Subgroups — C₅×#26922 #11949642

Order 1280.

732 conjugacy classes of subgroups.

The subgroup lattice has 650 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
3	C₅×#2950	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2949	C₂	1	1	yes	maximal, characteristic
5	C₅×#2047	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2046	C₂	1	1	yes	maximal, characteristic
7	C₅×#2028	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2015	C₂	1	1	yes	maximal, characteristic
9	C₅×#1931	C₂	1	1	yes	maximal, characteristic
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
14	C₅×#1885	C₂	1	1	yes	maximal, characteristic
15	C₅×#1857	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₅×Q₁₆	C₂²	1	1	yes	characteristic
17	C₂²×C₅×SD₁₆	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×#519	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×#441	—	2	1	no	—
32	C₅×#441	—	2	1	no	—
33	C₅×#440	—	2	1	no	—
34	C₅×#440	—	2	1	no	—
35	C₄×C₅×Q₁₆	—	2	1	no	—
36	C₄×C₅×Q₁₆	—	2	1	no	—
37	C₄×C₅×SD₁₆	—	2	1	no	—
38	C₄×C₅×SD₁₆	—	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×#419	C₂²	1	1	yes	characteristic
48	C₅×#419	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×#101	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×#391	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	#26922	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
68	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
69	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
70	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
71	C₂×C₅×Q₁₆	—	2	2	no	—
72	C₂×C₅×Q₁₆	—	2	2	no	—
73	C₂×C₅×Q₁₆	—	2	1	no	—
74	C₂×C₅×Q₁₆	—	2	1	no	—
75	C₂×C₅×SD₁₆	—	2	2	no	—
76	C₂×C₅×SD₁₆	—	2	2	no	—
77	C₂×C₅×SD₁₆	—	2	1	no	—
78	C₂×C₅×SD₁₆	—	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×Q₈	—	2	1	no	—
97	C₄×C₅×Q₈	—	2	1	no	—
98	C₄×C₅×Q₈	—	2	1	no	—
99	C₄×C₅×Q₈	—	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	—	4	1	no	—
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	C₅×#117	C₂³	1	1	yes	characteristic
110	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
111	C₂×C₅×C₂²⋊C₄	—	4	1	no	—
112	C₂×C₅×C₂²⋊C₄	—	4	1	no	—
113	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
114	C₅×#107	—	2	1	no	—
115	C₅×#107	—	2	1	no	—
116	C₅×#107	D₄	1	1	yes	characteristic
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×#106	—	2	1	no	—
121	C₅×#106	—	2	1	no	—
122	C₅×#106	D₄	1	1	yes	characteristic
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×C₄⋊C₈	—	2	1	no	—
127	C₅×C₄⋊C₈	—	2	1	no	—
128	C₅×C₄⋊C₈	—	2	1	no	—
129	C₅×C₄⋊C₈	—	2	1	no	—
130	C₅×#103	—	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×#103	—	2	1	no	—
138	C₅×#103	—	2	1	no	—
139	C₅×#103	—	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×#101	—	2	2	no	—
