Subgroups — C₁₀₁×#23429 #38805580

Order 25856.

2066 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#137×C₁₀₁	C₂	1	2	yes	maximal, complemented
2	C₂×#532×C₁₀₁	C₂	1	1	yes	maximal, characteristic
3	C₂×#417×C₁₀₁	C₂	1	2	yes	maximal, complemented
4	C₂×#391×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₀₁×#2016	C₂	1	2	yes	maximal, complemented
6	C₁₀₁×#2015	C₂	1	4	yes	maximal, complemented
7	C₁₀₁×#2014	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×Q₈×C₁₀₁	C₂²	1	1	yes	characteristic
11	C₂×#137×C₁₀₁	—	2	8	no	—
12	C₂×#137×C₁₀₁	—	2	8	no	—
13	C₂×#137×C₁₀₁	—	2	8	no	—
14	C₂²×Q₁₆×C₁₀₁	C₂²	1	4	yes	—
15	C₂²×SD₁₆×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
19	C₂×#127×C₁₀₁	C₂²	1	1	yes	characteristic
20	C₂×#124×C₁₀₁	C₂²	1	2	yes	—
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×C₄²×C₁₀₁	C₂²	1	1	yes	characteristic
25	#417×C₁₀₁	—	2	8	no	—
26	C₂×#103×C₁₀₁	C₂²	1	4	yes	—
27	C₂×#102×C₁₀₁	C₂²	1	4	yes	—
28	#391×C₁₀₁	—	2	2	no	—
29	#391×C₁₀₁	C₂²	1	2	yes	—
30	#391×C₁₀₁	C₂²	1	2	yes	—
31	C₂×#95×C₁₀₁	—	2	2	no	—
32	#336×C₁₀₁	C₂²	1	2	yes	—
33	#336×C₁₀₁	C₂²	1	2	yes	—
34	C₂×#41×C₁₀₁	—	2	4	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	D₄	1	8	yes	—
40	C₂²×Q₈×C₁₀₁	—	2	1	no	—
41	C₂²×Q₈×C₁₀₁	—	2	2	no	—
42	C₂²×Q₈×C₁₀₁	—	2	4	no	—
43	C₂²×Q₈×C₁₀₁	—	2	4	no	—
44	C₂²×Q₈×C₁₀₁	D₄	1	4	yes	complemented
45	C₂²×Q₈×C₁₀₁	C₂³	1	2	yes	—
46	C₂²×Q₈×C₁₀₁	C₂³	1	2	yes	—
47	C₂²×D₄×C₁₀₁	—	2	2	no	—
48	C₂²×D₄×C₁₀₁	—	2	2	no	—
49	C₂²×D₄×C₁₀₁	C₂³	1	2	yes	—
50	C₂³×C₄×C₁₀₁	—	2	1	no	—
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	#137×C₁₀₁	—	2	64	no	—
56	C₂×Q₁₆×C₁₀₁	—	2	8	no	—
57	C₂×Q₁₆×C₁₀₁	—	2	8	no	—
58	C₂×Q₁₆×C₁₀₁	—	2	8	no	—
59	C₂×SD₁₆×C₁₀₁	—	2	8	no	—
60	C₂×SD₁₆×C₁₀₁	—	2	8	no	—
61	C₂×SD₁₆×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×C₄²×C₁₀₁	—	2	4	no	—
78	C₂×C₄²×C₁₀₁	D₄	1	2	yes	—
79	C₂×C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
80	C₂×C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
81	#103×C₁₀₁	—	2	8	no	—
82	#102×C₁₀₁	—	2	8	no	—
83	#95×C₁₀₁	—	2	4	no	—
84	#95×C₁₀₁	—	2	4	no	—
85	C₂⁴×C₁₀₁	—	2	2	no	—
86	C₂⁴×C₁₀₁	C₂×D₄	1	1	yes	characteristic
87	#41×C₁₀₁	—	2	16	no	—
88	#41×C₁₀₁	—	2	16	no	—
89	#41×C₁₀₁	—	4	8	no	—
90	#41×C₁₀₁	—	4	8	no	—
91	C₂×Q₈×C₁₀₁	—	2	4	no	—
92	C₂×Q₈×C₁₀₁	—	2	2	no	—
