Subgroups — C₅×#70314 #14302397

Order 1920.

692 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5798	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#932	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#418	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5139	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5006	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4559	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4531	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1904	—	3	1	no	maximal, Hall
9	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
10	C₂×C₅×#235	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
12	C₃×C₅×#117	C₂²	1	1	yes	characteristic
13	C₂×C₅×#217	—	2	2	no	—
14	C₅×D₄×Dic₃	—	2	2	no	—
15	C₅×D₄×Dic₃	—	2	2	no	—
16	C₂×C₅×#214	C₄	1	2	yes	complemented
17	C₅×#932	—	2	2	no	—
18	C₅×#932	—	2	2	no	—
19	C₂×C₅×#213	C₄	1	2	yes	complemented
20	C₅×#926	C₂²	1	1	yes	characteristic
21	C₅×#926	C₂²	1	1	yes	characteristic
22	C₂×C₅×#208	C₂²	1	1	yes	characteristic
23	C₃×C₅×#102	—	2	2	no	—
24	C₅×#825	—	2	2	no	—
25	C₅×#806	—	2	2	no	—
26	#70314	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
27	C₂×C₅×AGL(1,ℤ/8)	—	3	1	no	—
28	C₅×#518	—	3	1	no	—
29	C₅×#421	—	3	1	no	—
30	C₅×#418	D₃	1	1	yes	characteristic, complemented
31	C₅×#410	—	3	1	no	—
32	C₅×#344	—	3	1	no	—
33	C₅×H(3,ℤ/4)	—	3	1	no	—
34	C₂⁴×C₃×C₅	—	2	1	no	—
35	C₂×C₃×C₅×D₄	—	2	1	no	—
36	C₂×C₃×C₅×D₄	—	2	1	no	—
37	C₂×C₃×C₅×D₄	—	2	1	no	—
38	C₂×C₃×C₅×D₄	C₂×C₄	1	2	yes	—
39	C₂×C₃×C₅×D₄	D₄	1	2	yes	—
40	C₂×C₃×C₅×D₄	D₄	1	2	yes	—
41	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
42	C₂×C₅×#67	—	2	1	no	—
43	C₂²×C₅×Dic₃	—	2	4	no	—
44	C₅×#235	—	2	1	no	—
45	C₅×#235	—	2	1	no	—
46	C₅×#235	—	2	1	no	—
47	C₅×#235	—	2	1	no	—
48	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic, complemented
49	C₂×C₄×C₅×D₃	—	2	1	no	—
50	C₂×C₅×Dic₆	C₂×C₄	1	1	yes	characteristic, complemented
51	C₃×C₅×M₁₆	—	2	1	no	—
52	C₃×C₅×M₁₆	—	2	1	no	—
53	C₂×C₃×C₅×C₈	—	2	1	no	—
54	C₃×C₅×C₄⋊C₄	—	2	1	no	—
55	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
56	C₃×C₄²×C₅	—	2	1	no	—
57	C₅×#217	—	2	4	no	—
58	C₅×#217	—	2	1	no	—
59	C₅×#217	D₄	1	2	yes	—
60	C₅×#214	—	2	4	no	—
61	C₅×#213	—	2	4	no	—
62	C₅×C₄⋊Dic₃	—	2	1	no	—
63	C₅×C₄⋊Dic₃	—	2	1	no	—
64	C₄×C₅×Dic₃	—	2	1	no	—
65	C₄×C₅×Dic₃	D₄	1	2	yes	—
66	C₅×#208	—	2	1	no	—
67	C₅×#208	—	2	1	no	—
68	C₂×C₅×C₃⋊C₈	C₂×C₄	1	2	yes	complemented
69	#5798	C₂×C₅	1	1	yes	characteristic, complemented
70	C₂×#932	C₂×C₅	1	1	yes	characteristic
71	C₃×#418	C₂×C₅	1	1	yes	characteristic, complemented
