Subgroups — C₂×#11749331 #14437765

Order 1920.

824 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	C₂×C₃×#4093	C₂	1	1	yes	maximal, characteristic
2	C₂×#91388	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#91119	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#835	C₂	1	1	yes	maximal, characteristic, complemented
5	#11749331	C₂	1	8	yes	maximal, direct product factor
6	C₂×#90965	C₂	1	1	yes	maximal, characteristic
7	C₂×#90964	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₅×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#65089	—	3	1	no	maximal, Hall
10	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
11	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊Dic₁₅	C₂²	1	1	yes	characteristic
13	C₂²×C₃⋊#168	C₂²	1	1	yes	characteristic
14	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
15	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
16	C₃×#4093	—	2	2	no	—
17	C₃×#4093	C₂²	1	4	yes	—
18	C₂×C₃×#685	—	2	1	no	—
19	C₂×C₃×#685	—	2	1	no	—
20	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
21	C₂×Dic₃⋊Dic₅	—	2	1	no	—
22	C₂×#6669	—	2	1	no	—
23	#91388	—	2	2	no	—
24	#91388	C₂²	1	4	yes	complemented
25	#91119	C₂²	1	4	yes	complemented
26	C₅×#835	C₂²	1	4	yes	complemented
27	#90965	C₂²	1	4	yes	—
28	#90964	C₂²	1	4	yes	—
29	Dic₅×C₃⋊C₈	C₂²	1	4	yes	complemented
30	C₂×#5056	—	5	1	no	maximal, Hall
31	C₂×#4093	D₃	1	1	yes	characteristic
32	C₂×#4036	—	3	1	no	—
33	C₂×C₅×#103	—	3	1	no	—
34	C₂×#3967	—	3	1	no	—
35	C₂×#3953	—	3	1	no	—
36	C₂×C₈×Dic₅	—	3	1	no	—
37	C₂×#3941	—	3	1	no	—
38	#65089	—	3	8	no	—
39	C₂³×C₃×D₅	—	2	1	no	—
40	C₂×C₃×C₅×Q₈	—	2	1	no	—
41	C₂×C₃×C₅×Q₈	—	2	2	no	—
42	C₂×C₃×C₅×Q₈	—	2	2	no	—
43	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
44	C₂²×C₃×C₄×C₅	—	2	1	no	—
45	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
46	C₂²×Dic₁₅	—	2	1	no	—
47	C₂²×C₅×Dic₃	—	2	1	no	—
48	C₂²×C₃×Dic₅	D₄	1	1	yes	characteristic
49	C₂²×C₃×Dic₅	D₄	1	1	yes	characteristic
50	C₂×C₃×D₂₀	—	2	2	no	—
51	C₂×C₃×D₂₀	—	2	2	no	—
52	C₂×C₃×D₂₀	—	2	1	no	—
53	C₂×C₃×D₂₀	C₂³	1	2	yes	—
54	C₄⋊Dic₁₅	—	2	1	no	—
55	C₄⋊Dic₁₅	C₂³	1	2	yes	—
56	C₂×C₃⋊#168	—	2	2	no	—
57	C₂×C₃⋊#168	C₂³	1	2	yes	—
58	C₅×C₄⋊Dic₃	—	2	1	no	—
59	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
