Subgroups — C₂×C₃×#65364 #14426008

Order 1920.

1168 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#127	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×#687	C₂	1	2	yes	maximal, complemented
3	C₂×C₃×C₄×Dic₁₀	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#3964	C₂	1	2	yes	maximal, complemented
5	C₃×#65364	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₃×C₄⋊#168	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#65364	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂²×C₃×C₅×D₄	—	2	1	no	—
9	C₂²×C₃×C₅×D₄	—	2	1	no	—
10	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
11	C₂²×C₃×Dic₁₀	C₂²	1	1	yes	characteristic
12	C₃×C₅×#127	—	2	2	no	—
13	C₃×C₅×#127	C₂²	1	4	yes	—
14	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
15	C₂×C₃×#687	—	2	8	no	—
16	C₂×C₃×#687	C₂²	1	8	yes	complemented
17	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
18	C₂×C₃×#683	—	2	1	no	—
19	C₂×C₃×C₄×Dic₅	—	2	1	no	—
20	C₂²×C₃×#168	C₂²	1	2	yes	—
21	C₃×C₄×Dic₁₀	—	2	2	no	—
22	C₃×C₄×Dic₁₀	C₂²	1	4	yes	complemented
23	C₃×#3964	C₂²	1	8	yes	complemented
24	C₃×C₄⋊#168	C₂²	1	4	yes	complemented
25	C₂×C₃×#460	—	5	1	no	maximal, Hall
26	C₂×C₅×#127	C₂×C₃	1	1	yes	characteristic
27	C₂²×#687	C₂×C₃	1	2	yes	complemented
28	C₂×C₄×Dic₁₀	C₂×C₃	1	1	yes	characteristic, complemented
29	C₂×#3964	C₂×C₃	1	2	yes	complemented
30	#65364	C₂×C₃	1	8	yes	direct product factor
31	C₂×C₄⋊#168	C₂×C₃	1	1	yes	characteristic, complemented
32	C₂⁴×C₃×C₅	—	2	2	no	—
33	C₂×C₃×C₅×D₄	—	2	4	no	—
34	C₂×C₃×C₅×D₄	—	2	4	no	—
35	C₂×C₃×C₅×D₄	—	2	4	no	—
36	C₂×C₃×C₅×D₄	—	2	2	no	—
37	C₂×C₃×C₅×D₄	—	2	4	no	—
38	C₂×C₃×C₅×D₄	—	4	4	no	—
39	C₂×C₃×C₅×D₄	—	4	4	no	—
40	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
41	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
42	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
43	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
44	C₂²×C₃×Dic₅	—	2	1	no	—
45	C₂²×C₃×Dic₅	—	2	1	no	—
46	C₂×C₃×Dic₁₀	—	2	1	no	—
47	C₂×C₃×Dic₁₀	—	2	2	no	—
48	C₂×C₃×Dic₁₀	D₄	1	4	yes	complemented
49	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
50	C₃×C₄²×C₅	D₄	1	2	yes	—
51	C₃×C₄²×C₅	C₂³	1	2	yes	—
52	C₃×#687	—	2	16	no	—
53	C₃×C₄⋊Dic₅	—	2	1	no	—
54	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
55	C₃×#683	—	2	4	no	—
56	C₃×C₄×Dic₅	—	2	4	no	—
57	C₂×C₃×#168	—	2	4	no	—
58	C₂×C₃×#168	C₂³	1	4	yes	—
59	C₂²×C₃×SD₁₆	—	5	2	no	—
60	C₂×C₃×#127	D₅	1	1	yes	characteristic
61	C₂×C₃×C₄×Q₈	—	5	1	no	—
