Subgroups — C₅×#19176 #11941896

Order 1280.

618 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×#3141	C₂	1	1	yes	maximal, characteristic
2	C₅×#3103	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#477	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×Q₈×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1704	C₂	1	2	yes	maximal, complemented
6	C₅×#1698	C₂	1	2	yes	maximal, complemented
7	C₅×#1684	C₂	1	2	yes	maximal, complemented
8	C₅×#1678	C₂	1	2	yes	maximal, complemented
9	C₅×#1565	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1548	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1547	C₂	1	1	yes	maximal, characteristic
12	C₅×#532	C₂²	1	1	yes	characteristic
13	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
15	C₅×#489	—	2	2	no	—
16	C₅×#487	C₂²	1	2	yes	—
17	C₅×#486	C₂²	1	2	yes	—
18	C₅×#481	—	2	1	no	—
19	C₅×#477	—	2	1	no	—
20	C₅×#477	—	2	1	no	—
21	C₅×#477	C₂²	1	2	yes	—
22	C₅×#477	C₂²	1	2	yes	—
23	C₅×#475	C₂²	1	1	yes	characteristic
24	C₅×#475	C₂²	1	1	yes	characteristic
25	C₅×#460	C₂²	1	1	yes	characteristic
26	C₅×#460	C₂²	1	1	yes	characteristic
27	C₅×#448	—	2	1	no	—
28	C₅×#446	—	2	2	no	—
29	C₅×#446	C₂²	1	2	yes	—
30	C₅×C₈×Q₈	C₂²	1	2	yes	—
31	C₄×C₅×SD₁₆	—	2	1	no	—
32	C₄×C₅×SD₁₆	—	2	1	no	—
33	C₅×#431	C₂²	1	1	yes	characteristic
34	C₂×C₅×#107	—	2	1	no	—
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×#333	C₂²	1	2	yes	—
46	C₅×#333	C₂²	1	2	yes	—
47	C₅×#332	C₂²	1	2	yes	—
48	C₅×#331	C₂²	1	2	yes	—
49	#19176	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×SD₁₆	—	2	1	no	—
54	C₂×C₅×SD₁₆	—	2	1	no	—
55	C₂×C₅×M₁₆	—	2	1	no	—
56	C₂×C₅×M₁₆	D₄	1	1	yes	characteristic
57	C₂×C₅×M₁₆	D₄	1	1	yes	characteristic
58	C₂²×C₅×C₈	—	2	1	no	—
59	C₅×C₄⋊Q₈	—	2	1	no	—
60	C₅×C₄⋊Q₈	—	2	1	no	—
61	C₅×C₄⋊Q₈	—	2	1	no	—
62	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
63	C₅×C₄⋊Q₈	C₂³	1	2	yes	—
64	C₅×#127	C₂³	1	1	yes	characteristic
65	C₅×#124	—	2	1	no	—
66	C₅×#121	—	2	1	no	—
67	C₅×#121	—	2	1	no	—
68	C₄×C₅×Q₈	—	2	1	no	—
69	C₄×C₅×Q₈	—	2	1	no	—
70	C₄×C₅×Q₈	D₄	1	1	yes	characteristic
71	C₄×C₅×Q₈	D₄	1	1	yes	characteristic
72	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
73	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
74	C₄×C₅×D₄	—	2	1	no	—
75	C₄×C₅×D₄	—	2	1	no	—
76	C₂×C₅×C₄⋊C₄	—	2	1	no	—
77	C₂×C₅×C₄⋊C₄	—	2	1	no	—
78	C₂×C₅×C₄⋊C₄	—	2	1	no	—
79	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
