Subgroups — C₁₀₁×#18142 #38800293

Order 25856.

1450 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#537×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₀₁×#3006	C₂	1	2	yes	maximal, complemented
3	C₁₀₁×#2406	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₀₁×#1604	C₂	1	4	yes	maximal, complemented
5	C₁₀₁×#1598	C₂	1	4	yes	maximal, complemented
6	C₁₀₁×#1510	C₂	1	2	yes	maximal, complemented
7	C₁₀₁×#1463	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#41×C₁₀₁	—	2	1	no	—
9	C₂²×#41×C₁₀₁	C₂²	1	1	yes	characteristic
10	C₂×AGL(1,ℤ/8)×C₁₀₁	—	2	2	no	—
11	#537×C₁₀₁	—	2	4	no	—
12	#537×C₁₀₁	—	2	2	no	—
13	#537×C₁₀₁	C₂²	1	4	yes	—
14	C₂×#123×C₁₀₁	—	2	1	no	—
15	C₂×C₂²⋊Q₈×C₁₀₁	—	2	2	no	—
16	C₂×#121×C₁₀₁	—	2	2	no	—
17	C₂×#121×C₁₀₁	—	2	1	no	—
18	C₂×#121×C₁₀₁	C₂²	1	2	yes	—
19	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
20	#449×C₁₀₁	—	2	4	no	—
21	#448×C₁₀₁	C₂²	1	4	yes	complemented
22	#447×C₁₀₁	C₂²	1	4	yes	complemented
23	#417×C₁₀₁	—	2	2	no	—
24	#407×C₁₀₁	C₂²	1	2	yes	—
25	#395×C₁₀₁	C₂²	1	2	yes	complemented
26	#394×C₁₀₁	C₂²	1	2	yes	complemented
27	#386×C₁₀₁	—	2	1	no	—
28	#385×C₁₀₁	—	2	2	no	—
29	#381×C₁₀₁	C₂²	1	1	yes	characteristic
30	#327×C₁₀₁	C₂²	1	8	yes	complemented
31	#324×C₁₀₁	C₂²	1	4	yes	complemented
32	C₂×#41×C₁₀₁	—	2	4	no	—
33	C₂×#41×C₁₀₁	—	2	4	no	—
34	C₂×#41×C₁₀₁	—	2	2	no	—
35	C₂×#41×C₁₀₁	—	2	2	no	—
36	C₂×#41×C₁₀₁	—	4	8	no	—
37	C₂×#41×C₁₀₁	—	4	4	no	—
38	C₂²×Q₈×C₁₀₁	—	2	1	no	—
39	C₂²×Q₈×C₁₀₁	C₂³	1	1	yes	characteristic
40	C₂²×D₄×C₁₀₁	—	2	1	no	—
41	C₂²×D₄×C₁₀₁	—	2	2	no	—
42	C₂²×D₄×C₁₀₁	—	2	1	no	—
43	C₂²×D₄×C₁₀₁	—	2	1	no	—
44	C₂²×D₄×C₁₀₁	D₄	1	2	yes	—
45	C₂²×D₄×C₁₀₁	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₁₀₁	—	2	2	no	—
47	C₂³×C₄×C₁₀₁	—	2	1	no	—
48	C₂³×C₄×C₁₀₁	D₄	1	1	yes	characteristic
49	C₂³×C₄×C₁₀₁	D₄	1	1	yes	characteristic
50	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
51	AGL(1,ℤ/8)×C₁₀₁	—	4	8	no	—
52	C₂×SD₁₆×C₁₀₁	—	2	4	no	—
53	C₂×D₈×C₁₀₁	—	2	4	no	—
54	C₂×M₁₆×C₁₀₁	—	2	2	no	—
55	#123×C₁₀₁	—	4	4	no	—
56	C₂²⋊Q₈×C₁₀₁	—	2	8	no	—
57	C₂²⋊Q₈×C₁₀₁	—	2	8	no	—
58	#121×C₁₀₁	—	2	4	no	—
59	#121×C₁₀₁	—	2	8	no	—
60	#121×C₁₀₁	—	2	8	no	—
61	#121×C₁₀₁	—	2	4	no	—
