Subgroups — C₁₀₁×#13878 #38796029

Order 25856.

2222 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#117×C₁₀₁	C₂	1	1	yes	maximal, characteristic
2	C₂×#381×C₁₀₁	C₂	1	1	yes	maximal, characteristic
3	C₂×#380×C₁₀₁	C₂	1	2	yes	maximal
4	C₂²×#95×C₁₀₁	C₂	1	1	yes	maximal, characteristic
5	C₁₀₁×#1444	C₂	1	2	yes	maximal, complemented
6	C₁₀₁×#1442	C₂	1	2	yes	maximal, complemented
7	C₁₀₁×#1436	C₂	1	4	yes	maximal, complemented
8	C₁₀₁×C₂²⋊#95	C₂	1	2	yes	maximal
9	C₂⁴×C₄×C₁₀₁	C₂²	1	2	yes	—
10	C₂⁴×C₄×C₁₀₁	C₂²	1	1	yes	characteristic
11	C₂×#117×C₁₀₁	—	2	4	no	—
12	C₂×#117×C₁₀₁	—	2	8	no	—
13	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	2	yes	—
14	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	4	yes	—
15	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
16	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
17	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	2	yes	—
18	C₂²×C₄²×C₁₀₁	C₂²	1	2	yes	—
19	#381×C₁₀₁	—	2	4	no	—
20	#380×C₁₀₁	—	2	8	no	—
21	C₂×#95×C₁₀₁	C₄	1	8	yes	complemented
22	C₂×#95×C₁₀₁	C₂²	1	4	yes	—
23	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
24	C₂×#95×C₁₀₁	C₂²	1	4	yes	—
25	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
26	C₂×#95×C₁₀₁	C₂²	1	4	yes	—
27	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
28	C₂×#95×C₁₀₁	C₂²	1	1	yes	characteristic
29	C₂×#95×C₁₀₁	C₂²	1	1	yes	characteristic
30	C₂⁵×C₁₀₁	C₂³	1	1	yes	characteristic
31	C₂³×C₄×C₁₀₁	—	2	4	no	—
32	C₂³×C₄×C₁₀₁	—	2	4	no	—
33	C₂³×C₄×C₁₀₁	—	2	4	no	—
34	C₂³×C₄×C₁₀₁	—	2	4	no	—
35	C₂³×C₄×C₁₀₁	—	2	8	no	—
36	C₂³×C₄×C₁₀₁	—	4	4	no	—
37	C₂³×C₄×C₁₀₁	C₂×C₄	1	8	yes	—
38	C₂³×C₄×C₁₀₁	C₂×C₄	1	4	yes	—
39	C₂³×C₄×C₁₀₁	D₄	1	4	yes	—
40	C₂³×C₄×C₁₀₁	Q₈	1	4	yes	—
41	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
42	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
43	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
44	C₂³×C₄×C₁₀₁	C₂³	1	4	yes	—
45	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
47	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
48	#117×C₁₀₁	—	2	32	no	—
49	C₂×C₄⋊C₄×C₁₀₁	—	2	8	no	—
50	C₂×C₄⋊C₄×C₁₀₁	—	2	4	no	—
51	C₂×C₄⋊C₄×C₁₀₁	—	2	8	no	—
52	C₂×C₄⋊C₄×C₁₀₁	—	2	8	no	—
53	C₂×C₄⋊C₄×C₁₀₁	—	4	4	no	—
