Subgroups — C₅×#26921 #11949641

Order 1280.

758 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3082	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#3081	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2949	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2948	C₂	1	1	yes	maximal, characteristic
5	C₅×#2046	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2045	C₂	1	1	yes	maximal, characteristic
7	C₅×#2027	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2012	C₂	1	1	yes	maximal, characteristic
9	C₅×#1931	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1930	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1922	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1922	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1888	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1885	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#1856	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₅×SD₁₆	C₂²	1	1	yes	characteristic
17	C₂²×C₅×D₈	C₂²	1	1	yes	characteristic
18	C₅×#544	C₂²	1	1	yes	characteristic
19	C₂×C₅×#124	C₂²	1	1	yes	characteristic
20	C₅×#519	C₂²	1	1	yes	characteristic
21	C₅×#518	C₂²	1	1	yes	characteristic
22	C₅×#518	C₂²	1	1	yes	characteristic
23	C₅×#479	—	2	1	no	—
24	C₅×#479	—	2	1	no	—
25	C₅×#478	—	2	1	no	—
26	C₅×#478	—	2	1	no	—
27	C₅×#477	—	2	1	no	—
28	C₅×#476	—	2	1	no	—
29	C₅×#475	—	2	1	no	—
30	C₅×#474	—	2	1	no	—
31	C₅×#442	—	2	1	no	—
32	C₅×#442	—	2	1	no	—
33	C₅×#440	—	2	1	no	—
34	C₅×#440	—	2	1	no	—
35	C₄×C₅×SD₁₆	—	2	1	no	—
36	C₄×C₅×SD₁₆	—	2	1	no	—
37	C₄×C₅×D₈	—	2	1	no	—
38	C₄×C₅×D₈	—	2	1	no	—
39	C₅×#428	C₂²	1	1	yes	characteristic
40	C₅×#428	C₂²	1	1	yes	characteristic
41	C₅×#427	C₂²	1	1	yes	characteristic
42	C₅×#427	C₂²	1	1	yes	characteristic
43	C₅×#424	C₂²	1	1	yes	characteristic
44	C₅×#424	C₂²	1	1	yes	characteristic
45	C₅×#419	C₂²	1	1	yes	characteristic
46	C₅×#419	C₂²	1	1	yes	characteristic
47	C₅×#418	C₂²	1	1	yes	characteristic
48	C₅×#418	C₂²	1	1	yes	characteristic
49	C₅×#418	C₂²	1	1	yes	characteristic
50	C₅×#418	C₂²	1	1	yes	characteristic
51	C₂×C₅×#103	C₂²	1	1	yes	characteristic
52	C₂×C₅×#102	C₂²	1	1	yes	characteristic
53	C₂×C₅×#101	C₂²	1	1	yes	characteristic
54	C₂×C₅×#100	C₂²	1	1	yes	characteristic
55	C₂×C₅×#100	C₂²	1	1	yes	characteristic
56	C₅×#405	C₂²	1	1	yes	characteristic
57	C₅×#405	C₂²	1	1	yes	characteristic
58	C₅×#390	C₂²	1	1	yes	characteristic
59	C₅×#343	C₂²	1	1	yes	characteristic
60	C₅×#341	C₂²	1	1	yes	characteristic
61	C₅×#341	C₂²	1	1	yes	characteristic
62	C₅×#339	C₂²	1	1	yes	characteristic
63	C₅×#339	C₂²	1	1	yes	characteristic
64	C₅×#339	C₂²	1	1	yes	characteristic
65	C₅×#339	C₂²	1	1	yes	characteristic
