Subgroups — C₂×Dic₃×#709 #14478930

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×C₃×#709	C₂	1	1	yes	maximal, characteristic
2	C₂×#91815	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₄×C₅×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×Dic₃×C₂²⋊D₅	C₂	1	4	yes	maximal, complemented
5	Dic₃×#709	C₂	1	16	yes	maximal, direct product factor
6	C₂×Dic₃×D₂₀	C₂	1	2	yes	maximal, complemented
7	C₂×C₄×D₅×Dic₃	C₂	1	2	yes	maximal, complemented
8	C₂×#91357	C₂	1	2	yes	maximal, complemented
9	C₂×Dic₃×Dic₁₀	C₂	1	2	yes	maximal, complemented
10	C₂×C₄×#709	—	3	1	no	maximal, Hall
11	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
12	C₂³×C₅×Dic₃	C₂²	1	2	yes	—
13	C₂²×C₃×C₂²⋊D₅	C₂²	1	2	yes	—
14	C₂×C₃×#709	C₄	1	16	yes	complemented
15	C₂×C₃×#709	C₂²	1	8	yes	—
16	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic
17	C₂²×C₃×C₄×D₅	C₂²	1	2	yes	—
18	C₂²×C₃×Dic₁₀	C₂²	1	1	yes	characteristic
19	C₂²×D₅×Dic₃	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×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	—
26	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₅×Dic₃	C₂²	1	8	yes	complemented
28	Dic₃×C₂²⋊D₅	C₂²	1	32	yes	complemented
29	C₂×#6668	C₂²	1	4	yes	—
30	C₂×#6665	C₂²	1	4	yes	—
31	C₂×Dic₃×Dic₅	C₂²	1	4	yes	—
32	Dic₃×D₂₀	C₂²	1	16	yes	complemented
33	C₄×D₅×Dic₃	C₂²	1	16	yes	complemented
34	#91357	C₂²	1	16	yes	complemented
35	Dic₃×Dic₁₀	C₂²	1	16	yes	complemented
36	C₂×Dic₃×#41	—	5	1	no	maximal, Hall
37	C₂²×#709	D₃	1	1	yes	characteristic
38	C₂²×C₄²×C₅	—	3	1	no	—
39	C₂×C₄×C₂²⋊D₅	—	3	4	no	—
40	C₂×#4072	—	3	1	no	—
41	C₄×#709	—	3	16	no	—
42	C₂×C₄×D₂₀	—	3	2	no	—
43	C₂×#4018	—	3	2	no	—
44	C₂×C₄²×D₅	—	3	2	no	—
45	C₂×C₄×Dic₁₀	—	3	2	no	—
46	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
47	C₂³×C₃×D₅	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	C₂²×C₅×Dic₃	—	2	8	no	—
54	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
55	C₂²×C₅×Dic₃	C₂³	1	8	yes	—
56	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
57	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	16	yes	complemented
58	C₂×C₃×C₂²⋊D₅	C₂³	1	8	yes	—
59	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
60	C₃×#709	C₂×C₄	1	64	yes	complemented
61	C₂×C₃×D₂₀	C₂×C₄	1	8	yes	complemented
62	C₂×C₃×D₂₀	C₂³	1	4	yes	—
63	C₂×C₃×C₄×D₅	C₂×C₄	1	16	yes	complemented
64	C₂×C₃×C₄×D₅	C₂³	1	8	yes	—
65	C₂×C₃×Dic₁₀	C₂×C₄	1	8	yes	complemented
66	C₂×C₃×Dic₁₀	C₂³	1	4	yes	—