54	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
55	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
56	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
57	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
58	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
59	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
60	C₂×C₂²⋊C₄×C₁₀₁	D₄	1	8	yes	—
61	C₂×C₄²×C₁₀₁	—	2	8	no	—
62	C₂×C₄²×C₁₀₁	—	2	4	no	—
63	#95×C₁₀₁	—	2	8	no	—
64	#95×C₁₀₁	—	2	4	no	—
65	#95×C₁₀₁	—	2	4	no	—
66	#95×C₁₀₁	—	2	8	no	—
67	#95×C₁₀₁	—	4	4	no	—
68	#95×C₁₀₁	C₂×C₄	1	4	yes	—
69	#95×C₁₀₁	C₂×C₄	1	8	yes	—
70	#95×C₁₀₁	C₂×C₄	1	4	yes	—
71	C₂⁴×C₁₀₁	—	2	4	no	—
72	C₂⁴×C₁₀₁	—	2	2	no	—
73	C₂⁴×C₁₀₁	—	2	2	no	—
74	C₂⁴×C₁₀₁	C₂²×C₄	1	2	yes	—
75	C₂⁴×C₁₀₁	C₂×D₄	1	2	yes	—
76	C₂⁴×C₁₀₁	C₂×D₄	1	4	yes	—
77	C₂⁴×C₁₀₁	C₂×Q₈	1	2	yes	—
78	C₂⁴×C₁₀₁	#41	1	4	yes	—
79	C₂⁴×C₁₀₁	C₂⁴	1	1	yes	characteristic
80	C₂²×C₄×C₁₀₁	—	2	16	no	—
81	C₂²×C₄×C₁₀₁	—	2	8	no	—
82	C₂²×C₄×C₁₀₁	—	2	16	no	—
83	C₂²×C₄×C₁₀₁	—	2	8	no	—
84	C₂²×C₄×C₁₀₁	—	2	2	no	—
85	C₂²×C₄×C₁₀₁	—	2	2	no	—
86	C₂²×C₄×C₁₀₁	—	2	2	no	—
87	C₂²×C₄×C₁₀₁	—	2	2	no	—
88	C₂²×C₄×C₁₀₁	—	2	2	no	—
89	C₂²×C₄×C₁₀₁	—	2	2	no	—
90	C₂²×C₄×C₁₀₁	—	2	4	no	—
91	C₂²×C₄×C₁₀₁	—	2	16	no	—
92	C₂²×C₄×C₁₀₁	—	2	2	no	—
93	C₂²×C₄×C₁₀₁	—	2	4	no	—
94	C₂²×C₄×C₁₀₁	—	2	4	no	—
95	C₂²×C₄×C₁₀₁	—	2	4	no	—
96	C₂²×C₄×C₁₀₁	—	2	4	no	—
97	C₂²×C₄×C₁₀₁	—	2	4	no	—
98	C₂²×C₄×C₁₀₁	—	2	2	no	—
99	C₂²×C₄×C₁₀₁	—	2	4	no	—
100	C₂²×C₄×C₁₀₁	—	2	4	no	—
101	C₂²×C₄×C₁₀₁	—	2	4	no	—
102	C₂²×C₄×C₁₀₁	—	2	16	no	—
103	C₂²×C₄×C₁₀₁	—	2	2	no	—
104	C₂²×C₄×C₁₀₁	—	2	2	no	—
105	C₂²×C₄×C₁₀₁	—	2	4	no	—
106	C₂²×C₄×C₁₀₁	—	2	4	no	—
107	C₂²×C₄×C₁₀₁	—	2	4	no	—
108	C₂²×C₄×C₁₀₁	—	2	4	no	—
109	C₂²×C₄×C₁₀₁	—	2	2	no	—
110	C₂²×C₄×C₁₀₁	—	2	2	no	—
111	C₂²×C₄×C₁₀₁	—	2	2	no	—
112	C₂²×C₄×C₁₀₁	—	2	2	no	—
113	C₂²×C₄×C₁₀₁	—	4	8	no	—
114	C₂²×C₄×C₁₀₁	—	4	16	no	—
115	C₂²×C₄×C₁₀₁	—	4	16	no	—
116	C₂²×C₄×C₁₀₁	C₄⋊C₄	1	16	yes	complemented
117	C₂²×C₄×C₁₀₁	C₂²×C₄	1	4	yes	—
118	C₂²×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
119	C₂²×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
120	C₂²×C₄×C₁₀₁	C₂²×C₄	1	4	yes	—
121	C₂²×C₄×C₁₀₁	C₂×D₄	1	8	yes	—
122	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