60	C₂×C₅×C₃⋊C₈	—	2	2	no	—
61	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
62	C₃×#685	—	2	4	no	—
63	C₃×#685	—	2	4	no	—
64	C₃×C₄×Dic₅	D₄	1	2	yes	—
65	C₃×C₄×Dic₅	C₂³	1	2	yes	—
66	Dic₃⋊Dic₅	—	2	4	no	—
67	#6669	—	2	4	no	—
68	C₂×C₃×#124	—	5	1	no	—
69	C₂×#870	—	5	1	no	—
70	C₂×#835	—	5	1	no	—
71	C₂×#835	D₅	1	1	yes	characteristic, complemented
72	C₂×#832	—	5	1	no	—
73	C₂×#832	—	5	1	no	—
74	#5056	—	5	8	no	—
75	C₂×C₄×C₃⋊C₈	—	5	1	no	—
76	C₂²×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
77	C₂²×D₂₀	C₂×D₃	1	1	yes	characteristic
78	C₂²×C₅×C₈	—	3	1	no	—
79	C₂×C₅×C₄⋊C₄	—	3	1	no	—
80	#4093	—	2	2	no	—
81	#4093	C₂×D₃	1	4	yes	—
82	C₂×#685	—	2	1	no	—
83	C₂×#685	—	2	1	no	—
84	C₂×C₄⋊Dic₅	—	3	1	no	—
85	C₂×C₄⋊Dic₅	—	6	1	no	—
86	C₂×#683	—	6	1	no	—
87	C₂×C₄×Dic₅	C₂×D₃	1	1	yes	characteristic
88	C₂²×#168	—	3	1	no	—
89	#4036	—	3	4	no	—
90	#4036	—	6	2	no	—
91	C₅×#103	—	3	4	no	—
92	#3967	—	3	4	no	—
93	#3953	—	3	4	no	—
94	C₈×Dic₅	—	3	4	no	—
95	#3941	—	3	4	no	—
96	C₂×#488	—	15	1	no	Sylow
97	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₃×D₅	—	2	2	no	—
99	C₂²×C₃×D₅	—	4	2	no	—
100	C₂²×C₃×D₅	—	4	2	no	—
101	C₂²×C₃×D₅	—	4	2	no	—
102	C₃×C₅×Q₈	—	2	2	no	—
103	C₃×C₅×Q₈	—	2	2	no	—
104	C₃×C₅×Q₈	—	4	2	no	—
105	C₂×C₃×C₄×C₅	—	2	2	no	—
106	C₂×C₃×C₄×C₅	—	4	2	no	—
107	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
108	C₂×C₃×C₄×C₅	#41	1	2	yes	—
109	C₂×C₃×C₄×C₅	#41	1	2	yes	—
110	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
111	C₂×Dic₁₅	—	2	2	no	—
112	C₂×Dic₁₅	—	4	2	no	—
113	C₂×C₅×Dic₃	—	2	2	no	—
114	C₂×C₅×Dic₃	—	4	2	no	—
115	C₂×C₃×Dic₅	—	2	2	no	—
116	C₂×C₃×Dic₅	—	2	2	no	—
117	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
118	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
119	C₃×D₂₀	—	2	2	no	—
120	C₃×D₂₀	—	2	2	no	—
121	C₃×D₂₀	—	4	2	no	—
122	C₃⋊#168	—	2	2	no	—
123	C₅×C₃⋊C₈	—	2	2	no	—
124	C₂²×C₃×Q₈	C₂×D₅	1	1	yes	characteristic
125	C₂²×C₃×D₄	—	5	1	no	—
126	C₃×#124	—	5	4	no	—
127	C₃×#124	—	10	2	no	—
128	C₂×C₃×C₂²⋊C₄	—	10	1	no	—
129	C₂×C₃×C₂²⋊C₄	—	10	1	no	—
130	C₂×C₃×C₄²	—	5	1	no	—
131	C₂×C₄⋊Dic₃	—	5	1	no	—
132	C₂×C₄⋊Dic₃	C₂×D₅	1	1	yes	characteristic
133	C₂×Dic₃⋊C₄	—	10	1	no	—
134	C₂×Dic₃⋊C₄	—	10	1	no	—
135	C₂²×C₃⋊C₈	—	5	1	no	—
136	C₂²×C₃⋊C₈	C₂×D₅	1	1	yes	characteristic
137	#870	—	5	4	no	—
