Subgroups — C₅×#19312 #11942032

Order 1280.

768 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3151	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#3115	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#3038	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2970	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1688	C₂	1	2	yes	maximal, complemented
6	C₅×#1686	C₂	1	2	yes	maximal, complemented
7	C₅×#1667	C₂	1	2	yes	maximal, complemented
8	C₅×#1665	C₂	1	2	yes	maximal, complemented
9	C₅×#1569	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1557	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1555	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×AGL(1,ℤ/8)	—	2	1	no	—
13	C₂×C₅×AGL(1,ℤ/8)	—	2	2	no	—
14	C₅×#532	C₂²	1	1	yes	characteristic
15	C₂×C₅×#127	C₂²	1	1	yes	characteristic
16	C₄×C₅×#41	C₂²	1	1	yes	characteristic
17	C₅×#496	—	2	1	no	—
18	C₅×#496	—	2	1	no	—
19	C₅×#493	C₂²	1	2	yes	—
20	C₅×#492	C₂²	1	2	yes	—
21	C₅×#482	—	2	1	no	—
22	C₅×#475	C₂²	1	1	yes	characteristic, complemented
23	C₅×#474	C₂²	1	1	yes	characteristic, complemented
24	C₅×#460	—	2	1	no	—
25	C₅×#460	C₂²	1	2	yes	—
26	C₅×#460	C₂²	1	1	yes	characteristic, complemented
27	C₅×#459	—	2	1	no	—
28	C₅×#459	C₂²	1	2	yes	—
29	C₅×#459	C₂²	1	1	yes	characteristic, complemented
30	C₅×#449	—	2	1	no	—
31	C₅×#446	C₂²	1	2	yes	complemented
32	C₅×#442	—	2	1	no	—
33	C₅×#440	—	2	1	no	—
34	C₅×#435	—	2	2	no	—
35	C₅×C₈×D₄	C₂²	1	2	yes	complemented
36	C₅×#432	—	2	1	no	—
37	C₅×#432	C₂²	1	1	yes	characteristic
38	C₅×#432	C₂²	1	1	yes	characteristic
39	C₅×#423	C₂²	1	1	yes	characteristic
40	C₅×#418	—	2	1	no	—
41	C₄×C₅×M₁₆	C₂²	1	1	yes	characteristic
42	C₂×C₅×#97	—	2	1	no	—
43	C₅×#335	C₂²	1	2	yes	complemented
44	C₅×#334	C₂²	1	2	yes	complemented
45	C₅×#332	C₂²	1	2	yes	complemented
46	C₅×#331	C₂²	1	2	yes	—
47	C₅×#331	C₂²	1	2	yes	—
48	C₅×#331	C₂²	1	2	yes	complemented
49	#19312	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
50	C₂×C₅×#41	—	2	1	no	—
51	C₂×C₅×#41	D₄	1	1	yes	characteristic
52	C₂²×C₅×D₄	—	2	1	no	—
53	C₂²×C₅×D₄	—	2	1	no	—
54	C₂²×C₅×D₄	—	2	1	no	—
55	C₅×AGL(1,ℤ/8)	—	4	8	no	—
56	C₅×AGL(1,ℤ/8)	—	4	4	no	—
57	C₂×C₅×SD₁₆	—	2	1	no	—
58	C₂×C₅×SD₁₆	—	2	2	no	—
59	C₂×C₅×SD₁₆	—	2	2	no	—
60	C₂×C₅×SD₁₆	—	2	2	no	—
61	C₂×C₅×D₈	—	2	1	no	—
62	C₂×C₅×D₈	—	2	2	no	—
63	C₂×C₅×D₈	—	2	2	no	—
64	C₂×C₅×D₈	—	2	2	no	—
65	C₂×C₅×M₁₆	—	2	1	no	—
66	C₂×C₅×M₁₆	D₄	1	2	yes	—
