Subgroups — C₁₀₁×#13918 #38796069

Order 25856.

1426 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	C₂×#389×C₁₀₁	C₂	1	2	yes	maximal
2	C₂×#382×C₁₀₁	C₂	1	2	yes	maximal
3	C₂×C₄×C₄⋊C₄×C₁₀₁	C₂	1	1	yes	maximal, characteristic
4	C₁₀₁×#1442	C₂	1	4	yes	maximal
5	C₁₀₁×C₄⋊#95	C₂	1	2	yes	maximal
6	C₁₀₁×C₄⋊#95	C₂	1	1	yes	maximal, characteristic
7	C₁₀₁×#1434	C₂	1	2	yes	maximal
8	C₄×#95×C₁₀₁	C₂	1	1	yes	maximal, characteristic
9	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	2	yes	—
10	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	4	yes	—
11	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
12	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
13	C₂²×C₄²×C₁₀₁	C₂²	1	2	yes	—
14	C₂²×C₄²×C₁₀₁	C₂²	1	1	yes	characteristic
15	C₂²×C₄²×C₁₀₁	C₂²	1	2	yes	—
16	#389×C₁₀₁	—	2	8	no	—
17	#382×C₁₀₁	—	2	8	no	—
18	C₄×C₄⋊C₄×C₁₀₁	C₄	1	8	yes	complemented
19	C₂×#95×C₁₀₁	C₂²	1	1	yes	characteristic
20	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
21	C₂×#95×C₁₀₁	C₂²	1	4	yes	—
22	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
23	C₂×#95×C₁₀₁	C₂²	1	4	yes	—
24	C₂×#95×C₁₀₁	C₂²	1	4	yes	—
25	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
26	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
27	C₂×#95×C₁₀₁	C₂²	1	1	yes	characteristic
28	C₂³×C₄×C₁₀₁	C₂³	1	4	yes	—
29	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
30	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
31	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
32	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
33	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
34	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
35	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
36	C₂×C₄⋊C₄×C₁₀₁	—	2	4	no	—
37	C₂×C₄⋊C₄×C₁₀₁	—	2	8	no	—
38	C₂×C₄⋊C₄×C₁₀₁	—	2	8	no	—
39	C₂×C₄⋊C₄×C₁₀₁	—	2	4	no	—
40	C₂×C₄⋊C₄×C₁₀₁	—	2	4	no	—
41	C₂×C₄⋊C₄×C₁₀₁	—	2	4	no	—
42	C₂×C₄⋊C₄×C₁₀₁	—	4	4	no	—
43	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	4	yes	—
44	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	4	yes	—
45	C₂×C₄⋊C₄×C₁₀₁	D₄	1	4	yes	—
46	C₂×C₄⋊C₄×C₁₀₁	Q₈	1	4	yes	—
47	C₂×C₄²×C₁₀₁	—	2	4	no	—
48	C₂×C₄²×C₁₀₁	—	2	4	no	—
49	C₂×C₄²×C₁₀₁	—	2	4	no	—
50	C₂×C₄²×C₁₀₁	—	2	4	no	—
51	C₂×C₄²×C₁₀₁	—	2	4	no	—
52	C₂×C₄²×C₁₀₁	—	2	4	no	—
53	C₂×C₄²×C₁₀₁	C₂×C₄	1	4	yes	—
54	C₂×C₄²×C₁₀₁	C₂×C₄	1	8	yes	—
55	#95×C₁₀₁	—	2	8	no	—
56	#95×C₁₀₁	—	2	4	no	—
57	#95×C₁₀₁	—	2	8	no	—
