Subgroups — C₂×C₁₀₁×#1900 #38803138

Order 25856.

2198 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×M₁₆×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#121×C₁₀₁	C₂	1	1	yes	maximal, characteristic
3	C₂²×#100×C₁₀₁	C₂	1	2	yes	maximal, complemented
4	C₂×#407×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₀₁×#1900	C₂	1	8	yes	maximal, direct product factor
6	C₂×#343×C₁₀₁	C₂	1	2	yes	maximal, complemented
7	C₂³×D₄×C₁₀₁	C₄	1	2	yes	—
8	C₂³×D₄×C₁₀₁	C₂²	1	1	yes	characteristic
9	C₂⁴×C₄×C₁₀₁	C₂²	1	1	yes	characteristic
10	C₂²×M₁₆×C₁₀₁	—	2	1	no	—
11	C₂²×M₁₆×C₁₀₁	—	2	2	no	—
12	C₂²×M₁₆×C₁₀₁	—	2	8	no	—
13	C₂²×M₁₆×C₁₀₁	C₂²	1	2	yes	—
14	C₂²×M₁₆×C₁₀₁	C₂²	1	2	yes	—
15	C₂²×M₁₆×C₁₀₁	C₂²	1	4	yes	complemented
16	C₂³×C₈×C₁₀₁	—	2	1	no	—
17	C₂×#121×C₁₀₁	—	2	1	no	—
18	C₂×#121×C₁₀₁	—	2	1	no	—
19	C₂×#121×C₁₀₁	—	2	2	no	—
20	C₂×#121×C₁₀₁	—	2	1	no	—
21	C₂×#121×C₁₀₁	—	2	2	no	—
22	C₂×#121×C₁₀₁	—	2	1	no	—
23	C₂×#121×C₁₀₁	C₄	1	4	yes	—
24	C₂×#121×C₁₀₁	C₂²	1	4	yes	—
25	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
26	C₂²×C₂²⋊C₄×C₁₀₁	C₄	1	2	yes	—
27	C₂×#100×C₁₀₁	—	2	8	no	—
28	C₂×#100×C₁₀₁	C₂²	1	8	yes	complemented
29	#407×C₁₀₁	—	2	2	no	—
30	#407×C₁₀₁	C₂²	1	4	yes	complemented
31	C₂×C₂²⋊C₈×C₁₀₁	—	2	1	no	—
32	C₂×C₂²⋊C₈×C₁₀₁	—	2	1	no	—
33	#343×C₁₀₁	C₂²	1	8	yes	complemented
34	C₂⁵×C₁₀₁	C₂×C₄	1	1	yes	characteristic
35	C₂⁵×C₁₀₁	C₂×C₄	1	2	yes	—
36	C₂²×D₄×C₁₀₁	—	2	4	no	—
37	C₂²×D₄×C₁₀₁	—	2	2	no	—
38	C₂²×D₄×C₁₀₁	—	2	2	no	—
39	C₂²×D₄×C₁₀₁	—	2	4	no	—
40	C₂²×D₄×C₁₀₁	—	2	1	no	—
41	C₂²×D₄×C₁₀₁	—	2	1	no	—
42	C₂²×D₄×C₁₀₁	—	2	1	no	—
43	C₂²×D₄×C₁₀₁	—	2	1	no	—
44	C₂²×D₄×C₁₀₁	—	2	4	no	—
45	C₂²×D₄×C₁₀₁	—	4	8	no	—
46	C₂²×D₄×C₁₀₁	C₂×C₄	1	2	yes	—
47	C₂²×D₄×C₁₀₁	C₂×C₄	1	8	yes	—
48	C₂²×D₄×C₁₀₁	C₂³	1	2	yes	—
49	C₂³×C₄×C₁₀₁	—	2	4	no	—
50	C₂³×C₄×C₁₀₁	—	2	4	no	—
51	C₂³×C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
52	C₂³×C₄×C₁₀₁	C₂×C₄	1	2	yes	—
53	C₂³×C₄×C₁₀₁	C₂×C₄	1	2	yes	—
54	C₂³×C₄×C₁₀₁	D₄	1	1	yes	characteristic
55	C₂³×C₄×C₁₀₁	D₄	1	1	yes	characteristic
56	C₂³×C₄×C₁₀₁	D₄	1	2	yes	—
57	C₂³×C₄×C₁₀₁	D₄	1	1	yes	characteristic
58	C₂³×C₄×C₁₀₁	D₄	1	2	yes	—
59	C₂³×C₄×C₁₀₁	D₄	1	1	yes	characteristic
60	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
61	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
62	C₂×M₁₆×C₁₀₁	—	2	16	no	—
63	C₂×M₁₆×C₁₀₁	—	2	8	no	—
64	C₂×M₁₆×C₁₀₁	—	2	4	no	—
65	C₂×M₁₆×C₁₀₁	—	2	2	no	—
66	C₂×M₁₆×C₁₀₁	—	2	4	no	—
67	C₂×M₁₆×C₁₀₁	—	2	16	no	—
68	C₂×M₁₆×C₁₀₁	—	2	2	no	—
69	C₂×M₁₆×C₁₀₁	—	2	4	no	—
70	C₂×M₁₆×C₁₀₁	—	2	4	no	—
71	C₂×M₁₆×C₁₀₁	D₄	1	8	yes	complemented
72	C₂×M₁₆×C₁₀₁	C₂³	1	4	yes	—
