Subgroups — C₅×#19177 #11941897

Order 1280.

650 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3141	C₂	1	1	yes	maximal, characteristic
2	C₅×#3103	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#462	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×Q₈×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1702	C₂	1	2	yes	maximal, complemented
6	C₅×#1700	C₂	1	2	yes	maximal, complemented
7	C₅×#1682	C₂	1	2	yes	maximal, complemented
8	C₅×#1680	C₂	1	2	yes	maximal, complemented
9	C₅×#1565	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1549	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1547	C₂	1	1	yes	maximal, characteristic
12	C₂²×C₅×Q₁₆	—	2	1	no	—
13	C₅×#532	C₂²	1	1	yes	characteristic
14	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
16	C₅×#489	—	2	2	no	—
17	C₅×#487	C₂²	1	2	yes	—
18	C₅×#486	C₂²	1	2	yes	—
19	C₅×#481	—	2	1	no	—
20	C₅×#475	C₂²	1	1	yes	characteristic
21	C₅×#475	C₂²	1	1	yes	characteristic
22	C₅×#462	—	2	1	no	—
23	C₅×#462	—	2	1	no	—
24	C₅×#462	C₂²	1	2	yes	—
25	C₅×#462	C₂²	1	2	yes	—
26	C₅×#460	C₂²	1	1	yes	characteristic
27	C₅×#460	C₂²	1	1	yes	characteristic
28	C₅×#448	—	2	1	no	—
29	C₅×#446	—	2	2	no	—
30	C₅×#446	C₂²	1	2	yes	—
31	C₅×C₈×Q₈	C₂²	1	2	yes	—
32	C₄×C₅×SD₁₆	—	2	1	no	—
33	C₄×C₅×SD₁₆	—	2	1	no	—
34	C₅×#431	C₂²	1	1	yes	characteristic
35	C₅×#423	—	2	1	no	—
36	C₅×#423	C₂²	1	1	yes	characteristic
37	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
38	C₅×#417	—	2	1	no	—
39	C₅×#417	—	2	1	no	—
40	C₂×C₅×#103	—	2	1	no	—
41	C₄×C₅×M₁₆	—	2	1	no	—
42	C₄×C₅×M₁₆	C₂²	1	1	yes	characteristic
43	C₅×#335	C₂²	1	2	yes	—
44	C₅×#334	C₂²	1	2	yes	—
45	C₅×#332	C₂²	1	2	yes	—
46	C₅×#332	C₂²	1	2	yes	—
47	C₅×#332	C₂²	1	2	yes	—
48	C₅×#331	C₂²	1	2	yes	—
49	#19177	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
50	C₂×C₅×#41	—	2	1	no	—
51	C₂²×C₅×Q₈	—	2	1	no	—
52	C₂²×C₅×Q₈	D₄	1	1	yes	characteristic
53	C₂×C₅×Q₁₆	—	2	2	no	—
54	C₂×C₅×Q₁₆	—	2	2	no	—
55	C₂×C₅×Q₁₆	—	4	4	no	—
56	C₂×C₅×SD₁₆	—	2	1	no	—
57	C₂×C₅×SD₁₆	—	2	1	no	—
58	C₂×C₅×M₁₆	—	2	1	no	—
59	C₂×C₅×M₁₆	D₄	1	1	yes	characteristic
60	C₂×C₅×M₁₆	D₄	1	1	yes	characteristic
61	C₂²×C₅×C₈	—	2	1	no	—
62	C₅×C₄⋊Q₈	—	2	1	no	—
63	C₅×C₄⋊Q₈	—	2	1	no	—
64	C₅×C₄⋊Q₈	—	2	1	no	—
65	C₅×C₄⋊Q₈	C₂³	1	2	yes	—
66	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
67	C₅×#127	C₂³	1	1	yes	characteristic
68	C₅×#124	—	2	1	no	—
69	C₅×#121	—	2	1	no	—
70	C₅×#121	—	2	1	no	—
71	C₄×C₅×Q₈	—	2	1	no	—
72	C₄×C₅×Q₈	—	2	1	no	—
73	C₄×C₅×Q₈	D₄	1	1	yes	characteristic