66	C₅×#336	C₂²	1	1	yes	characteristic
67	#26921	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
68	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
69	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
70	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
71	C₂×C₅×SD₁₆	—	2	2	no	—
72	C₂×C₅×SD₁₆	—	2	2	no	—
73	C₂×C₅×SD₁₆	—	2	1	no	—
74	C₂×C₅×SD₁₆	—	2	1	no	—
75	C₂×C₅×D₈	—	2	2	no	—
76	C₂×C₅×D₈	—	2	2	no	—
77	C₂×C₅×D₈	—	2	1	no	—
78	C₂×C₅×D₈	—	2	1	no	—
79	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
80	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
81	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
82	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
83	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
84	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
85	C₅×C₄⋊Q₈	—	2	1	no	—
86	C₅×C₄⋊Q₈	—	2	1	no	—
87	C₅×#125	—	2	1	no	—
88	C₅×#125	—	2	1	no	—
89	C₅×#124	—	2	2	no	—
90	C₅×#124	—	2	2	no	—
91	C₅×C₂²⋊Q₈	—	4	1	no	—
92	C₄×C₅×Q₈	—	2	1	no	—
93	C₄×C₅×Q₈	—	2	1	no	—
94	C₄×C₅×Q₈	—	2	1	no	—
95	C₄×C₅×Q₈	—	2	1	no	—
96	C₄×C₅×D₄	—	2	1	no	—
97	C₄×C₅×D₄	—	2	1	no	—
98	C₄×C₅×D₄	—	2	1	no	—
99	C₄×C₅×D₄	—	2	1	no	—
100	C₄×C₅×D₄	—	2	1	no	—
101	C₄×C₅×D₄	—	2	1	no	—
102	C₄×C₅×D₄	—	2	1	no	—
103	C₄×C₅×D₄	—	2	1	no	—
104	C₅×#117	—	4	1	no	—
105	C₅×#117	C₂³	1	1	yes	characteristic
106	C₅×#117	C₂³	1	1	yes	characteristic
107	C₅×#117	C₂³	1	1	yes	characteristic
108	C₅×#117	C₂³	1	1	yes	characteristic
109	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
110	C₂×C₅×C₂²⋊C₄	—	4	1	no	—
111	C₂×C₅×C₂²⋊C₄	—	4	1	no	—
112	C₂×C₅×C₂²⋊C₄	—	4	1	no	—
113	C₂×C₅×C₂²⋊C₄	—	4	1	no	—
114	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
115	C₅×#107	—	2	1	no	—
116	C₅×#107	—	2	1	no	—
117	C₅×#107	D₄	1	1	yes	characteristic
118	C₅×#107	D₄	1	1	yes	characteristic
119	C₅×#107	D₄	1	1	yes	characteristic
120	C₅×#107	D₄	1	1	yes	characteristic
121	C₅×#106	—	2	1	no	—
122	C₅×#106	—	2	1	no	—
123	C₅×#106	D₄	1	1	yes	characteristic
124	C₅×#106	D₄	1	1	yes	characteristic
125	C₅×#106	D₄	1	1	yes	characteristic
126	C₅×#106	D₄	1	1	yes	characteristic
127	C₅×C₄⋊C₈	—	2	1	no	—
128	C₅×C₄⋊C₈	—	2	1	no	—
129	C₅×C₄⋊C₈	—	2	1	no	—
130	C₅×C₄⋊C₈	—	2	1	no	—
131	C₅×#103	—	2	1	no	—
132	C₅×#103	—	2	1	no	—
133	C₅×#103	—	2	1	no	—
134	C₅×#103	—	2	1	no	—
135	C₅×#103	—	2	1	no	—
136	C₅×#103	—	2	1	no	—
137	C₅×#102	—	2	1	no	—
138	C₅×#102	—	2	1	no	—
139	C₅×#102	—	2	1	no	—
140	C₅×#102	—	2	1	no	—
141	C₅×#102	—	2	1	no	—
142	C₅×#102	—	2	1	no	—
143	C₅×#102	—	2	1	no	—
144	C₅×#102	—	2	1	no	—
145	C₅×#102	—	2	1	no	—
146	C₅×#102	—	2	1	no	—
147	C₅×#101	—	2	2	no	—
148	C₅×#100	—	2	2	no	—
149	C₅×#100	—	2	2	no	—
150	C₅×#97	—	2	1	no	—
151	C₅×#97	—	2	1	no	—
