Subgroups — C₂×#11750915 #14431607

Order 1920.

832 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×#91835	C₂	1	1	yes	maximal, characteristic
2	C₂×#91781	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×C₅×#103	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#91119	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#91104	C₂	1	1	yes	maximal, characteristic
6	C₂×#91102	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#91092	C₂	1	1	yes	maximal, characteristic, complemented
8	#11750915	C₂	1	8	yes	maximal, direct product factor
9	C₂×#65103	—	3	1	no	maximal, Hall
10	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
11	C₂²×C₄×D₁₅	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
14	#91835	—	2	2	no	—
15	#91835	C₂²	1	4	yes	—
16	C₂×#6714	—	2	1	no	—
17	C₂×#6714	—	2	1	no	—
18	C₂×C₄⋊Dic₁₅	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊Dic₁₅	C₂²	1	1	yes	characteristic
20	C₂×#6712	—	2	1	no	—
21	C₂×C₄×Dic₁₅	—	2	1	no	—
22	C₂²×C₃⋊#168	C₂²	1	1	yes	characteristic
23	#91781	—	2	2	no	—
24	#91781	C₂²	1	4	yes	—
25	C₃×C₅×#103	C₂²	1	4	yes	complemented
26	#91119	C₂²	1	4	yes	complemented
27	#91104	C₂²	1	4	yes	—
28	#91102	C₂²	1	4	yes	complemented
29	#91092	C₂²	1	4	yes	complemented
30	C₂×#4814	—	5	1	no	maximal, Hall
31	C₂×#4092	—	3	1	no	—
32	C₂×#4038	—	3	1	no	—
33	C₂×C₅×#103	D₃	1	1	yes	characteristic, complemented
34	C₂×#3967	—	3	1	no	—
35	C₂×#3952	—	3	1	no	—
36	C₂×#3950	—	3	1	no	—
37	C₂×#3940	—	3	1	no	—
38	#65103	—	3	8	no	—
39	C₂³×D₁₅	D₄	1	1	yes	characteristic
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	—	2	1	no	—
46	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
47	C₂²×Dic₁₅	—	2	1	no	—
48	C₂²×Dic₁₅	—	2	1	no	—
49	C₂²×Dic₁₅	D₄	1	1	yes	characteristic
50	C₂×C₄×D₁₅	—	2	2	no	—
51	C₂×C₄×D₁₅	—	2	2	no	—
52	C₂×C₄×D₁₅	D₄	1	2	yes	—
53	C₂×C₄×D₁₅	C₂³	1	2	yes	—
54	C₂×C₃×C₅×C₈	—	2	2	no	—
55	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
56	C₃×C₅×C₄⋊C₄	—	2	1	no	—
57	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
58	#6714	—	2	4	no	—
59	#6714	—	2	4	no	—
60	C₄⋊Dic₁₅	—	2	1	no	—
61	C₄⋊Dic₁₅	—	2	1	no	—
62	C₄⋊Dic₁₅	C₂³	1	2	yes	—
63	C₄⋊Dic₁₅	C₂³	1	2	yes	—
64	#6712	—	2	4	no	—
65	C₄×Dic₁₅	—	2	4	no	—
66	C₂×C₃⋊#168	—	2	2	no	—
67	C₂×C₃⋊#168	C₂³	1	2	yes	—
68	C₂×#946	—	5	1	no	—
69	C₂×#892	—	5	1	no	—
70	C₂×C₃×#103	D₅	1	1	yes	characteristic, complemented
71	C₂×#835	—	5	1	no	—
72	C₂×(C₂×D₃)⋊C₈	—	5	1	no	—
73	C₂×#818	—	5	1	no	—
74	C₂×#808	—	5	1	no	—
75	#4814	—	5	8	no	—
76	C₂²×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
77	C₂²×C₄×D₅	—	3	1	no	—
78	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
79	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
80	#4092	—	3	4	no	—
