Subgroups — C₁₀₁×#9468 #38791619

Order 25856.

934 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₀₁×#2972	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₀₁×#2408	C₂	1	1	yes	maximal, characteristic
3	C₁₀₁×#1799	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₀₁×#1786	C₂	1	2	yes	maximal, complemented
5	C₁₀₁×#1289	C₂	1	2	yes	maximal, complemented
6	C₂³×D₄×C₁₀₁	C₂²	1	1	yes	characteristic
7	C₂×#121×C₁₀₁	—	2	1	no	—
8	C₂×#120×C₁₀₁	—	2	1	no	—
9	C₂×C₄×D₄×C₁₀₁	C₂²	1	1	yes	characteristic
10	C₈×D₄×C₁₀₁	—	2	4	no	—
11	#431×C₁₀₁	—	2	1	no	—
12	C₂×#102×C₁₀₁	—	2	4	no	—
13	C₂×#99×C₁₀₁	—	2	1	no	—
14	C₂×C₂²⋊C₈×C₁₀₁	—	2	1	no	—
15	C₂×C₂²⋊C₈×C₁₀₁	C₂²	1	2	yes	—
16	#394×C₁₀₁	C₄	1	2	yes	complemented
17	#392×C₁₀₁	C₄	1	2	yes	complemented
18	#390×C₁₀₁	—	2	1	no	—
19	#380×C₁₀₁	C₂²	1	2	yes	—
20	#380×C₁₀₁	C₂²	1	1	yes	characteristic
21	#379×C₁₀₁	—	2	1	no	—
22	#342×C₁₀₁	—	2	1	no	—
23	C₂⁵×C₁₀₁	—	2	1	no	—
24	C₂²×D₄×C₁₀₁	—	2	2	no	—
25	C₂²×D₄×C₁₀₁	—	2	2	no	—
26	C₂²×D₄×C₁₀₁	—	2	1	no	—
27	C₂²×D₄×C₁₀₁	—	2	2	no	—
28	C₂²×D₄×C₁₀₁	—	4	4	no	—
29	C₂²×D₄×C₁₀₁	C₂×C₄	1	2	yes	—
30	C₂²×D₄×C₁₀₁	D₄	1	1	yes	characteristic
31	C₂³×C₄×C₁₀₁	D₄	1	1	yes	characteristic
32	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
33	C₂²×C₈×C₁₀₁	—	2	2	no	—
34	C₂²×C₈×C₁₀₁	D₄	1	4	yes	complemented
35	#121×C₁₀₁	—	4	4	no	—
36	#120×C₁₀₁	—	4	2	no	—
37	#120×C₁₀₁	—	4	2	no	—
38	C₄×D₄×C₁₀₁	—	2	2	no	—
39	C₄×D₄×C₁₀₁	—	2	2	no	—
40	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
41	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
42	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
43	C₂×C₂²⋊C₄×C₁₀₁	—	2	1	no	—
44	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
45	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
46	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
47	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
48	C₂×C₂²⋊C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
49	C₂×C₂²⋊C₄×C₁₀₁	D₄	1	1	yes	characteristic
50	C₂×C₄²×C₁₀₁	D₄	1	1	yes	characteristic
51	C₄⋊C₈×C₁₀₁	—	2	2	no	—
52	#102×C₁₀₁	—	4	8	no	—
53	#99×C₁₀₁	—	4	2	no	—
54	C₂²⋊C₈×C₁₀₁	—	2	2	no	—
55	C₂²⋊C₈×C₁₀₁	—	2	2	no	—
56	C₂²⋊C₈×C₁₀₁	—	2	2	no	—
57	C₄×C₈×C₁₀₁	—	2	2	no	—
