Subgroups — C₁₀₁×#21766 #38803917

Order 25856.

1486 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#525×C₁₀₁	C₂	1	1	yes	maximal, characteristic
2	C₂×#407×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₀₁×#2280	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₀₁×#1895	C₂	1	2	yes	maximal, complemented
5	C₁₀₁×#1894	C₂	1	2	yes	maximal, complemented
6	C₁₀₁×#1875	C₂	1	2	yes	maximal, complemented
7	C₁₀₁×#1873	C₂	1	2	yes	maximal, complemented
8	C₁₀₁×#1825	C₂	1	2	yes	maximal, complemented
9	C₁₀₁×#1788	C₂	1	2	yes	maximal, complemented
10	C₂²×#41×C₁₀₁	C₂²	1	1	yes	characteristic
11	C₂⁴×C₄×C₁₀₁	C₂²	1	1	yes	characteristic
12	C₂²×M₁₆×C₁₀₁	C₂²	1	2	yes	—
13	#525×C₁₀₁	—	2	4	no	—
14	#525×C₁₀₁	C₄	1	8	yes	complemented
15	C₂×#123×C₁₀₁	—	2	1	no	—
16	C₂×C₂²⋊Q₈×C₁₀₁	C₂²	1	1	yes	characteristic
17	C₂×C₂²⋊Q₈×C₁₀₁	C₂²	1	1	yes	characteristic
18	C₂×#121×C₁₀₁	C₂²	1	1	yes	characteristic
19	C₂×#121×C₁₀₁	C₂²	1	1	yes	characteristic
20	C₂×#120×C₁₀₁	—	2	1	no	—
21	C₂×C₄×D₄×C₁₀₁	—	2	1	no	—
22	C₂×C₄×D₄×C₁₀₁	—	2	1	no	—
23	C₂×#117×C₁₀₁	C₂²	1	1	yes	characteristic
24	C₂×#117×C₁₀₁	C₂²	1	2	yes	—
25	C₂×#103×C₁₀₁	C₂²	1	4	yes	complemented
26	C₂×#102×C₁₀₁	C₂²	1	4	yes	complemented
27	#407×C₁₀₁	—	2	4	no	—
28	C₂×C₂²⋊C₈×C₁₀₁	C₂²	1	2	yes	—
29	C₂×C₂²⋊C₈×C₁₀₁	C₂²	1	2	yes	—
30	#381×C₁₀₁	—	2	1	no	—
31	#380×C₁₀₁	C₂²	1	2	yes	—
32	#380×C₁₀₁	C₂²	1	2	yes	—
33	#379×C₁₀₁	—	2	1	no	—
34	C₄×C₂²⋊C₄×C₁₀₁	—	2	1	no	—
35	C₄×C₂²⋊C₄×C₁₀₁	—	2	1	no	—
36	#340×C₁₀₁	C₂²	1	4	yes	complemented
37	#340×C₁₀₁	C₂²	1	4	yes	complemented
38	C₂⁵×C₁₀₁	D₄	1	1	yes	characteristic
39	C₂×#41×C₁₀₁	—	2	2	no	—
40	C₂×#41×C₁₀₁	—	4	4	no	—
41	C₂×#41×C₁₀₁	C₂×C₄	1	4	yes	—
42	C₂²×Q₈×C₁₀₁	C₂³	1	1	yes	characteristic
43	C₂²×D₄×C₁₀₁	—	2	1	no	—
44	C₂²×D₄×C₁₀₁	—	2	1	no	—
45	C₂²×D₄×C₁₀₁	—	2	1	no	—
46	C₂²×D₄×C₁₀₁	C₂³	1	1	yes	characteristic
47	C₂³×C₄×C₁₀₁	—	2	1	no	—
48	C₂³×C₄×C₁₀₁	—	4	4	no	—
49	C₂³×C₄×C₁₀₁	C₂×C₄	1	4	yes	—
50	C₂³×C₄×C₁₀₁	D₄	1	1	yes	characteristic
51	C₂³×C₄×C₁₀₁	D₄	1	1	yes	characteristic
52	C₂³×C₄×C₁₀₁	D₄	1	1	yes	characteristic
53	C₂³×C₄×C₁₀₁	D₄	1	4	yes	—
54	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
55	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
56	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