73	C₂×M₁₆×C₁₀₁	C₂³	1	4	yes	—
74	C₂²×C₈×C₁₀₁	—	2	8	no	—
75	C₂²×C₈×C₁₀₁	—	2	2	no	—
76	C₂²×C₈×C₁₀₁	—	2	4	no	—
77	C₂²×C₈×C₁₀₁	—	2	2	no	—
78	#121×C₁₀₁	—	2	4	no	—
79	#121×C₁₀₁	—	2	4	no	—
80	#121×C₁₀₁	—	2	4	no	—
81	#121×C₁₀₁	—	2	4	no	—
82	#121×C₁₀₁	—	2	4	no	—
83	#121×C₁₀₁	—	2	4	no	—
84	#121×C₁₀₁	—	2	4	no	—
85	#121×C₁₀₁	—	2	4	no	—
86	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
87	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
88	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
89	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
90	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	2	yes	—
91	C₂×C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
92	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
93	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
94	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
95	C₂×C₂²⋊C₄×C₁₀₁	C₂×C₄	1	8	yes	—
96	#100×C₁₀₁	—	2	16	no	—
97	C₂²⋊C₈×C₁₀₁	—	2	4	no	—
98	C₂²⋊C₈×C₁₀₁	—	2	4	no	—
99	C₂⁴×C₁₀₁	—	2	4	no	—
100	C₂⁴×C₁₀₁	—	2	4	no	—
101	C₂⁴×C₁₀₁	—	2	2	no	—
102	C₂⁴×C₁₀₁	—	2	2	no	—
103	C₂⁴×C₁₀₁	—	2	8	no	—
104	C₂⁴×C₁₀₁	—	4	2	no	—
105	C₂⁴×C₁₀₁	—	4	4	no	—
106	C₂⁴×C₁₀₁	—	4	4	no	—
107	C₂⁴×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
108	C₂⁴×C₁₀₁	C₂²⋊C₄	1	2	yes	—
109	C₂⁴×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
110	C₂⁴×C₁₀₁	C₂²×C₄	1	2	yes	—
111	C₂⁴×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
112	C₂⁴×C₁₀₁	C₂²×C₄	1	4	yes	—
113	C₂×D₄×C₁₀₁	—	2	8	no	—
114	C₂×D₄×C₁₀₁	—	2	8	no	—
115	C₂×D₄×C₁₀₁	—	2	2	no	—
116	C₂×D₄×C₁₀₁	—	2	2	no	—
117	C₂×D₄×C₁₀₁	—	2	8	no	—
118	C₂×D₄×C₁₀₁	—	2	4	no	—
119	C₂×D₄×C₁₀₁	—	2	2	no	—
120	C₂×D₄×C₁₀₁	—	2	2	no	—
121	C₂×D₄×C₁₀₁	—	2	4	no	—
122	C₂×D₄×C₁₀₁	—	4	16	no	—
123	C₂×D₄×C₁₀₁	—	4	8	no	—
124	C₂×D₄×C₁₀₁	—	4	8	no	—
125	C₂×D₄×C₁₀₁	—	4	16	no	—
126	C₂×D₄×C₁₀₁	—	4	2	no	—
127	C₂×D₄×C₁₀₁	—	4	2	no	—
128	C₂×D₄×C₁₀₁	—	4	4	no	—
129	C₂×D₄×C₁₀₁	—	4	4	no	—
130	C₂×D₄×C₁₀₁	—	4	2	no	—
131	C₂×D₄×C₁₀₁	—	4	2	no	—
132	C₂²×C₄×C₁₀₁	—	2	4	no	—
133	C₂²×C₄×C₁₀₁	—	2	8	no	—
134	C₂²×C₄×C₁₀₁	—	2	2	no	—
135	C₂²×C₄×C₁₀₁	—	2	4	no	—
136	C₂²×C₄×C₁₀₁	—	2	2	no	—
137	C₂²×C₄×C₁₀₁	—	2	4	no	—
138	C₂²×C₄×C₁₀₁	—	2	4	no	—
139	C₂²×C₄×C₁₀₁	—	2	8	no	—
140	C₂²×C₄×C₁₀₁	—	2	2	no	—
141	C₂²×C₄×C₁₀₁	—	2	4	no	—
142	C₂²×C₄×C₁₀₁	—	2	2	no	—
143	C₂²×C₄×C₁₀₁	—	2	4	no	—
144	C₂²×C₄×C₁₀₁	—	2	4	no	—
145	C₂²×C₄×C₁₀₁	—	2	2	no	—
146	C₂²×C₄×C₁₀₁	—	2	2	no	—
147	C₂²×C₄×C₁₀₁	—	4	4	no	—
148	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	2	yes	—
149	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	2	yes	—
150	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	2	yes	—
