	no	—
296	C₅×Q₈	—	16	1	no	—
297	C₅×Q₈	C₂×SD₁₆	1	2	yes	—
298	C₅×D₄	—	2	1	no	—
299	C₅×D₄	—	2	1	no	—
300	C₅×D₄	—	2	1	no	—
301	C₅×D₄	—	4	1	no	—
302	C₅×D₄	—	4	1	no	—
303	C₅×D₄	—	4	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	—	4	1	no	—
309	C₅×D₄	—	8	2	no	—
310	C₅×D₄	—	8	1	no	—
311	C₅×D₄	—	8	1	no	—
312	C₅×D₄	—	8	2	no	—
313	C₅×D₄	—	8	2	no	—
314	C₅×D₄	—	16	1	no	—
315	C₅×D₄	C₂×SD₁₆	1	2	yes	—
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	—	2	1	no	—
320	C₂×C₄×C₅	—	2	1	no	—
321	C₂×C₄×C₅	—	2	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	—	16	1	no	—
330	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
331	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
332	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
333	C₅×C₈	—	2	2	no	—
334	C₅×C₈	—	2	1	no	—
335	C₅×C₈	—	2	1	no	—
336	C₅×C₈	—	2	1	no	—
337	C₅×C₈	—	4	1	no	—
338	C₅×C₈	—	4	1	no	—
339	C₅×C₈	—	4	1	no	—
340	C₅×C₈	—	4	1	no	—
341	C₅×C₈	C₂×SD₁₆	1	2	yes	—
342	C₂×#41	—	2	1	no	—
343	C₂²×D₄	—	2	1	no	—
344	C₂²×D₄	—	2	1	no	—
345	AGL(1,ℤ/8)	—	4	4	no	—
346	C₂×SD₁₆	—	2	1	no	—
347	C₂×SD₁₆	—	2	1	no	—
348	C₂×SD₁₆	—	2	1	no	—
349	C₂×SD₁₆	—	4	1	no	—
350	C₂×SD₁₆	—	4	1	no	—
351	C₂×SD₁₆	C₅×D₄	1	1	yes	characteristic
352	C₂×SD₁₆	C₅×D₄	1	1	yes	characteristic
353	C₂×D₈	—	2	1	no	—
354	C₂×D₈	—	2	1	no	—
355	C₂×D₈	—	2	1	no	—
356	C₂×M₁₆	—	2	1	no	—
357	C₂²×C₈	—	2	1	no	—
358	C₄⋊Q₈	—	2	1	no	—
359	C₄⋊Q₈	—	2	1	no	—
360	C₄⋊Q₈	—	4	1	no	—
361	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
362	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
363	#127	—	2	1	no	—
364	#127	C₂³×C₅	1	1	yes	characteristic
365	#127	C₂³×C₅	1	1	yes	characteristic
366	#125	—	2	1	no	—
367	C₂²⋊Q₈	—	2	1	no	—
368	C₂²⋊Q₈	—	4	1	no	—
369	#121	—	2	1	no	—
370	#121	—	2	1	no	—
371	#121	—	2	1	no	—
372	#121	—	4	1	no	—
373	#120	—	4	1	no	—
374	C₄×Q₈	—	2	1	no	—
375	C₄×Q₈	—	2	1	no	—
376	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
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	C₂×C₄⋊C₄	—	2	1	no	—
383	#107	—	2	1	no	—
384	#107	—	2	1	no	—
385	#107	—	2	1	no	—
386	#106	—	2	1	no	—
387	#106	—	2	1	no	—
388	#106	—	2	1	no	—
389	#106	C₅×D₄	1	1	yes	characteristic
390	#106	C₅×D₄	1	1	yes	characteristic
391	C₄⋊C₈	—	2	1	no	—
392	C₄⋊C₈	—	2	1	no	—
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	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
397	#103	—	2	1	no	—
398	#103	C₅×D₄	1	1	yes	characteristic
399	#103	C₅×D₄	1	1	yes	characteristic
400	#102	—	2	1	no	—
