Subgroups — C₅×#68343 #14284031

Order 1920.

528 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₃×#124	C₂	1	1	yes	maximal, characteristic
2	C₅×#4707	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#4705	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#329	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4540	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4464	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4464	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1527	—	3	1	no	maximal, Hall
9	C₂×C₅×D₃×Q₈	C₄	1	1	yes	characteristic
10	C₂×C₅×D₃×D₄	C₄	1	1	yes	characteristic
11	C₃×C₅×#124	C₂²	1	1	yes	characteristic
12	C₅×#947	C₄	1	1	yes	characteristic
13	C₅×#936	C₄	1	1	yes	characteristic
14	C₂×C₅×ΓL(1,𝔽₂₅)	—	2	1	no	—
15	C₅×#885	—	2	1	no	—
16	C₅×#885	—	2	1	no	—
17	C₅×D₃×C₂²⋊C₄	—	2	1	no	—
18	C₅×D₃×C₂²⋊C₄	—	2	1	no	—
19	C₅×#875	C₂²	1	1	yes	characteristic
20	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
21	C₃×C₅×#97	C₂²	1	1	yes	characteristic, complemented
22	C₃×C₅×#97	C₂²	1	1	yes	characteristic, complemented
23	C₅×(C₂×D₃)⋊C₈	—	2	1	no	—
24	C₅×Dic₃⋊C₈	—	2	1	no	—
25	C₅×C₈×Dic₃	—	2	1	no	—
26	C₅×#803	C₂²	1	1	yes	characteristic, complemented
27	C₅×#803	C₂²	1	1	yes	characteristic, complemented
28	#68343	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
29	C₂×C₅×#124	—	3	1	no	—
30	C₅×#432	—	3	1	no	—
31	C₄×C₅×M₁₆	—	3	1	no	—
32	C₅×#329	—	3	1	no	—
33	C₅×#329	—	3	1	no	—
34	C₅×#329	—	3	1	no	—
35	C₅×#329	D₃	1	1	yes	characteristic, complemented
36	C₂³×C₅×D₃	—	2	1	no	—
37	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
38	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
39	C₂×C₅×#67	—	2	1	no	—
40	C₅×D₃×Q₈	—	4	2	no	—
41	C₅×D₃×D₄	—	4	2	no	—
42	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄×C₅×D₃	—	2	1	no	—
44	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
46	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
47	C₂×C₅×Dic₆	—	2	1	no	—
48	C₂×C₅×Dic₆	C₂×C₄	1	1	yes	characteristic
49	C₂×C₃×C₅×C₈	—	2	1	no	—
50	C₂×C₃×C₅×C₈	—	2	1	no	—
51	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
52	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
53	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
54	C₅×#217	—	2	1	no	—
55	C₅×#217	—	2	1	no	—
56	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
57	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
58	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
59	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
60	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