151	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	2	yes	—
152	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	2	yes	—
153	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
154	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
155	C₂²×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
156	C₂²×C₄×C₁₀₁	C₂²×C₄	1	4	yes	—
157	C₂²×C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
158	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
159	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
160	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
161	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
162	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₁₀₁	C₂×D₄	1	4	yes	—
167	C₂²×C₄×C₁₀₁	#41	1	4	yes	—
168	C₂²×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
169	M₁₆×C₁₀₁	—	2	16	no	—
170	M₁₆×C₁₀₁	—	2	8	no	—
171	M₁₆×C₁₀₁	—	2	4	no	—
172	M₁₆×C₁₀₁	—	2	4	no	—
173	M₁₆×C₁₀₁	—	2	4	no	—
174	M₁₆×C₁₀₁	—	4	4	no	—
175	M₁₆×C₁₀₁	C₂×D₄	1	8	yes	complemented
176	C₂×C₈×C₁₀₁	—	2	16	no	—
177	C₂×C₈×C₁₀₁	—	2	8	no	—
178	C₂×C₈×C₁₀₁	—	2	4	no	—
179	C₂×C₈×C₁₀₁	—	2	4	no	—
180	C₂×C₈×C₁₀₁	—	4	4	no	—
181	C₄⋊C₄×C₁₀₁	—	2	2	no	—
182	C₄⋊C₄×C₁₀₁	—	2	2	no	—
183	C₄⋊C₄×C₁₀₁	—	2	2	no	—
184	C₄⋊C₄×C₁₀₁	—	2	2	no	—
185	C₂²⋊C₄×C₁₀₁	—	2	8	no	—
186	C₂²⋊C₄×C₁₀₁	—	2	8	no	—
187	C₂³×C₁₀₁	—	2	2	no	—
188	C₂³×C₁₀₁	—	2	2	no	—
189	C₂³×C₁₀₁	—	2	2	no	—
190	C₂³×C₁₀₁	—	2	2	no	—
191	C₂³×C₁₀₁	—	2	4	no	—
192	C₂³×C₁₀₁	—	2	4	no	—
193	C₂³×C₁₀₁	—	2	2	no	—
194	C₂³×C₁₀₁	—	2	2	no	—
195	C₂³×C₁₀₁	—	2	4	no	—
196	C₂³×C₁₀₁	—	2	4	no	—
197	C₂³×C₁₀₁	—	2	2	no	—
198	C₂³×C₁₀₁	—	2	4	no	—
199	C₂³×C₁₀₁	—	2	8	no	—
200	C₂³×C₁₀₁	—	4	2	no	—
201	C₂³×C₁₀₁	—	4	2	no	—
202	C₂³×C₁₀₁	—	4	16	no	—
203	C₂³×C₁₀₁	—	4	4	no	—
204	C₂³×C₁₀₁	—	4	4	no	—
205	C₂³×C₁₀₁	—	4	4	no	—
206	C₂³×C₁₀₁	—	4	4	no	—
207	C₂³×C₁₀₁	—	4	4	no	—
208	C₂³×C₁₀₁	—	4	4	no	—
209	C₂³×C₁₀₁	—	4	4	no	—
210	C₂³×C₁₀₁	—	4	4	no	—
211	C₂³×C₁₀₁	—	8	16	no	—
212	C₂³×C₁₀₁	#100	1	4	yes	complemented
213	C₂³×C₁₀₁	C₂×C₂²⋊C₄	1	2	yes	—
214	C₂³×C₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
215	C₂³×C₁₀₁	C₂×C₂²⋊C₄	1	2	yes	—
216	C₂³×C₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
217	C₂³×C₁₀₁	C₄×D₄	1	4	yes	—
218	C₂³×C₁₀₁	C₂³×C₄	1	1	yes	characteristic
219	D₄×C₁₀₁	—	4	16	no	—
220	D₄×C₁₀₁	—	4	16	no	—
221	D₄×C₁₀₁	—	4	2	no	—
222	D₄×C₁₀₁	—	4	4	no	—
223	D₄×C₁₀₁	—	4	2	no	—
224	D₄×C₁₀₁	—	4	4	no	—
225	D₄×C₁₀₁	—	4	4	no	—
226	C₂×C₄×C₁₀₁	—	2	4	no	—
227	C₂×C₄×C₁₀₁	—	2	4	no	—
228	C₂×C₄×C₁₀₁	—	2	2	no	—
229	C₂×C₄×C₁₀₁	—	2	2	no	—
230	C₂×C₄×C₁₀₁	—	2	2	no	—
231	C₂×C₄×C₁₀₁	—	2	2	no	—
