Subgroups — C₁₀₁×#13951 #38796102

Order 25856.

2006 conjugacy classes of subgroups.

The subgroup lattice has 540 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×#389×C₁₀₁	C₂	1	2	yes	maximal, complemented
3	C₂×#380×C₁₀₁	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×C₂²⋊C₄×C₁₀₁	C₂	1	1	yes	maximal, characteristic
5	C₁₀₁×#1439	C₂	1	4	yes	maximal
6	C₁₀₁×C₄⋊#95	C₂	1	2	yes	maximal, complemented
7	C₁₀₁×C₄⋊#95	C₂	1	2	yes	maximal, complemented
8	C₁₀₁×#1434	C₂	1	2	yes	maximal, complemented
9	C₂⁴×C₄×C₁₀₁	C₂²	1	1	yes	characteristic
10	C₂×#117×C₁₀₁	—	2	8	no	—
11	C₂×#117×C₁₀₁	C₄	1	8	yes	complemented
12	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	2	yes	—
13	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	4	yes	—
14	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
15	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
16	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	2	yes	—
17	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	2	yes	—
18	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	2	yes	—
19	C₂²×C₄²×C₁₀₁	C₂²	1	2	yes	—
20	C₂²×C₄²×C₁₀₁	C₂²	1	2	yes	—
21	#389×C₁₀₁	—	2	8	no	—
22	#380×C₁₀₁	—	2	4	no	—
23	C₄×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
24	C₂×#95×C₁₀₁	C₂²	1	1	yes	characteristic
25	C₂×#95×C₁₀₁	C₂²	1	4	yes	—
26	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
27	C₂×#95×C₁₀₁	C₂²	1	4	yes	—
28	C₂×#95×C₁₀₁	C₂²	1	1	yes	characteristic
29	C₂×#95×C₁₀₁	C₂²	1	4	yes	—
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	C₂×C₄	1	4	yes	—
34	C₂³×C₄×C₁₀₁	D₄	1	4	yes	—
35	C₂³×C₄×C₁₀₁	Q₈	1	4	yes	—
36	C₂³×C₄×C₁₀₁	C₂³	1	4	yes	—
37	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
38	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
39	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
40	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
41	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
42	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
43	#117×C₁₀₁	—	2	32	no	—
44	C₂×C₄⋊C₄×C₁₀₁	—	2	4	no	—
45	C₂×C₄⋊C₄×C₁₀₁	—	2	4	no	—
46	C₂×C₄⋊C₄×C₁₀₁	—	2	8	no	—
47	C₂×C₄⋊C₄×C₁₀₁	—	2	4	no	—
48	C₂×C₄⋊C₄×C₁₀₁	—	2	8	no	—
49	C₂×C₄⋊C₄×C₁₀₁	—	2	4	no	—
50	C₂×C₄⋊C₄×C₁₀₁	—	4	4	no	—