80	C₂×C₄²×C₅	—	2	1	no	—
81	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
82	C₅×#107	—	2	2	no	—
83	C₅×#107	—	2	2	no	—
84	C₅×#106	—	2	1	no	—
85	C₅×#106	—	2	1	no	—
86	C₅×C₄⋊C₈	—	2	2	no	—
87	C₅×C₄⋊C₈	—	2	2	no	—
88	C₅×C₄⋊C₈	—	2	1	no	—
89	C₅×C₄⋊C₈	—	2	1	no	—
90	C₅×C₄⋊C₈	C₂³	1	2	yes	—
91	C₅×C₄⋊C₈	C₂³	1	2	yes	—
92	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
93	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
94	C₅×#103	—	2	2	no	—
95	C₅×#103	—	2	2	no	—
96	C₅×#103	—	2	1	no	—
97	C₅×#103	—	2	1	no	—
98	C₅×#103	—	2	2	no	—
99	C₅×#103	—	2	2	no	—
100	C₅×#102	—	2	2	no	—
101	C₅×#102	—	2	2	no	—
102	C₅×#102	—	2	1	no	—
103	C₅×#102	—	2	1	no	—
104	C₅×C₂²⋊C₈	—	2	1	no	—
105	C₅×#97	—	2	2	no	—
106	C₅×#97	D₄	1	2	yes	—
107	C₄×C₅×C₈	—	2	2	no	—
108	C₄×C₅×C₈	—	2	1	no	—
109	C₄×C₅×C₈	C₂³	1	2	yes	—
110	#3141	C₂×C₅	1	1	yes	characteristic
111	#3103	C₂×C₅	1	1	yes	characteristic
112	C₂×#477	C₂×C₅	1	1	yes	characteristic, complemented
113	Q₈×M₁₆	C₂×C₅	1	1	yes	characteristic, complemented
114	#1704	C₂×C₅	1	2	yes	complemented
115	#1698	C₂×C₅	1	2	yes	complemented
116	#1684	C₂×C₅	1	2	yes	complemented
117	#1678	C₂×C₅	1	2	yes	complemented
118	#1565	C₂×C₅	1	1	yes	characteristic, complemented
119	#1548	C₂×C₅	1	1	yes	characteristic, complemented
120	#1547	C₂×C₅	1	1	yes	characteristic
121	C₅×#41	—	4	2	no	—
122	C₅×#41	—	4	2	no	—
123	C₂×C₅×Q₈	—	2	1	no	—
124	C₂×C₅×Q₈	—	2	2	no	—
125	C₂×C₅×Q₈	—	2	1	no	—
126	C₂×C₅×Q₈	—	2	2	no	—
127	C₂×C₅×Q₈	—	4	1	no	—
128	C₂×C₅×Q₈	—	4	1	no	—
129	C₂×C₅×Q₈	—	8	2	no	—
130	C₂×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
131	C₂×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
132	C₂×C₅×D₄	—	2	1	no	—
133	C₂×C₅×D₄	—	2	1	no	—
134	C₂×C₅×D₄	—	2	1	no	—
135	C₂×C₅×D₄	—	4	1	no	—
136	C₂²×C₄×C₅	—	2	1	no	—
137	C₂²×C₄×C₅	—	2	1	no	—
138	C₂²×C₄×C₅	—	4	1	no	—
139	C₂²×C₄×C₅	—	4	1	no	—
140	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₅	#41	1	1	yes	characteristic
143	C₅×SD₁₆	—	4	2	no	—
144	C₅×SD₁₆	—	4	2	no	—
145	C₅×M₁₆	—	2	2	no	—
146	C₅×M₁₆	—	2	2	no	—
147	C₅×M₁₆	—	4	2	no	—
148	C₂×C₅×C₈	—	2	2	no	—
149	C₂×C₅×C₈	—	2	2	no	—
150	C₂×C₅×C₈	—	2	1	no	—
151	C₂×C₅×C₈	—	2	1	no	—
152	C₂×C₅×C₈	—	4	2	no	—
153	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
154	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
155	C₅×C₄⋊C₄	—	2	1	no	—
156	C₅×C₄⋊C₄	—	2	1	no	—
157	C₅×C₄⋊C₄	—	2	1	no	—
158	C₅×C₄⋊C₄	—	2	1	no	—