72	#5139	C₂×C₅	1	1	yes	characteristic, complemented
73	#5006	C₂×C₅	1	1	yes	characteristic, complemented
74	#4559	C₂×C₅	1	1	yes	characteristic, complemented
75	#4531	C₂×C₅	1	1	yes	characteristic, complemented
76	C₂×C₅×#41	—	3	1	no	—
77	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
78	C₅×AGL(1,ℤ/8)	—	6	2	no	—
79	C₅×AGL(1,ℤ/8)	—	6	2	no	—
80	C₂×C₅×SD₁₆	—	3	2	no	—
81	C₂×C₅×D₈	—	3	2	no	—
82	C₂×C₅×M₁₆	—	3	1	no	—
83	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
84	C₄×C₅×D₄	—	6	2	no	—
85	C₄×C₅×D₄	—	6	2	no	—
86	C₅×#117	—	3	1	no	—
87	C₅×#117	—	3	1	no	—
88	C₅×#117	C₂×D₃	1	1	yes	characteristic
89	C₂×C₅×C₂²⋊C₄	—	6	2	no	—
90	C₅×#104	—	6	2	no	—
91	C₅×#102	—	2	2	no	—
92	C₅×#99	—	6	2	no	—
93	#1904	—	3	1	no	Sylow
94	C₂³×C₃×C₅	—	2	2	no	—
95	C₂³×C₃×C₅	—	2	2	no	—
96	C₂³×C₃×C₅	—	2	2	no	—
97	C₂³×C₃×C₅	—	8	2	no	—
98	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₅×D₃	—	2	1	no	—
100	C₃×C₅×D₄	—	2	2	no	—
101	C₃×C₅×D₄	—	2	2	no	—
102	C₃×C₅×D₄	—	2	2	no	—
103	C₃×C₅×D₄	C₂²⋊C₄	1	4	yes	—
104	C₂×C₃×C₄×C₅	—	4	1	no	—
105	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
107	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
108	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
109	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
110	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
111	C₅×#67	—	4	1	no	—
112	C₅×#67	—	4	1	no	—
113	C₂×C₅×Dic₃	—	2	1	no	—
114	C₂×C₅×Dic₃	—	2	2	no	—
115	C₂×C₅×Dic₃	—	2	2	no	—
116	C₂×C₅×Dic₃	—	8	4	no	—
117	C₅×D₁₂	—	2	1	no	—
118	C₅×D₁₂	—	2	1	no	—
119	C₄×C₅×D₃	—	4	1	no	—
120	C₄×C₅×D₃	—	4	1	no	—
121	C₅×Dic₆	—	2	1	no	—
122	C₅×Dic₆	—	2	1	no	—
123	C₃×C₅×C₈	—	4	1	no	—
124	C₅×C₃⋊C₈	—	2	2	no	—
125	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
126	C₂×#235	C₂²×C₅	1	1	yes	characteristic
127	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
128	C₃×#117	C₂²×C₅	1	1	yes	characteristic
129	C₂×#217	—	2	2	no	—
130	D₄×Dic₃	—	2	2	no	—
131	D₄×Dic₃	—	2	2	no	—
132	C₂×#214	C₄×C₅	1	2	yes	complemented
133	#932	—	2	2	no	—
134	#932	—	2	2	no	—
135	C₂×#213	C₄×C₅	1	2	yes	complemented
136	#926	C₂²×C₅	1	1	yes	characteristic
137	#926	C₂²×C₅	1	1	yes	characteristic
138	C₂×#208	C₂²×C₅	1	1	yes	characteristic
139	C₃×#102	—	2	2	no	—
140	#825	—	2	2	no	—
141	#806	—	2	2	no	—
142	C₂⁴×C₅	—	2	1	no	—
143	C₅×#41	—	6	1	no	—
144	C₅×#41	—	6	1	no	—
145	C₅×#41	—	6	1	no	—
146	C₅×#41	—	6	1	no	—
147	C₂×C₅×Q₈	—	3	1	no	—
148	C₂×C₅×D₄	—	2	1	no	—
149	C₂×C₅×D₄	—	2	1	no	—
150	C₂×C₅×D₄	—	2	1	no	—
151	C₂×C₅×D₄	—	3	1	no	—
152	C₂×C₅×D₄	—	6	1	no	—
153	C₂×C₅×D₄	C₄×D₃	1	2	yes	—
154	C₂×C₅×D₄	D₁₂	1	2	yes	—