62	C₃×#460	—	5	8	no	—
63	C₂×C₃×C₄⋊C₈	—	5	1	no	—
64	C₂×C₃×#102	—	5	2	no	—
65	C₂²×C₅×D₄	—	2	1	no	—
66	C₂²×C₅×D₄	—	2	1	no	—
67	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
68	C₂²×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
69	C₅×#127	—	2	2	no	—
70	C₅×#127	C₂²×C₃	1	4	yes	—
71	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
72	C₂×#687	—	2	8	no	—
73	C₂×#687	C₂²×C₃	1	8	yes	complemented
74	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
75	C₂×#683	—	2	1	no	—
76	C₂×C₄×Dic₅	—	2	1	no	—
77	C₂²×#168	C₂²×C₃	1	2	yes	—
78	C₄×Dic₁₀	—	2	2	no	—
79	C₄×Dic₁₀	C₂²×C₃	1	4	yes	complemented
80	#3964	C₂²×C₃	1	8	yes	complemented
81	C₄⋊#168	C₂²×C₃	1	4	yes	complemented
82	C₂×#460	—	5	1	no	Sylow
83	C₂³×C₃×C₅	—	2	4	no	—
84	C₂³×C₃×C₅	—	4	4	no	—
85	C₂³×C₃×C₅	—	4	4	no	—
86	C₂³×C₃×C₅	—	4	4	no	—
87	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
88	C₃×C₅×D₄	—	2	4	no	—
89	C₃×C₅×D₄	—	2	4	no	—
90	C₃×C₅×D₄	—	4	8	no	—
91	C₃×C₅×D₄	—	4	4	no	—
92	C₃×C₅×D₄	—	4	8	no	—
93	C₂×C₃×C₄×C₅	—	2	2	no	—
94	C₂×C₃×C₄×C₅	SD₁₆	1	4	yes	complemented
95	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
96	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
97	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
98	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
99	C₂×C₃×C₄×C₅	#41	1	2	yes	—
100	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
101	C₂×C₃×Dic₅	—	2	4	no	—
102	C₂×C₃×Dic₅	—	2	2	no	—
103	C₂×C₃×Dic₅	—	2	2	no	—
104	C₂×C₃×Dic₅	—	4	2	no	—
105	C₃×Dic₁₀	—	2	4	no	—
106	C₃×Dic₁₀	—	2	2	no	—
107	C₃×Dic₁₀	C₂×D₄	1	4	yes	complemented
108	C₃×#168	—	2	4	no	—
109	C₂²×C₃×Q₈	—	5	1	no	—
110	C₂²×C₃×D₄	—	2	1	no	—
111	C₂²×C₃×D₄	—	2	1	no	—
112	C₂²×C₃×D₄	C₂×D₅	1	2	yes	—
113	C₂×C₃×SD₁₆	—	5	8	no	—
114	C₂×C₃×SD₁₆	—	10	8	no	—
115	C₂²×C₃×C₈	—	5	2	no	—
116	C₃×#127	—	2	2	no	—
117	C₃×#127	C₂×D₅	1	4	yes	—
118	C₃×C₄×Q₈	—	5	4	no	—
119	C₃×C₄×Q₈	—	10	2	no	—
120	C₂×C₃×C₄⋊C₄	—	5	1	no	—
121	C₂×C₃×C₄⋊C₄	—	10	1	no	—
122	C₂×C₃×C₄²	—	10	1	no	—
123	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
124	C₃×C₄⋊C₈	—	5	4	no	—
125	C₃×#102	—	5	8	no	—
126	C₂⁴×C₅	—	2	2	no	—
127	C₂×C₅×D₄	—	2	4	no	—
128	C₂×C₅×D₄	—	2	2	no	—
129	C₂×C₅×D₄	—	2	4	no	—
130	C₂×C₅×D₄	—	2	4	no	—
131	C₂×C₅×D₄	—	2	4	no	—
132	C₂×C₅×D₄	—	4	4	no	—
133	C₂×C₅×D₄	—	4	4	no	—
134	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
135	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
138	C₂²×Dic₅	—	2	1	no	—
139	C₂²×Dic₅	—	2	1	no	—