57	C₂×M₁₆×C₁₀₁	—	2	4	no	—
58	C₂×M₁₆×C₁₀₁	—	4	4	no	—
59	C₂²×C₈×C₁₀₁	C₂³	1	4	yes	—
60	#123×C₁₀₁	—	2	8	no	—
61	C₂²⋊Q₈×C₁₀₁	—	2	2	no	—
62	C₂²⋊Q₈×C₁₀₁	—	2	2	no	—
63	C₂²⋊Q₈×C₁₀₁	C₂×C₄	1	4	yes	—
64	C₂²⋊Q₈×C₁₀₁	C₂×C₄	1	4	yes	—
65	#121×C₁₀₁	—	2	2	no	—
66	#121×C₁₀₁	—	2	2	no	—
67	#121×C₁₀₁	C₂×C₄	1	4	yes	—
68	#121×C₁₀₁	C₂×C₄	1	4	yes	—
69	#120×C₁₀₁	—	2	8	no	—
70	C₄×D₄×C₁₀₁	—	2	8	no	—
71	C₄×D₄×C₁₀₁	—	2	8	no	—
72	#117×C₁₀₁	—	2	2	no	—
73	#117×C₁₀₁	—	4	4	no	—
74	#117×C₁₀₁	C₂×C₄	1	4	yes	—
75	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
76	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
77	C₂×C₄⋊C₄×C₁₀₁	C₂³	1	4	yes	—
78	C₂×C₄⋊C₄×C₁₀₁	C₂³	1	1	yes	characteristic
79	C₂×C₄⋊C₄×C₁₀₁	C₂³	1	1	yes	characteristic
80	C₂×C₂²⋊C₄×C₁₀₁	—	2	1	no	—
81	C₂×C₂²⋊C₄×C₁₀₁	—	2	1	no	—
82	C₂×C₂²⋊C₄×C₁₀₁	—	2	1	no	—
83	C₂×C₂²⋊C₄×C₁₀₁	—	2	1	no	—
84	C₂×C₂²⋊C₄×C₁₀₁	—	2	1	no	—
85	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
86	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
87	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
88	C₂×C₄²×C₁₀₁	—	2	1	no	—
89	C₂×C₄²×C₁₀₁	—	2	2	no	—
90	#103×C₁₀₁	—	4	4	no	—
91	#102×C₁₀₁	—	4	4	no	—
92	C₂²⋊C₈×C₁₀₁	—	2	4	no	—
93	C₂²⋊C₈×C₁₀₁	—	2	4	no	—
94	#95×C₁₀₁	—	2	2	no	—
95	#95×C₁₀₁	—	2	2	no	—
96	C₂⁴×C₁₀₁	—	2	1	no	—
97	C₂⁴×C₁₀₁	—	4	2	no	—
98	C₂⁴×C₁₀₁	—	4	2	no	—
99	C₂⁴×C₁₀₁	—	4	2	no	—
100	C₂⁴×C₁₀₁	C₂²⋊C₄	1	4	yes	—
101	C₂⁴×C₁₀₁	C₂×D₄	1	1	yes	characteristic
102	C₂⁴×C₁₀₁	C₂×D₄	1	1	yes	characteristic
103	C₂⁴×C₁₀₁	C₂×D₄	1	1	yes	characteristic
104	#41×C₁₀₁	—	4	8	no	—
105	#41×C₁₀₁	—	4	8	no	—
106	C₂×Q₈×C₁₀₁	—	2	1	no	—
107	C₂×Q₈×C₁₀₁	—	2	4	no	—
108	C₂×Q₈×C₁₀₁	C₂²×C₄	1	2	yes	—
109	C₂×D₄×C₁₀₁	—	2	4	no	—
110	C₂×D₄×C₁₀₁	—	2	4	no	—
111	C₂×D₄×C₁₀₁	—	2	4	no	—
112	C₂×D₄×C₁₀₁	—	2	1	no	—
113	C₂×D₄×C₁₀₁	—	2	4	no	—
114	C₂×D₄×C₁₀₁	—	4	4	no	—
115	C₂×D₄×C₁₀₁	—	4	4	no	—
116	C₂×D₄×C₁₀₁	—	4	4	no	—
117	C₂×D₄×C₁₀₁	C₂²×C₄	1	2	yes	—
118	C₂²×C₄×C₁₀₁	—	2	4	no	—
119	C₂²×C₄×C₁₀₁	—	2	4	no	—
120	C₂²×C₄×C₁₀₁	—	2	4	no	—
121	C₂²×C₄×C₁₀₁	—	2	1	no	—
122	C₂²×C₄×C₁₀₁	—	2	1	no	—
123	C₂²×C₄×C₁₀₁	—	2	1	no	—
124	C₂²×C₄×C₁₀₁	—	2	4	no	—
125	C₂²×C₄×C₁₀₁	—	2	4	no	—
126	C₂²×C₄×C₁₀₁	—	4	8	no	—
127	C₂²×C₄×C₁₀₁	—	4	8	no	—
128	C₂²×C₄×C₁₀₁	—	4	2	no	—
129	C₂²×C₄×C₁₀₁	—	4	2	no	—
130	C₂²×C₄×C₁₀₁	—	4	2	no	—