81	#4092	—	6	2	no	—
82	C₂×#685	—	6	1	no	—
83	C₂×#685	—	6	1	no	—
84	C₂×C₄⋊Dic₅	—	3	1	no	—
85	C₂×C₄⋊Dic₅	—	3	1	no	—
86	C₂×#683	—	6	1	no	—
87	C₂×C₄×Dic₅	—	6	1	no	—
88	C₂²×#168	—	3	1	no	—
89	#4038	—	3	4	no	—
90	#4038	—	6	2	no	—
91	C₅×#103	C₂×D₃	1	4	yes	complemented
92	#3967	—	3	4	no	—
93	#3952	—	3	4	no	—
94	#3950	—	3	4	no	—
95	#3940	—	3	4	no	—
96	C₂×#485	—	15	1	no	Sylow
97	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
98	C₂²×D₁₅	—	2	2	no	—
99	C₂²×D₁₅	—	2	2	no	—
100	C₂²×D₁₅	—	2	2	no	—
101	C₂²×D₁₅	C₂×D₄	1	2	yes	—
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	—	2	2	no	—
107	C₂×C₃×C₄×C₅	—	4	2	no	—
108	C₂×C₃×C₄×C₅	—	4	2	no	—
109	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
110	C₂×C₃×C₄×C₅	#41	1	2	yes	—
111	C₂×C₃×C₄×C₅	#41	1	2	yes	—
112	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
113	C₂×Dic₁₅	—	2	2	no	—
114	C₂×Dic₁₅	—	2	2	no	—
115	C₂×Dic₁₅	—	2	2	no	—
116	C₂×Dic₁₅	—	4	2	no	—
117	C₂×Dic₁₅	—	4	2	no	—
118	C₂×Dic₁₅	C₂×D₄	1	2	yes	—
119	C₄×D₁₅	—	2	4	no	—
120	C₄×D₁₅	—	2	2	no	—
121	C₄×D₁₅	—	2	2	no	—
122	C₃×C₅×C₈	—	2	2	no	—
123	C₃⋊#168	—	2	2	no	—
124	C₂²×C₃×Q₈	C₂×D₅	1	1	yes	characteristic
125	C₂²×C₄×D₃	—	5	1	no	—
126	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
127	C₂×C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
128	#946	—	5	4	no	—
129	#946	—	10	2	no	—
130	C₂×(C₂×D₃)⋊C₄	—	10	1	no	—
131	C₂×(C₂×D₃)⋊C₄	—	10	1	no	—
132	C₂×C₄⋊Dic₃	—	5	1	no	—
133	C₂×C₄⋊Dic₃	—	5	1	no	—
134	C₂×Dic₃⋊C₄	—	10	1	no	—
135	C₂×C₄×Dic₃	—	10	1	no	—
136	C₂²×C₃⋊C₈	—	5	1	no	—
137	#892	—	5	4	no	—
138	#892	—	10	2	no	—
139	C₃×#103	C₂×D₅	1	4	yes	complemented
140	#835	—	5	4	no	—
141	(C₂×D₃)⋊C₈	—	5	4	no	—
142	#818	—	5	4	no	—
143	#808	—	5	4	no	—
144	C₂³×D₅	—	3	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	—	2	1	no	—
151	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
152	C₂²×Dic₅	—	3	1	no	—
153	C₂²×Dic₅	—	6	1	no	—
154	C₂²×Dic₅	—	6	1	no	—
155	C₂×C₄×D₅	—	3	2	no	—
156	C₂×C₄×D₅	—	3	2	no	—
157	C₂×C₄×D₅	—	6	2	no	—
158	C₂×C₄×D₅	—	6	2	no	—
159	C₂×C₅×C₈	—	2	2	no	—
160	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
161	C₅×C₄⋊C₄	—	2	1	no	—
162	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
163	#685	—	6	4	no	—
164	#685	—	6	4	no	—
165	C₄⋊Dic₅	—	3	2	no	—
166	C₄⋊Dic₅	—	3	2	no	—
167	C₄⋊Dic₅	—	6	1	no	—
168	C₄⋊Dic₅	—	6	1	no	—
169	#683	—	6	4	no	—
170	C₄×Dic₅	—	6	4	no	—
171	C₂×#168	—	3	2	no	—
172	C₂×#168	—	6	2	no	—
173	C₂×C₂²⋊Q₈	—	15	1	no	—
174	C₂×#117	—	15	1	no	—
175	#485	—	15	8	no	—
176	C₂×#107	—	15	1	no	—
177	C₂×#106	—	15	1	no	—
178	C₂×#103	—	15	1	no	—
179	C₂×#103	D₁₅	1	1	yes	characteristic, complemented
180	C₂×C₂²⋊C₈	—	15	1	no	—
181	C₂²×C₃×C₅	#123	1	2	yes	—
182	C₂²×C₃×C₅	#135	1	2	yes	—
