Subgroups — C₅×#68383 #14284765

Order 1920.

688 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₃×#127	C₂	1	1	yes	maximal, characteristic
2	C₅×#4837	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#4833	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#331	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4544	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4485	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4485	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1545	—	3	1	no	maximal, Hall
9	C₂×C₅×D₃×D₄	—	2	1	no	—
10	C₂×C₅×D₃×D₄	—	2	1	no	—
11	C₂×C₅×D₃×D₄	C₄	1	2	yes	—
12	C₃×C₅×#127	C₂²	1	1	yes	characteristic
13	C₅×#940	—	2	1	no	—
14	C₅×#940	—	2	1	no	—
15	C₅×#940	C₄	1	2	yes	—
16	C₂×C₅×ΓL(1,𝔽₂₅)	—	2	1	no	—
17	C₅×#874	C₂²	1	1	yes	characteristic
18	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
19	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
20	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
21	C₅×(C₂×D₃)⋊C₈	—	2	1	no	—
22	C₅×Dic₃⋊C₈	—	2	1	no	—
23	C₅×C₈×Dic₃	—	2	1	no	—
24	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
25	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
26	#68383	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
27	C₂×C₅×#127	—	3	1	no	—
28	C₅×#431	—	3	1	no	—
29	C₅×#423	—	3	1	no	—
30	C₅×#331	—	3	1	no	—
31	C₅×#331	—	3	1	no	—
32	C₅×#331	—	3	1	no	—
33	C₅×#331	D₃	1	1	yes	characteristic, complemented
34	C₂³×C₅×D₃	—	2	2	no	—
35	C₂×C₃×C₅×D₄	—	2	1	no	—
36	C₂×C₃×C₅×D₄	—	2	1	no	—
37	C₂×C₃×C₅×D₄	C₂×C₄	1	2	yes	—
38	C₂×C₅×#67	—	2	2	no	—
39	C₂×C₅×#67	—	2	2	no	—
40	C₂×C₅×#67	—	2	2	no	—
41	C₅×D₃×D₄	—	4	2	no	—
42	C₅×D₃×D₄	—	4	2	no	—
43	C₅×D₃×D₄	—	4	4	no	—
44	C₅×D₃×D₄	—	4	2	no	—
45	C₅×D₃×D₄	—	4	2	no	—
46	C₂×C₅×D₁₂	—	2	1	no	—
47	C₂×C₅×D₁₂	—	2	1	no	—
48	C₂×C₅×D₁₂	C₂×C₄	1	2	yes	—
49	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
51	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
52	C₂×C₃×C₅×C₈	—	2	1	no	—
53	C₂×C₃×C₅×C₈	—	2	1	no	—
54	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
55	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
56	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
57	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
58	C₂×C₅×C₃⋊C₈	—	2	1	no	—
59	C₂×C₅×C₃⋊C₈	—	2	1	no	—
60	C₅×ΓL(1,𝔽₂₅)	—	4	2	no	—
61	D₃×#127	C₂×C₅	1	1	yes	characteristic
62	#4837	C₂×C₅	1	1	yes	characteristic, complemented
63	#4833	C₂×C₅	1	1	yes	characteristic, complemented
64	C₃×#331	C₂×C₅	1	1	yes	characteristic, complemented
65	#4544	C₂×C₅	1	1	yes	characteristic, complemented