232	C₂×C₄×C₁₀₁	—	2	4	no	—
233	C₂×C₄×C₁₀₁	—	2	4	no	—
234	C₂×C₄×C₁₀₁	—	2	2	no	—
235	C₂×C₄×C₁₀₁	—	2	2	no	—
236	C₂×C₄×C₁₀₁	—	2	4	no	—
237	C₂×C₄×C₁₀₁	—	2	4	no	—
238	C₂×C₄×C₁₀₁	—	2	4	no	—
239	C₂×C₄×C₁₀₁	—	2	4	no	—
240	C₂×C₄×C₁₀₁	—	2	4	no	—
241	C₂×C₄×C₁₀₁	—	4	4	no	—
242	C₂×C₄×C₁₀₁	—	4	4	no	—
243	C₂×C₄×C₁₀₁	—	4	4	no	—
244	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	2	yes	—
245	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	2	yes	—
246	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
247	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
248	C₂×C₄×C₁₀₁	C₄×D₄	1	4	yes	—
249	C₂×C₄×C₁₀₁	#120	1	2	yes	—
250	C₂×C₄×C₁₀₁	#120	1	2	yes	—
251	C₂×C₄×C₁₀₁	#121	1	4	yes	—
252	C₂×C₄×C₁₀₁	#121	1	4	yes	—
253	C₂×C₄×C₁₀₁	#123	1	2	yes	—
254	C₂×C₄×C₁₀₁	#123	1	2	yes	—
255	C₂×C₄×C₁₀₁	C₂²×D₄	1	2	yes	—
256	C₂×C₄×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
257	C₂×C₄×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
258	C₂×C₄×C₁₀₁	C₂×#41	1	2	yes	—
259	C₈×C₁₀₁	—	2	8	no	—
260	C₈×C₁₀₁	—	4	4	no	—
261	C₂²×C₁₀₁	—	2	1	no	—
262	C₂²×C₁₀₁	—	2	1	no	—
263	C₂²×C₁₀₁	—	2	1	no	—
264	C₂²×C₁₀₁	—	2	1	no	—
265	C₂²×C₁₀₁	—	2	2	no	—
266	C₂²×C₁₀₁	—	2	8	no	—
267	C₂²×C₁₀₁	—	2	8	no	—
268	C₂²×C₁₀₁	—	2	2	no	—
269	C₂²×C₁₀₁	—	2	2	no	—
270	C₂²×C₁₀₁	—	2	2	no	—
271	C₂²×C₁₀₁	—	2	2	no	—
272	C₂²×C₁₀₁	—	4	8	no	—
273	C₂²×C₁₀₁	—	4	8	no	—
274	C₂²×C₁₀₁	—	4	4	no	—
275	C₂²×C₁₀₁	—	4	4	no	—
276	C₂²×C₁₀₁	—	4	4	no	—
277	C₂²×C₁₀₁	—	4	4	no	—
278	C₂²×C₁₀₁	—	8	8	no	—
279	C₂²×C₁₀₁	—	8	8	no	—
280	C₂²×C₁₀₁	—	8	8	no	—
281	C₂²×C₁₀₁	#386	1	2	yes	—
282	C₂²×C₁₀₁	#386	1	2	yes	—
283	C₂²×C₁₀₁	C₂×#100	1	2	yes	—
284	C₂²×C₁₀₁	C₂×#100	1	4	yes	complemented
285	C₂²×C₁₀₁	#413	1	2	yes	—
286	C₂²×C₁₀₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
287	C₂²×C₁₀₁	C₂×C₄×D₄	1	2	yes	—
288	C₄×C₁₀₁	—	2	2	no	—
289	C₄×C₁₀₁	—	2	2	no	—
290	C₄×C₁₀₁	—	4	4	no	—
291	C₄×C₁₀₁	#386	1	2	yes	—
292	C₄×C₁₀₁	#386	1	2	yes	—
293	C₄×C₁₀₁	C₂×#120	1	1	yes	characteristic
294	C₄×C₁₀₁	C₂×#121	1	2	yes	—
295	C₄×C₁₀₁	C₂×#123	1	1	yes	characteristic
296	C₂×#1900	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
297	C₂×C₁₀₁	—	2	2	no	—
298	C₂×C₁₀₁	—	2	2	no	—
299	C₂×C₁₀₁	—	2	4	no	—
300	C₂×C₁₀₁	—	4	2	no	—
301	C₂×C₁₀₁	—	8	4	no	—
302	C₂×C₁₀₁	#1900	1	4	yes	direct product factor
303	C₂×C₁₀₁	C₂×#386	1	1	yes	characteristic
304	C₂×C₁₀₁	C₂²×#100	1	1	yes	characteristic
305	C₂×C₁₀₁	C₂×#413	1	1	yes	characteristic
306	C₂³×M₁₆	C₂×C₁₀₁	1	1	yes	characteristic, complemented
307	C₂²×#121	C₂×C₁₀₁	1	1	yes	characteristic
308	C₂²×#100	C₂×C₁₀₁	1	2	yes	complemented
309	C₂×#407	C₂×C₁₀₁	1	1	yes	characteristic, complemented