61	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
62	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
63	C₂×C₅×C₃⋊C₈	—	2	1	no	—
64	C₂×C₅×C₃⋊C₈	—	2	1	no	—
65	C₅×ΓL(1,𝔽₂₅)	—	2	4	no	—
66	D₃×#124	C₂×C₅	1	1	yes	characteristic
67	#4707	C₂×C₅	1	1	yes	characteristic, complemented
68	#4705	C₂×C₅	1	1	yes	characteristic, complemented
69	C₃×#329	C₂×C₅	1	1	yes	characteristic, complemented
70	#4540	C₂×C₅	1	1	yes	characteristic, complemented
71	#4464	C₂×C₅	1	1	yes	characteristic, complemented
72	#4464	C₂×C₅	1	1	yes	characteristic, complemented
73	C₂²×C₅×Q₈	—	3	1	no	—
74	C₂²×C₅×D₄	—	3	1	no	—
75	C₂×C₅×M₁₆	—	6	1	no	—
76	C₅×#124	—	3	1	no	—
77	C₅×#124	—	3	1	no	—
78	C₅×#124	—	3	1	no	—
79	C₅×#124	—	6	1	no	—
80	C₅×#124	—	6	1	no	—
81	C₅×#124	C₂×D₃	1	1	yes	characteristic
82	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
83	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
84	C₂×C₄²×C₅	—	3	1	no	—
85	C₅×C₄⋊C₈	—	6	1	no	—
86	C₅×C₂²⋊C₈	—	6	1	no	—
87	C₅×#97	—	3	1	no	—
88	C₅×#97	—	3	1	no	—
89	C₅×#97	C₂×D₃	1	1	yes	characteristic, complemented
90	C₅×#97	C₂×D₃	1	1	yes	characteristic, complemented
91	C₄×C₅×C₈	—	6	1	no	—
92	#1527	—	3	1	no	Sylow
93	C₂³×C₃×C₅	—	2	1	no	—
94	C₂²×C₅×D₃	—	2	1	no	—
95	C₂²×C₅×D₃	—	4	2	no	—
96	C₂²×C₅×D₃	—	4	2	no	—
97	C₂²×C₅×D₃	—	4	2	no	—
98	C₂²×C₅×D₃	C₂²⋊C₄	1	1	yes	characteristic
99	C₃×C₅×Q₈	—	4	1	no	—
100	C₃×C₅×D₄	—	4	1	no	—
101	C₂×C₃×C₄×C₅	—	2	1	no	—
102	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
103	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
104	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
105	C₅×#67	—	4	2	no	—
106	C₂×C₅×Dic₃	—	2	1	no	—
107	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
108	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
109	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
110	C₅×D₁₂	—	4	1	no	—
111	C₄×C₅×D₃	—	2	2	no	—
112	C₄×C₅×D₃	—	2	2	no	—
113	C₄×C₅×D₃	—	4	1	no	—
114	C₄×C₅×D₃	—	4	2	no	—
115	C₅×Dic₆	—	4	2	no	—
116	C₅×Dic₆	—	4	1	no	—
117	C₃×C₅×C₈	—	2	2	no	—
118	C₃×C₅×C₈	—	4	1	no	—
119	C₅×C₃⋊C₈	—	2	2	no	—
120	C₅×C₃⋊C₈	—	4	1	no	—
121	C₂×D₃×Q₈	C₄×C₅	1	1	yes	characteristic
122	C₂×D₃×D₄	C₄×C₅	1	1	yes	characteristic
123	C₃×#124	C₂²×C₅	1	1	yes	characteristic
124	#947	C₄×C₅	1	1	yes	characteristic
125	#936	C₄×C₅	1	1	yes	characteristic
126	C₂×ΓL(1,𝔽₂₅)	—	2	1	no	—
127	#885	—	2	1	no	—
128	#885	—	2	1	no	—
129	D₃×C₂²⋊C₄	—	2	1	no	—
130	D₃×C₂²⋊C₄	—	2	1	no	—
131	#875	C₂²×C₅	1	1	yes	characteristic
132	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