62	#121×C₁₀₁	—	2	2	no	—
63	#121×C₁₀₁	—	2	2	no	—
64	#121×C₁₀₁	D₄	1	4	yes	—
65	#121×C₁₀₁	C₂³	1	4	yes	—
66	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
67	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
68	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
69	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
70	C₂×C₄⋊C₄×C₁₀₁	D₄	1	2	yes	—
71	C₂×C₄⋊C₄×C₁₀₁	D₄	1	2	yes	—
72	C₂×C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
73	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
74	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
75	C₂×C₂²⋊C₄×C₁₀₁	—	2	1	no	—
76	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
77	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
78	#103×C₁₀₁	—	2	4	no	—
79	#102×C₁₀₁	—	2	4	no	—
80	C₂²⋊C₈×C₁₀₁	—	2	2	no	—
81	C₂²⋊C₈×C₁₀₁	C₂³	1	4	yes	—
82	#95×C₁₀₁	—	2	2	no	—
83	#95×C₁₀₁	—	2	1	no	—
84	#95×C₁₀₁	C₂³	1	2	yes	—
85	C₂⁴×C₁₀₁	—	2	2	no	—
86	C₂⁴×C₁₀₁	—	2	1	no	—
87	C₂⁴×C₁₀₁	C₂×D₄	1	1	yes	characteristic
88	#41×C₁₀₁	—	2	8	no	—
89	#41×C₁₀₁	—	4	16	no	—
90	#41×C₁₀₁	—	4	8	no	—
91	#41×C₁₀₁	—	4	4	no	—
92	#41×C₁₀₁	—	4	4	no	—
93	#41×C₁₀₁	—	4	4	no	—
94	#41×C₁₀₁	—	4	8	no	—
95	C₂×Q₈×C₁₀₁	—	2	4	no	—
96	C₂×Q₈×C₁₀₁	—	2	2	no	—
97	C₂×Q₈×C₁₀₁	—	4	2	no	—
98	C₂×Q₈×C₁₀₁	—	4	4	no	—
99	C₂×D₄×C₁₀₁	—	2	4	no	—
100	C₂×D₄×C₁₀₁	—	2	4	no	—
101	C₂×D₄×C₁₀₁	—	2	4	no	—
102	C₂×D₄×C₁₀₁	—	2	4	no	—
103	C₂×D₄×C₁₀₁	—	2	4	no	—
104	C₂×D₄×C₁₀₁	—	2	2	no	—
105	C₂×D₄×C₁₀₁	—	2	2	no	—
106	C₂×D₄×C₁₀₁	—	4	4	no	—
107	C₂×D₄×C₁₀₁	—	4	4	no	—
108	C₂×D₄×C₁₀₁	—	4	2	no	—
109	C₂×D₄×C₁₀₁	—	4	8	no	—
110	C₂×D₄×C₁₀₁	—	4	2	no	—
111	C₂×D₄×C₁₀₁	—	4	1	no	—
112	C₂×D₄×C₁₀₁	—	4	1	no	—
113	C₂×D₄×C₁₀₁	—	8	2	no	—
114	C₂×D₄×C₁₀₁	C₂×D₄	1	4	yes	—
115	C₂²×C₄×C₁₀₁	—	2	1	no	—
116	C₂²×C₄×C₁₀₁	—	2	1	no	—
117	C₂²×C₄×C₁₀₁	—	2	4	no	—
118	C₂²×C₄×C₁₀₁	—	2	8	no	—
119	C₂²×C₄×C₁₀₁	—	2	1	no	—
120	C₂²×C₄×C₁₀₁	—	2	2	no	—
121	C₂²×C₄×C₁₀₁	—	2	1	no	—
122	C₂²×C₄×C₁₀₁	—	2	1	no	—
123	C₂²×C₄×C₁₀₁	—	2	2	no	—
124	C₂²×C₄×C₁₀₁	—	4	2	no	—
125	C₂²×C₄×C₁₀₁	—	4	8	no	—
126	C₂²×C₄×C₁₀₁	—	4	2	no	—
127	C₂²×C₄×C₁₀₁	—	4	2	no	—
128	C₂²×C₄×C₁₀₁	—	4	2	no	—
129	C₂²×C₄×C₁₀₁	—	4	2	no	—
130	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