147	C₅×#101	—	2	2	no	—
148	C₅×#100	—	2	2	no	—
149	C₅×#97	—	2	1	no	—
150	C₅×#97	—	2	1	no	—
151	C₄×C₅×C₈	—	2	1	no	—
152	C₄×C₅×C₈	—	2	1	no	—
153	C₅×#95	—	4	1	no	—
154	#3082	C₂×C₅	1	1	yes	characteristic, complemented
155	#3081	C₂×C₅	1	1	yes	characteristic
156	#2950	C₂×C₅	1	1	yes	characteristic, complemented
157	#2949	C₂×C₅	1	1	yes	characteristic
158	#2047	C₂×C₅	1	1	yes	characteristic, complemented
159	#2046	C₂×C₅	1	1	yes	characteristic
160	#2028	C₂×C₅	1	1	yes	characteristic, complemented
161	#2015	C₂×C₅	1	1	yes	characteristic
162	#1931	C₂×C₅	1	1	yes	characteristic
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
167	#1885	C₂×C₅	1	1	yes	characteristic
168	#1857	C₂×C₅	1	1	yes	characteristic, complemented
169	C₂⁴×C₅	—	2	1	no	—
170	C₂×C₅×Q₈	—	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	—	2	1	no	—
177	C₂×C₅×Q₈	—	2	1	no	—
178	C₂×C₅×Q₈	—	2	1	no	—
179	C₂×C₅×Q₈	—	2	1	no	—
180	C₂×C₅×Q₈	—	4	1	no	—
181	C₂×C₅×Q₈	#41	1	2	yes	—
182	C₂×C₅×Q₈	#41	1	2	yes	—
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	C₂²×C₄×C₅	—	2	1	no	—
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	C₂⁴	1	1	yes	characteristic
196	C₅×Q₁₆	—	2	4	no	—
197	C₅×Q₁₆	—	2	4	no	—
198	C₅×SD₁₆	—	2	4	no	—
199	C₅×SD₁₆	—	2	4	no	—
200	C₅×M₁₆	—	2	1	no	—
201	C₅×M₁₆	—	2	1	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	C₂×C₅×C₈	—	2	1	no	—
209	C₂×C₅×C₈	—	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	C₂×D₄	1	1	yes	characteristic
217	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
218	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
219	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
220	C₅×C₄⋊C₄	—	2	1	no	—
221	C₅×C₄⋊C₄	—	2	1	no	—
222	C₅×C₄⋊C₄	—	4	1	no	—
223	C₅×C₄⋊C₄	—	4	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	4	no	—
244	C₄²×C₅	—	2	1	no	—
245	C₄²×C₅	—	2	1	no	—
246	C₄²×C₅	—	2	1	no	—
247	C₄²×C₅	—	2	1	no	—
248	C₄²×C₅	—	2	1	no	—
249	C₄²×C₅	—	2	1	no	—
250	C₄²×C₅	—	4	1	no	—
251	C₄²×C₅	—	4	1	no	—
252	C₄²×C₅	—	4	1	no	—
253	C₄²×C₅	—	4	1	no	—
254	C₂²×Q₁₆	C₂²×C₅	1	1	yes	characteristic
255	C₂²×SD₁₆	C₂²×C₅	1	1	yes	characteristic
256	#544	C₂²×C₅	1	1	yes	characteristic
257	C₂×#124	C₂²×C₅	1	1	yes	characteristic
258	#519	C₂²×C₅	1	1	yes	characteristic
259	#519	C₂²×C₅	1	1	yes	characteristic
260	#518	C₂²×C₅	1	1	yes	characteristic
261	#479	—	2	1	no	—
262	#479	—	2	1	no	—
263	#478	—	2	1	no	—
264	#478	—	2	1	no	—
265	#477	—	2	1	no	—
266	#476	—	2	1	no	—
267	#475	—	2	1	no	—
268	#474	—	2	1	no	—
269	#441	—	2	1	no	—
270	#441	—	2	1	no	—
271	#440	—	2	1	no	—
272	#440	—	2	1	no	—
273	C₄×Q₁₆	—	2	1	no	—
274	C₄×Q₁₆	—	2	1	no	—
275	C₄×SD₁₆	—	2	1	no	—
276	C₄×SD₁₆	—	2	1	no	—
277	#428	C₂²×C₅	1	1	yes	characteristic
278	#428	C₂²×C₅	1	1	yes	characteristic