310	#1900	C₂×C₁₀₁	1	8	yes	direct product factor
311	C₂×#343	C₂×C₁₀₁	1	2	yes	complemented
312	C₁₀₁	C₂×#1900	1	1	yes	characteristic, direct product factor, Sylow
313	C₂³×D₄	C₄×C₁₀₁	1	2	yes	—
314	C₂³×D₄	C₂²×C₁₀₁	1	1	yes	characteristic
315	C₂⁴×C₄	C₂²×C₁₀₁	1	1	yes	characteristic
316	C₂²×M₁₆	—	2	1	no	—
317	C₂²×M₁₆	—	2	2	no	—
318	C₂²×M₁₆	—	2	8	no	—
319	C₂²×M₁₆	C₂²×C₁₀₁	1	2	yes	—
320	C₂²×M₁₆	C₂²×C₁₀₁	1	2	yes	—
321	C₂²×M₁₆	C₂²×C₁₀₁	1	4	yes	complemented
322	C₂³×C₈	—	2	1	no	—
323	C₂×#121	—	2	1	no	—
324	C₂×#121	—	2	1	no	—
325	C₂×#121	—	2	2	no	—
326	C₂×#121	—	2	1	no	—
327	C₂×#121	—	2	1	no	—
328	C₂×#121	—	2	2	no	—
329	C₂×#121	C₄×C₁₀₁	1	4	yes	—
330	C₂×#121	C₂²×C₁₀₁	1	4	yes	—
331	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
332	C₂²×C₂²⋊C₄	C₄×C₁₀₁	1	2	yes	—
333	C₂×#100	—	2	8	no	—
334	C₂×#100	C₂²×C₁₀₁	1	8	yes	complemented
335	#407	—	2	2	no	—
336	#407	C₂²×C₁₀₁	1	4	yes	complemented
337	C₂×C₂²⋊C₈	—	2	1	no	—
338	C₂×C₂²⋊C₈	—	2	1	no	—
339	#343	C₂²×C₁₀₁	1	8	yes	complemented
340	C₂⁵	C₂×C₄×C₁₀₁	1	1	yes	characteristic
341	C₂⁵	C₂×C₄×C₁₀₁	1	2	yes	—
342	C₂²×D₄	—	2	2	no	—
343	C₂²×D₄	—	2	4	no	—
344	C₂²×D₄	—	2	2	no	—
345	C₂²×D₄	—	2	1	no	—
346	C₂²×D₄	—	2	1	no	—
347	C₂²×D₄	—	2	1	no	—
348	C₂²×D₄	—	2	1	no	—
349	C₂²×D₄	—	2	4	no	—
350	C₂²×D₄	—	2	4	no	—
351	C₂²×D₄	—	4	8	no	—
352	C₂²×D₄	C₂×C₄×C₁₀₁	1	2	yes	—
353	C₂²×D₄	C₂×C₄×C₁₀₁	1	8	yes	—
354	C₂²×D₄	C₂³×C₁₀₁	1	2	yes	—
355	C₂³×C₄	—	2	4	no	—
356	C₂³×C₄	—	2	4	no	—
357	C₂³×C₄	C₂×C₄×C₁₀₁	1	1	yes	characteristic
358	C₂³×C₄	C₂×C₄×C₁₀₁	1	2	yes	—
359	C₂³×C₄	C₂×C₄×C₁₀₁	1	2	yes	—
360	C₂³×C₄	D₄×C₁₀₁	1	1	yes	characteristic
361	C₂³×C₄	D₄×C₁₀₁	1	2	yes	—
362	C₂³×C₄	D₄×C₁₀₁	1	1	yes	characteristic
363	C₂³×C₄	D₄×C₁₀₁	1	1	yes	characteristic
364	C₂³×C₄	D₄×C₁₀₁	1	1	yes	characteristic
365	C₂³×C₄	D₄×C₁₀₁	1	2	yes	—
366	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
367	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
368	C₂×M₁₆	—	2	16	no	—
369	C₂×M₁₆	—	2	8	no	—
370	C₂×M₁₆	—	2	4	no	—
371	C₂×M₁₆	—	2	2	no	—
372	C₂×M₁₆	—	2	4	no	—
373	C₂×M₁₆	—	2	16	no	—
374	C₂×M₁₆	—	2	2	no	—
375	C₂×M₁₆	—	2	4	no	—
376	C₂×M₁₆	—	2	4	no	—
377	C₂×M₁₆	D₄×C₁₀₁	1	8	yes	complemented
378	C₂×M₁₆	C₂³×C₁₀₁	1	4	yes	—
379	C₂×M₁₆	C₂³×C₁₀₁	1	4	yes	—
380	C₂²×C₈	—	2	8	no	—
381	C₂²×C₈	—	2	2	no	—
382	C₂²×C₈	—	2	4	no	—
383	C₂²×C₈	—	2	2	no	—
384	#121	—	2	4	no	—
385	#121	—	2	4	no	—
386	#121	—	2	4	no	—
387	#121	—	2	4	no	—
388	#121	—	2	4	no	—
389	#121	—	2	4	no	—
390	#121	—	2	4	no	—
391	#121	—	2	4	no	—
392	C₂×C₄⋊C₄	—	2	1	no	—
393	C₂×C₄⋊C₄	—	2	1	no	—
394	C₂×C₄⋊C₄	—	2	1	no	—
395	C₂×C₄⋊C₄	—	2	1	no	—
