Subgroups — C₅×#19288 #11942008

Order 1280.

608 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3167	C₂	1	1	yes	maximal, characteristic
2	C₅×#3113	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#3112	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×#446	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1704	C₂	1	2	yes	maximal, complemented
6	C₅×#1702	C₂	1	2	yes	maximal, complemented
7	C₅×#1692	C₂	1	2	yes	maximal, complemented
8	C₅×#1686	C₂	1	2	yes	maximal, complemented
9	C₅×#1568	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1552	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1551	C₂	1	1	yes	maximal, characteristic
12	C₅×#533	C₂²	1	1	yes	characteristic
13	C₅×#532	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
15	C₅×#498	C₂²	1	1	yes	characteristic
16	C₅×#492	C₂²	1	1	yes	characteristic
17	C₅×#487	C₂²	1	1	yes	characteristic
18	C₅×#486	C₂²	1	1	yes	characteristic
19	C₅×#483	—	2	1	no	—
20	C₅×#480	—	2	1	no	—
21	C₅×#477	C₂²	1	2	yes	—
22	C₅×#475	C₂²	1	2	yes	—
23	C₅×#465	—	2	1	no	—
24	C₅×#465	—	2	1	no	—
25	C₅×#462	C₂²	1	2	yes	—
26	C₅×#460	C₂²	1	2	yes	—
27	C₅×#451	—	2	1	no	—
28	C₅×#448	—	2	1	no	—
29	C₅×#446	—	2	1	no	—
30	C₅×#446	—	2	1	no	—
31	C₅×#446	C₂²	1	2	yes	—
32	C₅×#446	C₂²	1	2	yes	—
33	C₅×#441	—	2	2	no	—
34	C₅×#440	—	2	2	no	—
35	C₄×C₅×SD₁₆	—	2	1	no	—
36	C₄×C₅×SD₁₆	—	2	1	no	—
37	C₅×#432	C₂²	1	1	yes	characteristic
38	C₅×#432	C₂²	1	1	yes	characteristic
39	C₂×C₅×C₄⋊C₈	—	2	1	no	—
40	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
41	C₂×C₅×#97	—	2	1	no	—
42	C₂×C₄×C₅×C₈	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×#332	C₂²	1	2	yes	—
47	C₅×#332	C₂²	1	2	yes	—
48	C₅×#331	C₂²	1	2	yes	—
49	#19288	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
50	C₂×C₅×#41	—	2	1	no	—
51	C₂²×C₅×Q₈	D₄	1	1	yes	characteristic
52	C₂×C₅×Q₁₆	—	2	2	no	—
53	C₂×C₅×SD₁₆	—	2	2	no	—
54	C₂×C₅×SD₁₆	—	2	1	no	—
55	C₂×C₅×SD₁₆	—	2	1	no	—
56	C₂²×C₅×C₈	—	2	1	no	—
57	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
58	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
59	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
60	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
61	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
62	C₅×#127	C₂³	1	1	yes	characteristic
63	C₅×#125	—	2	1	no	—
64	C₅×#124	—	2	1	no	—
65	C₅×C₂²⋊Q₈	—	2	1	no	—
66	C₅×C₂²⋊Q₈	—	2	1	no	—
67	C₅×#121	—	2	1	no	—
68	C₅×#121	—	2	1	no	—
69	C₄×C₅×Q₈	—	2	1	no	—
70	C₄×C₅×Q₈	—	2	1	no	—
71	C₄×C₅×Q₈	—	2	1	no	—
72	C₄×C₅×Q₈	—	2	1	no	—
73	C₄×C₅×Q₈	D₄	1	2	yes	—
74	C₄×C₅×Q₈	C₂³	1	2	yes	—
75	C₄×C₅×D₄	—	2	1	no	—
76	C₄×C₅×D₄	—	2	1	no	—
77	C₅×#117	—	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×#106	—	2	1	no	—
84	C₅×#106	—	2	1	no	—
