Subgroups — C₁₀₁×#23930 #38806081

Order 25856.

1768 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#532×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#447×C₁₀₁	C₂	1	2	yes	maximal, complemented
3	C₂×#390×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₀₁×#2023	C₂	1	2	yes	maximal, complemented
5	C₁₀₁×#2011	C₂	1	2	yes	maximal, complemented
6	C₁₀₁×#1879	C₂	1	4	yes	maximal, complemented
7	C₁₀₁×#1874	C₂	1	2	yes	maximal, complemented
8	C₁₀₁×#1817	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#41×C₁₀₁	—	2	1	no	—
10	C₂³×D₄×C₁₀₁	C₂²	1	1	yes	characteristic
11	C₂²×D₈×C₁₀₁	C₂²	1	4	yes	—
12	#532×C₁₀₁	—	2	8	no	—
13	C₂×C₄⋊Q₈×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
14	C₂×#127×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
15	C₂×#124×C₁₀₁	—	2	1	no	—
16	C₂×#121×C₁₀₁	—	2	1	no	—
17	C₂×#121×C₁₀₁	C₂²	1	2	yes	—
18	C₂×C₄×D₄×C₁₀₁	—	2	1	no	—
19	C₂×C₄×D₄×C₁₀₁	C₂²	1	2	yes	complemented
20	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
21	C₂²×C₂²⋊C₄×C₁₀₁	—	2	1	no	—
22	C₂²×C₂²⋊C₄×C₁₀₁	—	2	1	no	—
23	C₂²×C₄²×C₁₀₁	C₂²	1	1	yes	characteristic
24	#447×C₁₀₁	—	2	8	no	—
25	C₂×#102×C₁₀₁	C₂²	1	4	yes	—
26	C₂×#102×C₁₀₁	C₂²	1	4	yes	complemented
27	C₂×C₂²⋊C₈×C₁₀₁	C₂²	1	2	yes	—
28	#390×C₁₀₁	—	2	1	no	—
29	#390×C₁₀₁	—	2	1	no	—
30	#390×C₁₀₁	C₂²	1	2	yes	—
31	#390×C₁₀₁	C₂²	1	2	yes	—
32	#340×C₁₀₁	C₂²	1	4	yes	complemented
33	#336×C₁₀₁	C₂²	1	2	yes	complemented
34	#336×C₁₀₁	C₂²	1	2	yes	complemented
35	C₂⁵×C₁₀₁	—	2	1	no	—
36	C₂×#41×C₁₀₁	—	2	8	no	—
37	C₂×#41×C₁₀₁	—	4	4	no	—
38	C₂×#41×C₁₀₁	—	4	4	no	—
39	C₂²×Q₈×C₁₀₁	—	2	1	no	—
40	C₂²×D₄×C₁₀₁	—	2	2	no	—
41	C₂²×D₄×C₁₀₁	—	2	4	no	—
42	C₂²×D₄×C₁₀₁	—	2	1	no	—
43	C₂²×D₄×C₁₀₁	—	2	1	no	—
44	C₂²×D₄×C₁₀₁	—	2	1	no	—
45	C₂²×D₄×C₁₀₁	—	2	4	no	—
46	C₂²×D₄×C₁₀₁	—	4	2	no	—
47	C₂²×D₄×C₁₀₁	C₂³	1	2	yes	—
48	C₂²×D₄×C₁₀₁	C₂³	1	2	yes	—
49	C₂³×C₄×C₁₀₁	—	2	2	no	—
50	C₂³×C₄×C₁₀₁	—	2	1	no	—
51	C₂³×C₄×C₁₀₁	D₄	1	1	yes	characteristic
52	C₂³×C₄×C₁₀₁	D₄	1	1	yes	characteristic
53	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
54	C₂×D₈×C₁₀₁	—	2	8	no	—
55	C₂×D₈×C₁₀₁	—	2	8	no	—
56	C₂×D₈×C₁₀₁	—	4	4	no	—
57	C₂²×C₈×C₁₀₁	C₂³	1	4	yes	—
58	C₄⋊Q₈×C₁₀₁	—	2	4	no	—
59	#127×C₁₀₁	—	2	4	no	—
60	#124×C₁₀₁	—	2	8	no	—