67	C₂×D₅×Dic₃	—	2	16	no	—
68	C₂×D₅×Dic₃	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	C₄×C₅×Dic₃	C₂³	1	8	yes	—
73	C₄×C₅×Dic₃	C₂³	1	4	yes	—
74	C₄×C₅×Dic₃	C₂³	1	4	yes	—
75	#6668	C₂³	1	16	yes	—
76	#6665	C₂³	1	16	yes	—
77	Dic₃×Dic₅	C₂³	1	16	yes	—
78	C₂²×C₃×#41	—	5	1	no	—
79	Dic₃×#41	—	5	16	no	—
80	C₂×Q₈×Dic₃	—	5	2	no	—
81	C₂×D₄×Dic₃	—	5	4	no	—
82	C₂×D₄×Dic₃	—	5	2	no	—
83	C₂×#926	—	5	1	no	—
84	C₂×#926	—	5	2	no	—
85	C₂²×C₄×Dic₃	—	5	2	no	—
86	C₂²×C₄×Dic₃	D₅	1	1	yes	characteristic, complemented
87	C₂³×C₄×C₅	—	3	2	no	—
88	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
89	C₂²×C₂²⋊D₅	C₂×D₃	1	2	yes	—
90	C₂×#709	Dic₃	1	16	yes	direct product factor
91	C₂×#709	C₂×D₃	1	8	yes	—
92	C₂²×D₂₀	C₂×D₃	1	1	yes	characteristic
93	C₂²×C₄×D₅	—	3	4	no	—
94	C₂²×C₄×D₅	C₂×D₃	1	2	yes	—
95	C₂²×Dic₁₀	C₂×D₃	1	1	yes	characteristic
96	C₂×C₄²×C₅	—	3	2	no	—
97	C₂×C₄²×C₅	—	3	1	no	—
98	C₂×C₄²×C₅	—	3	1	no	—
99	C₂×C₄²×C₅	—	3	8	no	—
100	C₂×C₂²⋊Dic₅	—	3	2	no	—
101	C₄×C₂²⋊D₅	—	3	32	no	—
102	C₂×#685	—	3	4	no	—
103	#4072	—	3	8	no	—
104	C₂×C₄⋊Dic₅	—	3	2	no	—
105	C₂×#683	—	3	4	no	—
106	C₂×C₄×Dic₅	—	3	2	no	—
107	C₂×C₄×Dic₅	—	3	4	no	—
108	C₄×D₂₀	—	3	16	no	—
109	#4018	—	3	16	no	—
110	C₄²×D₅	—	3	16	no	—
111	C₄×Dic₁₀	—	3	16	no	—
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×C₃×D₅	—	2	8	no	—
118	C₂²×C₃×D₅	C₂²×C₄	1	8	yes	—
119	C₂²×C₃×D₅	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	C₂×C₅×Dic₃	—	2	4	no	—
128	C₂×C₅×Dic₃	—	2	16	no	—
129	C₂×C₅×Dic₃	#41	1	8	yes	complemented
130	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
131	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
132	C₃×C₂²⋊D₅	C₂²×C₄	1	32	yes	complemented
133	C₂×C₃×Dic₅	C₂²×C₄	1	8	yes	—
134	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
135	C₃×D₂₀	C₂²×C₄	1	16	yes	complemented
136	C₃×C₄×D₅	C₂²×C₄	1	32	yes	complemented
137	C₃×Dic₁₀	C₂²×C₄	1	16	yes	complemented
138	D₅×Dic₃	—	2	32	no	—
139	C₂×C₃×#41	—	5	16	no	—
140	C₂×C₃×#41	—	5	8	no	—
141	C₂²×C₃×Q₈	—	5	1	no	—
142	C₂²×C₃×D₄	—	5	2	no	—
143	C₂²×C₃×D₄	—	5	1	no	—
144	C₂³×C₃×C₄	—	5	2	no	—
145	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
146	C₂³×Dic₃	—	5	4	no	—
147	C₂³×Dic₃	C₂×D₅	1	2	yes	—
148	C₂×#217	—	5	2	no	—
149	C₂×#217	—	5	4	no	—
150	Q₈×Dic₃	—	5	16	no	—
151	D₄×Dic₃	—	5	32	no	—
152	D₄×Dic₃	—	5	16	no	—
153	#926	—	5	8	no	—
154	#926	—	5	16	no	—
155	C₂×C₄⋊Dic₃	—	5	2	no	—
156	C₂×C₄⋊Dic₃	—	5	4	no	—
157	C₂×C₄×Dic₃	—	5	2	no	—