51	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	4	yes	—
52	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	4	yes	—
53	C₂×C₄⋊C₄×C₁₀₁	D₄	1	8	yes	—
54	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
55	C₂×C₂²⋊C₄×C₁₀₁	—	2	8	no	—
56	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
57	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
58	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
59	C₂×C₂²⋊C₄×C₁₀₁	—	4	2	no	—
60	C₂×C₂²⋊C₄×C₁₀₁	—	4	2	no	—
61	C₂×C₂²⋊C₄×C₁₀₁	C₂×C₄	1	8	yes	—
62	C₂×C₄²×C₁₀₁	—	2	8	no	—
63	C₂×C₄²×C₁₀₁	—	2	4	no	—
64	C₂×C₄²×C₁₀₁	—	2	4	no	—
65	C₂×C₄²×C₁₀₁	—	2	4	no	—
66	C₂×C₄²×C₁₀₁	C₂×C₄	1	8	yes	—
67	#95×C₁₀₁	—	2	2	no	—
68	#95×C₁₀₁	—	2	2	no	—
69	#95×C₁₀₁	—	2	4	no	—
70	#95×C₁₀₁	—	2	8	no	—
71	#95×C₁₀₁	—	2	8	no	—
72	#95×C₁₀₁	—	4	4	no	—
73	C₂⁴×C₁₀₁	—	2	2	no	—
74	C₂⁴×C₁₀₁	—	2	2	no	—
75	C₂⁴×C₁₀₁	—	2	2	no	—
76	C₂⁴×C₁₀₁	—	2	2	no	—
77	C₂⁴×C₁₀₁	—	2	1	no	—
78	C₂⁴×C₁₀₁	—	2	1	no	—
79	C₂⁴×C₁₀₁	—	2	1	no	—
80	C₂⁴×C₁₀₁	—	2	1	no	—
81	C₂⁴×C₁₀₁	C₂²×C₄	1	2	yes	—
82	C₂⁴×C₁₀₁	C₂×D₄	1	2	yes	—
83	C₂⁴×C₁₀₁	C₂×Q₈	1	2	yes	—
84	C₂⁴×C₁₀₁	C₂⁴	1	1	yes	characteristic
85	C₂²×C₄×C₁₀₁	—	2	2	no	—
86	C₂²×C₄×C₁₀₁	—	2	4	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	8	no	—
91	C₂²×C₄×C₁₀₁	—	2	8	no	—
92	C₂²×C₄×C₁₀₁	—	2	16	no	—
93	C₂²×C₄×C₁₀₁	—	2	16	no	—
94	C₂²×C₄×C₁₀₁	—	2	2	no	—
95	C₂²×C₄×C₁₀₁	—	2	2	no	—
96	C₂²×C₄×C₁₀₁	—	2	2	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	2	no	—
101	C₂²×C₄×C₁₀₁	—	2	2	no	—
102	C₂²×C₄×C₁₀₁	—	2	2	no	—
103	C₂²×C₄×C₁₀₁	—	2	2	no	—
104	C₂²×C₄×C₁₀₁	—	2	2	no	—
105	C₂²×C₄×C₁₀₁	—	2	2	no	—
106	C₂²×C₄×C₁₀₁	—	2	2	no	—
107	C₂²×C₄×C₁₀₁	—	2	2	no	—
108	C₂²×C₄×C₁₀₁	—	2	2	no	—
109	C₂²×C₄×C₁₀₁	—	2	2	no	—
110	C₂²×C₄×C₁₀₁	—	2	4	no	—
111	C₂²×C₄×C₁₀₁	—	2	4	no	—
112	C₂²×C₄×C₁₀₁	—	2	4	no	—
113	C₂²×C₄×C₁₀₁	—	2	4	no	—
114	C₂²×C₄×C₁₀₁	—	2	4	no	—
115	C₂²×C₄×C₁₀₁	—	2	4	no	—
116	C₂²×C₄×C₁₀₁	—	2	4	no	—
117	C₂²×C₄×C₁₀₁	C₄⋊C₄	1	16	yes	complemented
118	C₂²×C₄×C₁₀₁	C₂²×C₄	1	4	yes	—
119	C₂²×C₄×C₁₀₁	C₂²×C₄	1	4	yes	—
120	C₂²×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
121	C₂²×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
122	C₂²×C₄×C₁₀₁	C₂×D₄	1	8	yes	—
123	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₁₀₁	C₂×D₄	1	4	yes	—
