Subgroups — C₅×#61111 #11983831

Order 1280.

2600 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3586	C₂	1	4	yes	maximal, complemented
2	C₅×#3293	C₂	1	4	yes	maximal, complemented
3	C₅×#3291	C₂	1	4	yes	maximal, complemented
4	C₅×#3289	C₂	1	8	yes	maximal, complemented
5	C₅×#3152	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#3069	C₂	1	4	yes	maximal, complemented
7	C₅×#3018	C₂	1	2	yes	maximal, complemented
8	C₂×C₅×#456	C₂	1	2	yes	maximal, complemented
9	C₅×#2956	C₂	1	2	yes	maximal, complemented
10	C₅×#585	C₂²	1	2	yes	complemented
11	C₂×C₅×2₋¹⁺⁴	C₂²	1	2	yes	—
12	C₅×#578	—	2	8	no	—
13	C₅×#578	C₂²	1	16	yes	complemented
14	C₅×#577	—	2	8	no	—
15	C₅×#577	C₂²	1	16	yes	complemented
16	C₅×#575	—	2	8	no	—
17	C₅×#575	C₂²	1	4	yes	—
18	C₅×#575	C₂²	1	2	yes	—
19	C₂×C₅×#137	—	2	8	no	—
20	C₂×C₅×#137	C₂²	1	4	yes	complemented
21	C₂×C₅×#137	C₂²	1	4	yes	complemented
22	C₅×#568	C₂²	1	4	yes	complemented
23	C₅×#532	C₂²	1	1	yes	characteristic
24	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
25	C₅×#497	C₂²	1	4	yes	complemented
26	C₅×#494	C₂²	1	2	yes	complemented
27	C₅×#492	C₂²	1	2	yes	complemented
28	C₅×#473	C₂²	1	16	yes	complemented
29	C₅×#471	C₂²	1	16	yes	complemented
30	C₅×#456	C₂²	1	8	yes	complemented
31	C₅×#456	C₂²	1	8	yes	complemented
32	C₅×#456	C₂²	1	4	yes	complemented
33	C₅×#455	C₂²	1	4	yes	complemented
34	C₅×#454	C₂²	1	4	yes	complemented
35	C₅×#453	C₂²	1	4	yes	complemented
36	C₅×#444	C₂²	1	8	yes	complemented
37	C₅×#443	C₂²	1	8	yes	complemented
38	C₅×#430	C₂²	1	2	yes	complemented
39	C₂×C₅×#104	C₂²	1	4	yes	complemented
40	C₅×#413	C₂²	1	2	yes	complemented
41	C₂×C₅×#101	C₂²	1	2	yes	complemented
42	C₄×C₅×M₁₆	C₂²	1	1	yes	characteristic, complemented
43	#61111	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₅×2₋¹⁺⁴	—	2	8	no	—
45	C₅×2₋¹⁺⁴	—	2	4	no	—
46	C₅×2₋¹⁺⁴	—	4	2	no	—
47	C₅×2₋¹⁺⁴	C₂³	1	4	yes	—
48	C₅×2₋¹⁺⁴	C₂³	1	8	yes	—
49	C₅×H(5,𝔽₂)	—	2	4	no	—
50	C₅×H(5,𝔽₂)	—	4	2	no	—
51	C₅×H(5,𝔽₂)	C₂³	1	4	yes	—
52	C₂×C₅×#41	—	2	8	no	—
53	C₂×C₅×#41	—	2	4	no	—
54	C₂×C₅×#41	—	4	2	no	—
55	C₂×C₅×#41	—	4	2	no	—
56	C₂×C₅×#41	C₂³	1	4	yes	—
57	C₂×C₅×#41	C₂³	1	2	yes	—
58	C₂²×C₅×Q₈	—	2	4	no	—
59	C₂²×C₅×Q₈	C₂³	1	2	yes	—
60	C₅×#137	—	2	8	no	—
61	C₅×#137	—	2	4	no	—