58	#95×C₁₀₁	—	2	2	no	—
59	#95×C₁₀₁	C₂×C₄	1	2	yes	—
60	C₂⁴×C₁₀₁	—	2	2	no	—
61	C₂⁴×C₁₀₁	—	4	4	no	—
62	C₂⁴×C₁₀₁	—	4	2	no	—
63	C₂⁴×C₁₀₁	—	4	1	no	—
64	C₂⁴×C₁₀₁	—	4	1	no	—
65	C₂⁴×C₁₀₁	—	4	2	no	—
66	C₂⁴×C₁₀₁	—	8	2	no	—
67	C₂⁴×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
68	C₂⁴×C₁₀₁	C₂×D₄	1	1	yes	characteristic
69	C₂×D₄×C₁₀₁	—	2	2	no	—
70	C₂×D₄×C₁₀₁	—	2	2	no	—
71	C₂×D₄×C₁₀₁	—	2	8	no	—
72	C₂×D₄×C₁₀₁	—	2	4	no	—
73	C₂×D₄×C₁₀₁	—	2	4	no	—
74	C₂×D₄×C₁₀₁	—	4	4	no	—
75	C₂×D₄×C₁₀₁	—	4	2	no	—
76	C₂×D₄×C₁₀₁	—	4	4	no	—
77	C₂×D₄×C₁₀₁	—	4	8	no	—
78	C₂×D₄×C₁₀₁	—	4	4	no	—
79	C₂×D₄×C₁₀₁	—	4	4	no	—
80	C₂×D₄×C₁₀₁	—	4	1	no	—
81	C₂×D₄×C₁₀₁	—	4	1	no	—
82	C₂×D₄×C₁₀₁	—	8	2	no	—
83	C₂×D₄×C₁₀₁	D₈	1	2	yes	—
84	C₂×D₄×C₁₀₁	SD₁₆	1	2	yes	—
85	C₂²×C₄×C₁₀₁	—	2	1	no	—
86	C₂²×C₄×C₁₀₁	—	2	1	no	—
87	C₂²×C₄×C₁₀₁	—	2	2	no	—
88	C₂²×C₄×C₁₀₁	—	4	2	no	—
89	C₂²×C₄×C₁₀₁	—	4	2	no	—
90	C₂²×C₄×C₁₀₁	—	4	2	no	—
91	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
96	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₀₁	#41	1	2	yes	—
98	C₂×C₈×C₁₀₁	—	2	4	no	—
99	C₂×C₈×C₁₀₁	—	4	4	no	—
100	C₂×C₈×C₁₀₁	—	8	2	no	—
101	C₄⋊C₄×C₁₀₁	—	2	2	no	—
102	C₄⋊C₄×C₁₀₁	—	4	2	no	—
103	C₄⋊C₄×C₁₀₁	—	4	4	no	—
104	C₂²⋊C₄×C₁₀₁	—	2	2	no	—
105	C₂²⋊C₄×C₁₀₁	—	2	2	no	—
106	C₂²⋊C₄×C₁₀₁	—	4	4	no	—
107	C₂²⋊C₄×C₁₀₁	—	4	1	no	—
108	C₂²⋊C₄×C₁₀₁	—	4	1	no	—
109	C₂²⋊C₄×C₁₀₁	—	4	4	no	—
110	C₂²⋊C₄×C₁₀₁	—	4	2	no	—
111	C₂²⋊C₄×C₁₀₁	—	4	2	no	—
112	C₂²⋊C₄×C₁₀₁	—	8	2	no	—
113	C₄²×C₁₀₁	—	2	1	no	—
114	C₄²×C₁₀₁	—	2	1	no	—
115	C₂³×C₁₀₁	—	2	1	no	—
116	C₂³×C₁₀₁	—	2	1	no	—
117	C₂³×C₁₀₁	—	2	4	no	—
118	C₂³×C₁₀₁	—	4	1	no	—
119	C₂³×C₁₀₁	—	4	1	no	—
120	C₂³×C₁₀₁	—	4	1	no	—
121	C₂³×C₁₀₁	—	4	1	no	—
122	C₂³×C₁₀₁	—	4	2	no	—
123	C₂³×C₁₀₁	—	4	8	no	—
124	C₂³×C₁₀₁	—	4	2	no	—
125	C₂³×C₁₀₁	—	4	2	no	—
126	C₂³×C₁₀₁	—	4	2	no	—
127	C₂³×C₁₀₁	—	4	2	no	—
128	C₂³×C₁₀₁	—	4	2	no	—
129	C₂³×C₁₀₁	—	8	4	no	—
130	C₂³×C₁₀₁	—	8	4	no	—
131	C₂³×C₁₀₁	—	8	4	no	—
132	C₂³×C₁₀₁	—	8	8	no	—
133	C₂³×C₁₀₁	—	8	2	no	—
134	C₂³×C₁₀₁	—	8	2	no	—
135	C₂³×C₁₀₁	#102	1	2	yes	complemented
136	C₂³×C₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
137	C₂³×C₁₀₁	#121	1	2	yes	—
138	C₂³×C₁₀₁	C₂×D₈	1	1	yes	characteristic
139	C₂³×C₁₀₁	C₂×SD₁₆	1	1	yes	characteristic
