Subgroups — C₁₀₁×#23428 #38805579

Order 25856.

2282 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×AGL(1,ℤ/8)×C₁₀₁	C₂	1	2	yes	maximal, complemented
2	C₂×#532×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#417×C₁₀₁	C₂	1	2	yes	maximal, complemented
4	C₂×#390×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₀₁×#2013	C₂	1	2	yes	maximal, complemented
6	C₁₀₁×#2012	C₂	1	4	yes	maximal, complemented
7	C₁₀₁×#2011	C₂	1	2	yes	maximal, complemented
8	C₁₀₁×#1728	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#41×C₁₀₁	C₂²	1	2	yes	—
10	C₂³×D₄×C₁₀₁	C₂²	1	1	yes	characteristic
11	C₂×AGL(1,ℤ/8)×C₁₀₁	—	2	8	no	—
12	C₂×AGL(1,ℤ/8)×C₁₀₁	—	2	8	no	—
13	C₂×AGL(1,ℤ/8)×C₁₀₁	—	2	8	no	—
14	C₂²×SD₁₆×C₁₀₁	C₂²	1	4	yes	—
15	C₂²×D₈×C₁₀₁	C₂²	1	4	yes	—
16	C₂²×M₁₆×C₁₀₁	C₂²	1	2	yes	—
17	#532×C₁₀₁	—	2	8	no	—
18	C₂×C₄⋊Q₈×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
19	C₂×#127×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
20	C₂×#124×C₁₀₁	C₂²	1	2	yes	complemented
21	C₂×#121×C₁₀₁	—	2	2	no	—
22	C₂×C₄×D₄×C₁₀₁	—	2	2	no	—
23	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
24	C₂²×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
25	C₂²×C₄²×C₁₀₁	C₂²	1	1	yes	characteristic
26	#417×C₁₀₁	—	2	8	no	—
27	C₂×#103×C₁₀₁	C₂²	1	4	yes	complemented
28	C₂×#102×C₁₀₁	C₂²	1	4	yes	complemented
29	#390×C₁₀₁	—	2	2	no	—
30	#390×C₁₀₁	C₂²	1	2	yes	—
31	#390×C₁₀₁	C₂²	1	2	yes	—
32	#336×C₁₀₁	C₂²	1	2	yes	complemented
33	#336×C₁₀₁	C₂²	1	2	yes	complemented
34	C₂⁵×C₁₀₁	—	2	1	no	—
35	C₂×#41×C₁₀₁	—	2	4	no	—
36	C₂×#41×C₁₀₁	—	2	4	no	—
37	C₂×#41×C₁₀₁	—	2	4	no	—
38	C₂×#41×C₁₀₁	—	2	4	no	—
39	C₂×#41×C₁₀₁	—	2	4	no	—
40	C₂×#41×C₁₀₁	D₄	1	8	yes	—
41	C₂²×Q₈×C₁₀₁	C₂³	1	2	yes	—
42	C₂²×D₄×C₁₀₁	—	2	2	no	—
43	C₂²×D₄×C₁₀₁	—	2	4	no	—
44	C₂²×D₄×C₁₀₁	—	2	4	no	—
45	C₂²×D₄×C₁₀₁	—	2	2	no	—
46	C₂²×D₄×C₁₀₁	—	2	1	no	—
47	C₂²×D₄×C₁₀₁	—	2	2	no	—
48	C₂²×D₄×C₁₀₁	D₄	1	4	yes	complemented
49	C₂²×D₄×C₁₀₁	C₂³	1	2	yes	—
50	C₂²×D₄×C₁₀₁	C₂³	1	2	yes	—
51	C₂³×C₄×C₁₀₁	—	2	2	no	—
52	C₂³×C₄×C₁₀₁	—	2	1	no	—
53	C₂³×C₄×C₁₀₁	D₄	1	2	yes	—
54	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
