Subgroups — C₂×Dic₅×#235 #14478932

Order 1920.

3456 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×#235	C₂	1	1	yes	maximal, characteristic
2	C₂×#91815	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃×C₄×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×Dic₅×#67	C₂	1	4	yes	maximal, complemented
5	Dic₅×#235	C₂	1	16	yes	maximal, direct product factor
6	C₂×Dic₅×D₁₂	C₂	1	2	yes	maximal, complemented
7	C₂×C₄×D₃×Dic₅	C₂	1	2	yes	maximal, complemented
8	C₂×#91371	C₂	1	2	yes	maximal, complemented
9	C₂×Dic₅×Dic₆	C₂	1	2	yes	maximal, complemented
10	C₂×#41×Dic₅	—	3	1	no	maximal, Hall
11	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
12	C₂²×C₅×#67	C₂²	1	2	yes	—
13	C₂×C₅×#235	C₄	1	16	yes	complemented
14	C₂×C₅×#235	C₂²	1	8	yes	—
15	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
16	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
17	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
18	C₂³×C₃×Dic₅	C₂²	1	2	yes	—
19	C₂²×D₃×Dic₅	C₂²	1	4	yes	—
20	C₂×#6719	C₂²	1	2	yes	—
21	#91815	C₂²	1	8	yes	complemented
22	C₂×C₄⋊Dic₁₅	C₂²	1	2	yes	—
23	C₂×C₄×Dic₁₅	C₂²	1	2	yes	—
24	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
25	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
26	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	—
27	C₂×C₃×C₄×Dic₅	C₂²	1	8	yes	complemented
28	Dic₅×#67	C₂²	1	32	yes	complemented
29	C₂×Dic₃⋊Dic₅	C₂²	1	4	yes	—
30	C₂×(C₂×D₃)⋊Dic₅	C₂²	1	4	yes	—
31	C₂×Dic₃×Dic₅	C₂²	1	4	yes	—
32	Dic₅×D₁₂	C₂²	1	16	yes	complemented
33	C₄×D₃×Dic₅	C₂²	1	16	yes	complemented
34	#91371	C₂²	1	16	yes	complemented
35	Dic₅×Dic₆	C₂²	1	16	yes	complemented
36	C₂×C₄×#235	—	5	1	no	maximal, Hall
37	C₂²×C₅×#41	—	3	1	no	—
38	#41×Dic₅	—	3	16	no	—
39	C₂×Q₈×Dic₅	—	3	2	no	—
40	C₂×D₄×Dic₅	—	3	2	no	—
41	C₂×D₄×Dic₅	—	3	4	no	—
42	C₂×#4072	—	3	2	no	—
43	C₂×#4072	—	3	1	no	—
44	C₂²×C₄×Dic₅	—	3	2	no	—
45	C₂²×C₄×Dic₅	D₃	1	1	yes	characteristic, complemented
46	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
47	C₂³×C₅×D₃	C₂³	1	2	yes	—
48	C₂²×C₃×C₄×C₅	C₂×C₄	1	8	yes	complemented
49	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
