Subgroups — C₂×C₄×#6717 #14416054

Order 1920.

1104 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×C₅×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#6717	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×D₆₀	C₂	1	1	yes	maximal, characteristic
4	C₂×#91119	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×#6717	C₂	1	8	yes	maximal, direct product factor
6	C₂×#91093	C₂	1	1	yes	maximal, characteristic
7	C₂×#91092	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×C₃⋊#168	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₄×#688	—	3	1	no	maximal, Hall
10	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
11	C₂²×D₆₀	C₂²	1	1	yes	characteristic
12	C₂²×C₄×D₁₅	—	2	1	no	—
13	C₃×C₄×C₅×Q₈	—	2	2	no	—
14	C₃×C₄×C₅×Q₈	C₂²	1	4	yes	complemented
15	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
16	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₄²×C₅	—	2	1	no	—
18	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
19	C₂×#6717	C₄	1	8	yes	direct product factor
20	C₂×#6717	C₂²	1	4	yes	—
21	C₂×#6714	—	2	1	no	—
22	C₂×C₄⋊Dic₁₅	C₂²	1	1	yes	characteristic
23	C₂²×C₃⋊#168	C₂²	1	1	yes	characteristic
24	C₂²×C₃⋊#168	C₂²	1	1	yes	characteristic
25	C₄×D₆₀	—	2	2	no	—
26	C₄×D₆₀	C₂²	1	4	yes	—
27	#91119	C₂²	1	4	yes	complemented
28	#91093	C₂²	1	4	yes	—
29	#91092	C₂²	1	4	yes	complemented
30	C₄×C₃⋊#168	C₂²	1	4	yes	complemented
31	C₂×C₄×#215	—	5	1	no	maximal, Hall
32	C₂×C₄×C₅×Q₈	D₃	1	1	yes	characteristic, complemented
33	C₂²×#688	—	3	1	no	—
34	C₂×C₄×D₂₀	—	3	1	no	—
35	C₂×#3967	—	3	1	no	—
36	C₄×#688	—	3	8	no	—
37	C₂×#3941	—	3	1	no	—
38	C₂×#3940	—	3	1	no	—
39	C₂×C₄×#168	—	3	1	no	—
40	C₂³×D₁₅	—	2	1	no	—
41	C₂×C₃×C₅×Q₈	—	2	1	no	—
42	C₂×C₃×C₅×Q₈	—	2	2	no	—
43	C₂×C₃×C₅×Q₈	C₂×C₄	1	4	yes	complemented
44	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
45	C₂²×C₃×C₄×C₅	—	2	1	no	—
46	C₂²×C₃×C₄×C₅	—	2	1	no	—
47	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
48	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
49	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
50	C₂²×Dic₁₅	—	2	1	no	—
51	C₂×D₆₀	—	2	1	no	—
52	C₂×D₆₀	—	2	2	no	—
53	C₂×D₆₀	C₂×C₄	1	4	yes	—
54	C₂×D₆₀	C₂³	1	2	yes	—
55	C₂×C₄×D₁₅	—	2	4	no	—
56	C₂×C₄×D₁₅	—	4	4	no	—
57	C₃×C₅×C₄⋊C₄	—	2	4	no	—
58	C₃×C₅×C₄⋊C₄	—	2	1	no	—
