Subgroups — C₂×C₃×#66059 #14480031

Order 1920.

3456 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×#713	C₂	1	2	yes	maximal, complemented
2	C₂×C₃×C₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#4093	C₂	1	2	yes	maximal, complemented
4	C₃×#66059	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₃×#4041	C₂	1	4	yes	maximal, complemented
6	C₂×C₃×#4039	C₂	1	4	yes	maximal, complemented
7	C₂×C₃×#4020	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃×C₄²×D₅	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#66059	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂²×C₃×C₅×Q₈	C₂²	1	2	yes	—
11	C₂×C₃×#713	—	2	16	no	—
12	C₂×C₃×#713	C₂²	1	16	yes	complemented
13	C₂²×C₃×D₂₀	C₂²	1	2	yes	—
14	C₂²×C₃×D₂₀	C₂²	1	4	yes	—
15	C₂²×C₃×D₂₀	C₂²	1	4	yes	—
16	C₂²×C₃×C₄×D₅	C₂²	1	4	yes	—
17	C₂²×C₃×C₄×D₅	C₂²	1	2	yes	—
18	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
19	C₃×C₅×C₄⋊Q₈	C₂²	1	8	yes	complemented
20	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	4	yes	—
21	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
22	C₃×#4093	C₂²	1	16	yes	complemented
23	C₂×C₃×#685	C₂²	1	8	yes	—
24	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
25	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	—
26	C₃×#4041	C₂²	1	32	yes	complemented
27	C₃×#4039	C₂²	1	32	yes	complemented
28	C₃×#4020	C₂²	1	8	yes	complemented
29	C₃×C₄²×D₅	C₂²	1	8	yes	complemented
30	C₂×C₃×#532	—	5	1	no	maximal, Hall
31	C₂²×#713	C₂×C₃	1	2	yes	complemented
32	C₂×C₅×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
33	C₂×#4093	C₂×C₃	1	2	yes	complemented
34	#66059	C₂×C₃	1	16	yes	direct product factor
35	C₂×#4041	C₂×C₃	1	4	yes	complemented
36	C₂×#4039	C₂×C₃	1	4	yes	complemented
37	C₂×#4020	C₂×C₃	1	1	yes	characteristic, complemented
38	C₂×C₄²×D₅	C₂×C₃	1	1	yes	characteristic, complemented
39	C₂³×C₃×D₅	C₂³	1	4	yes	—
40	C₂³×C₃×D₅	C₂³	1	1	yes	characteristic
41	C₂×C₃×C₅×Q₈	—	2	8	no	—
42	C₂×C₃×C₅×Q₈	C₂³	1	8	yes	—
43	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
44	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
45	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
46	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
47	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
48	C₃×#713	—	2	64	no	—
49	C₂×C₃×D₂₀	—	2	16	no	—
50	C₂×C₃×D₂₀	—	2	8	no	—
51	C₂×C₃×D₂₀	—	2	16	no	—
52	C₂×C₃×D₂₀	C₂³	1	8	yes	—
53	C₂×C₃×D₂₀	C₂³	1	16	yes	—
54	C₂×C₃×D₂₀	C₂³	1	16	yes	—
55	C₂×C₃×C₄×D₅	—	2	8	no	—
56	C₂×C₃×C₄×D₅	—	2	16	no	—
57	C₂×C₃×C₄×D₅	D₄	1	8	yes	complemented
58	C₂×C₃×C₄×D₅	C₂³	1	16	yes	—
