Subgroups — C₁₀₁×#25896 #38808047

Order 25856.

1322 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#548×C₁₀₁	C₂	1	1	yes	maximal, characteristic
2	C₂×#489×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#477×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₀₁×#2547	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₀₁×#2036	C₂	1	2	yes	maximal, complemented
6	C₁₀₁×#2033	C₂	1	2	yes	maximal, complemented
7	C₁₀₁×#1983	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₀₁×#1955	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₀₁×#1788	C₂	1	2	yes	maximal, complemented
10	C₁₀₁×#1787	C₂	1	2	yes	maximal, complemented
11	C₁₀₁×#1763	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₁₀₁	C₂²	1	1	yes	characteristic
13	C₂³×Q₈×C₁₀₁	C₂²	1	1	yes	characteristic
14	#548×C₁₀₁	—	2	4	no	—
15	#548×C₁₀₁	—	2	4	no	—
16	C₂×C₄⋊Q₈×C₁₀₁	C₂²	1	1	yes	characteristic
17	C₂×#124×C₁₀₁	—	2	1	no	—
18	C₂×#124×C₁₀₁	—	2	1	no	—
19	C₂×#124×C₁₀₁	C₂²	1	1	yes	characteristic
20	C₂×C₂²⋊Q₈×C₁₀₁	—	2	1	no	—
21	C₂×C₂²⋊Q₈×C₁₀₁	C₂²	1	1	yes	characteristic
22	C₂×#121×C₁₀₁	—	2	1	no	—
23	C₂×#121×C₁₀₁	C₂²	1	1	yes	characteristic
24	C₂×C₄×Q₈×C₁₀₁	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₁₀₁	—	2	1	no	—
26	C₂×C₄×D₄×C₁₀₁	C₂²	1	1	yes	characteristic
27	#489×C₁₀₁	—	2	4	no	—
28	#477×C₁₀₁	—	2	4	no	—
29	C₂×#107×C₁₀₁	C₂²	1	2	yes	—
30	C₂×C₄⋊C₈×C₁₀₁	C₂²	1	1	yes	characteristic
31	C₂×#103×C₁₀₁	C₂²	1	2	yes	—
32	C₂×#103×C₁₀₁	C₂²	1	2	yes	—
33	C₂×#103×C₁₀₁	C₂²	1	2	yes	—
34	C₂×#103×C₁₀₁	C₂²	1	2	yes	—
35	C₂×#102×C₁₀₁	C₂²	1	2	yes	—
36	C₂×#102×C₁₀₁	C₂²	1	2	yes	—
37	C₂×C₂²⋊C₈×C₁₀₁	C₂²	1	2	yes	—
38	C₂×C₂²⋊C₈×C₁₀₁	C₂²	1	2	yes	—
39	C₂×#97×C₁₀₁	C₂²	1	1	yes	characteristic
40	#397×C₁₀₁	—	2	1	no	—
41	#397×C₁₀₁	—	2	1	no	—
42	#391×C₁₀₁	—	2	1	no	—
43	#380×C₁₀₁	C₂²	1	2	yes	—
44	#380×C₁₀₁	C₂²	1	2	yes	—
45	C₄×C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
46	#340×C₁₀₁	C₂²	1	2	yes	—
47	C₂×#41×C₁₀₁	—	2	2	no	—
48	C₂×#41×C₁₀₁	—	2	2	no	—
49	C₂×#41×C₁₀₁	—	2	4	no	—
50	C₂×#41×C₁₀₁	—	4	2	no	—
51	C₂²×Q₈×C₁₀₁	—	2	2	no	—
52	C₂²×Q₈×C₁₀₁	—	2	2	no	—
53	C₂²×Q₈×C₁₀₁	—	2	1	no	—
54	C₂²×Q₈×C₁₀₁	—	2	1	no	—
55	C₂²×Q₈×C₁₀₁	—	2	4	no	—
56	C₂²×Q₈×C₁₀₁	—	4	2	no	—
57	C₂²×Q₈×C₁₀₁	C₂³	1	1	yes	characteristic
58	C₂²×Q₈×C₁₀₁	C₂³	1	1	yes	characteristic
59	C₂²×D₄×C₁₀₁	—	2	1	no	—
60	C₂²×D₄×C₁₀₁	—	2	1	no	—
61	C₂²×D₄×C₁₀₁	D₄	1	1	yes	characteristic
62	C₂²×D₄×C₁₀₁	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₁₀₁	—	2	1	no	—