131	C₂²×C₄×C₁₀₁	—	4	4	no	—
132	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	4	yes	—
133	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	4	yes	—
134	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	4	yes	—
135	C₂²×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
136	C₂²×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
137	C₂²×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
138	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
142	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
143	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
144	C₂²×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
145	M₁₆×C₁₀₁	—	4	8	no	—
146	C₂×C₈×C₁₀₁	—	2	4	no	—
147	C₂×C₈×C₁₀₁	—	2	4	no	—
148	C₂×C₈×C₁₀₁	—	2	4	no	—
149	C₄⋊C₄×C₁₀₁	—	2	4	no	—
150	C₄⋊C₄×C₁₀₁	—	2	4	no	—
151	C₄⋊C₄×C₁₀₁	—	2	1	no	—
152	C₄⋊C₄×C₁₀₁	—	2	1	no	—
153	C₄⋊C₄×C₁₀₁	—	2	4	no	—
154	C₄⋊C₄×C₁₀₁	—	2	4	no	—
155	C₄⋊C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
156	C₄⋊C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
157	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
158	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
159	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
160	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
161	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
162	C₂²⋊C₄×C₁₀₁	—	4	4	no	—
163	C₂²⋊C₄×C₁₀₁	—	4	4	no	—
164	C₂²⋊C₄×C₁₀₁	—	4	4	no	—
165	C₄²×C₁₀₁	—	2	4	no	—
166	C₄²×C₁₀₁	—	4	4	no	—
167	C₂³×C₁₀₁	—	2	2	no	—
168	C₂³×C₁₀₁	—	2	2	no	—
169	C₂³×C₁₀₁	—	2	2	no	—
170	C₂³×C₁₀₁	—	2	2	no	—
171	C₂³×C₁₀₁	—	2	2	no	—
172	C₂³×C₁₀₁	—	2	2	no	—
173	C₂³×C₁₀₁	—	2	2	no	—
174	C₂³×C₁₀₁	—	2	2	no	—
175	C₂³×C₁₀₁	—	2	2	no	—
176	C₂³×C₁₀₁	—	2	2	no	—
177	C₂³×C₁₀₁	—	4	4	no	—
178	C₂³×C₁₀₁	—	4	4	no	—
179	C₂³×C₁₀₁	—	4	4	no	—
180	C₂³×C₁₀₁	—	4	16	no	—
181	C₂³×C₁₀₁	—	4	2	no	—
182	C₂³×C₁₀₁	—	4	2	no	—
183	C₂³×C₁₀₁	—	4	2	no	—
184	C₂³×C₁₀₁	C₂×C₂²⋊C₄	1	2	yes	—
185	C₂³×C₁₀₁	C₂×C₂²⋊C₄	1	2	yes	—
186	C₂³×C₁₀₁	C₂×C₂²⋊C₄	1	2	yes	—
187	C₂³×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
188	Q₈×C₁₀₁	—	2	4	no	—
189	Q₈×C₁₀₁	—	4	2	no	—
190	D₄×C₁₀₁	—	2	4	no	—
191	D₄×C₁₀₁	—	4	8	no	—
192	D₄×C₁₀₁	—	4	8	no	—
193	D₄×C₁₀₁	—	4	8	no	—
194	D₄×C₁₀₁	—	4	2	no	—
