Subgroups — C₂×#11750940 #14413052

Order 1920.

1024 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#6705	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₈×D₁₅	C₂	1	1	yes	maximal, characteristic
3	C₂×#91761	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃×C₅×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#91098	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#91098	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄⋊(C₃⋊#168)	C₂	1	1	yes	maximal, characteristic, complemented
8	#11750940	C₂	1	8	yes	maximal, direct product factor
9	C₂×#65128	—	3	1	no	maximal, Hall
10	C₂²×C₄×D₁₅	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
14	C₂×#6714	C₄	1	1	yes	characteristic
15	C₂×#6714	C₄	1	1	yes	characteristic
16	C₂×#6712	C₄	1	1	yes	characteristic
17	C₂×#6712	C₄	1	1	yes	characteristic
18	C₂×C₄×Dic₁₅	C₂²	1	1	yes	characteristic
19	C₂²×C₃⋊#168	C₂²	1	1	yes	characteristic
20	C₂²×C₃⋊#168	C₂²	1	1	yes	characteristic
21	C₂×#6705	—	2	4	no	—
22	C₂×#6705	C₂²	1	4	yes	—
23	C₂×C₈×D₁₅	—	2	4	no	—
24	C₂×C₈×D₁₅	C₂²	1	4	yes	—
25	#91761	C₄	1	4	yes	—
26	#91761	C₂²	1	4	yes	—
27	C₃×C₅×C₄⋊C₈	C₂²	1	4	yes	complemented
28	#91098	C₂²	1	4	yes	complemented
29	#91098	C₂²	1	4	yes	complemented
30	C₄⋊(C₃⋊#168)	C₂²	1	4	yes	complemented
31	C₂×#4839	—	5	1	no	maximal, Hall
32	C₂²×#676	—	3	1	no	—
33	C₂²×C₈×D₅	—	3	1	no	—
34	C₂×#4018	—	3	1	no	—
35	C₂×C₅×C₄⋊C₈	D₃	1	1	yes	characteristic, complemented
36	C₂×#3946	—	3	1	no	—
37	C₂×#3946	—	3	1	no	—
38	C₂×C₄⋊#168	—	3	1	no	—
39	#65128	—	3	8	no	—
40	C₂³×D₁₅	C₂×C₄	1	1	yes	characteristic
41	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
43	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
44	C₂²×Dic₁₅	C₂×C₄	1	1	yes	characteristic
45	C₂²×Dic₁₅	C₂×C₄	1	1	yes	characteristic
46	C₂²×Dic₁₅	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄×D₁₅	C₂×C₄	1	2	yes	—
48	C₂×C₄×D₁₅	D₄	1	4	yes	—
49	C₂×C₄×D₁₅	Q₈	1	4	yes	—
50	C₂×C₄×D₁₅	C₂³	1	2	yes	—
51	C₂×C₃×C₅×C₈	—	2	2	no	—
52	C₂×C₃×C₅×C₈	—	2	2	no	—
53	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
54	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
55	C₃×C₄²×C₅	C₂×C₄	1	2	yes	—
56	C₃×C₄²×C₅	C₂³	1	2	yes	—
57	#6714	C₂×C₄	1	4	yes	—
58	#6714	C₂×C₄	1	4	yes	—
59	#6712	C₂×C₄	1	4	yes	—
60	#6712	C₂×C₄	1	4	yes	—
61	C₄×Dic₁₅	C₂×C₄	1	2	yes	—
62	C₄×Dic₁₅	C₂³	1	2	yes	—
63	C₂×C₃⋊#168	—	2	2	no	—
64	C₂×C₃⋊#168	—	2	2	no	—
65	C₂×C₃⋊#168	C₂³	1	2	yes	—
66	C₂×C₃⋊#168	C₂³	1	2	yes	—