50	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
51	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
52	C₂²×Dic₁₅	C₂³	1	4	yes	—
53	C₂×C₅×#67	C₂×C₄	1	16	yes	complemented
54	C₂×C₅×#67	C₂³	1	8	yes	—
55	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
56	C₅×#235	C₂×C₄	1	64	yes	complemented
57	C₂×C₅×D₁₂	C₂×C₄	1	8	yes	complemented
58	C₂×C₅×D₁₂	C₂³	1	4	yes	—
59	C₂×C₄×C₅×D₃	C₂×C₄	1	16	yes	complemented
60	C₂×C₄×C₅×D₃	C₂³	1	8	yes	—
61	C₂×C₅×Dic₆	C₂×C₄	1	8	yes	complemented
62	C₂×C₅×Dic₆	C₂³	1	4	yes	—
63	C₂²×C₃×Dic₅	—	2	8	no	—
64	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
65	C₂²×C₃×Dic₅	C₂³	1	8	yes	—
66	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
67	C₂×D₃×Dic₅	—	2	16	no	—
68	C₂×D₃×Dic₅	C₂³	1	16	yes	—
69	#6719	C₂³	1	8	yes	—
70	C₄⋊Dic₁₅	C₂³	1	8	yes	—
71	C₄×Dic₁₅	C₂³	1	8	yes	—
72	C₃×C₄×Dic₅	C₂³	1	4	yes	—
73	C₃×C₄×Dic₅	C₂³	1	8	yes	—
74	C₃×C₄×Dic₅	C₂³	1	4	yes	—
75	Dic₃⋊Dic₅	C₂³	1	16	yes	—
76	(C₂×D₃)⋊Dic₅	C₂³	1	16	yes	—
77	Dic₃×Dic₅	C₂³	1	16	yes	—
78	C₂²×#235	D₅	1	1	yes	characteristic
79	C₂²×C₃×C₄²	—	5	1	no	—
80	C₂×C₄×#67	—	5	4	no	—
81	C₂×#926	—	5	1	no	—
82	C₄×#235	—	5	16	no	—
83	C₂×C₄×D₁₂	—	5	2	no	—
84	C₂×#872	—	5	2	no	—
85	C₂×C₄²×D₃	—	5	2	no	—
86	C₂×C₄×Dic₆	—	5	2	no	—
87	C₂×C₅×#41	—	3	16	no	—
88	C₂×C₅×#41	—	3	8	no	—
89	C₂²×C₅×Q₈	—	3	1	no	—
90	C₂²×C₅×D₄	—	3	2	no	—
91	C₂²×C₅×D₄	—	3	1	no	—
92	C₂³×C₄×C₅	—	3	2	no	—
93	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
94	C₂³×Dic₅	—	3	4	no	—
95	C₂³×Dic₅	C₂×D₃	1	2	yes	—
96	C₂×C₂²⋊Dic₅	—	3	2	no	—
97	C₂×C₂²⋊Dic₅	—	3	4	no	—
98	Q₈×Dic₅	—	3	16	no	—
99	D₄×Dic₅	—	3	32	no	—
100	D₄×Dic₅	—	3	16	no	—
101	#4072	—	3	8	no	—
102	#4072	—	3	16	no	—
103	C₂×C₄⋊Dic₅	—	3	2	no	—
104	C₂×C₄⋊Dic₅	—	3	4	no	—
105	C₂×C₄×Dic₅	—	3	2	no	—
106	C₂×C₄×Dic₅	—	3	4	no	—
107	C₂×C₄×Dic₅	—	3	16	no	—
108	C₂×C₄×Dic₅	C₂×D₃	1	1	yes	characteristic
109	C₂×C₄×Dic₅	C₂×D₃	1	1	yes	characteristic
110	C₂×C₄×Dic₅	C₂×D₃	1	2	yes	—
111	C₂×C₄×Dic₅	C₂×D₃	1	8	yes	complemented
112	C₂×C₄×#41	—	15	1	no	Sylow
113	C₂³×C₃×C₅	—	2	4	no	—
114	C₂³×C₃×C₅	C₂²×C₄	1	4	yes	—
115	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