125	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₁₀₁	C₂×Q₈	1	2	yes	—
127	C₂²×C₄×C₁₀₁	C₂×Q₈	1	2	yes	—
128	C₂²×C₄×C₁₀₁	#41	1	4	yes	—
129	C₂²×C₄×C₁₀₁	#41	1	4	yes	—
130	C₂²×C₄×C₁₀₁	#41	1	4	yes	—
131	C₄⋊C₄×C₁₀₁	—	2	8	no	—
132	C₄⋊C₄×C₁₀₁	—	4	16	no	—
133	C₄⋊C₄×C₁₀₁	—	4	8	no	—
134	C₄⋊C₄×C₁₀₁	C₂²⋊C₄	1	16	yes	complemented
135	C₂²⋊C₄×C₁₀₁	—	2	16	no	—
136	C₂²⋊C₄×C₁₀₁	—	2	16	no	—
137	C₂²⋊C₄×C₁₀₁	—	4	8	no	—
138	C₄²×C₁₀₁	—	2	16	no	—
139	C₄²×C₁₀₁	—	4	8	no	—
140	C₂³×C₁₀₁	—	2	2	no	—
141	C₂³×C₁₀₁	—	2	2	no	—
142	C₂³×C₁₀₁	—	2	2	no	—
143	C₂³×C₁₀₁	—	2	2	no	—
144	C₂³×C₁₀₁	—	2	2	no	—
145	C₂³×C₁₀₁	—	2	2	no	—
146	C₂³×C₁₀₁	—	2	4	no	—
147	C₂³×C₁₀₁	—	2	4	no	—
148	C₂³×C₁₀₁	—	2	4	no	—
149	C₂³×C₁₀₁	—	2	4	no	—
150	C₂³×C₁₀₁	—	2	2	no	—
151	C₂³×C₁₀₁	—	2	2	no	—
152	C₂³×C₁₀₁	—	2	2	no	—
153	C₂³×C₁₀₁	—	2	2	no	—
154	C₂³×C₁₀₁	—	4	2	no	—
155	C₂³×C₁₀₁	—	4	2	no	—
156	C₂³×C₁₀₁	—	4	2	no	—
157	C₂³×C₁₀₁	—	4	2	no	—
158	C₂³×C₁₀₁	—	4	2	no	—
159	C₂³×C₁₀₁	—	4	2	no	—
160	C₂³×C₁₀₁	—	4	2	no	—
161	C₂³×C₁₀₁	—	4	2	no	—
162	C₂³×C₁₀₁	C₂×C₄⋊C₄	1	4	yes	—
163	C₂³×C₁₀₁	C₂³×C₄	1	1	yes	characteristic
164	C₂³×C₁₀₁	C₂²×D₄	1	2	yes	—
165	C₂³×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
166	C₂³×C₁₀₁	C₂²×Q₈	1	1	yes	characteristic
167	C₂³×C₁₀₁	C₂×#41	1	2	yes	—
168	C₂³×C₁₀₁	C₂×#41	1	2	yes	—
169	C₂³×C₁₀₁	C₂×#41	1	2	yes	—
170	C₂³×C₁₀₁	H(5,𝔽₂)	1	1	yes	characteristic
171	C₂³×C₁₀₁	H(5,𝔽₂)	1	1	yes	characteristic
172	C₂³×C₁₀₁	2₋¹⁺⁴	1	1	yes	characteristic
173	C₂³×C₁₀₁	2₋¹⁺⁴	1	1	yes	characteristic
174	C₂×C₄×C₁₀₁	—	2	2	no	—
175	C₂×C₄×C₁₀₁	—	2	2	no	—
176	C₂×C₄×C₁₀₁	—	2	4	no	—
177	C₂×C₄×C₁₀₁	—	2	4	no	—
178	C₂×C₄×C₁₀₁	—	2	4	no	—
179	C₂×C₄×C₁₀₁	—	2	4	no	—
180	C₂×C₄×C₁₀₁	—	2	8	no	—
181	C₂×C₄×C₁₀₁	—	2	8	no	—
182	C₂×C₄×C₁₀₁	—	2	32	no	—
183	C₂×C₄×C₁₀₁	—	2	4	no	—
184	C₂×C₄×C₁₀₁	—	2	4	no	—
185	C₂×C₄×C₁₀₁	—	2	4	no	—
186	C₂×C₄×C₁₀₁	—	2	4	no	—
187	C₂×C₄×C₁₀₁	—	2	4	no	—
188	C₂×C₄×C₁₀₁	—	2	4	no	—
189	C₂×C₄×C₁₀₁	—	2	4	no	—
190	C₂×C₄×C₁₀₁	—	2	4	no	—
191	C₂×C₄×C₁₀₁	—	2	4	no	—
192	C₂×C₄×C₁₀₁	—	4	2	no	—
193	C₂×C₄×C₁₀₁	—	4	2	no	—
194	C₂×C₄×C₁₀₁	—	4	2	no	—
195	C₂×C₄×C₁₀₁	—	4	2	no	—
196	C₂×C₄×C₁₀₁	—	4	2	no	—
197	C₂×C₄×C₁₀₁	—	4	4	no	—
198	C₂×C₄×C₁₀₁	—	4	4	no	—
199	C₂×C₄×C₁₀₁	—	4	2	no	—