62	C₅×#137	—	2	16	no	—
63	C₅×#137	—	2	16	no	—
64	C₅×#137	—	2	16	no	—
65	C₅×#137	—	2	8	no	—
66	C₅×#137	—	2	8	no	—
67	C₅×#137	D₄	1	8	yes	complemented
68	C₅×#137	C₂³	1	8	yes	—
69	C₅×#137	C₂³	1	16	yes	—
70	C₅×AGL(1,ℤ/8)	—	2	4	no	—
71	C₅×AGL(1,ℤ/8)	—	2	16	no	—
72	C₅×AGL(1,ℤ/8)	D₄	1	8	yes	complemented
73	C₅×AGL(1,ℤ/8)	C₂³	1	8	yes	—
74	C₅×#135	—	2	8	no	—
75	C₅×#135	—	2	16	no	—
76	C₅×#135	—	2	16	no	—
77	C₅×#135	C₂³	1	8	yes	—
78	C₂×C₅×Q₁₆	—	2	4	no	—
79	C₂×C₅×Q₁₆	—	2	16	no	—
80	C₂×C₅×Q₁₆	C₂³	1	8	yes	—
81	C₂×C₅×SD₁₆	—	2	4	no	—
82	C₂×C₅×SD₁₆	—	2	16	no	—
83	C₂×C₅×SD₁₆	C₂³	1	8	yes	—
84	C₅×#131	—	2	8	no	—
85	C₅×#131	C₂³	1	16	yes	—
86	C₂×C₅×M₁₆	—	2	8	no	—
87	C₂×C₅×M₁₆	C₂³	1	4	yes	—
88	C₂×C₅×M₁₆	C₂³	1	2	yes	—
89	C₅×C₄⋊Q₈	—	4	1	no	—
90	C₅×C₄⋊Q₈	C₂³	1	2	yes	—
91	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
92	C₅×C₄⋊Q₈	C₂³	1	2	yes	—
93	C₅×#127	C₂³	1	1	yes	characteristic
94	C₅×#124	C₂³	1	2	yes	—
95	C₅×#121	—	4	1	no	—
96	C₄×C₅×D₄	—	4	1	no	—
97	C₂×C₅×C₄⋊C₄	—	4	1	no	—
98	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
99	C₅×#108	C₂³	1	8	yes	—
100	C₅×#104	C₂³	1	8	yes	—
101	C₅×#104	C₂³	1	8	yes	—
102	C₅×#101	C₂³	1	8	yes	—
103	C₅×#101	C₂³	1	4	yes	—
104	C₅×#100	C₂³	1	4	yes	—
105	C₅×#97	C₂³	1	2	yes	—
106	C₄×C₅×C₈	C₂³	1	2	yes	—
107	#3586	C₂×C₅	1	4	yes	complemented
108	#3293	C₂×C₅	1	4	yes	complemented
109	#3291	C₂×C₅	1	4	yes	complemented
110	#3289	C₂×C₅	1	8	yes	complemented
111	#3152	C₂×C₅	1	1	yes	characteristic, complemented
112	#3069	C₂×C₅	1	4	yes	complemented
113	#3018	C₂×C₅	1	2	yes	complemented
114	C₂×#456	C₂×C₅	1	2	yes	complemented
115	#2956	C₂×C₅	1	2	yes	complemented
116	C₅×#41	—	2	4	no	—
117	C₅×#41	—	2	4	no	—
118	C₅×#41	—	2	8	no	—
119	C₅×#41	—	2	16	no	—
120	C₅×#41	—	2	8	no	—
121	C₅×#41	—	2	4	no	—
122	C₅×#41	—	2	4	no	—
123	C₅×#41	—	4	4	no	—
124	C₅×#41	—	4	4	no	—
125	C₅×#41	—	4	8	no	—
126	C₅×#41	—	4	8	no	—
127	C₅×#41	—	4	8	no	—
128	C₅×#41	—	4	8	no	—
129	C₅×#41	—	4	4	no	—
130	C₅×#41	C₂×D₄	1	8	yes	—
131	C₅×#41	C₂⁴	1	8	yes	—
132	C₂×C₅×Q₈	—	2	2	no	—
133	C₂×C₅×Q₈	—	2	16	no	—
134	C₂×C₅×Q₈	—	2	8	no	—
135	C₂×C₅×Q₈	—	2	4	no	—
136	C₂×C₅×Q₈	—	2	4	no	—
137	C₂×C₅×Q₈	—	4	2	no	—
138	C₂×C₅×Q₈	—	4	8	no	—
139	C₂×C₅×Q₈	—	4	2	no	—
140	C₂×C₅×Q₈	C₂×D₄	1	4	yes	—