74	C₄×C₅×Q₈	D₄	1	1	yes	characteristic
75	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
76	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
77	C₄×C₅×D₄	—	2	1	no	—
78	C₄×C₅×D₄	—	2	1	no	—
79	C₂×C₅×C₄⋊C₄	—	2	1	no	—
80	C₂×C₅×C₄⋊C₄	—	2	1	no	—
81	C₂×C₅×C₄⋊C₄	—	2	1	no	—
82	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
83	C₂×C₄²×C₅	—	2	1	no	—
84	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
85	C₅×#106	—	2	1	no	—
86	C₅×#106	—	2	1	no	—
87	C₅×C₄⋊C₈	—	2	2	no	—
88	C₅×C₄⋊C₈	—	2	2	no	—
89	C₅×C₄⋊C₈	—	2	1	no	—
90	C₅×C₄⋊C₈	—	2	1	no	—
91	C₅×C₄⋊C₈	C₂³	1	2	yes	—
92	C₅×C₄⋊C₈	C₂³	1	2	yes	—
93	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
94	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
95	C₅×#103	—	2	1	no	—
96	C₅×#103	—	2	1	no	—
97	C₅×#103	—	2	2	no	—
98	C₅×#103	—	2	2	no	—
99	C₅×#103	—	2	2	no	—
100	C₅×#103	—	2	2	no	—
101	C₅×#102	—	2	2	no	—
102	C₅×#102	—	2	2	no	—
103	C₅×#102	—	2	1	no	—
104	C₅×#102	—	2	1	no	—
105	C₅×C₂²⋊C₈	—	2	1	no	—
106	C₅×#97	—	2	2	no	—
107	C₅×#97	D₄	1	2	yes	—
108	C₄×C₅×C₈	—	2	2	no	—
109	C₄×C₅×C₈	—	2	1	no	—
110	C₄×C₅×C₈	C₂³	1	2	yes	—
111	#3141	C₂×C₅	1	1	yes	characteristic
112	#3103	C₂×C₅	1	1	yes	characteristic
113	C₂×#462	C₂×C₅	1	1	yes	characteristic, complemented
114	Q₈×M₁₆	C₂×C₅	1	1	yes	characteristic, complemented
115	#1702	C₂×C₅	1	2	yes	complemented
116	#1700	C₂×C₅	1	2	yes	complemented
117	#1682	C₂×C₅	1	2	yes	complemented
118	#1680	C₂×C₅	1	2	yes	complemented
119	#1565	C₂×C₅	1	1	yes	characteristic, complemented
120	#1549	C₂×C₅	1	1	yes	characteristic, complemented
121	#1547	C₂×C₅	1	1	yes	characteristic
122	C₅×#41	—	4	2	no	—
123	C₅×#41	—	4	2	no	—
124	C₂×C₅×Q₈	—	2	1	no	—
125	C₂×C₅×Q₈	—	2	2	no	—
126	C₂×C₅×Q₈	—	2	1	no	—
127	C₂×C₅×Q₈	—	2	2	no	—
128	C₂×C₅×Q₈	—	4	1	no	—
129	C₂×C₅×Q₈	—	4	2	no	—
130	C₂×C₅×Q₈	—	4	2	no	—
131	C₂×C₅×Q₈	—	4	1	no	—
132	C₂×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
133	C₂×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
134	C₂×C₅×D₄	—	2	1	no	—
135	C₂×C₅×D₄	—	2	1	no	—
136	C₂×C₅×D₄	—	2	1	no	—
137	C₂×C₅×D₄	—	4	1	no	—
138	C₂²×C₄×C₅	—	2	1	no	—
139	C₂²×C₄×C₅	—	2	1	no	—
140	C₂²×C₄×C₅	—	4	1	no	—
141	C₂²×C₄×C₅	—	4	1	no	—
142	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₅	#41	1	1	yes	characteristic
145	C₅×Q₁₆	—	4	4	no	—
146	C₅×Q₁₆	—	4	4	no	—
147	C₅×SD₁₆	—	4	2	no	—
148	C₅×SD₁₆	—	4	2	no	—
149	C₅×M₁₆	—	2	2	no	—
150	C₅×M₁₆	—	2	2	no	—
151	C₅×M₁₆	—	4	2	no	—
152	C₂×C₅×C₈	—	2	2	no	—
153	C₂×C₅×C₈	—	2	2	no	—
154	C₂×C₅×C₈	—	2	1	no	—
155	C₂×C₅×C₈	—	2	1	no	—
156	C₂×C₅×C₈	—	4	2	no	—