200	C₂×C₄×C₁₀₁	—	4	2	no	—
201	C₂×C₄×C₁₀₁	—	4	2	no	—
202	C₂×C₄×C₁₀₁	—	4	4	no	—
203	C₂×C₄×C₁₀₁	—	4	4	no	—
204	C₂×C₄×C₁₀₁	—	4	4	no	—
205	C₂×C₄×C₁₀₁	—	4	4	no	—
206	C₂×C₄×C₁₀₁	—	4	4	no	—
207	C₂×C₄×C₁₀₁	—	4	4	no	—
208	C₂×C₄×C₁₀₁	—	4	4	no	—
209	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	8	yes	—
210	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	4	yes	—
211	C₂×C₄×C₁₀₁	C₂×C₄⋊C₄	1	4	yes	—
212	C₂×C₄×C₁₀₁	C₂×C₄⋊C₄	1	4	yes	—
213	C₂×C₄×C₁₀₁	#117	1	4	yes	—
214	C₂×C₄×C₁₀₁	#121	1	8	yes	—
215	C₂×C₄×C₁₀₁	C₂²⋊Q₈	1	8	yes	—
216	C₂²×C₁₀₁	—	2	4	no	—
217	C₂²×C₁₀₁	—	2	4	no	—
218	C₂²×C₁₀₁	—	2	4	no	—
219	C₂²×C₁₀₁	—	4	2	no	—
220	C₂²×C₁₀₁	—	4	2	no	—
221	C₂²×C₁₀₁	—	4	2	no	—
222	C₂²×C₁₀₁	—	4	2	no	—
223	C₂²×C₁₀₁	—	4	4	no	—
224	C₂²×C₁₀₁	—	4	4	no	—
225	C₂²×C₁₀₁	—	4	4	no	—
226	C₂²×C₁₀₁	—	4	4	no	—
227	C₂²×C₁₀₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
228	C₂²×C₁₀₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
229	C₂²×C₁₀₁	C₂×#117	1	1	yes	characteristic
230	C₂²×C₁₀₁	C₄×#41	1	1	yes	characteristic
231	C₂²×C₁₀₁	C₄×#41	1	1	yes	characteristic
232	C₂²×C₁₀₁	#520	1	1	yes	characteristic
233	C₂²×C₁₀₁	#520	1	1	yes	characteristic
234	C₂²×C₁₀₁	C₂×#121	1	2	yes	—
235	C₂²×C₁₀₁	C₂×C₂²⋊Q₈	1	2	yes	—
236	C₂²×C₁₀₁	#525	1	2	yes	—
237	C₂²×C₁₀₁	#533	1	2	yes	—
238	C₂²×C₁₀₁	#535	1	1	yes	characteristic
239	C₂²×C₁₀₁	#536	1	1	yes	characteristic
240	C₂²×C₁₀₁	#544	1	1	yes	characteristic
241	C₂²×C₁₀₁	#544	1	1	yes	characteristic
242	C₂²×C₁₀₁	#546	1	2	yes	—
243	C₂²×C₁₀₁	#547	1	2	yes	—
244	C₂²×C₁₀₁	#548	1	2	yes	—
245	C₂²×C₁₀₁	#550	1	2	yes	—
246	C₂²×C₁₀₁	#552	1	2	yes	—
247	C₂²×C₁₀₁	#553	1	2	yes	—
248	C₂²×C₁₀₁	#555	1	2	yes	—
249	C₂²×C₁₀₁	#556	1	2	yes	—
250	C₄×C₁₀₁	—	2	8	no	—
251	C₄×C₁₀₁	—	2	4	no	—
252	C₄×C₁₀₁	—	4	4	no	—
253	C₄×C₁₀₁	—	4	4	no	—
254	C₄×C₁₀₁	—	4	4	no	—
255	C₄×C₁₀₁	—	8	4	no	—
256	C₄×C₁₀₁	#380	1	8	yes	—
257	#13951	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
258	C₂×C₁₀₁	—	4	4	no	—
259	C₂×C₁₀₁	C₂×#380	1	1	yes	characteristic
260	C₂×C₁₀₁	#2296	1	1	yes	characteristic
261	C₂×C₁₀₁	#2317	1	1	yes	characteristic
262	C₂×C₁₀₁	#2339	1	1	yes	characteristic
263	C₂×C₁₀₁	#2341	1	1	yes	characteristic
264	C₂×C₁₀₁	#2346	1	1	yes	characteristic
265	C₂×C₁₀₁	#2347	1	1	yes	characteristic
