Subgroups — C₂×Q₈×#1220 #14482904

Order 1920.

3136 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×C₅×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×Q₈×D₁₅	C₂	1	1	yes	maximal, characteristic, complemented
3	Q₈×#1220	C₂	1	16	yes	maximal, direct product factor
4	C₂×#91835	C₂	1	3	yes	maximal, complemented
5	C₂×Q₈×Dic₁₅	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#91833	C₂	1	3	yes	maximal, complemented
7	C₂×C₄×#1220	C₂	1	3	yes	maximal
8	C₂×#91813	C₂	1	3	yes	maximal, complemented
9	C₂×Q₈×C₂²⋊D₅	—	3	1	no	maximal, Hall
10	C₂²×C₃×C₅×Q₈	—	2	8	no	—
11	C₂²×C₃×C₅×Q₈	C₂²	1	3	yes	—
12	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
13	C₂²×C₃×C₅×Q₈	C₂²	1	8	yes	complemented
14	C₂³×C₃×C₄×C₅	C₂²	1	3	yes	—
15	C₂²×#1220	C₂²	1	1	yes	characteristic
16	C₂×Q₈×D₁₅	—	2	8	no	—
17	C₂×Q₈×D₁₅	C₂²	1	8	yes	complemented
18	C₂²×C₄×D₁₅	C₂²	1	3	yes	—
19	C₂²×Dic₃₀	C₂²	1	3	yes	—
20	C₂×#6719	C₂²	1	3	yes	—
21	#91835	C₂²	1	24	yes	complemented
22	Q₈×Dic₁₅	C₂²	1	8	yes	complemented
23	#91833	C₂²	1	24	yes	complemented
24	C₄×#1220	C₂²	1	24	yes	—
25	C₂×#6714	C₂²	1	3	yes	—
26	C₂×C₄⋊Dic₁₅	C₂²	1	3	yes	—
27	#91813	C₂²	1	24	yes	complemented
28	C₂×#6712	C₂²	1	3	yes	—
29	C₂×#6712	C₂²	1	6	yes	—
30	C₂×C₄×Dic₁₅	C₂²	1	3	yes	—
31	C₂×Q₈×#67	—	5	1	no	maximal, Hall
32	C₂³×C₅×Q₈	D₃	1	1	yes	characteristic, complemented
33	C₂²×Q₈×D₅	—	3	1	no	—
34	Q₈×C₂²⋊D₅	—	3	16	no	—
35	C₂×#4092	—	3	3	no	—
36	C₂×Q₈×Dic₅	—	3	1	no	—
37	C₂×#4090	—	3	3	no	—
38	C₂×C₄×C₂²⋊D₅	—	3	3	no	—
39	C₂×#4070	—	3	3	no	—
40	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
41	C₂³×D₁₅	C₂³	1	1	yes	characteristic
42	C₂×C₃×C₅×Q₈	—	2	32	no	—
43	C₂×C₃×C₅×Q₈	—	2	12	no	—
44	C₂×C₃×C₅×Q₈	D₄	1	8	yes	complemented
45	C₂×C₃×C₅×Q₈	C₂³	1	12	yes	—
46	C₂×C₃×C₅×Q₈	C₂³	1	4	yes	—
47	C₂²×C₃×C₄×C₅	—	2	12	no	—
48	C₂²×C₃×C₄×C₅	C₂³	1	3	yes	—
49	C₂²×C₃×C₄×C₅	C₂³	1	12	yes	—
50	C₂²×C₃×C₄×C₅	C₂³	1	3	yes	—
51	C₂×#1220	Q₈	1	8	yes	direct product factor
52	C₂×#1220	C₂³	1	4	yes	—
53	C₂²×Dic₁₅	C₂³	1	3	yes	—
54	C₂²×Dic₁₅	C₂³	1	3	yes	—
55	C₂²×Dic₁₅	C₂³	1	1	yes	characteristic
56	Q₈×D₁₅	—	2	32	no	—