67	C₂²×C₅×C₈	—	2	2	no	—
68	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
69	C₅×#127	—	2	1	no	—
70	C₅×#127	—	2	1	no	—
71	C₅×#127	—	2	1	no	—
72	C₅×#127	C₂³	1	2	yes	—
73	C₅×#127	C₂³	1	1	yes	characteristic
74	C₅×#124	—	2	1	no	—
75	C₅×#121	—	2	1	no	—
76	C₅×#121	—	2	1	no	—
77	C₄×C₅×Q₈	D₄	1	1	yes	characteristic
78	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
79	C₄×C₅×D₄	—	2	1	no	—
80	C₄×C₅×D₄	—	2	1	no	—
81	C₄×C₅×D₄	—	2	1	no	—
82	C₄×C₅×D₄	—	2	1	no	—
83	C₄×C₅×D₄	D₄	1	1	yes	characteristic
84	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
85	C₅×#117	—	2	1	no	—
86	C₅×#117	D₄	1	1	yes	characteristic
87	C₂×C₄²×C₅	—	2	1	no	—
88	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
89	C₅×#107	—	2	1	no	—
90	C₅×#106	—	2	1	no	—
91	C₅×C₄⋊C₈	—	2	2	no	—
92	C₅×C₄⋊C₈	—	2	1	no	—
93	C₅×C₄⋊C₈	C₂³	1	2	yes	—
94	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
95	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
96	C₅×C₄⋊C₈	C₂³	1	2	yes	—
97	C₅×#103	—	2	1	no	—
98	C₅×#102	—	2	1	no	—
99	C₅×#102	—	2	2	no	—
100	C₅×#102	—	2	2	no	—
101	C₅×#102	—	2	1	no	—
102	C₅×#102	—	2	1	no	—
103	C₅×C₂²⋊C₈	—	2	1	no	—
104	C₅×C₂²⋊C₈	—	2	1	no	—
105	C₅×C₂²⋊C₈	—	2	2	no	—
106	C₅×#97	—	2	2	no	—
107	C₅×#97	—	2	1	no	—
108	C₅×#97	—	2	1	no	—
109	C₅×#97	D₄	1	1	yes	characteristic
110	C₅×#97	D₄	1	1	yes	characteristic
111	C₄×C₅×C₈	C₂³	1	2	yes	—
112	#3151	C₂×C₅	1	1	yes	characteristic, complemented
113	#3115	C₂×C₅	1	1	yes	characteristic, complemented
114	#3038	C₂×C₅	1	1	yes	characteristic, complemented
115	#2970	C₂×C₅	1	1	yes	characteristic, complemented
116	#1688	C₂×C₅	1	2	yes	complemented
117	#1686	C₂×C₅	1	2	yes	complemented
118	#1667	C₂×C₅	1	2	yes	complemented
119	#1665	C₂×C₅	1	2	yes	complemented
120	#1569	C₂×C₅	1	1	yes	characteristic, complemented
121	#1557	C₂×C₅	1	1	yes	characteristic, complemented
122	#1555	C₂×C₅	1	1	yes	characteristic, complemented
123	C₂⁴×C₅	—	4	1	no	—
124	C₅×#41	—	2	2	no	—
125	C₅×#41	—	4	1	no	—
126	C₅×#41	—	4	4	no	—
127	C₂×C₅×Q₈	—	2	1	no	—
128	C₂×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
129	C₂×C₅×D₄	—	2	1	no	—
130	C₂×C₅×D₄	—	2	1	no	—
131	C₂×C₅×D₄	—	2	1	no	—
132	C₂×C₅×D₄	—	2	2	no	—
133	C₂×C₅×D₄	—	2	2	no	—
134	C₂×C₅×D₄	—	2	1	no	—
135	C₂×C₅×D₄	—	2	2	no	—
136	C₂×C₅×D₄	—	4	4	no	—
137	C₂×C₅×D₄	—	4	2	no	—
138	C₂×C₅×D₄	—	4	2	no	—
139	C₂×C₅×D₄	—	4	1	no	—
140	C₂×C₅×D₄	—	4	1	no	—
141	C₂×C₅×D₄	—	4	1	no	—
142	C₂×C₅×D₄	—	4	1	no	—