266	C₂×C₁₀₁	#2414	1	2	yes	—
267	C₂×C₁₀₁	#2415	1	2	yes	—
268	C₂×C₁₀₁	#2439	1	2	yes	—
269	C₂×C₁₀₁	#2441	1	2	yes	—
270	C₂²×#117	C₂×C₁₀₁	1	1	yes	characteristic
271	C₂×#389	C₂×C₁₀₁	1	2	yes	complemented
272	C₂×#380	C₂×C₁₀₁	1	1	yes	characteristic
273	C₂×C₄×C₂²⋊C₄	C₂×C₁₀₁	1	1	yes	characteristic
274	#1439	C₂×C₁₀₁	1	4	yes	—
275	C₄⋊#95	C₂×C₁₀₁	1	2	yes	complemented
276	C₄⋊#95	C₂×C₁₀₁	1	2	yes	complemented
277	#1434	C₂×C₁₀₁	1	2	yes	complemented
278	C₁₀₁	#13951	1	1	yes	characteristic, direct product factor, Sylow
279	C₂⁴×C₄	C₂²×C₁₀₁	1	1	yes	characteristic
280	C₂×#117	—	2	8	no	—
281	C₂×#117	C₄×C₁₀₁	1	8	yes	complemented
282	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	2	yes	—
283	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	4	yes	—
284	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
285	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
286	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	2	yes	—
287	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	2	yes	—
288	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	2	yes	—
289	C₂²×C₄²	C₂²×C₁₀₁	1	2	yes	—
290	C₂²×C₄²	C₂²×C₁₀₁	1	2	yes	—
291	#389	—	2	8	no	—
292	#380	—	2	4	no	—
293	C₄×C₂²⋊C₄	—	2	4	no	—
294	C₂×#95	C₂²×C₁₀₁	1	1	yes	characteristic
295	C₂×#95	C₂²×C₁₀₁	1	4	yes	—
296	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
297	C₂×#95	C₂²×C₁₀₁	1	4	yes	—
298	C₂×#95	C₂²×C₁₀₁	1	1	yes	characteristic
299	C₂×#95	C₂²×C₁₀₁	1	4	yes	—
300	C₂⁵	C₂³×C₁₀₁	1	1	yes	characteristic
301	C₂³×C₄	—	2	4	no	—
302	C₂³×C₄	—	2	4	no	—
303	C₂³×C₄	C₂×C₄×C₁₀₁	1	4	yes	—
304	C₂³×C₄	D₄×C₁₀₁	1	4	yes	—
305	C₂³×C₄	Q₈×C₁₀₁	1	4	yes	—
306	C₂³×C₄	C₂³×C₁₀₁	1	4	yes	—
307	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
308	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
309	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
310	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
311	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
312	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
313	#117	—	2	32	no	—
314	C₂×C₄⋊C₄	—	2	4	no	—
315	C₂×C₄⋊C₄	—	2	4	no	—
316	C₂×C₄⋊C₄	—	2	8	no	—
317	C₂×C₄⋊C₄	—	2	4	no	—
318	C₂×C₄⋊C₄	—	2	8	no	—
319	C₂×C₄⋊C₄	—	2	4	no	—