131	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
132	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
133	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
135	C₂²×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
136	SD₁₆×C₁₀₁	—	4	8	no	—
137	D₈×C₁₀₁	—	4	8	no	—
138	M₁₆×C₁₀₁	—	4	4	no	—
139	C₂×C₈×C₁₀₁	—	2	4	no	—
140	C₄⋊C₄×C₁₀₁	—	2	4	no	—
141	C₄⋊C₄×C₁₀₁	—	2	4	no	—
142	C₄⋊C₄×C₁₀₁	—	2	2	no	—
143	C₄⋊C₄×C₁₀₁	—	2	4	no	—
144	C₄⋊C₄×C₁₀₁	—	4	4	no	—
145	C₄⋊C₄×C₁₀₁	C₂×D₄	1	4	yes	—
146	C₂²⋊C₄×C₁₀₁	—	2	8	no	—
147	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
148	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
149	C₂²⋊C₄×C₁₀₁	—	4	4	no	—
150	C₂²⋊C₄×C₁₀₁	—	4	2	no	—
151	C₂²⋊C₄×C₁₀₁	—	4	4	no	—
152	C₂³×C₁₀₁	—	2	2	no	—
153	C₂³×C₁₀₁	—	2	2	no	—
154	C₂³×C₁₀₁	—	2	2	no	—
155	C₂³×C₁₀₁	—	2	4	no	—
156	C₂³×C₁₀₁	—	4	1	no	—
157	C₂³×C₁₀₁	—	4	4	no	—
158	C₂³×C₁₀₁	—	4	1	no	—
159	C₂³×C₁₀₁	—	4	2	no	—
160	C₂³×C₁₀₁	—	4	4	no	—
161	C₂³×C₁₀₁	—	4	1	no	—
162	C₂³×C₁₀₁	—	4	2	no	—
163	C₂³×C₁₀₁	—	4	4	no	—
164	C₂³×C₁₀₁	#120	1	1	yes	characteristic
165	C₂³×C₁₀₁	#120	1	1	yes	characteristic
166	C₂³×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
167	Q₈×C₁₀₁	—	2	4	no	—
168	Q₈×C₁₀₁	—	4	8	no	—
169	Q₈×C₁₀₁	—	4	2	no	—
170	D₄×C₁₀₁	—	2	4	no	—
171	D₄×C₁₀₁	—	4	4	no	—
172	D₄×C₁₀₁	—	4	8	no	—
173	D₄×C₁₀₁	—	4	2	no	—
174	D₄×C₁₀₁	—	4	8	no	—
175	D₄×C₁₀₁	—	4	4	no	—
176	D₄×C₁₀₁	—	4	8	no	—
177	D₄×C₁₀₁	—	4	4	no	—
178	D₄×C₁₀₁	—	8	2	no	—
179	D₄×C₁₀₁	—	8	4	no	—
180	C₂×C₄×C₁₀₁	—	2	4	no	—
181	C₂×C₄×C₁₀₁	—	2	4	no	—
182	C₂×C₄×C₁₀₁	—	2	2	no	—
183	C₂×C₄×C₁₀₁	—	2	2	no	—
184	C₂×C₄×C₁₀₁	—	2	4	no	—
185	C₂×C₄×C₁₀₁	—	2	2	no	—
186	C₂×C₄×C₁₀₁	—	2	2	no	—
187	C₂×C₄×C₁₀₁	—	2	4	no	—
188	C₂×C₄×C₁₀₁	—	4	1	no	—
189	C₂×C₄×C₁₀₁	—	4	2	no	—
190	C₂×C₄×C₁₀₁	—	4	1	no	—
191	C₂×C₄×C₁₀₁	—	4	16	no	—
192	C₂×C₄×C₁₀₁	—	4	8	no	—
193	C₂×C₄×C₁₀₁	—	4	4	no	—
194	C₂×C₄×C₁₀₁	—	4	1	no	—
195	C₂×C₄×C₁₀₁	—	4	1	no	—
196	C₂×C₄×C₁₀₁	—	4	2	no	—
197	C₂×C₄×C₁₀₁	—	4	2	no	—
198	C₂×C₄×C₁₀₁	—	4	2	no	—
199	C₂×C₄×C₁₀₁	—	4	2	no	—
200	C₂×C₄×C₁₀₁	—	4	2	no	—
201	C₂×C₄×C₁₀₁	—	8	1	no	—
202	C₂×C₄×C₁₀₁	#120	1	2	yes	—
203	C₂×C₄×C₁₀₁	AGL(1,ℤ/8)	1	4	yes	complemented