64	C₂³×C₄×C₁₀₁	—	2	1	no	—
65	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
67	C₂²×C₈×C₁₀₁	C₂³	1	2	yes	—
68	C₂²×C₈×C₁₀₁	C₂³	1	2	yes	—
69	C₄⋊Q₈×C₁₀₁	—	2	2	no	—
70	C₄⋊Q₈×C₁₀₁	—	2	2	no	—
71	#124×C₁₀₁	—	2	8	no	—
72	#124×C₁₀₁	—	2	2	no	—
73	#124×C₁₀₁	—	4	4	no	—
74	#124×C₁₀₁	D₄	1	4	yes	—
75	C₂²⋊Q₈×C₁₀₁	—	2	8	no	—
76	C₂²⋊Q₈×C₁₀₁	—	2	2	no	—
77	C₂²⋊Q₈×C₁₀₁	—	2	2	no	—
78	#121×C₁₀₁	—	2	8	no	—
79	#121×C₁₀₁	—	2	2	no	—
80	#121×C₁₀₁	—	2	2	no	—
81	C₄×Q₈×C₁₀₁	—	2	2	no	—
82	C₄×Q₈×C₁₀₁	D₄	1	4	yes	—
83	C₄×D₄×C₁₀₁	—	2	8	no	—
84	C₄×D₄×C₁₀₁	—	2	2	no	—
85	C₄×D₄×C₁₀₁	—	2	2	no	—
86	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
87	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
88	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
89	C₂×C₄⋊C₄×C₁₀₁	D₄	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
91	C₂×C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
92	C₂×C₄⋊C₄×C₁₀₁	C₂³	1	1	yes	characteristic
93	C₂×C₂²⋊C₄×C₁₀₁	—	2	1	no	—
94	C₂×C₂²⋊C₄×C₁₀₁	—	2	1	no	—
95	C₂×C₂²⋊C₄×C₁₀₁	—	2	1	no	—
96	C₂×C₂²⋊C₄×C₁₀₁	—	2	1	no	—
97	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
98	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
99	C₂×C₂²⋊C₄×C₁₀₁	D₄	1	1	yes	characteristic
100	C₂×C₂²⋊C₄×C₁₀₁	D₄	1	1	yes	characteristic
101	C₂×C₄²×C₁₀₁	—	2	1	no	—
102	C₂×C₄²×C₁₀₁	—	2	1	no	—
103	C₂×C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
104	#107×C₁₀₁	—	2	4	no	—
105	C₄⋊C₈×C₁₀₁	—	2	2	no	—
106	#103×C₁₀₁	—	2	4	no	—
107	#103×C₁₀₁	—	2	4	no	—
108	#103×C₁₀₁	—	2	4	no	—
109	#103×C₁₀₁	—	4	2	no	—
110	#102×C₁₀₁	—	2	4	no	—
111	#102×C₁₀₁	—	4	2	no	—
112	C₂²⋊C₈×C₁₀₁	—	4	2	no	—
113	C₂²⋊C₈×C₁₀₁	—	4	2	no	—
114	#97×C₁₀₁	—	2	2	no	—
115	#95×C₁₀₁	—	2	1	no	—
116	#95×C₁₀₁	—	2	2	no	—
117	#95×C₁₀₁	—	2	2	no	—
118	C₂⁴×C₁₀₁	—	2	1	no	—
119	C₂⁴×C₁₀₁	C₂×D₄	1	1	yes	characteristic
120	C₂⁴×C₁₀₁	C₂×D₄	1	1	yes	characteristic
121	#41×C₁₀₁	—	4	8	no	—
122	#41×C₁₀₁	—	4	4	no	—
123	#41×C₁₀₁	—	4	4	no	—
124	C₂×Q₈×C₁₀₁	—	2	4	no	—
125	C₂×Q₈×C₁₀₁	—	2	1	no	—
126	C₂×Q₈×C₁₀₁	—	2	1	no	—
127	C₂×Q₈×C₁₀₁	—	2	2	no	—
128	C₂×Q₈×C₁₀₁	—	2	2	no	—
129	C₂×Q₈×C₁₀₁	—	2	2	no	—
130	C₂×Q₈×C₁₀₁	—	4	4	no	—
131	C₂×Q₈×C₁₀₁	—	4	2	no	—
132	C₂×Q₈×C₁₀₁	—	4	2	no	—
133	C₂×Q₈×C₁₀₁	—	4	8	no	—
134	C₂×Q₈×C₁₀₁	—	4	4	no	—
135	C₂×Q₈×C₁₀₁	—	4	4	no	—
136	C₂×Q₈×C₁₀₁	—	4	2	no	—
137	C₂×Q₈×C₁₀₁	C₂×D₄	1	2	yes	—
138	C₂×Q₈×C₁₀₁	C₂×D₄	1	2	yes	—
139	C₂×Q₈×C₁₀₁	#41	1	4	yes	—
140	C₂×D₄×C₁₀₁	—	2	4	no	—