141	C₂×C₅×Q₈	C₂⁴	1	2	yes	—
142	C₂×C₅×Q₈	C₂⁴	1	4	yes	—
143	C₂×C₅×D₄	—	2	4	no	—
144	C₂×C₅×D₄	—	2	8	no	—
145	C₂×C₅×D₄	—	2	2	no	—
146	C₂×C₅×D₄	—	4	1	no	—
147	C₂×C₅×D₄	—	4	4	no	—
148	C₂×C₅×D₄	—	4	2	no	—
149	C₂×C₅×D₄	—	4	8	no	—
150	C₂×C₅×D₄	—	4	2	no	—
151	C₂×C₅×D₄	C₂×D₄	1	4	yes	—
152	C₂×C₅×D₄	C₂⁴	1	2	yes	—
153	C₂²×C₄×C₅	—	2	4	no	—
154	C₂²×C₄×C₅	—	2	1	no	—
155	C₂²×C₄×C₅	—	2	2	no	—
156	C₂²×C₄×C₅	—	2	2	no	—
157	C₂²×C₄×C₅	—	4	4	no	—
158	C₂²×C₄×C₅	—	4	4	no	—
159	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
160	C₅×Q₁₆	—	2	16	no	—
161	C₅×Q₁₆	—	2	8	no	—
162	C₅×Q₁₆	—	2	16	no	—
163	C₅×Q₁₆	C₂×D₄	1	8	yes	—
164	C₅×SD₁₆	—	2	8	no	—
165	C₅×SD₁₆	—	2	16	no	—
166	C₅×SD₁₆	—	2	8	no	—
167	C₅×SD₁₆	—	2	16	no	—
168	C₅×SD₁₆	C₂×D₄	1	16	yes	—
169	C₅×D₈	—	2	8	no	—
170	C₅×D₈	C₂×D₄	1	8	yes	—
171	C₅×M₁₆	—	2	4	no	—
172	C₅×M₁₆	—	2	16	no	—
173	C₅×M₁₆	C₂×D₄	1	8	yes	—
174	C₅×M₁₆	C₂⁴	1	8	yes	—
175	C₂×C₅×C₈	—	2	4	no	—
176	C₂×C₅×C₈	—	2	16	no	—
177	C₂×C₅×C₈	C₂⁴	1	4	yes	—
178	C₅×C₄⋊C₄	—	4	2	no	—
179	C₅×C₄⋊C₄	—	4	2	no	—
180	C₅×C₄⋊C₄	—	4	1	no	—
181	C₅×C₂²⋊C₄	—	4	2	no	—
182	C₄²×C₅	—	2	1	no	—
183	C₄²×C₅	C₂⁴	1	1	yes	characteristic
184	C₄²×C₅	C₂⁴	1	1	yes	characteristic
185	#585	C₂²×C₅	1	2	yes	complemented
186	C₂×2₋¹⁺⁴	C₂²×C₅	1	2	yes	—
187	#578	—	2	8	no	—
188	#578	C₂²×C₅	1	16	yes	complemented
189	#577	—	2	8	no	—
190	#577	C₂²×C₅	1	16	yes	complemented
191	#575	—	2	8	no	—
192	#575	C₂²×C₅	1	4	yes	—
193	#575	C₂²×C₅	1	2	yes	—
194	C₂×#137	—	2	8	no	—
195	C₂×#137	C₂²×C₅	1	4	yes	complemented
196	C₂×#137	C₂²×C₅	1	4	yes	complemented
197	#568	C₂²×C₅	1	4	yes	complemented
198	#532	C₂²×C₅	1	1	yes	characteristic
199	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
200	#497	C₂²×C₅	1	4	yes	complemented
201	#494	C₂²×C₅	1	2	yes	complemented
202	#492	C₂²×C₅	1	2	yes	complemented
203	#473	C₂²×C₅	1	16	yes	complemented
204	#471	C₂²×C₅	1	16	yes	complemented
205	#456	C₂²×C₅	1	8	yes	complemented
206	#456	C₂²×C₅	1	8	yes	complemented
207	#456	C₂²×C₅	1	4	yes	complemented
208	#455	C₂²×C₅	1	4	yes	complemented
209	#454	C₂²×C₅	1	4	yes	complemented
210	#453	C₂²×C₅	1	4	yes	complemented
211	#444	C₂²×C₅	1	8	yes	complemented
212	#443	C₂²×C₅	1	8	yes	complemented
213	#430	C₂²×C₅	1	2	yes	complemented
214	C₂×#104	C₂²×C₅	1	4	yes	complemented