66	#4485	C₂×C₅	1	1	yes	characteristic, complemented
67	#4485	C₂×C₅	1	1	yes	characteristic, complemented
68	C₂²×C₅×D₄	—	3	2	no	—
69	C₂²×C₅×D₄	—	6	1	no	—
70	C₂²×C₅×D₄	—	6	1	no	—
71	C₂×C₅×M₁₆	—	6	1	no	—
72	C₅×#127	—	3	2	no	—
73	C₅×#127	—	3	1	no	—
74	C₅×#127	—	6	1	no	—
75	C₅×#127	—	6	1	no	—
76	C₅×#127	C₂×D₃	1	1	yes	characteristic
77	C₂×C₄²×C₅	—	3	1	no	—
78	C₅×C₄⋊C₈	—	3	1	no	—
79	C₅×C₄⋊C₈	—	3	1	no	—
80	C₅×C₄⋊C₈	—	6	1	no	—
81	C₅×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic, complemented
82	C₅×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic, complemented
83	C₅×C₂²⋊C₈	—	6	1	no	—
84	C₄×C₅×C₈	—	6	1	no	—
85	#1545	—	3	1	no	Sylow
86	C₂³×C₃×C₅	—	2	2	no	—
87	C₂²×C₅×D₃	—	2	2	no	—
88	C₂²×C₅×D₃	—	4	4	no	—
89	C₂²×C₅×D₃	—	4	4	no	—
90	C₂²×C₅×D₃	—	4	4	no	—
91	C₂²×C₅×D₃	C₂²⋊C₄	1	1	yes	characteristic
92	C₃×C₅×D₄	—	4	2	no	—
93	C₃×C₅×D₄	—	4	1	no	—
94	C₃×C₅×D₄	—	4	1	no	—
95	C₃×C₅×D₄	—	4	1	no	—
96	C₃×C₅×D₄	—	4	1	no	—
97	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
98	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
99	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
100	C₅×#67	—	4	4	no	—
101	C₅×#67	—	4	4	no	—
102	C₅×#67	—	4	4	no	—
103	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
104	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
105	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
106	C₅×D₁₂	—	4	2	no	—
107	C₅×D₁₂	—	4	1	no	—
108	C₅×D₁₂	—	4	1	no	—
109	C₅×D₁₂	—	4	1	no	—
110	C₅×D₁₂	—	4	1	no	—
111	C₄×C₅×D₃	—	2	1	no	—
112	C₄×C₅×D₃	—	2	1	no	—
113	C₄×C₅×D₃	—	2	2	no	—
114	C₄×C₅×D₃	D₈	1	2	yes	—
115	C₄×C₅×D₃	SD₁₆	1	2	yes	—
116	C₃×C₅×C₈	—	4	1	no	—
117	C₃×C₅×C₈	—	4	1	no	—
118	C₅×C₃⋊C₈	—	4	1	no	—
119	C₅×C₃⋊C₈	—	4	1	no	—
120	C₂×D₃×D₄	—	2	1	no	—
121	C₂×D₃×D₄	—	2	1	no	—
122	C₂×D₃×D₄	C₄×C₅	1	2	yes	—
123	C₃×#127	C₂²×C₅	1	1	yes	characteristic
124	#940	—	2	1	no	—
125	#940	—	2	1	no	—
126	#940	C₄×C₅	1	2	yes	—
127	C₂×ΓL(1,𝔽₂₅)	—	2	1	no	—
128	#874	C₂²×C₅	1	1	yes	characteristic
129	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
130	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
131	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
132	(C₂×D₃)⋊C₈	—	2	1	no	—
133	Dic₃⋊C₈	—	2	1	no	—
134	C₈×Dic₃	—	2	1	no	—
135	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic, complemented
136	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic, complemented
137	C₂⁴×C₅	—	6	2	no	—
138	C₂×C₅×D₄	—	2	1	no	—
139	C₂×C₅×D₄	—	2	1	no	—
140	C₂×C₅×D₄	—	3	2	no	—
141	C₂×C₅×D₄	—	6	2	no	—
142	C₂×C₅×D₄	—	6	2	no	—
143	C₂×C₅×D₄	—	6	2	no	—
144	C₂×C₅×D₄	—	6	1	no	—