143	C₂×C₅×D₄	—	8	2	no	—
144	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₅	—	2	1	no	—
146	C₂²×C₄×C₅	—	2	1	no	—
147	C₂²×C₄×C₅	—	2	1	no	—
148	C₂²×C₄×C₅	—	4	1	no	—
149	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₅	#41	1	1	yes	characteristic
152	C₅×SD₁₆	—	4	4	no	—
153	C₅×SD₁₆	—	4	2	no	—
154	C₅×SD₁₆	—	4	4	no	—
155	C₅×SD₁₆	—	4	4	no	—
156	C₅×D₈	—	4	4	no	—
157	C₅×D₈	—	4	2	no	—
158	C₅×D₈	—	4	4	no	—
159	C₅×D₈	—	4	4	no	—
160	C₅×M₁₆	—	2	4	no	—
161	C₅×M₁₆	—	4	2	no	—
162	C₂×C₅×C₈	—	2	2	no	—
163	C₂×C₅×C₈	—	2	2	no	—
164	C₂×C₅×C₈	—	2	1	no	—
165	C₂×C₅×C₈	—	2	1	no	—
166	C₂×C₅×C₈	—	4	4	no	—
167	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
168	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
169	C₅×C₄⋊C₄	—	2	1	no	—
170	C₅×C₄⋊C₄	—	2	1	no	—
171	C₅×C₄⋊C₄	—	2	1	no	—
172	C₅×C₄⋊C₄	—	2	1	no	—
173	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
174	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
175	C₅×C₂²⋊C₄	—	2	1	no	—
176	C₅×C₂²⋊C₄	—	2	1	no	—
177	C₅×C₂²⋊C₄	—	2	1	no	—
178	C₅×C₂²⋊C₄	—	4	1	no	—
179	C₅×C₂²⋊C₄	—	4	1	no	—
180	C₄²×C₅	—	2	1	no	—
181	C₄²×C₅	—	2	1	no	—
182	C₄²×C₅	—	2	1	no	—
183	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
184	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
185	C₄²×C₅	#41	1	1	yes	characteristic
186	C₄²×C₅	C₂⁴	1	1	yes	characteristic
187	C₂×AGL(1,ℤ/8)	—	2	1	no	—
188	C₂×AGL(1,ℤ/8)	—	2	2	no	—
189	#532	C₂²×C₅	1	1	yes	characteristic
190	C₂×#127	C₂²×C₅	1	1	yes	characteristic
191	C₄×#41	C₂²×C₅	1	1	yes	characteristic
192	#496	—	2	1	no	—
193	#496	—	2	1	no	—
194	#493	C₂²×C₅	1	2	yes	—
195	#492	C₂²×C₅	1	2	yes	—
196	#482	—	2	1	no	—
197	#475	C₂²×C₅	1	1	yes	characteristic, complemented
198	#474	C₂²×C₅	1	1	yes	characteristic, complemented
199	#460	—	2	1	no	—
200	#460	C₂²×C₅	1	2	yes	—
201	#460	C₂²×C₅	1	1	yes	characteristic, complemented
202	#459	—	2	1	no	—
203	#459	C₂²×C₅	1	2	yes	—
204	#459	C₂²×C₅	1	1	yes	characteristic, complemented
205	#449	—	2	1	no	—
206	#446	C₂²×C₅	1	2	yes	complemented
207	#442	—	2	1	no	—
208	#440	—	2	1	no	—
209	#435	—	2	2	no	—
210	C₈×D₄	C₂²×C₅	1	2	yes	complemented
211	#432	—	2	1	no	—
212	#432	C₂²×C₅	1	1	yes	characteristic
213	#432	C₂²×C₅	1	1	yes	characteristic
214	#423	C₂²×C₅	1	1	yes	characteristic
215	#418	—	2	1	no	—
216	C₄×M₁₆	C₂²×C₅	1	1	yes	characteristic
217	C₂×#97	—	2	1	no	—
218	#335	C₂²×C₅	1	2	yes	complemented
219	#334	C₂²×C₅	1	2	yes	complemented