159	C₅×C₄⋊C₄	—	2	1	no	—
160	C₅×C₄⋊C₄	—	2	2	no	—
161	C₅×C₄⋊C₄	—	2	2	no	—
162	C₅×C₄⋊C₄	—	2	1	no	—
163	C₅×C₄⋊C₄	—	2	1	no	—
164	C₅×C₄⋊C₄	—	4	1	no	—
165	C₅×C₄⋊C₄	—	4	1	no	—
166	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
167	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
168	C₅×C₂²⋊C₄	—	4	1	no	—
169	C₅×C₂²⋊C₄	—	4	1	no	—
170	C₄²×C₅	—	2	1	no	—
171	C₄²×C₅	—	2	1	no	—
172	C₄²×C₅	—	2	1	no	—
173	C₄²×C₅	—	2	1	no	—
174	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
175	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
176	C₄²×C₅	#41	1	1	yes	characteristic
177	C₄²×C₅	C₂⁴	1	1	yes	characteristic
178	#532	C₂²×C₅	1	1	yes	characteristic
179	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
180	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
181	#489	—	2	2	no	—
182	#487	C₂²×C₅	1	2	yes	—
183	#486	C₂²×C₅	1	2	yes	—
184	#481	—	2	1	no	—
185	#477	—	2	1	no	—
186	#477	—	2	1	no	—
187	#477	C₂²×C₅	1	2	yes	—
188	#477	C₂²×C₅	1	2	yes	—
189	#475	C₂²×C₅	1	1	yes	characteristic
190	#475	C₂²×C₅	1	1	yes	characteristic
191	#460	C₂²×C₅	1	1	yes	characteristic
192	#460	C₂²×C₅	1	1	yes	characteristic
193	#448	—	2	1	no	—
194	#446	—	2	2	no	—
195	#446	C₂²×C₅	1	2	yes	—
196	C₈×Q₈	C₂²×C₅	1	2	yes	—
197	C₄×SD₁₆	—	2	1	no	—
198	C₄×SD₁₆	—	2	1	no	—
199	#431	C₂²×C₅	1	1	yes	characteristic
200	C₂×#107	—	2	1	no	—
201	#423	—	2	1	no	—
202	#423	C₂²×C₅	1	1	yes	characteristic
203	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
204	#417	—	2	1	no	—
205	#417	—	2	1	no	—
206	C₂×#103	—	2	1	no	—
207	C₄×M₁₆	—	2	1	no	—
208	C₄×M₁₆	C₂²×C₅	1	1	yes	characteristic
209	#335	C₂²×C₅	1	2	yes	—
210	#334	C₂²×C₅	1	2	yes	—
211	#333	C₂²×C₅	1	2	yes	—
212	#333	C₂²×C₅	1	2	yes	—
213	#332	C₂²×C₅	1	2	yes	—
214	#331	C₂²×C₅	1	2	yes	—
215	C₂³×C₅	—	4	1	no	—
216	C₂³×C₅	#121	1	1	yes	characteristic
217	C₅×Q₈	—	2	1	no	—
218	C₅×Q₈	—	2	1	no	—
219	C₅×Q₈	—	2	1	no	—
220	C₅×Q₈	—	4	2	no	—
221	C₅×Q₈	—	4	1	no	—
222	C₅×Q₈	—	4	1	no	—
223	C₅×Q₈	—	8	2	no	—
224	C₅×Q₈	—	8	2	no	—
225	C₅×Q₈	#137	1	2	yes	—
226	C₅×D₄	—	4	1	no	—
227	C₅×D₄	—	4	1	no	—
228	C₅×D₄	—	4	1	no	—
229	C₅×D₄	—	4	1	no	—
230	C₅×D₄	—	8	1	no	—
231	C₅×D₄	—	8	2	no	—
232	C₂×C₄×C₅	—	2	1	no	—
233	C₂×C₄×C₅	—	2	1	no	—
234	C₂×C₄×C₅	—	2	1	no	—
235	C₂×C₄×C₅	—	2	1	no	—
236	C₂×C₄×C₅	—	2	1	no	—
237	C₂×C₄×C₅	—	2	1	no	—
238	C₂×C₄×C₅	—	4	1	no	—
239	C₂×C₄×C₅	—	4	2	no	—
240	C₂×C₄×C₅	—	4	1	no	—
241	C₂×C₄×C₅	—	4	2	no	—