59	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
60	C₃×C₄²×C₅	—	2	4	no	—
61	C₃×C₄²×C₅	D₄	1	2	yes	—
62	C₃×C₄²×C₅	C₂³	1	2	yes	—
63	#6717	C₂×C₄	1	16	yes	direct product factor
64	#6714	—	2	4	no	—
65	C₄⋊Dic₁₅	—	2	1	no	—
66	C₄⋊Dic₁₅	C₂³	1	2	yes	—
67	C₂×C₃⋊#168	—	2	2	no	—
68	C₂×C₃⋊#168	C₂×C₄	1	4	yes	complemented
69	C₂×C₃⋊#168	C₂³	1	2	yes	—
70	C₂×C₃⋊#168	C₂³	1	2	yes	—
71	C₂×C₃×C₄×Q₈	D₅	1	1	yes	characteristic, complemented
72	C₂²×#215	—	5	1	no	—
73	C₂×C₄×D₁₂	—	5	1	no	—
74	C₂×#835	—	5	1	no	—
75	C₄×#215	—	5	8	no	—
76	C₂×#809	—	5	1	no	—
77	C₂×#808	—	5	1	no	—
78	C₂×C₄×C₃⋊C₈	—	5	1	no	—
79	C₂²×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
80	C₂²×D₂₀	—	3	1	no	—
81	C₂²×C₄×D₅	—	6	1	no	—
82	C₄×C₅×Q₈	—	2	2	no	—
83	C₄×C₅×Q₈	C₂×D₃	1	4	yes	complemented
84	C₂×C₅×C₄⋊C₄	—	2	1	no	—
85	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
86	C₂×C₄²×C₅	—	2	1	no	—
87	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
88	C₂×#688	—	3	8	no	—
89	C₂×#688	—	3	4	no	—
90	C₂×#685	—	6	1	no	—
91	C₂×C₄⋊Dic₅	—	3	1	no	—
92	C₂²×#168	—	3	1	no	—
93	C₂²×#168	—	3	1	no	—
94	C₄×D₂₀	—	3	4	no	—
95	C₄×D₂₀	—	6	2	no	—
96	#3967	—	3	4	no	—
97	#3941	—	3	4	no	—
98	#3940	—	3	4	no	—
99	C₄×#168	—	3	4	no	—
100	C₂×C₄×SD₁₆	—	15	1	no	Sylow
101	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
102	C₂²×D₁₅	—	2	4	no	—
103	C₂²×D₁₅	—	2	2	no	—
104	C₂²×D₁₅	—	4	2	no	—
105	C₂²×D₁₅	—	4	2	no	—
106	C₃×C₅×Q₈	—	2	4	no	—
107	C₃×C₅×Q₈	—	2	2	no	—
108	C₃×C₅×Q₈	C₂²×C₄	1	4	yes	complemented
109	C₂×C₃×C₄×C₅	—	2	4	no	—
110	C₂×C₃×C₄×C₅	—	2	2	no	—
111	C₂×C₃×C₄×C₅	—	2	2	no	—
112	C₂×C₃×C₄×C₅	—	2	2	no	—
113	C₂×C₃×C₄×C₅	—	4	2	no	—
114	C₂×C₃×C₄×C₅	SD₁₆	1	4	yes	complemented
115	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
116	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
117	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
118	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
119	C₂×C₃×C₄×C₅	#41	1	2	yes	—
120	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
121	C₂×Dic₁₅	—	2	2	no	—
122	C₂×Dic₁₅	—	4	2	no	—
123	D₆₀	—	2	4	no	—
124	D₆₀	—	2	2	no	—
125	D₆₀	C₂²×C₄	1	4	yes	—
126	C₄×D₁₅	—	4	8	no	—
127	C₃⋊#168	—	2	2	no	—
128	C₃⋊#168	C₂²×C₄	1	4	yes	complemented
129	C₂²×C₃×Q₈	C₂×D₅	1	1	yes	characteristic
130	C₂²×D₁₂	—	5	1	no	—