55	AGL(1,ℤ/8)×C₁₀₁	—	2	64	no	—
56	C₂×SD₁₆×C₁₀₁	—	2	8	no	—
57	C₂×SD₁₆×C₁₀₁	—	2	8	no	—
58	C₂×SD₁₆×C₁₀₁	—	2	8	no	—
59	C₂×D₈×C₁₀₁	—	2	8	no	—
60	C₂×D₈×C₁₀₁	—	2	8	no	—
61	C₂×D₈×C₁₀₁	—	2	8	no	—
62	C₂×M₁₆×C₁₀₁	—	2	4	no	—
63	C₂×M₁₆×C₁₀₁	—	2	4	no	—
64	C₂×M₁₆×C₁₀₁	D₄	1	8	yes	complemented
65	C₂²×C₈×C₁₀₁	C₂³	1	4	yes	—
66	C₄⋊Q₈×C₁₀₁	—	2	4	no	—
67	#127×C₁₀₁	—	2	4	no	—
68	#124×C₁₀₁	—	2	4	no	—
69	#124×C₁₀₁	—	2	4	no	—
70	#121×C₁₀₁	—	2	16	no	—
71	C₄×D₄×C₁₀₁	—	2	16	no	—
72	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
73	C₂×C₄⋊C₄×C₁₀₁	—	2	4	no	—
74	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
75	C₂×C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
76	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
77	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
78	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
79	C₂×C₂²⋊C₄×C₁₀₁	—	4	8	no	—
80	C₂×C₄²×C₁₀₁	—	2	4	no	—
81	C₂×C₄²×C₁₀₁	D₄	1	2	yes	—
82	C₂×C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
83	C₂×C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
84	#103×C₁₀₁	—	2	8	no	—
85	#102×C₁₀₁	—	2	8	no	—
86	C₂⁴×C₁₀₁	—	2	4	no	—
87	C₂⁴×C₁₀₁	—	2	2	no	—
88	C₂⁴×C₁₀₁	—	2	2	no	—
89	C₂⁴×C₁₀₁	—	4	4	no	—
90	C₂⁴×C₁₀₁	—	4	4	no	—
91	C₂⁴×C₁₀₁	—	4	2	no	—
92	C₂⁴×C₁₀₁	—	4	2	no	—
93	C₂⁴×C₁₀₁	C₂×D₄	1	1	yes	characteristic
94	#41×C₁₀₁	—	2	16	no	—
95	#41×C₁₀₁	—	2	16	no	—
96	#41×C₁₀₁	—	4	8	no	—
97	#41×C₁₀₁	—	4	8	no	—
98	C₂×Q₈×C₁₀₁	—	2	2	no	—
99	C₂×Q₈×C₁₀₁	—	2	2	no	—
100	C₂×Q₈×C₁₀₁	—	2	2	no	—
101	C₂×Q₈×C₁₀₁	—	2	2	no	—
102	C₂×Q₈×C₁₀₁	—	2	2	no	—
103	C₂×Q₈×C₁₀₁	C₂×D₄	1	4	yes	—
104	C₂×D₄×C₁₀₁	—	2	8	no	—
105	C₂×D₄×C₁₀₁	—	2	8	no	—
106	C₂×D₄×C₁₀₁	—	2	16	no	—
107	C₂×D₄×C₁₀₁	—	2	4	no	—
108	C₂×D₄×C₁₀₁	—	2	2	no	—
109	C₂×D₄×C₁₀₁	—	2	2	no	—
110	C₂×D₄×C₁₀₁	—	2	2	no	—
111	C₂×D₄×C₁₀₁	—	2	4	no	—
112	C₂×D₄×C₁₀₁	—	2	4	no	—
113	C₂×D₄×C₁₀₁	—	2	2	no	—
114	C₂×D₄×C₁₀₁	—	2	2	no	—
115	C₂×D₄×C₁₀₁	—	2	2	no	—
116	C₂×D₄×C₁₀₁	—	4	4	no	—
117	C₂×D₄×C₁₀₁	—	4	4	no	—
118	C₂×D₄×C₁₀₁	—	4	4	no	—
119	C₂×D₄×C₁₀₁	—	4	2	no	—
120	C₂×D₄×C₁₀₁	—	4	8	no	—
121	C₂×D₄×C₁₀₁	—	4	2	no	—
