Subgroups — C₅×#19299 #11942019

Order 1280.

700 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#486	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#3079	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#3038	C₂	1	1	yes	maximal, characteristic
4	C₅×#2965	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1698	C₂	1	4	yes	maximal, complemented
6	C₅×#1697	C₂	1	4	yes	maximal, complemented
7	C₅×#1567	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1548	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1545	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₅×AGL(1,ℤ/8)	—	2	1	no	—
11	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
12	C₂×C₅×#127	C₂²	1	1	yes	characteristic
13	C₄×C₅×#41	C₂²	1	1	yes	characteristic
14	C₅×#486	—	2	1	no	—
15	C₅×#486	—	2	1	no	—
16	C₅×#486	C₂²	1	4	yes	—
17	C₅×#477	C₂²	1	2	yes	complemented
18	C₅×#476	C₂²	1	2	yes	complemented
19	C₅×#475	—	2	1	no	—
20	C₅×#474	—	2	1	no	—
21	C₅×#460	—	2	1	no	—
22	C₅×#460	C₂²	1	2	yes	—
23	C₅×#459	—	2	1	no	—
24	C₅×#459	C₂²	1	2	yes	—
25	C₅×#446	C₂²	1	2	yes	complemented
26	C₅×#436	C₂²	1	2	yes	complemented
27	C₅×#435	—	2	2	no	—
28	C₅×#431	—	2	1	no	—
29	C₅×#431	C₂²	1	1	yes	characteristic
30	C₅×#428	—	2	1	no	—
31	C₅×#423	C₂²	1	1	yes	characteristic
32	C₅×#423	C₂²	1	1	yes	characteristic
33	C₅×#418	—	2	1	no	—
34	C₅×#417	—	2	1	no	—
35	C₂×C₅×#102	—	2	2	no	—
36	C₄×C₅×M₁₆	—	2	1	no	—
37	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
38	C₅×#335	C₂²	1	4	yes	complemented
39	C₅×#333	C₂²	1	4	yes	complemented
40	C₅×#331	C₂²	1	4	yes	—
41	#19299	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
42	C₂×C₅×#41	D₄	1	1	yes	characteristic
43	C₂²×C₅×Q₈	—	2	1	no	—
44	C₂²×C₅×D₄	—	2	1	no	—
45	C₂²×C₅×D₄	—	2	1	no	—
46	C₂²×C₅×D₄	—	2	1	no	—
47	C₅×AGL(1,ℤ/8)	—	4	4	no	—
48	C₂×C₅×SD₁₆	—	2	2	no	—
49	C₂×C₅×D₈	—	2	2	no	—
50	C₂×C₅×M₁₆	—	2	1	no	—
51	C₂×C₅×M₁₆	—	2	1	no	—
52	C₂×C₅×M₁₆	—	2	2	no	—
53	C₂²×C₅×C₈	D₄	1	2	yes	—
54	C₅×C₄⋊Q₈	—	2	1	no	—
55	C₅×C₄⋊Q₈	—	2	1	no	—
56	C₅×C₄⋊Q₈	—	2	1	no	—
57	C₅×C₄⋊Q₈	C₂³	1	2	yes	—
58	C₅×#127	—	2	1	no	—
59	C₅×#127	—	2	1	no	—
60	C₅×#127	—	2	1	no	—
61	C₅×#127	C₂³	1	2	yes	—
62	C₄×C₅×Q₈	D₄	1	1	yes	characteristic
63	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
64	C₄×C₅×D₄	—	2	1	no	—
65	C₄×C₅×D₄	—	2	1	no	—
66	C₄×C₅×D₄	D₄	1	1	yes	characteristic