131	C₂²×C₄×D₃	—	10	1	no	—
132	C₃×C₄×Q₈	—	2	2	no	—
133	C₃×C₄×Q₈	C₂×D₅	1	4	yes	complemented
134	C₂×C₃×C₄⋊C₄	—	2	1	no	—
135	C₂×C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
136	C₂×C₃×C₄²	—	2	1	no	—
137	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
138	C₂×#215	—	5	8	no	—
139	C₂×#215	—	5	4	no	—
140	C₂×(C₂×D₃)⋊C₄	—	10	1	no	—
141	C₂×C₄⋊Dic₃	—	5	1	no	—
142	C₂²×C₃⋊C₈	—	5	1	no	—
143	C₂²×C₃⋊C₈	—	5	1	no	—
144	C₄×D₁₂	—	5	4	no	—
145	C₄×D₁₂	—	10	2	no	—
146	#835	—	5	4	no	—
147	#809	—	5	4	no	—
148	#808	—	5	4	no	—
149	C₄×C₃⋊C₈	—	5	4	no	—
150	C₂³×D₅	—	6	1	no	—
151	C₂×C₅×Q₈	—	2	2	no	—
152	C₂×C₅×Q₈	—	2	1	no	—
153	C₂×C₅×Q₈	C₄×D₃	1	4	yes	complemented
154	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
155	C₂²×C₄×C₅	—	2	1	no	—
156	C₂²×C₄×C₅	—	2	1	no	—
157	C₂²×C₄×C₅	#67	1	1	yes	characteristic
158	C₂²×C₄×C₅	#67	1	1	yes	characteristic
159	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
160	C₂²×Dic₅	—	6	1	no	—
161	C₂×D₂₀	—	3	4	no	—
162	C₂×D₂₀	—	3	2	no	—
163	C₂×D₂₀	—	6	2	no	—
164	C₂×D₂₀	—	6	1	no	—
165	C₂×C₄×D₅	—	6	4	no	—
166	C₂×C₄×D₅	—	12	4	no	—
167	C₅×C₄⋊C₄	—	2	4	no	—
168	C₅×C₄⋊C₄	—	2	1	no	—
169	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
170	C₄²×C₅	—	2	4	no	—
171	C₄²×C₅	#67	1	2	yes	—
172	C₄²×C₅	C₂²×D₃	1	2	yes	—
173	#688	—	3	16	no	—
174	#685	—	6	4	no	—
175	C₄⋊Dic₅	—	3	2	no	—
176	C₄⋊Dic₅	—	6	1	no	—
177	C₂×#168	—	3	4	no	—
178	C₂×#168	—	3	2	no	—
179	C₂×#168	—	3	2	no	—
180	C₂×#168	—	6	2	no	—
181	C₂²×SD₁₆	—	15	1	no	—
182	C₂×C₄×Q₈	D₁₅	1	1	yes	characteristic, complemented
183	C₂×C₄×D₄	—	15	1	no	—
184	C₄×SD₁₆	—	15	8	no	—
185	C₂×#106	—	15	1	no	—
186	C₂×#103	—	15	1	no	—
187	C₂×#102	—	15	1	no	—
188	C₂×C₄×C₈	—	15	1	no	—
189	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
190	C₂²×C₃×C₅	C₂×SD₁₆	1	2	yes	—
191	C₂²×C₃×C₅	#135	1	2	yes	—
192	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
193	C₂×D₁₅	—	2	4	no	—
194	C₂×D₁₅	—	4	2	no	—
195	C₂×D₁₅	—	4	2	no	—
196	C₂×D₁₅	—	4	8	no	—
197	C₃×C₄×C₅	—	2	4	no	—
198	C₃×C₄×C₅	—	2	2	no	—
199	C₃×C₄×C₅	—	4	2	no	—
200	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
201	C₃×C₄×C₅	C₂×SD₁₆	1	4	yes	complemented
202	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
203	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