220	#332	C₂²×C₅	1	2	yes	complemented
221	#331	C₂²×C₅	1	2	yes	—
222	#331	C₂²×C₅	1	2	yes	—
223	#331	C₂²×C₅	1	2	yes	complemented
224	C₂³×C₅	—	2	1	no	—
225	C₂³×C₅	—	4	1	no	—
226	C₂³×C₅	—	4	2	no	—
227	C₂³×C₅	—	8	2	no	—
228	C₂³×C₅	—	8	2	no	—
229	C₂³×C₅	—	8	2	no	—
230	C₂³×C₅	#121	1	1	yes	characteristic
231	C₅×Q₈	—	2	1	no	—
232	C₅×Q₈	—	2	1	no	—
233	C₅×Q₈	—	4	2	no	—
234	C₅×D₄	—	2	1	no	—
235	C₅×D₄	—	4	2	no	—
236	C₅×D₄	—	4	2	no	—
237	C₅×D₄	—	4	2	no	—
238	C₅×D₄	—	4	2	no	—
239	C₅×D₄	—	4	2	no	—
240	C₅×D₄	—	4	1	no	—
241	C₅×D₄	—	4	1	no	—
242	C₅×D₄	—	4	2	no	—
243	C₅×D₄	—	8	1	no	—
244	C₅×D₄	—	8	2	no	—
245	C₅×D₄	—	8	2	no	—
246	C₅×D₄	—	8	2	no	—
247	C₅×D₄	—	8	2	no	—
248	C₅×D₄	—	8	2	no	—
249	C₅×D₄	AGL(1,ℤ/8)	1	2	yes	complemented
250	C₂×C₄×C₅	—	2	2	no	—
251	C₂×C₄×C₅	—	2	1	no	—
252	C₂×C₄×C₅	—	2	1	no	—
253	C₂×C₄×C₅	—	2	1	no	—
254	C₂×C₄×C₅	—	2	1	no	—
255	C₂×C₄×C₅	—	2	1	no	—
256	C₂×C₄×C₅	—	4	1	no	—
257	C₂×C₄×C₅	—	4	2	no	—
258	C₂×C₄×C₅	—	4	2	no	—
259	C₂×C₄×C₅	—	4	1	no	—
260	C₂×C₄×C₅	—	8	1	no	—
261	C₂×C₄×C₅	—	8	2	no	—
262	C₂×C₄×C₅	#121	1	1	yes	characteristic
263	C₂×C₄×C₅	#121	1	1	yes	characteristic
264	C₂×C₄×C₅	#121	1	1	yes	characteristic
265	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
266	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
267	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
268	C₅×C₈	—	2	2	no	—
269	C₅×C₈	—	4	2	no	—
270	C₅×C₈	—	4	2	no	—
271	C₅×C₈	—	4	1	no	—
272	C₅×C₈	—	4	1	no	—
273	C₅×C₈	AGL(1,ℤ/8)	1	4	yes	complemented
274	C₂×#41	—	2	1	no	—
275	C₂×#41	C₅×D₄	1	1	yes	characteristic
276	C₂²×D₄	—	2	1	no	—
277	C₂²×D₄	—	2	1	no	—
278	C₂²×D₄	—	2	1	no	—
279	AGL(1,ℤ/8)	—	4	8	no	—
280	AGL(1,ℤ/8)	—	4	4	no	—
281	C₂×SD₁₆	—	2	2	no	—
282	C₂×SD₁₆	—	2	1	no	—
283	C₂×SD₁₆	—	2	2	no	—
284	C₂×SD₁₆	—	2	2	no	—
285	C₂×D₈	—	2	2	no	—
286	C₂×D₈	—	2	1	no	—
287	C₂×D₈	—	2	2	no	—
288	C₂×D₈	—	2	2	no	—
289	C₂×M₁₆	—	2	1	no	—
290	C₂×M₁₆	C₅×D₄	1	2	yes	—
291	C₂²×C₈	—	2	2	no	—
292	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
293	#127	—	2	1	no	—
294	#127	—	2	1	no	—
295	#127	—	2	1	no	—
296	#127	C₂³×C₅	1	2	yes	—
297	#127	C₂³×C₅	1	1	yes	characteristic
298	#124	—	2	1	no	—
299	#121	—	2	1	no	—
300	#121	—	2	1	no	—
301	C₄×Q₈	C₅×D₄	1	1	yes	characteristic
302	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
303	C₄×D₄	—	2	1	no	—
304	C₄×D₄	—	2	1	no	—
305	C₄×D₄	—	2	1	no	—
306	C₄×D₄	—	2	1	no	—
307	C₄×D₄	C₅×D₄	1	1	yes	characteristic