195	C₂×C₄×C₁₀₁	—	2	2	no	—
196	C₂×C₄×C₁₀₁	—	2	2	no	—
197	C₂×C₄×C₁₀₁	—	2	2	no	—
198	C₂×C₄×C₁₀₁	—	2	4	no	—
199	C₂×C₄×C₁₀₁	—	2	4	no	—
200	C₂×C₄×C₁₀₁	—	2	4	no	—
201	C₂×C₄×C₁₀₁	—	2	4	no	—
202	C₂×C₄×C₁₀₁	—	2	4	no	—
203	C₂×C₄×C₁₀₁	—	2	4	no	—
204	C₂×C₄×C₁₀₁	—	2	2	no	—
205	C₂×C₄×C₁₀₁	—	2	2	no	—
206	C₂×C₄×C₁₀₁	—	2	2	no	—
207	C₂×C₄×C₁₀₁	—	4	4	no	—
208	C₂×C₄×C₁₀₁	—	4	4	no	—
209	C₂×C₄×C₁₀₁	—	4	4	no	—
210	C₂×C₄×C₁₀₁	—	4	8	no	—
211	C₂×C₄×C₁₀₁	—	4	2	no	—
212	C₂×C₄×C₁₀₁	—	4	2	no	—
213	C₂×C₄×C₁₀₁	—	4	2	no	—
214	C₂×C₄×C₁₀₁	—	4	4	no	—
215	C₂×C₄×C₁₀₁	—	4	4	no	—
216	C₂×C₄×C₁₀₁	—	4	4	no	—
217	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	2	yes	—
218	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	2	yes	—
219	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	2	yes	—
220	C₂×C₄×C₁₀₁	C₂³×C₄	1	1	yes	characteristic
221	C₂×C₄×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
222	C₂×C₄×C₁₀₁	H(5,𝔽₂)	1	4	yes	—
223	C₈×C₁₀₁	—	4	4	no	—
224	C₂²×C₁₀₁	—	2	2	no	—
225	C₂²×C₁₀₁	—	2	2	no	—
226	C₂²×C₁₀₁	—	2	2	no	—
227	C₂²×C₁₀₁	—	2	2	no	—
228	C₂²×C₁₀₁	—	2	2	no	—
229	C₂²×C₁₀₁	—	2	2	no	—
230	C₂²×C₁₀₁	—	2	2	no	—
231	C₂²×C₁₀₁	—	2	2	no	—
232	C₂²×C₁₀₁	—	2	2	no	—
233	C₂²×C₁₀₁	—	4	16	no	—
234	C₂²×C₁₀₁	—	4	4	no	—
235	C₂²×C₁₀₁	—	4	4	no	—
236	C₂²×C₁₀₁	—	4	4	no	—
237	C₂²×C₁₀₁	—	4	2	no	—
238	C₂²×C₁₀₁	—	4	2	no	—
239	C₂²×C₁₀₁	—	4	2	no	—
240	C₂²×C₁₀₁	—	8	4	no	—
241	C₂²×C₁₀₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
242	C₂²×C₁₀₁	#534	1	2	yes	—
243	C₂²×C₁₀₁	#575	1	2	yes	—
244	C₂²×C₁₀₁	#575	1	2	yes	—
245	C₄×C₁₀₁	—	2	2	no	—
246	C₄×C₁₀₁	—	2	2	no	—
247	C₄×C₁₀₁	—	2	2	no	—
248	C₄×C₁₀₁	—	4	2	no	—
249	C₄×C₁₀₁	—	4	2	no	—
250	C₄×C₁₀₁	—	4	2	no	—
251	C₄×C₁₀₁	—	8	4	no	—
252	C₄×C₁₀₁	#518	1	2	yes	—
253	C₄×C₁₀₁	#534	1	2	yes	—
254	#21766	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
255	C₂×C₁₀₁	—	4	2	no	—
256	C₂×C₁₀₁	—	4	2	no	—
257	C₂×C₁₀₁	—	4	2	no	—
258	C₂×C₁₀₁	—	8	2	no	—
259	C₂×C₁₀₁	#2308	1	1	yes	characteristic
260	C₂×C₁₀₁	#2896	1	1	yes	characteristic
261	C₂×C₁₀₁	#2896	1	1	yes	characteristic
262	C₂×C₁₀₁	#3197	1	4	yes	—
263	C₂×#525	C₂×C₁₀₁	1	1	yes	characteristic
264	C₂×#407	C₂×C₁₀₁	1	1	yes	characteristic, complemented
265	#2280	C₂×C₁₀₁	1	1	yes	characteristic, complemented