116	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
117	C₂²×C₅×D₃	—	2	8	no	—
118	C₂²×C₅×D₃	C₂²×C₄	1	8	yes	—
119	C₂²×C₅×D₃	C₂⁴	1	4	yes	—
120	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
121	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
122	C₂×C₃×C₄×C₅	C₂²×C₄	1	16	yes	complemented
123	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
124	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
125	C₂×Dic₁₅	—	2	8	no	—
126	C₂×Dic₁₅	C₂⁴	1	8	yes	—
127	C₅×#67	C₂²×C₄	1	32	yes	complemented
128	C₂×C₅×Dic₃	C₂²×C₄	1	8	yes	—
129	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
130	C₅×D₁₂	C₂²×C₄	1	16	yes	complemented
131	C₄×C₅×D₃	C₂²×C₄	1	32	yes	complemented
132	C₅×Dic₆	C₂²×C₄	1	16	yes	complemented
133	C₂×C₃×Dic₅	—	2	4	no	—
134	C₂×C₃×Dic₅	—	2	16	no	—
135	C₂×C₃×Dic₅	#41	1	8	yes	complemented
136	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
137	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
138	D₃×Dic₅	—	2	32	no	—
139	C₂³×C₃×C₄	—	5	2	no	—
140	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
141	C₂²×#67	C₂×D₅	1	2	yes	—
142	C₂×#235	Dic₅	1	16	yes	direct product factor
143	C₂×#235	C₂×D₅	1	8	yes	—
144	C₂²×D₁₂	C₂×D₅	1	1	yes	characteristic
145	C₂²×C₄×D₃	—	5	4	no	—
146	C₂²×C₄×D₃	C₂×D₅	1	2	yes	—
147	C₂²×Dic₆	C₂×D₅	1	1	yes	characteristic
148	C₂×C₃×C₄²	—	5	2	no	—
149	C₂×C₃×C₄²	—	5	1	no	—
150	C₂×C₃×C₄²	—	5	1	no	—
151	C₂×C₃×C₄²	—	5	8	no	—
152	C₂×#217	—	5	2	no	—
153	C₄×#67	—	5	32	no	—
154	C₂×(C₂×D₃)⋊C₄	—	5	4	no	—
155	#926	—	5	8	no	—
156	C₂×C₄⋊Dic₃	—	5	2	no	—
157	C₂×Dic₃⋊C₄	—	5	4	no	—
158	C₂×C₄×Dic₃	—	5	2	no	—
159	C₂×C₄×Dic₃	—	5	4	no	—
160	C₄×D₁₂	—	5	16	no	—
161	#872	—	5	16	no	—
162	C₄²×D₃	—	5	16	no	—
163	C₄×Dic₆	—	5	16	no	—
164	C₂⁴×C₅	—	3	2	no	—
165	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
166	C₅×#41	—	3	64	no	—
167	C₂×C₅×Q₈	—	3	8	no	—
168	C₂×C₅×Q₈	—	3	4	no	—
169	C₂×C₅×D₄	—	3	16	no	—
170	C₂×C₅×D₄	—	3	8	no	—
171	C₂×C₅×D₄	—	3	8	no	—
172	C₂×C₅×D₄	—	3	4	no	—
173	C₂²×C₄×C₅	—	3	2	no	—
174	C₂²×C₄×C₅	—	3	16	no	—
175	C₂²×C₄×C₅	—	3	8	no	—
176	C₂²×C₄×C₅	C₄×D₃	1	8	yes	complemented