138	#870	—	10	2	no	—
139	#835	—	5	4	no	—
140	#835	C₂×D₅	1	4	yes	complemented
141	#832	—	5	4	no	—
142	#832	—	5	4	no	—
143	C₄×C₃⋊C₈	—	5	4	no	—
144	C₂³×D₅	—	2	1	no	—
145	C₂×C₅×Q₈	—	2	1	no	—
146	C₂×C₅×Q₈	—	2	2	no	—
147	C₂×C₅×Q₈	—	2	2	no	—
148	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
149	C₂²×C₄×C₅	—	2	1	no	—
150	C₂²×C₄×C₅	—	6	1	no	—
151	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
152	C₂²×Dic₅	—	6	1	no	—
153	C₂²×Dic₅	#67	1	1	yes	characteristic
154	C₂²×Dic₅	#67	1	1	yes	characteristic
155	C₂×D₂₀	—	2	2	no	—
156	C₂×D₂₀	—	2	2	no	—
157	C₂×D₂₀	—	2	1	no	—
158	C₂×D₂₀	C₂²×D₃	1	2	yes	—
159	C₂×C₅×C₈	—	3	2	no	—
160	C₂×C₅×C₈	—	6	2	no	—
161	C₅×C₄⋊C₄	—	3	2	no	—
162	C₅×C₄⋊C₄	—	6	1	no	—
163	#685	—	2	4	no	—
164	#685	—	2	4	no	—
165	C₄⋊Dic₅	—	3	2	no	—
166	C₄⋊Dic₅	—	6	1	no	—
167	C₄⋊Dic₅	—	6	4	no	—
168	#683	—	6	4	no	—
169	C₄×Dic₅	#67	1	2	yes	—
170	C₄×Dic₅	C₂²×D₃	1	2	yes	—
171	C₂×#168	—	3	2	no	—
172	C₂×#168	—	6	2	no	—
173	C₂×#125	—	15	1	no	—
174	C₂×#124	—	5	1	no	—
175	#488	—	15	8	no	—
176	C₂×#103	—	3	1	no	—
177	C₂×#103	—	15	1	no	—
178	C₂×#102	—	15	1	no	—
179	C₂×#102	—	15	1	no	—
180	C₂×C₄×C₈	—	15	1	no	—
181	C₂²×C₃×C₅	#124	1	2	yes	—
182	C₂²×C₃×C₅	#135	1	2	yes	—
183	C₂²×C₃×C₅	#135	1	2	yes	—
184	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
185	C₂×C₃×D₅	—	4	2	no	—
186	C₂×C₃×D₅	—	4	2	no	—
187	C₂×C₃×D₅	—	4	2	no	—
188	C₂×C₃×D₅	—	8	4	no	—
189	C₃×C₄×C₅	—	4	2	no	—
190	C₃×C₄×C₅	#124	1	2	yes	—
191	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
192	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
193	Dic₁₅	—	4	2	no	—
194	C₃×Dic₅	—	2	2	no	—
195	C₃×Dic₅	—	2	2	no	—
196	C₅×Dic₃	—	4	2	no	—
197	C₂⁴×C₃	—	10	1	no	—
198	C₂×C₃×Q₈	—	2	1	no	—
199	C₂×C₃×Q₈	—	2	2	no	—
200	C₂×C₃×Q₈	—	2	2	no	—
201	C₂×C₃×Q₈	C₂²×D₅	1	2	yes	—
202	C₂×C₃×D₄	—	5	2	no	—
203	C₂×C₃×D₄	—	10	2	no	—
204	C₂×C₃×D₄	—	10	1	no	—
205	C₂×C₃×D₄	—	10	2	no	—
206	C₂²×C₃×C₄	—	2	1	no	—
207	C₂²×C₃×C₄	—	5	1	no	—
208	C₂²×C₃×C₄	—	5	1	no	—
209	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
210	C₂²×Dic₃	—	2	1	no	—
211	C₂²×Dic₃	—	10	1	no	—
212	C₃×C₂²⋊C₄	—	10	4	no	—
213	C₃×C₂²⋊C₄	—	10	4	no	—
214	C₃×C₄²	—	5	2	no	—
215	C₃×C₄²	—	5	2	no	—
216	C₄⋊Dic₃	—	2	1	no	—
217	C₄⋊Dic₃	—	5	2	no	—
218	C₄⋊Dic₃	—	10	1	no	—
219	C₄⋊Dic₃	C₂²×D₅	1	2	yes	—