59	C₂×C₃×C₄×D₅	C₂³	1	8	yes	—
60	C₂×C₃×C₄×D₅	C₂³	1	4	yes	—
61	C₃×C₅×C₄⋊C₄	C₂³	1	16	yes	—
62	C₃×C₄²×C₅	C₂³	1	4	yes	—
63	C₃×#685	C₂³	1	32	yes	—
64	C₃×C₄×Dic₅	C₂³	1	4	yes	—
65	C₃×C₄×Dic₅	C₂³	1	8	yes	—
66	C₂²×C₃×#41	—	5	2	no	—
67	C₃×#532	—	5	16	no	—
68	C₂×C₃×C₄⋊Q₈	D₅	1	1	yes	characteristic, complemented
69	C₂×C₃×#127	—	5	1	no	—
70	C₂×C₃×#124	—	5	2	no	—
71	C₂×C₃×#121	—	5	4	no	—
72	C₂×C₃×C₄×D₄	—	5	4	no	—
73	C₂²×C₃×C₄²	—	5	1	no	—
74	C₂²×C₅×Q₈	C₂²×C₃	1	2	yes	—
75	C₂×#713	—	2	16	no	—
76	C₂×#713	C₂²×C₃	1	16	yes	complemented
77	C₂²×D₂₀	C₂²×C₃	1	4	yes	—
78	C₂²×D₂₀	C₂²×C₃	1	2	yes	—
79	C₂²×D₂₀	C₂²×C₃	1	4	yes	—
80	C₂²×C₄×D₅	C₂²×C₃	1	2	yes	—
81	C₂²×C₄×D₅	C₂²×C₃	1	4	yes	—
82	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
83	C₅×C₄⋊Q₈	C₂²×C₃	1	8	yes	complemented
84	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	4	yes	—
85	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
86	#4093	C₂²×C₃	1	16	yes	complemented
87	C₂×#685	C₂²×C₃	1	8	yes	—
88	C₂×C₄×Dic₅	C₂²×C₃	1	2	yes	—
89	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
90	#4041	C₂²×C₃	1	32	yes	complemented
91	#4039	C₂²×C₃	1	32	yes	complemented
92	#4020	C₂²×C₃	1	8	yes	complemented
93	C₄²×D₅	C₂²×C₃	1	8	yes	complemented
94	C₂×#532	—	5	1	no	Sylow
95	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
96	C₂²×C₃×D₅	—	2	4	no	—
97	C₂²×C₃×D₅	—	2	8	no	—
98	C₂²×C₃×D₅	—	2	16	no	—
99	C₂²×C₃×D₅	C₂×D₄	1	4	yes	—
100	C₂²×C₃×D₅	C₂⁴	1	8	yes	—
101	C₂²×C₃×D₅	C₂⁴	1	2	yes	—
102	C₃×C₅×Q₈	—	2	16	no	—
103	C₂×C₃×C₄×C₅	—	2	8	no	—
104	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
105	C₂×C₃×C₄×C₅	#41	1	8	yes	complemented
106	C₂×C₃×C₄×C₅	C₂⁴	1	8	yes	—
107	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
108	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
109	C₂×C₃×Dic₅	—	2	4	no	—
110	C₂×C₃×Dic₅	C₂×D₄	1	4	yes	—
111	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
112	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
113	C₃×D₂₀	—	2	32	no	—
114	C₃×D₂₀	—	2	16	no	—
115	C₃×D₂₀	—	2	32	no	—
116	C₃×C₄×D₅	—	2	16	no	—
117	C₃×C₄×D₅	—	2	32	no	—
118	C₃×C₄×D₅	C₂×D₄	1	16	yes	complemented
119	C₂×C₃×#41	—	5	16	no	—
120	C₂×C₃×#41	—	10	16	no	—
121	C₂²×C₃×Q₈	C₂×D₅	1	2	yes	—
122	C₂²×C₃×D₄	—	5	4	no	—
123	C₂²×C₃×D₄	—	5	2	no	—
124	C₂²×C₃×D₄	—	5	4	no	—
125	C₂³×C₃×C₄	—	5	1	no	—
126	C₂³×C₃×C₄	—	5	4	no	—
127	C₂³×C₃×C₄	—	5	2	no	—
128	C₃×C₄⋊Q₈	C₂×D₅	1	8	yes	complemented
129	C₃×#127	—	5	8	no	—
130	C₃×#124	—	5	16	no	—
131	C₃×#121	—	5	32	no	—
132	C₃×C₄×D₄	—	5	32	no	—
133	C₂×C₃×C₄⋊C₄	C₂×D₅	1	4	yes	—
134	C₂×C₃×C₂²⋊C₄	—	5	8	no	—