133	C₃×#97	C₂²×C₅	1	1	yes	characteristic, complemented
134	C₃×#97	C₂²×C₅	1	1	yes	characteristic, complemented
135	(C₂×D₃)⋊C₈	—	2	1	no	—
136	Dic₃⋊C₈	—	2	1	no	—
137	C₈×Dic₃	—	2	1	no	—
138	#803	C₂²×C₅	1	1	yes	characteristic, complemented
139	#803	C₂²×C₅	1	1	yes	characteristic, complemented
140	C₂⁴×C₅	—	6	1	no	—
141	C₂×C₅×Q₈	—	3	1	no	—
142	C₂×C₅×Q₈	—	6	1	no	—
143	C₂×C₅×Q₈	—	12	2	no	—
144	C₂×C₅×Q₈	C₄×D₃	1	1	yes	characteristic
145	C₂×C₅×D₄	—	3	1	no	—
146	C₂×C₅×D₄	—	6	1	no	—
147	C₂×C₅×D₄	—	12	2	no	—
148	C₂×C₅×D₄	C₄×D₃	1	1	yes	characteristic
149	C₂²×C₄×C₅	—	3	1	no	—
150	C₂²×C₄×C₅	—	3	1	no	—
151	C₂²×C₄×C₅	—	3	1	no	—
152	C₂²×C₄×C₅	—	6	1	no	—
153	C₅×M₁₆	—	6	4	no	—
154	C₂×C₅×C₈	—	2	1	no	—
155	C₂×C₅×C₈	—	2	1	no	—
156	C₂×C₅×C₈	—	6	1	no	—
157	C₂×C₅×C₈	—	6	1	no	—
158	C₅×C₂²⋊C₄	—	2	1	no	—
159	C₅×C₂²⋊C₄	—	2	1	no	—
160	C₅×C₂²⋊C₄	—	6	1	no	—
161	C₅×C₂²⋊C₄	—	6	1	no	—
162	C₅×C₂²⋊C₄	—	6	1	no	—
163	C₅×C₂²⋊C₄	—	6	1	no	—
164	C₅×C₂²⋊C₄	—	6	1	no	—
165	C₅×C₂²⋊C₄	—	6	1	no	—
166	C₄²×C₅	—	3	1	no	—
167	C₄²×C₅	—	3	1	no	—
168	C₄²×C₅	—	3	1	no	—
169	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
170	C₂×#124	—	3	1	no	—
171	#432	—	3	1	no	—
172	C₄×M₁₆	—	3	1	no	—
173	#329	—	3	1	no	—
174	#329	—	3	1	no	—
175	#329	—	3	1	no	—
176	#329	C₅×D₃	1	1	yes	characteristic, complemented
177	C₂²×C₃×C₅	—	4	1	no	—
178	C₂²×C₃×C₅	—	4	1	no	—
179	C₂²×C₃×C₅	—	4	1	no	—
180	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
181	C₂×C₅×D₃	—	2	1	no	—
182	C₂×C₅×D₃	—	2	1	no	—
183	C₂×C₅×D₃	—	4	1	no	—
184	C₂×C₅×D₃	—	4	1	no	—
185	C₂×C₅×D₃	—	4	1	no	—
186	C₂×C₅×D₃	—	8	4	no	—
187	C₂×C₅×D₃	#104	1	2	yes	—
188	C₃×C₄×C₅	—	2	1	no	—
189	C₃×C₄×C₅	—	2	1	no	—
190	C₃×C₄×C₅	—	2	1	no	—
191	C₃×C₄×C₅	—	4	1	no	—
192	C₅×Dic₃	—	2	1	no	—
193	C₅×Dic₃	—	2	1	no	—
194	C₅×Dic₃	—	4	1	no	—
195	C₅×Dic₃	#100	1	2	yes	—
196	C₂³×D₃	—	2	1	no	—
197	C₂×C₃×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
198	C₂×C₃×D₄	C₂×C₄×C₅	1	1	yes	characteristic
199	C₂×#67	—	2	1	no	—
200	D₃×Q₈	—	4	2	no	—
201	D₃×D₄	—	4	2	no	—
202	C₂×D₁₂	C₂×C₄×C₅	1	1	yes	characteristic
203	C₂×C₄×D₃	—	2	1	no	—
204	C₂×C₄×D₃	C₂×C₄×C₅	1	1	yes	characteristic
205	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
206	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
207	C₂×Dic₆	—	2	1	no	—
208	C₂×Dic₆	C₂×C₄×C₅	1	1	yes	characteristic
209	C₂×C₃×C₈	—	2	1	no	—
210	C₂×C₃×C₈	—	2	1	no	—
211	C₃×C₂²⋊C₄	—	2	1	no	—
212	C₃×C₂²⋊C₄	—	2	1	no	—
213	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
214	#217	—	2	1	no	—
215	#217	—	2	1	no	—
216	(C₂×D₃)⋊C₄	—	2	1	no	—
217	(C₂×D₃)⋊C₄	—	2	1	no	—
218	(C₂×D₃)⋊C₄	—	2	1	no	—