141	C₂×D₄×C₁₀₁	—	2	4	no	—
142	C₂×D₄×C₁₀₁	—	2	2	no	—
143	C₂×D₄×C₁₀₁	—	2	2	no	—
144	C₂×D₄×C₁₀₁	—	2	1	no	—
145	C₂×D₄×C₁₀₁	—	2	2	no	—
146	C₂×D₄×C₁₀₁	—	2	2	no	—
147	C₂×D₄×C₁₀₁	—	4	1	no	—
148	C₂×D₄×C₁₀₁	—	4	4	no	—
149	C₂×D₄×C₁₀₁	—	4	2	no	—
150	C₂×D₄×C₁₀₁	—	4	2	no	—
151	C₂×D₄×C₁₀₁	C₂×D₄	1	2	yes	—
152	C₂²×C₄×C₁₀₁	—	2	1	no	—
153	C₂²×C₄×C₁₀₁	—	2	4	no	—
154	C₂²×C₄×C₁₀₁	—	2	4	no	—
155	C₂²×C₄×C₁₀₁	—	2	1	no	—
156	C₂²×C₄×C₁₀₁	—	2	1	no	—
157	C₂²×C₄×C₁₀₁	—	2	1	no	—
158	C₂²×C₄×C₁₀₁	—	2	1	no	—
159	C₂²×C₄×C₁₀₁	—	2	1	no	—
160	C₂²×C₄×C₁₀₁	—	2	1	no	—
161	C₂²×C₄×C₁₀₁	—	2	2	no	—
162	C₂²×C₄×C₁₀₁	—	2	2	no	—
163	C₂²×C₄×C₁₀₁	—	2	2	no	—
164	C₂²×C₄×C₁₀₁	—	2	2	no	—
165	C₂²×C₄×C₁₀₁	—	2	2	no	—
166	C₂²×C₄×C₁₀₁	—	2	2	no	—
167	C₂²×C₄×C₁₀₁	—	4	4	no	—
168	C₂²×C₄×C₁₀₁	—	4	4	no	—
169	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
174	C₂×C₈×C₁₀₁	—	2	2	no	—
175	C₂×C₈×C₁₀₁	—	2	2	no	—
176	C₂×C₈×C₁₀₁	—	2	2	no	—
177	C₂×C₈×C₁₀₁	—	2	2	no	—
178	C₂×C₈×C₁₀₁	—	2	2	no	—
179	C₂×C₈×C₁₀₁	—	2	2	no	—
180	C₄⋊C₄×C₁₀₁	—	2	4	no	—
181	C₄⋊C₄×C₁₀₁	—	2	4	no	—
182	C₄⋊C₄×C₁₀₁	—	2	2	no	—
183	C₄⋊C₄×C₁₀₁	—	2	1	no	—
184	C₄⋊C₄×C₁₀₁	—	2	2	no	—
185	C₄⋊C₄×C₁₀₁	—	2	2	no	—
186	C₄⋊C₄×C₁₀₁	—	2	2	no	—
187	C₄⋊C₄×C₁₀₁	—	2	2	no	—
188	C₄⋊C₄×C₁₀₁	—	4	2	no	—
189	C₄⋊C₄×C₁₀₁	C₂×D₄	1	2	yes	—
190	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
191	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
192	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
193	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
194	C₂²⋊C₄×C₁₀₁	—	2	2	no	—
195	C₂²⋊C₄×C₁₀₁	—	2	2	no	—
196	C₂²⋊C₄×C₁₀₁	—	4	4	no	—
197	C₂²⋊C₄×C₁₀₁	—	4	4	no	—
198	C₄²×C₁₀₁	—	2	4	no	—
199	C₄²×C₁₀₁	—	4	2	no	—
200	C₄²×C₁₀₁	C₂×D₄	1	2	yes	—
201	C₄²×C₁₀₁	C₂×D₄	1	2	yes	—
202	C₂³×C₁₀₁	—	2	1	no	—
203	C₂³×C₁₀₁	—	2	2	no	—
204	C₂³×C₁₀₁	—	2	1	no	—
205	C₂³×C₁₀₁	—	2	2	no	—
206	C₂³×C₁₀₁	—	2	1	no	—
207	C₂³×C₁₀₁	—	2	2	no	—
208	C₂³×C₁₀₁	—	2	2	no	—
209	C₂³×C₁₀₁	—	2	1	no	—
210	C₂³×C₁₀₁	—	2	1	no	—
211	C₂³×C₁₀₁	—	2	2	no	—
212	C₂³×C₁₀₁	—	4	2	no	—
213	C₂³×C₁₀₁	—	4	1	no	—
214	C₂³×C₁₀₁	—	4	1	no	—
215	C₂³×C₁₀₁	—	4	2	no	—
216	C₂³×C₁₀₁	AGL(1,ℤ/8)	1	2	yes	—
217	C₂³×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
218	Q₈×C₁₀₁	—	2	2	no	—
219	Q₈×C₁₀₁	—	2	4	no	—
220	Q₈×C₁₀₁	—	2	4	no	—
221	Q₈×C₁₀₁	—	4	8	no	—
222	Q₈×C₁₀₁	—	4	1	no	—
223	Q₈×C₁₀₁	—	4	1	no	—
224	Q₈×C₁₀₁	—	8	4	no	—
225	Q₈×C₁₀₁	#124	1	4	yes	complemented
226	D₄×C₁₀₁	—	2	4	no	—
227	D₄×C₁₀₁	—	4	4	no	—