220	Dic₃⋊C₄	—	10	4	no	—
221	Dic₃⋊C₄	—	10	4	no	—
222	C₂×C₃⋊C₈	—	2	2	no	—
223	C₂×C₃⋊C₈	—	5	2	no	—
224	C₂×C₃⋊C₈	—	10	2	no	—
225	C₂×C₃⋊C₈	C₂²×D₅	1	2	yes	—
226	C₂³×C₅	C₂×#67	1	1	yes	characteristic
227	C₂²×D₅	—	2	2	no	—
228	C₂²×D₅	—	4	2	no	—
229	C₂²×D₅	—	4	2	no	—
230	C₂²×D₅	—	4	2	no	—
231	C₅×Q₈	—	2	2	no	—
232	C₅×Q₈	—	2	2	no	—
233	C₅×Q₈	—	4	2	no	—
234	C₂×C₄×C₅	—	2	2	no	—
235	C₂×C₄×C₅	—	4	2	no	—
236	C₂×C₄×C₅	—	6	2	no	—
237	C₂×C₄×C₅	—	12	2	no	—
238	C₂×C₄×C₅	#237	1	2	yes	—
239	C₂×C₄×C₅	#237	1	2	yes	—
240	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
241	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
242	C₂×Dic₅	—	2	2	no	—
243	C₂×Dic₅	—	2	2	no	—
244	C₂×Dic₅	—	6	2	no	—
245	C₂×Dic₅	—	12	2	no	—
246	C₂×Dic₅	C₂×#67	1	2	yes	—
247	C₂×Dic₅	C₂×#67	1	2	yes	—
248	D₂₀	—	2	2	no	—
249	D₂₀	—	2	2	no	—
250	D₂₀	—	4	2	no	—
251	C₅×C₈	—	6	2	no	—
252	#168	—	6	2	no	—
253	C₂²×Q₈	D₃×D₅	1	1	yes	characteristic
254	C₂²×D₄	—	5	1	no	—
255	C₂²×C₈	—	3	1	no	—
256	C₂²×C₈	—	15	1	no	—
257	#125	—	15	4	no	—
258	#125	—	30	2	no	—
259	#124	—	5	4	no	—
260	#124	—	10	2	no	—
261	C₂×C₄⋊C₄	—	3	1	no	—
262	C₂×C₄⋊C₄	—	15	1	no	—
263	C₂×C₄⋊C₄	—	30	1	no	—
264	C₂×C₄⋊C₄	—	30	1	no	—
265	C₂×C₂²⋊C₄	—	10	1	no	—
266	C₂×C₂²⋊C₄	—	10	1	no	—
267	C₂×C₄²	—	5	1	no	—
268	#103	—	3	4	no	—
269	#103	—	15	4	no	—
270	#102	—	15	4	no	—
271	#102	—	15	4	no	—
272	C₄×C₈	—	15	4	no	—
273	C₂×C₃×C₅	#488	1	4	yes	complemented
274	C₂×C₃×C₅	C₂×#124	1	1	yes	characteristic
275	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
276	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
277	C₃×D₅	—	8	2	no	—
278	C₂³×C₃	—	10	2	no	—
279	C₂³×C₃	—	20	2	no	—
280	C₂³×C₃	—	20	2	no	—
281	C₂³×C₃	—	20	2	no	—
282	C₂³×C₃	D₄×D₅	1	1	yes	characteristic
283	C₃×Q₈	—	2	2	no	—
284	C₃×Q₈	—	2	2	no	—
285	C₃×Q₈	—	4	2	no	—
286	C₃×D₄	—	10	2	no	—
287	C₃×D₄	—	10	2	no	—
288	C₃×D₄	—	20	2	no	—
289	C₂×C₃×C₄	—	2	2	no	—
290	C₂×C₃×C₄	—	4	2	no	—
291	C₂×C₃×C₄	—	5	2	no	—
292	C₂×C₃×C₄	—	5	2	no	—
293	C₂×C₃×C₄	—	10	2	no	—
294	C₂×C₃×C₄	—	10	2	no	—
295	C₂×C₃×C₄	#709	1	2	yes	—
296	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
297	C₂×C₃×C₄	#711	1	2	yes	—
298	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
299	C₂×Dic₃	—	2	2	no	—
300	C₂×Dic₃	—	4	2	no	—
301	C₂×Dic₃	—	10	2	no	—
302	C₂×Dic₃	—	20	2	no	—