152	C₄×C₅×C₈	—	2	1	no	—
153	C₄×C₅×C₈	—	2	1	no	—
154	#3082	C₂×C₅	1	1	yes	characteristic, complemented
155	#3081	C₂×C₅	1	1	yes	characteristic, complemented
156	#2949	C₂×C₅	1	1	yes	characteristic, complemented
157	#2948	C₂×C₅	1	1	yes	characteristic
158	#2046	C₂×C₅	1	1	yes	characteristic, complemented
159	#2045	C₂×C₅	1	1	yes	characteristic
160	#2027	C₂×C₅	1	1	yes	characteristic, complemented
161	#2012	C₂×C₅	1	1	yes	characteristic
162	#1931	C₂×C₅	1	1	yes	characteristic, complemented
163	#1930	C₂×C₅	1	1	yes	characteristic, complemented
164	#1922	C₂×C₅	1	1	yes	characteristic, complemented
165	#1922	C₂×C₅	1	1	yes	characteristic, complemented
166	#1888	C₂×C₅	1	1	yes	characteristic, complemented
167	#1885	C₂×C₅	1	1	yes	characteristic, complemented
168	#1856	C₂×C₅	1	1	yes	characteristic, complemented
169	C₂⁴×C₅	—	2	1	no	—
170	C₂⁴×C₅	—	2	1	no	—
171	C₂×C₅×Q₈	—	2	1	no	—
172	C₂×C₅×Q₈	—	2	1	no	—
173	C₂×C₅×Q₈	—	2	1	no	—
174	C₂×C₅×Q₈	—	2	1	no	—
175	C₂×C₅×Q₈	—	2	1	no	—
176	C₂×C₅×Q₈	—	4	1	no	—
177	C₂×C₅×Q₈	#41	1	2	yes	—
178	C₂×C₅×D₄	—	2	1	no	—
179	C₂×C₅×D₄	—	2	1	no	—
180	C₂×C₅×D₄	—	2	1	no	—
181	C₂×C₅×D₄	—	2	1	no	—
182	C₂×C₅×D₄	—	2	1	no	—
183	C₂×C₅×D₄	—	2	1	no	—
184	C₂×C₅×D₄	—	2	1	no	—
185	C₂×C₅×D₄	—	2	1	no	—
186	C₂×C₅×D₄	—	2	1	no	—
187	C₂×C₅×D₄	—	2	1	no	—
188	C₂×C₅×D₄	#41	1	2	yes	—
189	C₂×C₅×D₄	#41	1	2	yes	—
190	C₂²×C₄×C₅	—	2	1	no	—
191	C₂²×C₄×C₅	—	2	1	no	—
192	C₂²×C₄×C₅	—	2	1	no	—
193	C₂²×C₄×C₅	—	4	1	no	—
194	C₂²×C₄×C₅	—	4	1	no	—
195	C₂²×C₄×C₅	—	4	1	no	—
196	C₂²×C₄×C₅	—	4	1	no	—
197	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
198	C₅×SD₁₆	—	2	4	no	—
199	C₅×SD₁₆	—	2	4	no	—
200	C₅×D₈	—	2	4	no	—
201	C₅×D₈	—	2	4	no	—
202	C₅×M₁₆	—	2	1	no	—
203	C₅×M₁₆	—	2	1	no	—
204	C₅×M₁₆	—	2	1	no	—
205	C₅×M₁₆	—	2	1	no	—
206	C₅×M₁₆	—	2	1	no	—
207	C₅×M₁₆	—	2	1	no	—
208	C₅×M₁₆	—	2	1	no	—
209	C₅×M₁₆	—	2	1	no	—
210	C₂×C₅×C₈	—	2	1	no	—
211	C₂×C₅×C₈	—	2	1	no	—
212	C₂×C₅×C₈	—	2	1	no	—
213	C₂×C₅×C₈	—	2	1	no	—
214	C₂×C₅×C₈	—	2	1	no	—
215	C₂×C₅×C₈	—	2	1	no	—
216	C₂×C₅×C₈	—	2	1	no	—
217	C₂×C₅×C₈	—	2	1	no	—
218	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
219	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
220	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
221	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
222	C₅×C₄⋊C₄	—	2	1	no	—
223	C₅×C₄⋊C₄	—	2	1	no	—
224	C₅×C₄⋊C₄	—	4	1	no	—
225	C₅×C₄⋊C₄	—	4	1	no	—
226	C₅×C₄⋊C₄	—	4	1	no	—
227	C₅×C₄⋊C₄	—	4	1	no	—
228	C₅×C₄⋊C₄	—	4	1	no	—
229	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
230	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
231	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
232	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