140	C₂³×C₁₀₁	#135	1	2	yes	—
141	D₄×C₁₀₁	—	2	4	no	—
142	D₄×C₁₀₁	—	2	4	no	—
143	D₄×C₁₀₁	—	2	8	no	—
144	D₄×C₁₀₁	—	4	4	no	—
145	D₄×C₁₀₁	—	4	4	no	—
146	D₄×C₁₀₁	—	4	4	no	—
147	D₄×C₁₀₁	—	8	8	no	—
148	C₂×C₄×C₁₀₁	—	2	1	no	—
149	C₂×C₄×C₁₀₁	—	2	1	no	—
150	C₂×C₄×C₁₀₁	—	2	4	no	—
151	C₂×C₄×C₁₀₁	—	2	2	no	—
152	C₂×C₄×C₁₀₁	—	2	1	no	—
153	C₂×C₄×C₁₀₁	—	2	1	no	—
154	C₂×C₄×C₁₀₁	—	4	1	no	—
155	C₂×C₄×C₁₀₁	—	4	2	no	—
156	C₂×C₄×C₁₀₁	—	4	2	no	—
157	C₂×C₄×C₁₀₁	—	4	1	no	—
158	C₂×C₄×C₁₀₁	—	4	1	no	—
159	C₂×C₄×C₁₀₁	—	4	2	no	—
160	C₂×C₄×C₁₀₁	—	4	2	no	—
161	C₂×C₄×C₁₀₁	—	4	2	no	—
162	C₂×C₄×C₁₀₁	—	8	1	no	—
163	C₂×C₄×C₁₀₁	—	8	2	no	—
164	C₂×C₄×C₁₀₁	—	8	2	no	—
165	C₂×C₄×C₁₀₁	—	8	2	no	—
166	C₂×C₄×C₁₀₁	#102	1	2	yes	complemented
167	C₂×C₄×C₁₀₁	C₄×D₄	1	2	yes	—
168	C₂×C₄×C₁₀₁	#120	1	1	yes	characteristic
169	C₂×C₄×C₁₀₁	#123	1	1	yes	characteristic
170	C₈×C₁₀₁	—	4	4	no	—
171	C₂²×C₁₀₁	—	2	1	no	—
172	C₂²×C₁₀₁	—	2	2	no	—
173	C₂²×C₁₀₁	—	2	1	no	—
174	C₂²×C₁₀₁	—	2	2	no	—
175	C₂²×C₁₀₁	—	2	2	no	—
176	C₂²×C₁₀₁	—	4	1	no	—
177	C₂²×C₁₀₁	—	4	1	no	—
178	C₂²×C₁₀₁	—	4	2	no	—
179	C₂²×C₁₀₁	—	4	2	no	—
180	C₂²×C₁₀₁	—	4	4	no	—
181	C₂²×C₁₀₁	—	4	4	no	—
182	C₂²×C₁₀₁	—	4	1	no	—
183	C₂²×C₁₀₁	—	4	1	no	—
184	C₂²×C₁₀₁	—	4	4	no	—
185	C₂²×C₁₀₁	—	8	1	no	—
186	C₂²×C₁₀₁	—	8	2	no	—
187	C₂²×C₁₀₁	—	8	2	no	—
188	C₂²×C₁₀₁	—	8	8	no	—
189	C₂²×C₁₀₁	—	8	8	no	—
190	C₂²×C₁₀₁	—	8	2	no	—
191	C₂²×C₁₀₁	—	8	2	no	—
192	C₂²×C₁₀₁	#386	1	1	yes	characteristic
193	C₂²×C₁₀₁	C₂×#102	1	1	yes	characteristic
194	C₂²×C₁₀₁	#416	1	1	yes	characteristic
195	C₂²×C₁₀₁	#465	1	2	yes	—
196	C₂²×C₁₀₁	#466	1	2	yes	—
197	C₄×C₁₀₁	—	2	1	no	—
198	C₄×C₁₀₁	—	2	2	no	—
199	C₄×C₁₀₁	—	2	2	no	—
200	C₄×C₁₀₁	—	4	1	no	—
201	C₄×C₁₀₁	—	4	1	no	—
202	C₄×C₁₀₁	—	8	2	no	—
203	C₄×C₁₀₁	—	16	2	no	—
204	C₄×C₁₀₁	B(4,𝔽₂)	1	2	yes	—
205	#9468	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
206	C₂×C₁₀₁	—	2	1	no	—
207	C₂×C₁₀₁	—	2	2	no	—
208	C₂×C₁₀₁	—	2	1	no	—
209	C₂×C₁₀₁	—	2	2	no	—
210	C₂×C₁₀₁	—	4	2	no	—
211	C₂×C₁₀₁	—	8	4	no	—
212	C₂×C₁₀₁	#1889	1	1	yes	characteristic
213	C₂×C₁₀₁	#1893	1	1	yes	characteristic
214	C₂×C₁₀₁	#1910	1	1	yes	characteristic
215	#2972	C₂×C₁₀₁	1	1	yes	characteristic, complemented
216	#2408	C₂×C₁₀₁	1	1	yes	characteristic