204	Dic₁₅	—	4	2	no	—
205	C₂³×D₃	—	10	1	no	—
206	C₂×C₃×Q₈	—	2	2	no	—
207	C₂×C₃×Q₈	—	2	1	no	—
208	C₂×C₃×Q₈	C₄×D₅	1	4	yes	complemented
209	C₂×C₃×Q₈	C₂²×D₅	1	2	yes	—
210	C₂²×C₃×C₄	—	2	1	no	—
211	C₂²×C₃×C₄	—	2	1	no	—
212	C₂²×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
213	C₂²×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
214	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
215	C₂²×Dic₃	—	10	1	no	—
216	C₂×D₁₂	—	5	4	no	—
217	C₂×D₁₂	—	5	2	no	—
218	C₂×D₁₂	—	10	2	no	—
219	C₂×D₁₂	—	10	1	no	—
220	C₂×C₄×D₃	—	10	4	no	—
221	C₂×C₄×D₃	—	20	4	no	—
222	C₃×C₄⋊C₄	—	2	4	no	—
223	C₃×C₄⋊C₄	—	2	1	no	—
224	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
225	C₃×C₄²	—	2	4	no	—
226	C₃×C₄²	C₂²⋊D₅	1	2	yes	—
227	C₃×C₄²	C₂²×D₅	1	2	yes	—
228	#215	—	5	16	no	—
229	(C₂×D₃)⋊C₄	—	10	4	no	—
230	C₄⋊Dic₃	—	5	2	no	—
231	C₄⋊Dic₃	—	10	1	no	—
232	C₂×C₃⋊C₈	—	5	4	no	—
233	C₂×C₃⋊C₈	—	5	2	no	—
234	C₂×C₃⋊C₈	—	5	2	no	—
235	C₂×C₃⋊C₈	—	10	2	no	—
236	C₂³×C₅	C₂×#67	1	1	yes	characteristic
237	C₂²×D₅	—	6	4	no	—
238	C₂²×D₅	—	6	2	no	—
239	C₂²×D₅	—	12	2	no	—
240	C₂²×D₅	—	12	2	no	—
241	C₅×Q₈	—	2	4	no	—
242	C₅×Q₈	—	2	2	no	—
243	C₅×Q₈	C₂×C₄×D₃	1	4	yes	complemented
244	C₂×C₄×C₅	—	2	4	no	—
245	C₂×C₄×C₅	—	2	2	no	—
246	C₂×C₄×C₅	—	2	2	no	—
247	C₂×C₄×C₅	—	2	2	no	—
248	C₂×C₄×C₅	—	4	2	no	—
249	C₂×C₄×C₅	#215	1	4	yes	complemented
250	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
251	C₂×C₄×C₅	#235	1	2	yes	—
252	C₂×C₄×C₅	C₂×#67	1	2	yes	—
253	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
254	C₂×C₄×C₅	C₂×#67	1	2	yes	—
255	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
256	C₂×Dic₅	—	6	2	no	—
257	C₂×Dic₅	—	12	2	no	—
258	D₂₀	—	3	4	no	—
259	D₂₀	—	6	4	no	—
260	D₂₀	—	6	2	no	—
261	C₄×D₅	—	12	8	no	—
262	#168	—	3	4	no	—
263	#168	—	6	2	no	—
264	C₂²×Q₈	C₂×D₁₅	1	1	yes	characteristic
265	C₂²×D₄	—	15	1	no	—
266	C₂³×C₄	—	30	1	no	—
267	C₂×SD₁₆	—	15	8	no	—
268	C₂×SD₁₆	—	15	4	no	—
269	C₂²×C₈	—	15	1	no	—
270	C₂²×C₈	—	15	1	no	—
271	C₄×Q₈	—	2	2	no	—
272	C₄×Q₈	C₂×D₁₅	1	4	yes	complemented
273	C₄×D₄	—	15	4	no	—
274	C₄×D₄	—	30	2	no	—
275	C₂×C₄⋊C₄	—	2	1	no	—
276	C₂×C₄⋊C₄	—	15	1	no	—
277	C₂×C₄⋊C₄	C₂×D₁₅	1	1	yes	characteristic
278	C₂×C₂²⋊C₄	—	30	1	no	—
279	C₂×C₄²	—	2	1	no	—
280	C₂×C₄²	C₂×D₁₅	1	1	yes	characteristic
281	#106	—	15	4	no	—