67	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
68	C₅×#117	—	2	1	no	—
69	C₅×#117	D₄	1	1	yes	characteristic
70	C₂×C₅×C₄⋊C₄	—	2	1	no	—
71	C₂×C₅×C₄⋊C₄	—	2	1	no	—
72	C₂×C₄²×C₅	—	2	1	no	—
73	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
74	C₅×#107	—	2	2	no	—
75	C₅×#106	—	2	2	no	—
76	C₅×C₄⋊C₈	—	2	2	no	—
77	C₅×C₄⋊C₈	—	2	1	no	—
78	C₅×C₄⋊C₈	—	2	1	no	—
79	C₅×C₄⋊C₈	C₂³	1	2	yes	—
80	C₅×C₄⋊C₈	C₂³	1	2	yes	—
81	C₅×C₄⋊C₈	C₂³	1	2	yes	—
82	C₅×#103	—	2	2	no	—
83	C₅×#102	—	2	2	no	—
84	C₅×#102	—	2	4	no	—
85	C₅×#102	—	2	4	no	—
86	C₅×#102	—	2	2	no	—
87	C₅×#102	—	2	2	no	—
88	C₅×C₂²⋊C₈	—	2	1	no	—
89	C₅×C₂²⋊C₈	—	2	2	no	—
90	C₅×#97	—	2	2	no	—
91	C₄×C₅×C₈	—	2	1	no	—
92	C₄×C₅×C₈	D₄	1	1	yes	characteristic
93	C₄×C₅×C₈	D₄	1	1	yes	characteristic
94	C₄×C₅×C₈	C₂³	1	2	yes	—
95	C₂×#486	C₂×C₅	1	1	yes	characteristic, complemented
96	#3079	C₂×C₅	1	1	yes	characteristic, complemented
97	#3038	C₂×C₅	1	1	yes	characteristic
98	#2965	C₂×C₅	1	1	yes	characteristic, complemented
99	#1698	C₂×C₅	1	4	yes	complemented
100	#1697	C₂×C₅	1	4	yes	complemented
101	#1567	C₂×C₅	1	1	yes	characteristic, complemented
102	#1548	C₂×C₅	1	1	yes	characteristic, complemented
103	#1545	C₂×C₅	1	1	yes	characteristic, complemented
104	C₂⁴×C₅	—	4	1	no	—
105	C₅×#41	—	2	2	no	—
106	C₅×#41	—	2	2	no	—
107	C₂×C₅×Q₈	—	2	2	no	—
108	C₂×C₅×Q₈	—	4	1	no	—
109	C₂×C₅×Q₈	—	8	2	no	—
110	C₂×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
111	C₂×C₅×D₄	—	2	1	no	—
112	C₂×C₅×D₄	—	2	2	no	—
113	C₂×C₅×D₄	—	2	2	no	—
114	C₂×C₅×D₄	—	2	2	no	—
115	C₂×C₅×D₄	—	4	4	no	—
116	C₂×C₅×D₄	—	4	1	no	—
117	C₂×C₅×D₄	—	4	1	no	—
118	C₂×C₅×D₄	—	4	1	no	—
119	C₂×C₅×D₄	—	4	2	no	—
120	C₂×C₅×D₄	—	4	2	no	—
121	C₂×C₅×D₄	—	8	2	no	—
122	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₅	—	2	1	no	—
124	C₂²×C₄×C₅	—	2	1	no	—
125	C₂²×C₄×C₅	—	2	1	no	—
126	C₂²×C₄×C₅	—	4	1	no	—
127	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₅	#41	1	1	yes	characteristic
130	C₅×SD₁₆	—	4	4	no	—
131	C₅×D₈	—	4	4	no	—
132	C₅×M₁₆	—	4	4	no	—
133	C₅×M₁₆	—	4	2	no	—
134	C₅×M₁₆	—	4	2	no	—
135	C₂×C₅×C₈	—	2	2	no	—
136	C₂×C₅×C₈	—	2	2	no	—
137	C₂×C₅×C₈	—	2	2	no	—
138	C₂×C₅×C₈	—	4	2	no	—
139	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
140	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
141	C₅×C₄⋊C₄	—	2	1	no	—
142	C₅×C₄⋊C₄	—	2	1	no	—
143	C₅×C₄⋊C₄	—	2	2	no	—