242	C₂×C₄×C₅	—	8	1	no	—
243	C₂×C₄×C₅	—	8	2	no	—
244	C₂×C₄×C₅	—	8	2	no	—
245	C₂×C₄×C₅	#121	1	1	yes	characteristic
246	C₂×C₄×C₅	#121	1	1	yes	characteristic
247	C₂×C₄×C₅	#121	1	1	yes	characteristic
248	C₂×C₄×C₅	#135	1	2	yes	—
249	C₂×C₄×C₅	#137	1	2	yes	—
250	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
251	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
252	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
253	C₅×C₈	—	2	2	no	—
254	C₅×C₈	—	2	2	no	—
255	C₅×C₈	—	4	2	no	—
256	C₅×C₈	—	4	1	no	—
257	C₅×C₈	—	4	2	no	—
258	C₅×C₈	—	4	1	no	—
259	C₂×#41	—	2	1	no	—
260	C₂²×Q₈	—	2	1	no	—
261	C₂²×Q₈	C₅×D₄	1	1	yes	characteristic
262	C₂×SD₁₆	—	2	1	no	—
263	C₂×SD₁₆	—	2	1	no	—
264	C₂×M₁₆	—	2	1	no	—
265	C₂×M₁₆	C₅×D₄	1	1	yes	characteristic
266	C₂×M₁₆	C₅×D₄	1	1	yes	characteristic
267	C₂²×C₈	—	2	1	no	—
268	C₄⋊Q₈	—	2	1	no	—
269	C₄⋊Q₈	—	2	1	no	—
270	C₄⋊Q₈	—	2	1	no	—
271	C₄⋊Q₈	C₂³×C₅	1	2	yes	—
272	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
273	#127	C₂³×C₅	1	1	yes	characteristic
274	#124	—	2	1	no	—
275	#121	—	2	1	no	—
276	#121	—	2	1	no	—
277	C₄×Q₈	—	2	1	no	—
278	C₄×Q₈	—	2	1	no	—
279	C₄×Q₈	C₅×D₄	1	1	yes	characteristic
280	C₄×Q₈	C₅×D₄	1	1	yes	characteristic
281	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
282	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
283	C₄×D₄	—	2	1	no	—
284	C₄×D₄	—	2	1	no	—
285	C₂×C₄⋊C₄	—	2	1	no	—
286	C₂×C₄⋊C₄	—	2	1	no	—
287	C₂×C₄⋊C₄	—	2	1	no	—
288	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
289	C₂×C₄²	—	2	1	no	—
290	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
291	#107	—	2	2	no	—
292	#107	—	2	2	no	—
293	#106	—	2	1	no	—
294	#106	—	2	1	no	—
295	C₄⋊C₈	—	2	2	no	—
296	C₄⋊C₈	—	2	2	no	—
297	C₄⋊C₈	—	2	1	no	—
298	C₄⋊C₈	—	2	1	no	—
299	C₄⋊C₈	C₂³×C₅	1	2	yes	—
300	C₄⋊C₈	C₂³×C₅	1	2	yes	—
301	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
302	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
303	#103	—	2	2	no	—
304	#103	—	2	2	no	—
305	#103	—	2	1	no	—
306	#103	—	2	1	no	—
307	#103	—	2	2	no	—
308	#103	—	2	2	no	—
309	#102	—	2	2	no	—
310	#102	—	2	2	no	—
311	#102	—	2	1	no	—
312	#102	—	2	1	no	—
313	C₂²⋊C₈	—	2	1	no	—
314	#97	—	2	2	no	—
315	#97	C₅×D₄	1	2	yes	—
316	C₄×C₈	—	2	2	no	—
317	C₄×C₈	—	2	1	no	—
318	C₄×C₈	C₂³×C₅	1	2	yes	—
319	C₂²×C₅	—	2	1	no	—
320	C₂²×C₅	—	2	1	no	—
321	C₂²×C₅	—	8	1	no	—
322	C₂²×C₅	—	8	1	no	—
323	C₂²×C₅	—	8	1	no	—
324	C₂²×C₅	#464	1	2	yes	—