217	#1799	C₂×C₁₀₁	1	1	yes	characteristic, complemented
218	#1786	C₂×C₁₀₁	1	2	yes	complemented
219	#1289	C₂×C₁₀₁	1	2	yes	complemented
220	C₁₀₁	#9468	1	1	yes	characteristic, direct product factor, Sylow
221	C₂³×D₄	C₂²×C₁₀₁	1	1	yes	characteristic
222	C₂×#121	—	2	1	no	—
223	C₂×#120	—	2	1	no	—
224	C₂×C₄×D₄	C₂²×C₁₀₁	1	1	yes	characteristic
225	C₈×D₄	—	2	4	no	—
226	#431	—	2	1	no	—
227	C₂×#102	—	2	4	no	—
228	C₂×#99	—	2	1	no	—
229	C₂×C₂²⋊C₈	—	2	1	no	—
230	C₂×C₂²⋊C₈	C₂²×C₁₀₁	1	2	yes	—
231	#394	C₄×C₁₀₁	1	2	yes	complemented
232	#392	C₄×C₁₀₁	1	2	yes	complemented
233	#390	—	2	1	no	—
234	#380	C₂²×C₁₀₁	1	2	yes	—
235	#380	C₂²×C₁₀₁	1	1	yes	characteristic
236	#379	—	2	1	no	—
237	#342	—	2	1	no	—
238	C₂⁵	—	2	1	no	—
239	C₂²×D₄	—	2	2	no	—
240	C₂²×D₄	—	2	2	no	—
241	C₂²×D₄	—	2	1	no	—
242	C₂²×D₄	—	2	2	no	—
243	C₂²×D₄	—	4	4	no	—
244	C₂²×D₄	C₂×C₄×C₁₀₁	1	2	yes	—
245	C₂²×D₄	D₄×C₁₀₁	1	1	yes	characteristic
246	C₂³×C₄	D₄×C₁₀₁	1	1	yes	characteristic
247	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
248	C₂²×C₈	—	2	2	no	—
249	C₂²×C₈	D₄×C₁₀₁	1	4	yes	complemented
250	#121	—	4	4	no	—
251	#120	—	4	2	no	—
252	#120	—	4	2	no	—
253	C₄×D₄	—	2	2	no	—
254	C₄×D₄	—	2	2	no	—
255	C₂×C₄⋊C₄	—	2	1	no	—
256	C₂×C₄⋊C₄	—	2	2	no	—
257	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	1	yes	characteristic
258	C₂×C₂²⋊C₄	—	2	1	no	—
259	C₂×C₂²⋊C₄	—	2	2	no	—
260	C₂×C₂²⋊C₄	—	2	2	no	—
261	C₂×C₂²⋊C₄	—	2	2	no	—
262	C₂×C₂²⋊C₄	—	2	2	no	—
263	C₂×C₂²⋊C₄	C₂×C₄×C₁₀₁	1	1	yes	characteristic
264	C₂×C₂²⋊C₄	D₄×C₁₀₁	1	1	yes	characteristic
265	C₂×C₄²	D₄×C₁₀₁	1	1	yes	characteristic
266	C₄⋊C₈	—	2	2	no	—
267	#102	—	4	8	no	—
268	#99	—	4	2	no	—
269	C₂²⋊C₈	—	2	2	no	—
270	C₂²⋊C₈	—	2	2	no	—
271	C₂²⋊C₈	—	2	2	no	—
272	C₄×C₈	—	2	2	no	—
273	#95	—	2	2	no	—
274	#95	C₂×C₄×C₁₀₁	1	2	yes	—
275	C₂⁴	—	2	2	no	—
276	C₂⁴	—	4	4	no	—
277	C₂⁴	—	4	2	no	—
278	C₂⁴	—	4	1	no	—
279	C₂⁴	—	4	1	no	—
280	C₂⁴	—	4	2	no	—
281	C₂⁴	—	8	2	no	—
282	C₂⁴	C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
283	C₂⁴	C₂×D₄×C₁₀₁	1	1	yes	characteristic
284	C₂×D₄	—	2	2	no	—
285	C₂×D₄	—	2	2	no	—
286	C₂×D₄	—	2	8	no	—
287	C₂×D₄	—	2	4	no	—
288	C₂×D₄	—	2	4	no	—
289	C₂×D₄	—	4	4	no	—
290	C₂×D₄	—	4	2	no	—
291	C₂×D₄	—	4	4	no	—