135	C₂×C₃×C₄²	—	5	2	no	—
136	C₂×C₃×C₄²	—	5	1	no	—
137	C₂×C₃×C₄²	—	5	8	no	—
138	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
139	C₂³×D₅	C₂³×C₃	1	4	yes	—
140	C₂³×D₅	C₂³×C₃	1	1	yes	characteristic
141	C₂×C₅×Q₈	—	2	8	no	—
142	C₂×C₅×Q₈	C₂³×C₃	1	8	yes	—
143	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
144	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
145	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
146	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
147	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
148	#713	—	2	64	no	—
149	C₂×D₂₀	—	2	16	no	—
150	C₂×D₂₀	—	2	8	no	—
151	C₂×D₂₀	—	2	16	no	—
152	C₂×D₂₀	C₂³×C₃	1	8	yes	—
153	C₂×D₂₀	C₂³×C₃	1	16	yes	—
154	C₂×D₂₀	C₂³×C₃	1	16	yes	—
155	C₂×C₄×D₅	—	2	8	no	—
156	C₂×C₄×D₅	—	2	16	no	—
157	C₂×C₄×D₅	C₃×D₄	1	8	yes	complemented
158	C₂×C₄×D₅	C₂³×C₃	1	16	yes	—
159	C₂×C₄×D₅	C₂³×C₃	1	8	yes	—
160	C₂×C₄×D₅	C₂³×C₃	1	4	yes	—
161	C₅×C₄⋊C₄	C₂³×C₃	1	16	yes	—
162	C₄²×C₅	C₂³×C₃	1	4	yes	—
163	#685	C₂³×C₃	1	32	yes	—
164	C₄×Dic₅	C₂³×C₃	1	8	yes	—
165	C₄×Dic₅	C₂³×C₃	1	4	yes	—
166	C₂²×#41	—	5	2	no	—
167	#532	—	5	16	no	—
168	C₂×C₄⋊Q₈	C₃×D₅	1	1	yes	characteristic, complemented
169	C₂×#127	—	5	1	no	—
170	C₂×#124	—	5	2	no	—
171	C₂×#121	—	5	4	no	—
172	C₂×C₄×D₄	—	5	4	no	—
173	C₂²×C₄²	—	5	1	no	—
174	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
175	C₂²×C₃×C₅	C₂×#41	1	4	yes	—
176	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
177	C₂×C₃×D₅	—	2	8	no	—
178	C₂×C₃×D₅	—	2	4	no	—
179	C₂×C₃×D₅	—	2	8	no	—
180	C₂×C₃×D₅	—	2	16	no	—
181	C₂×C₃×D₅	—	4	16	no	—
182	C₂×C₃×D₅	C₂²×D₄	1	4	yes	—
183	C₃×C₄×C₅	—	2	8	no	—
184	C₃×C₄×C₅	C₂²×D₄	1	4	yes	—
185	C₃×C₄×C₅	C₂×#41	1	8	yes	complemented
186	C₃×Dic₅	—	2	4	no	—
187	C₃×Dic₅	C₂²×D₄	1	4	yes	—
188	C₂⁴×C₃	—	5	1	no	—
189	C₂⁴×C₃	—	5	4	no	—
190	C₃×#41	—	10	64	no	—
191	C₂×C₃×Q₈	—	2	8	no	—
192	C₂×C₃×Q₈	C₂²×D₅	1	8	yes	—
193	C₂×C₃×D₄	—	5	16	no	—
194	C₂×C₃×D₄	—	5	16	no	—
195	C₂×C₃×D₄	—	5	8	no	—
196	C₂×C₃×D₄	—	10	16	no	—
197	C₂×C₃×D₄	—	10	8	no	—
198	C₂×C₃×D₄	—	10	16	no	—
199	C₂²×C₃×C₄	—	5	1	no	—
200	C₂²×C₃×C₄	—	5	8	no	—
201	C₂²×C₃×C₄	—	5	4	no	—
202	C₂²×C₃×C₄	—	5	2	no	—
203	C₂²×C₃×C₄	—	5	8	no	—
204	C₂²×C₃×C₄	—	5	16	no	—
205	C₂²×C₃×C₄	—	10	16	no	—
206	C₂²×C₃×C₄	—	10	8	no	—
207	C₂²×C₃×C₄	C₂²×D₅	1	4	yes	—
208	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
209	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
210	C₃×C₄⋊C₄	C₂²×D₅	1	16	yes	—
211	C₃×C₂²⋊C₄	—	5	32	no	—
212	C₃×C₄²	—	5	8	no	—
213	C₃×C₄²	—	5	4	no	—
214	C₃×C₄²	C₂²×D₅	1	4	yes	—