233	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
234	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
235	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
236	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
237	C₅×C₂²⋊C₄	—	2	1	no	—
238	C₅×C₂²⋊C₄	—	2	1	no	—
239	C₅×C₂²⋊C₄	—	2	1	no	—
240	C₅×C₂²⋊C₄	—	2	1	no	—
241	C₅×C₂²⋊C₄	—	4	1	no	—
242	C₅×C₂²⋊C₄	—	4	1	no	—
243	C₅×C₂²⋊C₄	—	4	1	no	—
244	C₅×C₂²⋊C₄	—	4	1	no	—
245	C₅×C₂²⋊C₄	—	4	4	no	—
246	C₅×C₂²⋊C₄	—	8	2	no	—
247	C₄²×C₅	—	2	1	no	—
248	C₄²×C₅	—	2	1	no	—
249	C₄²×C₅	—	2	1	no	—
250	C₄²×C₅	—	2	1	no	—
251	C₄²×C₅	—	2	1	no	—
252	C₄²×C₅	—	2	1	no	—
253	C₄²×C₅	—	4	1	no	—
254	C₄²×C₅	—	4	1	no	—
255	C₂²×SD₁₆	C₂²×C₅	1	1	yes	characteristic
256	C₂²×D₈	C₂²×C₅	1	1	yes	characteristic
257	#544	C₂²×C₅	1	1	yes	characteristic
258	C₂×#124	C₂²×C₅	1	1	yes	characteristic
259	#519	C₂²×C₅	1	1	yes	characteristic
260	#518	C₂²×C₅	1	1	yes	characteristic
261	#518	C₂²×C₅	1	1	yes	characteristic
262	#479	—	2	1	no	—
263	#479	—	2	1	no	—
264	#478	—	2	1	no	—
265	#478	—	2	1	no	—
266	#477	—	2	1	no	—
267	#476	—	2	1	no	—
268	#475	—	2	1	no	—
269	#474	—	2	1	no	—
270	#442	—	2	1	no	—
271	#442	—	2	1	no	—
272	#440	—	2	1	no	—
273	#440	—	2	1	no	—
274	C₄×SD₁₆	—	2	1	no	—
275	C₄×SD₁₆	—	2	1	no	—
276	C₄×D₈	—	2	1	no	—
277	C₄×D₈	—	2	1	no	—
278	#428	C₂²×C₅	1	1	yes	characteristic
279	#428	C₂²×C₅	1	1	yes	characteristic
280	#427	C₂²×C₅	1	1	yes	characteristic
281	#427	C₂²×C₅	1	1	yes	characteristic
282	#424	C₂²×C₅	1	1	yes	characteristic
283	#424	C₂²×C₅	1	1	yes	characteristic
284	#419	C₂²×C₅	1	1	yes	characteristic
285	#419	C₂²×C₅	1	1	yes	characteristic
286	#418	C₂²×C₅	1	1	yes	characteristic
287	#418	C₂²×C₅	1	1	yes	characteristic
288	#418	C₂²×C₅	1	1	yes	characteristic
289	#418	C₂²×C₅	1	1	yes	characteristic
290	C₂×#103	C₂²×C₅	1	1	yes	characteristic
291	C₂×#102	C₂²×C₅	1	1	yes	characteristic
292	C₂×#101	C₂²×C₅	1	1	yes	characteristic
293	C₂×#100	C₂²×C₅	1	1	yes	characteristic
294	C₂×#100	C₂²×C₅	1	1	yes	characteristic
295	#405	C₂²×C₅	1	1	yes	characteristic
296	#405	C₂²×C₅	1	1	yes	characteristic
297	#390	C₂²×C₅	1	1	yes	characteristic
298	#343	C₂²×C₅	1	1	yes	characteristic
299	#341	C₂²×C₅	1	1	yes	characteristic
300	#341	C₂²×C₅	1	1	yes	characteristic
301	#339	C₂²×C₅	1	1	yes	characteristic
302	#339	C₂²×C₅	1	1	yes	characteristic
303	#339	C₂²×C₅	1	1	yes	characteristic
304	#339	C₂²×C₅	1	1	yes	characteristic
305	#336	C₂²×C₅	1	1	yes	characteristic
306	C₂³×C₅	—	2	2	no	—
307	C₂³×C₅	—	2	2	no	—
308	C₂³×C₅	—	4	1	no	—
309	C₂³×C₅	—	4	1	no	—
310	C₂³×C₅	—	4	1	no	—
311	C₂³×C₅	—	4	1	no	—
312	C₂³×C₅	—	8	1	no	—
313	C₂³×C₅	—	8	1	no	—
314	C₂³×C₅	—	8	1	no	—
315	C₂³×C₅	—	8	1	no	—
316	C₂³×C₅	H(5,𝔽₂)	1	1	yes	characteristic