282	#103	—	15	4	no	—
283	#102	—	15	4	no	—
284	C₄×C₈	—	15	4	no	—
285	C₂×C₃×C₅	C₄×SD₁₆	1	4	yes	complemented
286	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
287	C₂×C₃×C₅	C₂²×SD₁₆	1	1	yes	characteristic
288	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
289	D₁₅	—	4	4	no	—
290	C₂³×C₃	C₂×C₂²⋊D₅	1	1	yes	characteristic
291	C₂²×D₃	—	10	2	no	—
292	C₂²×D₃	—	10	4	no	—
293	C₂²×D₃	—	20	2	no	—
294	C₂²×D₃	—	20	2	no	—
295	C₃×Q₈	—	2	2	no	—
296	C₃×Q₈	—	2	4	no	—
297	C₃×Q₈	C₂×C₄×D₅	1	4	yes	complemented
298	C₂×C₃×C₄	—	2	2	no	—
299	C₂×C₃×C₄	—	2	2	no	—
300	C₂×C₃×C₄	—	2	4	no	—
301	C₂×C₃×C₄	—	2	2	no	—
302	C₂×C₃×C₄	—	4	2	no	—
303	C₂×C₃×C₄	#688	1	4	yes	complemented
304	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
305	C₂×C₃×C₄	#709	1	2	yes	—
306	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
307	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
308	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
309	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
310	C₂×Dic₃	—	10	2	no	—
311	C₂×Dic₃	—	20	2	no	—
312	D₁₂	—	5	4	no	—
313	D₁₂	—	10	2	no	—
314	D₁₂	—	10	4	no	—
315	C₄×D₃	—	20	8	no	—
316	C₃⋊C₈	—	5	4	no	—
317	C₃⋊C₈	—	10	2	no	—
318	C₂²×C₅	C₄×#67	1	2	yes	—
319	C₂²×C₅	C₂×#215	1	2	yes	—
320	C₂²×C₅	#950	1	2	yes	—
321	C₂²×C₅	C₂²×#67	1	1	yes	characteristic
322	C₂×D₅	—	6	4	no	—
323	C₂×D₅	—	12	8	no	—
324	C₂×D₅	—	12	2	no	—
325	C₂×D₅	—	12	2	no	—
326	C₄×C₅	—	2	4	no	—
327	C₄×C₅	—	2	2	no	—
328	C₄×C₅	—	4	2	no	—
329	C₄×C₅	C₄×#67	1	2	yes	—
330	C₄×C₅	C₂×#215	1	4	yes	complemented
331	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
332	C₄×C₅	C₂×#235	1	1	yes	characteristic
333	Dic₅	—	12	2	no	—
334	C₂⁴	—	30	1	no	—
335	C₂×Q₈	—	2	2	no	—
336	C₂×Q₈	—	2	1	no	—
337	C₂×Q₈	C₄×D₁₅	1	4	yes	complemented
338	C₂×Q₈	C₂²×D₁₅	1	2	yes	—
339	C₂×D₄	—	15	4	no	—
340	C₂×D₄	—	15	2	no	—
341	C₂×D₄	—	30	2	no	—
342	C₂×D₄	—	30	1	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	30	1	no	—
346	C₂²×C₄	—	30	4	no	—
347	C₂²×C₄	—	60	4	no	—
348	C₂²×C₄	#1220	1	1	yes	characteristic
349	C₂²×C₄	#1220	1	1	yes	characteristic
350	C₂²×C₄	C₂²×D₁₅	1	1	yes	characteristic
351	SD₁₆	—	15	16	no	—
352	C₂×C₈	—	15	4	no	—
353	C₂×C₈	—	15	2	no	—
354	C₂×C₈	—	15	2	no	—
355	C₂×C₈	—	30	2	no	—
356	C₄⋊C₄	—	2	4	no	—