93	C₂×Q₈×C₁₀₁	—	2	2	no	—
94	C₂×Q₈×C₁₀₁	—	2	16	no	—
95	C₂×Q₈×C₁₀₁	—	2	2	no	—
96	C₂×Q₈×C₁₀₁	—	2	4	no	—
97	C₂×Q₈×C₁₀₁	—	2	4	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	—	4	2	no	—
102	C₂×Q₈×C₁₀₁	—	4	8	no	—
103	C₂×Q₈×C₁₀₁	—	4	2	no	—
104	C₂×Q₈×C₁₀₁	C₂×D₄	1	4	yes	—
105	C₂×Q₈×C₁₀₁	C₂×D₄	1	4	yes	—
106	C₂×D₄×C₁₀₁	—	2	8	no	—
107	C₂×D₄×C₁₀₁	—	2	8	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	2	no	—
112	C₂×D₄×C₁₀₁	—	2	2	no	—
113	C₂×D₄×C₁₀₁	—	4	4	no	—
114	C₂×D₄×C₁₀₁	—	4	4	no	—
115	C₂×D₄×C₁₀₁	—	4	4	no	—
116	C₂×D₄×C₁₀₁	—	4	4	no	—
117	C₂×D₄×C₁₀₁	C₂×D₄	1	4	yes	—
118	C₂²×C₄×C₁₀₁	—	2	4	no	—
119	C₂²×C₄×C₁₀₁	—	2	4	no	—
120	C₂²×C₄×C₁₀₁	—	2	2	no	—
121	C₂²×C₄×C₁₀₁	—	2	2	no	—
122	C₂²×C₄×C₁₀₁	—	2	8	no	—
123	C₂²×C₄×C₁₀₁	—	2	4	no	—
124	C₂²×C₄×C₁₀₁	—	2	2	no	—
125	C₂²×C₄×C₁₀₁	—	4	2	no	—
126	C₂²×C₄×C₁₀₁	—	4	2	no	—
127	C₂²×C₄×C₁₀₁	—	4	2	no	—
128	C₂²×C₄×C₁₀₁	—	4	4	no	—
129	C₂²×C₄×C₁₀₁	—	4	4	no	—
130	C₂²×C₄×C₁₀₁	—	4	4	no	—
131	C₂²×C₄×C₁₀₁	—	4	2	no	—
132	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
133	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
134	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
135	C₂²×C₄×C₁₀₁	C₂×D₄	1	4	yes	—
136	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₀₁	C₂×D₄	1	4	yes	—
138	C₂²×C₄×C₁₀₁	#41	1	2	yes	—
139	C₂²×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
140	Q₁₆×C₁₀₁	—	2	32	no	—
141	SD₁₆×C₁₀₁	—	2	32	no	—
142	M₁₆×C₁₀₁	—	2	16	no	—
143	C₂×C₈×C₁₀₁	—	2	4	no	—
144	C₂×C₈×C₁₀₁	—	2	4	no	—
145	C₂×C₈×C₁₀₁	C₂×D₄	1	8	yes	—
146	C₄⋊C₄×C₁₀₁	—	2	8	no	—
147	C₄⋊C₄×C₁₀₁	—	2	4	no	—
148	C₄⋊C₄×C₁₀₁	—	4	2	no	—
149	C₂²⋊C₄×C₁₀₁	—	2	16	no	—
150	C₄²×C₁₀₁	—	2	4	no	—
151	C₄²×C₁₀₁	—	2	2	no	—
152	C₄²×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	2	no	—
157	C₂³×C₁₀₁	—	4	2	no	—
158	C₂³×C₁₀₁	—	4	4	no	—
159	C₂³×C₁₀₁	—	4	4	no	—
160	C₂³×C₁₀₁	#120	1	2	yes	—
161	C₂³×C₁₀₁	#121	1	2	yes	—
162	C₂³×C₁₀₁	#127	1	2	yes	—
163	C₂³×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
164	Q₈×C₁₀₁	—	2	8	no	—
165	Q₈×C₁₀₁	—	2	4	no	—
166	Q₈×C₁₀₁	—	2	4	no	—
167	Q₈×C₁₀₁	—	4	2	no	—
168	Q₈×C₁₀₁	—	4	4	no	—
169	Q₈×C₁₀₁	—	4	2	no	—
170	Q₈×C₁₀₁	—	4	8	no	—
171	D₄×C₁₀₁	—	2	4	no	—
172	D₄×C₁₀₁	—	2	4	no	—
173	D₄×C₁₀₁	—	4	16	no	—
174	D₄×C₁₀₁	—	4	16	no	—
175	D₄×C₁₀₁	—	4	2	no	—
176	D₄×C₁₀₁	—	4	2	no	—
177	C₂×C₄×C₁₀₁	—	2	2	no	—