266	#1895	C₂×C₁₀₁	1	2	yes	complemented
267	#1894	C₂×C₁₀₁	1	2	yes	complemented
268	#1875	C₂×C₁₀₁	1	2	yes	complemented
269	#1873	C₂×C₁₀₁	1	2	yes	complemented
270	#1825	C₂×C₁₀₁	1	2	yes	complemented
271	#1788	C₂×C₁₀₁	1	2	yes	complemented
272	C₁₀₁	#21766	1	1	yes	characteristic, direct product factor, Sylow
273	C₂²×#41	C₂²×C₁₀₁	1	1	yes	characteristic
274	C₂⁴×C₄	C₂²×C₁₀₁	1	1	yes	characteristic
275	C₂²×M₁₆	C₂²×C₁₀₁	1	2	yes	—
276	#525	—	2	4	no	—
277	#525	C₄×C₁₀₁	1	8	yes	complemented
278	C₂×#123	—	2	1	no	—
279	C₂×C₂²⋊Q₈	C₂²×C₁₀₁	1	1	yes	characteristic
280	C₂×C₂²⋊Q₈	C₂²×C₁₀₁	1	1	yes	characteristic
281	C₂×#121	C₂²×C₁₀₁	1	1	yes	characteristic
282	C₂×#121	C₂²×C₁₀₁	1	1	yes	characteristic
283	C₂×#120	—	2	1	no	—
284	C₂×C₄×D₄	—	2	1	no	—
285	C₂×C₄×D₄	—	2	1	no	—
286	C₂×#117	C₂²×C₁₀₁	1	1	yes	characteristic
287	C₂×#117	C₂²×C₁₀₁	1	2	yes	—
288	C₂×#103	C₂²×C₁₀₁	1	4	yes	complemented
289	C₂×#102	C₂²×C₁₀₁	1	4	yes	complemented
290	#407	—	2	4	no	—
291	C₂×C₂²⋊C₈	C₂²×C₁₀₁	1	2	yes	—
292	C₂×C₂²⋊C₈	C₂²×C₁₀₁	1	2	yes	—
293	#381	—	2	1	no	—
294	#380	C₂²×C₁₀₁	1	2	yes	—
295	#380	C₂²×C₁₀₁	1	2	yes	—
296	#379	—	2	1	no	—
297	C₄×C₂²⋊C₄	—	2	1	no	—
298	C₄×C₂²⋊C₄	—	2	1	no	—
299	#340	C₂²×C₁₀₁	1	4	yes	complemented
300	#340	C₂²×C₁₀₁	1	4	yes	complemented
301	C₂⁵	D₄×C₁₀₁	1	1	yes	characteristic
302	C₂×#41	—	2	2	no	—
303	C₂×#41	—	4	4	no	—
304	C₂×#41	C₂×C₄×C₁₀₁	1	4	yes	—
305	C₂²×Q₈	C₂³×C₁₀₁	1	1	yes	characteristic
306	C₂²×D₄	—	2	1	no	—
307	C₂²×D₄	—	2	1	no	—
308	C₂²×D₄	—	2	1	no	—
309	C₂²×D₄	C₂³×C₁₀₁	1	1	yes	characteristic
310	C₂³×C₄	—	2	1	no	—
311	C₂³×C₄	—	4	4	no	—
312	C₂³×C₄	C₂×C₄×C₁₀₁	1	4	yes	—
313	C₂³×C₄	D₄×C₁₀₁	1	1	yes	characteristic
314	C₂³×C₄	D₄×C₁₀₁	1	1	yes	characteristic
315	C₂³×C₄	D₄×C₁₀₁	1	1	yes	characteristic
316	C₂³×C₄	D₄×C₁₀₁	1	4	yes	—
317	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
318	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
319	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
320	C₂×M₁₆	—	2	4	no	—
321	C₂×M₁₆	—	4	4	no	—
322	C₂²×C₈	C₂³×C₁₀₁	1	4	yes	—
323	#123	—	2	8	no	—
324	C₂²⋊Q₈	—	2	2	no	—
325	C₂²⋊Q₈	—	2	2	no	—
326	C₂²⋊Q₈	C₂×C₄×C₁₀₁	1	4	yes	—
327	C₂²⋊Q₈	C₂×C₄×C₁₀₁	1	4	yes	—
328	#121	—	2	2	no	—
329	#121	—	2	2	no	—
330	#121	C₂×C₄×C₁₀₁	1	4	yes	—
331	#121	C₂×C₄×C₁₀₁	1	4	yes	—