320	C₂×C₄⋊C₄	—	4	4	no	—
321	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	4	yes	—
322	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	4	yes	—
323	C₂×C₄⋊C₄	D₄×C₁₀₁	1	8	yes	—
324	C₂×C₂²⋊C₄	—	2	4	no	—
325	C₂×C₂²⋊C₄	—	2	8	no	—
326	C₂×C₂²⋊C₄	—	2	4	no	—
327	C₂×C₂²⋊C₄	—	2	4	no	—
328	C₂×C₂²⋊C₄	—	2	4	no	—
329	C₂×C₂²⋊C₄	—	4	2	no	—
330	C₂×C₂²⋊C₄	—	4	2	no	—
331	C₂×C₂²⋊C₄	C₂×C₄×C₁₀₁	1	8	yes	—
332	C₂×C₄²	—	2	8	no	—
333	C₂×C₄²	—	2	4	no	—
334	C₂×C₄²	—	2	4	no	—
335	C₂×C₄²	—	2	4	no	—
336	C₂×C₄²	C₂×C₄×C₁₀₁	1	8	yes	—
337	#95	—	2	2	no	—
338	#95	—	2	2	no	—
339	#95	—	2	4	no	—
340	#95	—	2	8	no	—
341	#95	—	2	8	no	—
342	#95	—	4	4	no	—
343	C₂⁴	—	2	2	no	—
344	C₂⁴	—	2	2	no	—
345	C₂⁴	—	2	2	no	—
346	C₂⁴	—	2	2	no	—
347	C₂⁴	—	2	1	no	—
348	C₂⁴	—	2	1	no	—
349	C₂⁴	—	2	1	no	—
350	C₂⁴	—	2	1	no	—
351	C₂⁴	C₂²×C₄×C₁₀₁	1	2	yes	—
352	C₂⁴	C₂×D₄×C₁₀₁	1	2	yes	—
353	C₂⁴	C₂×Q₈×C₁₀₁	1	2	yes	—
354	C₂⁴	C₂⁴×C₁₀₁	1	1	yes	characteristic
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	4	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	8	no	—
361	C₂²×C₄	—	2	8	no	—
362	C₂²×C₄	—	2	16	no	—
363	C₂²×C₄	—	2	16	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	4	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	4	no	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	—	2	4	no	—
381	C₂²×C₄	—	2	4	no	—
382	C₂²×C₄	—	2	4	no	—
383	C₂²×C₄	—	2	4	no	—
384	C₂²×C₄	—	2	4	no	—
385	C₂²×C₄	—	2	4	no	—
386	C₂²×C₄	—	2	4	no	—
387	C₂²×C₄	C₄⋊C₄×C₁₀₁	1	16	yes	complemented
388	C₂²×C₄	C₂²×C₄×C₁₀₁	1	4	yes	—
389	C₂²×C₄	C₂²×C₄×C₁₀₁	1	4	yes	—
390	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
391	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
392	C₂²×C₄	C₂×D₄×C₁₀₁	1	8	yes	—
393	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
394	C₂²×C₄	C₂×D₄×C₁₀₁	1	4	yes	—
395	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
396	C₂²×C₄	C₂×Q₈×C₁₀₁	1	2	yes	—
397	C₂²×C₄	C₂×Q₈×C₁₀₁	1	2	yes	—
398	C₂²×C₄	#41×C₁₀₁	1	4	yes	—
399	C₂²×C₄	#41×C₁₀₁	1	4	yes	—
400	C₂²×C₄	#41×C₁₀₁	1	4	yes	—
401	C₄⋊C₄	—	2	8	no	—
402	C₄⋊C₄	—	4	16	no	—
403	C₄⋊C₄	—	4	8	no	—
404	C₄⋊C₄	C₂²⋊C₄×C₁₀₁	1	16	yes	complemented
405	C₂²⋊C₄	—	2	16	no	—
406	C₂²⋊C₄	—	2	16	no	—
407	C₂²⋊C₄	—	4	8	no	—
408	C₄²	—	2	16	no	—
409	C₄²	—	4	8	no	—
