Subgroups — C₁₀₁×#23421 #38805572

Order 25856.

2094 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#135×C₁₀₁	C₂	1	2	yes	maximal, complemented
2	C₂×#532×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#416×C₁₀₁	C₂	1	2	yes	maximal, complemented
4	C₁₀₁×#2297	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₀₁×#2016	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₀₁×#2015	C₂	1	2	yes	maximal, complemented
7	C₁₀₁×#2014	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₀₁×#2013	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₀₁×#2012	C₂	1	2	yes	maximal, complemented
10	C₁₀₁×#2011	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#336×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₁₀₁	C₂²	1	2	yes	—
13	C₂²×#41×C₁₀₁	C₂²	1	1	yes	characteristic
14	C₂×#135×C₁₀₁	—	2	8	no	—
15	C₂×#135×C₁₀₁	—	2	8	no	—
16	C₂×#135×C₁₀₁	—	2	8	no	—
17	C₂²×Q₁₆×C₁₀₁	C₂²	1	2	yes	—
18	C₂²×SD₁₆×C₁₀₁	C₂²	1	2	yes	—
19	C₂²×SD₁₆×C₁₀₁	C₂²	1	2	yes	—
20	C₂²×D₈×C₁₀₁	C₂²	1	2	yes	—
21	C₂³×C₈×C₁₀₁	C₂²	1	2	yes	—
22	#532×C₁₀₁	—	2	8	no	—
23	C₂×C₄⋊Q₈×C₁₀₁	C₂²	1	1	yes	characteristic
24	C₂×#127×C₁₀₁	C₂²	1	1	yes	characteristic
25	C₂×#124×C₁₀₁	C₂²	1	2	yes	—
26	C₂×#121×C₁₀₁	—	2	2	no	—
27	C₂×C₄×D₄×C₁₀₁	—	2	2	no	—
28	C₂×#117×C₁₀₁	C₂²	1	1	yes	characteristic
29	C₂²×C₄²×C₁₀₁	C₂²	1	1	yes	characteristic
30	#416×C₁₀₁	—	2	8	no	—
31	C₂×#103×C₁₀₁	C₂²	1	2	yes	—
32	C₂×#103×C₁₀₁	C₂²	1	2	yes	—
33	C₂×#102×C₁₀₁	C₂²	1	2	yes	—
34	C₂×#102×C₁₀₁	C₂²	1	2	yes	—
35	#391×C₁₀₁	C₂²	1	1	yes	characteristic
36	#391×C₁₀₁	C₂²	1	1	yes	characteristic
37	#390×C₁₀₁	C₂²	1	1	yes	characteristic
38	#390×C₁₀₁	C₂²	1	1	yes	characteristic
39	#386×C₁₀₁	—	2	2	no	—
40	C₄×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
41	#336×C₁₀₁	C₂²	1	1	yes	characteristic
42	#336×C₁₀₁	C₂²	1	2	yes	—
43	#336×C₁₀₁	C₂²	1	1	yes	characteristic
44	C₂×#41×C₁₀₁	—	2	4	no	—
45	C₂×#41×C₁₀₁	—	2	2	no	—
46	C₂×#41×C₁₀₁	—	2	4	no	—
47	C₂×#41×C₁₀₁	—	2	4	no	—
48	C₂×#41×C₁₀₁	—	2	4	no	—