308	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
309	#117	—	2	1	no	—
310	#117	C₅×D₄	1	1	yes	characteristic
311	C₂×C₄²	—	2	1	no	—
312	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
313	#107	—	2	1	no	—
314	#106	—	2	1	no	—
315	C₄⋊C₈	—	2	2	no	—
316	C₄⋊C₈	—	2	1	no	—
317	C₄⋊C₈	C₂³×C₅	1	2	yes	—
318	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
319	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
320	C₄⋊C₈	C₂³×C₅	1	2	yes	—
321	#103	—	2	1	no	—
322	#102	—	2	1	no	—
323	#102	—	2	2	no	—
324	#102	—	2	2	no	—
325	#102	—	2	1	no	—
326	#102	—	2	1	no	—
327	C₂²⋊C₈	—	2	1	no	—
328	C₂²⋊C₈	—	2	1	no	—
329	C₂²⋊C₈	—	2	2	no	—
330	#97	—	2	2	no	—
331	#97	—	2	1	no	—
332	#97	—	2	1	no	—
333	#97	C₅×D₄	1	1	yes	characteristic
334	#97	C₅×D₄	1	1	yes	characteristic
335	C₄×C₈	C₂³×C₅	1	2	yes	—
336	C₂²×C₅	—	2	1	no	—
337	C₂²×C₅	—	2	1	no	—
338	C₂²×C₅	—	2	2	no	—
339	C₂²×C₅	—	2	1	no	—
340	C₂²×C₅	—	4	1	no	—
341	C₂²×C₅	—	4	1	no	—
342	C₂²×C₅	—	8	1	no	—
343	C₂²×C₅	—	8	2	no	—
344	C₂²×C₅	—	8	2	no	—
345	C₂²×C₅	—	8	1	no	—
346	C₂²×C₅	—	8	2	no	—
347	C₂²×C₅	—	8	1	no	—
348	C₂²×C₅	—	16	4	no	—
349	C₂²×C₅	C₂×#121	1	1	yes	characteristic
350	C₄×C₅	—	2	1	no	—
351	C₄×C₅	—	2	1	no	—
352	C₄×C₅	—	2	1	no	—
353	C₄×C₅	—	2	1	no	—
354	C₄×C₅	—	4	1	no	—
355	C₄×C₅	—	4	1	no	—
356	C₄×C₅	—	4	1	no	—
357	C₄×C₅	—	8	1	no	—
358	C₄×C₅	C₂×AGL(1,ℤ/8)	1	2	yes	—
359	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
360	C₄×C₅	#575	1	1	yes	characteristic
361	C₂⁴	—	4	1	no	—
362	#41	—	2	2	no	—
363	#41	—	4	1	no	—
364	#41	—	4	4	no	—
365	C₂×Q₈	—	2	1	no	—
366	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
367	C₂×D₄	—	2	1	no	—
368	C₂×D₄	—	2	1	no	—
369	C₂×D₄	—	2	2	no	—
370	C₂×D₄	—	2	1	no	—
371	C₂×D₄	—	2	2	no	—
372	C₂×D₄	—	2	1	no	—
373	C₂×D₄	—	2	2	no	—
374	C₂×D₄	—	4	4	no	—
375	C₂×D₄	—	4	2	no	—
376	C₂×D₄	—	4	2	no	—
377	C₂×D₄	—	4	1	no	—
378	C₂×D₄	—	4	1	no	—
379	C₂×D₄	—	4	1	no	—
380	C₂×D₄	—	4	1	no	—
381	C₂×D₄	—	8	2	no	—
382	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
383	C₂²×C₄	—	2	1	no	—
384	C₂²×C₄	—	2	1	no	—
385	C₂²×C₄	—	2	1	no	—
386	C₂²×C₄	—	4	1	no	—
387	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
388	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
389	C₂²×C₄	C₅×#41	1	1	yes	characteristic
390	SD₁₆	—	4	4	no	—
391	SD₁₆	—	4	4	no	—
392	SD₁₆	—	4	2	no	—
393	SD₁₆	—	4	4	no	—
394	D₈	—	4	4	no	—
395	D₈	—	4	4	no	—
396	D₈	—	4	2	no	—
397	D₈	—	4	4	no	—