219	(C₂×D₃)⋊C₄	—	2	1	no	—
220	C₄×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
221	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
222	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
223	C₂×C₃⋊C₈	—	2	1	no	—
224	C₂×C₃⋊C₈	—	2	1	no	—
225	ΓL(1,𝔽₂₅)	—	2	4	no	—
226	C₂³×C₅	—	2	1	no	—
227	C₂³×C₅	—	3	1	no	—
228	C₂³×C₅	—	6	1	no	—
229	C₂³×C₅	—	12	2	no	—
230	C₂³×C₅	—	12	2	no	—
231	C₂³×C₅	—	12	2	no	—
232	C₅×Q₈	—	4	1	no	—
233	C₅×Q₈	—	12	1	no	—
234	C₅×Q₈	—	12	2	no	—
235	C₅×D₄	—	4	1	no	—
236	C₅×D₄	—	12	1	no	—
237	C₅×D₄	—	12	2	no	—
238	C₂×C₄×C₅	—	2	1	no	—
239	C₂×C₄×C₅	—	3	1	no	—
240	C₂×C₄×C₅	—	3	1	no	—
241	C₂×C₄×C₅	—	3	1	no	—
242	C₂×C₄×C₅	—	6	2	no	—
243	C₂×C₄×C₅	—	6	2	no	—
244	C₂×C₄×C₅	—	6	1	no	—
245	C₂×C₄×C₅	—	12	1	no	—
246	C₂×C₄×C₅	—	12	2	no	—
247	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
248	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
249	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
250	C₅×C₈	—	2	2	no	—
251	C₅×C₈	—	4	1	no	—
252	C₅×C₈	—	6	2	no	—
253	C₅×C₈	—	12	1	no	—
254	C₂²×Q₈	—	3	1	no	—
255	C₂²×D₄	—	3	1	no	—
256	C₂×M₁₆	—	6	1	no	—
257	#124	—	3	1	no	—
258	#124	—	3	1	no	—
259	#124	—	3	1	no	—
260	#124	—	6	1	no	—
261	#124	—	6	1	no	—
262	#124	C₂×C₅×D₃	1	1	yes	characteristic
263	C₂×C₂²⋊C₄	—	6	1	no	—
264	C₂×C₂²⋊C₄	—	6	1	no	—
265	C₂×C₄²	—	3	1	no	—
266	C₄⋊C₈	—	6	1	no	—
267	C₂²⋊C₈	—	6	1	no	—
268	#97	—	3	1	no	—
269	#97	—	3	1	no	—
270	#97	C₂×C₅×D₃	1	1	yes	characteristic, complemented
271	#97	C₂×C₅×D₃	1	1	yes	characteristic, complemented
272	C₄×C₈	—	6	1	no	—
273	C₂×C₃×C₅	—	8	1	no	—
274	C₂×C₃×C₅	C₂×#100	1	1	yes	characteristic
275	C₂×C₃×C₅	C₂×#104	1	1	yes	characteristic
276	C₂×C₃×C₅	#421	1	1	yes	characteristic
277	C₅×D₃	—	2	2	no	—
278	C₅×D₃	—	8	1	no	—
279	C₂³×C₃	—	2	1	no	—
280	C₂²×D₃	—	2	1	no	—
281	C₂²×D₃	—	4	2	no	—
282	C₂²×D₃	—	4	2	no	—
283	C₂²×D₃	—	4	2	no	—
284	C₂²×D₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
285	C₃×Q₈	—	4	1	no	—
286	C₃×D₄	—	4	1	no	—
287	C₂×C₃×C₄	—	2	1	no	—
288	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
289	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
290	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
291	#67	—	4	2	no	—
292	C₂×Dic₃	—	2	1	no	—
293	C₂×Dic₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
294	C₂×Dic₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
295	C₂×Dic₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
296	D₁₂	—	4	1	no	—
297	C₄×D₃	—	2	2	no	—
298	C₄×D₃	—	2	2	no	—
299	C₄×D₃	—	4	1	no	—
300	C₄×D₃	—	4	2	no	—
301	Dic₆	—	4	2	no	—