85	C₅×#106	—	2	2	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	C₂³	1	2	yes	—
90	C₅×C₄⋊C₈	C₂³	1	2	yes	—
91	C₅×C₄⋊C₈	C₂³	1	2	yes	—
92	C₅×#103	—	2	2	no	—
93	C₅×#103	—	2	2	no	—
94	C₅×#103	—	2	1	no	—
95	C₅×#103	—	2	1	no	—
96	C₅×#103	—	2	2	no	—
97	C₅×#102	—	2	1	no	—
98	C₅×#102	—	2	1	no	—
99	C₅×#102	—	2	2	no	—
100	C₅×C₂²⋊C₈	—	2	1	no	—
101	C₅×C₂²⋊C₈	—	2	1	no	—
102	C₅×#97	—	2	2	no	—
103	C₅×#97	—	2	2	no	—
104	C₅×#97	—	2	1	no	—
105	C₅×#97	—	2	1	no	—
106	C₄×C₅×C₈	D₄	1	1	yes	characteristic
107	C₄×C₅×C₈	D₄	1	1	yes	characteristic
108	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
109	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
110	#3167	C₂×C₅	1	1	yes	characteristic
111	#3113	C₂×C₅	1	1	yes	characteristic, complemented
112	#3112	C₂×C₅	1	1	yes	characteristic
113	C₂×#446	C₂×C₅	1	1	yes	characteristic, complemented
114	#1704	C₂×C₅	1	2	yes	complemented
115	#1702	C₂×C₅	1	2	yes	complemented
116	#1692	C₂×C₅	1	2	yes	complemented
117	#1686	C₂×C₅	1	2	yes	complemented
118	#1568	C₂×C₅	1	1	yes	characteristic, complemented
119	#1552	C₂×C₅	1	1	yes	characteristic, complemented
120	#1551	C₂×C₅	1	1	yes	characteristic
121	C₅×#41	—	8	2	no	—
122	C₂×C₅×Q₈	—	2	1	no	—
123	C₂×C₅×Q₈	—	2	1	no	—
124	C₂×C₅×Q₈	—	2	1	no	—
125	C₂×C₅×Q₈	—	2	1	no	—
126	C₂×C₅×Q₈	—	4	2	no	—
127	C₂×C₅×Q₈	C₂×D₄	1	2	yes	—
128	C₂×C₅×D₄	—	2	1	no	—
129	C₂×C₅×D₄	—	2	1	no	—
130	C₂×C₅×D₄	—	2	1	no	—
131	C₂×C₅×D₄	—	4	1	no	—
132	C₂²×C₄×C₅	—	2	1	no	—
133	C₂²×C₄×C₅	—	2	1	no	—
134	C₂²×C₄×C₅	—	4	1	no	—
135	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₅	#41	1	1	yes	characteristic
138	C₅×Q₁₆	—	4	4	no	—
139	C₅×SD₁₆	—	4	2	no	—
140	C₅×SD₁₆	—	4	4	no	—
141	C₅×SD₁₆	—	4	2	no	—
142	C₂×C₅×C₈	—	2	2	no	—
143	C₂×C₅×C₈	—	2	2	no	—
144	C₂×C₅×C₈	—	2	2	no	—
145	C₂×C₅×C₈	—	2	2	no	—
146	C₂×C₅×C₈	—	4	1	no	—
147	C₂×C₅×C₈	—	4	2	no	—
148	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
149	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
150	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
151	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
152	C₅×C₄⋊C₄	—	2	2	no	—
153	C₅×C₄⋊C₄	—	2	1	no	—
154	C₅×C₄⋊C₄	—	2	2	no	—
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	1	no	—
161	C₅×C₄⋊C₄	—	4	1	no	—
162	C₅×C₄⋊C₄	—	4	1	no	—
163	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
164	C₅×C₂²⋊C₄	—	4	1	no	—
165	C₅×C₂²⋊C₄	—	4	1	no	—
166	C₅×C₂²⋊C₄	—	4	1	no	—
167	C₄²×C₅	—	2	2	no	—
168	C₄²×C₅	—	2	2	no	—
169	C₄²×C₅	—	4	1	no	—
170	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
171	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
172	C₄²×C₅	#41	1	1	yes	characteristic
173	C₄²×C₅	C₂⁴	1	1	yes	characteristic
174	#533	C₂²×C₅	1	1	yes	characteristic