215	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
216	C₂²×D₅	—	2	4	no	—
217	C₂²×D₅	—	2	8	no	—
218	C₂²×D₅	—	2	16	no	—
219	C₂²×D₅	C₂×C₃×D₄	1	4	yes	—
220	C₂²×D₅	C₂⁴×C₃	1	8	yes	—
221	C₂²×D₅	C₂⁴×C₃	1	2	yes	—
222	C₅×Q₈	—	2	16	no	—
223	C₂×C₄×C₅	—	2	8	no	—
224	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
225	C₂×C₄×C₅	C₃×#41	1	8	yes	complemented
226	C₂×C₄×C₅	C₂⁴×C₃	1	8	yes	—
227	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
228	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
229	C₂×Dic₅	—	2	4	no	—
230	C₂×Dic₅	C₂×C₃×D₄	1	4	yes	—
231	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
232	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
233	D₂₀	—	2	32	no	—
234	D₂₀	—	2	16	no	—
235	D₂₀	—	2	32	no	—
236	C₄×D₅	—	2	16	no	—
237	C₄×D₅	—	2	32	no	—
238	C₄×D₅	C₂×C₃×D₄	1	16	yes	complemented
239	C₂×#41	—	5	16	no	—
240	C₂×#41	—	10	16	no	—
241	C₂²×Q₈	C₂×C₃×D₅	1	2	yes	—
242	C₂²×D₄	—	5	4	no	—
243	C₂²×D₄	—	5	4	no	—
244	C₂²×D₄	—	5	2	no	—
245	C₂³×C₄	—	5	1	no	—
246	C₂³×C₄	—	5	4	no	—
247	C₂³×C₄	—	5	2	no	—
248	C₄⋊Q₈	C₂×C₃×D₅	1	8	yes	complemented
249	#127	—	5	8	no	—
250	#124	—	5	16	no	—
251	#121	—	5	32	no	—
252	C₄×D₄	—	5	32	no	—
253	C₂×C₄⋊C₄	C₂×C₃×D₅	1	4	yes	—
254	C₂×C₂²⋊C₄	—	5	8	no	—
255	C₂×C₄²	—	5	2	no	—
256	C₂×C₄²	—	5	1	no	—
257	C₂×C₄²	—	5	8	no	—
258	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
259	C₂×C₃×C₅	#532	1	4	yes	complemented
260	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
261	C₂×C₃×C₅	C₂²×#41	1	2	yes	—
262	C₃×D₅	—	2	4	no	—
263	C₃×D₅	—	4	8	no	—
264	C₂³×C₃	—	5	4	no	—
265	C₂³×C₃	—	5	2	no	—
266	C₂³×C₃	—	5	8	no	—
267	C₂³×C₃	—	10	4	no	—
268	C₂³×C₃	—	10	8	no	—
269	C₂³×C₃	—	10	16	no	—
270	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
271	C₃×Q₈	—	2	16	no	—
272	C₃×D₄	—	10	32	no	—
273	C₃×D₄	—	10	16	no	—
274	C₃×D₄	—	10	32	no	—
275	C₂×C₃×C₄	—	2	8	no	—
276	C₂×C₃×C₄	—	5	4	no	—
277	C₂×C₃×C₄	—	5	2	no	—
278	C₂×C₃×C₄	—	5	16	no	—
279	C₂×C₃×C₄	—	5	4	no	—
280	C₂×C₃×C₄	—	10	32	no	—
281	C₂×C₃×C₄	—	10	4	no	—
282	C₂×C₃×C₄	—	10	16	no	—
283	C₂×C₃×C₄	D₄×D₅	1	4	yes	—
284	C₂×C₃×C₄	#713	1	8	yes	complemented
285	C₂×C₃×C₄	C₂³×D₅	1	8	yes	—
286	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
287	C₂×C₃×C₄	C₂³×D₅	1	4	yes	—
288	C₂²×C₅	C₂²×C₃×D₄	1	2	yes	—
289	C₂²×C₅	C₂×C₃×#41	1	4	yes	—
290	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
291	C₂×D₅	—	2	4	no	—
292	C₂×D₅	—	2	8	no	—
293	C₂×D₅	—	2	8	no	—
294	C₂×D₅	—	2	16	no	—
295	C₂×D₅	—	4	16	no	—
296	C₂×D₅	C₂²×C₃×D₄	1	4	yes	—
297	C₄×C₅	—	2	8	no	—
298	C₄×C₅	C₂²×C₃×D₄	1	4	yes	—
299	C₄×C₅	C₂×C₃×#41	1	8	yes	complemented