398	M₁₆	—	2	4	no	—
399	M₁₆	—	4	2	no	—
400	C₂×C₈	—	2	2	no	—
401	C₂×C₈	—	2	1	no	—
402	C₂×C₈	—	2	1	no	—
403	C₂×C₈	—	2	2	no	—
404	C₂×C₈	—	4	4	no	—
405	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
406	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
407	C₄⋊C₄	—	2	1	no	—
408	C₄⋊C₄	—	2	1	no	—
409	C₄⋊C₄	—	2	1	no	—
410	C₄⋊C₄	—	2	1	no	—
411	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
412	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
413	C₂²⋊C₄	—	2	1	no	—
414	C₂²⋊C₄	—	2	1	no	—
415	C₂²⋊C₄	—	2	1	no	—
416	C₂²⋊C₄	—	4	1	no	—
417	C₂²⋊C₄	—	4	1	no	—
418	C₄²	—	2	1	no	—
419	C₄²	—	2	1	no	—
420	C₄²	—	2	1	no	—
421	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
422	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
423	C₄²	C₅×#41	1	1	yes	characteristic
424	C₄²	C₂⁴×C₅	1	1	yes	characteristic
425	C₂×C₅	—	4	1	no	—
426	C₂×C₅	—	4	2	no	—
427	C₂×C₅	—	16	1	no	—
428	C₂×C₅	—	16	2	no	—
429	C₂×C₅	#3038	1	1	yes	characteristic
430	C₂×C₅	#3055	1	1	yes	characteristic
431	C₂×C₅	#3068	1	1	yes	characteristic
432	C₂³	—	2	1	no	—
433	C₂³	—	4	1	no	—
434	C₂³	—	4	2	no	—
435	C₂³	—	8	2	no	—
436	C₂³	—	8	2	no	—
437	C₂³	—	8	2	no	—
438	C₂³	C₅×#121	1	1	yes	characteristic
439	Q₈	—	2	1	no	—
440	Q₈	—	2	1	no	—
441	Q₈	—	4	2	no	—
442	D₄	—	2	1	no	—
443	D₄	—	4	2	no	—
444	D₄	—	4	2	no	—
445	D₄	—	4	2	no	—
446	D₄	—	4	2	no	—
447	D₄	—	4	2	no	—
448	D₄	—	4	1	no	—
449	D₄	—	4	1	no	—
450	D₄	—	4	2	no	—
451	D₄	—	8	2	no	—
452	D₄	—	8	1	no	—
453	D₄	—	8	2	no	—
454	D₄	—	8	2	no	—
455	D₄	—	8	2	no	—
456	D₄	—	8	2	no	—
457	D₄	C₅×AGL(1,ℤ/8)	1	2	yes	complemented
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	1	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	4	1	no	—
465	C₂×C₄	—	4	2	no	—
466	C₂×C₄	—	4	2	no	—
467	C₂×C₄	—	4	1	no	—
468	C₂×C₄	—	8	1	no	—
469	C₂×C₄	—	8	2	no	—
470	C₂×C₄	C₅×#121	1	1	yes	characteristic
471	C₂×C₄	C₅×#121	1	1	yes	characteristic
472	C₂×C₄	C₅×#121	1	1	yes	characteristic
473	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
474	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
475	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
476	C₈	—	2	2	no	—
477	C₈	—	4	2	no	—
478	C₈	—	4	2	no	—
479	C₈	—	4	1	no	—
480	C₈	—	4	1	no	—
481	C₈	C₅×AGL(1,ℤ/8)	1	4	yes	complemented
482	C₅	#19312	1	1	yes	characteristic, direct product factor, Sylow
483	C₂²	—	2	1	no	—
484	C₂²	—	2	1	no	—
485	C₂²	—	2	2	no	—
486	C₂²	—	2	1	no	—
487	C₂²	—	4	1	no	—