61	#121×C₁₀₁	—	2	8	no	—
62	#121×C₁₀₁	—	2	4	no	—
63	#121×C₁₀₁	D₄	1	8	yes	—
64	C₄×D₄×C₁₀₁	—	2	8	no	—
65	C₄×D₄×C₁₀₁	—	2	4	no	—
66	C₄×D₄×C₁₀₁	—	2	4	no	—
67	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
68	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
69	C₂×C₄⋊C₄×C₁₀₁	—	4	2	no	—
70	C₂×C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
71	C₂×C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
72	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
73	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
74	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
75	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
76	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
77	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
78	C₂×C₂²⋊C₄×C₁₀₁	—	4	4	no	—
79	C₂×C₂²⋊C₄×C₁₀₁	—	4	4	no	—
80	C₂×C₄²×C₁₀₁	—	2	4	no	—
81	C₂×C₄²×C₁₀₁	D₄	1	1	yes	characteristic
82	C₂×C₄²×C₁₀₁	D₄	1	1	yes	characteristic
83	C₂×C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
84	C₂×C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
85	#102×C₁₀₁	—	2	8	no	—
86	#102×C₁₀₁	—	4	4	no	—
87	C₂²⋊C₈×C₁₀₁	—	2	4	no	—
88	C₂⁴×C₁₀₁	—	2	4	no	—
89	C₂⁴×C₁₀₁	—	2	2	no	—
90	C₂⁴×C₁₀₁	—	2	2	no	—
91	C₂⁴×C₁₀₁	—	4	2	no	—
92	C₂⁴×C₁₀₁	—	4	2	no	—
93	C₂⁴×C₁₀₁	—	4	2	no	—
94	C₂⁴×C₁₀₁	—	4	2	no	—
95	C₂⁴×C₁₀₁	—	4	2	no	—
96	C₂⁴×C₁₀₁	—	4	2	no	—
97	C₂⁴×C₁₀₁	C₂×D₄	1	1	yes	characteristic
98	#41×C₁₀₁	—	4	32	no	—
99	C₂×Q₈×C₁₀₁	—	2	4	no	—
100	C₂×Q₈×C₁₀₁	—	4	2	no	—
101	C₂×Q₈×C₁₀₁	—	4	2	no	—
102	C₂×D₄×C₁₀₁	—	2	4	no	—
103	C₂×D₄×C₁₀₁	—	2	4	no	—
104	C₂×D₄×C₁₀₁	—	2	4	no	—
105	C₂×D₄×C₁₀₁	—	2	8	no	—
106	C₂×D₄×C₁₀₁	—	2	4	no	—
107	C₂×D₄×C₁₀₁	—	2	2	no	—
108	C₂×D₄×C₁₀₁	—	2	4	no	—
109	C₂×D₄×C₁₀₁	—	2	2	no	—
110	C₂×D₄×C₁₀₁	—	2	4	no	—
111	C₂×D₄×C₁₀₁	—	2	4	no	—
112	C₂×D₄×C₁₀₁	—	4	16	no	—
113	C₂×D₄×C₁₀₁	—	4	2	no	—
114	C₂×D₄×C₁₀₁	—	4	2	no	—
115	C₂×D₄×C₁₀₁	—	4	2	no	—
116	C₂×D₄×C₁₀₁	—	4	4	no	—
117	C₂×D₄×C₁₀₁	—	4	4	no	—
118	C₂×D₄×C₁₀₁	—	4	2	no	—
119	C₂×D₄×C₁₀₁	—	4	2	no	—
120	C₂×D₄×C₁₀₁	—	4	2	no	—
121	C₂×D₄×C₁₀₁	C₂×D₄	1	4	yes	—
122	C₂×D₄×C₁₀₁	#41	1	4	yes	complemented
123	C₂²×C₄×C₁₀₁	—	2	2	no	—
124	C₂²×C₄×C₁₀₁	—	2	2	no	—
125	C₂²×C₄×C₁₀₁	—	2	2	no	—
126	C₂²×C₄×C₁₀₁	—	2	2	no	—
127	C₂²×C₄×C₁₀₁	—	2	8	no	—