58	#95×C₁₀₁	—	2	4	no	—
59	#95×C₁₀₁	—	2	2	no	—
60	#95×C₁₀₁	—	2	8	no	—
61	#95×C₁₀₁	—	4	2	no	—
62	#95×C₁₀₁	C₂×C₄	1	8	yes	—
63	#95×C₁₀₁	D₄	1	4	yes	—
64	C₂⁴×C₁₀₁	C₂⁴	1	1	yes	characteristic
65	C₂²×C₄×C₁₀₁	—	2	2	no	—
66	C₂²×C₄×C₁₀₁	—	2	2	no	—
67	C₂²×C₄×C₁₀₁	—	2	2	no	—
68	C₂²×C₄×C₁₀₁	—	2	2	no	—
69	C₂²×C₄×C₁₀₁	—	2	2	no	—
70	C₂²×C₄×C₁₀₁	—	2	2	no	—
71	C₂²×C₄×C₁₀₁	—	2	2	no	—
72	C₂²×C₄×C₁₀₁	—	2	2	no	—
73	C₂²×C₄×C₁₀₁	—	2	2	no	—
74	C₂²×C₄×C₁₀₁	—	2	4	no	—
75	C₂²×C₄×C₁₀₁	—	2	2	no	—
76	C₂²×C₄×C₁₀₁	—	2	2	no	—
77	C₂²×C₄×C₁₀₁	—	2	2	no	—
78	C₂²×C₄×C₁₀₁	—	2	2	no	—
79	C₂²×C₄×C₁₀₁	—	2	2	no	—
80	C₂²×C₄×C₁₀₁	—	2	2	no	—
81	C₂²×C₄×C₁₀₁	—	2	2	no	—
82	C₂²×C₄×C₁₀₁	—	2	2	no	—
83	C₂²×C₄×C₁₀₁	—	2	2	no	—
84	C₂²×C₄×C₁₀₁	—	2	4	no	—
85	C₂²×C₄×C₁₀₁	—	2	1	no	—
86	C₂²×C₄×C₁₀₁	—	2	2	no	—
87	C₂²×C₄×C₁₀₁	—	2	1	no	—
88	C₂²×C₄×C₁₀₁	—	2	2	no	—
89	C₂²×C₄×C₁₀₁	—	2	2	no	—
90	C₂²×C₄×C₁₀₁	—	2	2	no	—
91	C₂²×C₄×C₁₀₁	—	2	4	no	—
92	C₂²×C₄×C₁₀₁	—	2	4	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	C₂²×C₄	1	2	yes	—
99	C₂²×C₄×C₁₀₁	C₂²×C₄	1	4	yes	—
100	C₂²×C₄×C₁₀₁	C₂²×C₄	1	4	yes	—
101	C₂²×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
102	C₂²×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
103	C₂²×C₄×C₁₀₁	C₂×D₄	1	4	yes	—
104	C₂²×C₄×C₁₀₁	C₂×D₄	1	4	yes	—
105	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₁₀₁	C₂×Q₈	1	4	yes	—
108	C₂²×C₄×C₁₀₁	C₂×Q₈	1	2	yes	—
109	C₂²×C₄×C₁₀₁	#41	1	4	yes	—
110	C₂²×C₄×C₁₀₁	#41	1	2	yes	—
111	C₂²×C₄×C₁₀₁	#41	1	4	yes	—
112	C₂²×C₄×C₁₀₁	#41	1	4	yes	—
113	C₄⋊C₄×C₁₀₁	—	2	8	no	—
114	C₄⋊C₄×C₁₀₁	—	4	16	no	—
115	C₄⋊C₄×C₁₀₁	—	4	8	no	—
116	C₄⋊C₄×C₁₀₁	C₄⋊C₄	1	16	yes	—
117	C₄²×C₁₀₁	—	2	8	no	—
118	C₄²×C₁₀₁	—	2	16	no	—
119	C₄²×C₁₀₁	—	4	8	no	—
120	C₂³×C₁₀₁	C₂³×C₄	1	1	yes	characteristic
121	C₂³×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
122	C₂³×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
123	C₂³×C₁₀₁	C₂²×Q₈	1	1	yes	characteristic
124	C₂³×C₁₀₁	C₂×#41	1	2	yes	—
125	C₂³×C₁₀₁	C₂×#41	1	2	yes	—
126	C₂³×C₁₀₁	C₂×#41	1	1	yes	characteristic
127	C₂³×C₁₀₁	C₂×#41	1	2	yes	—
128	C₂³×C₁₀₁	H(5,𝔽₂)	1	1	yes	characteristic
129	C₂³×C₁₀₁	2₋¹⁺⁴	1	2	yes	—
130	C₂³×C₁₀₁	2₋¹⁺⁴	1	1	yes	characteristic
131	C₂×C₄×C₁₀₁	—	2	2	no	—
132	C₂×C₄×C₁₀₁	—	2	4	no	—
133	C₂×C₄×C₁₀₁	—	2	2	no	—
134	C₂×C₄×C₁₀₁	—	2	4	no	—
135	C₂×C₄×C₁₀₁	—	2	4	no	—
136	C₂×C₄×C₁₀₁	—	2	4	no	—
137	C₂×C₄×C₁₀₁	—	2	4	no	—
138	C₂×C₄×C₁₀₁	—	2	4	no	—
139	C₂×C₄×C₁₀₁	—	2	4	no	—