317	C₅×Q₈	—	2	2	no	—
318	C₅×Q₈	—	2	2	no	—
319	C₅×Q₈	—	4	1	no	—
320	C₅×Q₈	—	4	1	no	—
321	C₅×Q₈	—	16	1	no	—
322	C₅×D₄	—	2	2	no	—
323	C₅×D₄	—	2	2	no	—
324	C₅×D₄	—	2	2	no	—
325	C₅×D₄	—	2	2	no	—
326	C₅×D₄	—	4	1	no	—
327	C₅×D₄	—	4	1	no	—
328	C₅×D₄	—	4	1	no	—
329	C₅×D₄	—	4	1	no	—
330	C₂×C₄×C₅	—	2	1	no	—
331	C₂×C₄×C₅	—	2	1	no	—
332	C₂×C₄×C₅	—	2	1	no	—
333	C₂×C₄×C₅	—	2	1	no	—
334	C₂×C₄×C₅	—	2	1	no	—
335	C₂×C₄×C₅	—	2	1	no	—
336	C₂×C₄×C₅	—	2	1	no	—
337	C₂×C₄×C₅	—	2	1	no	—
338	C₂×C₄×C₅	—	2	2	no	—
339	C₂×C₄×C₅	—	4	1	no	—
340	C₂×C₄×C₅	—	4	1	no	—
341	C₂×C₄×C₅	—	4	1	no	—
342	C₂×C₄×C₅	—	4	1	no	—
343	C₂×C₄×C₅	—	4	1	no	—
344	C₂×C₄×C₅	—	4	1	no	—
345	C₂×C₄×C₅	—	8	1	no	—
346	C₂×C₄×C₅	—	16	1	no	—
347	C₂×C₄×C₅	—	16	1	no	—
348	C₂×C₄×C₅	—	16	1	no	—
349	C₂×C₄×C₅	—	16	1	no	—
350	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
351	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
352	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
353	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
354	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
355	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
356	C₅×C₈	—	2	1	no	—
357	C₅×C₈	—	2	1	no	—
358	C₅×C₈	—	2	1	no	—
359	C₅×C₈	—	2	1	no	—
360	C₅×C₈	—	4	1	no	—
361	C₅×C₈	—	4	1	no	—
362	C₅×C₈	—	4	1	no	—
363	C₅×C₈	—	4	1	no	—
364	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
365	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
366	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
367	C₂×SD₁₆	—	2	2	no	—
368	C₂×SD₁₆	—	2	2	no	—
369	C₂×SD₁₆	—	2	1	no	—
370	C₂×SD₁₆	—	2	1	no	—
371	C₂×D₈	—	2	2	no	—
372	C₂×D₈	—	2	2	no	—
373	C₂×D₈	—	2	1	no	—
374	C₂×D₈	—	2	1	no	—
375	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
376	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
377	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
378	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
379	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
380	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
381	C₄⋊Q₈	—	2	1	no	—
382	C₄⋊Q₈	—	2	1	no	—
383	#125	—	2	1	no	—
384	#125	—	2	1	no	—
385	#124	—	2	2	no	—
386	#124	—	2	2	no	—
387	C₂²⋊Q₈	—	4	1	no	—
388	C₄×Q₈	—	2	1	no	—
389	C₄×Q₈	—	2	1	no	—
390	C₄×Q₈	—	2	1	no	—
391	C₄×Q₈	—	2	1	no	—
392	C₄×D₄	—	2	1	no	—
393	C₄×D₄	—	2	1	no	—
394	C₄×D₄	—	2	1	no	—
395	C₄×D₄	—	2	1	no	—
396	C₄×D₄	—	2	1	no	—
397	C₄×D₄	—	2	1	no	—
398	C₄×D₄	—	2	1	no	—
399	C₄×D₄	—	2	1	no	—
400	#117	—	4	1	no	—
401	#117	C₂³×C₅	1	1	yes	characteristic
402	#117	C₂³×C₅	1	1	yes	characteristic
403	#117	C₂³×C₅	1	1	yes	characteristic
404	#117	C₂³×C₅	1	1	yes	characteristic
405	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