215	#413	C₂²×C₅	1	2	yes	complemented
216	C₂×#101	C₂²×C₅	1	2	yes	complemented
217	C₄×M₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
218	C₂³×C₅	—	2	4	no	—
219	C₂³×C₅	—	2	2	no	—
220	C₂³×C₅	—	4	4	no	—
221	C₂³×C₅	H(5,𝔽₂)	1	1	yes	characteristic
222	C₅×Q₈	—	2	4	no	—
223	C₅×Q₈	—	2	8	no	—
224	C₅×Q₈	—	2	4	no	—
225	C₅×Q₈	—	4	8	no	—
226	C₅×Q₈	—	4	4	no	—
227	C₅×Q₈	—	4	4	no	—
228	C₅×Q₈	C₂²×D₄	1	8	yes	—
229	C₅×D₄	—	2	8	no	—
230	C₅×D₄	—	2	8	no	—
231	C₅×D₄	—	2	4	no	—
232	C₅×D₄	—	2	4	no	—
233	C₅×D₄	—	4	8	no	—
234	C₅×D₄	—	4	4	no	—
235	C₅×D₄	—	4	8	no	—
236	C₅×D₄	—	4	4	no	—
237	C₅×D₄	—	8	2	no	—
238	C₅×D₄	C₂²×D₄	1	8	yes	—
239	C₂×C₄×C₅	—	2	4	no	—
240	C₂×C₄×C₅	—	2	1	no	—
241	C₂×C₄×C₅	—	2	8	no	—
242	C₂×C₄×C₅	—	2	8	no	—
243	C₂×C₄×C₅	—	2	1	no	—
244	C₂×C₄×C₅	—	2	2	no	—
245	C₂×C₄×C₅	—	2	4	no	—
246	C₂×C₄×C₅	—	4	4	no	—
247	C₂×C₄×C₅	—	4	8	no	—
248	C₂×C₄×C₅	—	4	16	no	—
249	C₂×C₄×C₅	—	4	2	no	—
250	C₂×C₄×C₅	—	4	2	no	—
251	C₂×C₄×C₅	—	4	2	no	—
252	C₂×C₄×C₅	—	4	2	no	—
253	C₂×C₄×C₅	—	4	2	no	—
254	C₂×C₄×C₅	C₂²×D₄	1	4	yes	—
255	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
256	C₂×C₄×C₅	C₂⁵	1	1	yes	characteristic
257	C₅×C₈	—	2	8	no	—
258	C₅×C₈	C₂²×D₄	1	8	yes	—
259	2₋¹⁺⁴	—	2	8	no	—
260	2₋¹⁺⁴	—	2	4	no	—
261	2₋¹⁺⁴	—	4	2	no	—
262	2₋¹⁺⁴	C₂³×C₅	1	8	yes	—
263	2₋¹⁺⁴	C₂³×C₅	1	4	yes	—
264	H(5,𝔽₂)	—	2	4	no	—
265	H(5,𝔽₂)	—	4	2	no	—
266	H(5,𝔽₂)	C₂³×C₅	1	4	yes	—
267	C₂×#41	—	2	8	no	—
268	C₂×#41	—	2	4	no	—
269	C₂×#41	—	4	2	no	—
270	C₂×#41	—	4	2	no	—
271	C₂×#41	C₂³×C₅	1	4	yes	—
272	C₂×#41	C₂³×C₅	1	2	yes	—
273	C₂²×Q₈	—	2	4	no	—
274	C₂²×Q₈	C₂³×C₅	1	2	yes	—
275	#137	—	2	8	no	—
276	#137	—	2	4	no	—
277	#137	—	2	16	no	—
278	#137	—	2	16	no	—
279	#137	—	2	16	no	—
280	#137	—	2	8	no	—
281	#137	—	2	8	no	—
282	#137	C₅×D₄	1	8	yes	complemented
283	#137	C₂³×C₅	1	16	yes	—
284	#137	C₂³×C₅	1	8	yes	—
285	AGL(1,ℤ/8)	—	2	4	no	—
286	AGL(1,ℤ/8)	—	2	16	no	—
287	AGL(1,ℤ/8)	C₅×D₄	1	8	yes	complemented
288	AGL(1,ℤ/8)	C₂³×C₅	1	8	yes	—
289	#135	—	2	8	no	—
290	#135	—	2	16	no	—
291	#135	—	2	16	no	—
292	#135	C₂³×C₅	1	8	yes	—
293	C₂×Q₁₆	—	2	4	no	—
294	C₂×Q₁₆	—	2	16	no	—
295	C₂×Q₁₆	C₂³×C₅	1	8	yes	—
296	C₂×SD₁₆	—	2	4	no	—
297	C₂×SD₁₆	—	2	16	no	—
298	C₂×SD₁₆	C₂³×C₅	1	8	yes	—
299	#131	—	2	8	no	—