140	C₂×C₄×C₁₀₁	—	2	4	no	—
141	C₂×C₄×C₁₀₁	—	2	2	no	—
142	C₂×C₄×C₁₀₁	—	2	4	no	—
143	C₂×C₄×C₁₀₁	—	2	4	no	—
144	C₂×C₄×C₁₀₁	—	2	2	no	—
145	C₂×C₄×C₁₀₁	—	2	4	no	—
146	C₂×C₄×C₁₀₁	—	2	2	no	—
147	C₂×C₄×C₁₀₁	—	2	4	no	—
148	C₂×C₄×C₁₀₁	—	2	4	no	—
149	C₂×C₄×C₁₀₁	—	2	4	no	—
150	C₂×C₄×C₁₀₁	—	2	4	no	—
151	C₂×C₄×C₁₀₁	—	2	4	no	—
152	C₂×C₄×C₁₀₁	—	2	4	no	—
153	C₂×C₄×C₁₀₁	—	4	2	no	—
154	C₂×C₄×C₁₀₁	—	4	2	no	—
155	C₂×C₄×C₁₀₁	—	4	4	no	—
156	C₂×C₄×C₁₀₁	—	4	4	no	—
157	C₂×C₄×C₁₀₁	—	4	2	no	—
158	C₂×C₄×C₁₀₁	—	4	2	no	—
159	C₂×C₄×C₁₀₁	—	4	2	no	—
160	C₂×C₄×C₁₀₁	—	4	2	no	—
161	C₂×C₄×C₁₀₁	—	4	2	no	—
162	C₂×C₄×C₁₀₁	—	4	2	no	—
163	C₂×C₄×C₁₀₁	—	4	2	no	—
164	C₂×C₄×C₁₀₁	—	4	2	no	—
165	C₂×C₄×C₁₀₁	—	4	4	no	—
166	C₂×C₄×C₁₀₁	—	4	4	no	—
167	C₂×C₄×C₁₀₁	—	4	4	no	—
168	C₂×C₄×C₁₀₁	—	4	4	no	—
169	C₂×C₄×C₁₀₁	—	4	4	no	—
170	C₂×C₄×C₁₀₁	—	4	4	no	—
171	C₂×C₄×C₁₀₁	—	4	4	no	—
172	C₂×C₄×C₁₀₁	C₂×C₄⋊C₄	1	8	yes	—
173	C₂×C₄×C₁₀₁	C₂×C₄⋊C₄	1	4	yes	—
174	C₂×C₄×C₁₀₁	#117	1	4	yes	—
175	C₂×C₄×C₁₀₁	#117	1	4	yes	—
176	C₂×C₄×C₁₀₁	C₄×D₄	1	4	yes	—
177	C₂×C₄×C₁₀₁	#124	1	8	yes	—
178	C₂×C₄×C₁₀₁	#125	1	8	yes	—
179	C₂²×C₁₀₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
180	C₂²×C₁₀₁	C₂×#117	1	1	yes	characteristic
181	C₂²×C₁₀₁	C₂×#117	1	1	yes	characteristic
182	C₂²×C₁₀₁	C₂×C₄×D₄	1	1	yes	characteristic
183	C₂²×C₁₀₁	C₄×#41	1	1	yes	characteristic
184	C₂²×C₁₀₁	#519	1	1	yes	characteristic
185	C₂²×C₁₀₁	#520	1	1	yes	characteristic
186	C₂²×C₁₀₁	C₂×#124	1	2	yes	—
187	C₂²×C₁₀₁	C₂×#125	1	2	yes	—
188	C₂²×C₁₀₁	#529	1	2	yes	—
189	C₂²×C₁₀₁	#532	1	2	yes	—
190	C₂²×C₁₀₁	#541	1	2	yes	—
191	C₂²×C₁₀₁	#542	1	2	yes	—
192	C₂²×C₁₀₁	D₄²	1	1	yes	characteristic
193	C₂²×C₁₀₁	#547	1	2	yes	—
194	C₂²×C₁₀₁	#547	1	1	yes	characteristic
195	C₂²×C₁₀₁	#548	1	2	yes	—
196	C₂²×C₁₀₁	D₄×Q₈	1	1	yes	characteristic
197	C₂²×C₁₀₁	#552	1	2	yes	—
198	C₂²×C₁₀₁	#552	1	2	yes	—
199	C₂²×C₁₀₁	#554	1	1	yes	characteristic
200	C₂²×C₁₀₁	#555	1	2	yes	—
201	C₂²×C₁₀₁	#557	1	2	yes	—
202	C₄×C₁₀₁	—	2	4	no	—
203	C₄×C₁₀₁	—	2	8	no	—
204	C₄×C₁₀₁	—	4	2	no	—
205	C₄×C₁₀₁	—	4	4	no	—
206	C₄×C₁₀₁	—	4	4	no	—
207	C₄×C₁₀₁	—	4	4	no	—
208	C₄×C₁₀₁	—	8	4	no	—
209	C₄×C₁₀₁	#382	1	8	yes	complemented
210	#13918	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
211	C₂×C₁₀₁	C₂×#382	1	1	yes	characteristic
212	C₂×C₁₀₁	#2293	1	1	yes	characteristic
213	C₂×C₁₀₁	#2320	1	1	yes	characteristic
214	C₂×C₁₀₁	#2344	1	1	yes	characteristic
215	C₂×C₁₀₁	#2346	1	1	yes	characteristic