128	C₂²×C₄×C₁₀₁	—	2	2	no	—
129	C₂²×C₄×C₁₀₁	—	2	2	no	—
130	C₂²×C₄×C₁₀₁	—	2	2	no	—
131	C₂²×C₄×C₁₀₁	—	2	2	no	—
132	C₂²×C₄×C₁₀₁	—	4	1	no	—
133	C₂²×C₄×C₁₀₁	—	4	4	no	—
134	C₂²×C₄×C₁₀₁	—	4	4	no	—
135	C₂²×C₄×C₁₀₁	—	4	2	no	—
136	C₂²×C₄×C₁₀₁	—	4	2	no	—
137	C₂²×C₄×C₁₀₁	—	4	2	no	—
138	C₂²×C₄×C₁₀₁	D₈	1	4	yes	complemented
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	4	yes	—
142	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
146	D₈×C₁₀₁	—	4	16	no	—
147	C₂×C₈×C₁₀₁	—	2	4	no	—
148	C₂×C₈×C₁₀₁	—	2	4	no	—
149	C₂×C₈×C₁₀₁	—	2	4	no	—
150	C₄⋊C₄×C₁₀₁	—	2	4	no	—
151	C₄⋊C₄×C₁₀₁	—	2	2	no	—
152	C₄⋊C₄×C₁₀₁	—	2	4	no	—
153	C₄⋊C₄×C₁₀₁	—	4	2	no	—
154	C₄⋊C₄×C₁₀₁	C₂×D₄	1	4	yes	—
155	C₂²⋊C₄×C₁₀₁	—	2	8	no	—
156	C₂²⋊C₄×C₁₀₁	—	2	8	no	—
157	C₂²⋊C₄×C₁₀₁	—	4	4	no	—
158	C₂²⋊C₄×C₁₀₁	—	4	4	no	—
159	C₂²⋊C₄×C₁₀₁	—	4	4	no	—
160	C₂²⋊C₄×C₁₀₁	—	4	4	no	—
161	C₄²×C₁₀₁	—	2	2	no	—
162	C₄²×C₁₀₁	—	2	2	no	—
163	C₄²×C₁₀₁	—	2	2	no	—
164	C₄²×C₁₀₁	—	2	2	no	—
165	C₂³×C₁₀₁	—	2	1	no	—
166	C₂³×C₁₀₁	—	2	1	no	—
167	C₂³×C₁₀₁	—	2	1	no	—
168	C₂³×C₁₀₁	—	2	1	no	—
169	C₂³×C₁₀₁	—	2	4	no	—
170	C₂³×C₁₀₁	—	2	4	no	—
171	C₂³×C₁₀₁	—	4	8	no	—
172	C₂³×C₁₀₁	—	4	8	no	—
173	C₂³×C₁₀₁	—	4	8	no	—
174	C₂³×C₁₀₁	—	4	2	no	—
175	C₂³×C₁₀₁	—	4	2	no	—
176	C₂³×C₁₀₁	—	4	2	no	—
177	C₂³×C₁₀₁	—	4	2	no	—
178	C₂³×C₁₀₁	—	4	2	no	—
179	C₂³×C₁₀₁	—	4	2	no	—
180	C₂³×C₁₀₁	—	4	2	no	—
181	C₂³×C₁₀₁	—	4	2	no	—
182	C₂³×C₁₀₁	—	4	2	no	—
183	C₂³×C₁₀₁	—	4	2	no	—
184	C₂³×C₁₀₁	—	4	2	no	—
185	C₂³×C₁₀₁	—	4	2	no	—
186	C₂³×C₁₀₁	—	8	4	no	—
187	C₂³×C₁₀₁	—	8	4	no	—
188	C₂³×C₁₀₁	—	8	4	no	—
189	C₂³×C₁₀₁	—	8	4	no	—
190	C₂³×C₁₀₁	#120	1	2	yes	—
191	C₂³×C₁₀₁	C₂×D₈	1	2	yes	—
192	C₂³×C₁₀₁	AGL(1,ℤ/8)	1	2	yes	—
193	C₂³×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
194	Q₈×C₁₀₁	—	4	8	no	—
195	D₄×C₁₀₁	—	2	8	no	—
196	D₄×C₁₀₁	—	2	8	no	—
197	D₄×C₁₀₁	—	4	8	no	—
198	D₄×C₁₀₁	—	4	8	no	—
199	D₄×C₁₀₁	—	4	8	no	—
200	D₄×C₁₀₁	—	4	16	no	—
201	D₄×C₁₀₁	—	4	4	no	—
202	D₄×C₁₀₁	—	4	4	no	—
203	C₂×C₄×C₁₀₁	—	2	1	no	—
204	C₂×C₄×C₁₀₁	—	2	1	no	—
205	C₂×C₄×C₁₀₁	—	2	1	no	—
206	C₂×C₄×C₁₀₁	—	2	1	no	—
207	C₂×C₄×C₁₀₁	—	2	1	no	—
208	C₂×C₄×C₁₀₁	—	2	1	no	—
209	C₂×C₄×C₁₀₁	—	2	1	no	—
210	C₂×C₄×C₁₀₁	—	2	1	no	—
211	C₂×C₄×C₁₀₁	—	2	8	no	—
212	C₂×C₄×C₁₀₁	—	2	8	no	—
213	C₂×C₄×C₁₀₁	—	2	1	no	—