332	#120	—	2	8	no	—
333	C₄×D₄	—	2	8	no	—
334	C₄×D₄	—	2	8	no	—
335	#117	—	2	2	no	—
336	#117	—	4	4	no	—
337	#117	C₂×C₄×C₁₀₁	1	4	yes	—
338	C₂×C₄⋊C₄	—	2	1	no	—
339	C₂×C₄⋊C₄	—	2	1	no	—
340	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	4	yes	—
341	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	1	yes	characteristic
342	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	1	yes	characteristic
343	C₂×C₂²⋊C₄	—	2	1	no	—
344	C₂×C₂²⋊C₄	—	2	1	no	—
345	C₂×C₂²⋊C₄	—	2	1	no	—
346	C₂×C₂²⋊C₄	—	2	1	no	—
347	C₂×C₂²⋊C₄	—	2	1	no	—
348	C₂×C₂²⋊C₄	—	2	2	no	—
349	C₂×C₂²⋊C₄	—	2	2	no	—
350	C₂×C₂²⋊C₄	—	2	2	no	—
351	C₂×C₄²	—	2	1	no	—
352	C₂×C₄²	—	2	2	no	—
353	#103	—	4	4	no	—
354	#102	—	4	4	no	—
355	C₂²⋊C₈	—	2	4	no	—
356	C₂²⋊C₈	—	2	4	no	—
357	#95	—	2	2	no	—
358	#95	—	2	2	no	—
359	C₂⁴	—	2	1	no	—
360	C₂⁴	—	4	2	no	—
361	C₂⁴	—	4	2	no	—
362	C₂⁴	—	4	2	no	—
363	C₂⁴	C₂²⋊C₄×C₁₀₁	1	4	yes	—
364	C₂⁴	C₂×D₄×C₁₀₁	1	1	yes	characteristic
365	C₂⁴	C₂×D₄×C₁₀₁	1	1	yes	characteristic
366	C₂⁴	C₂×D₄×C₁₀₁	1	1	yes	characteristic
367	#41	—	4	8	no	—
368	#41	—	4	8	no	—
369	C₂×Q₈	—	2	1	no	—
370	C₂×Q₈	—	2	4	no	—
371	C₂×Q₈	C₂²×C₄×C₁₀₁	1	2	yes	—
372	C₂×D₄	—	2	4	no	—
373	C₂×D₄	—	2	4	no	—
374	C₂×D₄	—	2	4	no	—
375	C₂×D₄	—	2	1	no	—
376	C₂×D₄	—	2	4	no	—
377	C₂×D₄	—	4	4	no	—
378	C₂×D₄	—	4	4	no	—
379	C₂×D₄	—	4	4	no	—
380	C₂×D₄	C₂²×C₄×C₁₀₁	1	2	yes	—
381	C₂²×C₄	—	2	4	no	—
382	C₂²×C₄	—	2	4	no	—
383	C₂²×C₄	—	2	4	no	—
384	C₂²×C₄	—	2	1	no	—
385	C₂²×C₄	—	2	1	no	—
386	C₂²×C₄	—	2	1	no	—
387	C₂²×C₄	—	2	4	no	—
388	C₂²×C₄	—	2	4	no	—
389	C₂²×C₄	—	4	8	no	—
390	C₂²×C₄	—	4	8	no	—
391	C₂²×C₄	—	4	2	no	—
392	C₂²×C₄	—	4	2	no	—
393	C₂²×C₄	—	4	2	no	—
394	C₂²×C₄	—	4	4	no	—
395	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	4	yes	—
396	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	4	yes	—
397	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	4	yes	—
398	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
399	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
400	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
401	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
402	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
403	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