123	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₁₀₁	C₂×Q₈	1	2	yes	—
125	C₂²×C₄×C₁₀₁	C₂×Q₈	1	2	yes	—
126	C₂²×C₄×C₁₀₁	#41	1	8	yes	—
127	C₄⋊C₄×C₁₀₁	—	2	16	no	—
128	C₄⋊C₄×C₁₀₁	—	4	16	no	—
129	C₂²⋊C₄×C₁₀₁	—	2	16	no	—
130	C₂²⋊C₄×C₁₀₁	—	4	4	no	—
131	C₂²⋊C₄×C₁₀₁	—	4	4	no	—
132	C₄²×C₁₀₁	—	2	16	no	—
133	C₂³×C₁₀₁	—	2	4	no	—
134	C₂³×C₁₀₁	—	2	2	no	—
135	C₂³×C₁₀₁	—	2	2	no	—
136	C₂³×C₁₀₁	—	2	4	no	—
137	C₂³×C₁₀₁	—	2	4	no	—
138	C₂³×C₁₀₁	—	2	4	no	—
139	C₂³×C₁₀₁	—	2	4	no	—
140	C₂³×C₁₀₁	—	2	8	no	—
141	C₂³×C₁₀₁	—	2	8	no	—
142	C₂³×C₁₀₁	—	2	8	no	—
143	C₂³×C₁₀₁	—	2	8	no	—
144	C₂³×C₁₀₁	C₂×C₄⋊C₄	1	4	yes	—
145	C₂³×C₁₀₁	C₄×D₄	1	8	yes	—
146	C₂³×C₁₀₁	#120	1	4	yes	—
147	C₂³×C₁₀₁	C₂²⋊Q₈	1	8	yes	—
148	C₂³×C₁₀₁	#123	1	4	yes	—
149	C₂³×C₁₀₁	C₂³×C₄	1	1	yes	characteristic
150	C₂³×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
151	C₂³×C₁₀₁	C₂²×D₄	1	2	yes	—
152	C₂³×C₁₀₁	C₂²×Q₈	1	1	yes	characteristic
153	C₂³×C₁₀₁	C₂×#41	1	4	yes	—
154	C₂³×C₁₀₁	C₂×#41	1	2	yes	—
155	C₂³×C₁₀₁	H(5,𝔽₂)	1	2	yes	—
156	C₂³×C₁₀₁	2₋¹⁺⁴	1	2	yes	—
157	C₂×C₄×C₁₀₁	—	2	4	no	—
158	C₂×C₄×C₁₀₁	—	2	4	no	—
159	C₂×C₄×C₁₀₁	—	2	4	no	—
160	C₂×C₄×C₁₀₁	—	2	4	no	—
161	C₂×C₄×C₁₀₁	—	2	2	no	—
162	C₂×C₄×C₁₀₁	—	2	2	no	—
163	C₂×C₄×C₁₀₁	—	2	4	no	—
164	C₂×C₄×C₁₀₁	—	2	4	no	—
165	C₂×C₄×C₁₀₁	—	2	2	no	—
166	C₂×C₄×C₁₀₁	—	2	2	no	—
167	C₂×C₄×C₁₀₁	—	2	8	no	—
168	C₂×C₄×C₁₀₁	—	2	8	no	—
169	C₂×C₄×C₁₀₁	—	2	32	no	—
170	C₂×C₄×C₁₀₁	—	2	4	no	—
171	C₂×C₄×C₁₀₁	—	2	4	no	—
172	C₂×C₄×C₁₀₁	—	2	4	no	—
173	C₂×C₄×C₁₀₁	—	2	8	no	—
174	C₂×C₄×C₁₀₁	—	2	8	no	—
175	C₂×C₄×C₁₀₁	—	2	8	no	—
176	C₂×C₄×C₁₀₁	—	4	32	no	—
177	C₂×C₄×C₁₀₁	—	4	4	no	—
178	C₂×C₄×C₁₀₁	—	4	4	no	—
179	C₂×C₄×C₁₀₁	—	4	4	no	—
180	C₂×C₄×C₁₀₁	—	4	4	no	—
181	C₂×C₄×C₁₀₁	—	4	4	no	—
182	C₂×C₄×C₁₀₁	—	4	4	no	—
183	C₂×C₄×C₁₀₁	—	4	2	no	—
184	C₂×C₄×C₁₀₁	—	4	2	no	—
185	C₂×C₄×C₁₀₁	—	4	2	no	—
186	C₂×C₄×C₁₀₁	—	4	2	no	—
187	C₂×C₄×C₁₀₁	—	4	2	no	—
188	C₂×C₄×C₁₀₁	—	4	2	no	—
189	C₂×C₄×C₁₀₁	—	4	4	no	—
190	C₂×C₄×C₁₀₁	—	4	4	no	—
191	C₂×C₄×C₁₀₁	—	4	4	no	—
192	C₂×C₄×C₁₀₁	—	4	4	no	—
193	C₂×C₄×C₁₀₁	C₂×C₄⋊C₄	1	4	yes	—
194	C₂×C₄×C₁₀₁	C₂×C₄⋊C₄	1	4	yes	—
195	C₂×C₄×C₁₀₁	#117	1	8	yes	complemented
196	C₂²×C₁₀₁	—	2	4	no	—
197	C₂²×C₁₀₁	—	2	8	no	—
198	C₂²×C₁₀₁	—	2	8	no	—
199	C₂²×C₁₀₁	—	2	8	no	—
200	C₂²×C₁₀₁	—	2	16	no	—
201	C₂²×C₁₀₁	—	2	8	no	—