488	C₂²	—	4	1	no	—
489	C₂²	—	8	1	no	—
490	C₂²	—	8	2	no	—
491	C₂²	—	8	2	no	—
492	C₂²	—	8	1	no	—
493	C₂²	—	8	2	no	—
494	C₂²	—	8	1	no	—
495	C₂²	—	16	4	no	—
496	C₂²	C₂×C₅×#121	1	1	yes	characteristic
497	C₄	—	2	1	no	—
498	C₄	—	2	1	no	—
499	C₄	—	2	1	no	—
500	C₄	—	2	1	no	—
501	C₄	—	4	1	no	—
502	C₄	—	4	1	no	—
503	C₄	—	4	1	no	—
504	C₄	—	8	1	no	—
505	C₄	C₂×C₅×AGL(1,ℤ/8)	1	2	yes	—
506	C₄	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
507	C₄	C₅×#575	1	1	yes	characteristic
508	C₂	—	4	1	no	—
509	C₂	—	4	2	no	—
510	C₂	—	16	2	no	—
511	C₂	—	16	1	no	—
512	C₂	C₅×#3038	1	1	yes	characteristic
513	C₂	C₅×#3055	1	1	yes	characteristic
514	C₂	C₅×#3068	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₅
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×#3151	C₂	semidirect
2. C₅×#3115	C₂	semidirect
3. C₅×#3038	C₂	semidirect
4. C₅×#2970	C₂	semidirect
5. C₅×#1688	C₂	semidirect
6. C₅×#1686	C₂	semidirect
7. C₅×#1667	C₂	semidirect
8. C₅×#1665	C₂	semidirect
9. C₅×#1569	C₂	semidirect
10. C₅×#1557	C₂	semidirect
11. C₅×#1555	C₂	semidirect
22. C₅×#475	C₂²	semidirect
23. C₅×#474	C₂²	semidirect
26. C₅×#460	C₂²	semidirect
29. C₅×#459	C₂²	semidirect
31. C₅×#446	C₂²	semidirect
35. C₅×C₈×D₄	C₂²	semidirect
43. C₅×#335	C₂²	semidirect
44. C₅×#334	C₂²	semidirect
45. C₅×#332	C₂²	semidirect
48. C₅×#331	C₂²	semidirect
49. #19312	C₅	direct (N × H)
112. #3151	C₂×C₅	semidirect
113. #3115	C₂×C₅	semidirect
114. #3038	C₂×C₅	semidirect
115. #2970	C₂×C₅	semidirect
116. #1688	C₂×C₅	semidirect
117. #1686	C₂×C₅	semidirect
118. #1667	C₂×C₅	semidirect
119. #1665	C₂×C₅	semidirect
120. #1569	C₂×C₅	semidirect
121. #1557	C₂×C₅	semidirect
122. #1555	C₂×C₅	semidirect
197. #475	C₂²×C₅	semidirect
198. #474	C₂²×C₅	semidirect
201. #460	C₂²×C₅	semidirect
204. #459	C₂²×C₅	semidirect
206. #446	C₂²×C₅	semidirect
210. C₈×D₄	C₂²×C₅	semidirect
218. #335	C₂²×C₅	semidirect
219. #334	C₂²×C₅	semidirect
220. #332	C₂²×C₅	semidirect
223. #331	C₂²×C₅	semidirect
249. C₅×D₄	AGL(1,ℤ/8)	semidirect
273. C₅×C₈	AGL(1,ℤ/8)	semidirect
457. D₄	C₅×AGL(1,ℤ/8)	semidirect
481. C₈	C₅×AGL(1,ℤ/8)	semidirect
482. C₅	#19312	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×#3151	2
C₅×#3115	2
C₅×#3038	2
C₅×#2970	2
C₅×#1688	2
C₅×#1686	2
C₅×#1667	2
C₅×#1665	2
C₅×#1569	2
C₅×#1557	2
C₅×#1555	2
#19312	5

Subgroups — C5×#19312 #11942032

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#19312 #11942032