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	15	2	no	—
359	C₄⋊C₄	—	30	1	no	—
360	C₄⋊C₄	C₂²×D₁₅	1	2	yes	—
361	C₂²⋊C₄	—	30	4	no	—
362	C₄²	—	2	4	no	—
363	C₄²	#1220	1	2	yes	—
364	C₄²	C₂²×D₁₅	1	2	yes	—
365	C₃×C₅	C₂×C₄×SD₁₆	1	1	yes	characteristic, complemented, Hall
366	C₂²×C₃	C₄×C₂²⋊D₅	1	2	yes	—
367	C₂²×C₃	C₂×#688	1	2	yes	—
368	C₂²×C₃	#4096	1	2	yes	—
369	C₂²×C₃	C₂²×C₂²⋊D₅	1	1	yes	characteristic
370	C₂×D₃	—	10	4	no	—
371	C₂×D₃	—	20	8	no	—
372	C₂×D₃	—	20	2	no	—
373	C₂×D₃	—	20	2	no	—
374	C₃×C₄	—	2	4	no	—
375	C₃×C₄	—	2	2	no	—
376	C₃×C₄	—	4	2	no	—
377	C₃×C₄	C₄×C₂²⋊D₅	1	2	yes	—
378	C₃×C₄	C₂×#688	1	4	yes	complemented
379	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
380	C₃×C₄	C₂×#709	1	1	yes	characteristic
381	Dic₃	—	20	2	no	—
382	C₂×C₅	C₄×#215	1	4	yes	complemented
383	C₂×C₅	C₂×C₄×#67	1	1	yes	characteristic
384	C₂×C₅	C₂²×#215	1	1	yes	characteristic
385	C₂×C₅	C₂×#950	1	1	yes	characteristic
386	D₅	—	12	4	no	—
387	C₂³	—	30	4	no	—
388	C₂³	—	30	2	no	—
389	C₂³	—	60	2	no	—
390	C₂³	—	60	2	no	—
391	C₂³	C₂×#1220	1	1	yes	characteristic
392	Q₈	—	2	4	no	—
393	Q₈	—	2	2	no	—
394	Q₈	C₂×C₄×D₁₅	1	4	yes	complemented
395	D₄	—	15	4	no	—
396	D₄	—	30	4	no	—
397	D₄	—	30	2	no	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	30	2	no	—
404	C₂×C₄	—	60	2	no	—
405	C₂×C₄	—	60	8	no	—
406	C₂×C₄	#6717	1	4	yes	direct product factor
407	C₂×C₄	C₂×C₄×D₁₅	1	2	yes	—
408	C₂×C₄	#6817	1	2	yes	—
409	C₂×C₄	C₂×#1220	1	2	yes	—
410	C₂×C₄	C₂×#1220	1	1	yes	characteristic
411	C₂×C₄	C₂×#1220	1	2	yes	—
412	C₂×C₄	C₂³×D₁₅	1	1	yes	characteristic
413	C₈	—	15	4	no	—
414	C₈	—	30	2	no	—
415	C₂×C₃	C₄×#688	1	4	yes	complemented
416	C₂×C₃	C₂×C₄×C₂²⋊D₅	1	1	yes	characteristic
417	C₂×C₃	C₂²×#688	1	1	yes	characteristic
418	C₂×C₃	C₂×#4096	1	1	yes	characteristic
419	D₃	—	20	4	no	—
420	C₅	C₂×C₄×#215	1	1	yes	characteristic, complemented, Sylow
421	C₂²	—	30	4	no	—
422	C₂²	—	60	2	no	—
423	C₂²	—	60	2	no	—
424	C₂²	—	60	8	no	—
425	C₂²	C₄×#1220	1	2	yes	—
426	C₂²	C₂×#6717	1	2	yes	—
427	C₂²	#91839	1	2	yes	—
428	C₂²	C₂²×#1220	1	1	yes	characteristic
429	C₄	—	2	4	no	—
430	C₄	—	2	2	no	—
431	C₄	—	4	2	no	—
432	C₄	—	60	2	no	—
433	C₄	C₄×#1220	1	2	yes	—
434	C₄	C₂×#6717	1	4	yes	direct product factor
435	C₄	C₂²×C₄×D₁₅	1	1	yes	characteristic
436	C₄	C₂×#6817	1	1	yes	characteristic