177	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
178	C₂²×C₄×C₅	C₂²×D₃	1	4	yes	—
179	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
180	C₂²×Dic₅	—	2	8	no	—
181	C₂²×Dic₅	—	3	4	no	—
182	C₂²×Dic₅	—	3	16	no	—
183	C₂²×Dic₅	—	6	16	no	—
184	C₂²×Dic₅	C₂²×D₃	1	2	yes	—
185	C₂²×Dic₅	C₂²×D₃	1	8	yes	—
186	C₂²×Dic₅	C₂²×D₃	1	2	yes	—
187	C₂²⋊Dic₅	—	3	8	no	—
188	C₂²⋊Dic₅	—	3	16	no	—
189	C₄⋊Dic₅	—	3	8	no	—
190	C₄⋊Dic₅	—	3	16	no	—
191	C₄×Dic₅	—	3	8	no	—
192	C₄×Dic₅	—	3	16	no	—
193	C₄×Dic₅	C₂²×D₃	1	4	yes	—
194	C₄×Dic₅	C₂²×D₃	1	4	yes	—
195	C₄×Dic₅	C₂²×D₃	1	8	yes	—
196	C₂²×#41	—	3	1	no	—
197	C₄×#41	—	15	16	no	—
198	C₂×C₄×Q₈	—	15	2	no	—
199	C₂×C₄×D₄	—	15	2	no	—
200	C₂×C₄×D₄	—	15	4	no	—
201	C₂×#117	—	15	2	no	—
202	C₂×#117	—	15	1	no	—
203	C₂²×C₄²	—	5	1	no	—
204	C₂²×C₄²	—	15	2	no	—
205	C₂²×C₃×C₅	—	2	8	no	—
206	C₂²×C₃×C₅	—	2	4	no	—
207	C₂²×C₃×C₅	C₂³×C₄	1	4	yes	—
208	C₂²×C₃×C₅	C₂³×C₄	1	2	yes	—
209	C₂²×C₃×C₅	C₂×#41	1	4	yes	—
210	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
211	C₂×C₅×D₃	—	2	16	no	—
212	C₂×C₅×D₃	—	2	8	no	—
213	C₂×C₅×D₃	C₂³×C₄	1	8	yes	—
214	C₃×C₄×C₅	C₂³×C₄	1	4	yes	—
215	C₃×C₄×C₅	C₂³×C₄	1	4	yes	—
216	Dic₁₅	—	2	8	no	—
217	C₃×Dic₅	—	2	4	no	—
218	C₃×Dic₅	C₂×#41	1	8	yes	complemented
219	C₅×Dic₃	C₂³×C₄	1	8	yes	—
220	C₂⁴×C₃	C₂²×D₅	1	1	yes	characteristic
221	C₂³×D₃	C₂²×D₅	1	2	yes	—
222	C₂²×C₃×C₄	—	5	2	no	—
223	C₂²×C₃×C₄	—	5	2	no	—
224	C₂²×C₃×C₄	—	5	8	no	—
225	C₂²×C₃×C₄	—	10	8	no	—
226	C₂²×C₃×C₄	C₂×Dic₅	1	8	yes	complemented
227	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
228	C₂²×C₃×C₄	C₂²×D₅	1	4	yes	—
229	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
230	C₂×#67	C₂×Dic₅	1	16	yes	complemented
231	C₂×#67	C₂²×D₅	1	8	yes	—
232	C₂²×Dic₃	—	5	4	no	—
233	C₂²×Dic₃	C₂²×D₅	1	2	yes	—
234	#235	C₂×Dic₅	1	64	yes	direct product factor
235	C₂×D₁₂	C₂×Dic₅	1	8	yes	complemented
236	C₂×D₁₂	C₂²×D₅	1	4	yes	—
237	C₂×C₄×D₃	—	5	16	no	—
238	C₂×C₄×D₃	—	10	16	no	—
239	C₂×C₄×D₃	C₂×Dic₅	1	16	yes	complemented
240	C₂×C₄×D₃	C₂²×D₅	1	8	yes	—
241	C₂×Dic₆	C₂×Dic₅	1	8	yes	complemented
242	C₂×Dic₆	C₂²×D₅	1	4	yes	—
243	C₃×C₄²	—	5	8	no	—
244	C₃×C₄²	—	5	4	no	—