155	C₂×C₅×D₄	#67	1	2	yes	—
156	C₂²×C₄×C₅	—	6	4	no	—
157	C₂²×C₄×C₅	—	6	1	no	—
158	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
159	C₅×SD₁₆	—	6	4	no	—
160	C₅×D₈	—	6	4	no	—
161	C₅×M₁₆	—	2	1	no	—
162	C₅×M₁₆	—	2	1	no	—
163	C₅×M₁₆	—	6	1	no	—
164	C₅×M₁₆	—	6	1	no	—
165	C₂×C₅×C₈	—	2	1	no	—
166	C₂×C₅×C₈	—	3	2	no	—
167	C₅×C₄⋊C₄	—	2	1	no	—
168	C₅×C₄⋊C₄	—	6	1	no	—
169	C₅×C₄⋊C₄	—	6	1	no	—
170	C₅×C₂²⋊C₄	—	2	1	no	—
171	C₅×C₂²⋊C₄	—	3	2	no	—
172	C₅×C₂²⋊C₄	—	6	4	no	—
173	C₅×C₂²⋊C₄	—	6	1	no	—
174	C₄²×C₅	—	2	1	no	—
175	C₄²×C₅	—	3	2	no	—
176	C₄²×C₅	—	6	1	no	—
177	C₂×AGL(1,ℤ/8)	—	3	1	no	—
178	#518	—	3	1	no	—
179	#421	—	3	1	no	—
180	#418	C₅×D₃	1	1	yes	characteristic, complemented
181	#410	—	3	1	no	—
182	#344	—	3	1	no	—
183	H(3,ℤ/4)	—	3	1	no	—
184	C₂²×C₃×C₅	—	2	4	no	—
185	C₂²×C₃×C₅	—	4	1	no	—
186	C₂²×C₃×C₅	—	4	4	no	—
187	C₂²×C₃×C₅	—	8	2	no	—
188	C₂²×C₃×C₅	—	8	2	no	—
189	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
190	C₂²×C₃×C₅	#120	1	1	yes	characteristic
191	C₂²×C₃×C₅	#121	1	1	yes	characteristic
192	C₂×C₅×D₃	—	4	1	no	—
193	C₂×C₅×D₃	—	8	1	no	—
194	C₃×C₄×C₅	—	8	1	no	—
195	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
196	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
197	C₃×C₄×C₅	#121	1	1	yes	characteristic
198	C₃×C₄×C₅	#123	1	1	yes	characteristic
199	C₅×Dic₃	—	4	2	no	—
200	C₅×Dic₃	—	4	2	no	—
201	C₅×Dic₃	—	4	1	no	—
202	C₂⁴×C₃	—	2	1	no	—
203	C₂×C₃×D₄	—	2	1	no	—
204	C₂×C₃×D₄	—	2	1	no	—
205	C₂×C₃×D₄	—	2	1	no	—
206	C₂×C₃×D₄	C₂×C₄×C₅	1	2	yes	—
207	C₂×C₃×D₄	C₅×D₄	1	2	yes	—
208	C₂×C₃×D₄	C₅×D₄	1	2	yes	—
209	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
210	C₂×#67	—	2	1	no	—
211	C₂²×Dic₃	—	2	4	no	—
212	#235	—	2	1	no	—
213	#235	—	2	1	no	—
214	#235	—	2	1	no	—
215	#235	—	2	1	no	—
216	C₂×D₁₂	C₂×C₄×C₅	1	1	yes	characteristic, complemented
217	C₂×C₄×D₃	—	2	1	no	—
218	C₂×Dic₆	C₂×C₄×C₅	1	1	yes	characteristic, complemented
219	C₃×M₁₆	—	2	1	no	—
220	C₃×M₁₆	—	2	1	no	—
221	C₂×C₃×C₈	—	2	1	no	—
222	C₃×C₄⋊C₄	—	2	1	no	—
223	C₃×C₂²⋊C₄	—	2	1	no	—
224	C₃×C₄²	—	2	1	no	—
225	#217	—	2	4	no	—
226	#217	—	2	1	no	—
227	#217	C₅×D₄	1	2	yes	—
228	#214	—	2	4	no	—
229	#213	—	2	4	no	—
230	C₄⋊Dic₃	—	2	1	no	—
231	C₄⋊Dic₃	—	2	1	no	—
232	C₄×Dic₃	—	2	1	no	—
233	C₄×Dic₃	C₅×D₄	1	2	yes	—
234	#208	—	2	1	no	—
235	#208	—	2	1	no	—
236	C₂×C₃⋊C₈	C₂×C₄×C₅	1	2	yes	complemented
237	C₂³×C₅	—	2	2	no	—
238	C₂³×C₅	—	2	2	no	—
239	C₂³×C₅	—	2	2	no	—
240	C₂³×C₅	—	6	1	no	—
241	C₂³×C₅	—	8	2	no	—
242	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
243	C₅×Q₈	—	6	1	no	—
244	C₅×Q₈	—	6	1	no	—
245	C₅×D₄	—	2	2	no	—