158	C₂×C₄×Dic₃	—	5	4	no	—
159	C₂×C₄×Dic₃	—	5	16	no	—
160	C₂×C₄×Dic₃	C₂×D₅	1	1	yes	characteristic
161	C₂×C₄×Dic₃	C₂×D₅	1	1	yes	characteristic
162	C₂×C₄×Dic₃	C₂×D₅	1	2	yes	—
163	C₂×C₄×Dic₃	C₂×D₅	1	8	yes	complemented
164	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
165	C₂³×D₅	C₂²×D₃	1	2	yes	—
166	C₂²×C₄×C₅	—	3	2	no	—
167	C₂²×C₄×C₅	—	3	2	no	—
168	C₂²×C₄×C₅	—	3	8	no	—
169	C₂²×C₄×C₅	—	6	8	no	—
170	C₂²×C₄×C₅	C₂×Dic₃	1	8	yes	complemented
171	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
172	C₂²×C₄×C₅	C₂²×D₃	1	4	yes	—
173	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
174	C₂×C₂²⋊D₅	C₂×Dic₃	1	16	yes	complemented
175	C₂×C₂²⋊D₅	C₂²×D₃	1	8	yes	—
176	C₂²×Dic₅	—	3	4	no	—
177	C₂²×Dic₅	C₂²×D₃	1	2	yes	—
178	#709	C₂×Dic₃	1	64	yes	direct product factor
179	C₂×D₂₀	C₂×Dic₃	1	8	yes	complemented
180	C₂×D₂₀	C₂²×D₃	1	4	yes	—
181	C₂×C₄×D₅	—	3	16	no	—
182	C₂×C₄×D₅	—	6	16	no	—
183	C₂×C₄×D₅	C₂×Dic₃	1	16	yes	complemented
184	C₂×C₄×D₅	C₂²×D₃	1	8	yes	—
185	C₂×Dic₁₀	C₂×Dic₃	1	8	yes	complemented
186	C₂×Dic₁₀	C₂²×D₃	1	4	yes	—
187	C₄²×C₅	—	3	8	no	—
188	C₄²×C₅	—	3	4	no	—
189	C₄²×C₅	—	3	4	no	—
190	C₂²⋊Dic₅	—	3	8	no	—
191	#685	—	3	16	no	—
192	C₄⋊Dic₅	—	3	8	no	—
193	#683	—	3	16	no	—
194	C₄×Dic₅	—	3	8	no	—
195	C₄×Dic₅	—	3	16	no	—
196	C₂²×#41	—	5	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	—	3	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×C₃×D₅	—	2	16	no	—
212	C₂×C₃×D₅	—	2	8	no	—
213	C₂×C₃×D₅	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	C₂³×C₄	1	8	yes	—
218	C₅×Dic₃	—	2	4	no	—
219	C₅×Dic₃	C₂×#41	1	8	yes	complemented
220	C₂⁴×C₃	—	5	2	no	—
221	C₂⁴×C₃	C₂²×D₅	1	1	yes	characteristic
222	C₃×#41	—	5	64	no	—
223	C₂×C₃×Q₈	—	5	8	no	—
224	C₂×C₃×Q₈	—	5	4	no	—
225	C₂×C₃×D₄	—	5	16	no	—
226	C₂×C₃×D₄	—	5	8	no	—
227	C₂×C₃×D₄	—	5	8	no	—
228	C₂×C₃×D₄	—	5	4	no	—
229	C₂²×C₃×C₄	—	5	2	no	—
230	C₂²×C₃×C₄	—	5	16	no	—
231	C₂²×C₃×C₄	—	5	8	no	—
232	C₂²×C₃×C₄	C₄×D₅	1	8	yes	complemented
233	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
234	C₂²×C₃×C₄	C₂²×D₅	1	4	yes	—
235	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
236	C₂²×Dic₃	—	2	8	no	—
237	C₂²×Dic₃	—	5	4	no	—
238	C₂²×Dic₃	—	5	16	no	—
239	C₂²×Dic₃	—	10	16	no	—
240	C₂²×Dic₃	C₂²×D₅	1	2	yes	—
241	C₂²×Dic₃	C₂²×D₅	1	8	yes	—
242	C₂²×Dic₃	C₂²×D₅	1	2	yes	—
243	#217	—	5	8	no	—
244	#217	—	5	16	no	—
245	C₄⋊Dic₃	—	5	8	no	—
246	C₄⋊Dic₃	—	5	16	no	—
247	C₄×Dic₃	—	5	8	no	—