49	C₂×#41×C₁₀₁	—	2	4	no	—
50	C₂×#41×C₁₀₁	—	2	4	no	—
51	C₂×#41×C₁₀₁	—	2	4	no	—
52	C₂×#41×C₁₀₁	D₄	1	8	yes	—
53	C₂×#41×C₁₀₁	D₄	1	4	yes	complemented
54	C₂²×Q₈×C₁₀₁	C₂³	1	2	yes	—
55	C₂²×Q₈×C₁₀₁	C₂³	1	1	yes	characteristic
56	C₂²×D₄×C₁₀₁	—	2	2	no	—
57	C₂²×D₄×C₁₀₁	—	2	1	no	—
58	C₂²×D₄×C₁₀₁	—	2	2	no	—
59	C₂²×D₄×C₁₀₁	C₂³	1	2	yes	—
60	C₂²×D₄×C₁₀₁	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₁₀₁	—	2	2	no	—
62	C₂³×C₄×C₁₀₁	—	2	1	no	—
63	C₂³×C₄×C₁₀₁	D₄	1	2	yes	—
64	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
65	#135×C₁₀₁	—	2	64	no	—
66	C₂×Q₁₆×C₁₀₁	—	2	4	no	—
67	C₂×Q₁₆×C₁₀₁	—	2	4	no	—
68	C₂×Q₁₆×C₁₀₁	—	2	4	no	—
69	C₂×SD₁₆×C₁₀₁	—	2	4	no	—
70	C₂×SD₁₆×C₁₀₁	—	2	4	no	—
71	C₂×SD₁₆×C₁₀₁	—	2	4	no	—
72	C₂×SD₁₆×C₁₀₁	—	2	4	no	—
73	C₂×SD₁₆×C₁₀₁	—	2	4	no	—
74	C₂×SD₁₆×C₁₀₁	—	2	4	no	—
75	C₂×D₈×C₁₀₁	—	2	4	no	—
76	C₂×D₈×C₁₀₁	—	2	4	no	—
77	C₂×D₈×C₁₀₁	—	2	4	no	—
78	C₂²×C₈×C₁₀₁	—	2	4	no	—
79	C₂²×C₈×C₁₀₁	—	2	4	no	—
80	C₂²×C₈×C₁₀₁	D₄	1	8	yes	complemented
81	C₂²×C₈×C₁₀₁	C₂³	1	2	yes	—
82	C₂²×C₈×C₁₀₁	C₂³	1	2	yes	—
83	C₄⋊Q₈×C₁₀₁	—	2	4	no	—
84	#127×C₁₀₁	—	2	4	no	—
85	#124×C₁₀₁	—	2	4	no	—
86	#124×C₁₀₁	—	2	4	no	—
87	#121×C₁₀₁	—	2	16	no	—
88	C₄×D₄×C₁₀₁	—	2	16	no	—
89	#117×C₁₀₁	—	2	4	no	—
90	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
91	C₂×C₄⋊C₄×C₁₀₁	C₂³	1	1	yes	characteristic
92	C₂×C₄⋊C₄×C₁₀₁	C₂³	1	1	yes	characteristic
93	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
94	C₂×C₂²⋊C₄×C₁₀₁	—	2	1	no	—
95	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
96	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
97	C₂×C₄²×C₁₀₁	—	2	4	no	—
98	C₂×C₄²×C₁₀₁	—	2	1	no	—
99	C₂×C₄²×C₁₀₁	D₄	1	2	yes	—
100	C₂×C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
101	C₂×C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
102	#103×C₁₀₁	—	2	4	no	—
103	#103×C₁₀₁	—	2	4	no	—
104	#102×C₁₀₁	—	2	4	no	—
105	#102×C₁₀₁	—	2	4	no	—
106	#95×C₁₀₁	—	2	2	no	—
107	#95×C₁₀₁	—	2	2	no	—
108	C₂⁴×C₁₀₁	—	2	1	no	—
109	C₂⁴×C₁₀₁	—	2	2	no	—