145	C₂×C₅×D₄	—	6	1	no	—
146	C₂×C₅×D₄	—	12	2	no	—
147	C₂×C₅×D₄	—	12	2	no	—
148	C₂×C₅×D₄	—	12	2	no	—
149	C₂×C₅×D₄	—	12	2	no	—
150	C₂×C₅×D₄	—	12	4	no	—
151	C₂×C₅×D₄	C₄×D₃	1	2	yes	—
152	C₂²×C₄×C₅	—	3	1	no	—
153	C₂²×C₄×C₅	—	3	1	no	—
154	C₂²×C₄×C₅	—	3	1	no	—
155	C₅×M₁₆	—	12	2	no	—
156	C₂×C₅×C₈	—	2	1	no	—
157	C₂×C₅×C₈	—	2	1	no	—
158	C₂×C₅×C₈	—	6	1	no	—
159	C₂×C₅×C₈	—	6	1	no	—
160	C₄²×C₅	—	3	1	no	—
161	C₄²×C₅	—	3	1	no	—
162	C₄²×C₅	—	3	1	no	—
163	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
164	C₂×#127	—	3	1	no	—
165	#431	—	3	1	no	—
166	#423	—	3	1	no	—
167	#331	—	3	1	no	—
168	#331	—	3	1	no	—
169	#331	—	3	1	no	—
170	#331	C₅×D₃	1	1	yes	characteristic, complemented
171	C₂²×C₃×C₅	—	4	2	no	—
172	C₂²×C₃×C₅	—	4	2	no	—
173	C₂²×C₃×C₅	—	4	2	no	—
174	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
175	C₂×C₅×D₃	—	2	1	no	—
176	C₂×C₅×D₃	—	2	1	no	—
177	C₂×C₅×D₃	—	4	2	no	—
178	C₂×C₅×D₃	—	4	2	no	—
179	C₂×C₅×D₃	—	4	2	no	—
180	C₂×C₅×D₃	—	8	8	no	—
181	C₂×C₅×D₃	#102	1	2	yes	—
182	C₃×C₄×C₅	—	2	1	no	—
183	C₃×C₄×C₅	C₂×D₈	1	1	yes	characteristic
184	C₃×C₄×C₅	C₂×SD₁₆	1	1	yes	characteristic
185	C₃×C₄×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
186	C₃×C₄×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
187	C₅×Dic₃	—	2	1	no	—
188	C₅×Dic₃	#100	1	2	yes	—
189	C₅×Dic₃	#102	1	2	yes	—
190	C₂³×D₃	—	2	2	no	—
191	C₂×C₃×D₄	—	2	1	no	—
192	C₂×C₃×D₄	—	2	1	no	—
193	C₂×C₃×D₄	C₂×C₄×C₅	1	2	yes	—
194	C₂×#67	—	2	2	no	—
195	C₂×#67	—	2	2	no	—
196	C₂×#67	—	2	2	no	—
197	D₃×D₄	—	4	2	no	—
198	D₃×D₄	—	4	2	no	—
199	D₃×D₄	—	4	4	no	—
200	D₃×D₄	—	4	2	no	—
201	D₃×D₄	—	4	2	no	—
202	C₂×D₁₂	—	2	1	no	—
203	C₂×D₁₂	—	2	1	no	—
204	C₂×D₁₂	C₂×C₄×C₅	1	2	yes	—
205	C₂×C₄×D₃	C₂×C₄×C₅	1	1	yes	characteristic
206	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
207	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
208	C₂×C₃×C₈	—	2	1	no	—
209	C₂×C₃×C₈	—	2	1	no	—
210	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
211	C₄×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
212	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
213	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
214	C₂×C₃⋊C₈	—	2	1	no	—
215	C₂×C₃⋊C₈	—	2	1	no	—
216	ΓL(1,𝔽₂₅)	—	4	2	no	—
217	C₂³×C₅	—	2	2	no	—
218	C₂³×C₅	—	3	1	no	—
219	C₂³×C₅	—	6	2	no	—
220	C₂³×C₅	—	12	4	no	—
221	C₂³×C₅	—	12	4	no	—
222	C₂³×C₅	—	12	4	no	—
223	C₅×D₄	—	4	2	no	—
224	C₅×D₄	—	4	1	no	—
225	C₅×D₄	—	4	1	no	—
226	C₅×D₄	—	4	1	no	—
227	C₅×D₄	—	4	1	no	—
228	C₅×D₄	—	12	2	no	—
229	C₅×D₄	—	12	4	no	—
230	C₅×D₄	—	12	4	no	—
231	C₅×D₄	—	12	4	no	—