216	C₂×C₁₀₁	D₄×C₄⋊C₄	1	1	yes	characteristic
217	C₂×C₁₀₁	#2351	1	1	yes	characteristic
218	C₂×C₁₀₁	#2489	1	2	yes	—
219	C₂×C₁₀₁	#2491	1	2	yes	—
220	C₂×C₁₀₁	#2506	1	2	yes	—
221	C₂×C₁₀₁	#2508	1	2	yes	—
222	C₂×#389	C₂×C₁₀₁	1	2	yes	—
223	C₂×#382	C₂×C₁₀₁	1	2	yes	—
224	C₂×C₄×C₄⋊C₄	C₂×C₁₀₁	1	1	yes	characteristic
225	#1442	C₂×C₁₀₁	1	4	yes	—
226	C₄⋊#95	C₂×C₁₀₁	1	1	yes	characteristic
227	C₄⋊#95	C₂×C₁₀₁	1	2	yes	—
228	#1434	C₂×C₁₀₁	1	2	yes	—
229	C₄×#95	C₂×C₁₀₁	1	1	yes	characteristic
230	C₁₀₁	#13918	1	1	yes	characteristic, direct product factor, Sylow
231	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	2	yes	—
232	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	4	yes	—
233	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
234	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
235	C₂²×C₄²	C₂²×C₁₀₁	1	2	yes	—
236	C₂²×C₄²	C₂²×C₁₀₁	1	1	yes	characteristic
237	C₂²×C₄²	C₂²×C₁₀₁	1	2	yes	—
238	#389	—	2	8	no	—
239	#382	—	2	8	no	—
240	C₄×C₄⋊C₄	C₄×C₁₀₁	1	8	yes	complemented
241	C₂×#95	C₂²×C₁₀₁	1	1	yes	characteristic
242	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
243	C₂×#95	C₂²×C₁₀₁	1	4	yes	—
244	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
245	C₂×#95	C₂²×C₁₀₁	1	4	yes	—
246	C₂×#95	C₂²×C₁₀₁	1	4	yes	—
247	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
248	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
249	C₂×#95	C₂²×C₁₀₁	1	1	yes	characteristic
250	C₂³×C₄	C₂³×C₁₀₁	1	4	yes	—
251	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
252	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
253	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
254	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
255	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
256	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
257	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
258	C₂×C₄⋊C₄	—	2	4	no	—
259	C₂×C₄⋊C₄	—	2	8	no	—
260	C₂×C₄⋊C₄	—	2	8	no	—
261	C₂×C₄⋊C₄	—	2	4	no	—
262	C₂×C₄⋊C₄	—	2	4	no	—
263	C₂×C₄⋊C₄	—	2	4	no	—
264	C₂×C₄⋊C₄	—	4	4	no	—
265	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	4	yes	—
266	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	4	yes	—
267	C₂×C₄⋊C₄	D₄×C₁₀₁	1	4	yes	—
268	C₂×C₄⋊C₄	Q₈×C₁₀₁	1	4	yes	—
269	C₂×C₄²	—	2	4	no	—
270	C₂×C₄²	—	2	4	no	—
271	C₂×C₄²	—	2	4	no	—
272	C₂×C₄²	—	2	4	no	—
273	C₂×C₄²	—	2	4	no	—
274	C₂×C₄²	—	2	4	no	—
275	C₂×C₄²	C₂×C₄×C₁₀₁	1	4	yes	—