175	#532	C₂²×C₅	1	1	yes	characteristic
176	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
177	#498	C₂²×C₅	1	1	yes	characteristic
178	#492	C₂²×C₅	1	1	yes	characteristic
179	#487	C₂²×C₅	1	1	yes	characteristic
180	#486	C₂²×C₅	1	1	yes	characteristic
181	#483	—	2	1	no	—
182	#480	—	2	1	no	—
183	#477	C₂²×C₅	1	2	yes	—
184	#475	C₂²×C₅	1	2	yes	—
185	#465	—	2	1	no	—
186	#465	—	2	1	no	—
187	#462	C₂²×C₅	1	2	yes	—
188	#460	C₂²×C₅	1	2	yes	—
189	#451	—	2	1	no	—
190	#448	—	2	1	no	—
191	#446	—	2	1	no	—
192	#446	—	2	1	no	—
193	#446	C₂²×C₅	1	2	yes	—
194	#446	C₂²×C₅	1	2	yes	—
195	#441	—	2	2	no	—
196	#440	—	2	2	no	—
197	C₄×SD₁₆	—	2	1	no	—
198	C₄×SD₁₆	—	2	1	no	—
199	#432	C₂²×C₅	1	1	yes	characteristic
200	#432	C₂²×C₅	1	1	yes	characteristic
201	C₂×C₄⋊C₈	—	2	1	no	—
202	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
203	C₂×#97	—	2	1	no	—
204	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
205	#335	C₂²×C₅	1	2	yes	—
206	#334	C₂²×C₅	1	2	yes	—
207	#333	C₂²×C₅	1	2	yes	—
208	#332	C₂²×C₅	1	2	yes	—
209	#332	C₂²×C₅	1	2	yes	—
210	#331	C₂²×C₅	1	2	yes	—
211	C₂³×C₅	—	4	1	no	—
212	C₂³×C₅	#121	1	1	yes	characteristic
213	C₅×Q₈	—	2	2	no	—
214	C₅×Q₈	—	2	2	no	—
215	C₅×Q₈	—	4	2	no	—
216	C₅×Q₈	—	4	1	no	—
217	C₅×Q₈	—	4	1	no	—
218	C₅×Q₈	—	4	2	no	—
219	C₅×Q₈	—	8	1	no	—
220	C₅×D₄	—	4	1	no	—
221	C₅×D₄	—	4	1	no	—
222	C₅×D₄	—	4	2	no	—
223	C₅×D₄	—	8	1	no	—
224	C₅×D₄	—	8	2	no	—
225	C₂×C₄×C₅	—	2	2	no	—
226	C₂×C₄×C₅	—	2	1	no	—
227	C₂×C₄×C₅	—	2	1	no	—
228	C₂×C₄×C₅	—	2	2	no	—
229	C₂×C₄×C₅	—	2	2	no	—
230	C₂×C₄×C₅	—	2	2	no	—
231	C₂×C₄×C₅	—	4	2	no	—
232	C₂×C₄×C₅	—	4	2	no	—
233	C₂×C₄×C₅	—	4	1	no	—
234	C₂×C₄×C₅	—	4	1	no	—
235	C₂×C₄×C₅	—	4	1	no	—
236	C₂×C₄×C₅	—	8	2	no	—
237	C₂×C₄×C₅	#121	1	1	yes	characteristic
238	C₂×C₄×C₅	#121	1	1	yes	characteristic
239	C₂×C₄×C₅	#121	1	1	yes	characteristic
240	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
241	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
242	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
243	C₅×C₈	—	2	1	no	—
244	C₅×C₈	—	2	1	no	—
245	C₅×C₈	—	2	1	no	—
246	C₅×C₈	—	4	2	no	—
247	C₅×C₈	—	4	2	no	—
248	C₅×C₈	—	4	2	no	—
249	C₅×C₈	#137	1	2	yes	—
250	C₂×#41	—	2	1	no	—
251	C₂²×Q₈	C₅×D₄	1	1	yes	characteristic
252	C₂×Q₁₆	—	2	2	no	—
253	C₂×SD₁₆	—	2	2	no	—
254	C₂×SD₁₆	—	2	1	no	—
255	C₂×SD₁₆	—	2	1	no	—
256	C₂²×C₈	—	2	1	no	—
257	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
258	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
259	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
260	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
261	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
262	#127	C₂³×C₅	1	1	yes	characteristic
263	#125	—	2	1	no	—
264	#124	—	2	1	no	—