292	C₂×D₄	—	4	8	no	—
293	C₂×D₄	—	4	4	no	—
294	C₂×D₄	—	4	4	no	—
295	C₂×D₄	—	4	1	no	—
296	C₂×D₄	—	4	1	no	—
297	C₂×D₄	—	8	2	no	—
298	C₂×D₄	D₈×C₁₀₁	1	2	yes	—
299	C₂×D₄	SD₁₆×C₁₀₁	1	2	yes	—
300	C₂²×C₄	—	2	1	no	—
301	C₂²×C₄	—	2	1	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	4	2	no	—
304	C₂²×C₄	—	4	2	no	—
305	C₂²×C₄	—	4	2	no	—
306	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
307	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
308	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
309	C₂²×C₄	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
310	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
311	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
312	C₂²×C₄	#41×C₁₀₁	1	2	yes	—
313	C₂×C₈	—	2	4	no	—
314	C₂×C₈	—	4	4	no	—
315	C₂×C₈	—	8	2	no	—
316	C₄⋊C₄	—	2	2	no	—
317	C₄⋊C₄	—	4	2	no	—
318	C₄⋊C₄	—	4	4	no	—
319	C₂²⋊C₄	—	2	2	no	—
320	C₂²⋊C₄	—	2	2	no	—
321	C₂²⋊C₄	—	4	4	no	—
322	C₂²⋊C₄	—	4	1	no	—
323	C₂²⋊C₄	—	4	1	no	—
324	C₂²⋊C₄	—	4	4	no	—
325	C₂²⋊C₄	—	4	2	no	—
326	C₂²⋊C₄	—	4	2	no	—
327	C₂²⋊C₄	—	8	2	no	—
328	C₄²	—	2	1	no	—
329	C₄²	—	2	1	no	—
330	C₂³	—	2	1	no	—
331	C₂³	—	2	1	no	—
332	C₂³	—	2	4	no	—
333	C₂³	—	4	1	no	—
334	C₂³	—	4	1	no	—
335	C₂³	—	4	1	no	—
336	C₂³	—	4	1	no	—
337	C₂³	—	4	2	no	—
338	C₂³	—	4	8	no	—
339	C₂³	—	4	2	no	—
340	C₂³	—	4	2	no	—
341	C₂³	—	4	2	no	—
342	C₂³	—	4	2	no	—
343	C₂³	—	4	2	no	—
344	C₂³	—	8	4	no	—
345	C₂³	—	8	4	no	—
346	C₂³	—	8	4	no	—
347	C₂³	—	8	8	no	—
348	C₂³	—	8	2	no	—
349	C₂³	—	8	2	no	—
350	C₂³	#102×C₁₀₁	1	2	yes	complemented
351	C₂³	C₂×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
352	C₂³	#121×C₁₀₁	1	2	yes	—
353	C₂³	C₂×D₈×C₁₀₁	1	1	yes	characteristic
354	C₂³	C₂×SD₁₆×C₁₀₁	1	1	yes	characteristic
355	C₂³	#135×C₁₀₁	1	2	yes	—
356	D₄	—	2	4	no	—
357	D₄	—	2	4	no	—
358	D₄	—	2	8	no	—
359	D₄	—	4	4	no	—
360	D₄	—	4	4	no	—
361	D₄	—	4	4	no	—
362	D₄	—	8	8	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	4	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	4	1	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	1	no	—
373	C₂×C₄	—	4	1	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	8	1	no	—
378	C₂×C₄	—	8	2	no	—
379	C₂×C₄	—	8	2	no	—
380	C₂×C₄	—	8	2	no	—