401	#102	—	2	1	no	—
402	#102	—	2	1	no	—
403	#102	—	2	1	no	—
404	#102	—	2	1	no	—
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	C₅×D₄	1	1	yes	characteristic
412	#102	C₅×D₄	1	1	yes	characteristic
413	C₂²⋊C₈	—	2	1	no	—
414	C₂²⋊C₈	—	2	1	no	—
415	#97	—	2	1	no	—
416	C₄×C₈	—	2	1	no	—
417	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
418	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
419	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
420	C₂²×C₅	—	2	2	no	—
421	C₂²×C₅	—	4	1	no	—
422	C₂²×C₅	—	4	1	no	—
423	C₂²×C₅	—	4	1	no	—
424	C₂²×C₅	—	4	1	no	—
425	C₂²×C₅	—	4	1	no	—
426	C₂²×C₅	—	8	1	no	—
427	C₂²×C₅	—	8	1	no	—
428	C₂²×C₅	—	8	1	no	—
429	C₂²×C₅	—	8	1	no	—
430	C₂²×C₅	—	8	1	no	—
431	C₂²×C₅	—	8	1	no	—
432	C₂²×C₅	—	16	4	no	—
433	C₂²×C₅	D₄²	1	1	yes	characteristic
434	C₄×C₅	—	2	2	no	—
435	C₄×C₅	—	2	1	no	—
436	C₄×C₅	—	4	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	C₂²×SD₁₆	1	1	yes	characteristic
444	C₄×C₅	#575	1	1	yes	characteristic
445	C₄×C₅	#577	1	1	yes	characteristic
446	C₄×C₅	#577	1	1	yes	characteristic
447	C₂⁴	—	4	1	no	—
448	#41	—	4	2	no	—
449	#41	—	8	1	no	—
450	C₂×Q₈	—	2	1	no	—
451	C₂×Q₈	—	2	1	no	—
452	C₂×Q₈	—	4	1	no	—
453	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
454	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
455	C₂×D₄	—	2	1	no	—
456	C₂×D₄	—	2	1	no	—
457	C₂×D₄	—	2	1	no	—
458	C₂×D₄	—	2	1	no	—
459	C₂×D₄	—	2	1	no	—
460	C₂×D₄	—	2	1	no	—
461	C₂×D₄	—	4	1	no	—
462	C₂×D₄	—	4	1	no	—
463	C₂×D₄	—	4	1	no	—
464	C₂×D₄	—	4	1	no	—
465	C₂×D₄	—	4	2	no	—
466	C₂×D₄	—	4	2	no	—
467	C₂×D₄	—	8	1	no	—
468	C₂×D₄	—	8	1	no	—
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	—	4	1	no	—
474	C₂²×C₄	—	4	1	no	—
475	SD₁₆	—	4	1	no	—
476	SD₁₆	—	4	2	no	—
477	SD₁₆	—	4	2	no	—
478	SD₁₆	—	8	2	no	—
479	SD₁₆	—	8	2	no	—
480	SD₁₆	—	8	1	no	—
481	SD₁₆	C₅×SD₁₆	1	4	yes	complemented
482	D₈	—	4	2	no	—
483	D₈	—	4	2	no	—
484	D₈	—	8	1	no	—
485	M₁₆	—	4	2	no	—
486	C₂×C₈	—	2	1	no	—
487	C₂×C₈	—	2	1	no	—
488	C₂×C₈	—	2	1	no	—
489	C₂×C₈	—	2	1	no	—
490	C₂×C₈	—	2	1	no	—
491	C₂×C₈	—	8	1	no	—
492	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
493	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
494	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
495	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
496	C₄⋊C₄	—	2	1	no	—
497	C₄⋊C₄	—	2	1	no	—
498	C₄⋊C₄	—	2	1	no	—
499	C₄⋊C₄	—	2	1	no	—
500	C₄⋊C₄	—	2	1	no	—
501	C₄⋊C₄	—	2	1	no	—
502	C₄⋊C₄	—	4	1	no	—