265	C₂²⋊Q₈	—	2	1	no	—
266	C₂²⋊Q₈	—	2	1	no	—
267	#121	—	2	1	no	—
268	#121	—	2	1	no	—
269	C₄×Q₈	—	2	1	no	—
270	C₄×Q₈	—	2	1	no	—
271	C₄×Q₈	—	2	1	no	—
272	C₄×Q₈	—	2	1	no	—
273	C₄×Q₈	C₅×D₄	1	2	yes	—
274	C₄×Q₈	C₂³×C₅	1	2	yes	—
275	C₄×D₄	—	2	1	no	—
276	C₄×D₄	—	2	1	no	—
277	#117	—	2	1	no	—
278	C₂×C₄⋊C₄	—	2	1	no	—
279	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
280	C₂×C₄²	—	2	1	no	—
281	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
282	#107	—	2	2	no	—
283	#106	—	2	1	no	—
284	#106	—	2	1	no	—
285	#106	—	2	2	no	—
286	C₄⋊C₈	—	2	2	no	—
287	C₄⋊C₈	—	2	2	no	—
288	C₄⋊C₈	—	2	1	no	—
289	C₄⋊C₈	C₂³×C₅	1	2	yes	—
290	C₄⋊C₈	C₂³×C₅	1	2	yes	—
291	C₄⋊C₈	C₂³×C₅	1	2	yes	—
292	#103	—	2	2	no	—
293	#103	—	2	2	no	—
294	#103	—	2	1	no	—
295	#103	—	2	1	no	—
296	#103	—	2	2	no	—
297	#102	—	2	1	no	—
298	#102	—	2	1	no	—
299	#102	—	2	2	no	—
300	C₂²⋊C₈	—	2	1	no	—
301	C₂²⋊C₈	—	2	1	no	—
302	#97	—	2	2	no	—
303	#97	—	2	2	no	—
304	#97	—	2	1	no	—
305	#97	—	2	1	no	—
306	C₄×C₈	C₅×D₄	1	1	yes	characteristic
307	C₄×C₈	C₅×D₄	1	1	yes	characteristic
308	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
309	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
310	C₂²×C₅	—	2	1	no	—
311	C₂²×C₅	—	2	1	no	—
312	C₂²×C₅	—	8	1	no	—
313	C₂²×C₅	—	8	1	no	—
314	C₂²×C₅	—	8	1	no	—
315	C₂²×C₅	#471	1	2	yes	—
316	C₂²×C₅	C₂×#121	1	1	yes	characteristic
317	C₄×C₅	—	2	1	no	—
318	C₄×C₅	—	2	1	no	—
319	C₄×C₅	—	2	1	no	—
320	C₄×C₅	—	2	1	no	—
321	C₄×C₅	—	4	2	no	—
322	C₄×C₅	—	4	2	no	—
323	C₄×C₅	—	8	1	no	—
324	C₄×C₅	—	8	1	no	—
325	C₄×C₅	—	8	1	no	—
326	C₄×C₅	C₂×#137	1	1	yes	characteristic
327	C₄×C₅	#575	1	1	yes	characteristic
328	C₄×C₅	#575	1	2	yes	—
329	#41	—	8	2	no	—
330	C₂×Q₈	—	2	1	no	—
331	C₂×Q₈	—	2	1	no	—
332	C₂×Q₈	—	2	1	no	—
333	C₂×Q₈	—	2	1	no	—
334	C₂×Q₈	—	4	2	no	—
335	C₂×Q₈	C₂×C₅×D₄	1	2	yes	—
336	C₂×D₄	—	2	1	no	—
337	C₂×D₄	—	2	1	no	—
338	C₂×D₄	—	2	1	no	—
339	C₂×D₄	—	4	1	no	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	4	1	no	—
343	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
344	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
345	C₂²×C₄	C₅×#41	1	1	yes	characteristic
346	Q₁₆	—	4	4	no	—
347	SD₁₆	—	4	2	no	—
348	SD₁₆	—	4	4	no	—
349	SD₁₆	—	4	2	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	4	1	no	—
355	C₂×C₈	—	4	2	no	—
356	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
357	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
358	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
359	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	—	2	1	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	—	4	1	no	—
370	C₄⋊C₄	—	4	1	no	—
371	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
372	C₂²⋊C₄	—	4	1	no	—
373	C₂²⋊C₄	—	4	1	no	—