202	C₂²×C₁₀₁	—	2	4	no	—
203	C₂²×C₁₀₁	#385	1	8	yes	—
204	C₂²×C₁₀₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
205	C₂²×C₁₀₁	C₂×#117	1	2	yes	—
206	C₂²×C₁₀₁	C₂×C₄×D₄	1	2	yes	—
207	C₂²×C₁₀₁	#518	1	1	yes	characteristic
208	C₂²×C₁₀₁	#519	1	1	yes	characteristic
209	C₂²×C₁₀₁	C₂×#120	1	1	yes	characteristic
210	C₂²×C₁₀₁	C₂×C₂²⋊Q₈	1	2	yes	—
211	C₂²×C₁₀₁	C₂×#123	1	1	yes	characteristic
212	C₂²×C₁₀₁	#532	1	2	yes	—
213	C₂²×C₁₀₁	#533	1	2	yes	—
214	C₂²×C₁₀₁	#537	1	2	yes	—
215	C₂²×C₁₀₁	#544	1	2	yes	—
216	C₂²×C₁₀₁	#546	1	4	yes	—
217	C₂²×C₁₀₁	#547	1	4	yes	—
218	C₂²×C₁₀₁	#551	1	4	yes	—
219	C₂²×C₁₀₁	#552	1	4	yes	—
220	C₄×C₁₀₁	—	2	8	no	—
221	C₄×C₁₀₁	—	2	4	no	—
222	C₄×C₁₀₁	—	2	4	no	—
223	C₄×C₁₀₁	—	4	4	no	—
224	C₄×C₁₀₁	—	4	8	no	—
225	C₄×C₁₀₁	—	8	2	no	—
226	C₄×C₁₀₁	—	8	2	no	—
227	#13878	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
228	C₂×C₁₀₁	—	2	8	no	—
229	C₂×C₁₀₁	#2285	1	1	yes	characteristic
230	C₂×C₁₀₁	C₂×#385	1	1	yes	characteristic
231	C₂×C₁₀₁	#2316	1	1	yes	characteristic
232	C₂×C₁₀₁	#2342	1	2	yes	—
233	C₂×C₁₀₁	#2344	1	2	yes	—
234	C₂×C₁₀₁	#2430	1	2	yes	—
235	C₂×C₁₀₁	#2438	1	4	yes	—
236	C₂×C₁₀₁	#2498	1	2	yes	—
237	C₂²×#117	C₂×C₁₀₁	1	1	yes	characteristic
238	C₂×#381	C₂×C₁₀₁	1	1	yes	characteristic
239	C₂×#380	C₂×C₁₀₁	1	2	yes	—
240	C₂²×#95	C₂×C₁₀₁	1	1	yes	characteristic
241	#1444	C₂×C₁₀₁	1	2	yes	complemented
242	#1442	C₂×C₁₀₁	1	2	yes	complemented
243	#1436	C₂×C₁₀₁	1	4	yes	complemented
244	C₂²⋊#95	C₂×C₁₀₁	1	2	yes	—
245	C₁₀₁	#13878	1	1	yes	characteristic, direct product factor, Sylow
246	C₂⁴×C₄	C₂²×C₁₀₁	1	2	yes	—
247	C₂⁴×C₄	C₂²×C₁₀₁	1	1	yes	characteristic
248	C₂×#117	—	2	4	no	—
249	C₂×#117	—	2	8	no	—
250	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	2	yes	—
251	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	4	yes	—
252	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
253	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
254	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	2	yes	—
255	C₂²×C₄²	C₂²×C₁₀₁	1	2	yes	—
256	#381	—	2	4	no	—
257	#380	—	2	8	no	—
258	C₂×#95	C₄×C₁₀₁	1	8	yes	complemented
259	C₂×#95	C₂²×C₁₀₁	1	4	yes	—
260	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
261	C₂×#95	C₂²×C₁₀₁	1	4	yes	—