503	C₄⋊C₄	—	4	1	no	—
504	C₄⋊C₄	—	4	1	no	—
505	C₄⋊C₄	—	4	1	no	—
506	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
507	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
508	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
509	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
510	C₂²⋊C₄	—	2	1	no	—
511	C₂²⋊C₄	—	2	1	no	—
512	C₂²⋊C₄	—	4	1	no	—
513	C₂²⋊C₄	—	4	1	no	—
514	C₂²⋊C₄	—	4	1	no	—
515	C₄²	—	2	1	no	—
516	C₄²	—	2	1	no	—
517	C₄²	—	4	1	no	—
518	C₄²	C₂⁴×C₅	1	1	yes	characteristic
519	C₂×C₅	—	4	2	no	—
520	C₂×C₅	—	8	1	no	—
521	C₂×C₅	—	16	1	no	—
522	C₂×C₅	—	16	1	no	—
523	C₂×C₅	#3275	1	1	yes	characteristic
524	C₂×C₅	D₄×SD₁₆	1	1	yes	characteristic
525	C₂×C₅	#3292	1	1	yes	characteristic
526	C₂³	—	2	1	no	—
527	C₂³	—	2	1	no	—
528	C₂³	—	4	1	no	—
529	C₂³	—	4	1	no	—
530	C₂³	—	8	2	no	—
531	C₂³	—	8	2	no	—
532	C₂³	—	16	1	no	—
533	Q₈	—	2	1	no	—
534	Q₈	—	2	1	no	—
535	Q₈	—	2	1	no	—
536	Q₈	—	8	1	no	—
537	Q₈	—	8	1	no	—
538	Q₈	—	16	1	no	—
539	Q₈	C₂×C₅×SD₁₆	1	2	yes	—
540	D₄	—	2	1	no	—
541	D₄	—	2	1	no	—
542	D₄	—	2	1	no	—
543	D₄	—	4	1	no	—
544	D₄	—	4	1	no	—
545	D₄	—	4	1	no	—
546	D₄	—	4	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	1	no	—
554	D₄	—	8	2	no	—
555	D₄	—	8	2	no	—
556	D₄	—	16	1	no	—
557	D₄	C₂×C₅×SD₁₆	1	2	yes	—
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	—	2	1	no	—
563	C₂×C₄	—	2	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	—	8	2	no	—
571	C₂×C₄	—	16	1	no	—
572	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
573	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
574	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
575	C₈	—	2	2	no	—
576	C₈	—	2	1	no	—
577	C₈	—	2	1	no	—
578	C₈	—	2	1	no	—
579	C₈	—	4	1	no	—
580	C₈	—	4	1	no	—
581	C₈	—	4	1	no	—
582	C₈	—	4	1	no	—
583	C₈	C₂×C₅×SD₁₆	1	2	yes	—
584	C₅	#19893	1	1	yes	characteristic, direct product factor, Sylow
585	C₂²	—	2	2	no	—
586	C₂²	—	4	1	no	—
587	C₂²	—	4	1	no	—
588	C₂²	—	4	1	no	—
589	C₂²	—	4	1	no	—
590	C₂²	—	4	1	no	—
591	C₂²	—	8	1	no	—
592	C₂²	—	8	1	no	—
593	C₂²	—	8	1	no	—
594	C₂²	—	8	1	no	—
595	C₂²	—	8	1	no	—
596	C₂²	—	8	1	no	—
597	C₂²	—	16	4	no	—
598	C₂²	C₅×D₄²	1	1	yes	characteristic
599	C₄	—	2	2	no	—
600	C₄	—	2	1	no	—
601	C₄	—	4	1	no	—
602	C₄	—	4	1	no	—
603	C₄	—	4	1	no	—
604	C₄	—	4	1	no	—
605	C₄	—	4	1	no	—
606	C₄	—	8	1	no	—
607	C₄	—	8	1	no	—
608	C₄	C₂²×C₅×SD₁₆	1	1	yes	characteristic
609	C₄	C₅×#575	1	1	yes	characteristic
610	C₄	C₅×#577	1	1	yes	characteristic
