Subgroups — C₂×#11749225 #14416378

Order 1920.

1088 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	C₂²×#6717	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×Q₈×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#91418	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×#835	C₂	1	1	yes	maximal, characteristic, complemented
5	#11749225	C₂	1	8	yes	maximal, direct product factor
6	C₂×#90989	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#90968	C₂	1	1	yes	maximal, characteristic
8	C₂×#90952	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#65106	—	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×#1200	—	2	1	no	—
13	C₂×#6717	C₄	1	8	yes	complemented
14	C₂×#6717	C₂²	1	4	yes	—
15	C₂²×C₃⋊#168	C₂²	1	1	yes	characteristic
16	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
17	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
18	C₃×Q₈×Dic₅	—	2	2	no	—
19	C₃×Q₈×Dic₅	C₂²	1	4	yes	complemented
20	C₂×C₃×C₄⋊Dic₅	—	2	1	no	—
21	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₄×Dic₅	—	2	1	no	—
23	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
24	C₂×#6667	—	2	1	no	—
25	#91418	—	2	2	no	—
26	#91418	C₂²	1	4	yes	—
27	C₅×#835	C₂²	1	4	yes	complemented
28	#90989	C₂²	1	4	yes	complemented
29	#90968	C₂²	1	4	yes	—
30	#90952	C₂²	1	4	yes	complemented
31	C₂×#5026	—	5	1	no	maximal, Hall
32	C₂×Q₈×Dic₅	D₃	1	1	yes	characteristic, complemented
33	C₂²×#688	—	3	1	no	—
34	C₂×#4039	—	3	1	no	—
35	C₂×C₅×#103	—	3	1	no	—
36	C₂×#3953	—	3	1	no	—
37	C₂×#3947	—	3	1	no	—
38	C₂×#3939	—	3	1	no	—
39	#65106	—	3	8	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	C₂³	1	1	yes	characteristic
47	C₂×D₆₀	—	2	1	no	—
48	C₂×D₆₀	—	2	2	no	—
49	C₂×D₆₀	C₂×C₄	1	4	yes	—
50	C₂×D₆₀	C₂³	1	2	yes	—
51	C₂²×C₅×Dic₃	—	2	1	no	—
52	C₂²×C₃×Dic₅	—	2	1	no	—
53	C₂²×C₃×Dic₅	D₄	1	1	yes	characteristic
54	C₂²×C₃×Dic₅	D₄	1	1	yes	characteristic
55	C₂×#1200	—	2	4	no	—
56	C₂×#1200	—	4	4	no	—
57	#6717	C₂×C₄	1	16	yes	complemented
58	C₂×C₃⋊#168	C₂×C₄	1	4	yes	complemented
59	C₂×C₃⋊#168	C₂³	1	2	yes	—
60	C₅×C₄⋊Dic₃	—	2	1	no	—
61	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
62	C₂×C₅×C₃⋊C₈	—	2	2	no	—
63	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
64	C₃×C₄⋊Dic₅	—	2	1	no	—
65	C₃×C₄⋊Dic₅	—	2	4	no	—
66	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
67	C₃×C₄×Dic₅	—	2	4	no	—
68	C₃×C₄×Dic₅	D₄	1	2	yes	—
69	C₃×C₄×Dic₅	C₂³	1	2	yes	—
70	#6667	—	2	4	no	—
71	C₂×C₃×C₄×Q₈	—	5	1	no	—
72	C₂²×#215	—	5	1	no	—
73	C₂×C₄×D₁₂	—	5	1	no	—
74	C₂×#835	D₅	1	1	yes	characteristic, complemented
75	#5026	—	5	8	no	—
76	C₂×#809	—	5	1	no	—