67	#6705	—	2	8	no	—
68	C₈×D₁₅	—	2	8	no	—
69	C₂²×ΓL(1,𝔽₂₅)	—	5	1	no	—
70	C₂²×D₃×C₈	—	5	1	no	—
71	C₂×#872	—	5	1	no	—
72	C₂×C₃×C₄⋊C₈	D₅	1	1	yes	characteristic, complemented
73	C₂×Dic₃⋊C₈	—	5	1	no	—
74	C₂×Dic₃⋊C₈	—	5	1	no	—
75	C₂×C₄⋊(C₃⋊C₈)	—	5	1	no	—
76	#4839	—	5	8	no	—
77	C₂²×C₄×D₅	—	3	1	no	—
78	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
79	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
80	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
81	C₂×#685	—	3	1	no	—
82	C₂×#685	—	3	1	no	—
83	C₂×#683	—	3	1	no	—
84	C₂×#683	—	3	1	no	—
85	C₂×C₄×Dic₅	—	3	1	no	—
86	C₂²×#168	—	3	1	no	—
87	C₂²×#168	—	3	1	no	—
88	C₂×#676	—	3	4	no	—
89	C₂×#676	—	6	4	no	—
90	C₂×C₈×D₅	—	3	4	no	—
91	C₂×C₈×D₅	—	6	4	no	—
92	#4018	—	3	4	no	—
93	#4018	—	3	4	no	—
94	C₅×C₄⋊C₈	C₂×D₃	1	4	yes	complemented
95	#3946	—	3	4	no	—
96	#3946	—	3	4	no	—
97	C₄⋊#168	—	3	4	no	—
98	C₂×#424	—	15	1	no	Sylow
99	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
100	C₂²×D₁₅	—	2	2	no	—
101	C₂²×D₁₅	—	2	2	no	—
102	C₂²×D₁₅	C₄⋊C₄	1	4	yes	—
103	C₂²×D₁₅	C₂²×C₄	1	2	yes	—
104	C₂×C₃×C₄×C₅	—	2	2	no	—
105	C₂×C₃×C₄×C₅	—	2	2	no	—
106	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
107	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
108	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
110	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
111	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
112	C₂×Dic₁₅	—	2	2	no	—
113	C₂×Dic₁₅	—	2	2	no	—
114	C₂×Dic₁₅	C₄⋊C₄	1	4	yes	—
115	C₂×Dic₁₅	C₂²×C₄	1	2	yes	—
116	C₂×Dic₁₅	C₂²×C₄	1	2	yes	—
117	C₂×Dic₁₅	C₂²×C₄	1	2	yes	—
118	C₄×D₁₅	C₄⋊C₄	1	8	yes	—
119	C₄×D₁₅	C₂×D₄	1	4	yes	—
120	C₄×D₁₅	C₂×Q₈	1	4	yes	—
121	C₃×C₅×C₈	—	2	2	no	—
122	C₃×C₅×C₈	—	2	2	no	—
123	C₃⋊#168	—	2	2	no	—
124	C₃⋊#168	—	2	2	no	—
125	C₂²×C₄×D₃	—	5	1	no	—
126	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
127	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
128	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
129	C₂×(C₂×D₃)⋊C₄	—	5	1	no	—
130	C₂×(C₂×D₃)⋊C₄	—	5	1	no	—
131	C₂×Dic₃⋊C₄	—	5	1	no	—
132	C₂×Dic₃⋊C₄	—	5	1	no	—
133	C₂×C₄×Dic₃	—	5	1	no	—
134	C₂²×C₃⋊C₈	—	5	1	no	—
135	C₂²×C₃⋊C₈	—	5	1	no	—
136	C₂×ΓL(1,𝔽₂₅)	—	5	4	no	—
137	C₂×ΓL(1,𝔽₂₅)	—	10	4	no	—
138	C₂×D₃×C₈	—	5	4	no	—
139	C₂×D₃×C₈	—	10	4	no	—
140	#872	—	5	4	no	—
141	#872	—	5	4	no	—
142	C₃×C₄⋊C₈	C₂×D₅	1	4	yes	complemented
143	Dic₃⋊C₈	—	5	4	no	—
144	Dic₃⋊C₈	—	5	4	no	—
145	C₄⋊(C₃⋊C₈)	—	5	4	no	—
146	C₂³×D₅	—	3	1	no	—