406	C₂×C₂²⋊C₄	—	4	1	no	—
407	C₂×C₂²⋊C₄	—	4	1	no	—
408	C₂×C₂²⋊C₄	—	4	1	no	—
409	C₂×C₂²⋊C₄	—	4	1	no	—
410	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
411	#107	—	2	1	no	—
412	#107	—	2	1	no	—
413	#107	C₅×D₄	1	1	yes	characteristic
414	#107	C₅×D₄	1	1	yes	characteristic
415	#107	C₅×D₄	1	1	yes	characteristic
416	#107	C₅×D₄	1	1	yes	characteristic
417	#106	—	2	1	no	—
418	#106	—	2	1	no	—
419	#106	C₅×D₄	1	1	yes	characteristic
420	#106	C₅×D₄	1	1	yes	characteristic
421	#106	C₅×D₄	1	1	yes	characteristic
422	#106	C₅×D₄	1	1	yes	characteristic
423	C₄⋊C₈	—	2	1	no	—
424	C₄⋊C₈	—	2	1	no	—
425	C₄⋊C₈	—	2	1	no	—
426	C₄⋊C₈	—	2	1	no	—
427	#103	—	2	1	no	—
428	#103	—	2	1	no	—
429	#103	—	2	1	no	—
430	#103	—	2	1	no	—
431	#103	—	2	1	no	—
432	#103	—	2	1	no	—
433	#102	—	2	1	no	—
434	#102	—	2	1	no	—
435	#102	—	2	1	no	—
436	#102	—	2	1	no	—
437	#102	—	2	1	no	—
438	#102	—	2	1	no	—
439	#102	—	2	1	no	—
440	#102	—	2	1	no	—
441	#102	—	2	1	no	—
442	#102	—	2	1	no	—
443	#101	—	2	2	no	—
444	#100	—	2	2	no	—
445	#100	—	2	2	no	—
446	#97	—	2	1	no	—
447	#97	—	2	1	no	—
448	C₄×C₈	—	2	1	no	—
449	C₄×C₈	—	2	1	no	—
450	C₂²×C₅	—	2	1	no	—
451	C₂²×C₅	—	2	1	no	—
452	C₂²×C₅	—	4	2	no	—
453	C₂²×C₅	—	4	2	no	—
454	C₂²×C₅	—	8	2	no	—
455	C₂²×C₅	—	8	2	no	—
456	C₂²×C₅	—	8	1	no	—
457	C₂²×C₅	—	8	1	no	—
458	C₂²×C₅	—	8	1	no	—
459	C₂²×C₅	—	8	1	no	—
460	C₂²×C₅	—	16	1	no	—
461	C₂²×C₅	—	16	1	no	—
462	C₂²×C₅	#539	1	1	yes	characteristic
463	C₂²×C₅	D₄²	1	1	yes	characteristic
464	C₂²×C₅	#551	1	1	yes	characteristic
465	C₄×C₅	—	4	2	no	—
466	C₄×C₅	—	4	1	no	—
467	C₄×C₅	—	4	1	no	—
468	C₄×C₅	—	4	1	no	—
469	C₄×C₅	—	4	1	no	—
470	C₄×C₅	—	4	1	no	—
471	C₄×C₅	—	4	1	no	—
472	C₄×C₅	—	4	1	no	—
473	C₄×C₅	—	4	1	no	—
474	C₄×C₅	—	8	1	no	—
475	C₄×C₅	—	8	1	no	—
476	C₄×C₅	#525	1	1	yes	characteristic
477	C₄×C₅	#525	1	1	yes	characteristic
478	C₄×C₅	#548	1	1	yes	characteristic
479	C₄×C₅	#548	1	1	yes	characteristic
480	C₂⁴	—	2	1	no	—
481	C₂⁴	—	2	1	no	—
482	C₂×Q₈	—	2	1	no	—
483	C₂×Q₈	—	2	1	no	—
484	C₂×Q₈	—	2	1	no	—
485	C₂×Q₈	—	2	1	no	—
486	C₂×Q₈	—	2	1	no	—
487	C₂×Q₈	—	4	1	no	—
488	C₂×Q₈	C₅×#41	1	2	yes	—
489	C₂×D₄	—	2	1	no	—
490	C₂×D₄	—	2	1	no	—
491	C₂×D₄	—	2	1	no	—
492	C₂×D₄	—	2	1	no	—
493	C₂×D₄	—	2	1	no	—
494	C₂×D₄	—	2	1	no	—
495	C₂×D₄	—	2	1	no	—
496	C₂×D₄	—	2	1	no	—
497	C₂×D₄	—	2	1	no	—
498	C₂×D₄	—	2	1	no	—
499	C₂×D₄	C₅×#41	1	2	yes	—
500	C₂×D₄	C₅×#41	1	2	yes	—
501	C₂²×C₄	—	2	1	no	—
502	C₂²×C₄	—	2	1	no	—
503	C₂²×C₄	—	2	1	no	—
504	C₂²×C₄	—	4	1	no	—
505	C₂²×C₄	—	4	1	no	—
506	C₂²×C₄	—	4	1	no	—
507	C₂²×C₄	—	4	1	no	—
508	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
509	SD₁₆	—	2	4	no	—
510	SD₁₆	—	2	4	no	—
511	D₈	—	2	4	no	—
512	D₈	—	2	4	no	—
513	M₁₆	—	2	1	no	—