178	C₂×C₄×C₁₀₁	—	2	2	no	—
179	C₂×C₄×C₁₀₁	—	2	2	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	—	4	8	no	—
185	C₂×C₄×C₁₀₁	—	4	2	no	—
186	C₂×C₄×C₁₀₁	—	4	2	no	—
187	C₂×C₄×C₁₀₁	—	4	2	no	—
188	C₂×C₄×C₁₀₁	—	4	2	no	—
189	C₂×C₄×C₁₀₁	—	4	8	no	—
190	C₂×C₄×C₁₀₁	—	4	16	no	—
191	C₂×C₄×C₁₀₁	—	4	2	no	—
192	C₂×C₄×C₁₀₁	—	4	4	no	—
193	C₂×C₄×C₁₀₁	—	8	4	no	—
194	C₂×C₄×C₁₀₁	#120	1	8	yes	—
195	C₂×C₄×C₁₀₁	#120	1	2	yes	—
196	C₂×C₄×C₁₀₁	#121	1	8	yes	—
197	C₂×C₄×C₁₀₁	#121	1	2	yes	—
198	C₂×C₄×C₁₀₁	#127	1	2	yes	—
199	C₂×C₄×C₁₀₁	#137	1	4	yes	complemented
200	C₂×C₄×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
201	C₂×C₄×C₁₀₁	C₂²×D₄	1	2	yes	—
202	C₂×C₄×C₁₀₁	C₂²×D₄	1	2	yes	—
203	C₂×C₄×C₁₀₁	C₂×#41	1	1	yes	characteristic
204	C₈×C₁₀₁	—	2	8	no	—
205	C₂²×C₁₀₁	—	2	2	no	—
206	C₂²×C₁₀₁	—	2	2	no	—
207	C₂²×C₁₀₁	—	2	4	no	—
208	C₂²×C₁₀₁	—	2	4	no	—
209	C₂²×C₁₀₁	—	4	4	no	—
210	C₂²×C₁₀₁	—	4	8	no	—
211	C₂²×C₁₀₁	—	8	2	no	—
212	C₂²×C₁₀₁	—	8	2	no	—
213	C₂²×C₁₀₁	—	8	4	no	—
214	C₂²×C₁₀₁	#392	1	4	yes	—
215	C₂²×C₁₀₁	C₂×#120	1	1	yes	characteristic
216	C₂²×C₁₀₁	C₂×#121	1	1	yes	characteristic
217	C₂²×C₁₀₁	C₂×#127	1	1	yes	characteristic
218	C₂²×C₁₀₁	C₂×#137	1	2	yes	—
219	C₂²×C₁₀₁	#575	1	2	yes	—
220	C₄×C₁₀₁	—	2	4	no	—
221	C₄×C₁₀₁	—	4	4	no	—
222	C₄×C₁₀₁	—	4	4	no	—
223	C₄×C₁₀₁	—	4	2	no	—
224	C₄×C₁₀₁	—	8	2	no	—
225	C₄×C₁₀₁	#392	1	4	yes	—
226	C₄×C₁₀₁	C₂×#120	1	2	yes	—
227	C₄×C₁₀₁	C₂×#121	1	2	yes	—
228	#23429	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
229	C₂×C₁₀₁	—	2	4	no	—
230	C₂×C₁₀₁	—	8	4	no	—
231	C₂×C₁₀₁	C₂×#392	1	1	yes	characteristic
232	C₂×C₁₀₁	#3007	1	2	yes	—
233	C₂×C₁₀₁	#3037	1	2	yes	—
234	C₂×C₁₀₁	#3152	1	1	yes	characteristic
235	C₂×C₁₀₁	#3153	1	1	yes	characteristic
236	C₂²×#137	C₂×C₁₀₁	1	2	yes	complemented
237	C₂×#532	C₂×C₁₀₁	1	1	yes	characteristic
238	C₂×#417	C₂×C₁₀₁	1	2	yes	complemented
239	C₂×#391	C₂×C₁₀₁	1	1	yes	characteristic, complemented
240	#2016	C₂×C₁₀₁	1	2	yes	complemented
241	#2015	C₂×C₁₀₁	1	4	yes	complemented
242	#2014	C₂×C₁₀₁	1	2	yes	complemented
243	#1728	C₂×C₁₀₁	1	1	yes	characteristic, complemented
244	C₁₀₁	#23429	1	1	yes	characteristic, direct product factor, Sylow
245	C₂²×#41	C₂²×C₁₀₁	1	2	yes	—
246	C₂³×Q₈	C₂²×C₁₀₁	1	1	yes	characteristic
247	C₂×#137	—	2	8	no	—
248	C₂×#137	—	2	8	no	—
249	C₂×#137	—	2	8	no	—