262	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
263	C₂×#95	C₂²×C₁₀₁	1	4	yes	—
264	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
265	C₂×#95	C₂²×C₁₀₁	1	1	yes	characteristic
266	C₂×#95	C₂²×C₁₀₁	1	1	yes	characteristic
267	C₂⁵	C₂³×C₁₀₁	1	1	yes	characteristic
268	C₂³×C₄	—	2	4	no	—
269	C₂³×C₄	—	2	4	no	—
270	C₂³×C₄	—	2	4	no	—
271	C₂³×C₄	—	2	4	no	—
272	C₂³×C₄	—	2	8	no	—
273	C₂³×C₄	—	4	4	no	—
274	C₂³×C₄	C₂×C₄×C₁₀₁	1	8	yes	—
275	C₂³×C₄	C₂×C₄×C₁₀₁	1	4	yes	—
276	C₂³×C₄	D₄×C₁₀₁	1	4	yes	—
277	C₂³×C₄	Q₈×C₁₀₁	1	4	yes	—
278	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
279	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
280	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
281	C₂³×C₄	C₂³×C₁₀₁	1	4	yes	—
282	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
283	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
284	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
285	#117	—	2	32	no	—
286	C₂×C₄⋊C₄	—	2	8	no	—
287	C₂×C₄⋊C₄	—	2	4	no	—
288	C₂×C₄⋊C₄	—	2	8	no	—
289	C₂×C₄⋊C₄	—	2	8	no	—
290	C₂×C₄⋊C₄	—	4	4	no	—
291	C₂×C₂²⋊C₄	—	2	4	no	—
292	C₂×C₂²⋊C₄	—	2	4	no	—
293	C₂×C₂²⋊C₄	—	2	4	no	—
294	C₂×C₂²⋊C₄	—	2	2	no	—
295	C₂×C₂²⋊C₄	—	2	2	no	—
296	C₂×C₂²⋊C₄	—	2	4	no	—
297	C₂×C₂²⋊C₄	D₄×C₁₀₁	1	8	yes	—
298	C₂×C₄²	—	2	8	no	—
299	C₂×C₄²	—	2	4	no	—
300	#95	—	2	8	no	—
301	#95	—	2	4	no	—
302	#95	—	2	4	no	—
303	#95	—	2	8	no	—
304	#95	—	4	4	no	—
305	#95	C₂×C₄×C₁₀₁	1	4	yes	—
306	#95	C₂×C₄×C₁₀₁	1	8	yes	—
307	#95	C₂×C₄×C₁₀₁	1	4	yes	—
308	C₂⁴	—	2	4	no	—
309	C₂⁴	—	2	2	no	—
310	C₂⁴	—	2	2	no	—
311	C₂⁴	C₂²×C₄×C₁₀₁	1	2	yes	—
312	C₂⁴	C₂×D₄×C₁₀₁	1	2	yes	—
313	C₂⁴	C₂×D₄×C₁₀₁	1	4	yes	—
314	C₂⁴	C₂×Q₈×C₁₀₁	1	2	yes	—
315	C₂⁴	#41×C₁₀₁	1	4	yes	—
316	C₂⁴	C₂⁴×C₁₀₁	1	1	yes	characteristic
317	C₂²×C₄	—	2	16	no	—
318	C₂²×C₄	—	2	8	no	—
319	C₂²×C₄	—	2	16	no	—
320	C₂²×C₄	—	2	8	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	4	no	—
328	C₂²×C₄	—	2	16	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	2	4	no	—
331	C₂²×C₄	—	2	4	no	—
332	C₂²×C₄	—	2	4	no	—
333	C₂²×C₄	—	2	4	no	—
334	C₂²×C₄	—	2	4	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	4	no	—
337	C₂²×C₄	—	2	4	no	—
338	C₂²×C₄	—	2	4	no	—
339	C₂²×C₄	—	2	16	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	4	no	—