303	C₃⋊C₈	—	2	2	no	—
304	C₃⋊C₈	—	10	2	no	—
305	C₂²×C₅	#936	1	2	yes	—
306	C₂²×C₅	#950	1	2	yes	—
307	C₂²×C₅	#950	1	2	yes	—
308	C₂²×C₅	C₂²×#67	1	1	yes	characteristic
309	C₂×D₅	—	4	2	no	—
310	C₂×D₅	—	4	2	no	—
311	C₂×D₅	—	4	2	no	—
312	C₂×D₅	—	8	4	no	—
313	C₄×C₅	—	4	2	no	—
314	C₄×C₅	—	12	2	no	—
315	C₄×C₅	#936	1	2	yes	—
316	C₄×C₅	C₂×#237	1	1	yes	characteristic
317	C₄×C₅	C₂×#237	1	1	yes	characteristic
318	Dic₅	—	2	2	no	—
319	Dic₅	—	2	2	no	—
320	Dic₅	—	12	2	no	—
321	C₂⁴	—	10	1	no	—
322	C₂×Q₈	—	2	1	no	—
323	C₂×Q₈	—	2	2	no	—
324	C₂×Q₈	—	2	2	no	—
325	C₂×Q₈	C₂×D₃×D₅	1	2	yes	—
326	C₂×D₄	—	5	2	no	—
327	C₂×D₄	—	10	2	no	—
328	C₂×D₄	—	10	2	no	—
329	C₂×D₄	—	10	1	no	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	5	1	no	—
332	C₂²×C₄	—	5	1	no	—
333	C₂²×C₄	—	6	1	no	—
334	C₂²×C₄	—	30	1	no	—
335	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
336	C₂×C₈	—	3	2	no	—
337	C₂×C₈	—	6	2	no	—
338	C₂×C₈	—	15	2	no	—
339	C₂×C₈	—	30	2	no	—
340	C₄⋊C₄	—	3	2	no	—
341	C₄⋊C₄	—	6	1	no	—
342	C₄⋊C₄	—	15	2	no	—
343	C₄⋊C₄	—	30	4	no	—
344	C₄⋊C₄	—	30	4	no	—
345	C₄⋊C₄	—	30	1	no	—
346	C₂²⋊C₄	—	10	4	no	—
347	C₂²⋊C₄	—	10	4	no	—
348	C₄²	—	5	2	no	—
349	C₄²	—	5	2	no	—
350	C₃×C₅	C₂×#488	1	1	yes	characteristic, complemented, Hall
351	C₂²×C₃	—	20	2	no	—
352	C₂²×C₃	—	20	2	no	—
353	C₂²×C₃	—	20	2	no	—
354	C₂²×C₃	—	40	4	no	—
355	C₂²×C₃	#4031	1	2	yes	—
356	C₂²×C₃	#4062	1	2	yes	—
357	C₂²×C₃	#4065	1	2	yes	—
358	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
359	C₃×C₄	—	4	2	no	—
360	C₃×C₄	—	10	2	no	—
361	C₃×C₄	—	10	2	no	—
362	C₃×C₄	#4031	1	2	yes	—
363	C₃×C₄	C₂×#709	1	1	yes	characteristic
364	C₃×C₄	C₂×#711	1	1	yes	characteristic
365	Dic₃	—	4	2	no	—
366	Dic₃	—	20	2	no	—
367	C₂×C₅	#5056	1	4	yes	complemented
368	C₂×C₅	C₂×#936	1	1	yes	characteristic
369	C₂×C₅	C₂×#950	1	1	yes	characteristic
370	C₂×C₅	C₂×#950	1	1	yes	characteristic
371	D₅	—	8	2	no	—
372	C₂³	—	10	2	no	—
373	C₂³	—	20	2	no	—
374	C₂³	—	20	2	no	—
375	C₂³	—	20	2	no	—
376	C₂³	D₅×#67	1	1	yes	characteristic
377	Q₈	—	2	2	no	—
378	Q₈	—	2	2	no	—
379	Q₈	—	4	2	no	—
380	D₄	—	10	2	no	—
381	D₄	—	10	2	no	—
382	D₄	—	20	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	5	2	no	—
386	C₂×C₄	—	5	2	no	—
387	C₂×C₄	—	6	2	no	—
388	C₂×C₄	—	10	2	no	—
389	C₂×C₄	—	10	2	no	—