245	C₃×C₄²	—	5	4	no	—
246	#217	—	5	8	no	—
247	(C₂×D₃)⋊C₄	—	5	16	no	—
248	C₄⋊Dic₃	—	5	8	no	—
249	Dic₃⋊C₄	—	5	16	no	—
250	C₄×Dic₃	—	5	8	no	—
251	C₄×Dic₃	—	5	16	no	—
252	C₂³×C₅	—	2	4	no	—
253	C₂³×C₅	—	3	8	no	—
254	C₂³×C₅	—	3	4	no	—
255	C₂³×C₅	—	6	8	no	—
256	C₂³×C₅	C₂×C₄×D₃	1	4	yes	—
257	C₂³×C₅	C₂³×D₃	1	2	yes	—
258	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
259	C₅×Q₈	—	3	16	no	—
260	C₅×D₄	—	3	32	no	—
261	C₅×D₄	—	3	16	no	—
262	C₂×C₄×C₅	—	3	8	no	—
263	C₂×C₄×C₅	—	3	4	no	—
264	C₂×C₄×C₅	—	3	32	no	—
265	C₂×C₄×C₅	C₂×C₄×D₃	1	4	yes	—
266	C₂×C₄×C₅	C₂×C₄×D₃	1	4	yes	—
267	C₂×C₄×C₅	C₂×C₄×D₃	1	16	yes	complemented
268	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
269	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
270	C₂×Dic₅	—	2	4	no	—
271	C₂×Dic₅	—	2	16	no	—
272	C₂×Dic₅	—	3	8	no	—
273	C₂×Dic₅	—	6	8	no	—
274	C₂×Dic₅	—	6	32	no	—
275	C₂×Dic₅	#235	1	8	yes	direct product factor
276	C₂×Dic₅	C₂³×D₃	1	4	yes	—
277	C₂×Dic₅	C₂³×D₃	1	4	yes	—
278	C₂×#41	—	3	16	no	—
279	C₂×#41	—	3	8	no	—
280	C₂²×Q₈	—	3	1	no	—
281	C₂²×D₄	—	3	2	no	—
282	C₂²×D₄	—	3	1	no	—
283	C₂³×C₄	—	3	2	no	—
284	C₂³×C₄	—	5	2	no	—
285	C₂³×C₄	—	15	4	no	—
286	C₂³×C₄	D₃×D₅	1	1	yes	characteristic
287	C₄×Q₈	—	15	16	no	—
288	C₄×D₄	—	15	16	no	—
289	C₄×D₄	—	15	32	no	—
290	#117	—	15	16	no	—
291	#117	—	15	8	no	—
292	C₂×C₄⋊C₄	—	15	4	no	—
293	C₂×C₄⋊C₄	—	15	2	no	—
294	C₂×C₂²⋊C₄	—	15	4	no	—
295	C₂×C₂²⋊C₄	—	15	2	no	—
296	C₂×C₄²	—	5	2	no	—
297	C₂×C₄²	—	5	8	no	—
298	C₂×C₄²	—	5	1	no	—
299	C₂×C₄²	—	5	1	no	—
300	C₂×C₄²	—	15	16	no	—
301	C₂×C₄²	—	15	4	no	—
302	C₂×C₄²	—	15	2	no	—
303	C₂×C₃×C₅	—	2	4	no	—
304	C₂×C₃×C₅	C₄×#41	1	4	yes	complemented
305	C₂×C₃×C₅	C₂⁴×C₄	1	1	yes	characteristic
306	C₂×C₃×C₅	C₂²×#41	1	2	yes	—
307	C₅×D₃	—	2	8	no	—
308	C₂³×C₃	—	2	4	no	—
309	C₂³×C₃	C₂²×Dic₅	1	4	yes	—
310	C₂³×C₃	C₂³×D₅	1	2	yes	—
311	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
312	C₂²×D₃	—	2	8	no	—
313	C₂²×D₃	C₂²×Dic₅	1	8	yes	—
314	C₂²×D₃	C₂³×D₅	1	4	yes	—
315	C₂×C₃×C₄	—	5	8	no	—
316	C₂×C₃×C₄	—	5	4	no	—
317	C₂×C₃×C₄	—	5	4	no	—
318	C₂×C₃×C₄	—	10	16	no	—
319	C₂×C₃×C₄	—	10	4	no	—
320	C₂×C₃×C₄	C₂²×Dic₅	1	4	yes	—