343	C₂²×C₄	—	2	4	no	—
344	C₂²×C₄	—	2	4	no	—
345	C₂²×C₄	—	2	4	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	4	8	no	—
351	C₂²×C₄	—	4	16	no	—
352	C₂²×C₄	—	4	16	no	—
353	C₂²×C₄	C₄⋊C₄×C₁₀₁	1	16	yes	complemented
354	C₂²×C₄	C₂²×C₄×C₁₀₁	1	4	yes	—
355	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
356	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
357	C₂²×C₄	C₂²×C₄×C₁₀₁	1	4	yes	—
358	C₂²×C₄	C₂×D₄×C₁₀₁	1	8	yes	—
359	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
360	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
361	C₂²×C₄	C₂×Q₈×C₁₀₁	1	2	yes	—
362	C₂²×C₄	C₂×Q₈×C₁₀₁	1	2	yes	—
363	C₂²×C₄	#41×C₁₀₁	1	8	yes	—
364	C₄⋊C₄	—	2	16	no	—
365	C₄⋊C₄	—	4	16	no	—
366	C₂²⋊C₄	—	2	16	no	—
367	C₂²⋊C₄	—	4	4	no	—
368	C₂²⋊C₄	—	4	4	no	—
369	C₄²	—	2	16	no	—
370	C₂³	—	2	4	no	—
371	C₂³	—	2	2	no	—
372	C₂³	—	2	2	no	—
373	C₂³	—	2	4	no	—
374	C₂³	—	2	4	no	—
375	C₂³	—	2	4	no	—
376	C₂³	—	2	4	no	—
377	C₂³	—	2	8	no	—
378	C₂³	—	2	8	no	—
379	C₂³	—	2	8	no	—
380	C₂³	—	2	8	no	—
381	C₂³	C₂×C₄⋊C₄×C₁₀₁	1	4	yes	—
382	C₂³	C₄×D₄×C₁₀₁	1	8	yes	—
383	C₂³	#120×C₁₀₁	1	4	yes	—
384	C₂³	C₂²⋊Q₈×C₁₀₁	1	8	yes	—
385	C₂³	#123×C₁₀₁	1	4	yes	—
386	C₂³	C₂³×C₄×C₁₀₁	1	1	yes	characteristic
387	C₂³	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
388	C₂³	C₂²×D₄×C₁₀₁	1	2	yes	—
389	C₂³	C₂²×Q₈×C₁₀₁	1	1	yes	characteristic
390	C₂³	C₂×#41×C₁₀₁	1	4	yes	—
391	C₂³	C₂×#41×C₁₀₁	1	2	yes	—
392	C₂³	H(5,𝔽₂)×C₁₀₁	1	2	yes	—
393	C₂³	2₋¹⁺⁴×C₁₀₁	1	2	yes	—
394	C₂×C₄	—	2	4	no	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	2	4	no	—
397	C₂×C₄	—	2	4	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	4	no	—
401	C₂×C₄	—	2	4	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	8	no	—
405	C₂×C₄	—	2	8	no	—
406	C₂×C₄	—	2	32	no	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	2	8	no	—
411	C₂×C₄	—	2	8	no	—
412	C₂×C₄	—	2	8	no	—
413	C₂×C₄	—	4	32	no	—
414	C₂×C₄	—	4	4	no	—
415	C₂×C₄	—	4	4	no	—
416	C₂×C₄	—	4	4	no	—
417	C₂×C₄	—	4	4	no	—
418	C₂×C₄	—	4	4	no	—
419	C₂×C₄	—	4	4	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	4	no	—
427	C₂×C₄	—	4	4	no	—
428	C₂×C₄	—	4	4	no	—
429	C₂×C₄	—	4	4	no	—
430	C₂×C₄	C₂×C₄⋊C₄×C₁₀₁	1	4	yes	—
431	C₂×C₄	C₂×C₄⋊C₄×C₁₀₁	1	4	yes	—