232	C₅×D₄	—	12	1	no	—
233	C₅×D₄	—	12	1	no	—
234	C₅×D₄	—	12	1	no	—
235	C₅×D₄	—	12	1	no	—
236	C₂×C₄×C₅	—	3	1	no	—
237	C₂×C₄×C₅	—	3	1	no	—
238	C₂×C₄×C₅	—	3	2	no	—
239	C₂×C₄×C₅	—	3	2	no	—
240	C₂×C₄×C₅	—	3	1	no	—
241	C₂×C₄×C₅	—	6	2	no	—
242	C₂×C₄×C₅	—	6	1	no	—
243	C₂×C₄×C₅	—	6	1	no	—
244	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
245	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
246	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
247	C₅×C₈	—	4	1	no	—
248	C₅×C₈	—	4	1	no	—
249	C₅×C₈	—	12	1	no	—
250	C₅×C₈	—	12	1	no	—
251	C₂²×D₄	—	3	2	no	—
252	C₂²×D₄	—	6	1	no	—
253	C₂²×D₄	—	6	1	no	—
254	C₂×M₁₆	—	6	1	no	—
255	#127	—	3	2	no	—
256	#127	—	3	1	no	—
257	#127	—	6	1	no	—
258	#127	—	6	1	no	—
259	#127	C₂×C₅×D₃	1	1	yes	characteristic
260	C₂×C₄²	—	3	1	no	—
261	C₄⋊C₈	—	3	1	no	—
262	C₄⋊C₈	—	3	1	no	—
263	C₄⋊C₈	—	6	1	no	—
264	C₄⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
265	C₄⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
266	C₂²⋊C₈	—	6	1	no	—
267	C₄×C₈	—	6	1	no	—
268	C₂×C₃×C₅	—	8	2	no	—
269	C₂×C₃×C₅	C₂×#100	1	1	yes	characteristic
270	C₂×C₃×C₅	C₂×#102	1	1	yes	characteristic
271	C₂×C₃×C₅	#418	1	1	yes	characteristic
272	C₅×D₃	—	2	2	no	—
273	C₅×D₃	—	8	2	no	—
274	C₂³×C₃	—	2	2	no	—
275	C₂²×D₃	—	2	2	no	—
276	C₂²×D₃	—	4	4	no	—
277	C₂²×D₃	—	4	4	no	—
278	C₂²×D₃	—	4	4	no	—
279	C₂²×D₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
280	C₃×D₄	—	4	2	no	—
281	C₃×D₄	—	4	1	no	—
282	C₃×D₄	—	4	1	no	—
283	C₃×D₄	—	4	1	no	—
284	C₃×D₄	—	4	1	no	—
285	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
286	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
287	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
288	#67	—	4	4	no	—
289	#67	—	4	4	no	—
290	#67	—	4	4	no	—
291	C₂×Dic₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
292	C₂×Dic₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
293	C₂×Dic₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
294	D₁₂	—	4	2	no	—
295	D₁₂	—	4	1	no	—
296	D₁₂	—	4	1	no	—
297	D₁₂	—	4	1	no	—
298	D₁₂	—	4	1	no	—
299	C₄×D₃	—	2	1	no	—
300	C₄×D₃	—	2	1	no	—
301	C₄×D₃	—	2	2	no	—
302	C₄×D₃	C₅×D₈	1	2	yes	—
303	C₄×D₃	C₅×SD₁₆	1	2	yes	—
304	C₃×C₈	—	4	1	no	—
305	C₃×C₈	—	4	1	no	—
306	C₃⋊C₈	—	4	1	no	—
307	C₃⋊C₈	—	4	1	no	—
308	C₂²×C₅	—	3	2	no	—
309	C₂²×C₅	—	4	2	no	—
310	C₂²×C₅	—	4	2	no	—
311	C₂²×C₅	—	4	2	no	—
312	C₂²×C₅	—	6	1	no	—
313	C₂²×C₅	—	6	1	no	—
314	C₂²×C₅	—	12	2	no	—
315	C₂²×C₅	—	12	2	no	—
316	C₂²×C₅	—	12	2	no	—
317	C₂²×C₅	—	24	8	no	—
318	C₂²×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
319	C₄×C₅	—	2	1	no	—