204	C₂×C₄×C₁₀₁	C₂²×D₄	1	2	yes	—
205	C₈×C₁₀₁	—	4	4	no	—
206	C₂²×C₁₀₁	—	2	1	no	—
207	C₂²×C₁₀₁	—	2	1	no	—
208	C₂²×C₁₀₁	—	2	1	no	—
209	C₂²×C₁₀₁	—	2	1	no	—
210	C₂²×C₁₀₁	—	2	1	no	—
211	C₂²×C₁₀₁	—	2	1	no	—
212	C₂²×C₁₀₁	—	2	1	no	—
213	C₂²×C₁₀₁	—	4	4	no	—
214	C₂²×C₁₀₁	—	4	4	no	—
215	C₂²×C₁₀₁	—	4	4	no	—
216	C₂²×C₁₀₁	—	4	4	no	—
217	C₂²×C₁₀₁	—	4	2	no	—
218	C₂²×C₁₀₁	—	4	4	no	—
219	C₂²×C₁₀₁	—	8	2	no	—
220	C₂²×C₁₀₁	—	8	8	no	—
221	C₂²×C₁₀₁	—	8	1	no	—
222	C₂²×C₁₀₁	—	8	1	no	—
223	C₂²×C₁₀₁	B(4,𝔽₂)	1	2	yes	—
224	C₂²×C₁₀₁	C₂×#120	1	1	yes	characteristic
225	C₂²×C₁₀₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
226	C₄×C₁₀₁	—	2	4	no	—
227	C₄×C₁₀₁	—	2	2	no	—
228	C₄×C₁₀₁	—	2	2	no	—
229	C₄×C₁₀₁	—	4	4	no	—
230	C₄×C₁₀₁	—	4	2	no	—
231	C₄×C₁₀₁	—	4	2	no	—
232	C₄×C₁₀₁	—	8	2	no	—
233	#18142	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
234	C₂×C₁₀₁	—	2	2	no	—
235	C₂×C₁₀₁	—	2	2	no	—
236	C₂×C₁₀₁	—	4	1	no	—
237	C₂×C₁₀₁	—	8	2	no	—
238	C₂×C₁₀₁	—	8	4	no	—
239	C₂×C₁₀₁	#3003	1	1	yes	characteristic
240	C₂×C₁₀₁	#3020	1	1	yes	characteristic
241	C₂×C₁₀₁	C₂×B(4,𝔽₂)	1	1	yes	characteristic
242	C₂×#537	C₂×C₁₀₁	1	1	yes	characteristic, complemented
243	#3006	C₂×C₁₀₁	1	2	yes	complemented
244	#2406	C₂×C₁₀₁	1	1	yes	characteristic, complemented
245	#1604	C₂×C₁₀₁	1	4	yes	complemented
246	#1598	C₂×C₁₀₁	1	4	yes	complemented
247	#1510	C₂×C₁₀₁	1	2	yes	complemented
248	#1463	C₂×C₁₀₁	1	1	yes	characteristic, complemented
249	C₁₀₁	#18142	1	1	yes	characteristic, direct product factor, Sylow
250	C₂²×#41	—	2	1	no	—
251	C₂²×#41	C₂²×C₁₀₁	1	1	yes	characteristic
252	C₂×AGL(1,ℤ/8)	—	2	2	no	—
253	#537	—	2	4	no	—
254	#537	—	2	2	no	—
255	#537	C₂²×C₁₀₁	1	4	yes	—
256	C₂×#123	—	2	1	no	—
257	C₂×C₂²⋊Q₈	—	2	2	no	—
258	C₂×#121	—	2	2	no	—
259	C₂×#121	—	2	1	no	—
260	C₂×#121	C₂²×C₁₀₁	1	2	yes	—
261	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
262	#449	—	2	4	no	—
263	#448	C₂²×C₁₀₁	1	4	yes	complemented
264	#447	C₂²×C₁₀₁	1	4	yes	complemented
265	#417	—	2	2	no	—
266	#407	C₂²×C₁₀₁	1	2	yes	—
267	#395	C₂²×C₁₀₁	1	2	yes	complemented
268	#394	C₂²×C₁₀₁	1	2	yes	complemented
269	#386	—	2	1	no	—
270	#385	—	2	2	no	—
271	#381	C₂²×C₁₀₁	1	1	yes	characteristic