300	#131	C₂³×C₅	1	16	yes	—
301	C₂×M₁₆	—	2	8	no	—
302	C₂×M₁₆	C₂³×C₅	1	4	yes	—
303	C₂×M₁₆	C₂³×C₅	1	2	yes	—
304	C₄⋊Q₈	—	4	1	no	—
305	C₄⋊Q₈	C₂³×C₅	1	2	yes	—
306	C₄⋊Q₈	C₂³×C₅	1	2	yes	—
307	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
308	#127	C₂³×C₅	1	1	yes	characteristic
309	#124	C₂³×C₅	1	2	yes	—
310	#121	—	4	1	no	—
311	C₄×D₄	—	4	1	no	—
312	C₂×C₄⋊C₄	—	4	1	no	—
313	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
314	#108	C₂³×C₅	1	8	yes	—
315	#104	C₂³×C₅	1	8	yes	—
316	#104	C₂³×C₅	1	8	yes	—
317	#101	C₂³×C₅	1	8	yes	—
318	#101	C₂³×C₅	1	4	yes	—
319	#100	C₂³×C₅	1	4	yes	—
320	#97	C₂³×C₅	1	2	yes	—
321	C₄×C₈	C₂³×C₅	1	2	yes	—
322	C₂²×C₅	—	2	8	no	—
323	C₂²×C₅	—	4	1	no	—
324	C₂²×C₅	—	4	2	no	—
325	C₂²×C₅	—	8	4	no	—
326	C₂²×C₅	—	8	2	no	—
327	C₂²×C₅	—	16	4	no	—
328	C₂²×C₅	D₄²	1	2	yes	—
329	C₂²×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
330	C₄×C₅	—	2	2	no	—
331	C₄×C₅	—	2	8	no	—
332	C₄×C₅	—	4	1	no	—
333	C₄×C₅	—	4	2	no	—
334	C₄×C₅	—	4	4	no	—
335	C₄×C₅	D₄²	1	2	yes	—
336	C₄×C₅	C₂³×D₄	1	2	yes	—
337	#41	—	2	4	no	—
338	#41	—	2	4	no	—
339	#41	—	2	8	no	—
340	#41	—	2	16	no	—
341	#41	—	2	8	no	—
342	#41	—	2	4	no	—
343	#41	—	2	4	no	—
344	#41	—	4	4	no	—
345	#41	—	4	4	no	—
346	#41	—	4	8	no	—
347	#41	—	4	8	no	—
348	#41	—	4	8	no	—
349	#41	—	4	8	no	—
350	#41	—	4	4	no	—
351	#41	C₂×C₅×D₄	1	8	yes	—
352	#41	C₂⁴×C₅	1	8	yes	—
353	C₂×Q₈	—	2	2	no	—
354	C₂×Q₈	—	2	16	no	—
355	C₂×Q₈	—	2	8	no	—
356	C₂×Q₈	—	2	4	no	—
357	C₂×Q₈	—	2	4	no	—
358	C₂×Q₈	—	4	2	no	—
359	C₂×Q₈	—	4	8	no	—
360	C₂×Q₈	—	4	2	no	—
361	C₂×Q₈	C₂×C₅×D₄	1	4	yes	—
362	C₂×Q₈	C₂⁴×C₅	1	2	yes	—
363	C₂×Q₈	C₂⁴×C₅	1	4	yes	—
364	C₂×D₄	—	2	4	no	—
365	C₂×D₄	—	2	8	no	—
366	C₂×D₄	—	2	2	no	—
367	C₂×D₄	—	4	1	no	—
368	C₂×D₄	—	4	4	no	—
369	C₂×D₄	—	4	2	no	—
370	C₂×D₄	—	4	8	no	—
371	C₂×D₄	—	4	2	no	—
372	C₂×D₄	C₂×C₅×D₄	1	4	yes	—
373	C₂×D₄	C₂⁴×C₅	1	2	yes	—
374	C₂²×C₄	—	2	4	no	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	4	4	no	—
379	C₂²×C₄	—	4	4	no	—
380	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
381	Q₁₆	—	2	16	no	—
382	Q₁₆	—	2	8	no	—
383	Q₁₆	—	2	16	no	—
384	Q₁₆	C₂×C₅×D₄	1	8	yes	—
385	SD₁₆	—	2	8	no	—
386	SD₁₆	—	2	16	no	—
387	SD₁₆	—	2	8	no	—
388	SD₁₆	—	2	16	no	—
389	SD₁₆	C₂×C₅×D₄	1	16	yes	—
390	D₈	—	2	8	no	—