183	C₂²×C₃×C₅	#137	1	2	yes	—
184	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
185	C₂×D₁₅	—	2	2	no	—
186	C₂×D₁₅	—	2	2	no	—
187	C₂×D₁₅	—	2	2	no	—
188	C₂×D₁₅	—	4	4	no	—
189	C₃×C₄×C₅	—	4	2	no	—
190	C₃×C₄×C₅	—	4	2	no	—
191	C₃×C₄×C₅	#123	1	2	yes	—
192	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
193	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
194	Dic₁₅	—	2	2	no	—
195	Dic₁₅	—	4	2	no	—
196	Dic₁₅	—	4	2	no	—
197	C₂³×D₃	—	5	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	C₂²×C₃×C₄	—	2	1	no	—
203	C₂²×C₃×C₄	—	2	1	no	—
204	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
205	C₂²×Dic₃	—	5	1	no	—
206	C₂²×Dic₃	—	10	1	no	—
207	C₂²×Dic₃	—	10	1	no	—
208	C₂×C₄×D₃	—	5	2	no	—
209	C₂×C₄×D₃	—	5	2	no	—
210	C₂×C₄×D₃	—	10	2	no	—
211	C₂×C₄×D₃	—	10	2	no	—
212	C₂×C₃×C₈	—	2	2	no	—
213	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
214	C₃×C₄⋊C₄	—	2	1	no	—
215	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
216	(C₂×D₃)⋊C₄	—	10	4	no	—
217	(C₂×D₃)⋊C₄	—	10	4	no	—
218	C₄⋊Dic₃	—	5	2	no	—
219	C₄⋊Dic₃	—	5	2	no	—
220	C₄⋊Dic₃	—	10	1	no	—
221	C₄⋊Dic₃	—	10	1	no	—
222	Dic₃⋊C₄	—	10	4	no	—
223	C₄×Dic₃	—	10	4	no	—
224	C₂×C₃⋊C₈	—	5	2	no	—
225	C₂×C₃⋊C₈	—	10	2	no	—
226	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
227	C₂²×D₅	—	3	2	no	—
228	C₂²×D₅	—	6	2	no	—
229	C₂²×D₅	—	6	2	no	—
230	C₂²×D₅	—	6	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	—	2	2	no	—
236	C₂×C₄×C₅	—	4	2	no	—
237	C₂×C₄×C₅	—	4	2	no	—
238	C₂×C₄×C₅	#235	1	2	yes	—
239	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
240	C₂×C₄×C₅	#237	1	2	yes	—
241	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
242	C₂×Dic₅	—	3	2	no	—
243	C₂×Dic₅	—	6	2	no	—
244	C₂×Dic₅	—	6	2	no	—
245	C₂×Dic₅	—	6	2	no	—
246	C₂×Dic₅	—	12	2	no	—
247	C₂×Dic₅	—	12	2	no	—
248	C₄×D₅	—	6	4	no	—
249	C₄×D₅	—	6	2	no	—
250	C₄×D₅	—	6	2	no	—
251	C₅×C₈	—	2	2	no	—
252	#168	—	6	2	no	—
253	C₂²×Q₈	C₂×D₁₅	1	1	yes	characteristic
254	C₂³×C₄	—	15	1	no	—
255	C₂²×C₈	—	15	1	no	—
256	C₂²×C₈	C₂×D₁₅	1	1	yes	characteristic
257	C₂²⋊Q₈	—	15	4	no	—
258	C₂²⋊Q₈	—	30	2	no	—
259	#117	—	15	4	no	—
260	#117	—	30	2	no	—
261	C₂×C₄⋊C₄	—	15	1	no	—
262	C₂×C₄⋊C₄	—	15	1	no	—
263	C₂×C₄⋊C₄	—	30	1	no	—
264	C₂×C₄⋊C₄	C₂×D₁₅	1	1	yes	characteristic
265	C₂×C₂²⋊C₄	—	30	1	no	—
266	C₂×C₂²⋊C₄	—	30	1	no	—
267	C₂×C₄²	—	30	1	no	—
268	#107	—	15	4	no	—
269	#106	—	15	4	no	—
270	#103	—	15	4	no	—
271	#103	C₂×D₁₅	1	4	yes	complemented
272	C₂²⋊C₈	—	15	4	no	—
273	C₂×C₃×C₅	#485	1	4	yes	complemented
274	C₂×C₃×C₅	C₂×#123	1	1	yes	characteristic
275	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
276	C₂×C₃×C₅	C₂×#137	1	1	yes	characteristic
277	D₁₅	—	4	2	no	—
278	C₂³×C₃	D₄×D₅	1	1	yes	characteristic