57	C₂×C₄×D₁₅	—	2	12	no	—
58	C₂×C₄×D₁₅	C₂³	1	12	yes	—
59	C₂×Dic₃₀	—	2	12	no	—
60	C₂×Dic₃₀	C₂³	1	12	yes	—
61	#6719	C₂³	1	12	yes	—
62	#6714	C₂³	1	12	yes	—
63	C₄⋊Dic₁₅	C₂³	1	12	yes	—
64	#6712	C₂³	1	24	yes	—
65	#6712	C₂³	1	12	yes	—
66	C₄×Dic₁₅	C₂³	1	12	yes	—
67	C₂³×C₃×Q₈	D₅	1	1	yes	characteristic, complemented
68	C₂²×D₃×Q₈	—	5	1	no	—
69	Q₈×#67	—	5	16	no	—
70	C₂×#946	—	5	3	no	—
71	C₂×Q₈×Dic₃	—	5	1	no	—
72	C₂×#944	—	5	3	no	—
73	C₂×C₄×#67	—	5	3	no	—
74	C₂×#924	—	5	3	no	—
75	C₂²×C₅×Q₈	—	2	8	no	—
76	C₂²×C₅×Q₈	C₂×D₃	1	3	yes	—
77	C₂²×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
78	C₂²×C₅×Q₈	C₂×D₃	1	8	yes	complemented
79	C₂³×C₄×C₅	C₂×D₃	1	3	yes	—
80	C₂²×C₂²⋊D₅	—	3	1	no	—
81	C₂×Q₈×D₅	—	3	8	no	—
82	C₂×Q₈×D₅	—	6	8	no	—
83	C₂²×C₄×D₅	—	3	3	no	—
84	C₂²×Dic₁₀	—	3	3	no	—
85	C₂×C₂²⋊Dic₅	—	3	3	no	—
86	#4092	—	3	24	no	—
87	Q₈×Dic₅	—	3	8	no	—
88	#4090	—	3	24	no	—
89	C₄×C₂²⋊D₅	—	3	24	no	—
90	C₂×#685	—	3	3	no	—
91	C₂×C₄⋊Dic₅	—	3	3	no	—
92	#4070	—	3	24	no	—
93	C₂×#683	—	3	6	no	—
94	C₂×#683	—	3	3	no	—
95	C₂×C₄×Dic₅	—	3	3	no	—
96	C₂×D₄×Q₈	—	15	1	no	Sylow
97	C₂³×C₃×C₅	—	2	2	no	—
98	C₂³×C₃×C₅	—	2	2	no	—
99	C₂³×C₃×C₅	C₂×Q₈	1	4	yes	complemented
100	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
101	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
102	C₂²×D₁₅	—	2	2	no	—
103	C₂²×D₁₅	—	2	2	no	—
104	C₂²×D₁₅	C₂×Q₈	1	4	yes	complemented
105	C₂²×D₁₅	C₂⁴	1	2	yes	—
106	C₃×C₅×Q₈	—	2	24	no	—
107	C₃×C₅×Q₈	C₂×D₄	1	16	yes	complemented
108	C₂×C₃×C₄×C₅	—	2	6	no	—
109	C₂×C₃×C₄×C₅	—	2	24	no	—
110	C₂×C₃×C₄×C₅	C₂×D₄	1	12	yes	—
111	C₂×C₃×C₄×C₅	C₂⁴	1	6	yes	—
112	C₂×C₃×C₄×C₅	C₂⁴	1	6	yes	—
113	#1220	C₂×Q₈	1	16	yes	direct product factor
114	C₂×Dic₁₅	—	2	6	no	—
115	C₂×Dic₁₅	—	2	6	no	—
116	C₂×Dic₁₅	C₂×Q₈	1	4	yes	complemented
117	C₂×Dic₁₅	C₂⁴	1	6	yes	—
118	C₂×Dic₁₅	C₂⁴	1	6	yes	—
119	C₂×Dic₁₅	C₂⁴	1	2	yes	—
120	C₄×D₁₅	—	2	24	no	—
121	Dic₃₀	—	2	24	no	—
122	C₂²×C₃×Q₈	—	2	8	no	—
123	C₂²×C₃×Q₈	C₂×D₅	1	3	yes	—
124	C₂²×C₃×Q₈	C₂×D₅	1	1	yes	characteristic
125	C₂²×C₃×Q₈	C₂×D₅	1	8	yes	complemented
126	C₂³×C₃×C₄	C₂×D₅	1	3	yes	—
127	C₂²×#67	—	5	1	no	—