250	C₂²×Q₁₆	C₂²×C₁₀₁	1	4	yes	—
251	C₂²×SD₁₆	C₂²×C₁₀₁	1	4	yes	—
252	C₂²×M₁₆	C₂²×C₁₀₁	1	2	yes	—
253	#532	—	2	8	no	—
254	C₂×C₄⋊Q₈	C₂²×C₁₀₁	1	1	yes	characteristic
255	C₂×#127	C₂²×C₁₀₁	1	1	yes	characteristic
256	C₂×#124	C₂²×C₁₀₁	1	2	yes	—
257	C₂×#121	—	2	2	no	—
258	C₂×C₄×D₄	—	2	2	no	—
259	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
260	C₂²×C₄²	C₂²×C₁₀₁	1	1	yes	characteristic
261	#417	—	2	8	no	—
262	C₂×#103	C₂²×C₁₀₁	1	4	yes	—
263	C₂×#102	C₂²×C₁₀₁	1	4	yes	—
264	#391	—	2	2	no	—
265	#391	C₂²×C₁₀₁	1	2	yes	—
266	#391	C₂²×C₁₀₁	1	2	yes	—
267	C₂×#95	—	2	2	no	—
268	#336	C₂²×C₁₀₁	1	2	yes	—
269	#336	C₂²×C₁₀₁	1	2	yes	—
270	C₂×#41	—	2	4	no	—
271	C₂×#41	—	2	4	no	—
272	C₂×#41	—	2	4	no	—
273	C₂×#41	—	2	4	no	—
274	C₂×#41	—	2	4	no	—
275	C₂×#41	D₄×C₁₀₁	1	8	yes	—
276	C₂²×Q₈	—	2	1	no	—
277	C₂²×Q₈	—	2	2	no	—
278	C₂²×Q₈	—	2	4	no	—
279	C₂²×Q₈	—	2	4	no	—
280	C₂²×Q₈	D₄×C₁₀₁	1	4	yes	complemented
281	C₂²×Q₈	C₂³×C₁₀₁	1	2	yes	—
282	C₂²×Q₈	C₂³×C₁₀₁	1	2	yes	—
283	C₂²×D₄	—	2	2	no	—
284	C₂²×D₄	—	2	2	no	—
285	C₂²×D₄	C₂³×C₁₀₁	1	2	yes	—
286	C₂³×C₄	—	2	1	no	—
287	C₂³×C₄	—	2	2	no	—
288	C₂³×C₄	—	2	1	no	—
289	C₂³×C₄	D₄×C₁₀₁	1	2	yes	—
290	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
291	#137	—	2	64	no	—
292	C₂×Q₁₆	—	2	8	no	—
293	C₂×Q₁₆	—	2	8	no	—
294	C₂×Q₁₆	—	2	8	no	—
295	C₂×SD₁₆	—	2	8	no	—
296	C₂×SD₁₆	—	2	8	no	—
297	C₂×SD₁₆	—	2	8	no	—
298	C₂×M₁₆	—	2	4	no	—
299	C₂×M₁₆	—	2	4	no	—
300	C₂×M₁₆	D₄×C₁₀₁	1	8	yes	complemented
301	C₂²×C₈	C₂³×C₁₀₁	1	4	yes	—
302	C₄⋊Q₈	—	2	4	no	—
303	#127	—	2	4	no	—
304	#124	—	2	4	no	—
305	#124	—	2	4	no	—
306	#121	—	2	16	no	—
307	C₄×D₄	—	2	16	no	—
308	C₂×C₄⋊C₄	—	2	2	no	—
309	C₂×C₄⋊C₄	—	2	4	no	—
310	C₂×C₄⋊C₄	—	2	1	no	—
311	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	2	yes	—
312	C₂×C₂²⋊C₄	—	2	4	no	—
313	C₂×C₄²	—	2	4	no	—
314	C₂×C₄²	D₄×C₁₀₁	1	2	yes	—
315	C₂×C₄²	C₂³×C₁₀₁	1	1	yes	characteristic
316	C₂×C₄²	C₂³×C₁₀₁	1	1	yes	characteristic
317	#103	—	2	8	no	—
318	#102	—	2	8	no	—
319	#95	—	2	4	no	—
320	#95	—	2	4	no	—
321	C₂⁴	—	2	2	no	—
322	C₂⁴	C₂×D₄×C₁₀₁	1	1	yes	characteristic
323	#41	—	2	16	no	—
324	#41	—	2	16	no	—
325	#41	—	4	8	no	—
326	#41	—	4	8	no	—
327	C₂×Q₈	—	2	4	no	—
328	C₂×Q₈	—	2	2	no	—
329	C₂×Q₈	—	2	2	no	—
330	C₂×Q₈	—	2	16	no	—
331	C₂×Q₈	—	2	2	no	—
332	C₂×Q₈	—	2	4	no	—
333	C₂×Q₈	—	2	4	no	—