140	C₂×Dic₁₀	—	2	1	no	—
141	C₂×Dic₁₀	—	2	2	no	—
142	C₂×Dic₁₀	C₃×D₄	1	4	yes	complemented
143	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
144	C₄²×C₅	C₃×D₄	1	2	yes	—
145	C₄²×C₅	C₂³×C₃	1	2	yes	—
146	#687	—	2	16	no	—
147	C₄⋊Dic₅	—	2	1	no	—
148	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
149	#683	—	2	4	no	—
150	C₄×Dic₅	—	2	4	no	—
151	C₂×#168	—	2	4	no	—
152	C₂×#168	C₂³×C₃	1	4	yes	—
153	C₂²×SD₁₆	—	5	2	no	—
154	C₂×#127	C₃×D₅	1	1	yes	characteristic
155	C₂×C₄×Q₈	—	5	1	no	—
156	#460	—	5	8	no	—
157	C₂×C₄⋊C₈	—	5	1	no	—
158	C₂×#102	—	5	2	no	—
159	C₂²×C₃×C₅	—	4	4	no	—
160	C₂²×C₃×C₅	—	4	4	no	—
161	C₂²×C₃×C₅	—	4	4	no	—
162	C₂²×C₃×C₅	—	8	8	no	—
163	C₂²×C₃×C₅	#121	1	2	yes	—
164	C₂²×C₃×C₅	C₂×SD₁₆	1	2	yes	—
165	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	2	yes	—
166	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
167	C₃×C₄×C₅	—	2	2	no	—
168	C₃×C₄×C₅	#121	1	2	yes	—
169	C₃×C₄×C₅	C₂×SD₁₆	1	4	yes	complemented
170	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
171	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
172	C₃×Dic₅	—	2	4	no	—
173	C₃×Dic₅	—	4	2	no	—
174	C₂⁴×C₃	—	2	2	no	—
175	C₂×C₃×Q₈	—	5	4	no	—
176	C₂×C₃×Q₈	—	5	2	no	—
177	C₂×C₃×Q₈	—	10	2	no	—
178	C₂×C₃×Q₈	—	10	1	no	—
179	C₂×C₃×D₄	—	2	4	no	—
180	C₂×C₃×D₄	—	2	4	no	—
181	C₂×C₃×D₄	—	2	2	no	—
182	C₂×C₃×D₄	—	2	4	no	—
183	C₂×C₃×D₄	—	2	4	no	—
184	C₂×C₃×D₄	—	4	4	no	—
185	C₂×C₃×D₄	—	4	4	no	—
186	C₂×C₃×D₄	C₂²×D₅	1	4	yes	—
187	C₂²×C₃×C₄	—	10	1	no	—
188	C₂²×C₃×C₄	—	10	1	no	—
189	C₂²×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
190	C₂²×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
191	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
192	C₃×SD₁₆	—	10	16	no	—
193	C₂×C₃×C₈	—	5	4	no	—
194	C₂×C₃×C₈	—	10	4	no	—
195	C₃×C₄⋊C₄	—	5	2	no	—
196	C₃×C₄⋊C₄	—	10	4	no	—
197	C₃×C₄⋊C₄	—	10	1	no	—
198	C₃×C₄²	—	10	4	no	—
199	C₃×C₄²	C₂²⋊D₅	1	2	yes	—
200	C₃×C₄²	C₂²×D₅	1	2	yes	—
201	C₂³×C₅	—	2	4	no	—
202	C₂³×C₅	—	4	4	no	—
203	C₂³×C₅	—	4	4	no	—
204	C₂³×C₅	—	4	4	no	—
205	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
206	C₅×D₄	—	2	4	no	—
207	C₅×D₄	—	2	4	no	—
208	C₅×D₄	—	4	8	no	—
209	C₅×D₄	—	4	4	no	—
210	C₅×D₄	—	4	8	no	—
211	C₂×C₄×C₅	—	2	2	no	—
212	C₂×C₄×C₅	C₃×SD₁₆	1	4	yes	complemented
213	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
214	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
215	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