611	C₄	C₅×#577	1	1	yes	characteristic
612	C₂	—	4	2	no	—
613	C₂	—	8	1	no	—
614	C₂	—	16	1	no	—
615	C₂	—	16	1	no	—
616	C₂	C₅×#3275	1	1	yes	characteristic
617	C₂	C₅×D₄×SD₁₆	1	1	yes	characteristic
618	C₂	C₅×#3292	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₅
prime radical	C₅×#3274	C₂
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×#3385	C₂	semidirect
2. C₅×#3362	C₂	semidirect
3. C₅×#3295	C₂	semidirect
5. C₅×#1706	C₂	semidirect
6. C₅×#1695	C₂	semidirect
7. C₅×#1688	C₂	semidirect
8. C₅×#1678	C₂	semidirect
9. C₅×#1677	C₂	semidirect
10. C₅×#1631	C₂	semidirect
11. C₅×#1629	C₂	semidirect
12. C₅×#1623	C₂	semidirect
13. C₅×#1622	C₂	semidirect
14. C₅×#1590	C₂	semidirect
15. C₅×C₈×SD₁₆	C₂	semidirect
17. C₅×Q₈²	C₂²	semidirect
22. C₅×#500	C₂²	semidirect
25. C₅×#492	C₂²	semidirect
28. C₅×#486	C₂²	semidirect
31. C₅×#477	C₂²	semidirect
42. C₅×#460	C₂²	semidirect
47. C₅×#446	C₂²	semidirect
48. C₅×C₈×Q₈	C₂²	semidirect
56. C₅×#334	C₂²	semidirect
57. C₅×#334	C₂²	semidirect
58. C₅×#333	C₂²	semidirect
59. C₅×#333	C₂²	semidirect
61. C₅×#331	C₂²	semidirect
62. C₅×Q₈⋊C₈	C₂²	semidirect
63. C₅×Q₈⋊C₈	C₂²	semidirect
66. C₅×C₈²	C₂²	semidirect
67. #19893	C₅	direct (N × H)
146. #3385	C₂×C₅	semidirect
147. #3362	C₂×C₅	semidirect
148. #3295	C₂×C₅	semidirect
150. #1706	C₂×C₅	semidirect
151. #1695	C₂×C₅	semidirect
152. #1688	C₂×C₅	semidirect
153. #1678	C₂×C₅	semidirect
154. #1677	C₂×C₅	semidirect
155. #1631	C₂×C₅	semidirect
156. #1629	C₂×C₅	semidirect
157. #1623	C₂×C₅	semidirect
158. #1622	C₂×C₅	semidirect
159. #1590	C₂×C₅	semidirect
160. C₈×SD₁₆	C₂×C₅	semidirect
195. C₅×SD₁₆	SD₁₆	semidirect
234. Q₈²	C₂²×C₅	semidirect
239. #500	C₂²×C₅	semidirect
242. #492	C₂²×C₅	semidirect
245. #486	C₂²×C₅	semidirect
248. #477	C₂²×C₅	semidirect
259. #460	C₂²×C₅	semidirect
264. #446	C₂²×C₅	semidirect
265. C₈×Q₈	C₂²×C₅	semidirect
273. #334	C₂²×C₅	semidirect
274. #334	C₂²×C₅	semidirect
275. #333	C₂²×C₅	semidirect
276. #333	C₂²×C₅	semidirect
278. #331	C₂²×C₅	semidirect
279. Q₈⋊C₈	C₂²×C₅	semidirect
280. Q₈⋊C₈	C₂²×C₅	semidirect
283. C₈²	C₂²×C₅	semidirect
481. SD₁₆	C₅×SD₁₆	semidirect
584. C₅	#19893	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×#3385	2
C₅×#3362	2
C₅×#3295	2
C₅×#3274	2
C₅×#1706	2
C₅×#1695	2
C₅×#1688	2
C₅×#1678	2
C₅×#1677	2
C₅×#1631	2
C₅×#1629	2
C₅×#1623	2
C₅×#1622	2
C₅×#1590	2
C₅×C₈×SD₁₆	2
#19893	5

Subgroups — C5×#19893 #11942613

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#19893 #11942613