272	#327	C₂²×C₁₀₁	1	8	yes	complemented
273	#324	C₂²×C₁₀₁	1	4	yes	complemented
274	C₂×#41	—	2	4	no	—
275	C₂×#41	—	2	4	no	—
276	C₂×#41	—	2	2	no	—
277	C₂×#41	—	2	2	no	—
278	C₂×#41	—	4	8	no	—
279	C₂×#41	—	4	4	no	—
280	C₂²×Q₈	—	2	1	no	—
281	C₂²×Q₈	C₂³×C₁₀₁	1	1	yes	characteristic
282	C₂²×D₄	—	2	1	no	—
283	C₂²×D₄	—	2	2	no	—
284	C₂²×D₄	—	2	1	no	—
285	C₂²×D₄	—	2	1	no	—
286	C₂²×D₄	D₄×C₁₀₁	1	2	yes	—
287	C₂²×D₄	C₂³×C₁₀₁	1	1	yes	characteristic
288	C₂³×C₄	—	2	2	no	—
289	C₂³×C₄	—	2	1	no	—
290	C₂³×C₄	D₄×C₁₀₁	1	1	yes	characteristic
291	C₂³×C₄	D₄×C₁₀₁	1	1	yes	characteristic
292	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
293	AGL(1,ℤ/8)	—	4	8	no	—
294	C₂×SD₁₆	—	2	4	no	—
295	C₂×D₈	—	2	4	no	—
296	C₂×M₁₆	—	2	2	no	—
297	#123	—	4	4	no	—
298	C₂²⋊Q₈	—	2	8	no	—
299	C₂²⋊Q₈	—	2	8	no	—
300	#121	—	2	4	no	—
301	#121	—	2	8	no	—
302	#121	—	2	8	no	—
303	#121	—	2	4	no	—
304	#121	—	2	2	no	—
305	#121	—	2	2	no	—
306	#121	D₄×C₁₀₁	1	4	yes	—
307	#121	C₂³×C₁₀₁	1	4	yes	—
308	C₂×C₄⋊C₄	—	2	1	no	—
309	C₂×C₄⋊C₄	—	2	2	no	—
310	C₂×C₄⋊C₄	—	2	2	no	—
311	C₂×C₄⋊C₄	—	2	2	no	—
312	C₂×C₄⋊C₄	D₄×C₁₀₁	1	2	yes	—
313	C₂×C₄⋊C₄	D₄×C₁₀₁	1	2	yes	—
314	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	2	yes	—
315	C₂×C₂²⋊C₄	—	2	2	no	—
316	C₂×C₂²⋊C₄	—	2	2	no	—
317	C₂×C₂²⋊C₄	—	2	1	no	—
318	C₂×C₂²⋊C₄	—	2	2	no	—
319	C₂×C₂²⋊C₄	—	2	2	no	—
320	#103	—	2	4	no	—
321	#102	—	2	4	no	—
322	C₂²⋊C₈	—	2	2	no	—
323	C₂²⋊C₈	C₂³×C₁₀₁	1	4	yes	—
324	#95	—	2	1	no	—
325	#95	—	2	2	no	—
326	#95	C₂³×C₁₀₁	1	2	yes	—
327	C₂⁴	—	2	2	no	—
328	C₂⁴	—	2	1	no	—
329	C₂⁴	C₂×D₄×C₁₀₁	1	1	yes	characteristic
330	#41	—	2	8	no	—
331	#41	—	4	16	no	—
332	#41	—	4	4	no	—
333	#41	—	4	8	no	—
334	#41	—	4	4	no	—
335	#41	—	4	4	no	—
336	#41	—	4	8	no	—
337	C₂×Q₈	—	2	4	no	—
338	C₂×Q₈	—	2	2	no	—
339	C₂×Q₈	—	4	2	no	—
340	C₂×Q₈	—	4	4	no	—
341	C₂×D₄	—	2	4	no	—
342	C₂×D₄	—	2	4	no	—
343	C₂×D₄	—	2	4	no	—
344	C₂×D₄	—	2	4	no	—
345	C₂×D₄	—	2	4	no	—
346	C₂×D₄	—	2	2	no	—
347	C₂×D₄	—	2	2	no	—
348	C₂×D₄	—	4	4	no	—
349	C₂×D₄	—	4	4	no	—
350	C₂×D₄	—	4	2	no	—
351	C₂×D₄	—	4	2	no	—
352	C₂×D₄	—	4	8	no	—
353	C₂×D₄	—	4	1	no	—
354	C₂×D₄	—	4	1	no	—
355	C₂×D₄	—	8	2	no	—
356	C₂×D₄	C₂×D₄×C₁₀₁	1	4	yes	—