279	#427	C₂²×C₅	1	1	yes	characteristic
280	#427	C₂²×C₅	1	1	yes	characteristic
281	#424	C₂²×C₅	1	1	yes	characteristic
282	#424	C₂²×C₅	1	1	yes	characteristic
283	#419	C₂²×C₅	1	1	yes	characteristic
284	#419	C₂²×C₅	1	1	yes	characteristic
285	#419	C₂²×C₅	1	1	yes	characteristic
286	#419	C₂²×C₅	1	1	yes	characteristic
287	#418	C₂²×C₅	1	1	yes	characteristic
288	#418	C₂²×C₅	1	1	yes	characteristic
289	C₂×#103	C₂²×C₅	1	1	yes	characteristic
290	C₂×#102	C₂²×C₅	1	1	yes	characteristic
291	C₂×#101	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	#405	C₂²×C₅	1	1	yes	characteristic
295	#405	C₂²×C₅	1	1	yes	characteristic
296	#391	C₂²×C₅	1	1	yes	characteristic
297	#343	C₂²×C₅	1	1	yes	characteristic
298	#341	C₂²×C₅	1	1	yes	characteristic
299	#341	C₂²×C₅	1	1	yes	characteristic
300	#339	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	#336	C₂²×C₅	1	1	yes	characteristic
305	C₂³×C₅	—	2	2	no	—
306	C₂³×C₅	—	4	1	no	—
307	C₂³×C₅	—	4	1	no	—
308	C₂³×C₅	—	8	1	no	—
309	C₂³×C₅	—	8	1	no	—
310	C₂³×C₅	H(5,𝔽₂)	1	1	yes	characteristic
311	C₅×Q₈	—	2	2	no	—
312	C₅×Q₈	—	2	2	no	—
313	C₅×Q₈	—	2	2	no	—
314	C₅×Q₈	—	2	2	no	—
315	C₅×Q₈	—	4	1	no	—
316	C₅×Q₈	—	4	1	no	—
317	C₅×Q₈	—	4	1	no	—
318	C₅×Q₈	—	4	1	no	—
319	C₅×Q₈	—	16	1	no	—
320	C₅×D₄	—	2	2	no	—
321	C₅×D₄	—	2	2	no	—
322	C₅×D₄	—	4	1	no	—
323	C₅×D₄	—	4	1	no	—
324	C₂×C₄×C₅	—	2	2	no	—
325	C₂×C₄×C₅	—	2	1	no	—
326	C₂×C₄×C₅	—	2	1	no	—
327	C₂×C₄×C₅	—	2	1	no	—
328	C₂×C₄×C₅	—	2	1	no	—
329	C₂×C₄×C₅	—	2	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	2	no	—
334	C₂×C₄×C₅	—	4	1	no	—
335	C₂×C₄×C₅	—	4	1	no	—
336	C₂×C₄×C₅	—	4	1	no	—
337	C₂×C₄×C₅	—	4	1	no	—
338	C₂×C₄×C₅	—	4	1	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	—	8	1	no	—
343	C₂×C₄×C₅	—	16	1	no	—
344	C₂×C₄×C₅	—	16	1	no	—
345	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
346	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
347	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
348	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
349	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
350	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
351	C₅×C₈	—	2	1	no	—
352	C₅×C₈	—	2	1	no	—
353	C₅×C₈	—	2	1	no	—
354	C₅×C₈	—	2	1	no	—
355	C₅×C₈	—	4	1	no	—
356	C₅×C₈	—	4	1	no	—
357	C₅×C₈	—	4	1	no	—
358	C₅×C₈	—	4	1	no	—
359	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
360	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
361	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
362	C₂×Q₁₆	—	2	2	no	—
363	C₂×Q₁₆	—	2	2	no	—
364	C₂×Q₁₆	—	2	1	no	—
365	C₂×Q₁₆	—	2	1	no	—
366	C₂×SD₁₆	—	2	2	no	—
367	C₂×SD₁₆	—	2	2	no	—
368	C₂×SD₁₆	—	2	1	no	—
369	C₂×SD₁₆	—	2	1	no	—
370	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
371	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