122	C₂×D₄×C₁₀₁	—	4	4	no	—
123	C₂×D₄×C₁₀₁	C₂×D₄	1	4	yes	—
124	C₂×D₄×C₁₀₁	C₂×D₄	1	4	yes	—
125	C₂²×C₄×C₁₀₁	—	2	4	no	—
126	C₂²×C₄×C₁₀₁	—	2	2	no	—
127	C₂²×C₄×C₁₀₁	—	2	8	no	—
128	C₂²×C₄×C₁₀₁	—	2	4	no	—
129	C₂²×C₄×C₁₀₁	—	2	2	no	—
130	C₂²×C₄×C₁₀₁	—	4	2	no	—
131	C₂²×C₄×C₁₀₁	—	4	4	no	—
132	C₂²×C₄×C₁₀₁	—	4	4	no	—
133	C₂²×C₄×C₁₀₁	—	4	4	no	—
134	C₂²×C₄×C₁₀₁	—	4	2	no	—
135	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
136	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
137	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
138	C₂²×C₄×C₁₀₁	C₂×D₄	1	4	yes	—
139	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₁₀₁	C₂×D₄	1	4	yes	—
141	C₂²×C₄×C₁₀₁	#41	1	2	yes	—
142	C₂²×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
143	SD₁₆×C₁₀₁	—	2	32	no	—
144	D₈×C₁₀₁	—	2	32	no	—
145	M₁₆×C₁₀₁	—	2	16	no	—
146	C₂×C₈×C₁₀₁	—	2	4	no	—
147	C₂×C₈×C₁₀₁	—	2	4	no	—
148	C₂×C₈×C₁₀₁	C₂×D₄	1	8	yes	—
149	C₄⋊C₄×C₁₀₁	—	2	8	no	—
150	C₄⋊C₄×C₁₀₁	—	2	4	no	—
151	C₄⋊C₄×C₁₀₁	—	4	2	no	—
152	C₂²⋊C₄×C₁₀₁	—	2	16	no	—
153	C₂²⋊C₄×C₁₀₁	—	4	8	no	—
154	C₂²⋊C₄×C₁₀₁	—	4	8	no	—
155	C₄²×C₁₀₁	—	2	4	no	—
156	C₄²×C₁₀₁	—	2	2	no	—
157	C₄²×C₁₀₁	—	2	2	no	—
158	C₂³×C₁₀₁	—	2	2	no	—
159	C₂³×C₁₀₁	—	2	2	no	—
160	C₂³×C₁₀₁	—	2	4	no	—
161	C₂³×C₁₀₁	—	2	4	no	—
162	C₂³×C₁₀₁	—	4	16	no	—
163	C₂³×C₁₀₁	—	4	2	no	—
164	C₂³×C₁₀₁	—	4	2	no	—
165	C₂³×C₁₀₁	—	4	2	no	—
166	C₂³×C₁₀₁	—	4	2	no	—
167	C₂³×C₁₀₁	—	4	4	no	—
168	C₂³×C₁₀₁	—	4	4	no	—
169	C₂³×C₁₀₁	—	4	4	no	—
170	C₂³×C₁₀₁	—	4	4	no	—
171	C₂³×C₁₀₁	—	4	8	no	—
172	C₂³×C₁₀₁	—	8	4	no	—
173	C₂³×C₁₀₁	—	8	4	no	—
174	C₂³×C₁₀₁	—	8	8	no	—
175	C₂³×C₁₀₁	#120	1	2	yes	—
176	C₂³×C₁₀₁	#121	1	2	yes	—
177	C₂³×C₁₀₁	#127	1	2	yes	—
178	C₂³×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
179	Q₈×C₁₀₁	—	2	4	no	—
180	Q₈×C₁₀₁	—	2	4	no	—
181	Q₈×C₁₀₁	—	4	2	no	—
182	Q₈×C₁₀₁	—	4	2	no	—
183	D₄×C₁₀₁	—	2	4	no	—
184	D₄×C₁₀₁	—	2	8	no	—
185	D₄×C₁₀₁	—	2	4	no	—
186	D₄×C₁₀₁	—	4	16	no	—
187	D₄×C₁₀₁	—	4	16	no	—
188	D₄×C₁₀₁	—	4	2	no	—
189	D₄×C₁₀₁	—	4	4	no	—
190	D₄×C₁₀₁	—	4	2	no	—
191	D₄×C₁₀₁	—	4	8	no	—
192	C₂×C₄×C₁₀₁	—	2	2	no	—
193	C₂×C₄×C₁₀₁	—	2	2	no	—
194	C₂×C₄×C₁₀₁	—	2	2	no	—