357	C₂²×C₄	—	2	1	no	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	—	2	4	no	—
360	C₂²×C₄	—	2	8	no	—
361	C₂²×C₄	—	2	1	no	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	2	1	no	—
364	C₂²×C₄	—	2	1	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	4	2	no	—
367	C₂²×C₄	—	4	8	no	—
368	C₂²×C₄	—	4	2	no	—
369	C₂²×C₄	—	4	2	no	—
370	C₂²×C₄	—	4	2	no	—
371	C₂²×C₄	—	4	2	no	—
372	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
373	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
374	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
375	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
376	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
377	C₂²×C₄	C₂⁴×C₁₀₁	1	1	yes	characteristic
378	SD₁₆	—	4	8	no	—
379	D₈	—	4	8	no	—
380	M₁₆	—	4	4	no	—
381	C₂×C₈	—	2	4	no	—
382	C₄⋊C₄	—	2	4	no	—
383	C₄⋊C₄	—	2	4	no	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	2	4	no	—
386	C₄⋊C₄	—	4	4	no	—
387	C₄⋊C₄	C₂×D₄×C₁₀₁	1	4	yes	—
388	C₂²⋊C₄	—	2	8	no	—
389	C₂²⋊C₄	—	2	4	no	—
390	C₂²⋊C₄	—	2	4	no	—
391	C₂²⋊C₄	—	4	4	no	—
392	C₂²⋊C₄	—	4	2	no	—
393	C₂²⋊C₄	—	4	4	no	—
394	C₂³	—	2	2	no	—
395	C₂³	—	2	2	no	—
396	C₂³	—	2	2	no	—
397	C₂³	—	2	4	no	—
398	C₂³	—	4	1	no	—
399	C₂³	—	4	4	no	—
400	C₂³	—	4	1	no	—
401	C₂³	—	4	2	no	—
402	C₂³	—	4	4	no	—
403	C₂³	—	4	4	no	—
404	C₂³	—	4	1	no	—
405	C₂³	—	4	2	no	—
406	C₂³	#120×C₁₀₁	1	1	yes	characteristic
407	C₂³	#120×C₁₀₁	1	1	yes	characteristic
408	C₂³	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
409	Q₈	—	2	4	no	—
410	Q₈	—	4	8	no	—
411	Q₈	—	4	2	no	—
412	D₄	—	2	4	no	—
413	D₄	—	4	4	no	—
414	D₄	—	4	8	no	—
415	D₄	—	4	2	no	—
416	D₄	—	4	8	no	—
417	D₄	—	4	4	no	—
418	D₄	—	4	4	no	—
419	D₄	—	4	8	no	—
420	D₄	—	8	2	no	—
421	D₄	—	8	4	no	—
422	C₂×C₄	—	2	4	no	—
423	C₂×C₄	—	2	4	no	—
424	C₂×C₄	—	2	4	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	4	no	—
430	C₂×C₄	—	4	1	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	4	16	no	—
434	C₂×C₄	—	4	8	no	—
435	C₂×C₄	—	4	4	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	8	1	no	—
444	C₂×C₄	#120×C₁₀₁	1	2	yes	—
445	C₂×C₄	AGL(1,ℤ/8)×C₁₀₁	1	4	yes	complemented
446	C₂×C₄	C₂²×D₄×C₁₀₁	1	2	yes	—
447	C₈	—	4	4	no	—