390	C₂×C₄	—	12	2	no	—
391	C₂×C₄	—	30	2	no	—
392	C₂×C₄	—	60	2	no	—
393	C₂×C₄	#6779	1	2	yes	—
394	C₂×C₄	#6780	1	2	yes	—
395	C₂×C₄	D₅×#67	1	1	yes	characteristic
396	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
397	C₈	—	6	2	no	—
398	C₈	—	30	2	no	—
399	C₂×C₃	—	40	2	no	—
400	C₂×C₃	#65089	1	4	yes	complemented
401	C₂×C₃	C₂×#4031	1	1	yes	characteristic
402	C₂×C₃	C₂×#4062	1	1	yes	characteristic
403	C₂×C₃	C₂×#4065	1	1	yes	characteristic
404	C₅	C₂×#5056	1	1	yes	characteristic, complemented, Sylow
405	C₂²	—	20	2	no	—
406	C₂²	—	20	2	no	—
407	C₂²	—	20	2	no	—
408	C₂²	—	40	4	no	—
409	C₂²	#91514	1	2	yes	—
410	C₂²	#91516	1	2	yes	—
411	C₂²	#91534	1	2	yes	—
412	C₂²	C₂×D₅×#67	1	1	yes	characteristic
413	C₄	—	4	2	no	—
414	C₄	—	10	2	no	—
415	C₄	—	10	2	no	—
416	C₄	—	12	2	no	—
417	C₄	—	60	2	no	—
418	C₄	#91534	1	2	yes	—
419	C₄	C₂×#6779	1	1	yes	characteristic
420	C₄	C₂×#6780	1	1	yes	characteristic
421	C₃	C₂×#65089	1	1	yes	characteristic, complemented, Sylow
422	C₂	—	40	2	no	—
423	C₂	#11749331	1	4	yes	direct product factor
424	C₂	C₂×#91514	1	1	yes	characteristic
425	C₂	C₂×#91516	1	1	yes	characteristic
426	C₂	C₂×#91534	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₅×#67
commutator, cosocle	C₂×C₃×C₄×C₅	C₂⁴
Frattini	C₂×C₄	C₂²×D₃×D₅
Fitting	C₂²×C₃×C₅×Q₈	C₂²
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂²×C₃×D₂₀	C₂²
hypercenter	C₂²×Q₈	D₃×D₅
hypocenter	C₃×C₅	C₂×#488
LCS	G ▷ C₂×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×#91388	C₂	semidirect
3. C₂×#91119	C₂	semidirect
4. C₂×C₅×#835	C₂	semidirect
5. #11749331	C₂	direct (N × H)
8. C₂×Dic₅×C₃⋊C₈	C₂	semidirect
24. #91388	C₂²	semidirect
25. #91119	C₂²	semidirect
26. C₅×#835	C₂²	semidirect
29. Dic₅×C₃⋊C₈	C₂²	semidirect
71. C₂×#835	D₅	semidirect
140. #835	C₂×D₅	semidirect
273. C₂×C₃×C₅	#488	semidirect
350. C₃×C₅	C₂×#488	semidirect
367. C₂×C₅	#5056	semidirect
400. C₂×C₃	#65089	semidirect
404. C₅	C₂×#5056	semidirect
421. C₃	C₂×#65089	semidirect
423. C₂	#11749331	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×#4093	2
C₂×#91388	2
C₂×#91119	2
C₂×C₅×#835	2
#11749331	2
C₂×#90965	2
C₂×#90964	2
C₂×Dic₅×C₃⋊C₈	2
C₂×#65089	3
C₂×#5056	5

Subgroups — C2×#11749331 #14437765

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11749331 #14437765