147	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
148	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
149	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
150	C₂²×Dic₅	—	3	1	no	—
151	C₂²×Dic₅	—	3	1	no	—
152	C₂²×Dic₅	—	3	1	no	—
153	C₂×C₄×D₅	—	3	2	no	—
154	C₂×C₄×D₅	—	3	4	no	—
155	C₂×C₄×D₅	—	3	4	no	—
156	C₂×C₄×D₅	—	3	2	no	—
157	C₂×C₅×C₈	—	2	2	no	—
158	C₂×C₅×C₈	—	2	2	no	—
159	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
160	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
161	C₄²×C₅	C₄×D₃	1	2	yes	—
162	C₄²×C₅	C₂²×D₃	1	2	yes	—
163	#685	—	3	4	no	—
164	#685	—	3	4	no	—
165	#683	—	3	4	no	—
166	#683	—	3	4	no	—
167	C₄×Dic₅	—	3	2	no	—
168	C₄×Dic₅	—	3	2	no	—
169	C₂×#168	—	3	2	no	—
170	C₂×#168	—	3	2	no	—
171	C₂×#168	—	6	2	no	—
172	C₂×#168	—	6	2	no	—
173	#676	—	6	8	no	—
174	C₈×D₅	—	6	8	no	—
175	C₂²×M₁₆	—	15	1	no	—
176	C₂³×C₈	—	15	1	no	—
177	C₂×#117	—	15	1	no	—
178	#424	—	15	8	no	—
179	C₂×C₄⋊C₈	—	15	1	no	—
180	C₂×C₄⋊C₈	—	15	1	no	—
181	C₂×C₄⋊C₈	—	15	1	no	—
182	C₂×C₄⋊C₈	D₁₅	1	1	yes	characteristic, complemented
183	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	2	yes	—
184	C₂²×C₃×C₅	#131	1	2	yes	—
185	C₂²×C₃×C₅	#131	1	2	yes	—
186	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
187	C₂×D₁₅	—	2	2	no	—
188	C₂×D₁₅	—	2	2	no	—
189	C₂×D₁₅	—	2	8	no	—
190	C₂×D₁₅	C₂×C₄⋊C₄	1	4	yes	—
191	C₃×C₄×C₅	—	2	2	no	—
192	C₃×C₄×C₅	—	2	2	no	—
193	C₃×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
194	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
195	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
196	Dic₁₅	—	2	2	no	—
197	Dic₁₅	—	2	2	no	—
198	Dic₁₅	C₂×C₄⋊C₄	1	4	yes	—
199	C₂³×D₃	—	5	1	no	—
200	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
201	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
202	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
203	C₂²×Dic₃	—	5	1	no	—
204	C₂²×Dic₃	—	5	1	no	—
205	C₂²×Dic₃	—	5	1	no	—
206	C₂×C₄×D₃	—	5	2	no	—
207	C₂×C₄×D₃	—	5	4	no	—
208	C₂×C₄×D₃	—	5	4	no	—
209	C₂×C₄×D₃	—	5	2	no	—
210	C₂×C₃×C₈	—	2	2	no	—
211	C₂×C₃×C₈	—	2	2	no	—
212	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
213	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
214	C₃×C₄²	C₄×D₅	1	2	yes	—
215	C₃×C₄²	C₂²×D₅	1	2	yes	—
216	(C₂×D₃)⋊C₄	—	5	4	no	—
217	(C₂×D₃)⋊C₄	—	5	4	no	—
218	Dic₃⋊C₄	—	5	4	no	—
219	Dic₃⋊C₄	—	5	4	no	—
220	C₄×Dic₃	—	5	2	no	—
221	C₄×Dic₃	—	5	2	no	—
222	C₂×C₃⋊C₈	—	5	2	no	—