216	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
217	C₂×C₄×C₅	C₃×#41	1	2	yes	—
218	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
219	C₂×Dic₅	—	2	4	no	—
220	C₂×Dic₅	—	2	2	no	—
221	C₂×Dic₅	—	2	2	no	—
222	C₂×Dic₅	—	4	2	no	—
223	Dic₁₀	—	2	4	no	—
224	Dic₁₀	—	2	2	no	—
225	Dic₁₀	C₂×C₃×D₄	1	4	yes	complemented
226	#168	—	2	4	no	—
227	C₂²×Q₈	—	5	1	no	—
228	C₂²×D₄	—	2	1	no	—
229	C₂²×D₄	—	2	1	no	—
230	C₂²×D₄	C₂×C₃×D₅	1	2	yes	—
231	C₂×SD₁₆	—	5	8	no	—
232	C₂×SD₁₆	—	10	8	no	—
233	C₂²×C₈	—	5	2	no	—
234	#127	—	2	2	no	—
235	#127	C₂×C₃×D₅	1	4	yes	—
236	C₄×Q₈	—	5	4	no	—
237	C₄×Q₈	—	10	2	no	—
238	C₂×C₄⋊C₄	—	5	1	no	—
239	C₂×C₄⋊C₄	—	10	1	no	—
240	C₂×C₄²	—	10	1	no	—
241	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
242	C₄⋊C₈	—	5	4	no	—
243	#102	—	5	8	no	—
244	C₂×C₃×C₅	—	8	4	no	—
245	C₂×C₃×C₅	#460	1	4	yes	complemented
246	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
247	C₂×C₃×C₅	C₂²×SD₁₆	1	1	yes	characteristic
248	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
249	C₂³×C₃	—	2	4	no	—
250	C₂³×C₃	—	4	4	no	—
251	C₂³×C₃	—	4	4	no	—
252	C₂³×C₃	—	4	4	no	—
253	C₂³×C₃	C₂×C₂²⋊D₅	1	1	yes	characteristic
254	C₃×Q₈	—	5	4	no	—
255	C₃×Q₈	—	10	2	no	—
256	C₃×Q₈	—	10	4	no	—
257	C₃×D₄	—	2	4	no	—
258	C₃×D₄	—	2	4	no	—
259	C₃×D₄	—	4	8	no	—
260	C₃×D₄	—	4	8	no	—
261	C₃×D₄	—	4	4	no	—
262	C₂×C₃×C₄	—	2	2	no	—
263	C₂×C₃×C₄	—	10	2	no	—
264	C₂×C₃×C₄	—	10	4	no	—
265	C₂×C₃×C₄	—	10	2	no	—
266	C₂×C₃×C₄	—	20	2	no	—
267	C₂×C₃×C₄	#687	1	4	yes	complemented
268	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
269	C₂×C₃×C₄	#711	1	2	yes	—
270	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
271	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
272	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
273	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
274	C₃×C₈	—	10	4	no	—
275	C₂²×C₅	—	4	4	no	—
276	C₂²×C₅	—	4	4	no	—
277	C₂²×C₅	—	4	4	no	—
278	C₂²×C₅	—	8	8	no	—
279	C₂²×C₅	C₃×#121	1	2	yes	—
280	C₂²×C₅	C₂×C₃×SD₁₆	1	2	yes	—
281	C₂²×C₅	C₃×AGL(1,ℤ/8)	1	2	yes	—
282	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
283	C₄×C₅	—	2	2	no	—
284	C₄×C₅	C₃×#121	1	2	yes	—
285	C₄×C₅	C₂×C₃×SD₁₆	1	4	yes	complemented
286	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
287	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
288	Dic₅	—	2	4	no	—
289	Dic₅	—	4	2	no	—
290	C₂⁴	—	2	2	no	—
291	C₂×Q₈	—	5	4	no	—
292	C₂×Q₈	—	5	2	no	—
293	C₂×Q₈	—	10	2	no	—
294	C₂×Q₈	—	10	1	no	—
295	C₂×D₄	—	2	4	no	—