334	C₂×Q₈	—	2	2	no	—
335	C₂×Q₈	—	2	2	no	—
336	C₂×Q₈	—	2	2	no	—
337	C₂×Q₈	—	4	2	no	—
338	C₂×Q₈	—	4	8	no	—
339	C₂×Q₈	—	4	2	no	—
340	C₂×Q₈	C₂×D₄×C₁₀₁	1	4	yes	—
341	C₂×Q₈	C₂×D₄×C₁₀₁	1	4	yes	—
342	C₂×D₄	—	2	8	no	—
343	C₂×D₄	—	2	8	no	—
344	C₂×D₄	—	2	2	no	—
345	C₂×D₄	—	2	2	no	—
346	C₂×D₄	—	2	2	no	—
347	C₂×D₄	—	2	2	no	—
348	C₂×D₄	—	2	2	no	—
349	C₂×D₄	—	4	4	no	—
350	C₂×D₄	—	4	4	no	—
351	C₂×D₄	—	4	4	no	—
352	C₂×D₄	—	4	4	no	—
353	C₂×D₄	C₂×D₄×C₁₀₁	1	4	yes	—
354	C₂²×C₄	—	2	4	no	—
355	C₂²×C₄	—	2	4	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	8	no	—
359	C₂²×C₄	—	2	4	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	4	2	no	—
362	C₂²×C₄	—	4	2	no	—
363	C₂²×C₄	—	4	2	no	—
364	C₂²×C₄	—	4	4	no	—
365	C₂²×C₄	—	4	4	no	—
366	C₂²×C₄	—	4	4	no	—
367	C₂²×C₄	—	4	2	no	—
368	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
369	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
370	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
371	C₂²×C₄	C₂×D₄×C₁₀₁	1	4	yes	—
372	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
373	C₂²×C₄	C₂×D₄×C₁₀₁	1	4	yes	—
374	C₂²×C₄	#41×C₁₀₁	1	2	yes	—
375	C₂²×C₄	C₂⁴×C₁₀₁	1	1	yes	characteristic
376	Q₁₆	—	2	32	no	—
377	SD₁₆	—	2	32	no	—
378	M₁₆	—	2	16	no	—
379	C₂×C₈	—	2	4	no	—
380	C₂×C₈	—	2	4	no	—
381	C₂×C₈	C₂×D₄×C₁₀₁	1	8	yes	—
382	C₄⋊C₄	—	2	8	no	—
383	C₄⋊C₄	—	2	4	no	—
384	C₄⋊C₄	—	4	2	no	—
385	C₂²⋊C₄	—	2	16	no	—
386	C₄²	—	2	4	no	—
387	C₄²	—	2	2	no	—
388	C₄²	—	2	2	no	—
389	C₂³	—	2	2	no	—
390	C₂³	—	2	2	no	—
391	C₂³	—	2	4	no	—
392	C₂³	—	4	2	no	—
393	C₂³	—	4	2	no	—
394	C₂³	—	4	4	no	—
395	C₂³	—	4	4	no	—
396	C₂³	#120×C₁₀₁	1	2	yes	—
397	C₂³	#121×C₁₀₁	1	2	yes	—
398	C₂³	#127×C₁₀₁	1	2	yes	—
399	C₂³	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
400	Q₈	—	2	8	no	—
401	Q₈	—	2	4	no	—
402	Q₈	—	2	4	no	—
403	Q₈	—	4	2	no	—
404	Q₈	—	4	4	no	—
405	Q₈	—	4	2	no	—
406	Q₈	—	4	8	no	—
407	D₄	—	2	4	no	—
408	D₄	—	2	4	no	—
409	D₄	—	4	16	no	—
410	D₄	—	4	16	no	—
411	D₄	—	4	2	no	—
412	D₄	—	4	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	4	no	—
417	C₂×C₄	—	2	4	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	4	8	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	8	no	—
426	C₂×C₄	—	4	16	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	4	no	—
429	C₂×C₄	—	8	4	no	—
430	C₂×C₄	#120×C₁₀₁	1	8	yes	—