325	C₂²×C₅	C₂×#121	1	1	yes	characteristic
326	C₄×C₅	—	2	1	no	—
327	C₄×C₅	—	2	2	no	—
328	C₄×C₅	—	2	1	no	—
329	C₄×C₅	—	2	1	no	—
330	C₄×C₅	—	4	1	no	—
331	C₄×C₅	—	4	1	no	—
332	C₄×C₅	—	4	1	no	—
333	C₄×C₅	—	8	1	no	—
334	C₄×C₅	—	8	2	no	—
335	C₄×C₅	#464	1	2	yes	—
336	C₄×C₅	C₂×#135	1	1	yes	characteristic
337	C₄×C₅	C₂×#137	1	1	yes	characteristic
338	C₄×C₅	C₂×#137	1	1	yes	characteristic
339	C₄×C₅	#575	1	1	yes	characteristic
340	#41	—	4	2	no	—
341	#41	—	4	2	no	—
342	C₂×Q₈	—	2	1	no	—
343	C₂×Q₈	—	2	2	no	—
344	C₂×Q₈	—	2	1	no	—
345	C₂×Q₈	—	2	2	no	—
346	C₂×Q₈	—	4	1	no	—
347	C₂×Q₈	—	4	1	no	—
348	C₂×Q₈	—	8	2	no	—
349	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
350	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
351	C₂×D₄	—	2	1	no	—
352	C₂×D₄	—	2	1	no	—
353	C₂×D₄	—	2	1	no	—
354	C₂×D₄	—	4	1	no	—
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	2	1	no	—
357	C₂²×C₄	—	4	1	no	—
358	C₂²×C₄	—	4	1	no	—
359	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
360	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
361	C₂²×C₄	C₅×#41	1	1	yes	characteristic
362	SD₁₆	—	4	2	no	—
363	SD₁₆	—	4	2	no	—
364	M₁₆	—	2	2	no	—
365	M₁₆	—	2	2	no	—
366	M₁₆	—	4	2	no	—
367	C₂×C₈	—	2	2	no	—
368	C₂×C₈	—	2	1	no	—
369	C₂×C₈	—	2	1	no	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	—	4	2	no	—
372	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
373	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
374	C₄⋊C₄	—	2	1	no	—
375	C₄⋊C₄	—	2	1	no	—
376	C₄⋊C₄	—	2	1	no	—
377	C₄⋊C₄	—	2	1	no	—
378	C₄⋊C₄	—	2	1	no	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	—	2	1	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	—	4	1	no	—
384	C₄⋊C₄	—	4	1	no	—
385	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
386	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
387	C₂²⋊C₄	—	4	1	no	—
388	C₂²⋊C₄	—	4	1	no	—
389	C₄²	—	2	1	no	—
390	C₄²	—	2	1	no	—
391	C₄²	—	2	1	no	—
392	C₄²	—	2	1	no	—
393	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
394	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
395	C₄²	C₅×#41	1	1	yes	characteristic
396	C₄²	C₂⁴×C₅	1	1	yes	characteristic
397	C₂×C₅	—	2	2	no	—
398	C₂×C₅	—	16	1	no	—
399	C₂×C₅	C₂×#464	1	1	yes	characteristic
400	C₂×C₅	#3056	1	1	yes	characteristic
401	C₂×C₅	#3068	1	1	yes	characteristic
402	C₂³	—	4	1	no	—
403	C₂³	C₅×#121	1	1	yes	characteristic
404	Q₈	—	2	1	no	—
405	Q₈	—	2	1	no	—
406	Q₈	—	2	1	no	—