514	M₁₆	—	2	1	no	—
515	M₁₆	—	2	1	no	—
516	M₁₆	—	2	1	no	—
517	M₁₆	—	2	1	no	—
518	M₁₆	—	2	1	no	—
519	M₁₆	—	2	1	no	—
520	M₁₆	—	2	1	no	—
521	C₂×C₈	—	2	1	no	—
522	C₂×C₈	—	2	1	no	—
523	C₂×C₈	—	2	1	no	—
524	C₂×C₈	—	2	1	no	—
525	C₂×C₈	—	2	1	no	—
526	C₂×C₈	—	2	1	no	—
527	C₂×C₈	—	2	1	no	—
528	C₂×C₈	—	2	1	no	—
529	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
530	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
531	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
532	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
533	C₄⋊C₄	—	2	1	no	—
534	C₄⋊C₄	—	2	1	no	—
535	C₄⋊C₄	—	4	1	no	—
536	C₄⋊C₄	—	4	1	no	—
537	C₄⋊C₄	—	4	1	no	—
538	C₄⋊C₄	—	4	1	no	—
539	C₄⋊C₄	—	4	1	no	—
540	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
541	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
542	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
543	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
544	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
545	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
546	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
547	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
548	C₂²⋊C₄	—	2	1	no	—
549	C₂²⋊C₄	—	2	1	no	—
550	C₂²⋊C₄	—	2	1	no	—
551	C₂²⋊C₄	—	2	1	no	—
552	C₂²⋊C₄	—	4	1	no	—
553	C₂²⋊C₄	—	4	1	no	—
554	C₂²⋊C₄	—	4	1	no	—
555	C₂²⋊C₄	—	4	1	no	—
556	C₂²⋊C₄	—	4	4	no	—
557	C₂²⋊C₄	—	8	2	no	—
558	C₄²	—	2	1	no	—
559	C₄²	—	2	1	no	—
560	C₄²	—	2	1	no	—
561	C₄²	—	2	1	no	—
562	C₄²	—	2	1	no	—
563	C₄²	—	2	1	no	—
564	C₄²	—	4	1	no	—
565	C₄²	—	4	1	no	—
566	C₂×C₅	—	2	1	no	—
567	C₂×C₅	—	2	1	no	—
568	C₂×C₅	—	8	2	no	—
569	C₂×C₅	—	8	2	no	—
570	C₂×C₅	#2463	1	1	yes	characteristic
571	C₂×C₅	#3288	1	1	yes	characteristic
572	C₂×C₅	#3290	1	1	yes	characteristic
573	C₂³	—	2	2	no	—
574	C₂³	—	2	2	no	—
575	C₂³	—	4	1	no	—
576	C₂³	—	4	1	no	—
577	C₂³	—	4	1	no	—
578	C₂³	—	4	1	no	—
579	C₂³	—	8	1	no	—
580	C₂³	—	8	1	no	—
581	C₂³	—	8	1	no	—
582	C₂³	—	8	1	no	—
583	C₂³	C₅×H(5,𝔽₂)	1	1	yes	characteristic
584	Q₈	—	2	2	no	—
585	Q₈	—	2	2	no	—
586	Q₈	—	4	1	no	—
587	Q₈	—	4	1	no	—
588	Q₈	—	16	1	no	—
589	D₄	—	2	2	no	—
590	D₄	—	2	2	no	—
591	D₄	—	2	2	no	—
592	D₄	—	2	2	no	—
593	D₄	—	4	1	no	—
594	D₄	—	4	1	no	—
595	D₄	—	4	1	no	—
596	D₄	—	4	1	no	—
597	C₂×C₄	—	2	1	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	2	1	no	—
600	C₂×C₄	—	2	1	no	—
601	C₂×C₄	—	2	1	no	—
602	C₂×C₄	—	2	1	no	—
603	C₂×C₄	—	2	1	no	—
604	C₂×C₄	—	2	1	no	—
605	C₂×C₄	—	2	2	no	—
606	C₂×C₄	—	4	1	no	—
607	C₂×C₄	—	4	1	no	—
608	C₂×C₄	—	4	1	no	—
609	C₂×C₄	—	4	1	no	—
610	C₂×C₄	—	4	1	no	—
611	C₂×C₄	—	4	1	no	—
612	C₂×C₄	—	8	1	no	—
613	C₂×C₄	—	16	1	no	—
614	C₂×C₄	—	16	1	no	—
615	C₂×C₄	—	16	1	no	—
616	C₂×C₄	—	16	1	no	—