246	C₅×D₄	—	2	2	no	—
247	C₅×D₄	—	2	2	no	—
248	C₅×D₄	—	6	1	no	—
249	C₅×D₄	—	6	1	no	—
250	C₅×D₄	—	12	1	no	—
251	C₅×D₄	—	12	1	no	—
252	C₅×D₄	(C₂×D₃)⋊C₄	1	4	yes	—
253	C₂×C₄×C₅	—	4	1	no	—
254	C₂×C₄×C₅	—	6	1	no	—
255	C₂×C₄×C₅	—	6	2	no	—
256	C₂×C₄×C₅	—	6	2	no	—
257	C₂×C₄×C₅	—	12	1	no	—
258	C₂×C₄×C₅	—	12	1	no	—
259	C₂×C₄×C₅	—	24	4	no	—
260	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
261	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
262	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
263	C₂×C₄×C₅	#237	1	1	yes	characteristic
264	C₂×C₄×C₅	#237	1	1	yes	characteristic
265	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
266	C₅×C₈	—	4	1	no	—
267	C₅×C₈	—	6	2	no	—
268	C₂×#41	—	3	1	no	—
269	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
270	AGL(1,ℤ/8)	—	6	2	no	—
271	AGL(1,ℤ/8)	—	6	2	no	—
272	C₂×SD₁₆	—	3	2	no	—
273	C₂×D₈	—	3	2	no	—
274	C₂×M₁₆	—	3	1	no	—
275	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
276	C₄×D₄	—	6	2	no	—
277	C₄×D₄	—	6	2	no	—
278	#117	—	3	1	no	—
279	#117	—	3	1	no	—
280	#117	C₂×C₅×D₃	1	1	yes	characteristic
281	C₂×C₂²⋊C₄	—	6	2	no	—
282	#104	—	6	2	no	—
283	#102	—	2	2	no	—
284	#99	—	6	2	no	—
285	C₂×C₃×C₅	—	2	1	no	—
286	C₂×C₃×C₅	—	2	1	no	—
287	C₂×C₃×C₅	—	2	1	no	—
288	C₂×C₃×C₅	—	4	4	no	—
289	C₂×C₃×C₅	#386	1	1	yes	characteristic
290	C₅×D₃	—	8	1	no	—
291	C₂³×C₃	—	2	2	no	—
292	C₂³×C₃	—	2	2	no	—
293	C₂³×C₃	—	2	2	no	—
294	C₂³×C₃	—	8	2	no	—
295	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
296	C₂²×D₃	—	2	1	no	—
297	C₃×D₄	—	2	2	no	—
298	C₃×D₄	—	2	2	no	—
299	C₃×D₄	—	2	2	no	—
300	C₃×D₄	C₅×C₂²⋊C₄	1	4	yes	—
301	C₂×C₃×C₄	—	4	1	no	—
302	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
303	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
304	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
305	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
306	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
307	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
308	#67	—	4	1	no	—
309	#67	—	4	1	no	—
310	C₂×Dic₃	—	2	1	no	—
311	C₂×Dic₃	—	2	2	no	—
312	C₂×Dic₃	—	2	2	no	—
313	C₂×Dic₃	—	8	4	no	—
314	D₁₂	—	2	1	no	—
315	D₁₂	—	2	1	no	—
316	C₄×D₃	—	4	1	no	—
317	C₄×D₃	—	4	1	no	—
318	Dic₆	—	2	1	no	—
319	Dic₆	—	2	1	no	—
320	C₃×C₈	—	4	1	no	—
321	C₃⋊C₈	—	2	2	no	—
322	C₂²×C₅	—	2	4	no	—
323	C₂²×C₅	—	4	1	no	—
324	C₂²×C₅	—	4	4	no	—
325	C₂²×C₅	—	8	2	no	—
326	C₂²×C₅	—	8	2	no	—
327	C₂²×C₅	—	12	1	no	—
328	C₂²×C₅	—	24	1	no	—
329	C₂²×C₅	#67⋊C₄	1	1	yes	characteristic
330	C₂²×C₅	#882	1	1	yes	characteristic
331	C₂²×C₅	#939	1	1	yes	characteristic
332	C₄×C₅	—	8	1	no	—