300	Dic₅	—	2	4	no	—
301	Dic₅	C₂²×C₃×D₄	1	4	yes	—
302	C₂⁴	—	5	1	no	—
303	C₂⁴	—	5	4	no	—
304	#41	—	10	64	no	—
305	C₂×Q₈	—	2	8	no	—
306	C₂×Q₈	C₂²×C₃×D₅	1	8	yes	—
307	C₂×D₄	—	5	16	no	—
308	C₂×D₄	—	5	16	no	—
309	C₂×D₄	—	5	8	no	—
310	C₂×D₄	—	10	16	no	—
311	C₂×D₄	—	10	8	no	—
312	C₂×D₄	—	10	16	no	—
313	C₂²×C₄	—	5	1	no	—
314	C₂²×C₄	—	5	8	no	—
315	C₂²×C₄	—	5	4	no	—
316	C₂²×C₄	—	5	2	no	—
317	C₂²×C₄	—	5	8	no	—
318	C₂²×C₄	—	5	16	no	—
319	C₂²×C₄	—	10	16	no	—
320	C₂²×C₄	—	10	8	no	—
321	C₂²×C₄	C₂²×C₃×D₅	1	4	yes	—
322	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
323	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
324	C₄⋊C₄	C₂²×C₃×D₅	1	16	yes	—
325	C₂²⋊C₄	—	5	32	no	—
326	C₄²	—	5	8	no	—
327	C₄²	—	5	4	no	—
328	C₄²	C₂²×C₃×D₅	1	4	yes	—
329	C₃×C₅	C₂×#532	1	1	yes	characteristic, complemented, Hall
330	C₂²×C₃	—	5	4	no	—
331	C₂²×C₃	—	10	8	no	—
332	C₂²×C₃	—	10	4	no	—
333	C₂²×C₃	—	10	8	no	—
334	C₂²×C₃	—	10	16	no	—
335	C₂²×C₃	—	20	16	no	—
336	C₂²×C₃	C₂×D₄×D₅	1	2	yes	—
337	C₂²×C₃	C₂×#713	1	4	yes	—
338	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
339	C₃×C₄	—	2	8	no	—
340	C₃×C₄	—	5	4	no	—
341	C₃×C₄	—	10	4	no	—
342	C₃×C₄	C₂×D₄×D₅	1	4	yes	—
343	C₃×C₄	C₂×#713	1	8	yes	complemented
344	C₂×C₅	C₃×#532	1	4	yes	complemented
345	C₂×C₅	C₂³×C₃×D₄	1	1	yes	characteristic
346	C₂×C₅	C₂²×C₃×#41	1	2	yes	—
347	D₅	—	2	4	no	—
348	D₅	—	4	8	no	—
349	C₂³	—	5	4	no	—
350	C₂³	—	5	2	no	—
351	C₂³	—	5	8	no	—
352	C₂³	—	10	4	no	—
353	C₂³	—	10	8	no	—
354	C₂³	—	10	16	no	—
355	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
356	Q₈	—	2	16	no	—
357	D₄	—	10	32	no	—
358	D₄	—	10	16	no	—
359	D₄	—	10	32	no	—
360	C₂×C₄	—	2	8	no	—
361	C₂×C₄	—	5	4	no	—
362	C₂×C₄	—	5	2	no	—
363	C₂×C₄	—	5	16	no	—
364	C₂×C₄	—	5	4	no	—
365	C₂×C₄	—	10	32	no	—
366	C₂×C₄	—	10	4	no	—
367	C₂×C₄	—	10	16	no	—
368	C₂×C₄	C₃×D₄×D₅	1	4	yes	—
369	C₂×C₄	C₃×#713	1	8	yes	complemented
370	C₂×C₄	C₂³×C₃×D₅	1	8	yes	—
371	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
372	C₂×C₄	C₂³×C₃×D₅	1	4	yes	—
373	C₂×C₃	—	10	4	no	—
374	C₂×C₃	—	20	8	no	—
375	C₂×C₃	#66059	1	4	yes	direct product factor
376	C₂×C₃	C₂²×D₄×D₅	1	1	yes	characteristic
377	C₂×C₃	C₂²×#713	1	2	yes	—
378	C₅	C₂×C₃×#532	1	1	yes	characteristic, complemented, Sylow
379	C₂²	—	5	4	no	—
380	C₂²	—	10	4	no	—
381	C₂²	—	10	8	no	—
382	C₂²	—	10	8	no	—
383	C₂²	—	10	16	no	—
384	C₂²	—	20	16	no	—
385	C₂²	C₂×C₃×D₄×D₅	1	2	yes	—
386	C₂²	C₂×C₃×#713	1	4	yes	—
387	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
388	C₄	—	2	8	no	—
389	C₄	—	5	4	no	—
390	C₄	—	10	4	no	—
391	C₄	C₂×C₃×D₄×D₅	1	4	yes	—