321	C₂×C₃×C₄	C₂²×Dic₅	1	4	yes	—
322	C₂×C₃×C₄	C₂²×Dic₅	1	16	yes	complemented
323	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
324	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
325	#67	C₂²×Dic₅	1	32	yes	complemented
326	C₂×Dic₃	—	5	8	no	—
327	C₂×Dic₃	—	10	8	no	—
328	C₂×Dic₃	C₂²×Dic₅	1	8	yes	—
329	C₂×Dic₃	C₂³×D₅	1	4	yes	—
330	D₁₂	C₂²×Dic₅	1	16	yes	complemented
331	C₄×D₃	—	10	32	no	—
332	C₄×D₃	C₂²×Dic₅	1	32	yes	complemented
333	Dic₆	C₂²×Dic₅	1	16	yes	complemented
334	C₂²×C₅	—	2	4	no	—
335	C₂²×C₅	—	2	8	no	—
336	C₂²×C₅	—	3	8	no	—
337	C₂²×C₅	—	6	8	no	—
338	C₂²×C₅	—	6	16	no	—
339	C₂²×C₅	C₂²×C₄×D₃	1	4	yes	—
340	C₂²×C₅	C₂²×C₄×D₃	1	2	yes	—
341	C₂²×C₅	C₂×#235	1	4	yes	—
342	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
343	C₄×C₅	—	3	8	no	—
344	C₄×C₅	C₂²×C₄×D₃	1	4	yes	—
345	C₄×C₅	C₂²×C₄×D₃	1	4	yes	—
346	Dic₅	—	2	4	no	—
347	Dic₅	—	6	8	no	—
348	Dic₅	C₂×#235	1	8	yes	direct product factor
349	C₂⁴	—	3	2	no	—
350	C₂⁴	C₂×D₃×D₅	1	1	yes	characteristic
351	#41	—	3	64	no	—
352	C₂×Q₈	—	3	8	no	—
353	C₂×Q₈	—	3	4	no	—
354	C₂×D₄	—	3	16	no	—
355	C₂×D₄	—	3	8	no	—
356	C₂×D₄	—	3	8	no	—
357	C₂×D₄	—	3	4	no	—
358	C₂²×C₄	—	3	2	no	—
359	C₂²×C₄	—	3	16	no	—
360	C₂²×C₄	—	3	8	no	—
361	C₂²×C₄	—	5	2	no	—
362	C₂²×C₄	—	5	2	no	—
363	C₂²×C₄	—	5	8	no	—
364	C₂²×C₄	—	10	8	no	—
365	C₂²×C₄	—	15	16	no	—
366	C₂²×C₄	—	15	4	no	—
367	C₂²×C₄	—	30	16	no	—
368	C₂²×C₄	D₃×Dic₅	1	8	yes	complemented
369	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
370	C₂²×C₄	C₂×D₃×D₅	1	4	yes	—
371	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
372	C₄⋊C₄	—	15	16	no	—
373	C₄⋊C₄	—	15	8	no	—
374	C₂²⋊C₄	—	15	16	no	—
375	C₂²⋊C₄	—	15	8	no	—
376	C₄²	—	5	4	no	—
377	C₄²	—	5	4	no	—
378	C₄²	—	5	8	no	—
379	C₄²	—	15	16	no	—
380	C₄²	—	15	8	no	—
381	C₃×C₅	C₂×C₄×#41	1	1	yes	characteristic, complemented, Hall
382	C₂²×C₃	—	2	8	no	—
383	C₂²×C₃	—	2	4	no	—
384	C₂²×C₃	D₅×#41	1	4	yes	—
385	C₂²×C₃	C₂³×Dic₅	1	4	yes	—
386	C₂²×C₃	C₂³×Dic₅	1	2	yes	—
387	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
388	C₂×D₃	—	2	16	no	—
389	C₂×D₃	—	2	8	no	—
390	C₂×D₃	C₂³×Dic₅	1	8	yes	—
391	C₃×C₄	—	5	8	no	—