276	C₂×C₄²	C₂×C₄×C₁₀₁	1	8	yes	—
277	#95	—	2	8	no	—
278	#95	—	2	4	no	—
279	#95	—	2	8	no	—
280	#95	—	2	4	no	—
281	#95	—	2	2	no	—
282	#95	—	2	8	no	—
283	#95	—	4	2	no	—
284	#95	C₂×C₄×C₁₀₁	1	8	yes	—
285	#95	D₄×C₁₀₁	1	4	yes	—
286	C₂⁴	C₂⁴×C₁₀₁	1	1	yes	characteristic
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	2	4	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	2	4	no	—
307	C₂²×C₄	—	2	1	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	2	4	no	—
314	C₂²×C₄	—	2	4	no	—
315	C₂²×C₄	—	2	4	no	—
316	C₂²×C₄	—	2	4	no	—
317	C₂²×C₄	—	2	4	no	—
318	C₂²×C₄	—	2	4	no	—
319	C₂²×C₄	—	2	4	no	—
320	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
321	C₂²×C₄	C₂²×C₄×C₁₀₁	1	4	yes	—
322	C₂²×C₄	C₂²×C₄×C₁₀₁	1	4	yes	—
323	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
324	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
325	C₂²×C₄	C₂×D₄×C₁₀₁	1	4	yes	—
326	C₂²×C₄	C₂×D₄×C₁₀₁	1	4	yes	—
327	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
328	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
329	C₂²×C₄	C₂×Q₈×C₁₀₁	1	4	yes	—
330	C₂²×C₄	C₂×Q₈×C₁₀₁	1	2	yes	—
331	C₂²×C₄	#41×C₁₀₁	1	4	yes	—
332	C₂²×C₄	#41×C₁₀₁	1	2	yes	—
333	C₂²×C₄	#41×C₁₀₁	1	4	yes	—
334	C₂²×C₄	#41×C₁₀₁	1	4	yes	—
335	C₄⋊C₄	—	2	8	no	—
336	C₄⋊C₄	—	4	16	no	—
337	C₄⋊C₄	—	4	8	no	—
338	C₄⋊C₄	C₄⋊C₄×C₁₀₁	1	16	yes	—
339	C₄²	—	2	8	no	—
340	C₄²	—	2	16	no	—
341	C₄²	—	4	8	no	—
342	C₂³	C₂³×C₄×C₁₀₁	1	1	yes	characteristic
343	C₂³	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
344	C₂³	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
345	C₂³	C₂²×Q₈×C₁₀₁	1	1	yes	characteristic
346	C₂³	C₂×#41×C₁₀₁	1	2	yes	—
347	C₂³	C₂×#41×C₁₀₁	1	2	yes	—
348	C₂³	C₂×#41×C₁₀₁	1	1	yes	characteristic
349	C₂³	C₂×#41×C₁₀₁	1	2	yes	—
350	C₂³	H(5,𝔽₂)×C₁₀₁	1	1	yes	characteristic
351	C₂³	2₋¹⁺⁴×C₁₀₁	1	2	yes	—
352	C₂³	2₋¹⁺⁴×C₁₀₁	1	1	yes	characteristic
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	4	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	4	no	—
357	C₂×C₄	—	2	4	no	—
358	C₂×C₄	—	2	4	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	2	4	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	4	no	—
370	C₂×C₄	—	2	4	no	—
371	C₂×C₄	—	2	4	no	—
372	C₂×C₄	—	2	4	no	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	2	4	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	4	no	—
378	C₂×C₄	—	4	4	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	4	4	no	—