437	C₃	C₂×C₄×#688	1	1	yes	characteristic, complemented, Sylow
438	C₂	—	60	4	no	—
439	C₂	C₄×#6717	1	4	yes	direct product factor
440	C₂	C₂×C₄×#1220	1	1	yes	characteristic
441	C₂	C₂²×#6717	1	1	yes	characteristic
442	C₂	C₂×#91839	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	#1220
commutator	C₃×C₄×C₅	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₁₅
Fitting	C₂×C₃×C₄×C₅×Q₈	C₂
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂²×D₆₀	C₂²
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₂×C₄×Q₈	D₁₅
hypocenter	C₃×C₅	C₂×C₄×SD₁₆
LCS	G ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×C₄×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₄×C₅×Q₈	C₂	semidirect
4. C₂×#91119	C₂	semidirect
5. C₄×#6717	C₂	direct (N × H)
7. C₂×#91092	C₂	semidirect
8. C₂×C₄×C₃⋊#168	C₂	semidirect
14. C₃×C₄×C₅×Q₈	C₂²	semidirect
19. C₂×#6717	C₄	direct (N × H)
27. #91119	C₂²	semidirect
29. #91092	C₂²	semidirect
30. C₄×C₃⋊#168	C₂²	semidirect
32. C₂×C₄×C₅×Q₈	D₃	semidirect
43. C₂×C₃×C₅×Q₈	C₂×C₄	semidirect
63. #6717	C₂×C₄	direct (N × H)
68. C₂×C₃⋊#168	C₂×C₄	semidirect
71. C₂×C₃×C₄×Q₈	D₅	semidirect
83. C₄×C₅×Q₈	C₂×D₃	semidirect
108. C₃×C₅×Q₈	C₂²×C₄	semidirect
114. C₂×C₃×C₄×C₅	SD₁₆	semidirect
128. C₃⋊#168	C₂²×C₄	semidirect
133. C₃×C₄×Q₈	C₂×D₅	semidirect
153. C₂×C₅×Q₈	C₄×D₃	semidirect
182. C₂×C₄×Q₈	D₁₅	semidirect
201. C₃×C₄×C₅	C₂×SD₁₆	semidirect
208. C₂×C₃×Q₈	C₄×D₅	semidirect
243. C₅×Q₈	C₂×C₄×D₃	semidirect
249. C₂×C₄×C₅	#215	semidirect
272. C₄×Q₈	C₂×D₁₅	semidirect
285. C₂×C₃×C₅	C₄×SD₁₆	semidirect
297. C₃×Q₈	C₂×C₄×D₅	semidirect
303. C₂×C₃×C₄	#688	semidirect
330. C₄×C₅	C₂×#215	semidirect
337. C₂×Q₈	C₄×D₁₅	semidirect
365. C₃×C₅	C₂×C₄×SD₁₆	semidirect
378. C₃×C₄	C₂×#688	semidirect
382. C₂×C₅	C₄×#215	semidirect
394. Q₈	C₂×C₄×D₁₅	semidirect
406. C₂×C₄	#6717	direct (N × H)
415. C₂×C₃	C₄×#688	semidirect
420. C₅	C₂×C₄×#215	semidirect
434. C₄	C₂×#6717	direct (N × H)
437. C₃	C₂×C₄×#688	semidirect
439. C₂	C₄×#6717	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×C₄×C₅×Q₈	2
C₂²×#6717	2
C₂×C₄×D₆₀	2
C₂×#91119	2
C₄×#6717	2
C₂×#91093	2
C₂×#91092	2
C₂×C₄×C₃⋊#168	2
C₂×C₄×#688	3
C₂×C₄×#215	5

Subgroups — C2×C4×#6717 #14416054

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×#6717 #14416054