228	D₄×C₁₀₁	—	4	8	no	—
229	D₄×C₁₀₁	—	4	8	no	—
230	D₄×C₁₀₁	—	4	1	no	—
231	D₄×C₁₀₁	—	4	1	no	—
232	C₂×C₄×C₁₀₁	—	2	2	no	—
233	C₂×C₄×C₁₀₁	—	2	4	no	—
234	C₂×C₄×C₁₀₁	—	2	1	no	—
235	C₂×C₄×C₁₀₁	—	2	1	no	—
236	C₂×C₄×C₁₀₁	—	2	2	no	—
237	C₂×C₄×C₁₀₁	—	2	2	no	—
238	C₂×C₄×C₁₀₁	—	2	2	no	—
239	C₂×C₄×C₁₀₁	—	2	1	no	—
240	C₂×C₄×C₁₀₁	—	2	1	no	—
241	C₂×C₄×C₁₀₁	—	2	2	no	—
242	C₂×C₄×C₁₀₁	—	2	2	no	—
243	C₂×C₄×C₁₀₁	—	4	8	no	—
244	C₂×C₄×C₁₀₁	—	4	8	no	—
245	C₂×C₄×C₁₀₁	—	4	2	no	—
246	C₂×C₄×C₁₀₁	—	4	1	no	—
247	C₂×C₄×C₁₀₁	—	4	1	no	—
248	C₂×C₄×C₁₀₁	—	4	1	no	—
249	C₂×C₄×C₁₀₁	—	4	1	no	—
250	C₂×C₄×C₁₀₁	—	4	1	no	—
251	C₂×C₄×C₁₀₁	—	4	1	no	—
252	C₂×C₄×C₁₀₁	—	4	2	no	—
253	C₂×C₄×C₁₀₁	—	4	2	no	—
254	C₂×C₄×C₁₀₁	—	4	2	no	—
255	C₂×C₄×C₁₀₁	—	4	2	no	—
256	C₂×C₄×C₁₀₁	—	4	2	no	—
257	C₂×C₄×C₁₀₁	—	4	2	no	—
258	C₂×C₄×C₁₀₁	—	4	2	no	—
259	C₂×C₄×C₁₀₁	—	4	2	no	—
260	C₂×C₄×C₁₀₁	#120	1	2	yes	—
261	C₂×C₄×C₁₀₁	#120	1	2	yes	—
262	C₂×C₄×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
263	C₂×C₄×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
264	C₂×C₄×C₁₀₁	C₂×#41	1	2	yes	—
265	C₂×C₄×C₁₀₁	H(5,𝔽₂)	1	2	yes	—
266	C₈×C₁₀₁	—	4	2	no	—
267	C₈×C₁₀₁	—	4	2	no	—
268	C₂²×C₁₀₁	—	2	2	no	—
269	C₂²×C₁₀₁	—	2	4	no	—
270	C₂²×C₁₀₁	—	4	1	no	—
271	C₂²×C₁₀₁	—	4	1	no	—
272	C₂²×C₁₀₁	—	4	2	no	—
273	C₂²×C₁₀₁	—	4	2	no	—
274	C₂²×C₁₀₁	—	4	1	no	—
275	C₂²×C₁₀₁	—	4	1	no	—
276	C₂²×C₁₀₁	—	4	2	no	—
277	C₂²×C₁₀₁	—	4	1	no	—
278	C₂²×C₁₀₁	—	4	2	no	—
279	C₂²×C₁₀₁	—	4	2	no	—
280	C₂²×C₁₀₁	—	4	2	no	—
281	C₂²×C₁₀₁	—	8	2	no	—
282	C₂²×C₁₀₁	—	8	2	no	—
283	C₂²×C₁₀₁	C₂×#120	1	1	yes	characteristic
284	C₂²×C₁₀₁	#546	1	2	yes	—
285	C₂²×C₁₀₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
286	C₂²×C₁₀₁	#575	1	1	yes	characteristic
287	C₂²×C₁₀₁	#578	1	2	yes	—
288	C₄×C₁₀₁	—	2	4	no	—
289	C₄×C₁₀₁	—	2	2	no	—
290	C₄×C₁₀₁	—	2	2	no	—
291	C₄×C₁₀₁	—	4	1	no	—
292	C₄×C₁₀₁	—	4	1	no	—
293	C₄×C₁₀₁	—	4	2	no	—
294	C₄×C₁₀₁	—	4	2	no	—
295	C₄×C₁₀₁	—	8	2	no	—
296	C₄×C₁₀₁	—	8	2	no	—
297	C₄×C₁₀₁	C₂×#124	1	1	yes	characteristic
298	C₄×C₁₀₁	#535	1	1	yes	characteristic
299	C₄×C₁₀₁	#546	1	2	yes	—
300	#25896	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
301	C₂×C₁₀₁	—	4	2	no	—
302	C₂×C₁₀₁	—	8	1	no	—
303	C₂×C₁₀₁	—	8	2	no	—
304	C₂×C₁₀₁	#2435	1	1	yes	characteristic
305	C₂×C₁₀₁	#3006	1	1	yes	characteristic
306	C₂×C₁₀₁	#3011	1	1	yes	characteristic
307	C₂×C₁₀₁	#3308	1	2	yes	—
308	C₂×C₁₀₁	#3313	1	2	yes	—
309	C₂×#548	C₂×C₁₀₁	1	1	yes	characteristic