128	C₂×D₃×Q₈	—	5	8	no	—
129	C₂×D₃×Q₈	—	10	8	no	—
130	C₂²×C₄×D₃	—	5	3	no	—
131	C₂²×Dic₆	—	5	3	no	—
132	C₂×#217	—	5	3	no	—
133	#946	—	5	24	no	—
134	Q₈×Dic₃	—	5	8	no	—
135	#944	—	5	24	no	—
136	C₄×#67	—	5	24	no	—
137	C₂×(C₂×D₃)⋊C₄	—	5	3	no	—
138	C₂×C₄⋊Dic₃	—	5	3	no	—
139	#924	—	5	24	no	—
140	C₂×Dic₃⋊C₄	—	5	6	no	—
141	C₂×Dic₃⋊C₄	—	5	3	no	—
142	C₂×C₄×Dic₃	—	5	3	no	—
143	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
144	C₂³×D₅	—	3	1	no	—
145	C₂×C₅×Q₈	—	2	32	no	—
146	C₂×C₅×Q₈	—	2	12	no	—
147	C₂×C₅×Q₈	#67	1	8	yes	complemented
148	C₂×C₅×Q₈	C₂²×D₃	1	12	yes	—
149	C₂×C₅×Q₈	C₂²×D₃	1	4	yes	—
150	C₂²×C₄×C₅	—	2	12	no	—
151	C₂²×C₄×C₅	C₂²×D₃	1	3	yes	—
152	C₂²×C₄×C₅	C₂²×D₃	1	12	yes	—
153	C₂²×C₄×C₅	C₂²×D₃	1	3	yes	—
154	C₂×C₂²⋊D₅	—	3	8	no	—
155	C₂×C₂²⋊D₅	—	3	4	no	—
156	C₂²×Dic₅	—	3	1	no	—
157	C₂²×Dic₅	—	3	3	no	—
158	C₂²×Dic₅	—	3	3	no	—
159	Q₈×D₅	—	6	32	no	—
160	C₂×C₄×D₅	—	3	12	no	—
161	C₂×C₄×D₅	—	6	12	no	—
162	C₂×Dic₁₀	—	3	12	no	—
163	C₂×Dic₁₀	—	6	12	no	—
164	C₂²⋊Dic₅	—	3	12	no	—
165	#685	—	3	12	no	—
166	C₄⋊Dic₅	—	3	12	no	—
167	#683	—	3	24	no	—
168	#683	—	3	12	no	—
169	C₄×Dic₅	—	3	12	no	—
170	C₂³×Q₈	—	15	1	no	—
171	C₂³×Q₈	D₁₅	1	1	yes	characteristic, complemented
172	D₄×Q₈	—	15	16	no	—
173	C₂×C₄⋊Q₈	—	15	3	no	—
174	C₂×C₂²⋊Q₈	—	15	3	no	—
175	C₂×C₂²⋊Q₈	—	15	3	no	—
176	C₂×C₄×Q₈	—	15	1	no	—
177	C₂×C₄×D₄	—	15	3	no	—
178	C₂²×C₃×C₅	—	2	8	no	—
179	C₂²×C₃×C₅	—	2	2	no	—
180	C₂²×C₃×C₅	—	2	2	no	—
181	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
182	C₂²×C₃×C₅	C₂²×Q₈	1	2	yes	—
183	C₂²×C₃×C₅	C₂²×Q₈	1	4	yes	complemented
184	C₂²×C₃×C₅	2₋¹⁺⁴	1	2	yes	—
185	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
186	C₂×D₁₅	—	2	8	no	—
187	C₂×D₁₅	—	2	2	no	—
188	C₂×D₁₅	—	2	2	no	—
189	C₂×D₁₅	C₂²×Q₈	1	4	yes	complemented
190	C₃×C₄×C₅	—	2	6	no	—
191	C₃×C₄×C₅	C₂²×D₄	1	12	yes	—
192	Dic₁₅	—	2	6	no	—
193	Dic₁₅	—	2	6	no	—
194	Dic₁₅	C₂²×Q₈	1	4	yes	complemented
195	C₂⁴×C₃	C₂²×D₅	1	1	yes	characteristic
196	C₂³×D₃	—	5	1	no	—
197	C₂×C₃×Q₈	—	2	32	no	—
198	C₂×C₃×Q₈	—	2	12	no	—
199	C₂×C₃×Q₈	C₂²⋊D₅	1	8	yes	complemented
200	C₂×C₃×Q₈	C₂²×D₅	1	12	yes	—