333	C₄×C₅	—	12	2	no	—
334	C₄×C₅	—	12	2	no	—
335	C₄×C₅	—	12	1	no	—
336	C₄×C₅	#67⋊C₄	1	1	yes	characteristic
337	C₄×C₅	#886	1	1	yes	characteristic
338	C₄×C₅	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
339	C₄×C₅	#939	1	1	yes	characteristic
340	C₂⁴	—	2	1	no	—
341	#41	—	6	1	no	—
342	#41	—	6	1	no	—
343	#41	—	6	1	no	—
344	#41	—	6	1	no	—
345	C₂×Q₈	—	3	1	no	—
346	C₂×D₄	—	2	1	no	—
347	C₂×D₄	—	2	1	no	—
348	C₂×D₄	—	2	1	no	—
349	C₂×D₄	—	3	1	no	—
350	C₂×D₄	—	6	1	no	—
351	C₂×D₄	C₄×C₅×D₃	1	2	yes	—
352	C₂×D₄	C₅×D₁₂	1	2	yes	—
353	C₂×D₄	C₅×#67	1	2	yes	—
354	C₂²×C₄	—	6	4	no	—
355	C₂²×C₄	—	6	1	no	—
356	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
357	SD₁₆	—	6	4	no	—
358	D₈	—	6	4	no	—
359	M₁₆	—	2	1	no	—
360	M₁₆	—	2	1	no	—
361	M₁₆	—	6	1	no	—
362	M₁₆	—	6	1	no	—
363	C₂×C₈	—	2	1	no	—
364	C₂×C₈	—	3	2	no	—
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	—	6	1	no	—
367	C₄⋊C₄	—	6	1	no	—
368	C₂²⋊C₄	—	2	1	no	—
369	C₂²⋊C₄	—	3	2	no	—
370	C₂²⋊C₄	—	6	4	no	—
371	C₂²⋊C₄	—	6	1	no	—
372	C₄²	—	2	1	no	—
373	C₄²	—	3	2	no	—
374	C₄²	—	6	1	no	—
375	C₃×C₅	#1904	1	1	yes	characteristic, complemented, Hall
376	C₂²×C₃	—	2	4	no	—
377	C₂²×C₃	—	4	1	no	—
378	C₂²×C₃	—	4	4	no	—
379	C₂²×C₃	—	8	2	no	—
380	C₂²×C₃	—	8	2	no	—
381	C₂²×C₃	C₄×C₅×D₄	1	1	yes	characteristic
382	C₂²×C₃	C₅×#120	1	1	yes	characteristic
383	C₂²×C₃	C₅×#121	1	1	yes	characteristic
384	C₂×D₃	—	4	1	no	—
385	C₂×D₃	—	8	1	no	—
386	C₃×C₄	—	8	1	no	—
387	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
388	C₃×C₄	C₄×C₅×D₄	1	1	yes	characteristic
389	C₃×C₄	C₅×#121	1	1	yes	characteristic
390	C₃×C₄	C₅×#123	1	1	yes	characteristic
391	Dic₃	—	4	2	no	—
392	Dic₃	—	4	2	no	—
393	Dic₃	—	4	1	no	—
394	C₂×C₅	—	2	1	no	—
395	C₂×C₅	—	2	1	no	—
396	C₂×C₅	—	2	1	no	—
397	C₂×C₅	—	4	4	no	—
398	C₂×C₅	—	24	1	no	—
399	C₂×C₅	#4958	1	1	yes	characteristic
400	C₂³	—	2	2	no	—
401	C₂³	—	2	2	no	—
402	C₂³	—	2	2	no	—
403	C₂³	—	6	1	no	—
404	C₂³	—	8	2	no	—
405	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
406	Q₈	—	6	1	no	—
407	Q₈	—	6	1	no	—
408	D₄	—	2	2	no	—
409	D₄	—	2	2	no	—
410	D₄	—	2	2	no	—
411	D₄	—	6	1	no	—
412	D₄	—	6	1	no	—
413	D₄	—	12	1	no	—
414	D₄	—	12	1	no	—
415	D₄	C₅×(C₂×D₃)⋊C₄	1	4	yes	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	6	1	no	—
418	C₂×C₄	—	6	2	no	—
419	C₂×C₄	—	6	2	no	—
420	C₂×C₄	—	12	1	no	—
421	C₂×C₄	—	12	1	no	—
422	C₂×C₄	—	24	4	no	—
423	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
424	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
425	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
426	C₂×C₄	C₅×#237	1	1	yes	characteristic