279	C₂²×D₃	—	5	2	no	—
280	C₂²×D₃	—	10	2	no	—
281	C₂²×D₃	—	10	2	no	—
282	C₂²×D₃	—	10	2	no	—
283	C₃×Q₈	—	2	2	no	—
284	C₃×Q₈	—	2	2	no	—
285	C₃×Q₈	—	4	2	no	—
286	C₂×C₃×C₄	—	2	2	no	—
287	C₂×C₃×C₄	—	2	2	no	—
288	C₂×C₃×C₄	—	4	2	no	—
289	C₂×C₃×C₄	—	4	2	no	—
290	C₂×C₃×C₄	#709	1	2	yes	—
291	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
292	C₂×C₃×C₄	#711	1	2	yes	—
293	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
294	C₂×Dic₃	—	5	2	no	—
295	C₂×Dic₃	—	10	2	no	—
296	C₂×Dic₃	—	10	2	no	—
297	C₂×Dic₃	—	10	2	no	—
298	C₂×Dic₃	—	20	2	no	—
299	C₂×Dic₃	—	20	2	no	—
300	C₄×D₃	—	10	2	no	—
301	C₄×D₃	—	10	2	no	—
302	C₄×D₃	—	10	4	no	—
303	C₃×C₈	—	2	2	no	—
304	C₃⋊C₈	—	10	2	no	—
305	C₂²×C₅	#883	1	2	yes	—
306	C₂²×C₅	#915	1	2	yes	—
307	C₂²×C₅	#919	1	2	yes	—
308	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
309	C₂×D₅	—	6	2	no	—
310	C₂×D₅	—	6	2	no	—
311	C₂×D₅	—	6	2	no	—
312	C₂×D₅	—	12	4	no	—
313	C₄×C₅	—	4	2	no	—
314	C₄×C₅	—	4	2	no	—
315	C₄×C₅	#883	1	2	yes	—
316	C₄×C₅	C₂×#235	1	1	yes	characteristic
317	C₄×C₅	C₂×#237	1	1	yes	characteristic
318	Dic₅	—	6	2	no	—
319	Dic₅	—	12	2	no	—
320	Dic₅	—	12	2	no	—
321	C₂⁴	—	15	1	no	—
322	C₂×Q₈	—	2	1	no	—
323	C₂×Q₈	—	2	2	no	—
324	C₂×Q₈	—	2	2	no	—
325	C₂×Q₈	C₂²×D₁₅	1	2	yes	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	15	1	no	—
329	C₂²×C₄	—	15	2	no	—
330	C₂²×C₄	—	15	2	no	—
331	C₂²×C₄	—	30	2	no	—
332	C₂²×C₄	—	30	2	no	—
333	C₂²×C₄	—	30	1	no	—
334	C₂²×C₄	—	30	1	no	—
335	C₂²×C₄	C₂²×D₁₅	1	1	yes	characteristic
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	15	2	no	—
338	C₂×C₈	—	30	2	no	—
339	C₂×C₈	C₂²×D₁₅	1	2	yes	—
340	C₄⋊C₄	—	2	1	no	—
341	C₄⋊C₄	—	15	2	no	—
342	C₄⋊C₄	—	15	2	no	—
343	C₄⋊C₄	—	30	4	no	—
344	C₄⋊C₄	—	30	1	no	—
345	C₄⋊C₄	—	30	1	no	—
346	C₄⋊C₄	C₂²×D₁₅	1	2	yes	—
347	C₂²⋊C₄	—	30	4	no	—
348	C₂²⋊C₄	—	30	4	no	—
349	C₄²	—	30	4	no	—
350	C₃×C₅	C₂×#485	1	1	yes	characteristic, complemented, Hall
351	C₂²×C₃	#4029	1	2	yes	—
352	C₂²×C₃	#4061	1	2	yes	—
353	C₂²×C₃	#4065	1	2	yes	—
354	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
355	C₂×D₃	—	10	2	no	—
356	C₂×D₃	—	10	2	no	—
357	C₂×D₃	—	10	2	no	—
358	C₂×D₃	—	20	4	no	—
359	C₃×C₄	—	4	2	no	—
360	C₃×C₄	—	4	2	no	—
361	C₃×C₄	#4029	1	2	yes	—
362	C₃×C₄	C₂×#709	1	1	yes	characteristic
363	C₃×C₄	C₂×#711	1	1	yes	characteristic
364	Dic₃	—	10	2	no	—
365	Dic₃	—	20	2	no	—
366	Dic₃	—	20	2	no	—
367	C₂×C₅	#4814	1	4	yes	complemented
368	C₂×C₅	C₂×#883	1	1	yes	characteristic
369	C₂×C₅	C₂×#915	1	1	yes	characteristic
370	C₂×C₅	C₂×#919	1	1	yes	characteristic
371	D₅	—	12	2	no	—
372	C₂³	—	15	2	no	—
373	C₂³	—	30	2	no	—
374	C₂³	—	30	2	no	—
375	C₂³	—	30	2	no	—
376	C₂³	D₄×D₁₅	1	1	yes	characteristic
377	Q₈	—	2	2	no	—