617	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
618	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
619	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
620	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
621	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
622	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
623	C₈	—	2	1	no	—
624	C₈	—	2	1	no	—
625	C₈	—	2	1	no	—
626	C₈	—	2	1	no	—
627	C₈	—	4	1	no	—
628	C₈	—	4	1	no	—
629	C₈	—	4	1	no	—
630	C₈	—	4	1	no	—
631	C₅	#26921	1	1	yes	characteristic, direct product factor, Sylow
632	C₂²	—	2	1	no	—
633	C₂²	—	2	1	no	—
634	C₂²	—	4	2	no	—
635	C₂²	—	4	2	no	—
636	C₂²	—	8	2	no	—
637	C₂²	—	8	2	no	—
638	C₂²	—	8	1	no	—
639	C₂²	—	8	1	no	—
640	C₂²	—	8	1	no	—
641	C₂²	—	8	1	no	—
642	C₂²	—	16	1	no	—
643	C₂²	—	16	1	no	—
644	C₂²	C₅×#539	1	1	yes	characteristic
645	C₂²	C₅×D₄²	1	1	yes	characteristic
646	C₂²	C₅×#551	1	1	yes	characteristic
647	C₄	—	4	1	no	—
648	C₄	—	4	1	no	—
649	C₄	—	4	1	no	—
650	C₄	—	4	1	no	—
651	C₄	—	4	1	no	—
652	C₄	—	4	1	no	—
653	C₄	—	4	1	no	—
654	C₄	—	4	1	no	—
655	C₄	—	4	2	no	—
656	C₄	—	8	1	no	—
657	C₄	—	8	1	no	—
658	C₄	C₅×#525	1	1	yes	characteristic
659	C₄	C₅×#525	1	1	yes	characteristic
660	C₄	C₅×#548	1	1	yes	characteristic
661	C₄	C₅×#548	1	1	yes	characteristic
662	C₂	—	2	1	no	—
663	C₂	—	2	1	no	—
664	C₂	—	8	2	no	—
665	C₂	—	8	2	no	—
666	C₂	C₅×#2463	1	1	yes	characteristic
667	C₂	C₅×#3288	1	1	yes	characteristic
668	C₂	C₅×#3290	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	D₄²
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
prime radical	C₂²×C₅×D₈	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×#3082	C₂	semidirect
2. C₅×#3081	C₂	semidirect
3. C₅×#2949	C₂	semidirect
5. C₅×#2046	C₂	semidirect
7. C₅×#2027	C₂	semidirect
9. C₅×#1931	C₂	semidirect
10. C₅×#1930	C₂	semidirect
11. C₅×#1922	C₂	semidirect
12. C₅×#1922	C₂	semidirect
13. C₅×#1888	C₂	semidirect
14. C₅×#1885	C₂	semidirect
15. C₅×#1856	C₂	semidirect
67. #26921	C₅	direct (N × H)
154. #3082	C₂×C₅	semidirect
155. #3081	C₂×C₅	semidirect
156. #2949	C₂×C₅	semidirect
158. #2046	C₂×C₅	semidirect
160. #2027	C₂×C₅	semidirect
162. #1931	C₂×C₅	semidirect
163. #1930	C₂×C₅	semidirect
164. #1922	C₂×C₅	semidirect
165. #1922	C₂×C₅	semidirect
166. #1888	C₂×C₅	semidirect
167. #1885	C₂×C₅	semidirect
168. #1856	C₂×C₅	semidirect
631. C₅	#26921	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×#3082	2
C₅×#3081	2
C₅×#2949	2
C₅×#2948	2
C₅×#2046	2
C₅×#2045	2
C₅×#2027	2
C₅×#2012	2
C₅×#1931	2
C₅×#1930	2
C₅×#1922	2
C₅×#1888	2
C₅×#1885	2
C₅×#1856	2
#26921	5

Subgroups — C5×#26921 #11949641

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#26921 #11949641