110	C₂⁴×C₁₀₁	C₂×D₄	1	1	yes	characteristic
111	#41×C₁₀₁	—	2	16	no	—
112	#41×C₁₀₁	—	2	16	no	—
113	#41×C₁₀₁	—	2	16	no	—
114	#41×C₁₀₁	—	4	8	no	—
115	#41×C₁₀₁	—	4	8	no	—
116	#41×C₁₀₁	—	4	8	no	—
117	C₂×Q₈×C₁₀₁	—	2	2	no	—
118	C₂×Q₈×C₁₀₁	—	2	1	no	—
119	C₂×Q₈×C₁₀₁	—	2	2	no	—
120	C₂×Q₈×C₁₀₁	—	2	2	no	—
121	C₂×Q₈×C₁₀₁	—	2	2	no	—
122	C₂×Q₈×C₁₀₁	—	2	2	no	—
123	C₂×Q₈×C₁₀₁	—	2	2	no	—
124	C₂×Q₈×C₁₀₁	—	2	2	no	—
125	C₂×Q₈×C₁₀₁	C₂×D₄	1	4	yes	—
126	C₂×Q₈×C₁₀₁	C₂×D₄	1	2	yes	—
127	C₂×D₄×C₁₀₁	—	2	8	no	—
128	C₂×D₄×C₁₀₁	—	2	8	no	—
129	C₂×D₄×C₁₀₁	—	2	4	no	—
130	C₂×D₄×C₁₀₁	—	2	2	no	—
131	C₂×D₄×C₁₀₁	—	2	2	no	—
132	C₂×D₄×C₁₀₁	—	2	2	no	—
133	C₂×D₄×C₁₀₁	—	2	2	no	—
134	C₂×D₄×C₁₀₁	—	2	2	no	—
135	C₂×D₄×C₁₀₁	—	2	2	no	—
136	C₂×D₄×C₁₀₁	—	2	2	no	—
137	C₂×D₄×C₁₀₁	—	2	1	no	—
138	C₂×D₄×C₁₀₁	—	4	4	no	—
139	C₂×D₄×C₁₀₁	—	4	2	no	—
140	C₂×D₄×C₁₀₁	—	4	4	no	—
141	C₂×D₄×C₁₀₁	—	4	4	no	—
142	C₂×D₄×C₁₀₁	—	4	2	no	—
143	C₂×D₄×C₁₀₁	—	4	4	no	—
144	C₂×D₄×C₁₀₁	C₂×D₄	1	4	yes	—
145	C₂×D₄×C₁₀₁	C₂×D₄	1	2	yes	—
146	C₂²×C₄×C₁₀₁	—	2	4	no	—
147	C₂²×C₄×C₁₀₁	—	2	1	no	—
148	C₂²×C₄×C₁₀₁	—	2	2	no	—
149	C₂²×C₄×C₁₀₁	—	2	8	no	—
150	C₂²×C₄×C₁₀₁	—	2	4	no	—
151	C₂²×C₄×C₁₀₁	—	2	4	no	—
152	C₂²×C₄×C₁₀₁	—	2	1	no	—
153	C₂²×C₄×C₁₀₁	—	2	1	no	—
154	C₂²×C₄×C₁₀₁	—	4	2	no	—
155	C₂²×C₄×C₁₀₁	—	4	2	no	—
156	C₂²×C₄×C₁₀₁	—	4	4	no	—
157	C₂²×C₄×C₁₀₁	—	4	4	no	—
158	C₂²×C₄×C₁₀₁	—	4	2	no	—
159	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
160	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
161	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
162	C₂²×C₄×C₁₀₁	C₂×D₄	1	4	yes	—
163	C₂²×C₄×C₁₀₁	C₂×D₄	1	4	yes	—
164	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₁₀₁	#41	1	2	yes	—
166	C₂²×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
167	Q₁₆×C₁₀₁	—	2	16	no	—
168	SD₁₆×C₁₀₁	—	2	16	no	—
169	SD₁₆×C₁₀₁	—	2	16	no	—
170	D₈×C₁₀₁	—	2	16	no	—
171	C₂×C₈×C₁₀₁	—	2	16	no	—
172	C₂×C₈×C₁₀₁	—	2	2	no	—
173	C₂×C₈×C₁₀₁	—	2	2	no	—
174	C₂×C₈×C₁₀₁	—	2	2	no	—
175	C₂×C₈×C₁₀₁	—	2	2	no	—