302	Dic₆	—	4	1	no	—
303	C₃×C₈	—	2	2	no	—
304	C₃×C₈	—	4	1	no	—
305	C₃⋊C₈	—	2	2	no	—
306	C₃⋊C₈	—	4	1	no	—
307	C₂²×C₅	—	3	2	no	—
308	C₂²×C₅	—	4	1	no	—
309	C₂²×C₅	—	4	1	no	—
310	C₂²×C₅	—	4	1	no	—
311	C₂²×C₅	—	6	1	no	—
312	C₂²×C₅	—	6	1	no	—
313	C₂²×C₅	—	12	1	no	—
314	C₂²×C₅	—	12	1	no	—
315	C₂²×C₅	—	12	1	no	—
316	C₂²×C₅	—	24	4	no	—
317	C₂²×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
318	C₄×C₅	—	2	1	no	—
319	C₄×C₅	—	2	1	no	—
320	C₄×C₅	—	2	1	no	—
321	C₄×C₅	—	3	2	no	—
322	C₄×C₅	—	4	1	no	—
323	C₄×C₅	—	6	1	no	—
324	C₄×C₅	—	6	1	no	—
325	C₄×C₅	—	12	1	no	—
326	C₂⁴	—	6	1	no	—
327	C₂×Q₈	—	3	1	no	—
328	C₂×Q₈	—	6	1	no	—
329	C₂×Q₈	—	12	2	no	—
330	C₂×Q₈	C₄×C₅×D₃	1	1	yes	characteristic
331	C₂×D₄	—	3	1	no	—
332	C₂×D₄	—	6	1	no	—
333	C₂×D₄	—	12	2	no	—
334	C₂×D₄	C₄×C₅×D₃	1	1	yes	characteristic
335	C₂²×C₄	—	3	1	no	—
336	C₂²×C₄	—	3	1	no	—
337	C₂²×C₄	—	3	1	no	—
338	C₂²×C₄	—	6	1	no	—
339	M₁₆	—	6	4	no	—
340	C₂×C₈	—	2	1	no	—
341	C₂×C₈	—	2	1	no	—
342	C₂×C₈	—	6	1	no	—
343	C₂×C₈	—	6	1	no	—
344	C₂²⋊C₄	—	2	1	no	—
345	C₂²⋊C₄	—	2	1	no	—
346	C₂²⋊C₄	—	6	1	no	—
347	C₂²⋊C₄	—	6	1	no	—
348	C₂²⋊C₄	—	6	1	no	—
349	C₂²⋊C₄	—	6	1	no	—
350	C₂²⋊C₄	—	6	1	no	—
351	C₂²⋊C₄	—	6	1	no	—
352	C₄²	—	3	1	no	—
353	C₄²	—	3	1	no	—
354	C₄²	—	3	1	no	—
355	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
356	C₃×C₅	#1527	1	1	yes	characteristic, complemented, Hall
357	C₂²×C₃	—	4	1	no	—
358	C₂²×C₃	—	4	1	no	—
359	C₂²×C₃	—	4	1	no	—
360	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
361	C₂×D₃	—	2	1	no	—
362	C₂×D₃	—	2	1	no	—
363	C₂×D₃	—	4	1	no	—
364	C₂×D₃	—	4	1	no	—
365	C₂×D₃	—	4	1	no	—
366	C₂×D₃	—	8	4	no	—
367	C₂×D₃	C₅×#104	1	2	yes	—
368	C₃×C₄	—	2	1	no	—
369	C₃×C₄	—	2	1	no	—
370	C₃×C₄	—	2	1	no	—
371	C₃×C₄	—	4	1	no	—
372	Dic₃	—	2	1	no	—
373	Dic₃	—	2	1	no	—
374	Dic₃	—	4	1	no	—
375	Dic₃	C₅×#100	1	2	yes	—
376	C₂×C₅	—	6	2	no	—
377	C₂×C₅	—	8	1	no	—
378	C₂×C₅	—	24	1	no	—
379	C₂×C₅	D₃×#100	1	1	yes	characteristic
380	C₂×C₅	D₃×#104	1	1	yes	characteristic
381	C₂×C₅	#4821	1	1	yes	characteristic
382	C₂³	—	2	1	no	—
383	C₂³	—	3	1	no	—
384	C₂³	—	6	1	no	—
385	C₂³	—	12	2	no	—
386	C₂³	—	12	2	no	—
387	C₂³	—	12	2	no	—
388	Q₈	—	4	1	no	—
389	Q₈	—	12	1	no	—
390	Q₈	—	12	2	no	—
391	D₄	—	4	1	no	—
392	D₄	—	12	1	no	—
393	D₄	—	12	2	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	3	1	no	—
396	C₂×C₄	—	3	1	no	—
397	C₂×C₄	—	3	1	no	—
398	C₂×C₄	—	6	2	no	—
399	C₂×C₄	—	6	2	no	—
400	C₂×C₄	—	6	1	no	—
401	C₂×C₄	—	12	1	no	—
402	C₂×C₄	—	12	2	no	—
403	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
404	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