248	C₄×Dic₃	—	5	16	no	—
249	C₄×Dic₃	C₂²×D₅	1	4	yes	—
250	C₄×Dic₃	C₂²×D₅	1	4	yes	—
251	C₄×Dic₃	C₂²×D₅	1	8	yes	—
252	C₂³×C₅	—	2	4	no	—
253	C₂³×C₅	C₂²×Dic₃	1	4	yes	—
254	C₂³×C₅	C₂³×D₃	1	2	yes	—
255	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
256	C₂²×D₅	—	2	8	no	—
257	C₂²×D₅	C₂²×Dic₃	1	8	yes	—
258	C₂²×D₅	C₂³×D₃	1	4	yes	—
259	C₂×C₄×C₅	—	3	8	no	—
260	C₂×C₄×C₅	—	3	4	no	—
261	C₂×C₄×C₅	—	3	4	no	—
262	C₂×C₄×C₅	—	6	16	no	—
263	C₂×C₄×C₅	—	6	4	no	—
264	C₂×C₄×C₅	C₂²×Dic₃	1	4	yes	—
265	C₂×C₄×C₅	C₂²×Dic₃	1	4	yes	—
266	C₂×C₄×C₅	C₂²×Dic₃	1	16	yes	complemented
267	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
268	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
269	C₂²⋊D₅	C₂²×Dic₃	1	32	yes	complemented
270	C₂×Dic₅	—	3	8	no	—
271	C₂×Dic₅	—	6	8	no	—
272	C₂×Dic₅	C₂²×Dic₃	1	8	yes	—
273	C₂×Dic₅	C₂³×D₃	1	4	yes	—
274	D₂₀	C₂²×Dic₃	1	16	yes	complemented
275	C₄×D₅	—	6	32	no	—
276	C₄×D₅	C₂²×Dic₃	1	32	yes	complemented
277	Dic₁₀	C₂²×Dic₃	1	16	yes	complemented
278	C₂×#41	—	5	16	no	—
279	C₂×#41	—	5	8	no	—
280	C₂²×Q₈	—	5	1	no	—
281	C₂²×D₄	—	5	2	no	—
282	C₂²×D₄	—	5	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	—	3	2	no	—
297	C₂×C₄²	—	3	8	no	—
298	C₂×C₄²	—	3	1	no	—
299	C₂×C₄²	—	3	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	C₃×D₅	—	2	8	no	—
308	C₂³×C₃	—	2	4	no	—
309	C₂³×C₃	—	5	8	no	—
310	C₂³×C₃	—	5	4	no	—
311	C₂³×C₃	—	10	8	no	—
312	C₂³×C₃	C₂×C₄×D₅	1	4	yes	—
313	C₂³×C₃	C₂³×D₅	1	2	yes	—
314	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
315	C₃×Q₈	—	5	16	no	—
316	C₃×D₄	—	5	32	no	—
317	C₃×D₄	—	5	16	no	—
318	C₂×C₃×C₄	—	5	8	no	—
319	C₂×C₃×C₄	—	5	4	no	—
320	C₂×C₃×C₄	—	5	32	no	—
321	C₂×C₃×C₄	C₂×C₄×D₅	1	4	yes	—
322	C₂×C₃×C₄	C₂×C₄×D₅	1	4	yes	—
323	C₂×C₃×C₄	C₂×C₄×D₅	1	16	yes	complemented
324	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
325	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
326	C₂×Dic₃	—	2	4	no	—
327	C₂×Dic₃	—	2	16	no	—
328	C₂×Dic₃	—	5	8	no	—
329	C₂×Dic₃	—	10	8	no	—
330	C₂×Dic₃	—	10	32	no	—
331	C₂×Dic₃	#709	1	8	yes	direct product factor
332	C₂×Dic₃	C₂³×D₅	1	4	yes	—
333	C₂×Dic₃	C₂³×D₅	1	4	yes	—
334	C₂²×C₅	—	2	4	no	—
335	C₂²×C₅	—	2	8	no	—
336	C₂²×C₅	D₃×#41	1	4	yes	—
337	C₂²×C₅	C₂³×Dic₃	1	4	yes	—
338	C₂²×C₅	C₂³×Dic₃	1	2	yes	—
339	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
340	C₂×D₅	—	2	8	no	—
341	C₂×D₅	—	2	16	no	—
342	C₂×D₅	C₂³×Dic₃	1	8	yes	—
343	C₄×C₅	—	3	8	no	—
344	C₄×C₅	—	6	4	no	—