214	C₂×C₄×C₁₀₁	—	2	4	no	—
215	C₂×C₄×C₁₀₁	—	2	1	no	—
216	C₂×C₄×C₁₀₁	—	2	1	no	—
217	C₂×C₄×C₁₀₁	—	4	4	no	—
218	C₂×C₄×C₁₀₁	—	4	16	no	—
219	C₂×C₄×C₁₀₁	—	4	2	no	—
220	C₂×C₄×C₁₀₁	—	4	2	no	—
221	C₂×C₄×C₁₀₁	—	4	2	no	—
222	C₂×C₄×C₁₀₁	—	4	2	no	—
223	C₂×C₄×C₁₀₁	—	4	2	no	—
224	C₂×C₄×C₁₀₁	—	8	4	no	—
225	C₂×C₄×C₁₀₁	#120	1	2	yes	—
226	C₂×C₄×C₁₀₁	C₂×D₈	1	2	yes	—
227	C₂×C₄×C₁₀₁	C₂×D₈	1	2	yes	—
228	C₂×C₄×C₁₀₁	AGL(1,ℤ/8)	1	2	yes	—
229	C₂×C₄×C₁₀₁	C₂²×D₄	1	2	yes	—
230	C₂×C₄×C₁₀₁	C₂×#41	1	2	yes	—
231	C₂×C₄×C₁₀₁	H(5,𝔽₂)	1	2	yes	—
232	C₈×C₁₀₁	—	4	4	no	—
233	C₂²×C₁₀₁	—	2	2	no	—
234	C₂²×C₁₀₁	—	2	2	no	—
235	C₂²×C₁₀₁	—	2	2	no	—
236	C₂²×C₁₀₁	—	2	2	no	—
237	C₂²×C₁₀₁	—	2	2	no	—
238	C₂²×C₁₀₁	—	2	2	no	—
239	C₂²×C₁₀₁	—	4	4	no	—
240	C₂²×C₁₀₁	—	4	4	no	—
241	C₂²×C₁₀₁	—	4	4	no	—
242	C₂²×C₁₀₁	—	4	4	no	—
243	C₂²×C₁₀₁	—	4	4	no	—
244	C₂²×C₁₀₁	—	4	4	no	—
245	C₂²×C₁₀₁	—	8	16	no	—
246	C₂²×C₁₀₁	—	8	2	no	—
247	C₂²×C₁₀₁	—	8	2	no	—
248	C₂²×C₁₀₁	—	8	2	no	—
249	C₂²×C₁₀₁	—	8	2	no	—
250	C₂²×C₁₀₁	—	8	2	no	—
251	C₂²×C₁₀₁	—	8	2	no	—
252	C₂²×C₁₀₁	—	8	2	no	—
253	C₂²×C₁₀₁	—	8	2	no	—
254	C₂²×C₁₀₁	#447	1	4	yes	—
255	C₂²×C₁₀₁	C₂×#120	1	1	yes	characteristic
256	C₂²×C₁₀₁	#525	1	1	yes	characteristic
257	C₂²×C₁₀₁	#535	1	1	yes	characteristic
258	C₂²×C₁₀₁	C₂²×D₈	1	1	yes	characteristic
259	C₂²×C₁₀₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
260	C₂²×C₁₀₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
261	C₂²×C₁₀₁	#575	1	1	yes	characteristic
262	C₄×C₁₀₁	—	2	2	no	—
263	C₄×C₁₀₁	—	2	2	no	—
264	C₄×C₁₀₁	—	2	2	no	—
265	C₄×C₁₀₁	—	2	2	no	—
266	C₄×C₁₀₁	—	4	4	no	—
267	C₄×C₁₀₁	—	4	1	no	—
268	C₄×C₁₀₁	—	8	2	no	—
269	C₄×C₁₀₁	#546	1	4	yes	—
270	#23930	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
271	C₂×C₁₀₁	—	2	4	no	—
272	C₂×C₁₀₁	—	8	4	no	—
273	C₂×C₁₀₁	—	8	4	no	—
274	C₂×C₁₀₁	#2404	1	1	yes	characteristic
275	C₂×C₁₀₁	C₂×#447	1	1	yes	characteristic
276	C₂×C₁₀₁	#3006	1	1	yes	characteristic
277	C₂×C₁₀₁	#3100	1	1	yes	characteristic
278	C₂×C₁₀₁	#3109	1	1	yes	characteristic
279	C₂×C₁₀₁	#3205	1	1	yes	characteristic
280	C₂×C₁₀₁	#3213	1	1	yes	characteristic
281	C₂×#532	C₂×C₁₀₁	1	1	yes	characteristic, complemented
282	C₂×#447	C₂×C₁₀₁	1	2	yes	complemented
283	C₂×#390	C₂×C₁₀₁	1	1	yes	characteristic, complemented