310	C₂×#489	C₂×C₁₀₁	1	1	yes	characteristic, complemented
311	C₂×#477	C₂×C₁₀₁	1	1	yes	characteristic, complemented
312	#2547	C₂×C₁₀₁	1	1	yes	characteristic, complemented
313	#2036	C₂×C₁₀₁	1	2	yes	complemented
314	#2033	C₂×C₁₀₁	1	2	yes	complemented
315	#1983	C₂×C₁₀₁	1	1	yes	characteristic, complemented
316	#1955	C₂×C₁₀₁	1	1	yes	characteristic, complemented
317	#1788	C₂×C₁₀₁	1	2	yes	complemented
318	#1787	C₂×C₁₀₁	1	2	yes	complemented
319	#1763	C₂×C₁₀₁	1	1	yes	characteristic, complemented
320	C₁₀₁	#25896	1	1	yes	characteristic, direct product factor, Sylow
321	C₂²×#41	C₂²×C₁₀₁	1	1	yes	characteristic
322	C₂³×Q₈	C₂²×C₁₀₁	1	1	yes	characteristic
323	#548	—	2	4	no	—
324	#548	—	2	4	no	—
325	C₂×C₄⋊Q₈	C₂²×C₁₀₁	1	1	yes	characteristic
326	C₂×#124	—	2	1	no	—
327	C₂×#124	—	2	1	no	—
328	C₂×#124	C₂²×C₁₀₁	1	1	yes	characteristic
329	C₂×C₂²⋊Q₈	—	2	1	no	—
330	C₂×C₂²⋊Q₈	C₂²×C₁₀₁	1	1	yes	characteristic
331	C₂×#121	—	2	1	no	—
332	C₂×#121	C₂²×C₁₀₁	1	1	yes	characteristic
333	C₂×C₄×Q₈	C₂²×C₁₀₁	1	1	yes	characteristic
334	C₂×C₄×D₄	—	2	1	no	—
335	C₂×C₄×D₄	C₂²×C₁₀₁	1	1	yes	characteristic
336	#489	—	2	4	no	—
337	#477	—	2	4	no	—
338	C₂×#107	C₂²×C₁₀₁	1	2	yes	—
339	C₂×C₄⋊C₈	C₂²×C₁₀₁	1	1	yes	characteristic
340	C₂×#103	C₂²×C₁₀₁	1	2	yes	—
341	C₂×#103	C₂²×C₁₀₁	1	2	yes	—
342	C₂×#103	C₂²×C₁₀₁	1	2	yes	—
343	C₂×#103	C₂²×C₁₀₁	1	2	yes	—
344	C₂×#102	C₂²×C₁₀₁	1	2	yes	—
345	C₂×#102	C₂²×C₁₀₁	1	2	yes	—
346	C₂×C₂²⋊C₈	C₂²×C₁₀₁	1	2	yes	—
347	C₂×C₂²⋊C₈	C₂²×C₁₀₁	1	2	yes	—
348	C₂×#97	C₂²×C₁₀₁	1	1	yes	characteristic
349	#397	—	2	1	no	—
350	#397	—	2	1	no	—
351	#391	—	2	1	no	—
352	#380	C₂²×C₁₀₁	1	2	yes	—
353	#380	C₂²×C₁₀₁	1	2	yes	—
354	C₄×C₄⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
355	#340	C₂²×C₁₀₁	1	2	yes	—
356	C₂×#41	—	2	2	no	—
357	C₂×#41	—	2	2	no	—
358	C₂×#41	—	2	4	no	—
359	C₂×#41	—	4	2	no	—
360	C₂²×Q₈	—	2	2	no	—
361	C₂²×Q₈	—	2	2	no	—
362	C₂²×Q₈	—	2	1	no	—
363	C₂²×Q₈	—	2	1	no	—
364	C₂²×Q₈	—	2	4	no	—
365	C₂²×Q₈	—	4	2	no	—
366	C₂²×Q₈	C₂³×C₁₀₁	1	1	yes	characteristic
367	C₂²×Q₈	C₂³×C₁₀₁	1	1	yes	characteristic
368	C₂²×D₄	—	2	1	no	—
369	C₂²×D₄	—	2	1	no	—
370	C₂²×D₄	D₄×C₁₀₁	1	1	yes	characteristic
371	C₂²×D₄	C₂³×C₁₀₁	1	1	yes	characteristic
372	C₂³×C₄	—	2	1	no	—
373	C₂³×C₄	—	2	1	no	—
374	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
375	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
376	C₂²×C₈	C₂³×C₁₀₁	1	2	yes	—
377	C₂²×C₈	C₂³×C₁₀₁	1	2	yes	—