396	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	2	yes	—
397	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	2	yes	—
398	C₂×C₂²⋊C₄	—	2	4	no	—
399	C₂×C₂²⋊C₄	—	2	2	no	—
400	C₂×C₂²⋊C₄	—	2	2	no	—
401	C₂×C₂²⋊C₄	C₂×C₄×C₁₀₁	1	8	yes	—
402	#100	—	2	16	no	—
403	C₂²⋊C₈	—	2	4	no	—
404	C₂²⋊C₈	—	2	4	no	—
405	C₂⁴	—	2	4	no	—
406	C₂⁴	—	2	4	no	—
407	C₂⁴	—	2	2	no	—
408	C₂⁴	—	2	2	no	—
409	C₂⁴	—	2	8	no	—
410	C₂⁴	—	4	2	no	—
411	C₂⁴	—	4	4	no	—
412	C₂⁴	—	4	4	no	—
413	C₂⁴	C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
414	C₂⁴	C₂²⋊C₄×C₁₀₁	1	2	yes	—
415	C₂⁴	C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
416	C₂⁴	C₂²×C₄×C₁₀₁	1	2	yes	—
417	C₂⁴	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
418	C₂⁴	C₂²×C₄×C₁₀₁	1	4	yes	—
419	C₂×D₄	—	2	8	no	—
420	C₂×D₄	—	2	8	no	—
421	C₂×D₄	—	2	2	no	—
422	C₂×D₄	—	2	2	no	—
423	C₂×D₄	—	2	8	no	—
424	C₂×D₄	—	2	4	no	—
425	C₂×D₄	—	2	2	no	—
426	C₂×D₄	—	2	2	no	—
427	C₂×D₄	—	2	4	no	—
428	C₂×D₄	—	4	16	no	—
429	C₂×D₄	—	4	8	no	—
430	C₂×D₄	—	4	8	no	—
431	C₂×D₄	—	4	16	no	—
432	C₂×D₄	—	4	2	no	—
433	C₂×D₄	—	4	2	no	—
434	C₂×D₄	—	4	4	no	—
435	C₂×D₄	—	4	4	no	—
436	C₂×D₄	—	4	2	no	—
437	C₂×D₄	—	4	2	no	—
438	C₂²×C₄	—	2	4	no	—
439	C₂²×C₄	—	2	8	no	—
440	C₂²×C₄	—	2	2	no	—
441	C₂²×C₄	—	2	4	no	—
442	C₂²×C₄	—	2	2	no	—
443	C₂²×C₄	—	2	4	no	—
444	C₂²×C₄	—	2	4	no	—
445	C₂²×C₄	—	2	8	no	—
446	C₂²×C₄	—	2	2	no	—
447	C₂²×C₄	—	2	4	no	—
448	C₂²×C₄	—	2	2	no	—
449	C₂²×C₄	—	2	4	no	—
450	C₂²×C₄	—	2	4	no	—
451	C₂²×C₄	—	2	2	no	—
452	C₂²×C₄	—	2	2	no	—
453	C₂²×C₄	—	4	4	no	—
454	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	2	yes	—
455	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
456	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
457	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	2	yes	—
458	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	2	yes	—
459	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	2	yes	—
460	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	2	yes	—
461	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
462	C₂²×C₄	C₂²×C₄×C₁₀₁	1	4	yes	—
463	C₂²×C₄	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
464	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
465	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
466	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
467	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
468	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
469	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
470	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