405	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
406	C₈	—	2	2	no	—
407	C₈	—	4	1	no	—
408	C₈	—	6	2	no	—
409	C₈	—	12	1	no	—
410	C₂×C₃	—	8	1	no	—
411	C₂×C₃	C₂×C₅×#100	1	1	yes	characteristic
412	C₂×C₃	C₂×C₅×#104	1	1	yes	characteristic
413	C₂×C₃	C₅×#421	1	1	yes	characteristic
414	D₃	—	2	2	no	—
415	D₃	—	8	1	no	—
416	C₅	#68343	1	1	yes	characteristic, direct product factor, Sylow
417	C₂²	—	3	2	no	—
418	C₂²	—	4	1	no	—
419	C₂²	—	4	1	no	—
420	C₂²	—	4	1	no	—
421	C₂²	—	6	1	no	—
422	C₂²	—	6	1	no	—
423	C₂²	—	12	1	no	—
424	C₂²	—	12	1	no	—
425	C₂²	—	12	1	no	—
426	C₂²	—	24	4	no	—
427	C₂²	C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
428	C₄	—	2	1	no	—
429	C₄	—	2	1	no	—
430	C₄	—	2	1	no	—
431	C₄	—	3	2	no	—
432	C₄	—	4	1	no	—
433	C₄	—	6	1	no	—
434	C₄	—	6	1	no	—
435	C₄	—	12	1	no	—
436	C₃	C₅×#1527	1	1	yes	characteristic, complemented, Sylow
437	C₂	—	6	2	no	—
438	C₂	—	8	1	no	—
439	C₂	—	24	1	no	—
440	C₂	C₅×D₃×#100	1	1	yes	characteristic
441	C₂	C₅×D₃×#104	1	1	yes	characteristic
442	C₂	C₅×#4821	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×#329	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₂×C₅×D₃×D₄	C₄
cosocle	C₃×C₄²	C₂³×C₅
hypercenter	C₅×#329	D₃
hypocenter	C₃	C₅×#1527
LCS	G ▷ C₂×C₃×C₄ ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×#329

Complements

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

N	H ≅ G/N	type
2. C₅×#4707	C₂	semidirect
3. C₅×#4705	C₂	semidirect
4. C₃×C₅×#329	C₂	semidirect
5. C₅×#4540	C₂	semidirect
6. C₅×#4464	C₂	semidirect
7. C₅×#4464	C₂	semidirect
21. C₃×C₅×#97	C₂²	semidirect
22. C₃×C₅×#97	C₂²	semidirect
26. C₅×#803	C₂²	semidirect
27. C₅×#803	C₂²	semidirect
28. #68343	C₅	direct (N × H)
35. C₅×#329	D₃	semidirect
67. #4707	C₂×C₅	semidirect
68. #4705	C₂×C₅	semidirect
69. C₃×#329	C₂×C₅	semidirect
70. #4540	C₂×C₅	semidirect
71. #4464	C₂×C₅	semidirect
72. #4464	C₂×C₅	semidirect
89. C₅×#97	C₂×D₃	semidirect
90. C₅×#97	C₂×D₃	semidirect
133. C₃×#97	C₂²×C₅	semidirect
134. C₃×#97	C₂²×C₅	semidirect
138. #803	C₂²×C₅	semidirect
139. #803	C₂²×C₅	semidirect
176. #329	C₅×D₃	semidirect
270. #97	C₂×C₅×D₃	semidirect
271. #97	C₂×C₅×D₃	semidirect
356. C₃×C₅	#1527	semidirect
416. C₅	#68343	direct (N × H)
436. C₃	C₅×#1527	semidirect

Maximal subgroups

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

subgroup	index
C₅×D₃×#124	2
C₅×#4707	2
C₅×#4705	2
C₃×C₅×#329	2
C₅×#4540	2
C₅×#4464	2
C₅×#1527	3
#68343	5

Subgroups — C5×#68343 #14284031

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#68343 #14284031