378	C₄⋊Q₈	—	2	2	no	—
379	C₄⋊Q₈	—	2	2	no	—
380	#124	—	2	8	no	—
381	#124	—	2	2	no	—
382	#124	—	4	4	no	—
383	#124	D₄×C₁₀₁	1	4	yes	—
384	C₂²⋊Q₈	—	2	8	no	—
385	C₂²⋊Q₈	—	2	2	no	—
386	C₂²⋊Q₈	—	2	2	no	—
387	#121	—	2	8	no	—
388	#121	—	2	2	no	—
389	#121	—	2	2	no	—
390	C₄×Q₈	—	2	2	no	—
391	C₄×Q₈	D₄×C₁₀₁	1	4	yes	—
392	C₄×D₄	—	2	8	no	—
393	C₄×D₄	—	2	2	no	—
394	C₄×D₄	—	2	2	no	—
395	C₂×C₄⋊C₄	—	2	1	no	—
396	C₂×C₄⋊C₄	—	2	1	no	—
397	C₂×C₄⋊C₄	—	2	1	no	—
398	C₂×C₄⋊C₄	D₄×C₁₀₁	1	1	yes	characteristic
399	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	2	yes	—
400	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	2	yes	—
401	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	1	yes	characteristic
402	C₂×C₂²⋊C₄	—	2	1	no	—
403	C₂×C₂²⋊C₄	—	2	1	no	—
404	C₂×C₂²⋊C₄	—	2	1	no	—
405	C₂×C₂²⋊C₄	—	2	1	no	—
406	C₂×C₂²⋊C₄	—	2	2	no	—
407	C₂×C₂²⋊C₄	—	2	2	no	—
408	C₂×C₂²⋊C₄	D₄×C₁₀₁	1	1	yes	characteristic
409	C₂×C₂²⋊C₄	D₄×C₁₀₁	1	1	yes	characteristic
410	C₂×C₄²	—	2	1	no	—
411	C₂×C₄²	—	2	1	no	—
412	C₂×C₄²	C₂³×C₁₀₁	1	1	yes	characteristic
413	#107	—	2	4	no	—
414	C₄⋊C₈	—	2	2	no	—
415	#103	—	2	4	no	—
416	#103	—	2	4	no	—
417	#103	—	2	4	no	—
418	#103	—	4	2	no	—
419	#102	—	2	4	no	—
420	#102	—	4	2	no	—
421	C₂²⋊C₈	—	4	2	no	—
422	C₂²⋊C₈	—	4	2	no	—
423	#97	—	2	2	no	—
424	#95	—	2	1	no	—
425	#95	—	2	2	no	—
426	#95	—	2	2	no	—
427	C₂⁴	—	2	1	no	—
428	C₂⁴	C₂×D₄×C₁₀₁	1	1	yes	characteristic
429	C₂⁴	C₂×D₄×C₁₀₁	1	1	yes	characteristic
430	#41	—	4	8	no	—
431	#41	—	4	4	no	—
432	#41	—	4	4	no	—
433	C₂×Q₈	—	2	4	no	—
434	C₂×Q₈	—	2	1	no	—
435	C₂×Q₈	—	2	1	no	—
436	C₂×Q₈	—	2	2	no	—
437	C₂×Q₈	—	2	2	no	—
438	C₂×Q₈	—	2	2	no	—
439	C₂×Q₈	—	4	4	no	—
440	C₂×Q₈	—	4	2	no	—
441	C₂×Q₈	—	4	2	no	—
442	C₂×Q₈	—	4	8	no	—
443	C₂×Q₈	—	4	4	no	—
444	C₂×Q₈	—	4	4	no	—
445	C₂×Q₈	—	4	2	no	—
446	C₂×Q₈	C₂×D₄×C₁₀₁	1	2	yes	—
447	C₂×Q₈	C₂×D₄×C₁₀₁	1	2	yes	—
448	C₂×Q₈	#41×C₁₀₁	1	4	yes	—
449	C₂×D₄	—	2	4	no	—
450	C₂×D₄	—	2	4	no	—
451	C₂×D₄	—	2	2	no	—
452	C₂×D₄	—	2	2	no	—
453	C₂×D₄	—	2	1	no	—
454	C₂×D₄	—	2	2	no	—
455	C₂×D₄	—	2	2	no	—
456	C₂×D₄	—	4	1	no	—
457	C₂×D₄	—	4	4	no	—
458	C₂×D₄	—	4	2	no	—
459	C₂×D₄	—	4	2	no	—
460	C₂×D₄	C₂×D₄×C₁₀₁	1	2	yes	—
461	C₂²×C₄	—	2	1	no	—
462	C₂²×C₄	—	2	4	no	—
463	C₂²×C₄	—	2	4	no	—
464	C₂²×C₄	—	2	1	no	—
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	—	2	1	no	—
468	C₂²×C₄	—	2	1	no	—
469	C₂²×C₄	—	2	1	no	—
470	C₂²×C₄	—	2	2	no	—
471	C₂²×C₄	—	2	2	no	—
472	C₂²×C₄	—	2	2	no	—
473	C₂²×C₄	—	2	2	no	—