427	C₂×C₄	C₅×#237	1	1	yes	characteristic
428	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
429	C₈	—	4	1	no	—
430	C₈	—	6	2	no	—
431	C₂×C₃	—	2	1	no	—
432	C₂×C₃	—	2	1	no	—
433	C₂×C₃	—	2	1	no	—
434	C₂×C₃	—	4	4	no	—
435	C₂×C₃	C₅×#386	1	1	yes	characteristic
436	D₃	—	8	1	no	—
437	C₅	#70314	1	1	yes	characteristic, direct product factor, Sylow
438	C₂²	—	2	4	no	—
439	C₂²	—	4	1	no	—
440	C₂²	—	4	4	no	—
441	C₂²	—	8	2	no	—
442	C₂²	—	8	2	no	—
443	C₂²	—	12	1	no	—
444	C₂²	—	24	1	no	—
445	C₂²	C₅×#67⋊C₄	1	1	yes	characteristic
446	C₂²	C₅×#882	1	1	yes	characteristic
447	C₂²	C₅×#939	1	1	yes	characteristic
448	C₄	—	8	1	no	—
449	C₄	—	12	2	no	—
450	C₄	—	12	2	no	—
451	C₄	—	12	1	no	—
452	C₄	C₅×#67⋊C₄	1	1	yes	characteristic
453	C₄	C₅×#886	1	1	yes	characteristic
454	C₄	C₂×C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
455	C₄	C₅×#939	1	1	yes	characteristic
456	C₃	C₅×#1904	1	1	yes	characteristic, complemented, Sylow
457	C₂	—	2	1	no	—
458	C₂	—	2	1	no	—
459	C₂	—	2	1	no	—
460	C₂	—	4	4	no	—
461	C₂	—	24	1	no	—
462	C₂	C₅×#4958	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₅	#4958
commutator	C₂×C₃×C₄	C₂²×C₄×C₅
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting	C₃×C₅×#418	C₂
socle	C₂×C₃×C₅	#386
prime radical	C₂×C₅×#932	C₂
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₅×#418	D₃
hypocenter	C₃	C₅×#1904
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#418

Complements

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

N	H ≅ G/N	type
1. C₅×#5798	C₂	semidirect
3. C₃×C₅×#418	C₂	semidirect
4. C₅×#5139	C₂	semidirect
5. C₅×#5006	C₂	semidirect
6. C₅×#4559	C₂	semidirect
7. C₅×#4531	C₂	semidirect
16. C₂×C₅×#214	C₄	semidirect
19. C₂×C₅×#213	C₄	semidirect
26. #70314	C₅	direct (N × H)
30. C₅×#418	D₃	semidirect
48. C₂×C₅×D₁₂	C₂×C₄	semidirect
50. C₂×C₅×Dic₆	C₂×C₄	semidirect
68. C₂×C₅×C₃⋊C₈	C₂×C₄	semidirect
69. #5798	C₂×C₅	semidirect
71. C₃×#418	C₂×C₅	semidirect
72. #5139	C₂×C₅	semidirect
73. #5006	C₂×C₅	semidirect
74. #4559	C₂×C₅	semidirect
75. #4531	C₂×C₅	semidirect
132. C₂×#214	C₄×C₅	semidirect
135. C₂×#213	C₄×C₅	semidirect
180. #418	C₅×D₃	semidirect
216. C₂×D₁₂	C₂×C₄×C₅	semidirect
218. C₂×Dic₆	C₂×C₄×C₅	semidirect
236. C₂×C₃⋊C₈	C₂×C₄×C₅	semidirect
375. C₃×C₅	#1904	semidirect
437. C₅	#70314	direct (N × H)
456. C₃	C₅×#1904	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5798	2
C₂×C₅×#932	2
C₃×C₅×#418	2
C₅×#5139	2
C₅×#5006	2
C₅×#4559	2
C₅×#4531	2
C₅×#1904	3
#70314	5

Subgroups — C5×#70314 #14302397

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#70314 #14302397