176	C₂×C₈×C₁₀₁	C₂×D₄	1	4	yes	—
177	C₂×C₈×C₁₀₁	C₂×D₄	1	4	yes	—
178	C₄⋊C₄×C₁₀₁	—	2	8	no	—
179	C₄⋊C₄×C₁₀₁	—	2	2	no	—
180	C₄⋊C₄×C₁₀₁	—	2	2	no	—
181	C₂²⋊C₄×C₁₀₁	—	2	16	no	—
182	C₂²⋊C₄×C₁₀₁	—	4	4	no	—
183	C₂²⋊C₄×C₁₀₁	—	4	2	no	—
184	C₂²⋊C₄×C₁₀₁	—	4	4	no	—
185	C₄²×C₁₀₁	—	2	4	no	—
186	C₄²×C₁₀₁	—	2	2	no	—
187	C₄²×C₁₀₁	—	2	2	no	—
188	C₄²×C₁₀₁	—	4	2	no	—
189	C₂³×C₁₀₁	—	2	2	no	—
190	C₂³×C₁₀₁	—	2	2	no	—
191	C₂³×C₁₀₁	—	2	4	no	—
192	C₂³×C₁₀₁	—	2	2	no	—
193	C₂³×C₁₀₁	—	4	1	no	—
194	C₂³×C₁₀₁	—	4	2	no	—
195	C₂³×C₁₀₁	—	4	2	no	—
196	C₂³×C₁₀₁	—	4	1	no	—
197	C₂³×C₁₀₁	—	4	2	no	—
198	C₂³×C₁₀₁	—	4	4	no	—
199	C₂³×C₁₀₁	—	4	2	no	—
200	C₂³×C₁₀₁	—	4	4	no	—
201	C₂³×C₁₀₁	#120	1	2	yes	—
202	C₂³×C₁₀₁	#121	1	2	yes	—
203	C₂³×C₁₀₁	#127	1	2	yes	—
204	C₂³×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
205	Q₈×C₁₀₁	—	2	4	no	—
206	Q₈×C₁₀₁	—	2	4	no	—
207	Q₈×C₁₀₁	—	2	4	no	—
208	Q₈×C₁₀₁	—	4	2	no	—
209	Q₈×C₁₀₁	—	4	2	no	—
210	Q₈×C₁₀₁	—	4	2	no	—
211	D₄×C₁₀₁	—	2	4	no	—
212	D₄×C₁₀₁	—	2	4	no	—
213	D₄×C₁₀₁	—	2	4	no	—
214	D₄×C₁₀₁	—	4	16	no	—
215	D₄×C₁₀₁	—	4	16	no	—
216	D₄×C₁₀₁	—	4	8	no	—
217	D₄×C₁₀₁	—	4	2	no	—
218	D₄×C₁₀₁	—	4	2	no	—
219	D₄×C₁₀₁	—	4	2	no	—
220	C₂×C₄×C₁₀₁	—	2	2	no	—
221	C₂×C₄×C₁₀₁	—	2	2	no	—
222	C₂×C₄×C₁₀₁	—	2	2	no	—
223	C₂×C₄×C₁₀₁	—	2	4	no	—
224	C₂×C₄×C₁₀₁	—	2	2	no	—
225	C₂×C₄×C₁₀₁	—	2	2	no	—
226	C₂×C₄×C₁₀₁	—	2	2	no	—
227	C₂×C₄×C₁₀₁	—	4	8	no	—
228	C₂×C₄×C₁₀₁	—	4	1	no	—
229	C₂×C₄×C₁₀₁	—	4	2	no	—
230	C₂×C₄×C₁₀₁	—	4	1	no	—
231	C₂×C₄×C₁₀₁	—	4	2	no	—
232	C₂×C₄×C₁₀₁	—	4	16	no	—
233	C₂×C₄×C₁₀₁	—	4	8	no	—
234	C₂×C₄×C₁₀₁	—	4	1	no	—
235	C₂×C₄×C₁₀₁	—	4	1	no	—
236	C₂×C₄×C₁₀₁	—	4	2	no	—
237	C₂×C₄×C₁₀₁	—	4	2	no	—
238	C₂×C₄×C₁₀₁	#120	1	8	yes	—
239	C₂×C₄×C₁₀₁	#120	1	2	yes	—
240	C₂×C₄×C₁₀₁	#121	1	8	yes	—
241	C₂×C₄×C₁₀₁	#121	1	2	yes	—
242	C₂×C₄×C₁₀₁	#127	1	2	yes	—
243	C₂×C₄×C₁₀₁	#135	1	4	yes	complemented
244	C₂×C₄×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
245	C₂×C₄×C₁₀₁	C₂²×D₄	1	2	yes	—
246	C₂×C₄×C₁₀₁	C₂²×D₄	1	2	yes	—