195	C₂×C₄×C₁₀₁	—	2	4	no	—
196	C₂×C₄×C₁₀₁	—	2	2	no	—
197	C₂×C₄×C₁₀₁	—	2	2	no	—
198	C₂×C₄×C₁₀₁	—	4	8	no	—
199	C₂×C₄×C₁₀₁	—	4	2	no	—
200	C₂×C₄×C₁₀₁	—	4	2	no	—
201	C₂×C₄×C₁₀₁	—	4	16	no	—
202	C₂×C₄×C₁₀₁	—	4	2	no	—
203	C₂×C₄×C₁₀₁	—	4	4	no	—
204	C₂×C₄×C₁₀₁	—	8	4	no	—
205	C₂×C₄×C₁₀₁	#120	1	8	yes	—
206	C₂×C₄×C₁₀₁	#120	1	2	yes	—
207	C₂×C₄×C₁₀₁	#121	1	8	yes	—
208	C₂×C₄×C₁₀₁	#121	1	2	yes	—
209	C₂×C₄×C₁₀₁	#127	1	2	yes	—
210	C₂×C₄×C₁₀₁	AGL(1,ℤ/8)	1	4	yes	complemented
211	C₂×C₄×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
212	C₂×C₄×C₁₀₁	C₂²×D₄	1	2	yes	—
213	C₂×C₄×C₁₀₁	C₂²×D₄	1	2	yes	—
214	C₂×C₄×C₁₀₁	C₂×#41	1	1	yes	characteristic
215	C₈×C₁₀₁	—	2	8	no	—
216	C₂²×C₁₀₁	—	2	2	no	—
217	C₂²×C₁₀₁	—	2	2	no	—
218	C₂²×C₁₀₁	—	2	4	no	—
219	C₂²×C₁₀₁	—	2	4	no	—
220	C₂²×C₁₀₁	—	4	4	no	—
221	C₂²×C₁₀₁	—	4	4	no	—
222	C₂²×C₁₀₁	—	4	8	no	—
223	C₂²×C₁₀₁	—	4	8	no	—
224	C₂²×C₁₀₁	—	8	16	no	—
225	C₂²×C₁₀₁	—	8	2	no	—
226	C₂²×C₁₀₁	—	8	2	no	—
227	C₂²×C₁₀₁	—	8	2	no	—
228	C₂²×C₁₀₁	—	8	2	no	—
229	C₂²×C₁₀₁	—	8	4	no	—
230	C₂²×C₁₀₁	—	8	4	no	—
231	C₂²×C₁₀₁	#392	1	4	yes	—
232	C₂²×C₁₀₁	C₂×#120	1	1	yes	characteristic
233	C₂²×C₁₀₁	C₂×#121	1	1	yes	characteristic
234	C₂²×C₁₀₁	C₂×#127	1	1	yes	characteristic
235	C₂²×C₁₀₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
236	C₂²×C₁₀₁	#575	1	2	yes	—
237	C₄×C₁₀₁	—	2	4	no	—
238	C₄×C₁₀₁	—	4	4	no	—
239	C₄×C₁₀₁	—	4	2	no	—
240	C₄×C₁₀₁	—	8	2	no	—
241	C₄×C₁₀₁	#392	1	4	yes	—
242	C₄×C₁₀₁	C₂×#120	1	2	yes	—
243	C₄×C₁₀₁	C₂×#121	1	2	yes	—
244	#23428	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
245	C₂×C₁₀₁	—	2	4	no	—
246	C₂×C₁₀₁	—	8	4	no	—
247	C₂×C₁₀₁	—	8	4	no	—
248	C₂×C₁₀₁	C₂×#392	1	1	yes	characteristic
249	C₂×C₁₀₁	#3006	1	2	yes	—
250	C₂×C₁₀₁	#3036	1	2	yes	—
251	C₂×C₁₀₁	#3151	1	1	yes	characteristic
252	C₂×C₁₀₁	#3153	1	1	yes	characteristic
253	C₂²×AGL(1,ℤ/8)	C₂×C₁₀₁	1	2	yes	complemented
254	C₂×#532	C₂×C₁₀₁	1	1	yes	characteristic, complemented
255	C₂×#417	C₂×C₁₀₁	1	2	yes	complemented
256	C₂×#390	C₂×C₁₀₁	1	1	yes	characteristic, complemented
257	#2013	C₂×C₁₀₁	1	2	yes	complemented
258	#2012	C₂×C₁₀₁	1	4	yes	complemented