320	C₄×C₅	—	3	2	no	—
321	C₄×C₅	—	3	2	no	—
322	C₄×C₅	—	6	1	no	—
323	C₄×C₅	D₃×D₈	1	1	yes	characteristic
324	C₄×C₅	#911	1	1	yes	characteristic
325	C₄×C₅	D₃×SD₁₆	1	1	yes	characteristic
326	C₄×C₅	#914	1	1	yes	characteristic
327	C₂⁴	—	6	2	no	—
328	C₂×D₄	—	2	1	no	—
329	C₂×D₄	—	2	1	no	—
330	C₂×D₄	—	3	2	no	—
331	C₂×D₄	—	6	2	no	—
332	C₂×D₄	—	6	2	no	—
333	C₂×D₄	—	6	2	no	—
334	C₂×D₄	—	6	1	no	—
335	C₂×D₄	—	6	1	no	—
336	C₂×D₄	—	12	2	no	—
337	C₂×D₄	—	12	2	no	—
338	C₂×D₄	—	12	2	no	—
339	C₂×D₄	—	12	2	no	—
340	C₂×D₄	—	12	4	no	—
341	C₂×D₄	C₄×C₅×D₃	1	2	yes	—
342	C₂²×C₄	—	3	1	no	—
343	C₂²×C₄	—	3	1	no	—
344	C₂²×C₄	—	3	1	no	—
345	M₁₆	—	12	2	no	—
346	C₂×C₈	—	2	1	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	6	1	no	—
349	C₂×C₈	—	6	1	no	—
350	C₄²	—	3	1	no	—
351	C₄²	—	3	1	no	—
352	C₄²	—	3	1	no	—
353	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
354	C₃×C₅	#1545	1	1	yes	characteristic, complemented, Hall
355	C₂²×C₃	—	4	2	no	—
356	C₂²×C₃	—	4	2	no	—
357	C₂²×C₃	—	4	2	no	—
358	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
359	C₂×D₃	—	2	1	no	—
360	C₂×D₃	—	2	1	no	—
361	C₂×D₃	—	4	2	no	—
362	C₂×D₃	—	4	2	no	—
363	C₂×D₃	—	4	2	no	—
364	C₂×D₃	—	8	8	no	—
365	C₂×D₃	C₅×#102	1	2	yes	—
366	C₃×C₄	—	2	1	no	—
367	C₃×C₄	C₂×C₅×D₈	1	1	yes	characteristic
368	C₃×C₄	C₂×C₅×SD₁₆	1	1	yes	characteristic
369	C₃×C₄	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
370	C₃×C₄	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
371	Dic₃	—	2	1	no	—
372	Dic₃	C₅×#100	1	2	yes	—
373	Dic₃	C₅×#102	1	2	yes	—
374	C₂×C₅	—	6	2	no	—
375	C₂×C₅	—	8	2	no	—
376	C₂×C₅	—	24	2	no	—
377	C₂×C₅	D₃×#100	1	1	yes	characteristic
378	C₂×C₅	D₃×#102	1	1	yes	characteristic
379	C₂×C₅	#4770	1	1	yes	characteristic
380	C₂³	—	2	2	no	—
381	C₂³	—	3	1	no	—
382	C₂³	—	6	2	no	—
383	C₂³	—	12	4	no	—
384	C₂³	—	12	4	no	—
385	C₂³	—	12	4	no	—
386	D₄	—	4	2	no	—
387	D₄	—	4	1	no	—
388	D₄	—	4	1	no	—
389	D₄	—	4	1	no	—
390	D₄	—	4	1	no	—
391	D₄	—	12	2	no	—
392	D₄	—	12	4	no	—
393	D₄	—	12	4	no	—
394	D₄	—	12	4	no	—
395	D₄	—	12	1	no	—
396	D₄	—	12	1	no	—
397	D₄	—	12	1	no	—
398	D₄	—	12	1	no	—
399	C₂×C₄	—	3	1	no	—
400	C₂×C₄	—	3	1	no	—
401	C₂×C₄	—	3	2	no	—
402	C₂×C₄	—	3	2	no	—
403	C₂×C₄	—	3	1	no	—
404	C₂×C₄	—	6	2	no	—
405	C₂×C₄	—	6	1	no	—
406	C₂×C₄	—	6	1	no	—
407	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
408	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
409	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
410	C₈	—	4	1	no	—
411	C₈	—	4	1	no	—
412	C₈	—	12	1	no	—
413	C₈	—	12	1	no	—
414	C₂×C₃	—	8	2	no	—