201	C₂×C₃×Q₈	C₂²×D₅	1	4	yes	—
202	C₂²×C₃×C₄	—	2	12	no	—
203	C₂²×C₃×C₄	C₂²×D₅	1	3	yes	—
204	C₂²×C₃×C₄	C₂²×D₅	1	12	yes	—
205	C₂²×C₃×C₄	C₂²×D₅	1	3	yes	—
206	C₂×#67	—	5	8	no	—
207	C₂×#67	—	5	4	no	—
208	C₂²×Dic₃	—	5	1	no	—
209	C₂²×Dic₃	—	5	3	no	—
210	C₂²×Dic₃	—	5	3	no	—
211	D₃×Q₈	—	10	32	no	—
212	C₂×C₄×D₃	—	5	12	no	—
213	C₂×C₄×D₃	—	10	12	no	—
214	C₂×Dic₆	—	5	12	no	—
215	C₂×Dic₆	—	10	12	no	—
216	#217	—	5	12	no	—
217	(C₂×D₃)⋊C₄	—	5	12	no	—
218	C₄⋊Dic₃	—	5	12	no	—
219	Dic₃⋊C₄	—	5	24	no	—
220	Dic₃⋊C₄	—	5	12	no	—
221	C₄×Dic₃	—	5	12	no	—
222	C₂³×C₅	—	2	2	no	—
223	C₂³×C₅	—	2	2	no	—
224	C₂³×C₅	D₃×Q₈	1	4	yes	complemented
225	C₂³×C₅	C₂³×D₃	1	2	yes	—
226	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
227	C₂²×D₅	—	3	4	no	—
228	C₂²×D₅	—	3	2	no	—
229	C₂²×D₅	—	6	2	no	—
230	C₂²×D₅	—	6	2	no	—
231	C₅×Q₈	—	2	24	no	—
232	C₅×Q₈	C₂×#67	1	16	yes	complemented
233	C₂×C₄×C₅	—	2	6	no	—
234	C₂×C₄×C₅	—	2	24	no	—
235	C₂×C₄×C₅	C₂×#67	1	12	yes	—
236	C₂×C₄×C₅	C₂³×D₃	1	6	yes	—
237	C₂×C₄×C₅	C₂³×D₃	1	6	yes	—
238	C₂²⋊D₅	—	3	16	no	—
239	C₂×Dic₅	—	3	4	no	—
240	C₂×Dic₅	—	3	2	no	—
241	C₂×Dic₅	—	3	6	no	—
242	C₂×Dic₅	—	3	6	no	—
243	C₂×Dic₅	—	6	6	no	—
244	C₂×Dic₅	—	6	6	no	—
245	C₄×D₅	—	6	24	no	—
246	Dic₁₀	—	6	24	no	—
247	C₂²×Q₈	—	2	8	no	—
248	C₂²×Q₈	—	15	8	no	—
249	C₂²×Q₈	—	15	3	no	—
250	C₂²×Q₈	—	30	8	no	—
251	C₂²×Q₈	C₂×D₁₅	1	3	yes	—
252	C₂²×Q₈	C₂×D₁₅	1	1	yes	characteristic
253	C₂²×Q₈	C₂×D₁₅	1	8	yes	complemented
254	C₂²×D₄	—	15	1	no	—
255	C₂³×C₄	—	15	3	no	—
256	C₂³×C₄	C₂×D₁₅	1	3	yes	—
257	C₄⋊Q₈	—	15	24	no	—
258	C₂²⋊Q₈	—	15	24	no	—
259	C₂²⋊Q₈	—	15	24	no	—
260	C₄×Q₈	—	15	8	no	—
261	C₄×D₄	—	15	24	no	—
262	C₂×C₄⋊C₄	—	15	3	no	—
263	C₂×C₄⋊C₄	—	15	3	no	—
264	C₂×C₄⋊C₄	—	15	6	no	—
265	C₂×C₂²⋊C₄	—	15	3	no	—
266	C₂×C₂²⋊C₄	—	15	3	no	—
267	C₂×C₄²	—	15	3	no	—
268	C₂×C₃×C₅	—	2	4	no	—
269	C₂×C₃×C₅	D₄×Q₈	1	4	yes	complemented
270	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
271	C₂×C₃×C₅	C₂³×Q₈	1	1	yes	characteristic
272	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
273	D₁₅	—	2	4	no	—
274	C₂³×C₃	—	2	2	no	—
275	C₂³×C₃	—	2	2	no	—