157	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
158	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
159	C₅×C₄⋊C₄	—	2	1	no	—
160	C₅×C₄⋊C₄	—	2	1	no	—
161	C₅×C₄⋊C₄	—	2	1	no	—
162	C₅×C₄⋊C₄	—	2	1	no	—
163	C₅×C₄⋊C₄	—	2	1	no	—
164	C₅×C₄⋊C₄	—	2	2	no	—
165	C₅×C₄⋊C₄	—	2	1	no	—
166	C₅×C₄⋊C₄	—	2	2	no	—
167	C₅×C₄⋊C₄	—	2	1	no	—
168	C₅×C₄⋊C₄	—	4	1	no	—
169	C₅×C₄⋊C₄	—	4	1	no	—
170	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
171	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
172	C₅×C₂²⋊C₄	—	4	1	no	—
173	C₅×C₂²⋊C₄	—	4	1	no	—
174	C₄²×C₅	—	2	1	no	—
175	C₄²×C₅	—	2	1	no	—
176	C₄²×C₅	—	2	1	no	—
177	C₄²×C₅	—	2	1	no	—
178	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
179	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
180	C₄²×C₅	#41	1	1	yes	characteristic
181	C₄²×C₅	C₂⁴	1	1	yes	characteristic
182	C₂²×Q₁₆	—	2	1	no	—
183	#532	C₂²×C₅	1	1	yes	characteristic
184	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
185	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
186	#489	—	2	2	no	—
187	#487	C₂²×C₅	1	2	yes	—
188	#486	C₂²×C₅	1	2	yes	—
189	#481	—	2	1	no	—
190	#475	C₂²×C₅	1	1	yes	characteristic
191	#475	C₂²×C₅	1	1	yes	characteristic
192	#462	—	2	1	no	—
193	#462	—	2	1	no	—
194	#462	C₂²×C₅	1	2	yes	—
195	#462	C₂²×C₅	1	2	yes	—
196	#460	C₂²×C₅	1	1	yes	characteristic
197	#460	C₂²×C₅	1	1	yes	characteristic
198	#448	—	2	1	no	—
199	#446	—	2	2	no	—
200	#446	C₂²×C₅	1	2	yes	—
201	C₈×Q₈	C₂²×C₅	1	2	yes	—
202	C₄×SD₁₆	—	2	1	no	—
203	C₄×SD₁₆	—	2	1	no	—
204	#431	C₂²×C₅	1	1	yes	characteristic
205	#423	—	2	1	no	—
206	#423	C₂²×C₅	1	1	yes	characteristic
207	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
208	#417	—	2	1	no	—
209	#417	—	2	1	no	—
210	C₂×#103	—	2	1	no	—
211	C₄×M₁₆	—	2	1	no	—
212	C₄×M₁₆	C₂²×C₅	1	1	yes	characteristic
213	#335	C₂²×C₅	1	2	yes	—
214	#334	C₂²×C₅	1	2	yes	—
215	#332	C₂²×C₅	1	2	yes	—
216	#332	C₂²×C₅	1	2	yes	—
217	#332	C₂²×C₅	1	2	yes	—
218	#331	C₂²×C₅	1	2	yes	—
219	C₂³×C₅	—	4	1	no	—
220	C₂³×C₅	#121	1	1	yes	characteristic
221	C₅×Q₈	—	2	1	no	—
222	C₅×Q₈	—	2	1	no	—
223	C₅×Q₈	—	2	1	no	—
224	C₅×Q₈	—	4	2	no	—
225	C₅×Q₈	—	4	1	no	—
226	C₅×Q₈	—	4	2	no	—
227	C₅×Q₈	—	4	1	no	—
228	C₅×Q₈	—	4	2	no	—
229	C₅×Q₈	—	8	2	no	—
230	C₅×Q₈	AGL(1,ℤ/8)	1	2	yes	—
231	C₅×D₄	—	4	1	no	—
232	C₅×D₄	—	4	1	no	—
233	C₅×D₄	—	4	1	no	—
234	C₅×D₄	—	4	1	no	—
235	C₅×D₄	—	8	1	no	—
236	C₅×D₄	—	8	2	no	—
237	C₂×C₄×C₅	—	2	1	no	—
238	C₂×C₄×C₅	—	2	1	no	—
239	C₂×C₄×C₅	—	2	1	no	—
240	C₂×C₄×C₅	—	2	1	no	—
241	C₂×C₄×C₅	—	2	1	no	—