471	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
472	C₂²×C₄	C₂×D₄×C₁₀₁	1	4	yes	—
473	C₂²×C₄	#41×C₁₀₁	1	4	yes	—
474	C₂²×C₄	C₂⁴×C₁₀₁	1	1	yes	characteristic
475	M₁₆	—	2	16	no	—
476	M₁₆	—	2	8	no	—
477	M₁₆	—	2	4	no	—
478	M₁₆	—	2	4	no	—
479	M₁₆	—	2	4	no	—
480	M₁₆	—	4	4	no	—
481	M₁₆	C₂×D₄×C₁₀₁	1	8	yes	complemented
482	C₂×C₈	—	2	16	no	—
483	C₂×C₈	—	2	8	no	—
484	C₂×C₈	—	2	4	no	—
485	C₂×C₈	—	2	4	no	—
486	C₂×C₈	—	4	4	no	—
487	C₄⋊C₄	—	2	2	no	—
488	C₄⋊C₄	—	2	2	no	—
489	C₄⋊C₄	—	2	2	no	—
490	C₄⋊C₄	—	2	2	no	—
491	C₂²⋊C₄	—	2	8	no	—
492	C₂²⋊C₄	—	2	8	no	—
493	C₂³	—	2	2	no	—
494	C₂³	—	2	2	no	—
495	C₂³	—	2	2	no	—
496	C₂³	—	2	2	no	—
497	C₂³	—	2	2	no	—
498	C₂³	—	2	4	no	—
499	C₂³	—	2	4	no	—
500	C₂³	—	2	2	no	—
501	C₂³	—	2	4	no	—
502	C₂³	—	2	4	no	—
503	C₂³	—	2	2	no	—
504	C₂³	—	2	4	no	—
505	C₂³	—	2	8	no	—
506	C₂³	—	4	2	no	—
507	C₂³	—	4	2	no	—
508	C₂³	—	4	16	no	—
509	C₂³	—	4	4	no	—
510	C₂³	—	4	4	no	—
511	C₂³	—	4	4	no	—
512	C₂³	—	4	4	no	—
513	C₂³	—	4	4	no	—
514	C₂³	—	4	4	no	—
515	C₂³	—	4	4	no	—
516	C₂³	—	4	4	no	—
517	C₂³	—	8	16	no	—
518	C₂³	#100×C₁₀₁	1	4	yes	complemented
519	C₂³	C₂×C₂²⋊C₄×C₁₀₁	1	2	yes	—
520	C₂³	C₂×C₂²⋊C₄×C₁₀₁	1	2	yes	—
521	C₂³	C₂×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
522	C₂³	C₂×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
523	C₂³	C₄×D₄×C₁₀₁	1	4	yes	—
524	C₂³	C₂³×C₄×C₁₀₁	1	1	yes	characteristic
525	D₄	—	4	16	no	—
526	D₄	—	4	16	no	—
527	D₄	—	4	2	no	—
528	D₄	—	4	4	no	—
529	D₄	—	4	2	no	—
530	D₄	—	4	4	no	—
531	D₄	—	4	4	no	—
532	C₂×C₄	—	2	4	no	—
533	C₂×C₄	—	2	4	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	2	4	no	—
539	C₂×C₄	—	2	4	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	2	4	no	—
543	C₂×C₄	—	2	4	no	—
544	C₂×C₄	—	2	4	no	—
545	C₂×C₄	—	2	4	no	—
546	C₂×C₄	—	2	4	no	—
547	C₂×C₄	—	4	4	no	—
548	C₂×C₄	—	4	4	no	—
549	C₂×C₄	—	4	4	no	—
550	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	2	yes	—
551	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	2	yes	—
552	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
553	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
554	C₂×C₄	C₄×D₄×C₁₀₁	1	4	yes	—
555	C₂×C₄	#120×C₁₀₁	1	2	yes	—
556	C₂×C₄	#120×C₁₀₁	1	2	yes	—
557	C₂×C₄	#121×C₁₀₁	1	4	yes	—
558	C₂×C₄	#121×C₁₀₁	1	4	yes	—
559	C₂×C₄	#123×C₁₀₁	1	2	yes	—
560	C₂×C₄	#123×C₁₀₁	1	2	yes	—
561	C₂×C₄	C₂²×D₄×C₁₀₁	1	2	yes	—
562	C₂×C₄	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
563	C₂×C₄	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
564	C₂×C₄	C₂×#41×C₁₀₁	1	2	yes	—
565	C₈	—	2	8	no	—
566	C₈	—	4	4	no	—
567	C₂²	—	2	8	no	—
568	C₂²	—	2	8	no	—
569	C₂²	—	2	2	no	—
570	C₂²	—	2	1	no	—