276	C₂³×C₃	Q₈×D₅	1	4	yes	complemented
277	C₂³×C₃	C₂³×D₅	1	2	yes	—
278	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
279	C₂²×D₃	—	5	4	no	—
280	C₂²×D₃	—	5	2	no	—
281	C₂²×D₃	—	10	2	no	—
282	C₂²×D₃	—	10	2	no	—
283	C₃×Q₈	—	2	24	no	—
284	C₃×Q₈	C₂×C₂²⋊D₅	1	16	yes	complemented
285	C₂×C₃×C₄	—	2	6	no	—
286	C₂×C₃×C₄	—	2	24	no	—
287	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	12	yes	—
288	C₂×C₃×C₄	C₂³×D₅	1	6	yes	—
289	C₂×C₃×C₄	C₂³×D₅	1	6	yes	—
290	#67	—	5	16	no	—
291	C₂×Dic₃	—	5	4	no	—
292	C₂×Dic₃	—	5	2	no	—
293	C₂×Dic₃	—	5	6	no	—
294	C₂×Dic₃	—	5	6	no	—
295	C₂×Dic₃	—	10	6	no	—
296	C₂×Dic₃	—	10	6	no	—
297	C₄×D₃	—	10	24	no	—
298	Dic₆	—	10	24	no	—
299	C₂²×C₅	—	2	2	no	—
300	C₂²×C₅	—	2	2	no	—
301	C₂²×C₅	—	2	8	no	—
302	C₂²×C₅	C₂×D₃×Q₈	1	2	yes	—
303	C₂²×C₅	C₂×D₃×Q₈	1	4	yes	complemented
304	C₂²×C₅	#1007	1	2	yes	—
305	C₂²×C₅	C₂²×#67	1	2	yes	—
306	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
307	C₂×D₅	—	3	4	no	—
308	C₂×D₅	—	6	2	no	—
309	C₂×D₅	—	6	2	no	—
310	C₂×D₅	—	6	8	no	—
311	C₄×C₅	—	2	6	no	—
312	C₄×C₅	C₂²×#67	1	12	yes	—
313	Dic₅	—	3	4	no	—
314	Dic₅	—	6	6	no	—
315	Dic₅	—	6	6	no	—
316	C₂⁴	—	15	1	no	—
317	C₂⁴	C₂²×D₁₅	1	1	yes	characteristic
318	C₂×Q₈	—	2	32	no	—
319	C₂×Q₈	—	2	12	no	—
320	C₂×Q₈	—	15	12	no	—
321	C₂×Q₈	—	30	32	no	—
322	C₂×Q₈	—	30	12	no	—
323	C₂×Q₈	#1220	1	8	yes	direct product factor
324	C₂×Q₈	C₂²×D₁₅	1	12	yes	—
325	C₂×Q₈	C₂²×D₁₅	1	4	yes	—
326	C₂×D₄	—	15	8	no	—
327	C₂×D₄	—	15	4	no	—
328	C₂²×C₄	—	2	12	no	—
329	C₂²×C₄	—	15	1	no	—
330	C₂²×C₄	—	15	3	no	—
331	C₂²×C₄	—	15	3	no	—
332	C₂²×C₄	—	15	12	no	—
333	C₂²×C₄	—	30	12	no	—
334	C₂²×C₄	C₂²×D₁₅	1	12	yes	—
335	C₂²×C₄	C₂²×D₁₅	1	3	yes	—
336	C₂²×C₄	C₂²×D₁₅	1	3	yes	—
337	C₄⋊C₄	—	15	12	no	—
338	C₄⋊C₄	—	15	12	no	—
339	C₄⋊C₄	—	15	24	no	—
340	C₂²⋊C₄	—	15	12	no	—
341	C₂²⋊C₄	—	15	12	no	—
342	C₄²	—	15	12	no	—
343	C₃×C₅	C₂×D₄×Q₈	1	1	yes	characteristic, complemented, Hall
344	C₂²×C₃	—	2	8	no	—
345	C₂²×C₃	—	2	2	no	—
346	C₂²×C₃	—	2	2	no	—
347	C₂²×C₃	C₂×Q₈×D₅	1	2	yes	—
348	C₂²×C₃	C₂×Q₈×D₅	1	4	yes	complemented
349	C₂²×C₃	#4147	1	2	yes	—
350	C₂²×C₃	C₂²×C₂²⋊D₅	1	2	yes	—