296	C₂×D₄	—	2	4	no	—
297	C₂×D₄	—	2	2	no	—
298	C₂×D₄	—	2	4	no	—
299	C₂×D₄	—	2	4	no	—
300	C₂×D₄	—	4	4	no	—
301	C₂×D₄	—	4	4	no	—
302	C₂×D₄	C₂²×C₃×D₅	1	4	yes	—
303	C₂²×C₄	—	10	1	no	—
304	C₂²×C₄	—	10	1	no	—
305	C₂²×C₄	C₃×C₂²⋊D₅	1	1	yes	characteristic
306	C₂²×C₄	C₃×C₂²⋊D₅	1	1	yes	characteristic
307	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
308	SD₁₆	—	10	16	no	—
309	C₂×C₈	—	5	4	no	—
310	C₂×C₈	—	10	4	no	—
311	C₄⋊C₄	—	5	2	no	—
312	C₄⋊C₄	—	10	1	no	—
313	C₄⋊C₄	—	10	4	no	—
314	C₄²	—	10	4	no	—
315	C₄²	C₃×C₂²⋊D₅	1	2	yes	—
316	C₄²	C₂²×C₃×D₅	1	2	yes	—
317	C₃×C₅	C₂×#460	1	1	yes	characteristic, complemented, Hall
318	C₂²×C₃	—	4	4	no	—
319	C₂²×C₃	—	4	4	no	—
320	C₂²×C₃	—	4	4	no	—
321	C₂²×C₃	—	8	8	no	—
322	C₂²×C₃	#4078	1	2	yes	—
323	C₂²×C₃	C₂×#687	1	2	yes	—
324	C₂²×C₃	#4084	1	2	yes	—
325	C₂²×C₃	C₂²×C₂²⋊D₅	1	1	yes	characteristic
326	C₃×C₄	—	2	2	no	—
327	C₃×C₄	—	10	4	no	—
328	C₃×C₄	—	20	2	no	—
329	C₃×C₄	C₂×#687	1	4	yes	complemented
330	C₃×C₄	#4084	1	2	yes	—
331	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
332	C₃×C₄	C₂×#711	1	1	yes	characteristic
333	C₂×C₅	—	8	4	no	—
334	C₂×C₅	C₃×#460	1	4	yes	complemented
335	C₂×C₅	C₂×C₃×#121	1	1	yes	characteristic
336	C₂×C₅	C₂²×C₃×SD₁₆	1	1	yes	characteristic
337	C₂×C₅	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
338	C₂³	—	2	4	no	—
339	C₂³	—	4	4	no	—
340	C₂³	—	4	4	no	—
341	C₂³	—	4	4	no	—
342	C₂³	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
343	Q₈	—	5	4	no	—
344	Q₈	—	10	4	no	—
345	Q₈	—	10	2	no	—
346	D₄	—	2	4	no	—
347	D₄	—	2	4	no	—
348	D₄	—	4	8	no	—
349	D₄	—	4	8	no	—
350	D₄	—	4	4	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	10	4	no	—
353	C₂×C₄	—	10	2	no	—
354	C₂×C₄	—	10	2	no	—
355	C₂×C₄	—	20	2	no	—
356	C₂×C₄	C₃×#687	1	4	yes	complemented
357	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
358	C₂×C₄	C₃×#711	1	2	yes	—
359	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
360	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
361	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
362	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
363	C₈	—	10	4	no	—
364	C₂×C₃	—	8	4	no	—
365	C₂×C₃	#65364	1	4	yes	direct product factor
366	C₂×C₃	C₂×#4078	1	1	yes	characteristic
367	C₂×C₃	C₂²×#687	1	1	yes	characteristic
368	C₂×C₃	C₂×#4084	1	1	yes	characteristic
369	C₅	C₂×C₃×#460	1	1	yes	characteristic, complemented, Sylow
370	C₂²	—	4	4	no	—
371	C₂²	—	4	4	no	—
372	C₂²	—	4	4	no	—
373	C₂²	—	8	8	no	—