410	C₂³	—	2	2	no	—
411	C₂³	—	2	2	no	—
412	C₂³	—	2	2	no	—
413	C₂³	—	2	2	no	—
414	C₂³	—	2	2	no	—
415	C₂³	—	2	2	no	—
416	C₂³	—	2	4	no	—
417	C₂³	—	2	4	no	—
418	C₂³	—	2	4	no	—
419	C₂³	—	2	4	no	—
420	C₂³	—	2	2	no	—
421	C₂³	—	2	2	no	—
422	C₂³	—	2	2	no	—
423	C₂³	—	2	2	no	—
424	C₂³	—	4	2	no	—
425	C₂³	—	4	2	no	—
426	C₂³	—	4	2	no	—
427	C₂³	—	4	2	no	—
428	C₂³	—	4	2	no	—
429	C₂³	—	4	2	no	—
430	C₂³	—	4	2	no	—
431	C₂³	—	4	2	no	—
432	C₂³	C₂×C₄⋊C₄×C₁₀₁	1	4	yes	—
433	C₂³	C₂³×C₄×C₁₀₁	1	1	yes	characteristic
434	C₂³	C₂²×D₄×C₁₀₁	1	2	yes	—
435	C₂³	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
436	C₂³	C₂²×Q₈×C₁₀₁	1	1	yes	characteristic
437	C₂³	C₂×#41×C₁₀₁	1	2	yes	—
438	C₂³	C₂×#41×C₁₀₁	1	2	yes	—
439	C₂³	C₂×#41×C₁₀₁	1	2	yes	—
440	C₂³	H(5,𝔽₂)×C₁₀₁	1	1	yes	characteristic
441	C₂³	H(5,𝔽₂)×C₁₀₁	1	1	yes	characteristic
442	C₂³	2₋¹⁺⁴×C₁₀₁	1	1	yes	characteristic
443	C₂³	2₋¹⁺⁴×C₁₀₁	1	1	yes	characteristic
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	4	no	—
447	C₂×C₄	—	2	4	no	—
448	C₂×C₄	—	2	4	no	—
449	C₂×C₄	—	2	4	no	—
450	C₂×C₄	—	2	8	no	—
451	C₂×C₄	—	2	8	no	—
452	C₂×C₄	—	2	32	no	—
453	C₂×C₄	—	2	4	no	—
454	C₂×C₄	—	2	4	no	—
455	C₂×C₄	—	2	4	no	—
456	C₂×C₄	—	2	4	no	—
457	C₂×C₄	—	2	4	no	—
458	C₂×C₄	—	2	4	no	—
459	C₂×C₄	—	2	4	no	—
460	C₂×C₄	—	2	4	no	—
461	C₂×C₄	—	2	4	no	—
462	C₂×C₄	—	4	2	no	—
463	C₂×C₄	—	4	2	no	—
464	C₂×C₄	—	4	2	no	—
465	C₂×C₄	—	4	2	no	—
466	C₂×C₄	—	4	2	no	—
467	C₂×C₄	—	4	4	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	4	4	no	—
470	C₂×C₄	—	4	2	no	—
471	C₂×C₄	—	4	2	no	—
472	C₂×C₄	—	4	4	no	—
473	C₂×C₄	—	4	4	no	—
474	C₂×C₄	—	4	4	no	—
475	C₂×C₄	—	4	4	no	—
476	C₂×C₄	—	4	4	no	—
477	C₂×C₄	—	4	4	no	—
478	C₂×C₄	—	4	4	no	—
479	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	8	yes	—
480	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	4	yes	—
481	C₂×C₄	C₂×C₄⋊C₄×C₁₀₁	1	4	yes	—
482	C₂×C₄	C₂×C₄⋊C₄×C₁₀₁	1	4	yes	—
483	C₂×C₄	#117×C₁₀₁	1	4	yes	—
484	C₂×C₄	#121×C₁₀₁	1	8	yes	—
485	C₂×C₄	C₂²⋊Q₈×C₁₀₁	1	8	yes	—
486	C₂²	—	2	4	no	—
487	C₂²	—	2	4	no	—
488	C₂²	—	2	4	no	—
489	C₂²	—	4	4	no	—
490	C₂²	—	4	4	no	—
491	C₂²	—	4	4	no	—
492	C₂²	—	4	4	no	—
493	C₂²	—	4	2	no	—
494	C₂²	—	4	2	no	—
495	C₂²	—	4	2	no	—
496	C₂²	—	4	2	no	—