284	#2023	C₂×C₁₀₁	1	2	yes	complemented
285	#2011	C₂×C₁₀₁	1	2	yes	complemented
286	#1879	C₂×C₁₀₁	1	4	yes	complemented
287	#1874	C₂×C₁₀₁	1	2	yes	complemented
288	#1817	C₂×C₁₀₁	1	1	yes	characteristic, complemented
289	C₁₀₁	#23930	1	1	yes	characteristic, direct product factor, Sylow
290	C₂²×#41	—	2	1	no	—
291	C₂³×D₄	C₂²×C₁₀₁	1	1	yes	characteristic
292	C₂²×D₈	C₂²×C₁₀₁	1	4	yes	—
293	#532	—	2	8	no	—
294	C₂×C₄⋊Q₈	C₂²×C₁₀₁	1	1	yes	characteristic, complemented
295	C₂×#127	C₂²×C₁₀₁	1	1	yes	characteristic, complemented
296	C₂×#124	—	2	1	no	—
297	C₂×#121	—	2	1	no	—
298	C₂×#121	C₂²×C₁₀₁	1	2	yes	—
299	C₂×C₄×D₄	—	2	1	no	—
300	C₂×C₄×D₄	C₂²×C₁₀₁	1	2	yes	complemented
301	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
302	C₂²×C₂²⋊C₄	—	2	1	no	—
303	C₂²×C₂²⋊C₄	—	2	1	no	—
304	C₂²×C₄²	C₂²×C₁₀₁	1	1	yes	characteristic
305	#447	—	2	8	no	—
306	C₂×#102	C₂²×C₁₀₁	1	4	yes	—
307	C₂×#102	C₂²×C₁₀₁	1	4	yes	complemented
308	C₂×C₂²⋊C₈	C₂²×C₁₀₁	1	2	yes	—
309	#390	—	2	1	no	—
310	#390	—	2	1	no	—
311	#390	C₂²×C₁₀₁	1	2	yes	—
312	#390	C₂²×C₁₀₁	1	2	yes	—
313	#340	C₂²×C₁₀₁	1	4	yes	complemented
314	#336	C₂²×C₁₀₁	1	2	yes	complemented
315	#336	C₂²×C₁₀₁	1	2	yes	complemented
316	C₂⁵	—	2	1	no	—
317	C₂×#41	—	2	8	no	—
318	C₂×#41	—	4	4	no	—
319	C₂×#41	—	4	4	no	—
320	C₂²×Q₈	—	2	1	no	—
321	C₂²×D₄	—	2	2	no	—
322	C₂²×D₄	—	2	4	no	—
323	C₂²×D₄	—	2	1	no	—
324	C₂²×D₄	—	2	1	no	—
325	C₂²×D₄	—	2	1	no	—
326	C₂²×D₄	—	2	4	no	—
327	C₂²×D₄	—	4	2	no	—
328	C₂²×D₄	C₂³×C₁₀₁	1	2	yes	—
329	C₂²×D₄	C₂³×C₁₀₁	1	2	yes	—
330	C₂³×C₄	—	2	2	no	—
331	C₂³×C₄	—	2	1	no	—
332	C₂³×C₄	D₄×C₁₀₁	1	1	yes	characteristic
333	C₂³×C₄	D₄×C₁₀₁	1	1	yes	characteristic
334	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
335	C₂×D₈	—	2	8	no	—
336	C₂×D₈	—	2	8	no	—
337	C₂×D₈	—	4	4	no	—
338	C₂²×C₈	C₂³×C₁₀₁	1	4	yes	—
339	C₄⋊Q₈	—	2	4	no	—
340	#127	—	2	4	no	—
341	#124	—	2	8	no	—
342	#121	—	2	8	no	—
343	#121	—	2	4	no	—
344	#121	D₄×C₁₀₁	1	8	yes	—
345	C₄×D₄	—	2	8	no	—
346	C₄×D₄	—	2	4	no	—
347	C₄×D₄	—	2	4	no	—
348	C₂×C₄⋊C₄	—	2	1	no	—
349	C₂×C₄⋊C₄	—	2	1	no	—
350	C₂×C₄⋊C₄	—	4	2	no	—
351	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	2	yes	—
352	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	2	yes	—