391	D₈	C₂×C₅×D₄	1	8	yes	—
392	M₁₆	—	2	4	no	—
393	M₁₆	—	2	16	no	—
394	M₁₆	C₂×C₅×D₄	1	8	yes	—
395	M₁₆	C₂⁴×C₅	1	8	yes	—
396	C₂×C₈	—	2	4	no	—
397	C₂×C₈	—	2	16	no	—
398	C₂×C₈	C₂⁴×C₅	1	4	yes	—
399	C₄⋊C₄	—	4	2	no	—
400	C₄⋊C₄	—	4	2	no	—
401	C₄⋊C₄	—	4	1	no	—
402	C₂²⋊C₄	—	4	2	no	—
403	C₄²	—	2	1	no	—
404	C₄²	C₂⁴×C₅	1	1	yes	characteristic
405	C₄²	C₂⁴×C₅	1	1	yes	characteristic
406	C₂×C₅	—	2	1	no	—
407	C₂×C₅	—	2	2	no	—
408	C₂×C₅	—	4	8	no	—
409	C₂×C₅	—	8	2	no	—
410	C₂×C₅	C₂×D₄²	1	1	yes	characteristic
411	C₂³	—	2	4	no	—
412	C₂³	—	2	2	no	—
413	C₂³	—	4	4	no	—
414	C₂³	C₅×H(5,𝔽₂)	1	1	yes	characteristic
415	Q₈	—	2	4	no	—
416	Q₈	—	2	8	no	—
417	Q₈	—	2	4	no	—
418	Q₈	—	4	8	no	—
419	Q₈	—	4	4	no	—
420	Q₈	—	4	4	no	—
421	Q₈	C₂²×C₅×D₄	1	8	yes	—
422	D₄	—	2	8	no	—
423	D₄	—	2	8	no	—
424	D₄	—	2	4	no	—
425	D₄	—	2	4	no	—
426	D₄	—	4	8	no	—
427	D₄	—	4	4	no	—
428	D₄	—	4	8	no	—
429	D₄	—	4	4	no	—
430	D₄	—	8	2	no	—
431	D₄	C₂²×C₅×D₄	1	8	yes	—
432	C₂×C₄	—	2	4	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	8	no	—
435	C₂×C₄	—	2	8	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	4	no	—
439	C₂×C₄	—	4	4	no	—
440	C₂×C₄	—	4	8	no	—
441	C₂×C₄	—	4	16	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	C₂²×C₅×D₄	1	4	yes	—
448	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
449	C₂×C₄	C₂⁵×C₅	1	1	yes	characteristic
450	C₈	—	2	8	no	—
451	C₈	C₂²×C₅×D₄	1	8	yes	—
452	C₅	#61111	1	1	yes	characteristic, direct product factor, Sylow
453	C₂²	—	2	8	no	—
454	C₂²	—	4	1	no	—
455	C₂²	—	4	2	no	—
456	C₂²	—	8	4	no	—
457	C₂²	—	8	2	no	—
458	C₂²	—	16	4	no	—
459	C₂²	C₅×D₄²	1	2	yes	—
460	C₂²	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
461	C₄	—	2	2	no	—
462	C₄	—	2	8	no	—
463	C₄	—	4	1	no	—
464	C₄	—	4	2	no	—
465	C₄	—	4	4	no	—
466	C₄	C₅×D₄²	1	2	yes	—
467	C₄	C₂³×C₅×D₄	1	2	yes	—
468	C₂	—	2	1	no	—
469	C₂	—	2	2	no	—
470	C₂	—	4	8	no	—
471	C₂	—	8	2	no	—
472	C₂	C₂×C₅×D₄²	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₅	C₂×D₄²
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₅ ◁ C₂²×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×#3586	C₂	semidirect
2. C₅×#3293	C₂	semidirect
3. C₅×#3291	C₂	semidirect
4. C₅×#3289	C₂	semidirect
5. C₅×#3152	C₂	semidirect
6. C₅×#3069	C₂	semidirect