144	C₅×C₄⋊C₄	—	2	2	no	—
145	C₅×C₄⋊C₄	—	4	1	no	—
146	C₅×C₄⋊C₄	—	4	1	no	—
147	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
148	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
149	C₅×C₂²⋊C₄	—	2	1	no	—
150	C₅×C₂²⋊C₄	—	2	1	no	—
151	C₅×C₂²⋊C₄	—	2	1	no	—
152	C₄²×C₅	—	2	1	no	—
153	C₄²×C₅	—	2	1	no	—
154	C₄²×C₅	—	2	1	no	—
155	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
156	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
157	C₄²×C₅	#41	1	1	yes	characteristic
158	C₄²×C₅	C₂⁴	1	1	yes	characteristic
159	C₂×AGL(1,ℤ/8)	—	2	1	no	—
160	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
161	C₂×#127	C₂²×C₅	1	1	yes	characteristic
162	C₄×#41	C₂²×C₅	1	1	yes	characteristic
163	#486	—	2	1	no	—
164	#486	—	2	1	no	—
165	#486	C₂²×C₅	1	4	yes	—
166	#477	C₂²×C₅	1	2	yes	complemented
167	#476	C₂²×C₅	1	2	yes	complemented
168	#475	—	2	1	no	—
169	#474	—	2	1	no	—
170	#460	—	2	1	no	—
171	#460	C₂²×C₅	1	2	yes	—
172	#459	—	2	1	no	—
173	#459	C₂²×C₅	1	2	yes	—
174	#446	C₂²×C₅	1	2	yes	complemented
175	#436	C₂²×C₅	1	2	yes	complemented
176	#435	—	2	2	no	—
177	#431	—	2	1	no	—
178	#431	C₂²×C₅	1	1	yes	characteristic
179	#428	—	2	1	no	—
180	#423	C₂²×C₅	1	1	yes	characteristic
181	#423	C₂²×C₅	1	1	yes	characteristic
182	#418	—	2	1	no	—
183	#417	—	2	1	no	—
184	C₂×#102	—	2	2	no	—
185	C₄×M₁₆	—	2	1	no	—
186	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
187	#335	C₂²×C₅	1	4	yes	complemented
188	#333	C₂²×C₅	1	4	yes	complemented
189	#331	C₂²×C₅	1	4	yes	—
190	C₂³×C₅	—	2	1	no	—
191	C₂³×C₅	—	4	2	no	—
192	C₂³×C₅	—	8	2	no	—
193	C₂³×C₅	—	8	2	no	—
194	C₂³×C₅	—	8	2	no	—
195	C₂³×C₅	#121	1	1	yes	characteristic
196	C₅×Q₈	—	2	1	no	—
197	C₅×Q₈	—	2	1	no	—
198	C₅×Q₈	—	8	2	no	—
199	C₅×Q₈	—	8	2	no	—
200	C₅×D₄	—	2	1	no	—
201	C₅×D₄	—	2	1	no	—
202	C₅×D₄	—	4	2	no	—
203	C₅×D₄	—	4	2	no	—
204	C₅×D₄	—	4	2	no	—
205	C₅×D₄	—	4	4	no	—
206	C₅×D₄	—	8	2	no	—
207	C₅×D₄	—	8	2	no	—
208	C₅×D₄	—	8	2	no	—
209	C₅×D₄	—	8	2	no	—
210	C₂×C₄×C₅	—	2	2	no	—
211	C₂×C₄×C₅	—	2	2	no	—
212	C₂×C₄×C₅	—	2	1	no	—
213	C₂×C₄×C₅	—	2	1	no	—
214	C₂×C₄×C₅	—	2	1	no	—
215	C₂×C₄×C₅	—	4	2	no	—
216	C₂×C₄×C₅	—	4	2	no	—
217	C₂×C₄×C₅	—	4	2	no	—
218	C₂×C₄×C₅	—	4	2	no	—
219	C₂×C₄×C₅	—	8	2	no	—
220	C₂×C₄×C₅	#121	1	1	yes	characteristic
221	C₂×C₄×C₅	#121	1	1	yes	characteristic
222	C₂×C₄×C₅	#121	1	1	yes	characteristic