474	C₂²×C₄	—	2	2	no	—
475	C₂²×C₄	—	2	2	no	—
476	C₂²×C₄	—	4	4	no	—
477	C₂²×C₄	—	4	4	no	—
478	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
479	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
480	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
481	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
482	C₂²×C₄	C₂⁴×C₁₀₁	1	1	yes	characteristic
483	C₂×C₈	—	2	2	no	—
484	C₂×C₈	—	2	2	no	—
485	C₂×C₈	—	2	2	no	—
486	C₂×C₈	—	2	2	no	—
487	C₂×C₈	—	2	2	no	—
488	C₂×C₈	—	2	2	no	—
489	C₄⋊C₄	—	2	4	no	—
490	C₄⋊C₄	—	2	4	no	—
491	C₄⋊C₄	—	2	2	no	—
492	C₄⋊C₄	—	2	1	no	—
493	C₄⋊C₄	—	2	2	no	—
494	C₄⋊C₄	—	2	2	no	—
495	C₄⋊C₄	—	2	2	no	—
496	C₄⋊C₄	—	2	2	no	—
497	C₄⋊C₄	—	4	2	no	—
498	C₄⋊C₄	C₂×D₄×C₁₀₁	1	2	yes	—
499	C₂²⋊C₄	—	2	4	no	—
500	C₂²⋊C₄	—	2	4	no	—
501	C₂²⋊C₄	—	2	4	no	—
502	C₂²⋊C₄	—	2	4	no	—
503	C₂²⋊C₄	—	2	2	no	—
504	C₂²⋊C₄	—	2	2	no	—
505	C₂²⋊C₄	—	4	4	no	—
506	C₂²⋊C₄	—	4	4	no	—
507	C₄²	—	2	4	no	—
508	C₄²	—	4	2	no	—
509	C₄²	C₂×D₄×C₁₀₁	1	2	yes	—
510	C₄²	C₂×D₄×C₁₀₁	1	2	yes	—
511	C₂³	—	2	1	no	—
512	C₂³	—	2	2	no	—
513	C₂³	—	2	1	no	—
514	C₂³	—	2	2	no	—
515	C₂³	—	2	1	no	—
516	C₂³	—	2	2	no	—
517	C₂³	—	2	2	no	—
518	C₂³	—	2	1	no	—
519	C₂³	—	2	1	no	—
520	C₂³	—	2	2	no	—
521	C₂³	—	4	2	no	—
522	C₂³	—	4	1	no	—
523	C₂³	—	4	1	no	—
524	C₂³	—	4	2	no	—
525	C₂³	AGL(1,ℤ/8)×C₁₀₁	1	2	yes	—
526	C₂³	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
527	Q₈	—	2	2	no	—
528	Q₈	—	2	4	no	—
529	Q₈	—	2	4	no	—
530	Q₈	—	4	8	no	—
531	Q₈	—	4	1	no	—
532	Q₈	—	4	1	no	—
533	Q₈	—	8	4	no	—
534	Q₈	#124×C₁₀₁	1	4	yes	complemented
535	D₄	—	2	4	no	—
536	D₄	—	4	4	no	—
537	D₄	—	4	8	no	—
538	D₄	—	4	8	no	—
539	D₄	—	4	1	no	—
540	D₄	—	4	1	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	2	4	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	2	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	2	2	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	4	8	no	—
553	C₂×C₄	—	4	8	no	—
554	C₂×C₄	—	4	2	no	—
555	C₂×C₄	—	4	1	no	—
556	C₂×C₄	—	4	1	no	—
557	C₂×C₄	—	4	1	no	—
558	C₂×C₄	—	4	1	no	—
559	C₂×C₄	—	4	1	no	—
560	C₂×C₄	—	4	1	no	—
561	C₂×C₄	—	4	2	no	—
562	C₂×C₄	—	4	2	no	—
563	C₂×C₄	—	4	2	no	—
564	C₂×C₄	—	4	2	no	—
565	C₂×C₄	—	4	2	no	—
566	C₂×C₄	—	4	2	no	—
567	C₂×C₄	—	4	2	no	—
568	C₂×C₄	—	4	2	no	—
569	C₂×C₄	#120×C₁₀₁	1	2	yes	—
570	C₂×C₄	#120×C₁₀₁	1	2	yes	—
571	C₂×C₄	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
572	C₂×C₄	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