571	C₂²	—	2	1	no	—
572	C₂²	—	2	1	no	—
573	C₂²	—	2	1	no	—
574	C₂²	—	2	2	no	—
575	C₂²	—	2	2	no	—
576	C₂²	—	2	2	no	—
577	C₂²	—	2	2	no	—
578	C₂²	—	4	8	no	—
579	C₂²	—	4	8	no	—
580	C₂²	—	4	4	no	—
581	C₂²	—	4	4	no	—
582	C₂²	—	4	4	no	—
583	C₂²	—	4	4	no	—
584	C₂²	—	8	8	no	—
585	C₂²	—	8	8	no	—
586	C₂²	—	8	8	no	—
587	C₂²	#386×C₁₀₁	1	2	yes	—
588	C₂²	#386×C₁₀₁	1	2	yes	—
589	C₂²	C₂×#100×C₁₀₁	1	2	yes	—
590	C₂²	C₂×#100×C₁₀₁	1	4	yes	complemented
591	C₂²	#413×C₁₀₁	1	2	yes	—
592	C₂²	C₂²×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
593	C₂²	C₂×C₄×D₄×C₁₀₁	1	2	yes	—
594	C₄	—	2	2	no	—
595	C₄	—	2	2	no	—
596	C₄	—	4	4	no	—
597	C₄	#386×C₁₀₁	1	2	yes	—
598	C₄	#386×C₁₀₁	1	2	yes	—
599	C₄	C₂×#120×C₁₀₁	1	1	yes	characteristic
600	C₄	C₂×#121×C₁₀₁	1	2	yes	—
601	C₄	C₂×#123×C₁₀₁	1	1	yes	characteristic
602	C₂	—	2	2	no	—
603	C₂	—	2	2	no	—
604	C₂	—	2	4	no	—
605	C₂	—	4	2	no	—
606	C₂	—	8	4	no	—
607	C₂	C₁₀₁×#1900	1	4	yes	direct product factor
608	C₂	C₂×#386×C₁₀₁	1	1	yes	characteristic
609	C₂	C₂²×#100×C₁₀₁	1	1	yes	characteristic
610	C₂	C₂×#413×C₁₀₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₀₁	C₂×C₂²⋊C₄
commutator	C₂³	C₂³×C₄×C₁₀₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₀₁
prime radical	C₂²×#121×C₁₀₁	C₂
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₀₁ ◁ C₂⁴×C₄×C₁₀₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂³×M₁₆×C₁₀₁	C₂	semidirect
3. C₂²×#100×C₁₀₁	C₂	semidirect
4. C₂×#407×C₁₀₁	C₂	semidirect
5. C₁₀₁×#1900	C₂	direct (N × H)
6. C₂×#343×C₁₀₁	C₂	semidirect
15. C₂²×M₁₆×C₁₀₁	C₂²	semidirect
28. C₂×#100×C₁₀₁	C₂²	semidirect
30. #407×C₁₀₁	C₂²	semidirect
33. #343×C₁₀₁	C₂²	semidirect
71. C₂×M₁₆×C₁₀₁	D₄	semidirect
175. M₁₆×C₁₀₁	C₂×D₄	semidirect
212. C₂³×C₁₀₁	#100	semidirect
284. C₂²×C₁₀₁	C₂×#100	semidirect
296. C₂×#1900	C₁₀₁	direct (N × H)
302. C₂×C₁₀₁	#1900	direct (N × H)
306. C₂³×M₁₆	C₂×C₁₀₁	semidirect
308. C₂²×#100	C₂×C₁₀₁	semidirect
309. C₂×#407	C₂×C₁₀₁	semidirect
310. #1900	C₂×C₁₀₁	direct (N × H)
311. C₂×#343	C₂×C₁₀₁	semidirect
312. C₁₀₁	C₂×#1900	direct (N × H)
321. C₂²×M₁₆	C₂²×C₁₀₁	semidirect
334. C₂×#100	C₂²×C₁₀₁	semidirect
336. #407	C₂²×C₁₀₁	semidirect
339. #343	C₂²×C₁₀₁	semidirect
377. C₂×M₁₆	D₄×C₁₀₁	semidirect
481. M₁₆	C₂×D₄×C₁₀₁	semidirect
518. C₂³	#100×C₁₀₁	semidirect
590. C₂²	C₂×#100×C₁₀₁	semidirect
607. C₂	C₁₀₁×#1900	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×M₁₆×C₁₀₁	2
C₂²×#121×C₁₀₁	2
C₂²×#100×C₁₀₁	2
C₂×#407×C₁₀₁	2
C₁₀₁×#1900	2
C₂×#343×C₁₀₁	2
C₂×#1900	101

Subgroups — C2×C101×#1900 #38803138

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₀₁×#1900 #38803138