259	#2011	C₂×C₁₀₁	1	2	yes	complemented
260	#1728	C₂×C₁₀₁	1	1	yes	characteristic, complemented
261	C₁₀₁	#23428	1	1	yes	characteristic, direct product factor, Sylow
262	C₂²×#41	C₂²×C₁₀₁	1	2	yes	—
263	C₂³×D₄	C₂²×C₁₀₁	1	1	yes	characteristic
264	C₂×AGL(1,ℤ/8)	—	2	8	no	—
265	C₂×AGL(1,ℤ/8)	—	2	8	no	—
266	C₂×AGL(1,ℤ/8)	—	2	8	no	—
267	C₂²×SD₁₆	C₂²×C₁₀₁	1	4	yes	—
268	C₂²×D₈	C₂²×C₁₀₁	1	4	yes	—
269	C₂²×M₁₆	C₂²×C₁₀₁	1	2	yes	—
270	#532	—	2	8	no	—
271	C₂×C₄⋊Q₈	C₂²×C₁₀₁	1	1	yes	characteristic, complemented
272	C₂×#127	C₂²×C₁₀₁	1	1	yes	characteristic, complemented
273	C₂×#124	C₂²×C₁₀₁	1	2	yes	complemented
274	C₂×#121	—	2	2	no	—
275	C₂×C₄×D₄	—	2	2	no	—
276	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
277	C₂²×C₂²⋊C₄	—	2	2	no	—
278	C₂²×C₄²	C₂²×C₁₀₁	1	1	yes	characteristic
279	#417	—	2	8	no	—
280	C₂×#103	C₂²×C₁₀₁	1	4	yes	complemented
281	C₂×#102	C₂²×C₁₀₁	1	4	yes	complemented
282	#390	—	2	2	no	—
283	#390	C₂²×C₁₀₁	1	2	yes	—
284	#390	C₂²×C₁₀₁	1	2	yes	—
285	#336	C₂²×C₁₀₁	1	2	yes	complemented
286	#336	C₂²×C₁₀₁	1	2	yes	complemented
287	C₂⁵	—	2	1	no	—
288	C₂×#41	—	2	4	no	—
289	C₂×#41	—	2	4	no	—
290	C₂×#41	—	2	4	no	—
291	C₂×#41	—	2	4	no	—
292	C₂×#41	—	2	4	no	—
293	C₂×#41	D₄×C₁₀₁	1	8	yes	—
294	C₂²×Q₈	C₂³×C₁₀₁	1	2	yes	—
295	C₂²×D₄	—	2	2	no	—
296	C₂²×D₄	—	2	4	no	—
297	C₂²×D₄	—	2	4	no	—
298	C₂²×D₄	—	2	2	no	—
299	C₂²×D₄	—	2	1	no	—
300	C₂²×D₄	—	2	2	no	—
301	C₂²×D₄	D₄×C₁₀₁	1	4	yes	complemented
302	C₂²×D₄	C₂³×C₁₀₁	1	2	yes	—
303	C₂²×D₄	C₂³×C₁₀₁	1	2	yes	—
304	C₂³×C₄	—	2	2	no	—
305	C₂³×C₄	—	2	1	no	—
306	C₂³×C₄	D₄×C₁₀₁	1	2	yes	—
307	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
308	AGL(1,ℤ/8)	—	2	64	no	—
309	C₂×SD₁₆	—	2	8	no	—
310	C₂×SD₁₆	—	2	8	no	—
311	C₂×SD₁₆	—	2	8	no	—
312	C₂×D₈	—	2	8	no	—
313	C₂×D₈	—	2	8	no	—
314	C₂×D₈	—	2	8	no	—
315	C₂×M₁₆	—	2	4	no	—
316	C₂×M₁₆	—	2	4	no	—
317	C₂×M₁₆	D₄×C₁₀₁	1	8	yes	complemented
318	C₂²×C₈	C₂³×C₁₀₁	1	4	yes	—
319	C₄⋊Q₈	—	2	4	no	—
320	#127	—	2	4	no	—
321	#124	—	2	4	no	—
322	#124	—	2	4	no	—
323	#121	—	2	16	no	—
324	C₄×D₄	—	2	16	no	—
325	C₂×C₄⋊C₄	—	2	2	no	—
326	C₂×C₄⋊C₄	—	2	4	no	—