392	C₄	C₂×C₃×#713	1	8	yes	complemented
393	C₃	C₂×#66059	1	1	yes	characteristic, direct product factor, Sylow
394	C₂	—	10	4	no	—
395	C₂	—	20	8	no	—
396	C₂	C₃×#66059	1	4	yes	direct product factor
397	C₂	C₂²×C₃×D₄×D₅	1	1	yes	characteristic
398	C₂	C₂²×C₃×#713	1	2	yes	—

	subgroup	G/H
center	C₂³×C₃	C₂³×D₅
commutator, cosocle	C₂²×C₅	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₅
Fitting	C₂×C₃×C₅×C₄⋊Q₈	C₂
socle	C₂³×C₃×C₅	C₂⁴
hypercenter	C₂×C₃×C₄⋊Q₈	D₅
hypocenter	C₅	C₂×C₃×#532
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×#713	C₂	semidirect
2. C₂×C₃×C₅×C₄⋊Q₈	C₂	semidirect
3. C₂×C₃×#4093	C₂	semidirect
4. C₃×#66059	C₂	direct (N × H)
5. C₂×C₃×#4041	C₂	semidirect
6. C₂×C₃×#4039	C₂	semidirect
7. C₂×C₃×#4020	C₂	semidirect
8. C₂×C₃×C₄²×D₅	C₂	semidirect
9. C₂×#66059	C₃	direct (N × H)
12. C₂×C₃×#713	C₂²	semidirect
19. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
22. C₃×#4093	C₂²	semidirect
26. C₃×#4041	C₂²	semidirect
27. C₃×#4039	C₂²	semidirect
28. C₃×#4020	C₂²	semidirect
29. C₃×C₄²×D₅	C₂²	semidirect
31. C₂²×#713	C₂×C₃	semidirect
32. C₂×C₅×C₄⋊Q₈	C₂×C₃	semidirect
33. C₂×#4093	C₂×C₃	semidirect
34. #66059	C₂×C₃	direct (N × H)
35. C₂×#4041	C₂×C₃	semidirect
36. C₂×#4039	C₂×C₃	semidirect
37. C₂×#4020	C₂×C₃	semidirect
38. C₂×C₄²×D₅	C₂×C₃	semidirect
57. C₂×C₃×C₄×D₅	D₄	semidirect
68. C₂×C₃×C₄⋊Q₈	D₅	semidirect
76. C₂×#713	C₂²×C₃	semidirect
83. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
86. #4093	C₂²×C₃	semidirect
90. #4041	C₂²×C₃	semidirect
91. #4039	C₂²×C₃	semidirect
92. #4020	C₂²×C₃	semidirect
93. C₄²×D₅	C₂²×C₃	semidirect
105. C₂×C₃×C₄×C₅	#41	semidirect
118. C₃×C₄×D₅	C₂×D₄	semidirect
128. C₃×C₄⋊Q₈	C₂×D₅	semidirect
157. C₂×C₄×D₅	C₃×D₄	semidirect
168. C₂×C₄⋊Q₈	C₃×D₅	semidirect
185. C₃×C₄×C₅	C₂×#41	semidirect
225. C₂×C₄×C₅	C₃×#41	semidirect
238. C₄×D₅	C₂×C₃×D₄	semidirect
248. C₄⋊Q₈	C₂×C₃×D₅	semidirect
259. C₂×C₃×C₅	#532	semidirect
284. C₂×C₃×C₄	#713	semidirect
299. C₄×C₅	C₂×C₃×#41	semidirect
329. C₃×C₅	C₂×#532	semidirect
343. C₃×C₄	C₂×#713	semidirect
344. C₂×C₅	C₃×#532	semidirect
369. C₂×C₄	C₃×#713	semidirect
375. C₂×C₃	#66059	direct (N × H)
378. C₅	C₂×C₃×#532	semidirect
392. C₄	C₂×C₃×#713	semidirect
393. C₃	C₂×#66059	direct (N × H)
396. C₂	C₃×#66059	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×#713	2
C₂×C₃×C₅×C₄⋊Q₈	2
C₂×C₃×#4093	2
C₃×#66059	2
C₂×C₃×#4041	2
C₂×C₃×#4039	2
C₂×C₃×#4020	2
C₂×C₃×C₄²×D₅	2
C₂×#66059	3
C₂×C₃×#532	5

Subgroups — C2×C3×#66059 #14480031

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#66059 #14480031