388	C₂×C₄	—	4	4	no	—
389	C₂×C₄	—	4	4	no	—
390	C₂×C₄	—	4	4	no	—
391	C₂×C₄	—	4	4	no	—
392	C₂×C₄	—	4	4	no	—
393	C₂×C₄	—	4	4	no	—
394	C₂×C₄	C₂×C₄⋊C₄×C₁₀₁	1	8	yes	—
395	C₂×C₄	C₂×C₄⋊C₄×C₁₀₁	1	4	yes	—
396	C₂×C₄	#117×C₁₀₁	1	4	yes	—
397	C₂×C₄	#117×C₁₀₁	1	4	yes	—
398	C₂×C₄	C₄×D₄×C₁₀₁	1	4	yes	—
399	C₂×C₄	#124×C₁₀₁	1	8	yes	—
400	C₂×C₄	#125×C₁₀₁	1	8	yes	—
401	C₂²	C₂²×C₄⋊C₄×C₁₀₁	1	1	yes	characteristic
402	C₂²	C₂×#117×C₁₀₁	1	1	yes	characteristic
403	C₂²	C₂×#117×C₁₀₁	1	1	yes	characteristic
404	C₂²	C₂×C₄×D₄×C₁₀₁	1	1	yes	characteristic
405	C₂²	C₄×#41×C₁₀₁	1	1	yes	characteristic
406	C₂²	#519×C₁₀₁	1	1	yes	characteristic
407	C₂²	#520×C₁₀₁	1	1	yes	characteristic
408	C₂²	C₂×#124×C₁₀₁	1	2	yes	—
409	C₂²	C₂×#125×C₁₀₁	1	2	yes	—
410	C₂²	#529×C₁₀₁	1	2	yes	—
411	C₂²	#532×C₁₀₁	1	2	yes	—
412	C₂²	#541×C₁₀₁	1	2	yes	—
413	C₂²	#542×C₁₀₁	1	2	yes	—
414	C₂²	D₄²×C₁₀₁	1	1	yes	characteristic
415	C₂²	#547×C₁₀₁	1	1	yes	characteristic
416	C₂²	#547×C₁₀₁	1	2	yes	—
417	C₂²	#548×C₁₀₁	1	2	yes	—
418	C₂²	D₄×Q₈×C₁₀₁	1	1	yes	characteristic
419	C₂²	#552×C₁₀₁	1	2	yes	—
420	C₂²	#552×C₁₀₁	1	2	yes	—
421	C₂²	#554×C₁₀₁	1	1	yes	characteristic
422	C₂²	#555×C₁₀₁	1	2	yes	—
423	C₂²	#557×C₁₀₁	1	2	yes	—
424	C₄	—	2	4	no	—
425	C₄	—	2	8	no	—
426	C₄	—	4	4	no	—
427	C₄	—	4	4	no	—
428	C₄	—	4	4	no	—
429	C₄	—	4	2	no	—
430	C₄	—	8	4	no	—
431	C₄	#382×C₁₀₁	1	8	yes	complemented
432	C₂	C₂×#382×C₁₀₁	1	1	yes	characteristic
433	C₂	C₁₀₁×#2293	1	1	yes	characteristic
434	C₂	C₁₀₁×#2320	1	1	yes	characteristic
435	C₂	C₁₀₁×#2344	1	1	yes	characteristic
436	C₂	C₁₀₁×#2346	1	1	yes	characteristic
437	C₂	D₄×C₄⋊C₄×C₁₀₁	1	1	yes	characteristic
438	C₂	C₁₀₁×#2351	1	1	yes	characteristic
439	C₂	C₁₀₁×#2489	1	2	yes	—
440	C₂	C₁₀₁×#2491	1	2	yes	—
441	C₂	C₁₀₁×#2506	1	2	yes	—
442	C₂	C₁₀₁×#2508	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₁₀₁	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₀₁
Frattini, cosocle	C₂⁴	C₂⁴×C₁₀₁
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
18. C₄×C₄⋊C₄×C₁₀₁	C₄	semidirect
209. C₄×C₁₀₁	#382	semidirect
210. #13918	C₁₀₁	direct (N × H)
230. C₁₀₁	#13918	direct (N × H)
240. C₄×C₄⋊C₄	C₄×C₁₀₁	semidirect
431. C₄	#382×C₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#389×C₁₀₁	2
C₂×#382×C₁₀₁	2
C₂×C₄×C₄⋊C₄×C₁₀₁	2
C₁₀₁×#1442	2
C₁₀₁×C₄⋊#95	2
C₁₀₁×#1434	2
C₄×#95×C₁₀₁	2
#13918	101

Subgroups — C101×#13918 #38796069

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#13918 #38796069