223	C₂×C₃⋊C₈	—	5	2	no	—
224	C₂×C₃⋊C₈	—	10	2	no	—
225	C₂×C₃⋊C₈	—	10	2	no	—
226	ΓL(1,𝔽₂₅)	—	10	8	no	—
227	D₃×C₈	—	10	8	no	—
228	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
229	C₂²×D₅	—	3	4	no	—
230	C₂²×D₅	—	3	2	no	—
231	C₂²×D₅	—	6	2	no	—
232	C₂²×D₅	—	6	2	no	—
233	C₂×C₄×C₅	—	2	2	no	—
234	C₂×C₄×C₅	—	2	2	no	—
235	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
236	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
237	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
238	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
239	C₂×C₄×C₅	D₃×Q₈	1	2	yes	—
240	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
241	C₂×Dic₅	—	3	4	no	—
242	C₂×Dic₅	—	3	2	no	—
243	C₂×Dic₅	—	3	2	no	—
244	C₂×Dic₅	—	3	2	no	—
245	C₂×Dic₅	—	6	2	no	—
246	C₂×Dic₅	—	6	2	no	—
247	C₄×D₅	—	3	8	no	—
248	C₄×D₅	—	3	4	no	—
249	C₄×D₅	—	3	4	no	—
250	C₅×C₈	—	2	2	no	—
251	C₅×C₈	—	2	2	no	—
252	#168	—	6	2	no	—
253	#168	—	6	2	no	—
254	C₂³×C₄	—	15	1	no	—
255	C₂×M₁₆	—	15	4	no	—
256	C₂×M₁₆	—	30	4	no	—
257	C₂²×C₈	—	15	1	no	—
258	C₂²×C₈	—	15	1	no	—
259	C₂²×C₈	—	15	4	no	—
260	C₂²×C₈	—	30	4	no	—
261	C₂²×C₈	C₂×D₁₅	1	1	yes	characteristic
262	C₂²×C₈	C₂×D₁₅	1	1	yes	characteristic
263	#117	—	15	4	no	—
264	#117	—	15	4	no	—
265	C₂×C₄⋊C₄	—	15	1	no	—
266	C₂×C₄⋊C₄	—	15	1	no	—
267	C₂×C₂²⋊C₄	—	15	1	no	—
268	C₂×C₂²⋊C₄	—	15	1	no	—
269	C₂×C₄²	—	15	1	no	—
270	C₂×C₄²	C₂×D₁₅	1	1	yes	characteristic
271	C₄⋊C₈	—	15	4	no	—
272	C₄⋊C₈	—	15	4	no	—
273	C₄⋊C₈	—	15	4	no	—
274	C₄⋊C₈	C₂×D₁₅	1	4	yes	complemented
275	C₂×C₃×C₅	#424	1	4	yes	complemented
276	C₂×C₃×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
277	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
278	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
279	D₁₅	—	2	4	no	—
280	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
281	C₂²×D₃	—	5	2	no	—
282	C₂²×D₃	—	5	4	no	—
283	C₂²×D₃	—	10	2	no	—
284	C₂²×D₃	—	10	2	no	—
285	C₂×C₃×C₄	—	2	2	no	—
286	C₂×C₃×C₄	—	2	2	no	—
287	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
288	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
289	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
290	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
291	C₂×C₃×C₄	Q₈×D₅	1	2	yes	—
292	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
293	C₂×Dic₃	—	5	2	no	—
294	C₂×Dic₃	—	5	4	no	—
295	C₂×Dic₃	—	5	2	no	—
296	C₂×Dic₃	—	5	2	no	—
297	C₂×Dic₃	—	10	2	no	—
298	C₂×Dic₃	—	10	2	no	—
299	C₄×D₃	—	5	4	no	—