351	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
352	C₂×D₃	—	5	4	no	—
353	C₂×D₃	—	10	8	no	—
354	C₂×D₃	—	10	2	no	—
355	C₂×D₃	—	10	2	no	—
356	C₃×C₄	—	2	6	no	—
357	C₃×C₄	C₂²×C₂²⋊D₅	1	12	yes	—
358	Dic₃	—	5	4	no	—
359	Dic₃	—	10	6	no	—
360	Dic₃	—	10	6	no	—
361	C₂×C₅	—	2	4	no	—
362	C₂×C₅	Q₈×#67	1	4	yes	complemented
363	C₂×C₅	C₂²×D₃×Q₈	1	1	yes	characteristic
364	C₂×C₅	C₂×#1007	1	1	yes	characteristic
365	C₂×C₅	C₂³×#67	1	1	yes	characteristic
366	D₅	—	6	4	no	—
367	C₂³	—	2	2	no	—
368	C₂³	—	2	2	no	—
369	C₂³	—	15	4	no	—
370	C₂³	—	15	2	no	—
371	C₂³	—	30	2	no	—
372	C₂³	—	30	2	no	—
373	C₂³	Q₈×D₁₅	1	4	yes	complemented
374	C₂³	C₂³×D₁₅	1	2	yes	—
375	C₂³	C₂³×D₁₅	1	1	yes	characteristic
376	Q₈	—	2	24	no	—
377	Q₈	—	30	24	no	—
378	Q₈	C₂×#1220	1	16	yes	direct product factor
379	D₄	—	15	16	no	—
380	C₂×C₄	—	2	6	no	—
381	C₂×C₄	—	2	24	no	—
382	C₂×C₄	—	15	4	no	—
383	C₂×C₄	—	15	2	no	—
384	C₂×C₄	—	15	6	no	—
385	C₂×C₄	—	15	6	no	—
386	C₂×C₄	—	30	6	no	—
387	C₂×C₄	—	30	6	no	—
388	C₂×C₄	—	30	24	no	—
389	C₂×C₄	C₂×#1220	1	12	yes	—
390	C₂×C₄	C₂³×D₁₅	1	6	yes	—
391	C₂×C₄	C₂³×D₁₅	1	6	yes	—
392	C₂×C₃	—	2	4	no	—
393	C₂×C₃	Q₈×C₂²⋊D₅	1	4	yes	complemented
394	C₂×C₃	C₂²×Q₈×D₅	1	1	yes	characteristic
395	C₂×C₃	C₂×#4147	1	1	yes	characteristic
396	C₂×C₃	C₂³×C₂²⋊D₅	1	1	yes	characteristic
397	D₃	—	10	4	no	—
398	C₅	C₂×Q₈×#67	1	1	yes	characteristic, complemented, Sylow
399	C₂²	—	2	8	no	—
400	C₂²	—	2	2	no	—
401	C₂²	—	2	2	no	—
402	C₂²	—	15	4	no	—
403	C₂²	—	30	8	no	—
404	C₂²	—	30	2	no	—
405	C₂²	—	30	2	no	—
406	C₂²	C₂×Q₈×D₁₅	1	2	yes	—
407	C₂²	C₂×Q₈×D₁₅	1	4	yes	complemented
408	C₂²	#92098	1	2	yes	—
409	C₂²	C₂²×#1220	1	2	yes	—
410	C₂²	C₂⁴×D₁₅	1	1	yes	characteristic
411	C₄	—	2	6	no	—
412	C₄	—	15	4	no	—
413	C₄	—	30	6	no	—
414	C₄	—	30	6	no	—
415	C₄	C₂²×#1220	1	12	yes	—
416	C₃	C₂×Q₈×C₂²⋊D₅	1	1	yes	characteristic, complemented, Sylow
417	C₂	—	2	4	no	—
418	C₂	—	30	4	no	—
419	C₂	Q₈×#1220	1	4	yes	direct product factor
420	C₂	C₂²×Q₈×D₁₅	1	1	yes	characteristic
421	C₂	C₂×#92098	1	1	yes	characteristic
422	C₂	C₂³×#1220	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂³×D₁₅