378	Q₈	—	2	2	no	—
379	Q₈	—	4	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	15	2	no	—
385	C₂×C₄	—	30	2	no	—
386	C₂×C₄	—	30	4	no	—
387	C₂×C₄	—	30	2	no	—
388	C₂×C₄	—	30	2	no	—
389	C₂×C₄	—	30	2	no	—
390	C₂×C₄	—	30	2	no	—
391	C₂×C₄	—	60	2	no	—
392	C₂×C₄	—	60	2	no	—
393	C₂×C₄	#6817	1	2	yes	—
394	C₂×C₄	D₄×D₁₅	1	1	yes	characteristic
395	C₂×C₄	#6819	1	2	yes	—
396	C₂×C₄	C₂³×D₁₅	1	1	yes	characteristic
397	C₈	—	2	2	no	—
398	C₈	—	30	2	no	—
399	C₂×C₃	#65103	1	4	yes	complemented
400	C₂×C₃	C₂×#4029	1	1	yes	characteristic
401	C₂×C₃	C₂×#4061	1	1	yes	characteristic
402	C₂×C₃	C₂×#4065	1	1	yes	characteristic
403	D₃	—	20	2	no	—
404	C₅	C₂×#4814	1	1	yes	characteristic, complemented, Sylow
405	C₂²	—	30	2	no	—
406	C₂²	—	30	2	no	—
407	C₂²	—	30	2	no	—
408	C₂²	—	60	4	no	—
409	C₂²	#91772	1	2	yes	—
410	C₂²	#91804	1	2	yes	—
411	C₂²	#91808	1	2	yes	—
412	C₂²	C₂×D₄×D₁₅	1	1	yes	characteristic
413	C₄	—	4	2	no	—
414	C₄	—	4	2	no	—
415	C₄	—	30	2	no	—
416	C₄	—	60	2	no	—
417	C₄	—	60	2	no	—
418	C₄	#91772	1	2	yes	—
419	C₄	C₂×#6817	1	1	yes	characteristic
420	C₄	C₂×#6819	1	1	yes	characteristic
421	C₃	C₂×#65103	1	1	yes	characteristic, complemented, Sylow
422	C₂	—	60	2	no	—
423	C₂	#11750915	1	4	yes	direct product factor
424	C₂	C₂×#91772	1	1	yes	characteristic
425	C₂	C₂×#91804	1	1	yes	characteristic
426	C₂	C₂×#91808	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₄×D₁₅
commutator, cosocle	C₂×C₃×C₄×C₅	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₅
Fitting	C₂×C₃×C₅×#103	C₂
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂³×D₁₅	D₄
hypercenter	C₂×#103	D₁₅
hypocenter	C₃×C₅	C₂×#485
LCS	G ▷ C₂×C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#103

Complements

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

N	H ≅ G/N	type
3. C₂×C₃×C₅×#103	C₂	semidirect
4. C₂×#91119	C₂	semidirect
6. C₂×#91102	C₂	semidirect
7. C₂×#91092	C₂	semidirect
8. #11750915	C₂	direct (N × H)
25. C₃×C₅×#103	C₂²	semidirect
26. #91119	C₂²	semidirect
28. #91102	C₂²	semidirect
29. #91092	C₂²	semidirect
33. C₂×C₅×#103	D₃	semidirect
70. C₂×C₃×#103	D₅	semidirect
91. C₅×#103	C₂×D₃	semidirect
139. C₃×#103	C₂×D₅	semidirect
179. C₂×#103	D₁₅	semidirect
271. #103	C₂×D₁₅	semidirect
273. C₂×C₃×C₅	#485	semidirect
350. C₃×C₅	C₂×#485	semidirect
367. C₂×C₅	#4814	semidirect
399. C₂×C₃	#65103	semidirect
404. C₅	C₂×#4814	semidirect
421. C₃	C₂×#65103	semidirect
423. C₂	#11750915	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×#91835	2
C₂×#91781	2
C₂×C₃×C₅×#103	2
C₂×#91119	2
C₂×#91104	2
C₂×#91102	2
C₂×#91092	2
#11750915	2
C₂×#65103	3
C₂×#4814	5

Subgroups — C2×#11750915 #14431607

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11750915 #14431607