404	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
405	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
406	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
407	C₂²×C₄	C₂⁴×C₁₀₁	1	1	yes	characteristic
408	M₁₆	—	4	8	no	—
409	C₂×C₈	—	2	4	no	—
410	C₂×C₈	—	2	4	no	—
411	C₂×C₈	—	2	4	no	—
412	C₄⋊C₄	—	2	4	no	—
413	C₄⋊C₄	—	2	4	no	—
414	C₄⋊C₄	—	2	1	no	—
415	C₄⋊C₄	—	2	1	no	—
416	C₄⋊C₄	—	2	4	no	—
417	C₄⋊C₄	—	2	4	no	—
418	C₄⋊C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
419	C₄⋊C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
420	C₂²⋊C₄	—	2	4	no	—
421	C₂²⋊C₄	—	2	4	no	—
422	C₂²⋊C₄	—	2	4	no	—
423	C₂²⋊C₄	—	2	4	no	—
424	C₂²⋊C₄	—	2	4	no	—
425	C₂²⋊C₄	—	4	4	no	—
426	C₂²⋊C₄	—	4	4	no	—
427	C₂²⋊C₄	—	4	4	no	—
428	C₄²	—	2	4	no	—
429	C₄²	—	4	4	no	—
430	C₂³	—	2	2	no	—
431	C₂³	—	2	2	no	—
432	C₂³	—	2	2	no	—
433	C₂³	—	2	2	no	—
434	C₂³	—	2	2	no	—
435	C₂³	—	2	2	no	—
436	C₂³	—	2	2	no	—
437	C₂³	—	2	2	no	—
438	C₂³	—	2	2	no	—
439	C₂³	—	2	2	no	—
440	C₂³	—	4	4	no	—
441	C₂³	—	4	4	no	—
442	C₂³	—	4	4	no	—
443	C₂³	—	4	16	no	—
444	C₂³	—	4	2	no	—
445	C₂³	—	4	2	no	—
446	C₂³	—	4	2	no	—
447	C₂³	C₂×C₂²⋊C₄×C₁₀₁	1	2	yes	—
448	C₂³	C₂×C₂²⋊C₄×C₁₀₁	1	2	yes	—
449	C₂³	C₂×C₂²⋊C₄×C₁₀₁	1	2	yes	—
450	C₂³	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
451	Q₈	—	2	4	no	—
452	Q₈	—	4	2	no	—
453	D₄	—	2	4	no	—
454	D₄	—	4	8	no	—
455	D₄	—	4	8	no	—
456	D₄	—	4	8	no	—
457	D₄	—	4	2	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	4	no	—
462	C₂×C₄	—	2	4	no	—
463	C₂×C₄	—	2	4	no	—
464	C₂×C₄	—	2	4	no	—
465	C₂×C₄	—	2	4	no	—
466	C₂×C₄	—	2	4	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	4	4	no	—
471	C₂×C₄	—	4	4	no	—
472	C₂×C₄	—	4	4	no	—
473	C₂×C₄	—	4	8	no	—
474	C₂×C₄	—	4	2	no	—
475	C₂×C₄	—	4	2	no	—
476	C₂×C₄	—	4	2	no	—
477	C₂×C₄	—	4	4	no	—
478	C₂×C₄	—	4	4	no	—
479	C₂×C₄	—	4	4	no	—
480	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	2	yes	—
481	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	2	yes	—
482	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	2	yes	—
483	C₂×C₄	C₂³×C₄×C₁₀₁	1	1	yes	characteristic
484	C₂×C₄	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
485	C₂×C₄	H(5,𝔽₂)×C₁₀₁	1	4	yes	—
486	C₈	—	4	4	no	—
487	C₂²	—	2	2	no	—
488	C₂²	—	2	2	no	—
489	C₂²	—	2	2	no	—