374	C₂²⋊C₄	—	4	1	no	—
375	C₄²	—	2	2	no	—
376	C₄²	—	2	2	no	—
377	C₄²	—	4	1	no	—
378	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
379	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
380	C₄²	C₅×#41	1	1	yes	characteristic
381	C₄²	C₂⁴×C₅	1	1	yes	characteristic
382	C₂×C₅	—	2	2	no	—
383	C₂×C₅	—	16	1	no	—
384	C₂×C₅	#3037	1	1	yes	characteristic
385	C₂×C₅	#3054	1	1	yes	characteristic
386	C₂×C₅	C₂×#471	1	1	yes	characteristic
387	C₂³	—	4	1	no	—
388	C₂³	C₅×#121	1	1	yes	characteristic
389	Q₈	—	2	2	no	—
390	Q₈	—	2	2	no	—
391	Q₈	—	4	2	no	—
392	Q₈	—	4	1	no	—
393	Q₈	—	4	1	no	—
394	Q₈	—	4	2	no	—
395	Q₈	—	8	1	no	—
396	D₄	—	4	1	no	—
397	D₄	—	4	1	no	—
398	D₄	—	4	2	no	—
399	D₄	—	8	1	no	—
400	D₄	—	8	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	8	2	no	—
413	C₂×C₄	C₅×#121	1	1	yes	characteristic
414	C₂×C₄	C₅×#121	1	1	yes	characteristic
415	C₂×C₄	C₅×#121	1	1	yes	characteristic
416	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
417	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
418	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
419	C₈	—	2	1	no	—
420	C₈	—	2	1	no	—
421	C₈	—	2	1	no	—
422	C₈	—	4	2	no	—
423	C₈	—	4	2	no	—
424	C₈	—	4	2	no	—
425	C₈	C₅×#137	1	2	yes	—
426	C₅	#19288	1	1	yes	characteristic, direct product factor, Sylow
427	C₂²	—	2	1	no	—
428	C₂²	—	2	1	no	—
429	C₂²	—	8	1	no	—
430	C₂²	—	8	1	no	—
431	C₂²	—	8	1	no	—
432	C₂²	C₅×#471	1	2	yes	—
433	C₂²	C₂×C₅×#121	1	1	yes	characteristic
434	C₄	—	2	1	no	—
435	C₄	—	2	1	no	—
436	C₄	—	2	1	no	—
437	C₄	—	2	1	no	—
438	C₄	—	4	2	no	—
439	C₄	—	4	2	no	—
440	C₄	—	8	1	no	—
441	C₄	—	8	1	no	—
442	C₄	—	8	1	no	—
443	C₄	C₂×C₅×#137	1	1	yes	characteristic
444	C₄	C₅×#575	1	1	yes	characteristic
445	C₄	C₅×#575	1	2	yes	—
446	C₂	—	2	2	no	—
447	C₂	—	16	1	no	—
448	C₂	C₅×#3037	1	1	yes	characteristic
449	C₂	C₅×#3054	1	1	yes	characteristic
450	C₂	C₂×C₅×#471	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
2. C₅×#3113	C₂	semidirect
4. C₂×C₅×#446	C₂	semidirect
5. C₅×#1704	C₂	semidirect
6. C₅×#1702	C₂	semidirect
7. C₅×#1692	C₂	semidirect
8. C₅×#1686	C₂	semidirect
9. C₅×#1568	C₂	semidirect
10. C₅×#1552	C₂	semidirect
49. #19288	C₅	direct (N × H)
111. #3113	C₂×C₅	semidirect
113. C₂×#446	C₂×C₅	semidirect
114. #1704	C₂×C₅	semidirect
115. #1702	C₂×C₅	semidirect
116. #1692	C₂×C₅	semidirect
117. #1686	C₂×C₅	semidirect
118. #1568	C₂×C₅	semidirect
119. #1552	C₂×C₅	semidirect
426. C₅	#19288	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×#3167	2
C₅×#3113	2
C₅×#3112	2
C₂×C₅×#446	2
C₅×#1704	2
C₅×#1702	2
C₅×#1692	2
C₅×#1686	2
C₅×#1568	2
C₅×#1552	2
C₅×#1551	2
#19288	5

Subgroups — C5×#19288 #11942008

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#19288 #11942008