345	C₄×C₅	C₂³×Dic₃	1	4	yes	—
346	C₄×C₅	C₂³×Dic₃	1	4	yes	—
347	Dic₅	—	6	8	no	—
348	Dic₅	C₂³×Dic₃	1	8	yes	—
349	C₂⁴	—	5	2	no	—
350	C₂⁴	C₂×D₃×D₅	1	1	yes	characteristic
351	#41	—	5	64	no	—
352	C₂×Q₈	—	5	8	no	—
353	C₂×Q₈	—	5	4	no	—
354	C₂×D₄	—	5	16	no	—
355	C₂×D₄	—	5	8	no	—
356	C₂×D₄	—	5	8	no	—
357	C₂×D₄	—	5	4	no	—
358	C₂²×C₄	—	3	2	no	—
359	C₂²×C₄	—	3	2	no	—
360	C₂²×C₄	—	3	8	no	—
361	C₂²×C₄	—	5	2	no	—
362	C₂²×C₄	—	5	16	no	—
363	C₂²×C₄	—	5	8	no	—
364	C₂²×C₄	—	6	8	no	—
365	C₂²×C₄	—	15	16	no	—
366	C₂²×C₄	—	15	4	no	—
367	C₂²×C₄	—	30	16	no	—
368	C₂²×C₄	D₅×Dic₃	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	—	3	4	no	—
377	C₄²	—	3	4	no	—
378	C₄²	—	3	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	—	5	8	no	—
385	C₂²×C₃	—	10	16	no	—
386	C₂²×C₃	—	10	8	no	—
387	C₂²×C₃	C₂²×C₄×D₅	1	4	yes	—
388	C₂²×C₃	C₂²×C₄×D₅	1	2	yes	—
389	C₂²×C₃	C₂×#709	1	4	yes	—
390	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
391	C₃×C₄	—	5	8	no	—
392	C₃×C₄	C₂²×C₄×D₅	1	4	yes	—
393	C₃×C₄	C₂²×C₄×D₅	1	4	yes	—
394	Dic₃	—	2	4	no	—
395	Dic₃	—	10	8	no	—
396	Dic₃	C₂×#709	1	8	yes	direct product factor
397	C₂×C₅	—	2	4	no	—
398	C₂×C₅	Dic₃×#41	1	4	yes	complemented
399	C₂×C₅	C₂×D₃×#41	1	2	yes	—
400	C₂×C₅	C₂⁴×Dic₃	1	1	yes	characteristic
401	D₅	—	2	8	no	—
402	C₂³	—	2	4	no	—
403	C₂³	—	5	8	no	—
404	C₂³	—	5	4	no	—
405	C₂³	—	10	8	no	—
406	C₂³	C₂×D₅×Dic₃	1	4	yes	—
407	C₂³	C₂²×D₃×D₅	1	2	yes	—
408	C₂³	C₂²×D₃×D₅	1	1	yes	characteristic
409	Q₈	—	5	16	no	—
410	D₄	—	5	32	no	—
411	D₄	—	5	16	no	—
412	C₂×C₄	—	3	8	no	—
413	C₂×C₄	—	3	4	no	—
414	C₂×C₄	—	3	4	no	—
415	C₂×C₄	—	5	8	no	—
416	C₂×C₄	—	5	4	no	—
417	C₂×C₄	—	5	32	no	—
418	C₂×C₄	—	6	16	no	—
419	C₂×C₄	—	6	4	no	—
420	C₂×C₄	—	15	8	no	—
421	C₂×C₄	—	30	32	no	—
422	C₂×C₄	—	30	8	no	—
423	C₂×C₄	C₂×D₅×Dic₃	1	4	yes	—
424	C₂×C₄	C₂×D₅×Dic₃	1	4	yes	—
425	C₂×C₄	C₂×D₅×Dic₃	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	—	10	8	no	—
430	C₂×C₃	C₄×#709	1	4	yes	complemented
431	C₂×C₃	C₂³×C₄×D₅	1	1	yes	characteristic
432	C₂×C₃	C₂²×#709	1	2	yes	—
433	C₅	C₂×Dic₃×#41	1	1	yes	characteristic, complemented, Sylow
434	C₂²	—	2	8	no	—
435	C₂²	—	2	4	no	—
436	C₂²	—	5	8	no	—
437	C₂²	—	10	16	no	—
438	C₂²	—	10	8	no	—
439	C₂²	D₃×#709	1	4	yes	—
440	C₂²	C₂²×D₅×Dic₃	1	4	yes	—
441	C₂²	C₂²×D₅×Dic₃	1	2	yes	—
442	C₂²	C₂³×D₃×D₅	1	1	yes	characteristic
443	C₄	—	3	8	no	—
444	C₄	—	5	8	no	—
445	C₄	—	6	4	no	—
446	C₄	—	30	8	no	—
447	C₄	C₂²×D₅×Dic₃	1	4	yes	—