77	C₂×#807	—	5	1	no	—
78	C₂×#803	—	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	C₂²×C₅×C₈	—	3	1	no	—
83	C₂×C₅×C₄⋊C₄	—	3	1	no	—
84	Q₈×Dic₅	—	2	2	no	—
85	Q₈×Dic₅	C₂×D₃	1	4	yes	complemented
86	C₂×#688	—	3	8	no	—
87	C₂×#688	—	3	4	no	—
88	C₂×#685	—	6	1	no	—
89	C₂×C₄⋊Dic₅	—	2	1	no	—
90	C₂×C₄⋊Dic₅	C₂×D₃	1	1	yes	characteristic
91	C₂×C₄×Dic₅	—	2	1	no	—
92	C₂×C₄×Dic₅	C₂×D₃	1	1	yes	characteristic
93	C₂²×#168	—	3	1	no	—
94	#4039	—	3	4	no	—
95	#4039	—	6	2	no	—
96	C₅×#103	—	3	4	no	—
97	#3953	—	3	4	no	—
98	#3947	—	3	4	no	—
99	#3939	—	3	4	no	—
100	C₂×#440	—	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	C₂²×C₄	1	2	yes	—
112	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
113	C₂×C₃×C₄×C₅	#41	1	2	yes	—
114	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
115	D₆₀	—	2	4	no	—
116	D₆₀	—	2	2	no	—
117	D₆₀	C₂²×C₄	1	4	yes	—
118	C₂×C₅×Dic₃	—	2	2	no	—
119	C₂×C₅×Dic₃	—	4	2	no	—
120	C₂×C₃×Dic₅	—	2	2	no	—
121	C₂×C₃×Dic₅	—	2	2	no	—
122	C₂×C₃×Dic₅	—	2	2	no	—
123	C₂×C₃×Dic₅	—	4	2	no	—
124	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
125	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
126	#1200	—	4	8	no	—
127	C₃⋊#168	C₂²×C₄	1	4	yes	complemented
128	C₅×C₃⋊C₈	—	2	2	no	—
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	—	5	4	no	—
133	C₃×C₄×Q₈	—	10	2	no	—
134	C₂×C₃×C₄⋊C₄	—	5	1	no	—
135	C₂×C₃×C₄⋊C₄	—	10	1	no	—
136	C₂×C₃×C₄²	—	5	1	no	—
137	C₂×C₃×C₄²	—	10	1	no	—
138	C₂×#215	—	5	8	no	—
139	C₂×#215	—	5	4	no	—
140	C₂×(C₂×D₃)⋊C₄	—	10	1	no	—
141	C₂×C₄⋊Dic₃	C₂×D₅	1	1	yes	characteristic
142	C₂²×C₃⋊C₈	—	5	1	no	—
143	C₂²×C₃⋊C₈	C₂×D₅	1	1	yes	characteristic
144	C₄×D₁₂	—	5	4	no	—
145	C₄×D₁₂	—	10	2	no	—
146	#835	C₂×D₅	1	4	yes	complemented
147	#809	—	5	4	no	—
148	#807	—	5	4	no	—
149	#803	—	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	—	6	1	no	—
157	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
158	C₂²×Dic₅	—	2	1	no	—
159	C₂²×Dic₅	#67	1	1	yes	characteristic
160	C₂²×Dic₅	#67	1	1	yes	characteristic
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	C₂×C₅×C₈	—	3	2	no	—
168	C₂×C₅×C₈	—	6	2	no	—
169	C₅×C₄⋊C₄	—	3	2	no	—
170	C₅×C₄⋊C₄	—	6	1	no	—
171	#688	—	3	16	no	—
172	#685	—	6	4	no	—
173	C₄⋊Dic₅	—	2	1	no	—
174	C₄⋊Dic₅	—	2	4	no	—
175	C₄⋊Dic₅	C₂²×D₃	1	2	yes	—
176	C₄×Dic₅	—	2	4	no	—
177	C₄×Dic₅	#67	1	2	yes	—
178	C₄×Dic₅	C₂²×D₃	1	2	yes	—
179	C₂×#168	—	3	4	no	—
180	C₂×#168	—	3	2	no	—
181	C₂²×SD₁₆	—	15	1	no	—
182	C₂×C₄×Q₈	—	5	1	no	—
183	C₂×C₄×D₄	—	15	1	no	—
184	#440	—	15	8	no	—
185	C₂×#107	—	15	1	no	—
186	C₂×#103	—	3	1	no	—
187	C₂×#102	—	15	1	no	—
188	C₂×#97	—	15	1	no	—
189	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