372	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
373	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
374	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
375	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
376	C₄⋊Q₈	—	2	1	no	—
377	C₄⋊Q₈	—	2	1	no	—
378	#125	—	2	1	no	—
379	#125	—	2	1	no	—
380	#124	—	2	2	no	—
381	#124	—	2	2	no	—
382	C₂²⋊Q₈	—	4	1	no	—
383	C₄×Q₈	—	2	1	no	—
384	C₄×Q₈	—	2	1	no	—
385	C₄×Q₈	—	2	1	no	—
386	C₄×Q₈	—	2	1	no	—
387	C₄×Q₈	—	2	1	no	—
388	C₄×Q₈	—	2	1	no	—
389	C₄×Q₈	—	2	1	no	—
390	C₄×Q₈	—	2	1	no	—
391	C₄×D₄	—	2	1	no	—
392	C₄×D₄	—	2	1	no	—
393	C₄×D₄	—	2	1	no	—
394	C₄×D₄	—	2	1	no	—
395	#117	—	4	1	no	—
396	#117	—	4	1	no	—
397	#117	C₂³×C₅	1	1	yes	characteristic
398	#117	C₂³×C₅	1	1	yes	characteristic
399	#117	C₂³×C₅	1	1	yes	characteristic
400	#117	C₂³×C₅	1	1	yes	characteristic
401	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
402	C₂×C₂²⋊C₄	—	4	1	no	—
403	C₂×C₂²⋊C₄	—	4	1	no	—
404	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
405	#107	—	2	1	no	—
406	#107	—	2	1	no	—
407	#107	C₅×D₄	1	1	yes	characteristic
408	#107	C₅×D₄	1	1	yes	characteristic
409	#107	C₅×D₄	1	1	yes	characteristic
410	#107	C₅×D₄	1	1	yes	characteristic
411	#106	—	2	1	no	—
412	#106	—	2	1	no	—
413	#106	C₅×D₄	1	1	yes	characteristic
414	#106	C₅×D₄	1	1	yes	characteristic
415	#106	C₅×D₄	1	1	yes	characteristic
416	#106	C₅×D₄	1	1	yes	characteristic
417	C₄⋊C₈	—	2	1	no	—
418	C₄⋊C₈	—	2	1	no	—
419	C₄⋊C₈	—	2	1	no	—
420	C₄⋊C₈	—	2	1	no	—
421	#103	—	2	1	no	—
422	#103	—	2	1	no	—
423	#103	—	2	1	no	—
424	#103	—	2	1	no	—
425	#103	—	2	1	no	—
426	#103	—	2	1	no	—
427	#103	—	2	1	no	—
428	#103	—	2	1	no	—
429	#103	—	2	1	no	—
430	#103	—	2	1	no	—
431	#102	—	2	1	no	—
432	#102	—	2	1	no	—
433	#102	—	2	1	no	—
434	#102	—	2	1	no	—
435	#102	—	2	1	no	—
436	#102	—	2	1	no	—
437	#101	—	2	2	no	—
438	#101	—	2	2	no	—
439	#100	—	2	2	no	—
440	#97	—	2	1	no	—
441	#97	—	2	1	no	—
442	C₄×C₈	—	2	1	no	—
443	C₄×C₈	—	2	1	no	—
444	#95	—	4	1	no	—
445	C₂²×C₅	—	2	1	no	—
446	C₂²×C₅	—	2	1	no	—
447	C₂²×C₅	—	4	2	no	—
448	C₂²×C₅	—	8	2	no	—
449	C₂²×C₅	—	8	1	no	—
450	C₂²×C₅	—	8	1	no	—
451	C₂²×C₅	—	16	1	no	—
452	C₂²×C₅	#539	1	1	yes	characteristic
453	C₂²×C₅	D₄²	1	1	yes	characteristic
454	C₂²×C₅	#551	1	1	yes	characteristic
455	C₄×C₅	—	4	2	no	—
456	C₄×C₅	—	4	2	no	—
457	C₄×C₅	—	4	1	no	—
458	C₄×C₅	—	4	1	no	—
459	C₄×C₅	—	4	1	no	—
460	C₄×C₅	—	4	1	no	—
461	C₄×C₅	—	4	1	no	—
462	C₄×C₅	—	4	1	no	—
463	C₄×C₅	—	4	1	no	—
464	C₄×C₅	—	4	1	no	—
465	C₄×C₅	—	8	1	no	—
466	C₄×C₅	—	8	1	no	—
467	C₄×C₅	#525	1	1	yes	characteristic
468	C₄×C₅	#525	1	1	yes	characteristic
469	C₄×C₅	#548	1	1	yes	characteristic
470	C₄×C₅	#548	1	1	yes	characteristic
471	C₂⁴	—	2	1	no	—
472	C₂×Q₈	—	2	1	no	—
473	C₂×Q₈	—	2	1	no	—