353	C₂×C₂²⋊C₄	—	2	2	no	—
354	C₂×C₂²⋊C₄	—	2	2	no	—
355	C₂×C₂²⋊C₄	—	2	2	no	—
356	C₂×C₂²⋊C₄	—	2	2	no	—
357	C₂×C₂²⋊C₄	—	2	2	no	—
358	C₂×C₂²⋊C₄	—	2	2	no	—
359	C₂×C₂²⋊C₄	—	4	4	no	—
360	C₂×C₂²⋊C₄	—	4	4	no	—
361	C₂×C₄²	—	2	4	no	—
362	C₂×C₄²	D₄×C₁₀₁	1	1	yes	characteristic
363	C₂×C₄²	D₄×C₁₀₁	1	1	yes	characteristic
364	C₂×C₄²	C₂³×C₁₀₁	1	1	yes	characteristic
365	C₂×C₄²	C₂³×C₁₀₁	1	1	yes	characteristic
366	#102	—	2	8	no	—
367	#102	—	4	4	no	—
368	C₂²⋊C₈	—	2	4	no	—
369	C₂⁴	—	2	4	no	—
370	C₂⁴	—	2	2	no	—
371	C₂⁴	—	2	2	no	—
372	C₂⁴	—	4	2	no	—
373	C₂⁴	—	4	2	no	—
374	C₂⁴	—	4	2	no	—
375	C₂⁴	—	4	2	no	—
376	C₂⁴	—	4	2	no	—
377	C₂⁴	—	4	2	no	—
378	C₂⁴	C₂×D₄×C₁₀₁	1	1	yes	characteristic
379	#41	—	4	32	no	—
380	C₂×Q₈	—	2	4	no	—
381	C₂×Q₈	—	4	2	no	—
382	C₂×Q₈	—	4	2	no	—
383	C₂×D₄	—	2	4	no	—
384	C₂×D₄	—	2	4	no	—
385	C₂×D₄	—	2	4	no	—
386	C₂×D₄	—	2	8	no	—
387	C₂×D₄	—	2	4	no	—
388	C₂×D₄	—	2	2	no	—
389	C₂×D₄	—	2	4	no	—
390	C₂×D₄	—	2	2	no	—
391	C₂×D₄	—	2	4	no	—
392	C₂×D₄	—	2	4	no	—
393	C₂×D₄	—	4	16	no	—
394	C₂×D₄	—	4	2	no	—
395	C₂×D₄	—	4	2	no	—
396	C₂×D₄	—	4	2	no	—
397	C₂×D₄	—	4	4	no	—
398	C₂×D₄	—	4	4	no	—
399	C₂×D₄	—	4	2	no	—
400	C₂×D₄	—	4	2	no	—
401	C₂×D₄	—	4	2	no	—
402	C₂×D₄	C₂×D₄×C₁₀₁	1	4	yes	—
403	C₂×D₄	#41×C₁₀₁	1	4	yes	complemented
404	C₂²×C₄	—	2	2	no	—
405	C₂²×C₄	—	2	2	no	—
406	C₂²×C₄	—	2	2	no	—
407	C₂²×C₄	—	2	2	no	—
408	C₂²×C₄	—	2	8	no	—
409	C₂²×C₄	—	2	2	no	—
410	C₂²×C₄	—	2	2	no	—
411	C₂²×C₄	—	2	2	no	—
412	C₂²×C₄	—	2	2	no	—
413	C₂²×C₄	—	4	1	no	—
414	C₂²×C₄	—	4	4	no	—
415	C₂²×C₄	—	4	4	no	—
416	C₂²×C₄	—	4	2	no	—
417	C₂²×C₄	—	4	2	no	—
418	C₂²×C₄	—	4	2	no	—
419	C₂²×C₄	D₈×C₁₀₁	1	4	yes	complemented
420	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
421	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
422	C₂²×C₄	C₂×D₄×C₁₀₁	1	4	yes	—
423	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
424	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
425	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
426	C₂²×C₄	C₂⁴×C₁₀₁	1	1	yes	characteristic
427	D₈	—	4	16	no	—
428	C₂×C₈	—	2	4	no	—
429	C₂×C₈	—	2	4	no	—
430	C₂×C₈	—	2	4	no	—
431	C₄⋊C₄	—	2	4	no	—
432	C₄⋊C₄	—	2	2	no	—
433	C₄⋊C₄	—	2	4	no	—
434	C₄⋊C₄	—	4	2	no	—
435	C₄⋊C₄	C₂×D₄×C₁₀₁	1	4	yes	—