242	C₂×C₄×C₅	—	2	1	no	—
243	C₂×C₄×C₅	—	4	1	no	—
244	C₂×C₄×C₅	—	4	2	no	—
245	C₂×C₄×C₅	—	4	1	no	—
246	C₂×C₄×C₅	—	4	2	no	—
247	C₂×C₄×C₅	—	8	1	no	—
248	C₂×C₄×C₅	—	8	2	no	—
249	C₂×C₄×C₅	—	8	2	no	—
250	C₂×C₄×C₅	#121	1	1	yes	characteristic
251	C₂×C₄×C₅	#121	1	1	yes	characteristic
252	C₂×C₄×C₅	#121	1	1	yes	characteristic
253	C₂×C₄×C₅	#135	1	2	yes	—
254	C₂×C₄×C₅	#137	1	2	yes	—
255	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
256	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
257	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
258	C₅×C₈	—	2	2	no	—
259	C₅×C₈	—	2	2	no	—
260	C₅×C₈	—	4	2	no	—
261	C₅×C₈	—	4	2	no	—
262	C₅×C₈	—	4	1	no	—
263	C₅×C₈	—	4	1	no	—
264	C₂×#41	—	2	1	no	—
265	C₂²×Q₈	—	2	1	no	—
266	C₂²×Q₈	C₅×D₄	1	1	yes	characteristic
267	C₂×Q₁₆	—	2	2	no	—
268	C₂×Q₁₆	—	2	2	no	—
269	C₂×Q₁₆	—	4	4	no	—
270	C₂×SD₁₆	—	2	1	no	—
271	C₂×SD₁₆	—	2	1	no	—
272	C₂×M₁₆	—	2	1	no	—
273	C₂×M₁₆	C₅×D₄	1	1	yes	characteristic
274	C₂×M₁₆	C₅×D₄	1	1	yes	characteristic
275	C₂²×C₈	—	2	1	no	—
276	C₄⋊Q₈	—	2	1	no	—
277	C₄⋊Q₈	—	2	1	no	—
278	C₄⋊Q₈	—	2	1	no	—
279	C₄⋊Q₈	C₂³×C₅	1	2	yes	—
280	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
281	#127	C₂³×C₅	1	1	yes	characteristic
282	#124	—	2	1	no	—
283	#121	—	2	1	no	—
284	#121	—	2	1	no	—
285	C₄×Q₈	—	2	1	no	—
286	C₄×Q₈	—	2	1	no	—
287	C₄×Q₈	C₅×D₄	1	1	yes	characteristic
288	C₄×Q₈	C₅×D₄	1	1	yes	characteristic
289	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
290	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
291	C₄×D₄	—	2	1	no	—
292	C₄×D₄	—	2	1	no	—
293	C₂×C₄⋊C₄	—	2	1	no	—
294	C₂×C₄⋊C₄	—	2	1	no	—
295	C₂×C₄⋊C₄	—	2	1	no	—
296	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
297	C₂×C₄²	—	2	1	no	—
298	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
299	#106	—	2	1	no	—
300	#106	—	2	1	no	—
301	C₄⋊C₈	—	2	2	no	—
302	C₄⋊C₈	—	2	2	no	—
303	C₄⋊C₈	—	2	1	no	—
304	C₄⋊C₈	—	2	1	no	—
305	C₄⋊C₈	C₂³×C₅	1	2	yes	—
306	C₄⋊C₈	C₂³×C₅	1	2	yes	—
307	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
308	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
309	#103	—	2	1	no	—
310	#103	—	2	1	no	—
311	#103	—	2	2	no	—
312	#103	—	2	2	no	—
313	#103	—	2	2	no	—
314	#103	—	2	2	no	—
315	#102	—	2	2	no	—
316	#102	—	2	2	no	—
317	#102	—	2	1	no	—
318	#102	—	2	1	no	—
319	C₂²⋊C₈	—	2	1	no	—
320	#97	—	2	2	no	—
321	#97	C₅×D₄	1	2	yes	—
322	C₄×C₈	—	2	2	no	—
323	C₄×C₈	—	2	1	no	—
324	C₄×C₈	C₂³×C₅	1	2	yes	—
325	C₂²×C₅	—	2	1	no	—
326	C₂²×C₅	—	2	1	no	—
327	C₂²×C₅	—	8	1	no	—
328	C₂²×C₅	—	8	1	no	—