7. C₅×#3018	C₂	semidirect
8. C₂×C₅×#456	C₂	semidirect
9. C₅×#2956	C₂	semidirect
10. C₅×#585	C₂²	semidirect
13. C₅×#578	C₂²	semidirect
15. C₅×#577	C₂²	semidirect
20. C₂×C₅×#137	C₂²	semidirect
21. C₂×C₅×#137	C₂²	semidirect
22. C₅×#568	C₂²	semidirect
24. C₂×C₅×C₄⋊Q₈	C₂²	semidirect
25. C₅×#497	C₂²	semidirect
26. C₅×#494	C₂²	semidirect
27. C₅×#492	C₂²	semidirect
28. C₅×#473	C₂²	semidirect
29. C₅×#471	C₂²	semidirect
30. C₅×#456	C₂²	semidirect
31. C₅×#456	C₂²	semidirect
32. C₅×#456	C₂²	semidirect
33. C₅×#455	C₂²	semidirect
34. C₅×#454	C₂²	semidirect
35. C₅×#453	C₂²	semidirect
36. C₅×#444	C₂²	semidirect
37. C₅×#443	C₂²	semidirect
38. C₅×#430	C₂²	semidirect
39. C₂×C₅×#104	C₂²	semidirect
40. C₅×#413	C₂²	semidirect
41. C₂×C₅×#101	C₂²	semidirect
42. C₄×C₅×M₁₆	C₂²	semidirect
43. #61111	C₅	direct (N × H)
67. C₅×#137	D₄	semidirect
72. C₅×AGL(1,ℤ/8)	D₄	semidirect
107. #3586	C₂×C₅	semidirect
108. #3293	C₂×C₅	semidirect
109. #3291	C₂×C₅	semidirect
110. #3289	C₂×C₅	semidirect
111. #3152	C₂×C₅	semidirect
112. #3069	C₂×C₅	semidirect
113. #3018	C₂×C₅	semidirect
114. C₂×#456	C₂×C₅	semidirect
115. #2956	C₂×C₅	semidirect
185. #585	C₂²×C₅	semidirect
188. #578	C₂²×C₅	semidirect
190. #577	C₂²×C₅	semidirect
195. C₂×#137	C₂²×C₅	semidirect
196. C₂×#137	C₂²×C₅	semidirect
197. #568	C₂²×C₅	semidirect
199. C₂×C₄⋊Q₈	C₂²×C₅	semidirect
200. #497	C₂²×C₅	semidirect
201. #494	C₂²×C₅	semidirect
202. #492	C₂²×C₅	semidirect
203. #473	C₂²×C₅	semidirect
204. #471	C₂²×C₅	semidirect
205. #456	C₂²×C₅	semidirect
206. #456	C₂²×C₅	semidirect
207. #456	C₂²×C₅	semidirect
208. #455	C₂²×C₅	semidirect
209. #454	C₂²×C₅	semidirect
210. #453	C₂²×C₅	semidirect
211. #444	C₂²×C₅	semidirect
212. #443	C₂²×C₅	semidirect
213. #430	C₂²×C₅	semidirect
214. C₂×#104	C₂²×C₅	semidirect
215. #413	C₂²×C₅	semidirect
216. C₂×#101	C₂²×C₅	semidirect
217. C₄×M₁₆	C₂²×C₅	semidirect
282. #137	C₅×D₄	semidirect
287. AGL(1,ℤ/8)	C₅×D₄	semidirect
452. C₅	#61111	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×#3586	2
C₅×#3293	2
C₅×#3291	2
C₅×#3289	2
C₅×#3152	2
C₅×#3069	2
C₅×#3018	2
C₂×C₅×#456	2
C₅×#2956	2
#61111	5

Subgroups — C5×#61111 #11983831

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#61111 #11983831