431	C₂×C₄	#120×C₁₀₁	1	2	yes	—
432	C₂×C₄	#121×C₁₀₁	1	8	yes	—
433	C₂×C₄	#121×C₁₀₁	1	2	yes	—
434	C₂×C₄	#127×C₁₀₁	1	2	yes	—
435	C₂×C₄	#137×C₁₀₁	1	4	yes	complemented
436	C₂×C₄	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
437	C₂×C₄	C₂²×D₄×C₁₀₁	1	2	yes	—
438	C₂×C₄	C₂²×D₄×C₁₀₁	1	2	yes	—
439	C₂×C₄	C₂×#41×C₁₀₁	1	1	yes	characteristic
440	C₈	—	2	8	no	—
441	C₂²	—	2	4	no	—
442	C₂²	—	2	4	no	—
443	C₂²	—	2	2	no	—
444	C₂²	—	2	2	no	—
445	C₂²	—	4	8	no	—
446	C₂²	—	4	4	no	—
447	C₂²	—	8	4	no	—
448	C₂²	—	8	2	no	—
449	C₂²	—	8	2	no	—
450	C₂²	#392×C₁₀₁	1	4	yes	—
451	C₂²	C₂×#120×C₁₀₁	1	1	yes	characteristic
452	C₂²	C₂×#121×C₁₀₁	1	1	yes	characteristic
453	C₂²	C₂×#127×C₁₀₁	1	1	yes	characteristic
454	C₂²	C₂×#137×C₁₀₁	1	2	yes	—
455	C₂²	#575×C₁₀₁	1	2	yes	—
456	C₄	—	2	4	no	—
457	C₄	—	4	2	no	—
458	C₄	—	4	4	no	—
459	C₄	—	4	4	no	—
460	C₄	—	8	2	no	—
461	C₄	#392×C₁₀₁	1	4	yes	—
462	C₄	C₂×#120×C₁₀₁	1	2	yes	—
463	C₄	C₂×#121×C₁₀₁	1	2	yes	—
464	C₂	—	2	4	no	—
465	C₂	—	8	4	no	—
466	C₂	C₂×#392×C₁₀₁	1	1	yes	characteristic
467	C₂	C₁₀₁×#3007	1	2	yes	—
468	C₂	C₁₀₁×#3037	1	2	yes	—
469	C₂	C₁₀₁×#3152	1	1	yes	characteristic
470	C₂	C₁₀₁×#3153	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₀₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₀₁
prime radical	C₂×#532×C₁₀₁	C₂
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×#137×C₁₀₁	C₂	semidirect
3. C₂×#417×C₁₀₁	C₂	semidirect
4. C₂×#391×C₁₀₁	C₂	semidirect
5. C₁₀₁×#2016	C₂	semidirect
6. C₁₀₁×#2015	C₂	semidirect
7. C₁₀₁×#2014	C₂	semidirect
8. C₁₀₁×#1728	C₂	semidirect
44. C₂²×Q₈×C₁₀₁	D₄	semidirect
64. C₂×M₁₆×C₁₀₁	D₄	semidirect
199. C₂×C₄×C₁₀₁	#137	semidirect
228. #23429	C₁₀₁	direct (N × H)
236. C₂²×#137	C₂×C₁₀₁	semidirect
238. C₂×#417	C₂×C₁₀₁	semidirect
239. C₂×#391	C₂×C₁₀₁	semidirect
240. #2016	C₂×C₁₀₁	semidirect
241. #2015	C₂×C₁₀₁	semidirect
242. #2014	C₂×C₁₀₁	semidirect
243. #1728	C₂×C₁₀₁	semidirect
244. C₁₀₁	#23429	direct (N × H)
280. C₂²×Q₈	D₄×C₁₀₁	semidirect
300. C₂×M₁₆	D₄×C₁₀₁	semidirect
435. C₂×C₄	#137×C₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#137×C₁₀₁	2
C₂×#532×C₁₀₁	2
C₂×#417×C₁₀₁	2
C₂×#391×C₁₀₁	2
C₁₀₁×#2016	2
C₁₀₁×#2015	2
C₁₀₁×#2014	2
C₁₀₁×#1728	2
#23429	101

Subgroups — C101×#23429 #38805580

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#23429 #38805580