497	C₂²	C₂²×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
498	C₂²	C₂²×C₄⋊C₄×C₁₀₁	1	1	yes	characteristic
499	C₂²	C₂×#117×C₁₀₁	1	1	yes	characteristic
500	C₂²	C₄×#41×C₁₀₁	1	1	yes	characteristic
501	C₂²	C₄×#41×C₁₀₁	1	1	yes	characteristic
502	C₂²	#520×C₁₀₁	1	1	yes	characteristic
503	C₂²	#520×C₁₀₁	1	1	yes	characteristic
504	C₂²	C₂×#121×C₁₀₁	1	2	yes	—
505	C₂²	C₂×C₂²⋊Q₈×C₁₀₁	1	2	yes	—
506	C₂²	#525×C₁₀₁	1	2	yes	—
507	C₂²	#533×C₁₀₁	1	2	yes	—
508	C₂²	#535×C₁₀₁	1	1	yes	characteristic
509	C₂²	#536×C₁₀₁	1	1	yes	characteristic
510	C₂²	#544×C₁₀₁	1	1	yes	characteristic
511	C₂²	#544×C₁₀₁	1	1	yes	characteristic
512	C₂²	#546×C₁₀₁	1	2	yes	—
513	C₂²	#547×C₁₀₁	1	2	yes	—
514	C₂²	#548×C₁₀₁	1	2	yes	—
515	C₂²	#550×C₁₀₁	1	2	yes	—
516	C₂²	#552×C₁₀₁	1	2	yes	—
517	C₂²	#553×C₁₀₁	1	2	yes	—
518	C₂²	#555×C₁₀₁	1	2	yes	—
519	C₂²	#556×C₁₀₁	1	2	yes	—
520	C₄	—	2	4	no	—
521	C₄	—	2	8	no	—
522	C₄	—	4	4	no	—
523	C₄	—	4	4	no	—
524	C₄	—	4	4	no	—
525	C₄	—	8	4	no	—
526	C₄	#380×C₁₀₁	1	8	yes	—
527	C₂	—	4	4	no	—
528	C₂	C₂×#380×C₁₀₁	1	1	yes	characteristic
529	C₂	C₁₀₁×#2296	1	1	yes	characteristic
530	C₂	C₁₀₁×#2317	1	1	yes	characteristic
531	C₂	C₁₀₁×#2339	1	1	yes	characteristic
532	C₂	C₁₀₁×#2341	1	1	yes	characteristic
533	C₂	C₁₀₁×#2346	1	1	yes	characteristic
534	C₂	C₁₀₁×#2347	1	1	yes	characteristic
535	C₂	C₁₀₁×#2414	1	2	yes	—
536	C₂	C₁₀₁×#2415	1	2	yes	—
537	C₂	C₁₀₁×#2439	1	2	yes	—
538	C₂	C₁₀₁×#2441	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
2. C₂×#389×C₁₀₁	C₂	semidirect
6. C₁₀₁×C₄⋊#95	C₂	semidirect
7. C₁₀₁×C₄⋊#95	C₂	semidirect
8. C₁₀₁×#1434	C₂	semidirect
11. C₂×#117×C₁₀₁	C₄	semidirect
117. C₂²×C₄×C₁₀₁	C₄⋊C₄	semidirect
134. C₄⋊C₄×C₁₀₁	C₂²⋊C₄	semidirect
257. #13951	C₁₀₁	direct (N × H)
271. C₂×#389	C₂×C₁₀₁	semidirect
275. C₄⋊#95	C₂×C₁₀₁	semidirect
276. C₄⋊#95	C₂×C₁₀₁	semidirect
277. #1434	C₂×C₁₀₁	semidirect
278. C₁₀₁	#13951	direct (N × H)
281. C₂×#117	C₄×C₁₀₁	semidirect
387. C₂²×C₄	C₄⋊C₄×C₁₀₁	semidirect
404. C₄⋊C₄	C₂²⋊C₄×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×#389×C₁₀₁	2
C₂×#380×C₁₀₁	2
C₂×C₄×C₂²⋊C₄×C₁₀₁	2
C₁₀₁×#1439	2
C₁₀₁×C₄⋊#95	2
C₁₀₁×#1434	2
#13951	101

Subgroups — C101×#13951 #38796102

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#13951 #38796102