448	C₂²	—	2	1	no	—
449	C₂²	—	2	1	no	—
450	C₂²	—	2	1	no	—
451	C₂²	—	2	1	no	—
452	C₂²	—	2	1	no	—
453	C₂²	—	2	1	no	—
454	C₂²	—	2	1	no	—
455	C₂²	—	4	4	no	—
456	C₂²	—	4	4	no	—
457	C₂²	—	4	4	no	—
458	C₂²	—	4	4	no	—
459	C₂²	—	4	2	no	—
460	C₂²	—	4	4	no	—
461	C₂²	—	8	2	no	—
462	C₂²	—	8	8	no	—
463	C₂²	—	8	1	no	—
464	C₂²	—	8	1	no	—
465	C₂²	B(4,𝔽₂)×C₁₀₁	1	2	yes	—
466	C₂²	C₂×#120×C₁₀₁	1	1	yes	characteristic
467	C₂²	C₂×AGL(1,ℤ/8)×C₁₀₁	1	2	yes	—
468	C₄	—	2	4	no	—
469	C₄	—	2	2	no	—
470	C₄	—	2	2	no	—
471	C₄	—	4	4	no	—
472	C₄	—	4	2	no	—
473	C₄	—	4	2	no	—
474	C₄	—	8	2	no	—
475	C₂	—	2	2	no	—
476	C₂	—	2	2	no	—
477	C₂	—	4	1	no	—
478	C₂	—	8	2	no	—
479	C₂	—	8	4	no	—
480	C₂	C₁₀₁×#3003	1	1	yes	characteristic
481	C₂	C₁₀₁×#3020	1	1	yes	characteristic
482	C₂	C₂×B(4,𝔽₂)×C₁₀₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₀₁	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₀₁
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₁ ◁ C₂³×C₄×C₁₀₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#537×C₁₀₁	C₂	semidirect
2. C₁₀₁×#3006	C₂	semidirect
3. C₁₀₁×#2406	C₂	semidirect
4. C₁₀₁×#1604	C₂	semidirect
5. C₁₀₁×#1598	C₂	semidirect
6. C₁₀₁×#1510	C₂	semidirect
7. C₁₀₁×#1463	C₂	semidirect
21. #448×C₁₀₁	C₂²	semidirect
22. #447×C₁₀₁	C₂²	semidirect
25. #395×C₁₀₁	C₂²	semidirect
26. #394×C₁₀₁	C₂²	semidirect
30. #327×C₁₀₁	C₂²	semidirect
31. #324×C₁₀₁	C₂²	semidirect
203. C₂×C₄×C₁₀₁	AGL(1,ℤ/8)	semidirect
233. #18142	C₁₀₁	direct (N × H)
242. C₂×#537	C₂×C₁₀₁	semidirect
243. #3006	C₂×C₁₀₁	semidirect
244. #2406	C₂×C₁₀₁	semidirect
245. #1604	C₂×C₁₀₁	semidirect
246. #1598	C₂×C₁₀₁	semidirect
247. #1510	C₂×C₁₀₁	semidirect
248. #1463	C₂×C₁₀₁	semidirect
249. C₁₀₁	#18142	direct (N × H)
263. #448	C₂²×C₁₀₁	semidirect
264. #447	C₂²×C₁₀₁	semidirect
267. #395	C₂²×C₁₀₁	semidirect
268. #394	C₂²×C₁₀₁	semidirect
272. #327	C₂²×C₁₀₁	semidirect
273. #324	C₂²×C₁₀₁	semidirect
445. 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
C₂×#537×C₁₀₁	2
C₁₀₁×#3006	2
C₁₀₁×#2406	2
C₁₀₁×#1604	2
C₁₀₁×#1598	2
C₁₀₁×#1510	2
C₁₀₁×#1463	2
#18142	101

Subgroups — C101×#18142 #38800293

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#18142 #38800293