327	C₂×C₄⋊C₄	—	2	1	no	—
328	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	2	yes	—
329	C₂×C₂²⋊C₄	—	2	4	no	—
330	C₂×C₂²⋊C₄	—	2	4	no	—
331	C₂×C₂²⋊C₄	—	2	4	no	—
332	C₂×C₂²⋊C₄	—	4	8	no	—
333	C₂×C₄²	—	2	4	no	—
334	C₂×C₄²	D₄×C₁₀₁	1	2	yes	—
335	C₂×C₄²	C₂³×C₁₀₁	1	1	yes	characteristic
336	C₂×C₄²	C₂³×C₁₀₁	1	1	yes	characteristic
337	#103	—	2	8	no	—
338	#102	—	2	8	no	—
339	C₂⁴	—	2	4	no	—
340	C₂⁴	—	2	2	no	—
341	C₂⁴	—	2	2	no	—
342	C₂⁴	—	4	4	no	—
343	C₂⁴	—	4	4	no	—
344	C₂⁴	—	4	2	no	—
345	C₂⁴	—	4	2	no	—
346	C₂⁴	C₂×D₄×C₁₀₁	1	1	yes	characteristic
347	#41	—	2	16	no	—
348	#41	—	2	16	no	—
349	#41	—	4	8	no	—
350	#41	—	4	8	no	—
351	C₂×Q₈	—	2	2	no	—
352	C₂×Q₈	—	2	2	no	—
353	C₂×Q₈	—	2	2	no	—
354	C₂×Q₈	—	2	2	no	—
355	C₂×Q₈	—	2	2	no	—
356	C₂×Q₈	C₂×D₄×C₁₀₁	1	4	yes	—
357	C₂×D₄	—	2	8	no	—
358	C₂×D₄	—	2	8	no	—
359	C₂×D₄	—	2	16	no	—
360	C₂×D₄	—	2	4	no	—
361	C₂×D₄	—	2	2	no	—
362	C₂×D₄	—	2	2	no	—
363	C₂×D₄	—	2	2	no	—
364	C₂×D₄	—	2	4	no	—
365	C₂×D₄	—	2	4	no	—
366	C₂×D₄	—	2	2	no	—
367	C₂×D₄	—	2	2	no	—
368	C₂×D₄	—	2	2	no	—
369	C₂×D₄	—	4	4	no	—
370	C₂×D₄	—	4	4	no	—
371	C₂×D₄	—	4	4	no	—
372	C₂×D₄	—	4	2	no	—
373	C₂×D₄	—	4	8	no	—
374	C₂×D₄	—	4	2	no	—
375	C₂×D₄	—	4	4	no	—
376	C₂×D₄	C₂×D₄×C₁₀₁	1	4	yes	—
377	C₂×D₄	C₂×D₄×C₁₀₁	1	4	yes	—
378	C₂²×C₄	—	2	4	no	—
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	—	2	8	no	—
381	C₂²×C₄	—	2	4	no	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	4	2	no	—
384	C₂²×C₄	—	4	4	no	—
385	C₂²×C₄	—	4	4	no	—
386	C₂²×C₄	—	4	4	no	—
387	C₂²×C₄	—	4	2	no	—
388	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
389	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
390	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
391	C₂²×C₄	C₂×D₄×C₁₀₁	1	4	yes	—
392	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
393	C₂²×C₄	C₂×D₄×C₁₀₁	1	4	yes	—
394	C₂²×C₄	#41×C₁₀₁	1	2	yes	—
395	C₂²×C₄	C₂⁴×C₁₀₁	1	1	yes	characteristic
396	SD₁₆	—	2	32	no	—
397	D₈	—	2	32	no	—
398	M₁₆	—	2	16	no	—
399	C₂×C₈	—	2	4	no	—
400	C₂×C₈	—	2	4	no	—
401	C₂×C₈	C₂×D₄×C₁₀₁	1	8	yes	—
402	C₄⋊C₄	—	2	8	no	—
403	C₄⋊C₄	—	2	4	no	—