381	C₂×C₄	#102×C₁₀₁	1	2	yes	complemented
382	C₂×C₄	C₄×D₄×C₁₀₁	1	2	yes	—
383	C₂×C₄	#120×C₁₀₁	1	1	yes	characteristic
384	C₂×C₄	#123×C₁₀₁	1	1	yes	characteristic
385	C₈	—	4	4	no	—
386	C₂²	—	2	1	no	—
387	C₂²	—	2	2	no	—
388	C₂²	—	2	1	no	—
389	C₂²	—	2	2	no	—
390	C₂²	—	2	2	no	—
391	C₂²	—	4	1	no	—
392	C₂²	—	4	1	no	—
393	C₂²	—	4	2	no	—
394	C₂²	—	4	2	no	—
395	C₂²	—	4	4	no	—
396	C₂²	—	4	4	no	—
397	C₂²	—	4	1	no	—
398	C₂²	—	4	1	no	—
399	C₂²	—	4	4	no	—
400	C₂²	—	8	1	no	—
401	C₂²	—	8	2	no	—
402	C₂²	—	8	2	no	—
403	C₂²	—	8	8	no	—
404	C₂²	—	8	8	no	—
405	C₂²	—	8	2	no	—
406	C₂²	—	8	2	no	—
407	C₂²	#386×C₁₀₁	1	1	yes	characteristic
408	C₂²	C₂×#102×C₁₀₁	1	1	yes	characteristic
409	C₂²	#416×C₁₀₁	1	1	yes	characteristic
410	C₂²	#465×C₁₀₁	1	2	yes	—
411	C₂²	#466×C₁₀₁	1	2	yes	—
412	C₄	—	2	1	no	—
413	C₄	—	2	2	no	—
414	C₄	—	2	2	no	—
415	C₄	—	4	1	no	—
416	C₄	—	4	1	no	—
417	C₄	—	8	2	no	—
418	C₄	—	16	2	no	—
419	C₄	B(4,𝔽₂)×C₁₀₁	1	2	yes	—
420	C₂	—	2	1	no	—
421	C₂	—	2	2	no	—
422	C₂	—	2	1	no	—
423	C₂	—	2	2	no	—
424	C₂	—	4	2	no	—
425	C₂	—	8	4	no	—
426	C₂	C₁₀₁×#1889	1	1	yes	characteristic
427	C₂	C₁₀₁×#1893	1	1	yes	characteristic
428	C₂	C₁₀₁×#1910	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₀₁	#386
commutator	C₂²×C₄	C₂²×C₄×C₁₀₁
Frattini, cosocle	C₂³×C₄	C₂³×C₁₀₁
prime radical	C₁₀₁×#2408	C₂
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. C₁₀₁×#2972	C₂	semidirect
3. C₁₀₁×#1799	C₂	semidirect
4. C₁₀₁×#1786	C₂	semidirect
5. C₁₀₁×#1289	C₂	semidirect
16. #394×C₁₀₁	C₄	semidirect
17. #392×C₁₀₁	C₄	semidirect
34. C₂²×C₈×C₁₀₁	D₄	semidirect
135. C₂³×C₁₀₁	#102	semidirect
166. C₂×C₄×C₁₀₁	#102	semidirect
205. #9468	C₁₀₁	direct (N × H)
215. #2972	C₂×C₁₀₁	semidirect
217. #1799	C₂×C₁₀₁	semidirect
218. #1786	C₂×C₁₀₁	semidirect
219. #1289	C₂×C₁₀₁	semidirect
220. C₁₀₁	#9468	direct (N × H)
231. #394	C₄×C₁₀₁	semidirect
232. #392	C₄×C₁₀₁	semidirect
249. C₂²×C₈	D₄×C₁₀₁	semidirect
350. C₂³	#102×C₁₀₁	semidirect
381. C₂×C₄	#102×C₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₁₀₁×#2972	2
C₁₀₁×#2408	2
C₁₀₁×#1799	2
C₁₀₁×#1786	2
C₁₀₁×#1289	2
#9468	101

Subgroups — C101×#9468 #38791619

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#9468 #38791619