329	C₂²×C₅	—	8	1	no	—
330	C₂²×C₅	#464	1	2	yes	—
331	C₂²×C₅	C₂×#121	1	1	yes	characteristic
332	C₄×C₅	—	2	1	no	—
333	C₄×C₅	—	2	2	no	—
334	C₄×C₅	—	2	1	no	—
335	C₄×C₅	—	2	1	no	—
336	C₄×C₅	—	4	1	no	—
337	C₄×C₅	—	4	1	no	—
338	C₄×C₅	—	4	1	no	—
339	C₄×C₅	—	8	1	no	—
340	C₄×C₅	—	8	2	no	—
341	C₄×C₅	#464	1	2	yes	—
342	C₄×C₅	C₂×#135	1	1	yes	characteristic
343	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
344	C₄×C₅	C₂×#137	1	1	yes	characteristic
345	C₄×C₅	#575	1	1	yes	characteristic
346	#41	—	4	2	no	—
347	#41	—	4	2	no	—
348	C₂×Q₈	—	2	1	no	—
349	C₂×Q₈	—	2	2	no	—
350	C₂×Q₈	—	2	1	no	—
351	C₂×Q₈	—	2	2	no	—
352	C₂×Q₈	—	4	1	no	—
353	C₂×Q₈	—	4	2	no	—
354	C₂×Q₈	—	4	2	no	—
355	C₂×Q₈	—	4	1	no	—
356	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
357	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
358	C₂×D₄	—	2	1	no	—
359	C₂×D₄	—	2	1	no	—
360	C₂×D₄	—	2	1	no	—
361	C₂×D₄	—	4	1	no	—
362	C₂²×C₄	—	2	1	no	—
363	C₂²×C₄	—	2	1	no	—
364	C₂²×C₄	—	4	1	no	—
365	C₂²×C₄	—	4	1	no	—
366	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
367	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
368	C₂²×C₄	C₅×#41	1	1	yes	characteristic
369	Q₁₆	—	4	4	no	—
370	Q₁₆	—	4	4	no	—
371	SD₁₆	—	4	2	no	—
372	SD₁₆	—	4	2	no	—
373	M₁₆	—	2	2	no	—
374	M₁₆	—	2	2	no	—
375	M₁₆	—	4	2	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	2	1	no	—
378	C₂×C₈	—	2	1	no	—
379	C₂×C₈	—	2	2	no	—
380	C₂×C₈	—	4	2	no	—
381	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
382	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
383	C₄⋊C₄	—	2	1	no	—
384	C₄⋊C₄	—	2	1	no	—
385	C₄⋊C₄	—	2	1	no	—
386	C₄⋊C₄	—	2	1	no	—
387	C₄⋊C₄	—	2	1	no	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	—	2	1	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	2	1	no	—
392	C₄⋊C₄	—	4	1	no	—
393	C₄⋊C₄	—	4	1	no	—
394	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
395	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
396	C₂²⋊C₄	—	4	1	no	—
397	C₂²⋊C₄	—	4	1	no	—
398	C₄²	—	2	1	no	—
399	C₄²	—	2	1	no	—
400	C₄²	—	2	1	no	—
401	C₄²	—	2	1	no	—
402	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
403	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
404	C₄²	C₅×#41	1	1	yes	characteristic
405	C₄²	C₂⁴×C₅	1	1	yes	characteristic
406	C₂×C₅	—	2	2	no	—
407	C₂×C₅	—	16	1	no	—
408	C₂×C₅	C₂×#464	1	1	yes	characteristic
409	C₂×C₅	#3055	1	1	yes	characteristic
410	C₂×C₅	#3069	1	1	yes	characteristic
411	C₂³	—	4	1	no	—
412	C₂³	C₅×#121	1	1	yes	characteristic
413	Q₈	—	2	1	no	—
414	Q₈	—	2	1	no	—