404	C₄⋊C₄	—	4	2	no	—
405	C₂²⋊C₄	—	2	16	no	—
406	C₂²⋊C₄	—	4	8	no	—
407	C₂²⋊C₄	—	4	8	no	—
408	C₄²	—	2	4	no	—
409	C₄²	—	2	2	no	—
410	C₄²	—	2	2	no	—
411	C₂³	—	2	2	no	—
412	C₂³	—	2	2	no	—
413	C₂³	—	2	4	no	—
414	C₂³	—	2	4	no	—
415	C₂³	—	4	16	no	—
416	C₂³	—	4	2	no	—
417	C₂³	—	4	2	no	—
418	C₂³	—	4	2	no	—
419	C₂³	—	4	2	no	—
420	C₂³	—	4	4	no	—
421	C₂³	—	4	4	no	—
422	C₂³	—	4	4	no	—
423	C₂³	—	4	4	no	—
424	C₂³	—	4	8	no	—
425	C₂³	—	8	8	no	—
426	C₂³	—	8	4	no	—
427	C₂³	—	8	4	no	—
428	C₂³	#120×C₁₀₁	1	2	yes	—
429	C₂³	#121×C₁₀₁	1	2	yes	—
430	C₂³	#127×C₁₀₁	1	2	yes	—
431	C₂³	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
432	Q₈	—	2	4	no	—
433	Q₈	—	2	4	no	—
434	Q₈	—	4	2	no	—
435	Q₈	—	4	2	no	—
436	D₄	—	2	4	no	—
437	D₄	—	2	8	no	—
438	D₄	—	2	4	no	—
439	D₄	—	4	16	no	—
440	D₄	—	4	16	no	—
441	D₄	—	4	2	no	—
442	D₄	—	4	4	no	—
443	D₄	—	4	2	no	—
444	D₄	—	4	8	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	4	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	4	8	no	—
452	C₂×C₄	—	4	2	no	—
453	C₂×C₄	—	4	2	no	—
454	C₂×C₄	—	4	16	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	4	no	—
457	C₂×C₄	—	8	4	no	—
458	C₂×C₄	#120×C₁₀₁	1	8	yes	—
459	C₂×C₄	#120×C₁₀₁	1	2	yes	—
460	C₂×C₄	#121×C₁₀₁	1	8	yes	—
461	C₂×C₄	#121×C₁₀₁	1	2	yes	—
462	C₂×C₄	#127×C₁₀₁	1	2	yes	—
463	C₂×C₄	AGL(1,ℤ/8)×C₁₀₁	1	4	yes	complemented
464	C₂×C₄	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
465	C₂×C₄	C₂²×D₄×C₁₀₁	1	2	yes	—
466	C₂×C₄	C₂²×D₄×C₁₀₁	1	2	yes	—
467	C₂×C₄	C₂×#41×C₁₀₁	1	1	yes	characteristic
468	C₈	—	2	8	no	—
469	C₂²	—	2	4	no	—
470	C₂²	—	2	4	no	—
471	C₂²	—	2	2	no	—
472	C₂²	—	2	2	no	—
473	C₂²	—	4	8	no	—
474	C₂²	—	4	8	no	—
475	C₂²	—	4	4	no	—
476	C₂²	—	4	4	no	—
477	C₂²	—	8	16	no	—
478	C₂²	—	8	4	no	—
479	C₂²	—	8	4	no	—
480	C₂²	—	8	2	no	—
481	C₂²	—	8	2	no	—
482	C₂²	—	8	2	no	—
483	C₂²	—	8	2	no	—
484	C₂²	#392×C₁₀₁	1	4	yes	—
485	C₂²	C₂×#120×C₁₀₁	1	1	yes	characteristic
486	C₂²	C₂×#121×C₁₀₁	1	1	yes	characteristic
487	C₂²	C₂×#127×C₁₀₁	1	1	yes	characteristic
488	C₂²	C₂×AGL(1,ℤ/8)×C₁₀₁	1	2	yes	—
489	C₂²	#575×C₁₀₁	1	2	yes	—
490	C₄	—	2	4	no	—
491	C₄	—	4	2	no	—