392	C₃×C₄	—	10	4	no	—
393	C₃×C₄	C₂³×Dic₅	1	4	yes	—
394	C₃×C₄	C₂³×Dic₅	1	4	yes	—
395	Dic₃	—	10	8	no	—
396	Dic₃	C₂³×Dic₅	1	8	yes	—
397	C₂×C₅	—	2	4	no	—
398	C₂×C₅	—	6	8	no	—
399	C₂×C₅	C₄×#235	1	4	yes	complemented
400	C₂×C₅	C₂³×C₄×D₃	1	1	yes	characteristic
401	C₂×C₅	C₂²×#235	1	2	yes	—
402	C₂³	—	2	4	no	—
403	C₂³	—	3	8	no	—
404	C₂³	—	3	4	no	—
405	C₂³	—	6	8	no	—
406	C₂³	C₂×D₃×Dic₅	1	4	yes	—
407	C₂³	C₂²×D₃×D₅	1	2	yes	—
408	C₂³	C₂²×D₃×D₅	1	1	yes	characteristic
409	Q₈	—	3	16	no	—
410	D₄	—	3	32	no	—
411	D₄	—	3	16	no	—
412	C₂×C₄	—	3	8	no	—
413	C₂×C₄	—	3	4	no	—
414	C₂×C₄	—	3	32	no	—
415	C₂×C₄	—	5	8	no	—
416	C₂×C₄	—	5	4	no	—
417	C₂×C₄	—	5	4	no	—
418	C₂×C₄	—	10	16	no	—
419	C₂×C₄	—	10	4	no	—
420	C₂×C₄	—	15	8	no	—
421	C₂×C₄	—	30	32	no	—
422	C₂×C₄	—	30	8	no	—
423	C₂×C₄	C₂×D₃×Dic₅	1	4	yes	—
424	C₂×C₄	C₂×D₃×Dic₅	1	4	yes	—
425	C₂×C₄	C₂×D₃×Dic₅	1	16	yes	complemented
426	C₂×C₄	C₂²×D₃×D₅	1	2	yes	—
427	C₂×C₄	C₂²×D₃×D₅	1	2	yes	—
428	C₂×C₃	—	2	4	no	—
429	C₂×C₃	#41×Dic₅	1	4	yes	complemented
430	C₂×C₃	C₂×D₅×#41	1	2	yes	—
431	C₂×C₃	C₂⁴×Dic₅	1	1	yes	characteristic
432	D₃	—	2	8	no	—
433	C₅	C₂×C₄×#235	1	1	yes	characteristic, complemented, Sylow
434	C₂²	—	2	8	no	—
435	C₂²	—	2	4	no	—
436	C₂²	—	3	8	no	—
437	C₂²	—	6	16	no	—
438	C₂²	—	6	8	no	—
439	C₂²	D₅×#235	1	4	yes	—
440	C₂²	C₂²×D₃×Dic₅	1	4	yes	—
441	C₂²	C₂²×D₃×Dic₅	1	2	yes	—
442	C₂²	C₂³×D₃×D₅	1	1	yes	characteristic
443	C₄	—	3	8	no	—
444	C₄	—	5	8	no	—
445	C₄	—	10	4	no	—
446	C₄	—	30	8	no	—
447	C₄	C₂²×D₃×Dic₅	1	4	yes	—
448	C₄	C₂²×D₃×Dic₅	1	4	yes	—
449	C₃	C₂×#41×Dic₅	1	1	yes	characteristic, complemented, Sylow
450	C₂	—	2	4	no	—
451	C₂	—	6	8	no	—
452	C₂	Dic₅×#235	1	4	yes	direct product factor
453	C₂	C₂×D₅×#235	1	2	yes	—
454	C₂	C₂³×D₃×Dic₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₃×D₅
commutator	C₂×C₃×C₅	C₂⁴×C₄
Frattini	C₂²	C₂³×D₃×D₅
Fitting	C₂³×C₃×C₄×C₅	C₂²
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂²×C₅×#235	C₂
cosocle	C₂²×C₃×C₅	C₂⁵
hypercenter	C₂³×C₄	D₃×D₅
hypocenter	C₃×C₅	C₂×C₄×#41
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₄

Complements

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