573	C₂×C₄	C₂×#41×C₁₀₁	1	2	yes	—
574	C₂×C₄	H(5,𝔽₂)×C₁₀₁	1	2	yes	—
575	C₈	—	4	2	no	—
576	C₈	—	4	2	no	—
577	C₂²	—	2	2	no	—
578	C₂²	—	2	4	no	—
579	C₂²	—	4	1	no	—
580	C₂²	—	4	1	no	—
581	C₂²	—	4	2	no	—
582	C₂²	—	4	2	no	—
583	C₂²	—	4	1	no	—
584	C₂²	—	4	1	no	—
585	C₂²	—	4	2	no	—
586	C₂²	—	4	1	no	—
587	C₂²	—	4	2	no	—
588	C₂²	—	4	2	no	—
589	C₂²	—	4	2	no	—
590	C₂²	—	8	2	no	—
591	C₂²	—	8	2	no	—
592	C₂²	C₂×#120×C₁₀₁	1	1	yes	characteristic
593	C₂²	#546×C₁₀₁	1	2	yes	—
594	C₂²	C₂×AGL(1,ℤ/8)×C₁₀₁	1	1	yes	characteristic
595	C₂²	#575×C₁₀₁	1	1	yes	characteristic
596	C₂²	#578×C₁₀₁	1	2	yes	—
597	C₄	—	2	4	no	—
598	C₄	—	2	2	no	—
599	C₄	—	2	2	no	—
600	C₄	—	4	1	no	—
601	C₄	—	4	1	no	—
602	C₄	—	4	2	no	—
603	C₄	—	4	2	no	—
604	C₄	—	8	2	no	—
605	C₄	—	8	2	no	—
606	C₄	C₂×#124×C₁₀₁	1	1	yes	characteristic
607	C₄	#535×C₁₀₁	1	1	yes	characteristic
608	C₄	#546×C₁₀₁	1	2	yes	—
609	C₂	—	4	2	no	—
610	C₂	—	8	1	no	—
611	C₂	—	8	2	no	—
612	C₂	C₁₀₁×#2435	1	1	yes	characteristic
613	C₂	C₁₀₁×#3006	1	1	yes	characteristic
614	C₂	C₁₀₁×#3011	1	1	yes	characteristic
615	C₂	C₁₀₁×#3308	1	2	yes	—
616	C₂	C₁₀₁×#3313	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₀₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₀₁
prime radical	C₂×#548×C₁₀₁	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₀₁ ◁ C₂×C₄×D₄×C₁₀₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#489×C₁₀₁	C₂	semidirect
3. C₂×#477×C₁₀₁	C₂	semidirect
4. C₁₀₁×#2547	C₂	semidirect
5. C₁₀₁×#2036	C₂	semidirect
6. C₁₀₁×#2033	C₂	semidirect
7. C₁₀₁×#1983	C₂	semidirect
8. C₁₀₁×#1955	C₂	semidirect
9. C₁₀₁×#1788	C₂	semidirect
10. C₁₀₁×#1787	C₂	semidirect
11. C₁₀₁×#1763	C₂	semidirect
225. Q₈×C₁₀₁	#124	semidirect
300. #25896	C₁₀₁	direct (N × H)
310. C₂×#489	C₂×C₁₀₁	semidirect
311. C₂×#477	C₂×C₁₀₁	semidirect
312. #2547	C₂×C₁₀₁	semidirect
313. #2036	C₂×C₁₀₁	semidirect
314. #2033	C₂×C₁₀₁	semidirect
315. #1983	C₂×C₁₀₁	semidirect
316. #1955	C₂×C₁₀₁	semidirect
317. #1788	C₂×C₁₀₁	semidirect
318. #1787	C₂×C₁₀₁	semidirect
319. #1763	C₂×C₁₀₁	semidirect
320. C₁₀₁	#25896	direct (N × H)
534. Q₈	#124×C₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#548×C₁₀₁	2
C₂×#489×C₁₀₁	2
C₂×#477×C₁₀₁	2
C₁₀₁×#2547	2
C₁₀₁×#2036	2
C₁₀₁×#2033	2
C₁₀₁×#1983	2
C₁₀₁×#1955	2
C₁₀₁×#1788	2
C₁₀₁×#1787	2
C₁₀₁×#1763	2
#25896	101

Subgroups — C101×#25896 #38808047

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#25896 #38808047