474	C₂×Q₈	—	2	1	no	—
475	C₂×Q₈	—	2	1	no	—
476	C₂×Q₈	—	2	1	no	—
477	C₂×Q₈	—	2	1	no	—
478	C₂×Q₈	—	2	1	no	—
479	C₂×Q₈	—	2	1	no	—
480	C₂×Q₈	—	2	1	no	—
481	C₂×Q₈	—	2	1	no	—
482	C₂×Q₈	—	4	1	no	—
483	C₂×Q₈	C₅×#41	1	2	yes	—
484	C₂×Q₈	C₅×#41	1	2	yes	—
485	C₂×D₄	—	2	1	no	—
486	C₂×D₄	—	2	1	no	—
487	C₂×D₄	—	2	1	no	—
488	C₂×D₄	—	2	1	no	—
489	C₂×D₄	—	2	1	no	—
490	C₂×D₄	C₅×#41	1	2	yes	—
491	C₂²×C₄	—	2	1	no	—
492	C₂²×C₄	—	2	1	no	—
493	C₂²×C₄	—	2	1	no	—
494	C₂²×C₄	—	2	1	no	—
495	C₂²×C₄	—	4	1	no	—
496	C₂²×C₄	—	4	1	no	—
497	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
498	Q₁₆	—	2	4	no	—
499	Q₁₆	—	2	4	no	—
500	SD₁₆	—	2	4	no	—
501	SD₁₆	—	2	4	no	—
502	M₁₆	—	2	1	no	—
503	M₁₆	—	2	1	no	—
504	M₁₆	—	2	1	no	—
505	M₁₆	—	2	1	no	—
506	M₁₆	—	2	1	no	—
507	M₁₆	—	2	1	no	—
508	M₁₆	—	2	1	no	—
509	M₁₆	—	2	1	no	—
510	C₂×C₈	—	2	1	no	—
511	C₂×C₈	—	2	1	no	—
512	C₂×C₈	—	2	1	no	—
513	C₂×C₈	—	2	1	no	—
514	C₂×C₈	—	2	1	no	—
515	C₂×C₈	—	2	1	no	—
516	C₂×C₈	—	2	1	no	—
517	C₂×C₈	—	2	1	no	—
518	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
519	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
520	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
521	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
522	C₄⋊C₄	—	2	1	no	—
523	C₄⋊C₄	—	2	1	no	—
524	C₄⋊C₄	—	4	1	no	—
525	C₄⋊C₄	—	4	1	no	—
526	C₄⋊C₄	—	4	1	no	—
527	C₄⋊C₄	—	4	1	no	—
528	C₄⋊C₄	—	4	1	no	—
529	C₄⋊C₄	—	4	1	no	—
530	C₄⋊C₄	—	4	1	no	—
531	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
532	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
533	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
534	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
535	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
536	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
537	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
538	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
539	C₂²⋊C₄	—	2	1	no	—
540	C₂²⋊C₄	—	2	1	no	—
541	C₂²⋊C₄	—	2	1	no	—
542	C₂²⋊C₄	—	2	1	no	—
543	C₂²⋊C₄	—	4	1	no	—
544	C₂²⋊C₄	—	4	1	no	—
545	C₂²⋊C₄	—	4	4	no	—
546	C₄²	—	2	1	no	—
547	C₄²	—	2	1	no	—
548	C₄²	—	2	1	no	—
549	C₄²	—	2	1	no	—
550	C₄²	—	2	1	no	—
551	C₄²	—	2	1	no	—
552	C₄²	—	4	1	no	—
553	C₄²	—	4	1	no	—
554	C₄²	—	4	1	no	—
555	C₄²	—	4	1	no	—
556	C₂×C₅	—	2	1	no	—
557	C₂×C₅	—	2	1	no	—
558	C₂×C₅	—	8	2	no	—
559	C₂×C₅	#2463	1	1	yes	characteristic
560	C₂×C₅	#3289	1	1	yes	characteristic
561	C₂×C₅	#3290	1	1	yes	characteristic
562	C₂³	—	2	2	no	—
563	C₂³	—	4	1	no	—
564	C₂³	—	4	1	no	—
565	C₂³	—	8	1	no	—
566	C₂³	—	8	1	no	—
567	C₂³	C₅×H(5,𝔽₂)	1	1	yes	characteristic
568	Q₈	—	2	2	no	—
569	Q₈	—	2	2	no	—
570	Q₈	—	2	2	no	—
571	Q₈	—	2	2	no	—
572	Q₈	—	4	1	no	—
573	Q₈	—	4	1	no	—
574	Q₈	—	4	1	no	—
575	Q₈	—	4	1	no	—
576	Q₈	—	16	1	no	—