commutator, cosocle	C₂²×C₃×C₅	C₂⁵
Frattini	C₂²	C₂⁴×D₁₅
Fitting	C₂³×C₃×C₅×Q₈	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂²×#1220	C₂²
hypercenter	C₂³×Q₈	D₁₅
hypocenter	C₃×C₅	C₂×D₄×Q₈
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂³ ◁ C₂³×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂³×C₃×C₅×Q₈	C₂	semidirect
2. C₂²×Q₈×D₁₅	C₂	semidirect
3. Q₈×#1220	C₂	direct (N × H)
4. C₂×#91835	C₂	semidirect
5. C₂×Q₈×Dic₁₅	C₂	semidirect
6. C₂×#91833	C₂	semidirect
8. C₂×#91813	C₂	semidirect
13. C₂²×C₃×C₅×Q₈	C₂²	semidirect
17. C₂×Q₈×D₁₅	C₂²	semidirect
21. #91835	C₂²	semidirect
22. Q₈×Dic₁₅	C₂²	semidirect
23. #91833	C₂²	semidirect
27. #91813	C₂²	semidirect
32. C₂³×C₅×Q₈	D₃	semidirect
44. C₂×C₃×C₅×Q₈	D₄	semidirect
51. C₂×#1220	Q₈	direct (N × H)
67. C₂³×C₃×Q₈	D₅	semidirect
78. C₂²×C₅×Q₈	C₂×D₃	semidirect
99. C₂³×C₃×C₅	C₂×Q₈	semidirect
104. C₂²×D₁₅	C₂×Q₈	semidirect
107. C₃×C₅×Q₈	C₂×D₄	semidirect
113. #1220	C₂×Q₈	direct (N × H)
116. C₂×Dic₁₅	C₂×Q₈	semidirect
125. C₂²×C₃×Q₈	C₂×D₅	semidirect
147. C₂×C₅×Q₈	#67	semidirect
171. C₂³×Q₈	D₁₅	semidirect
183. C₂²×C₃×C₅	C₂²×Q₈	semidirect
189. C₂×D₁₅	C₂²×Q₈	semidirect
194. Dic₁₅	C₂²×Q₈	semidirect
199. C₂×C₃×Q₈	C₂²⋊D₅	semidirect
224. C₂³×C₅	D₃×Q₈	semidirect
232. C₅×Q₈	C₂×#67	semidirect
253. C₂²×Q₈	C₂×D₁₅	semidirect
269. C₂×C₃×C₅	D₄×Q₈	semidirect
276. C₂³×C₃	Q₈×D₅	semidirect
284. C₃×Q₈	C₂×C₂²⋊D₅	semidirect
303. C₂²×C₅	C₂×D₃×Q₈	semidirect
323. C₂×Q₈	#1220	direct (N × H)
343. C₃×C₅	C₂×D₄×Q₈	semidirect
348. C₂²×C₃	C₂×Q₈×D₅	semidirect
362. C₂×C₅	Q₈×#67	semidirect
373. C₂³	Q₈×D₁₅	semidirect
378. Q₈	C₂×#1220	direct (N × H)
393. C₂×C₃	Q₈×C₂²⋊D₅	semidirect
398. C₅	C₂×Q₈×#67	semidirect
407. C₂²	C₂×Q₈×D₁₅	semidirect
416. C₃	C₂×Q₈×C₂²⋊D₅	semidirect
419. C₂	Q₈×#1220	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₃×C₅×Q₈	2
C₂²×Q₈×D₁₅	2
Q₈×#1220	2
C₂×#91835	2
C₂×Q₈×Dic₁₅	2
C₂×#91833	2
C₂×C₄×#1220	2
C₂×#91813	2
C₂×Q₈×C₂²⋊D₅	3
C₂×Q₈×#67	5

Subgroups — C2×Q8×#1220 #14482904

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×Q₈×#1220 #14482904