490	C₂²	—	2	2	no	—
491	C₂²	—	2	2	no	—
492	C₂²	—	2	2	no	—
493	C₂²	—	2	2	no	—
494	C₂²	—	2	2	no	—
495	C₂²	—	2	2	no	—
496	C₂²	—	4	16	no	—
497	C₂²	—	4	4	no	—
498	C₂²	—	4	4	no	—
499	C₂²	—	4	4	no	—
500	C₂²	—	4	2	no	—
501	C₂²	—	4	2	no	—
502	C₂²	—	4	2	no	—
503	C₂²	—	8	4	no	—
504	C₂²	C₂²×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
505	C₂²	#534×C₁₀₁	1	2	yes	—
506	C₂²	#575×C₁₀₁	1	2	yes	—
507	C₂²	#575×C₁₀₁	1	2	yes	—
508	C₄	—	2	2	no	—
509	C₄	—	2	2	no	—
510	C₄	—	2	2	no	—
511	C₄	—	4	2	no	—
512	C₄	—	4	2	no	—
513	C₄	—	4	2	no	—
514	C₄	—	8	4	no	—
515	C₄	#518×C₁₀₁	1	2	yes	—
516	C₄	#534×C₁₀₁	1	2	yes	—
517	C₂	—	4	2	no	—
518	C₂	—	4	2	no	—
519	C₂	—	4	2	no	—
520	C₂	—	8	2	no	—
521	C₂	C₁₀₁×#2308	1	1	yes	characteristic
522	C₂	C₁₀₁×#2896	1	1	yes	characteristic
523	C₂	C₁₀₁×#2896	1	1	yes	characteristic
524	C₂	C₁₀₁×#3197	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₀₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₀₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₀₁
prime radical	C₂×#525×C₁₀₁	C₂
LCS	G ▷ C₂×C₄ ▷ 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
2. C₂×#407×C₁₀₁	C₂	semidirect
3. C₁₀₁×#2280	C₂	semidirect
4. C₁₀₁×#1895	C₂	semidirect
5. C₁₀₁×#1894	C₂	semidirect
6. C₁₀₁×#1875	C₂	semidirect
7. C₁₀₁×#1873	C₂	semidirect
8. C₁₀₁×#1825	C₂	semidirect
9. C₁₀₁×#1788	C₂	semidirect
14. #525×C₁₀₁	C₄	semidirect
25. C₂×#103×C₁₀₁	C₂²	semidirect
26. C₂×#102×C₁₀₁	C₂²	semidirect
36. #340×C₁₀₁	C₂²	semidirect
37. #340×C₁₀₁	C₂²	semidirect
254. #21766	C₁₀₁	direct (N × H)
264. C₂×#407	C₂×C₁₀₁	semidirect
265. #2280	C₂×C₁₀₁	semidirect
266. #1895	C₂×C₁₀₁	semidirect
267. #1894	C₂×C₁₀₁	semidirect
268. #1875	C₂×C₁₀₁	semidirect
269. #1873	C₂×C₁₀₁	semidirect
270. #1825	C₂×C₁₀₁	semidirect
271. #1788	C₂×C₁₀₁	semidirect
272. C₁₀₁	#21766	direct (N × H)
277. #525	C₄×C₁₀₁	semidirect
288. C₂×#103	C₂²×C₁₀₁	semidirect
289. C₂×#102	C₂²×C₁₀₁	semidirect
299. #340	C₂²×C₁₀₁	semidirect
300. #340	C₂²×C₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#525×C₁₀₁	2
C₂×#407×C₁₀₁	2
C₁₀₁×#2280	2
C₁₀₁×#1895	2
C₁₀₁×#1894	2
C₁₀₁×#1875	2
C₁₀₁×#1873	2
C₁₀₁×#1825	2
C₁₀₁×#1788	2
#21766	101

Subgroups — C101×#21766 #38803917

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#21766 #38803917