223	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
224	C₂×C₄×C₅	#137	1	2	yes	—
225	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
226	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
227	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
228	C₅×C₈	—	2	2	no	—
229	C₅×C₈	—	2	2	no	—
230	C₅×C₈	—	4	2	no	—
231	C₅×C₈	—	4	2	no	—
232	C₅×C₈	—	4	2	no	—
233	C₂×#41	C₅×D₄	1	1	yes	characteristic
234	C₂²×Q₈	—	2	1	no	—
235	C₂²×D₄	—	2	1	no	—
236	C₂²×D₄	—	2	1	no	—
237	C₂²×D₄	—	2	1	no	—
238	AGL(1,ℤ/8)	—	4	4	no	—
239	C₂×SD₁₆	—	2	2	no	—
240	C₂×D₈	—	2	2	no	—
241	C₂×M₁₆	—	2	1	no	—
242	C₂×M₁₆	—	2	1	no	—
243	C₂×M₁₆	—	2	2	no	—
244	C₂²×C₈	C₅×D₄	1	2	yes	—
245	C₄⋊Q₈	—	2	1	no	—
246	C₄⋊Q₈	—	2	1	no	—
247	C₄⋊Q₈	—	2	1	no	—
248	C₄⋊Q₈	C₂³×C₅	1	2	yes	—
249	#127	—	2	1	no	—
250	#127	—	2	1	no	—
251	#127	—	2	1	no	—
252	#127	C₂³×C₅	1	2	yes	—
253	C₄×Q₈	C₅×D₄	1	1	yes	characteristic
254	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
255	C₄×D₄	—	2	1	no	—
256	C₄×D₄	—	2	1	no	—
257	C₄×D₄	C₅×D₄	1	1	yes	characteristic
258	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
259	#117	—	2	1	no	—
260	#117	C₅×D₄	1	1	yes	characteristic
261	C₂×C₄⋊C₄	—	2	1	no	—
262	C₂×C₄⋊C₄	—	2	1	no	—
263	C₂×C₄²	—	2	1	no	—
264	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
265	#107	—	2	2	no	—
266	#106	—	2	2	no	—
267	C₄⋊C₈	—	2	2	no	—
268	C₄⋊C₈	—	2	1	no	—
269	C₄⋊C₈	—	2	1	no	—
270	C₄⋊C₈	C₂³×C₅	1	2	yes	—
271	C₄⋊C₈	C₂³×C₅	1	2	yes	—
272	C₄⋊C₈	C₂³×C₅	1	2	yes	—
273	#103	—	2	2	no	—
274	#102	—	2	2	no	—
275	#102	—	2	4	no	—
276	#102	—	2	4	no	—
277	#102	—	2	2	no	—
278	#102	—	2	2	no	—
279	C₂²⋊C₈	—	2	1	no	—
280	C₂²⋊C₈	—	2	2	no	—
281	#97	—	2	2	no	—
282	C₄×C₈	—	2	1	no	—
283	C₄×C₈	C₅×D₄	1	1	yes	characteristic
284	C₄×C₈	C₅×D₄	1	1	yes	characteristic
285	C₄×C₈	C₂³×C₅	1	2	yes	—
286	C₂²×C₅	—	2	1	no	—
287	C₂²×C₅	—	2	1	no	—
288	C₂²×C₅	—	4	1	no	—
289	C₂²×C₅	—	4	1	no	—
290	C₂²×C₅	—	4	1	no	—
291	C₂²×C₅	—	8	2	no	—
292	C₂²×C₅	—	8	2	no	—
293	C₂²×C₅	—	8	2	no	—
294	C₂²×C₅	—	16	4	no	—
295	C₂²×C₅	#468	1	2	yes	—
296	C₂²×C₅	C₂×#121	1	1	yes	characteristic
297	C₄×C₅	—	2	1	no	—
298	C₄×C₅	—	2	1	no	—
299	C₄×C₅	—	4	1	no	—
300	C₄×C₅	—	4	1	no	—
301	C₄×C₅	—	4	1	no	—
302	C₄×C₅	—	8	2	no	—
303	C₄×C₅	#468	1	2	yes	—
304	C₄×C₅	#472	1	2	yes	—
305	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
306	C₄×C₅	C₂×#137	1	1	yes	characteristic