374	C₂²	C₃×#4078	1	2	yes	—
375	C₂²	C₂×C₃×#687	1	2	yes	—
376	C₂²	C₃×#4084	1	2	yes	—
377	C₂²	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
378	C₄	—	2	2	no	—
379	C₄	—	10	4	no	—
380	C₄	—	20	2	no	—
381	C₄	C₂×C₃×#687	1	4	yes	complemented
382	C₄	C₃×#4084	1	2	yes	—
383	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
384	C₄	C₂×C₃×#711	1	1	yes	characteristic
385	C₃	C₂×#65364	1	1	yes	characteristic, direct product factor, Sylow
386	C₂	—	8	4	no	—
387	C₂	C₃×#65364	1	4	yes	direct product factor
388	C₂	C₂×C₃×#4078	1	1	yes	characteristic
389	C₂	C₂²×C₃×#687	1	1	yes	characteristic
390	C₂	C₂×C₃×#4084	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	C₂×C₂²⋊D₅
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting, prime radical	C₂×C₃×C₅×#127	C₂
socle	C₂³×C₃×C₅	C₂×D₄
hypercenter	C₂×C₃×#127	D₅
hypocenter	C₅	C₂×C₃×#460
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×C₄² ◁ C₂×C₃×#127

Complements

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

N	H ≅ G/N	type
2. C₂²×C₃×#687	C₂	semidirect
3. C₂×C₃×C₄×Dic₁₀	C₂	semidirect
4. C₂×C₃×#3964	C₂	semidirect
5. C₃×#65364	C₂	direct (N × H)
6. C₂×C₃×C₄⋊#168	C₂	semidirect
7. C₂×#65364	C₃	direct (N × H)
16. C₂×C₃×#687	C₂²	semidirect
22. C₃×C₄×Dic₁₀	C₂²	semidirect
23. C₃×#3964	C₂²	semidirect
24. C₃×C₄⋊#168	C₂²	semidirect
27. C₂²×#687	C₂×C₃	semidirect
28. C₂×C₄×Dic₁₀	C₂×C₃	semidirect
29. C₂×#3964	C₂×C₃	semidirect
30. #65364	C₂×C₃	direct (N × H)
31. C₂×C₄⋊#168	C₂×C₃	semidirect
48. C₂×C₃×Dic₁₀	D₄	semidirect
73. C₂×#687	C₂²×C₃	semidirect
79. C₄×Dic₁₀	C₂²×C₃	semidirect
80. #3964	C₂²×C₃	semidirect
81. C₄⋊#168	C₂²×C₃	semidirect
94. C₂×C₃×C₄×C₅	SD₁₆	semidirect
107. C₃×Dic₁₀	C₂×D₄	semidirect
142. C₂×Dic₁₀	C₃×D₄	semidirect
169. C₃×C₄×C₅	C₂×SD₁₆	semidirect
212. C₂×C₄×C₅	C₃×SD₁₆	semidirect
225. Dic₁₀	C₂×C₃×D₄	semidirect
245. C₂×C₃×C₅	#460	semidirect
267. C₂×C₃×C₄	#687	semidirect
285. C₄×C₅	C₂×C₃×SD₁₆	semidirect
317. C₃×C₅	C₂×#460	semidirect
329. C₃×C₄	C₂×#687	semidirect
334. C₂×C₅	C₃×#460	semidirect
356. C₂×C₄	C₃×#687	semidirect
365. C₂×C₃	#65364	direct (N × H)
369. C₅	C₂×C₃×#460	semidirect
381. C₄	C₂×C₃×#687	semidirect
385. C₃	C₂×#65364	direct (N × H)
387. C₂	C₃×#65364	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅×#127	2
C₂²×C₃×#687	2
C₂×C₃×C₄×Dic₁₀	2
C₂×C₃×#3964	2
C₃×#65364	2
C₂×C₃×C₄⋊#168	2
C₂×#65364	3
C₂×C₃×#460	5

Subgroups — C2×C3×#65364 #14426008

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#65364 #14426008