436	C₂²⋊C₄	—	2	8	no	—
437	C₂²⋊C₄	—	2	8	no	—
438	C₂²⋊C₄	—	4	4	no	—
439	C₂²⋊C₄	—	4	4	no	—
440	C₂²⋊C₄	—	4	4	no	—
441	C₂²⋊C₄	—	4	4	no	—
442	C₄²	—	2	2	no	—
443	C₄²	—	2	2	no	—
444	C₄²	—	2	2	no	—
445	C₄²	—	2	2	no	—
446	C₂³	—	2	1	no	—
447	C₂³	—	2	1	no	—
448	C₂³	—	2	1	no	—
449	C₂³	—	2	1	no	—
450	C₂³	—	2	4	no	—
451	C₂³	—	2	4	no	—
452	C₂³	—	4	8	no	—
453	C₂³	—	4	8	no	—
454	C₂³	—	4	8	no	—
455	C₂³	—	4	2	no	—
456	C₂³	—	4	2	no	—
457	C₂³	—	4	2	no	—
458	C₂³	—	4	2	no	—
459	C₂³	—	4	2	no	—
460	C₂³	—	4	2	no	—
461	C₂³	—	4	2	no	—
462	C₂³	—	4	2	no	—
463	C₂³	—	4	2	no	—
464	C₂³	—	4	2	no	—
465	C₂³	—	4	2	no	—
466	C₂³	—	4	2	no	—
467	C₂³	—	8	4	no	—
468	C₂³	—	8	4	no	—
469	C₂³	—	8	4	no	—
470	C₂³	—	8	4	no	—
471	C₂³	#120×C₁₀₁	1	2	yes	—
472	C₂³	C₂×D₈×C₁₀₁	1	2	yes	—
473	C₂³	AGL(1,ℤ/8)×C₁₀₁	1	2	yes	—
474	C₂³	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
475	Q₈	—	4	8	no	—
476	D₄	—	2	8	no	—
477	D₄	—	2	8	no	—
478	D₄	—	4	8	no	—
479	D₄	—	4	8	no	—
480	D₄	—	4	8	no	—
481	D₄	—	4	16	no	—
482	D₄	—	4	4	no	—
483	D₄	—	4	4	no	—
484	C₂×C₄	—	2	8	no	—
485	C₂×C₄	—	2	1	no	—
486	C₂×C₄	—	2	1	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	2	1	no	—
489	C₂×C₄	—	2	1	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	2	8	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	2	4	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	4	4	no	—
499	C₂×C₄	—	4	16	no	—
500	C₂×C₄	—	4	2	no	—
501	C₂×C₄	—	4	2	no	—
502	C₂×C₄	—	4	2	no	—
503	C₂×C₄	—	4	2	no	—
504	C₂×C₄	—	4	2	no	—
505	C₂×C₄	—	8	4	no	—
506	C₂×C₄	#120×C₁₀₁	1	2	yes	—
507	C₂×C₄	C₂×D₈×C₁₀₁	1	2	yes	—
508	C₂×C₄	C₂×D₈×C₁₀₁	1	2	yes	—
509	C₂×C₄	AGL(1,ℤ/8)×C₁₀₁	1	2	yes	—
510	C₂×C₄	C₂²×D₄×C₁₀₁	1	2	yes	—
511	C₂×C₄	C₂×#41×C₁₀₁	1	2	yes	—
512	C₂×C₄	H(5,𝔽₂)×C₁₀₁	1	2	yes	—
513	C₈	—	4	4	no	—
514	C₂²	—	2	2	no	—
515	C₂²	—	2	2	no	—
516	C₂²	—	2	2	no	—
517	C₂²	—	2	2	no	—
518	C₂²	—	2	2	no	—
519	C₂²	—	2	2	no	—
520	C₂²	—	4	4	no	—
521	C₂²	—	4	4	no	—
522	C₂²	—	4	4	no	—
523	C₂²	—	4	4	no	—
524	C₂²	—	4	4	no	—
525	C₂²	—	4	4	no	—
526	C₂²	—	8	16	no	—
527	C₂²	—	8	2	no	—
528	C₂²	—	8	2	no	—
529	C₂²	—	8	2	no	—
530	C₂²	—	8	2	no	—
531	C₂²	—	8	2	no	—
532	C₂²	—	8	2	no	—
533	C₂²	—	8	2	no	—
534	C₂²	—	8	2	no	—
535	C₂²	#447×C₁₀₁	1	4	yes	—
536	C₂²	C₂×#120×C₁₀₁	1	1	yes	characteristic