190	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	2	yes	—
191	C₂²×C₃×C₅	#137	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	C₄×D₄	1	2	yes	—
199	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
200	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
201	C₃×Dic₅	—	2	2	no	—
202	C₃×Dic₅	—	2	2	no	—
203	C₃×Dic₅	—	4	2	no	—
204	C₅×Dic₃	—	4	2	no	—
205	C₂³×D₃	—	10	1	no	—
206	C₂×C₃×Q₈	—	2	1	no	—
207	C₂×C₃×Q₈	—	2	2	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	—	5	1	no	—
212	C₂²×C₃×C₄	—	5	1	no	—
213	C₂²×C₃×C₄	—	10	1	no	—
214	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
215	C₂²×Dic₃	—	2	1	no	—
216	C₂×D₁₂	—	5	4	no	—
217	C₂×D₁₂	—	5	2	no	—
218	C₂×D₁₂	—	10	1	no	—
219	C₂×D₁₂	—	10	2	no	—
220	C₂×C₄×D₃	—	10	4	no	—
221	C₂×C₄×D₃	—	20	4	no	—
222	C₃×C₄⋊C₄	—	5	2	no	—
223	C₃×C₄⋊C₄	—	10	4	no	—
224	C₃×C₄⋊C₄	—	10	1	no	—
225	C₃×C₄²	—	5	2	no	—
226	C₃×C₄²	—	5	2	no	—
227	C₃×C₄²	—	10	4	no	—
228	#215	—	5	16	no	—
229	(C₂×D₃)⋊C₄	—	10	4	no	—
230	C₄⋊Dic₃	—	2	1	no	—
231	C₄⋊Dic₃	C₂²×D₅	1	2	yes	—
232	C₂×C₃⋊C₈	—	2	2	no	—
233	C₂×C₃⋊C₈	—	5	4	no	—
234	C₂×C₃⋊C₈	—	5	2	no	—
235	C₂×C₃⋊C₈	C₂²×D₅	1	2	yes	—
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	—	6	2	no	—
247	C₂×C₄×C₅	—	12	2	no	—
248	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
249	C₂×C₄×C₅	#235	1	2	yes	—
250	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
251	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
252	C₂×Dic₅	—	2	2	no	—
253	C₂×Dic₅	—	2	2	no	—
254	C₂×Dic₅	—	2	2	no	—
255	C₂×Dic₅	—	4	2	no	—
256	C₂×Dic₅	C₂×#67	1	2	yes	—
257	C₂×Dic₅	C₂×#67	1	2	yes	—
258	D₂₀	—	3	4	no	—
259	D₂₀	—	6	4	no	—
260	D₂₀	—	6	2	no	—
261	C₄×D₅	—	12	8	no	—
262	C₅×C₈	—	6	2	no	—
263	#168	—	3	4	no	—
264	C₂²×Q₈	D₃×D₅	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	—	3	1	no	—
270	C₂²×C₈	—	15	1	no	—
271	C₄×Q₈	—	5	4	no	—
272	C₄×Q₈	—	10	2	no	—
273	C₄×D₄	—	15	4	no	—
274	C₄×D₄	—	30	2	no	—
275	C₂×C₄⋊C₄	—	3	1	no	—
276	C₂×C₄⋊C₄	—	5	1	no	—
277	C₂×C₄⋊C₄	—	10	1	no	—
278	C₂×C₂²⋊C₄	—	30	1	no	—
279	C₂×C₄²	—	5	1	no	—
280	C₂×C₄²	—	10	1	no	—
281	#107	—	15	4	no	—
282	#103	—	3	4	no	—
283	#102	—	15	4	no	—
284	#97	—	15	4	no	—
285	C₂×C₃×C₅	#440	1	4	yes	complemented
286	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
287	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
288	C₂×C₃×C₅	C₂×#137	1	1	yes	characteristic
289	D₁₅	—	4	4	no	—
290	C₂³×C₃	D₄×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	4	no	—
300	C₂×C₃×C₄	—	5	2	no	—
301	C₂×C₃×C₄	—	5	2	no	—
302	C₂×C₃×C₄	—	10	2	no	—
303	C₂×C₃×C₄	—	10	2	no	—
304	C₂×C₃×C₄	—	10	2	no	—