407	Q₈	—	4	2	no	—
408	Q₈	—	4	1	no	—
409	Q₈	—	4	1	no	—
410	Q₈	—	8	2	no	—
411	Q₈	—	8	2	no	—
412	Q₈	C₅×#137	1	2	yes	—
413	D₄	—	4	1	no	—
414	D₄	—	4	1	no	—
415	D₄	—	4	1	no	—
416	D₄	—	4	1	no	—
417	D₄	—	8	1	no	—
418	D₄	—	8	2	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	1	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	8	1	no	—
430	C₂×C₄	—	8	2	no	—
431	C₂×C₄	—	8	2	no	—
432	C₂×C₄	C₅×#121	1	1	yes	characteristic
433	C₂×C₄	C₅×#121	1	1	yes	characteristic
434	C₂×C₄	C₅×#121	1	1	yes	characteristic
435	C₂×C₄	C₅×#135	1	2	yes	—
436	C₂×C₄	C₅×#137	1	2	yes	—
437	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
438	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
439	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
440	C₈	—	2	2	no	—
441	C₈	—	2	2	no	—
442	C₈	—	4	2	no	—
443	C₈	—	4	1	no	—
444	C₈	—	4	2	no	—
445	C₈	—	4	1	no	—
446	C₅	#19176	1	1	yes	characteristic, direct product factor, Sylow
447	C₂²	—	2	1	no	—
448	C₂²	—	2	1	no	—
449	C₂²	—	8	1	no	—
450	C₂²	—	8	1	no	—
451	C₂²	—	8	1	no	—
452	C₂²	C₅×#464	1	2	yes	—
453	C₂²	C₂×C₅×#121	1	1	yes	characteristic
454	C₄	—	2	1	no	—
455	C₄	—	2	2	no	—
456	C₄	—	2	1	no	—
457	C₄	—	2	1	no	—
458	C₄	—	4	1	no	—
459	C₄	—	4	1	no	—
460	C₄	—	4	1	no	—
461	C₄	—	8	1	no	—
462	C₄	—	8	2	no	—
463	C₄	C₅×#464	1	2	yes	—
464	C₄	C₂×C₅×#135	1	1	yes	characteristic
465	C₄	C₂×C₅×#137	1	1	yes	characteristic
466	C₄	C₂×C₅×#137	1	1	yes	characteristic
467	C₄	C₅×#575	1	1	yes	characteristic
468	C₂	—	2	2	no	—
469	C₂	—	16	1	no	—
470	C₂	C₂×C₅×#464	1	1	yes	characteristic
471	C₂	C₅×#3056	1	1	yes	characteristic
472	C₂	C₅×#3068	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×#477	C₂	semidirect
4. C₅×Q₈×M₁₆	C₂	semidirect
5. C₅×#1704	C₂	semidirect
6. C₅×#1698	C₂	semidirect
7. C₅×#1684	C₂	semidirect
8. C₅×#1678	C₂	semidirect
9. C₅×#1565	C₂	semidirect
10. C₅×#1548	C₂	semidirect
49. #19176	C₅	direct (N × H)
112. C₂×#477	C₂×C₅	semidirect
113. Q₈×M₁₆	C₂×C₅	semidirect
114. #1704	C₂×C₅	semidirect
115. #1698	C₂×C₅	semidirect
116. #1684	C₂×C₅	semidirect
117. #1678	C₂×C₅	semidirect
118. #1565	C₂×C₅	semidirect
119. #1548	C₂×C₅	semidirect
446. C₅	#19176	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×#477	2
C₅×Q₈×M₁₆	2
C₅×#1704	2
C₅×#1698	2
C₅×#1684	2
C₅×#1678	2
C₅×#1565	2
C₅×#1548	2
C₅×#1547	2
#19176	5

Subgroups — C5×#19176 #11941896

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#19176 #11941896