448	C₄	C₂²×D₅×Dic₃	1	4	yes	—
449	C₃	C₂×C₄×#709	1	1	yes	characteristic, complemented, Sylow
450	C₂	—	2	4	no	—
451	C₂	—	10	8	no	—
452	C₂	Dic₃×#709	1	4	yes	direct product factor
453	C₂	C₂×D₃×#709	1	2	yes	—
454	C₂	C₂³×D₅×Dic₃	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×C₃×#709	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×C₄×C₅×Dic₃	C₂	semidirect
4. C₂×Dic₃×C₂²⋊D₅	C₂	semidirect
5. Dic₃×#709	C₂	direct (N × H)
6. C₂×Dic₃×D₂₀	C₂	semidirect
7. C₂×C₄×D₅×Dic₃	C₂	semidirect
8. C₂×#91357	C₂	semidirect
9. C₂×Dic₃×Dic₁₀	C₂	semidirect
14. C₂×C₃×#709	C₄	semidirect
21. #91815	C₂²	semidirect
27. C₂×C₄×C₅×Dic₃	C₂²	semidirect
28. Dic₃×C₂²⋊D₅	C₂²	semidirect
32. Dic₃×D₂₀	C₂²	semidirect
33. C₄×D₅×Dic₃	C₂²	semidirect
34. #91357	C₂²	semidirect
35. Dic₃×Dic₁₀	C₂²	semidirect
48. C₂²×C₃×C₄×C₅	C₂×C₄	semidirect
57. C₂×C₃×C₂²⋊D₅	C₂×C₄	semidirect
60. C₃×#709	C₂×C₄	semidirect
61. C₂×C₃×D₂₀	C₂×C₄	semidirect
63. C₂×C₃×C₄×D₅	C₂×C₄	semidirect
65. C₂×C₃×Dic₁₀	C₂×C₄	semidirect
86. C₂²×C₄×Dic₃	D₅	semidirect
90. C₂×#709	Dic₃	direct (N × H)
122. C₂×C₃×C₄×C₅	C₂²×C₄	semidirect
129. C₂×C₅×Dic₃	#41	semidirect
132. C₃×C₂²⋊D₅	C₂²×C₄	semidirect
135. C₃×D₂₀	C₂²×C₄	semidirect
136. C₃×C₄×D₅	C₂²×C₄	semidirect
137. C₃×Dic₁₀	C₂²×C₄	semidirect
163. C₂×C₄×Dic₃	C₂×D₅	semidirect
170. C₂²×C₄×C₅	C₂×Dic₃	semidirect
174. C₂×C₂²⋊D₅	C₂×Dic₃	semidirect
178. #709	C₂×Dic₃	direct (N × H)
179. C₂×D₂₀	C₂×Dic₃	semidirect
183. C₂×C₄×D₅	C₂×Dic₃	semidirect
185. C₂×Dic₁₀	C₂×Dic₃	semidirect
219. C₅×Dic₃	C₂×#41	semidirect
232. C₂²×C₃×C₄	C₄×D₅	semidirect
266. C₂×C₄×C₅	C₂²×Dic₃	semidirect
269. C₂²⋊D₅	C₂²×Dic₃	semidirect
274. D₂₀	C₂²×Dic₃	semidirect
276. C₄×D₅	C₂²×Dic₃	semidirect
277. Dic₁₀	C₂²×Dic₃	semidirect
304. C₂×C₃×C₅	C₄×#41	semidirect
323. C₂×C₃×C₄	C₂×C₄×D₅	semidirect
331. C₂×Dic₃	#709	direct (N × H)
368. C₂²×C₄	D₅×Dic₃	semidirect
381. C₃×C₅	C₂×C₄×#41	semidirect
396. Dic₃	C₂×#709	direct (N × H)
398. C₂×C₅	Dic₃×#41	semidirect
425. C₂×C₄	C₂×D₅×Dic₃	semidirect
430. C₂×C₃	C₄×#709	semidirect
433. C₅	C₂×Dic₃×#41	semidirect
449. C₃	C₂×C₄×#709	semidirect
452. C₂	Dic₃×#709	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×C₃×#709	2
C₂×#91815	2
C₂²×C₄×C₅×Dic₃	2
C₂×Dic₃×C₂²⋊D₅	2
Dic₃×#709	2
C₂×Dic₃×D₂₀	2
C₂×C₄×D₅×Dic₃	2
C₂×#91357	2
C₂×Dic₃×Dic₁₀	2
C₂×C₄×#709	3
C₂×Dic₃×#41	5

Subgroups — C2×Dic3×#709 #14478930

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×Dic₃×#709 #14478930