305	C₂×C₃×C₄	—	20	2	no	—
306	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
307	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
308	C₂×C₃×C₄	#711	1	2	yes	—
309	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
310	C₂×Dic₃	—	2	2	no	—
311	C₂×Dic₃	—	4	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	—	2	2	no	—
317	C₃⋊C₈	—	5	4	no	—
318	C₂²×C₅	C₄×#67	1	2	yes	—
319	C₂²×C₅	#942	1	2	yes	—
320	C₂²×C₅	#949	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	—	12	2	no	—
328	C₄×C₅	C₄×#67	1	2	yes	—
329	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
330	C₄×C₅	C₂×#235	1	1	yes	characteristic
331	Dic₅	—	2	2	no	—
332	Dic₅	—	2	2	no	—
333	Dic₅	—	4	2	no	—
334	C₂⁴	—	30	1	no	—
335	C₂×Q₈	—	2	2	no	—
336	C₂×Q₈	—	2	1	no	—
337	C₂×Q₈	#1200	1	4	yes	complemented
338	C₂×Q₈	C₂×D₃×D₅	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	—	5	1	no	—
345	C₂²×C₄	—	5	1	no	—
346	C₂²×C₄	—	6	1	no	—
347	C₂²×C₄	—	10	1	no	—
348	C₂²×C₄	—	30	4	no	—
349	C₂²×C₄	—	60	4	no	—
350	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
351	SD₁₆	—	15	16	no	—
352	C₂×C₈	—	3	2	no	—
353	C₂×C₈	—	6	2	no	—
354	C₂×C₈	—	15	4	no	—
355	C₂×C₈	—	15	2	no	—
356	C₄⋊C₄	—	3	2	no	—
357	C₄⋊C₄	—	5	2	no	—
358	C₄⋊C₄	—	6	1	no	—
359	C₄⋊C₄	—	10	4	no	—
360	C₄⋊C₄	—	10	1	no	—
361	C₂²⋊C₄	—	30	4	no	—
362	C₄²	—	5	2	no	—
363	C₄²	—	5	2	no	—
364	C₄²	—	10	4	no	—
365	C₃×C₅	C₂×#440	1	1	yes	characteristic, complemented, Hall
366	C₂²×C₃	#4027	1	2	yes	—
367	C₂²×C₃	#4060	1	2	yes	—
368	C₂²×C₃	#4064	1	2	yes	—
369	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
370	C₂×D₃	—	10	4	no	—
371	C₂×D₃	—	20	2	no	—
372	C₂×D₃	—	20	2	no	—
373	C₂×D₃	—	20	8	no	—
374	C₃×C₄	—	2	4	no	—
375	C₃×C₄	—	10	2	no	—
376	C₃×C₄	—	10	2	no	—
377	C₃×C₄	—	20	2	no	—
378	C₃×C₄	#4027	1	2	yes	—
379	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
380	C₃×C₄	C₂×#711	1	1	yes	characteristic
381	Dic₃	—	4	2	no	—
382	C₂×C₅	#5026	1	4	yes	complemented
383	C₂×C₅	C₂×C₄×#67	1	1	yes	characteristic
384	C₂×C₅	C₂×#942	1	1	yes	characteristic
385	C₂×C₅	C₂×#949	1	1	yes	characteristic
386	D₅	—	12	4	no	—
387	C₂³	—	30	2	no	—
388	C₂³	—	30	4	no	—
389	C₂³	—	60	2	no	—
390	C₂³	—	60	2	no	—
391	C₂³	D₅×#67	1	1	yes	characteristic
392	Q₈	—	2	2	no	—
393	Q₈	—	2	4	no	—
394	Q₈	C₂×#1200	1	4	yes	complemented
395	D₄	—	15	4	no	—
396	D₄	—	30	2	no	—
397	D₄	—	30	4	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	5	2	no	—
401	C₂×C₄	—	5	2	no	—
402	C₂×C₄	—	6	2	no	—
403	C₂×C₄	—	10	2	no	—
404	C₂×C₄	—	10	2	no	—
405	C₂×C₄	—	10	2	no	—
406	C₂×C₄	—	12	2	no	—
407	C₂×C₄	—	20	2	no	—
408	C₂×C₄	—	60	8	no	—
409	C₂×C₄	#6782	1	2	yes	—