300	C₄×D₃	—	5	4	no	—
301	C₄×D₃	—	5	8	no	—
302	C₃×C₈	—	2	2	no	—
303	C₃×C₈	—	2	2	no	—
304	C₃⋊C₈	—	10	2	no	—
305	C₃⋊C₈	—	10	2	no	—
306	C₂²×C₅	D₃×C₄⋊C₄	1	2	yes	—
307	C₂²×C₅	#901	1	2	yes	—
308	C₂²×C₅	#907	1	2	yes	—
309	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
310	C₂×D₅	—	3	4	no	—
311	C₂×D₅	—	6	2	no	—
312	C₂×D₅	—	6	2	no	—
313	C₂×D₅	—	6	8	no	—
314	C₄×C₅	—	2	2	no	—
315	C₄×C₅	—	2	2	no	—
316	C₄×C₅	D₃×C₄⋊C₄	1	2	yes	—
317	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
318	C₄×C₅	C₂×D₃×Q₈	1	1	yes	characteristic
319	Dic₅	—	3	4	no	—
320	Dic₅	—	6	2	no	—
321	Dic₅	—	6	2	no	—
322	C₂⁴	—	15	1	no	—
323	C₂²×C₄	—	15	1	no	—
324	C₂²×C₄	—	15	2	no	—
325	C₂²×C₄	—	15	4	no	—
326	C₂²×C₄	—	15	4	no	—
327	C₂²×C₄	—	15	2	no	—
328	C₂²×C₄	—	15	1	no	—
329	C₂²×C₄	—	15	1	no	—
330	C₂²×C₄	C₄×D₁₅	1	1	yes	characteristic
331	C₂²×C₄	C₄×D₁₅	1	1	yes	characteristic
332	C₂²×C₄	C₂²×D₁₅	1	1	yes	characteristic
333	M₁₆	—	30	8	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	15	2	no	—
337	C₂×C₈	—	15	2	no	—
338	C₂×C₈	—	30	8	no	—
339	C₂×C₈	—	30	2	no	—
340	C₂×C₈	—	30	2	no	—
341	C₂×C₈	C₂²×D₁₅	1	2	yes	—
342	C₂×C₈	C₂²×D₁₅	1	2	yes	—
343	C₄⋊C₄	—	15	4	no	—
344	C₄⋊C₄	—	15	4	no	—
345	C₂²⋊C₄	—	15	4	no	—
346	C₂²⋊C₄	—	15	4	no	—
347	C₄²	—	15	2	no	—
348	C₄²	—	15	2	no	—
349	C₄²	C₄×D₁₅	1	2	yes	—
350	C₄²	C₂²×D₁₅	1	2	yes	—
351	C₃×C₅	C₂×#424	1	1	yes	characteristic, complemented, Hall
352	C₂²×C₃	D₅×C₄⋊C₄	1	2	yes	—
353	C₂²×C₃	#4047	1	2	yes	—
354	C₂²×C₃	#4053	1	2	yes	—
355	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
356	C₂×D₃	—	5	4	no	—
357	C₂×D₃	—	10	2	no	—
358	C₂×D₃	—	10	2	no	—
359	C₂×D₃	—	10	8	no	—
360	C₃×C₄	—	2	2	no	—
361	C₃×C₄	—	2	2	no	—
362	C₃×C₄	D₅×C₄⋊C₄	1	2	yes	—
363	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
364	C₃×C₄	C₂×Q₈×D₅	1	1	yes	characteristic
365	Dic₃	—	5	4	no	—
366	Dic₃	—	10	2	no	—
367	Dic₃	—	10	2	no	—
368	C₂×C₅	#4839	1	4	yes	complemented
369	C₂×C₅	C₂×D₃×C₄⋊C₄	1	1	yes	characteristic
370	C₂×C₅	C₂×#901	1	1	yes	characteristic
371	C₂×C₅	C₂×#907	1	1	yes	characteristic
372	D₅	—	6	4	no	—
373	C₂³	—	15	4	no	—
374	C₂³	—	15	2	no	—
375	C₂³	—	30	2	no	—
376	C₂³	—	30	2	no	—
377	C₂³	C₂×C₄×D₁₅	1	1	yes	characteristic
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	15	4	no	—
381	C₂×C₄	—	15	2	no	—
382	C₂×C₄	—	15	8	no	—
383	C₂×C₄	—	15	4	no	—
384	C₂×C₄	—	15	4	no	—
385	C₂×C₄	—	15	2	no	—
386	C₂×C₄	—	15	2	no	—
387	C₂×C₄	—	30	2	no	—
388	C₂×C₄	—	30	2	no	—
389	C₂×C₄	C₂×C₄×D₁₅	1	2	yes	—