N	H ≅ G/N	type
2. C₂×#91815	C₂	semidirect
3. C₂²×C₃×C₄×Dic₅	C₂	semidirect
4. C₂×Dic₅×#67	C₂	semidirect
5. Dic₅×#235	C₂	direct (N × H)
6. C₂×Dic₅×D₁₂	C₂	semidirect
7. C₂×C₄×D₃×Dic₅	C₂	semidirect
8. C₂×#91371	C₂	semidirect
9. C₂×Dic₅×Dic₆	C₂	semidirect
13. C₂×C₅×#235	C₄	semidirect
21. #91815	C₂²	semidirect
27. C₂×C₃×C₄×Dic₅	C₂²	semidirect
28. Dic₅×#67	C₂²	semidirect
32. Dic₅×D₁₂	C₂²	semidirect
33. C₄×D₃×Dic₅	C₂²	semidirect
34. #91371	C₂²	semidirect
35. Dic₅×Dic₆	C₂²	semidirect
45. C₂²×C₄×Dic₅	D₃	semidirect
48. C₂²×C₃×C₄×C₅	C₂×C₄	semidirect
53. C₂×C₅×#67	C₂×C₄	semidirect
56. C₅×#235	C₂×C₄	semidirect
57. C₂×C₅×D₁₂	C₂×C₄	semidirect
59. C₂×C₄×C₅×D₃	C₂×C₄	semidirect
61. C₂×C₅×Dic₆	C₂×C₄	semidirect
111. C₂×C₄×Dic₅	C₂×D₃	semidirect
122. C₂×C₃×C₄×C₅	C₂²×C₄	semidirect
127. C₅×#67	C₂²×C₄	semidirect
130. C₅×D₁₂	C₂²×C₄	semidirect
131. C₄×C₅×D₃	C₂²×C₄	semidirect
132. C₅×Dic₆	C₂²×C₄	semidirect
135. C₂×C₃×Dic₅	#41	semidirect
142. C₂×#235	Dic₅	direct (N × H)
176. C₂²×C₄×C₅	C₄×D₃	semidirect
218. C₃×Dic₅	C₂×#41	semidirect
226. C₂²×C₃×C₄	C₂×Dic₅	semidirect
230. C₂×#67	C₂×Dic₅	semidirect
234. #235	C₂×Dic₅	direct (N × H)
235. C₂×D₁₂	C₂×Dic₅	semidirect
239. C₂×C₄×D₃	C₂×Dic₅	semidirect
241. C₂×Dic₆	C₂×Dic₅	semidirect
267. C₂×C₄×C₅	C₂×C₄×D₃	semidirect
275. C₂×Dic₅	#235	direct (N × H)
304. C₂×C₃×C₅	C₄×#41	semidirect
322. C₂×C₃×C₄	C₂²×Dic₅	semidirect
325. #67	C₂²×Dic₅	semidirect
330. D₁₂	C₂²×Dic₅	semidirect
332. C₄×D₃	C₂²×Dic₅	semidirect
333. Dic₆	C₂²×Dic₅	semidirect
348. Dic₅	C₂×#235	direct (N × H)
368. C₂²×C₄	D₃×Dic₅	semidirect
381. C₃×C₅	C₂×C₄×#41	semidirect
399. C₂×C₅	C₄×#235	semidirect
425. C₂×C₄	C₂×D₃×Dic₅	semidirect
429. C₂×C₃	#41×Dic₅	semidirect
433. C₅	C₂×C₄×#235	semidirect
449. C₃	C₂×#41×Dic₅	semidirect
452. C₂	Dic₅×#235	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₅×#235	2
C₂×#91815	2
C₂²×C₃×C₄×Dic₅	2
C₂×Dic₅×#67	2
Dic₅×#235	2
C₂×Dic₅×D₁₂	2
C₂×C₄×D₃×Dic₅	2
C₂×#91371	2
C₂×Dic₅×Dic₆	2
C₂×#41×Dic₅	3
C₂×C₄×#235	5

Subgroups — C2×Dic5×#235 #14478932

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×Dic₅×#235 #14478932