432	C₂×C₄	#117×C₁₀₁	1	8	yes	complemented
433	C₂²	—	2	8	no	—
434	C₂²	—	2	16	no	—
435	C₂²	—	2	8	no	—
436	C₂²	—	2	4	no	—
437	C₂²	—	2	4	no	—
438	C₂²	—	2	8	no	—
439	C₂²	—	2	8	no	—
440	C₂²	#385×C₁₀₁	1	8	yes	—
441	C₂²	C₂²×C₄⋊C₄×C₁₀₁	1	1	yes	characteristic
442	C₂²	C₂×#117×C₁₀₁	1	2	yes	—
443	C₂²	C₂×C₄×D₄×C₁₀₁	1	2	yes	—
444	C₂²	#518×C₁₀₁	1	1	yes	characteristic
445	C₂²	#519×C₁₀₁	1	1	yes	characteristic
446	C₂²	C₂×#120×C₁₀₁	1	1	yes	characteristic
447	C₂²	C₂×C₂²⋊Q₈×C₁₀₁	1	2	yes	—
448	C₂²	C₂×#123×C₁₀₁	1	1	yes	characteristic
449	C₂²	#532×C₁₀₁	1	2	yes	—
450	C₂²	#533×C₁₀₁	1	2	yes	—
451	C₂²	#537×C₁₀₁	1	2	yes	—
452	C₂²	#544×C₁₀₁	1	2	yes	—
453	C₂²	#546×C₁₀₁	1	4	yes	—
454	C₂²	#547×C₁₀₁	1	4	yes	—
455	C₂²	#551×C₁₀₁	1	4	yes	—
456	C₂²	#552×C₁₀₁	1	4	yes	—
457	C₄	—	2	4	no	—
458	C₄	—	2	4	no	—
459	C₄	—	2	8	no	—
460	C₄	—	4	8	no	—
461	C₄	—	4	4	no	—
462	C₄	—	8	2	no	—
463	C₄	—	8	2	no	—
464	C₂	—	2	8	no	—
465	C₂	C₁₀₁×#2285	1	1	yes	characteristic
466	C₂	C₂×#385×C₁₀₁	1	1	yes	characteristic
467	C₂	C₁₀₁×#2316	1	1	yes	characteristic
468	C₂	C₁₀₁×#2342	1	2	yes	—
469	C₂	C₁₀₁×#2344	1	2	yes	—
470	C₂	C₁₀₁×#2430	1	2	yes	—
471	C₂	C₁₀₁×#2438	1	4	yes	—
472	C₂	C₁₀₁×#2498	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₁₀₁	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₀₁
Frattini, cosocle	C₂⁴	C₂⁴×C₁₀₁
prime radical	C₂⁵×C₁₀₁	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₀₁ ◁ G

Complements

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

N	H ≅ G/N	type
5. C₁₀₁×#1444	C₂	semidirect
6. C₁₀₁×#1442	C₂	semidirect
7. C₁₀₁×#1436	C₂	semidirect
21. C₂×#95×C₁₀₁	C₄	semidirect
116. C₂²×C₄×C₁₀₁	C₄⋊C₄	semidirect
195. C₂×C₄×C₁₀₁	#117	semidirect
227. #13878	C₁₀₁	direct (N × H)
241. #1444	C₂×C₁₀₁	semidirect
242. #1442	C₂×C₁₀₁	semidirect
243. #1436	C₂×C₁₀₁	semidirect
245. C₁₀₁	#13878	direct (N × H)
258. C₂×#95	C₄×C₁₀₁	semidirect
353. C₂²×C₄	C₄⋊C₄×C₁₀₁	semidirect
432. C₂×C₄	#117×C₁₀₁	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×#117×C₁₀₁	2
C₂×#381×C₁₀₁	2
C₂×#380×C₁₀₁	2
C₂²×#95×C₁₀₁	2
C₁₀₁×#1444	2
C₁₀₁×#1442	2
C₁₀₁×#1436	2
C₁₀₁×C₂²⋊#95	2
#13878	101

Subgroups — C101×#13878 #38796029

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#13878 #38796029