537	C₂²	#525×C₁₀₁	1	1	yes	characteristic
538	C₂²	#535×C₁₀₁	1	1	yes	characteristic
539	C₂²	C₂²×D₈×C₁₀₁	1	1	yes	characteristic
540	C₂²	C₂×AGL(1,ℤ/8)×C₁₀₁	1	1	yes	characteristic
541	C₂²	C₂×AGL(1,ℤ/8)×C₁₀₁	1	1	yes	characteristic
542	C₂²	#575×C₁₀₁	1	1	yes	characteristic
543	C₄	—	2	2	no	—
544	C₄	—	2	2	no	—
545	C₄	—	2	2	no	—
546	C₄	—	2	2	no	—
547	C₄	—	4	4	no	—
548	C₄	—	4	1	no	—
549	C₄	—	8	2	no	—
550	C₄	#546×C₁₀₁	1	4	yes	—
551	C₂	—	2	4	no	—
552	C₂	—	8	4	no	—
553	C₂	—	8	4	no	—
554	C₂	C₁₀₁×#2404	1	1	yes	characteristic
555	C₂	C₂×#447×C₁₀₁	1	1	yes	characteristic
556	C₂	C₁₀₁×#3006	1	1	yes	characteristic
557	C₂	C₁₀₁×#3100	1	1	yes	characteristic
558	C₂	C₁₀₁×#3109	1	1	yes	characteristic
559	C₂	C₁₀₁×#3205	1	1	yes	characteristic
560	C₂	C₁₀₁×#3213	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. C₂×#532×C₁₀₁	C₂	semidirect
2. C₂×#447×C₁₀₁	C₂	semidirect
3. C₂×#390×C₁₀₁	C₂	semidirect
4. C₁₀₁×#2023	C₂	semidirect
5. C₁₀₁×#2011	C₂	semidirect
6. C₁₀₁×#1879	C₂	semidirect
7. C₁₀₁×#1874	C₂	semidirect
8. C₁₀₁×#1817	C₂	semidirect
13. C₂×C₄⋊Q₈×C₁₀₁	C₂²	semidirect
14. C₂×#127×C₁₀₁	C₂²	semidirect
19. C₂×C₄×D₄×C₁₀₁	C₂²	semidirect
26. C₂×#102×C₁₀₁	C₂²	semidirect
32. #340×C₁₀₁	C₂²	semidirect
33. #336×C₁₀₁	C₂²	semidirect
34. #336×C₁₀₁	C₂²	semidirect
122. C₂×D₄×C₁₀₁	#41	semidirect
138. C₂²×C₄×C₁₀₁	D₈	semidirect
270. #23930	C₁₀₁	direct (N × H)
281. C₂×#532	C₂×C₁₀₁	semidirect
282. C₂×#447	C₂×C₁₀₁	semidirect
283. C₂×#390	C₂×C₁₀₁	semidirect
284. #2023	C₂×C₁₀₁	semidirect
285. #2011	C₂×C₁₀₁	semidirect
286. #1879	C₂×C₁₀₁	semidirect
287. #1874	C₂×C₁₀₁	semidirect
288. #1817	C₂×C₁₀₁	semidirect
289. C₁₀₁	#23930	direct (N × H)
294. C₂×C₄⋊Q₈	C₂²×C₁₀₁	semidirect
295. C₂×#127	C₂²×C₁₀₁	semidirect
300. C₂×C₄×D₄	C₂²×C₁₀₁	semidirect
307. C₂×#102	C₂²×C₁₀₁	semidirect
313. #340	C₂²×C₁₀₁	semidirect
314. #336	C₂²×C₁₀₁	semidirect
315. #336	C₂²×C₁₀₁	semidirect
403. C₂×D₄	#41×C₁₀₁	semidirect
419. C₂²×C₄	D₈×C₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#532×C₁₀₁	2
C₂×#447×C₁₀₁	2
C₂×#390×C₁₀₁	2
C₁₀₁×#2023	2
C₁₀₁×#2011	2
C₁₀₁×#1879	2
C₁₀₁×#1874	2
C₁₀₁×#1817	2
#23930	101

Subgroups — C101×#23930 #38806081

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#23930 #38806081