390	C₂×C₄	C₂×C₄×D₁₅	1	2	yes	—
391	C₂×C₄	C₂×C₄×D₁₅	1	1	yes	characteristic
392	C₂×C₄	D₄×D₁₅	1	2	yes	—
393	C₂×C₄	Q₈×D₁₅	1	2	yes	—
394	C₂×C₄	C₂³×D₁₅	1	1	yes	characteristic
395	C₈	—	2	2	no	—
396	C₈	—	2	2	no	—
397	C₈	—	30	2	no	—
398	C₈	—	30	2	no	—
399	C₂×C₃	#65128	1	4	yes	complemented
400	C₂×C₃	C₂×D₅×C₄⋊C₄	1	1	yes	characteristic
401	C₂×C₃	C₂×#4047	1	1	yes	characteristic
402	C₂×C₃	C₂×#4053	1	1	yes	characteristic
403	D₃	—	10	4	no	—
404	C₅	C₂×#4839	1	1	yes	characteristic, complemented, Sylow
405	C₂²	—	15	4	no	—
406	C₂²	—	30	8	no	—
407	C₂²	—	30	2	no	—
408	C₂²	—	30	2	no	—
409	C₂²	C₄⋊C₄×D₁₅	1	2	yes	—
410	C₂²	#91790	1	2	yes	—
411	C₂²	#91796	1	2	yes	—
412	C₂²	C₂²×C₄×D₁₅	1	1	yes	characteristic
413	C₄	—	2	2	no	—
414	C₄	—	2	2	no	—
415	C₄	—	15	4	no	—
416	C₄	—	30	2	no	—
417	C₄	—	30	2	no	—
418	C₄	C₄⋊C₄×D₁₅	1	2	yes	—
419	C₄	C₂×D₄×D₁₅	1	1	yes	characteristic
420	C₄	C₂×Q₈×D₁₅	1	1	yes	characteristic
421	C₃	C₂×#65128	1	1	yes	characteristic, complemented, Sylow
422	C₂	—	30	4	no	—
423	C₂	#11750940	1	4	yes	direct product factor
424	C₂	C₂×C₄⋊C₄×D₁₅	1	1	yes	characteristic
425	C₂	C₂×#91790	1	1	yes	characteristic
426	C₂	C₂×#91796	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂²×D₁₅
commutator	C₂²×C₃×C₅	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₁₅
Fitting	C₂×C₃×C₅×C₄⋊C₈	C₂
socle	C₂³×C₃×C₅	C₂²×C₄
prime radical	C₂³×D₁₅	C₂×C₄
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₂×C₄⋊C₈	D₁₅
hypocenter	C₃×C₅	C₂×#424
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
4. C₂×C₃×C₅×C₄⋊C₈	C₂	semidirect
5. C₂×#91098	C₂	semidirect
6. C₂×#91098	C₂	semidirect
7. C₂×C₄⋊(C₃⋊#168)	C₂	semidirect
8. #11750940	C₂	direct (N × H)
27. C₃×C₅×C₄⋊C₈	C₂²	semidirect
28. #91098	C₂²	semidirect
29. #91098	C₂²	semidirect
30. C₄⋊(C₃⋊#168)	C₂²	semidirect
35. C₂×C₅×C₄⋊C₈	D₃	semidirect
72. C₂×C₃×C₄⋊C₈	D₅	semidirect
94. C₅×C₄⋊C₈	C₂×D₃	semidirect
142. C₃×C₄⋊C₈	C₂×D₅	semidirect
182. C₂×C₄⋊C₈	D₁₅	semidirect
274. C₄⋊C₈	C₂×D₁₅	semidirect
275. C₂×C₃×C₅	#424	semidirect
351. C₃×C₅	C₂×#424	semidirect
368. C₂×C₅	#4839	semidirect
399. C₂×C₃	#65128	semidirect
404. C₅	C₂×#4839	semidirect
421. C₃	C₂×#65128	semidirect
423. C₂	#11750940	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×#6705	2
C₂²×C₈×D₁₅	2
C₂×#91761	2
C₂×C₃×C₅×C₄⋊C₈	2
C₂×#91098	2
C₂×C₄⋊(C₃⋊#168)	2
#11750940	2
C₂×#65128	3
C₂×#4839	5

Subgroups — C2×#11750940 #14413052

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11750940 #14413052