307	C₄×C₅	#575	1	2	yes	—
308	C₂⁴	—	4	1	no	—
309	#41	—	2	2	no	—
310	#41	—	2	2	no	—
311	C₂×Q₈	—	2	2	no	—
312	C₂×Q₈	—	4	1	no	—
313	C₂×Q₈	—	8	2	no	—
314	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
315	C₂×D₄	—	2	1	no	—
316	C₂×D₄	—	2	2	no	—
317	C₂×D₄	—	2	2	no	—
318	C₂×D₄	—	2	2	no	—
319	C₂×D₄	—	4	4	no	—
320	C₂×D₄	—	4	1	no	—
321	C₂×D₄	—	4	1	no	—
322	C₂×D₄	—	4	1	no	—
323	C₂×D₄	—	4	2	no	—
324	C₂×D₄	—	4	2	no	—
325	C₂×D₄	—	8	2	no	—
326	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	4	1	no	—
331	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
332	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
333	C₂²×C₄	C₅×#41	1	1	yes	characteristic
334	SD₁₆	—	4	4	no	—
335	D₈	—	4	4	no	—
336	M₁₆	—	4	4	no	—
337	M₁₆	—	4	2	no	—
338	M₁₆	—	4	2	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	4	2	no	—
343	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
344	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
345	C₄⋊C₄	—	2	1	no	—
346	C₄⋊C₄	—	2	1	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	4	1	no	—
350	C₄⋊C₄	—	4	1	no	—
351	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
352	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
353	C₂²⋊C₄	—	2	1	no	—
354	C₂²⋊C₄	—	2	1	no	—
355	C₂²⋊C₄	—	2	1	no	—
356	C₄²	—	2	1	no	—
357	C₄²	—	2	1	no	—
358	C₄²	—	2	1	no	—
359	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
360	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
361	C₄²	C₅×#41	1	1	yes	characteristic
362	C₄²	C₂⁴×C₅	1	1	yes	characteristic
363	C₂×C₅	—	2	2	no	—
364	C₂×C₅	—	8	1	no	—
365	C₂×C₅	—	16	2	no	—
366	C₂×C₅	#3040	1	1	yes	characteristic
367	C₂×C₅	C₂×#468	1	1	yes	characteristic
368	C₂×C₅	C₂×#472	1	1	yes	characteristic
369	C₂³	—	2	1	no	—
370	C₂³	—	4	2	no	—
371	C₂³	—	8	2	no	—
372	C₂³	—	8	2	no	—
373	C₂³	—	8	2	no	—
374	C₂³	C₅×#121	1	1	yes	characteristic
375	Q₈	—	2	1	no	—
376	Q₈	—	2	1	no	—
377	Q₈	—	8	2	no	—
378	Q₈	—	8	2	no	—
379	D₄	—	2	1	no	—
380	D₄	—	2	1	no	—
381	D₄	—	4	2	no	—
382	D₄	—	4	2	no	—
383	D₄	—	4	2	no	—
384	D₄	—	4	4	no	—
385	D₄	—	8	2	no	—
386	D₄	—	8	2	no	—
387	D₄	—	8	2	no	—
388	D₄	—	8	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	8	2	no	—
399	C₂×C₄	C₅×#121	1	1	yes	characteristic
400	C₂×C₄	C₅×#121	1	1	yes	characteristic
401	C₂×C₄	C₅×#121	1	1	yes	characteristic