577	D₄	—	2	2	no	—
578	D₄	—	2	2	no	—
579	D₄	—	4	1	no	—
580	D₄	—	4	1	no	—
581	C₂×C₄	—	2	2	no	—
582	C₂×C₄	—	2	1	no	—
583	C₂×C₄	—	2	1	no	—
584	C₂×C₄	—	2	1	no	—
585	C₂×C₄	—	2	1	no	—
586	C₂×C₄	—	2	1	no	—
587	C₂×C₄	—	2	1	no	—
588	C₂×C₄	—	2	1	no	—
589	C₂×C₄	—	2	1	no	—
590	C₂×C₄	—	2	2	no	—
591	C₂×C₄	—	4	1	no	—
592	C₂×C₄	—	4	1	no	—
593	C₂×C₄	—	4	1	no	—
594	C₂×C₄	—	4	1	no	—
595	C₂×C₄	—	4	1	no	—
596	C₂×C₄	—	4	1	no	—
597	C₂×C₄	—	4	1	no	—
598	C₂×C₄	—	4	1	no	—
599	C₂×C₄	—	8	1	no	—
600	C₂×C₄	—	16	1	no	—
601	C₂×C₄	—	16	1	no	—
602	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
603	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
604	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
605	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
606	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
607	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
608	C₈	—	2	1	no	—
609	C₈	—	2	1	no	—
610	C₈	—	2	1	no	—
611	C₈	—	2	1	no	—
612	C₈	—	4	1	no	—
613	C₈	—	4	1	no	—
614	C₈	—	4	1	no	—
615	C₈	—	4	1	no	—
616	C₅	#26922	1	1	yes	characteristic, direct product factor, Sylow
617	C₂²	—	2	1	no	—
618	C₂²	—	2	1	no	—
619	C₂²	—	4	2	no	—
620	C₂²	—	8	2	no	—
621	C₂²	—	8	1	no	—
622	C₂²	—	8	1	no	—
623	C₂²	—	16	1	no	—
624	C₂²	C₅×#539	1	1	yes	characteristic
625	C₂²	C₅×D₄²	1	1	yes	characteristic
626	C₂²	C₅×#551	1	1	yes	characteristic
627	C₄	—	4	1	no	—
628	C₄	—	4	1	no	—
629	C₄	—	4	1	no	—
630	C₄	—	4	1	no	—
631	C₄	—	4	1	no	—
632	C₄	—	4	1	no	—
633	C₄	—	4	1	no	—
634	C₄	—	4	1	no	—
635	C₄	—	4	2	no	—
636	C₄	—	4	2	no	—
637	C₄	—	8	1	no	—
638	C₄	—	8	1	no	—
639	C₄	C₅×#525	1	1	yes	characteristic
640	C₄	C₅×#525	1	1	yes	characteristic
641	C₄	C₅×#548	1	1	yes	characteristic
642	C₄	C₅×#548	1	1	yes	characteristic
643	C₂	—	2	1	no	—
644	C₂	—	2	1	no	—
645	C₂	—	8	2	no	—
646	C₂	C₅×#2463	1	1	yes	characteristic
647	C₂	C₅×#3289	1	1	yes	characteristic
648	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×D₄	C₂³
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
3. C₅×#2950	C₂	semidirect
5. C₅×#2047	C₂	semidirect
7. C₅×#2028	C₂	semidirect
10. C₅×#1930	C₂	semidirect
11. C₅×#1922	C₂	semidirect
12. C₅×#1922	C₂	semidirect
15. C₅×#1857	C₂	semidirect
67. #26922	C₅	direct (N × H)
154. #3082	C₂×C₅	semidirect
156. #2950	C₂×C₅	semidirect
158. #2047	C₂×C₅	semidirect
160. #2028	C₂×C₅	semidirect
163. #1930	C₂×C₅	semidirect
164. #1922	C₂×C₅	semidirect
165. #1922	C₂×C₅	semidirect
168. #1857	C₂×C₅	semidirect
616. C₅	#26922	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×#2950	2
C₅×#2949	2
C₅×#2047	2
C₅×#2046	2
C₅×#2028	2
C₅×#2015	2
C₅×#1931	2
C₅×#1930	2
C₅×#1922	2
C₅×#1888	2
C₅×#1885	2
C₅×#1857	2
#26922	5

Subgroups — C5×#26922 #11949642

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#26922 #11949642