415	Q₈	—	2	1	no	—
416	Q₈	—	4	2	no	—
417	Q₈	—	4	1	no	—
418	Q₈	—	4	2	no	—
419	Q₈	—	4	1	no	—
420	Q₈	—	4	2	no	—
421	Q₈	—	8	2	no	—
422	Q₈	C₅×AGL(1,ℤ/8)	1	2	yes	—
423	D₄	—	4	1	no	—
424	D₄	—	4	1	no	—
425	D₄	—	4	1	no	—
426	D₄	—	4	1	no	—
427	D₄	—	8	1	no	—
428	D₄	—	8	2	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	8	1	no	—
440	C₂×C₄	—	8	2	no	—
441	C₂×C₄	—	8	2	no	—
442	C₂×C₄	C₅×#121	1	1	yes	characteristic
443	C₂×C₄	C₅×#121	1	1	yes	characteristic
444	C₂×C₄	C₅×#121	1	1	yes	characteristic
445	C₂×C₄	C₅×#135	1	2	yes	—
446	C₂×C₄	C₅×#137	1	2	yes	—
447	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
448	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
449	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
450	C₈	—	2	2	no	—
451	C₈	—	2	2	no	—
452	C₈	—	4	2	no	—
453	C₈	—	4	2	no	—
454	C₈	—	4	1	no	—
455	C₈	—	4	1	no	—
456	C₅	#19177	1	1	yes	characteristic, direct product factor, Sylow
457	C₂²	—	2	1	no	—
458	C₂²	—	2	1	no	—
459	C₂²	—	8	1	no	—
460	C₂²	—	8	1	no	—
461	C₂²	—	8	1	no	—
462	C₂²	C₅×#464	1	2	yes	—
463	C₂²	C₂×C₅×#121	1	1	yes	characteristic
464	C₄	—	2	1	no	—
465	C₄	—	2	2	no	—
466	C₄	—	2	1	no	—
467	C₄	—	2	1	no	—
468	C₄	—	4	1	no	—
469	C₄	—	4	1	no	—
470	C₄	—	4	1	no	—
471	C₄	—	8	1	no	—
472	C₄	—	8	2	no	—
473	C₄	C₅×#464	1	2	yes	—
474	C₄	C₂×C₅×#135	1	1	yes	characteristic
475	C₄	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
476	C₄	C₂×C₅×#137	1	1	yes	characteristic
477	C₄	C₅×#575	1	1	yes	characteristic
478	C₂	—	2	2	no	—
479	C₂	—	16	1	no	—
480	C₂	C₂×C₅×#464	1	1	yes	characteristic
481	C₂	C₅×#3055	1	1	yes	characteristic
482	C₂	C₅×#3069	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₅
prime radical	C₅×#532	C₂²
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
3. C₂×C₅×#462	C₂	semidirect
4. C₅×Q₈×M₁₆	C₂	semidirect
5. C₅×#1702	C₂	semidirect
6. C₅×#1700	C₂	semidirect
7. C₅×#1682	C₂	semidirect
8. C₅×#1680	C₂	semidirect
9. C₅×#1565	C₂	semidirect
10. C₅×#1549	C₂	semidirect
49. #19177	C₅	direct (N × H)
113. C₂×#462	C₂×C₅	semidirect
114. Q₈×M₁₆	C₂×C₅	semidirect
115. #1702	C₂×C₅	semidirect
116. #1700	C₂×C₅	semidirect
117. #1682	C₂×C₅	semidirect
118. #1680	C₂×C₅	semidirect
119. #1565	C₂×C₅	semidirect
120. #1549	C₂×C₅	semidirect
456. C₅	#19177	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×#3141	2
C₅×#3103	2
C₂×C₅×#462	2
C₅×Q₈×M₁₆	2
C₅×#1702	2
C₅×#1700	2
C₅×#1682	2
C₅×#1680	2
C₅×#1565	2
C₅×#1549	2
C₅×#1547	2
#19177	5

Subgroups — C5×#19177 #11941897

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#19177 #11941897