402	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
403	C₂×C₄	C₅×#137	1	2	yes	—
404	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
405	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
406	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
407	C₈	—	2	2	no	—
408	C₈	—	2	2	no	—
409	C₈	—	4	2	no	—
410	C₈	—	4	2	no	—
411	C₈	—	4	2	no	—
412	C₅	#19299	1	1	yes	characteristic, direct product factor, Sylow
413	C₂²	—	2	1	no	—
414	C₂²	—	2	1	no	—
415	C₂²	—	4	1	no	—
416	C₂²	—	4	1	no	—
417	C₂²	—	4	1	no	—
418	C₂²	—	8	2	no	—
419	C₂²	—	8	2	no	—
420	C₂²	—	8	2	no	—
421	C₂²	—	16	4	no	—
422	C₂²	C₅×#468	1	2	yes	—
423	C₂²	C₂×C₅×#121	1	1	yes	characteristic
424	C₄	—	2	1	no	—
425	C₄	—	2	1	no	—
426	C₄	—	4	1	no	—
427	C₄	—	4	1	no	—
428	C₄	—	4	1	no	—
429	C₄	—	8	2	no	—
430	C₄	C₅×#468	1	2	yes	—
431	C₄	C₅×#472	1	2	yes	—
432	C₄	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
433	C₄	C₂×C₅×#137	1	1	yes	characteristic
434	C₄	C₅×#575	1	2	yes	—
435	C₂	—	2	2	no	—
436	C₂	—	8	1	no	—
437	C₂	—	16	2	no	—
438	C₂	C₅×#3040	1	1	yes	characteristic
439	C₂	C₂×C₅×#468	1	1	yes	characteristic
440	C₂	C₂×C₅×#472	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₅
prime radical	C₅×#3038	C₂
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. C₂×C₅×#486	C₂	semidirect
2. C₅×#3079	C₂	semidirect
4. C₅×#2965	C₂	semidirect
5. C₅×#1698	C₂	semidirect
6. C₅×#1697	C₂	semidirect
7. C₅×#1567	C₂	semidirect
8. C₅×#1548	C₂	semidirect
9. C₅×#1545	C₂	semidirect
17. C₅×#477	C₂²	semidirect
18. C₅×#476	C₂²	semidirect
25. C₅×#446	C₂²	semidirect
26. C₅×#436	C₂²	semidirect
38. C₅×#335	C₂²	semidirect
39. C₅×#333	C₂²	semidirect
41. #19299	C₅	direct (N × H)
95. C₂×#486	C₂×C₅	semidirect
96. #3079	C₂×C₅	semidirect
98. #2965	C₂×C₅	semidirect
99. #1698	C₂×C₅	semidirect
100. #1697	C₂×C₅	semidirect
101. #1567	C₂×C₅	semidirect
102. #1548	C₂×C₅	semidirect
103. #1545	C₂×C₅	semidirect
166. #477	C₂²×C₅	semidirect
167. #476	C₂²×C₅	semidirect
174. #446	C₂²×C₅	semidirect
175. #436	C₂²×C₅	semidirect
187. #335	C₂²×C₅	semidirect
188. #333	C₂²×C₅	semidirect
412. C₅	#19299	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₅×#486	2
C₅×#3079	2
C₅×#3038	2
C₅×#2965	2
C₅×#1698	2
C₅×#1697	2
C₅×#1567	2
C₅×#1548	2
C₅×#1545	2
#19299	5

Subgroups — C5×#19299 #11942019

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#19299 #11942019