415	C₂×C₃	C₂×C₅×#100	1	1	yes	characteristic
416	C₂×C₃	C₂×C₅×#102	1	1	yes	characteristic
417	C₂×C₃	C₅×#418	1	1	yes	characteristic
418	D₃	—	2	2	no	—
419	D₃	—	8	2	no	—
420	C₅	#68383	1	1	yes	characteristic, direct product factor, Sylow
421	C₂²	—	3	2	no	—
422	C₂²	—	4	2	no	—
423	C₂²	—	4	2	no	—
424	C₂²	—	4	2	no	—
425	C₂²	—	6	1	no	—
426	C₂²	—	6	1	no	—
427	C₂²	—	12	2	no	—
428	C₂²	—	12	2	no	—
429	C₂²	—	12	2	no	—
430	C₂²	—	24	8	no	—
431	C₂²	C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
432	C₄	—	2	1	no	—
433	C₄	—	3	2	no	—
434	C₄	—	3	2	no	—
435	C₄	—	6	1	no	—
436	C₄	C₅×D₃×D₈	1	1	yes	characteristic
437	C₄	C₅×#911	1	1	yes	characteristic
438	C₄	C₅×D₃×SD₁₆	1	1	yes	characteristic
439	C₄	C₅×#914	1	1	yes	characteristic
440	C₃	C₅×#1545	1	1	yes	characteristic, complemented, Sylow
441	C₂	—	6	2	no	—
442	C₂	—	8	2	no	—
443	C₂	—	24	2	no	—
444	C₂	C₅×D₃×#100	1	1	yes	characteristic
445	C₂	C₅×D₃×#102	1	1	yes	characteristic
446	C₂	C₅×#4770	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	D₃×C₂²⋊C₄
commutator	C₂×C₃×C₄	C₂²×C₄×C₅
Frattini	C₄²	C₂²×C₅×D₃
Fitting	C₃×C₅×#331	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₅×D₃×#127	C₂
cosocle	C₃×C₄²	C₂³×C₅
hypercenter	C₅×#331	D₃
hypocenter	C₃	C₅×#1545
LCS	G ▷ C₂×C₃×C₄ ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×#331

Complements

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

N	H ≅ G/N	type
2. C₅×#4837	C₂	semidirect
3. C₅×#4833	C₂	semidirect
4. C₃×C₅×#331	C₂	semidirect
5. C₅×#4544	C₂	semidirect
6. C₅×#4485	C₂	semidirect
7. C₅×#4485	C₂	semidirect
19. C₃×C₅×C₄⋊C₈	C₂²	semidirect
20. C₃×C₅×C₄⋊C₈	C₂²	semidirect
24. C₅×C₄⋊(C₃⋊C₈)	C₂²	semidirect
25. C₅×C₄⋊(C₃⋊C₈)	C₂²	semidirect
26. #68383	C₅	direct (N × H)
33. C₅×#331	D₃	semidirect
62. #4837	C₂×C₅	semidirect
63. #4833	C₂×C₅	semidirect
64. C₃×#331	C₂×C₅	semidirect
65. #4544	C₂×C₅	semidirect
66. #4485	C₂×C₅	semidirect
67. #4485	C₂×C₅	semidirect
81. C₅×C₄⋊C₈	C₂×D₃	semidirect
82. C₅×C₄⋊C₈	C₂×D₃	semidirect
130. C₃×C₄⋊C₈	C₂²×C₅	semidirect
131. C₃×C₄⋊C₈	C₂²×C₅	semidirect
135. C₄⋊(C₃⋊C₈)	C₂²×C₅	semidirect
136. C₄⋊(C₃⋊C₈)	C₂²×C₅	semidirect
170. #331	C₅×D₃	semidirect
264. C₄⋊C₈	C₂×C₅×D₃	semidirect
265. C₄⋊C₈	C₂×C₅×D₃	semidirect
354. C₃×C₅	#1545	semidirect
420. C₅	#68383	direct (N × H)
440. C₃	C₅×#1545	semidirect

Maximal subgroups

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

subgroup	index
C₅×D₃×#127	2
C₅×#4837	2
C₅×#4833	2
C₃×C₅×#331	2
C₅×#4544	2
C₅×#4485	2
C₅×#1545	3
#68383	5

Subgroups — C5×#68383 #14284765

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#68383 #14284765