410	C₂×C₄	C₂×#1200	1	2	yes	—
411	C₂×C₄	D₅×#67	1	1	yes	characteristic
412	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
413	C₈	—	6	2	no	—
414	C₈	—	15	4	no	—
415	C₂×C₃	#65106	1	4	yes	complemented
416	C₂×C₃	C₂×#4027	1	1	yes	characteristic
417	C₂×C₃	C₂×#4060	1	1	yes	characteristic
418	C₂×C₃	C₂×#4064	1	1	yes	characteristic
419	D₃	—	20	4	no	—
420	C₅	C₂×#5026	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	#91502	1	2	yes	—
426	C₂²	#91515	1	2	yes	—
427	C₂²	#91552	1	2	yes	—
428	C₂²	C₂×D₅×#67	1	1	yes	characteristic
429	C₄	—	2	4	no	—
430	C₄	—	10	2	no	—
431	C₄	—	10	2	no	—
432	C₄	—	12	2	no	—
433	C₄	—	20	2	no	—
434	C₄	#91552	1	2	yes	—
435	C₄	C₂×#6782	1	1	yes	characteristic
436	C₄	C₂²×#1200	1	1	yes	characteristic
437	C₃	C₂×#65106	1	1	yes	characteristic, complemented, Sylow
438	C₂	—	60	4	no	—
439	C₂	#11749225	1	4	yes	direct product factor
440	C₂	C₂×#91502	1	1	yes	characteristic
441	C₂	C₂×#91515	1	1	yes	characteristic
442	C₂	C₂×#91552	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₅×#67
commutator	C₃×C₄×C₅	C₂³×C₄
Frattini	C₂×C₄	C₂²×D₃×D₅
Fitting	C₂²×C₃×C₅×Q₈	C₂²
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂²×D₆₀	C₂²
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₂²×Q₈	D₃×D₅
hypocenter	C₃×C₅	C₂×#440
LCS	G ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×Q₈

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×Q₈×Dic₅	C₂	semidirect
4. C₂×C₅×#835	C₂	semidirect
5. #11749225	C₂	direct (N × H)
6. C₂×#90989	C₂	semidirect
8. C₂×#90952	C₂	semidirect
13. C₂×#6717	C₄	semidirect
19. C₃×Q₈×Dic₅	C₂²	semidirect
27. C₅×#835	C₂²	semidirect
28. #90989	C₂²	semidirect
30. #90952	C₂²	semidirect
32. C₂×Q₈×Dic₅	D₃	semidirect
43. C₂×C₃×C₅×Q₈	C₂×C₄	semidirect
57. #6717	C₂×C₄	semidirect
58. C₂×C₃⋊#168	C₂×C₄	semidirect
74. C₂×#835	D₅	semidirect
85. Q₈×Dic₅	C₂×D₃	semidirect
108. C₃×C₅×Q₈	C₂²×C₄	semidirect
127. C₃⋊#168	C₂²×C₄	semidirect
146. #835	C₂×D₅	semidirect
153. C₂×C₅×Q₈	C₄×D₃	semidirect
208. C₂×C₃×Q₈	C₄×D₅	semidirect
243. C₅×Q₈	C₂×C₄×D₃	semidirect
285. C₂×C₃×C₅	#440	semidirect
297. C₃×Q₈	C₂×C₄×D₅	semidirect
337. C₂×Q₈	#1200	semidirect
365. C₃×C₅	C₂×#440	semidirect
382. C₂×C₅	#5026	semidirect
394. Q₈	C₂×#1200	semidirect
415. C₂×C₃	#65106	semidirect
420. C₅	C₂×#5026	semidirect
437. C₃	C₂×#65106	semidirect
439. C₂	#11749225	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×#6717	2
C₂×C₃×Q₈×Dic₅	2
C₂×#91418	2
C₂×C₅×#835	2
#11749225	2
C₂×#90989	2
C₂×#90968	2
C₂×#90952	2
C₂×#65106	3
C₂×#5026	5

Subgroups — C2×#11749225 #14416378

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11749225 #14416378