492	C₄	—	4	4	no	—
493	C₄	—	8	2	no	—
494	C₄	#392×C₁₀₁	1	4	yes	—
495	C₄	C₂×#120×C₁₀₁	1	2	yes	—
496	C₄	C₂×#121×C₁₀₁	1	2	yes	—
497	C₂	—	2	4	no	—
498	C₂	—	8	4	no	—
499	C₂	—	8	4	no	—
500	C₂	C₂×#392×C₁₀₁	1	1	yes	characteristic
501	C₂	C₁₀₁×#3006	1	2	yes	—
502	C₂	C₁₀₁×#3036	1	2	yes	—
503	C₂	C₁₀₁×#3151	1	1	yes	characteristic
504	C₂	C₁₀₁×#3153	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₀₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₀₁
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₀₁ ◁ C₂²×C₄²×C₁₀₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×AGL(1,ℤ/8)×C₁₀₁	C₂	semidirect
2. C₂×#532×C₁₀₁	C₂	semidirect
3. C₂×#417×C₁₀₁	C₂	semidirect
4. C₂×#390×C₁₀₁	C₂	semidirect
5. C₁₀₁×#2013	C₂	semidirect
6. C₁₀₁×#2012	C₂	semidirect
7. C₁₀₁×#2011	C₂	semidirect
8. C₁₀₁×#1728	C₂	semidirect
18. C₂×C₄⋊Q₈×C₁₀₁	C₂²	semidirect
19. C₂×#127×C₁₀₁	C₂²	semidirect
20. C₂×#124×C₁₀₁	C₂²	semidirect
27. C₂×#103×C₁₀₁	C₂²	semidirect
28. C₂×#102×C₁₀₁	C₂²	semidirect
32. #336×C₁₀₁	C₂²	semidirect
33. #336×C₁₀₁	C₂²	semidirect
48. C₂²×D₄×C₁₀₁	D₄	semidirect
64. C₂×M₁₆×C₁₀₁	D₄	semidirect
210. C₂×C₄×C₁₀₁	AGL(1,ℤ/8)	semidirect
244. #23428	C₁₀₁	direct (N × H)
253. C₂²×AGL(1,ℤ/8)	C₂×C₁₀₁	semidirect
254. C₂×#532	C₂×C₁₀₁	semidirect
255. C₂×#417	C₂×C₁₀₁	semidirect
256. C₂×#390	C₂×C₁₀₁	semidirect
257. #2013	C₂×C₁₀₁	semidirect
258. #2012	C₂×C₁₀₁	semidirect
259. #2011	C₂×C₁₀₁	semidirect
260. #1728	C₂×C₁₀₁	semidirect
261. C₁₀₁	#23428	direct (N × H)
271. C₂×C₄⋊Q₈	C₂²×C₁₀₁	semidirect
272. C₂×#127	C₂²×C₁₀₁	semidirect
273. C₂×#124	C₂²×C₁₀₁	semidirect
280. C₂×#103	C₂²×C₁₀₁	semidirect
281. C₂×#102	C₂²×C₁₀₁	semidirect
285. #336	C₂²×C₁₀₁	semidirect
286. #336	C₂²×C₁₀₁	semidirect
301. C₂²×D₄	D₄×C₁₀₁	semidirect
317. C₂×M₁₆	D₄×C₁₀₁	semidirect
463. C₂×C₄	AGL(1,ℤ/8)×C₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₂²×AGL(1,ℤ/8)×C₁₀₁	2
C₂×#532×C₁₀₁	2
C₂×#417×C₁₀₁	2
C₂×#390×C₁₀₁	2
C₁₀₁×#2013	2
C₁₀₁×#2012	2
C₁₀₁×#2011	2
C₁₀₁×#1728	2
#23428	101

Subgroups — C101×#23428 #38805579

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#23428 #38805579