247	C₂×C₄×C₁₀₁	C₂×#41	1	1	yes	characteristic
248	C₈×C₁₀₁	—	2	4	no	—
249	C₈×C₁₀₁	—	2	4	no	—
250	C₂²×C₁₀₁	—	2	2	no	—
251	C₂²×C₁₀₁	—	2	2	no	—
252	C₂²×C₁₀₁	—	2	4	no	—
253	C₂²×C₁₀₁	—	2	4	no	—
254	C₂²×C₁₀₁	—	4	2	no	—
255	C₂²×C₁₀₁	—	4	4	no	—
256	C₂²×C₁₀₁	—	4	8	no	—
257	C₂²×C₁₀₁	—	4	4	no	—
258	C₂²×C₁₀₁	—	8	1	no	—
259	C₂²×C₁₀₁	—	8	2	no	—
260	C₂²×C₁₀₁	—	8	1	no	—
261	C₂²×C₁₀₁	—	8	2	no	—
262	C₂²×C₁₀₁	—	8	2	no	—
263	C₂²×C₁₀₁	—	8	4	no	—
264	C₂²×C₁₀₁	#392	1	4	yes	—
265	C₂²×C₁₀₁	C₂×#120	1	1	yes	characteristic
266	C₂²×C₁₀₁	C₂×#121	1	1	yes	characteristic
267	C₂²×C₁₀₁	C₂×#127	1	1	yes	characteristic
268	C₂²×C₁₀₁	C₂×#135	1	2	yes	—
269	C₂²×C₁₀₁	#575	1	2	yes	—
270	C₄×C₁₀₁	—	2	4	no	—
271	C₄×C₁₀₁	—	4	4	no	—
272	C₄×C₁₀₁	—	4	2	no	—
273	C₄×C₁₀₁	—	4	2	no	—
274	C₄×C₁₀₁	—	8	1	no	—
275	C₄×C₁₀₁	—	8	1	no	—
276	C₄×C₁₀₁	#392	1	4	yes	—
277	C₄×C₁₀₁	C₂×#120	1	2	yes	—
278	C₄×C₁₀₁	C₂×#121	1	2	yes	—
279	#23421	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
280	C₂×C₁₀₁	—	2	4	no	—
281	C₂×C₁₀₁	—	8	4	no	—
282	C₂×C₁₀₁	—	8	2	no	—
283	C₂×C₁₀₁	C₂×#392	1	1	yes	characteristic
284	C₂×C₁₀₁	#3002	1	2	yes	—
285	C₂×C₁₀₁	#3035	1	2	yes	—
286	C₂×C₁₀₁	#3147	1	1	yes	characteristic
287	C₂×C₁₀₁	#3150	1	1	yes	characteristic
288	C₂²×#135	C₂×C₁₀₁	1	2	yes	complemented
289	C₂×#532	C₂×C₁₀₁	1	1	yes	characteristic, complemented
290	C₂×#416	C₂×C₁₀₁	1	2	yes	complemented
291	#2297	C₂×C₁₀₁	1	1	yes	characteristic, complemented
292	#2016	C₂×C₁₀₁	1	1	yes	characteristic, complemented
293	#2015	C₂×C₁₀₁	1	2	yes	complemented
294	#2014	C₂×C₁₀₁	1	1	yes	characteristic, complemented
295	#2013	C₂×C₁₀₁	1	1	yes	characteristic, complemented
296	#2012	C₂×C₁₀₁	1	2	yes	complemented
297	#2011	C₂×C₁₀₁	1	1	yes	characteristic, complemented
298	C₂×#336	C₂×C₁₀₁	1	1	yes	characteristic, complemented
299	C₁₀₁	#23421	1	1	yes	characteristic, direct product factor, Sylow
300	C₂²×#41	C₂²×C₁₀₁	1	2	yes	—
301	C₂²×#41	C₂²×C₁₀₁	1	1	yes	characteristic
302	C₂×#135	—	2	8	no	—
303	C₂×#135	—	2	8	no	—
304	C₂×#135	—	2	8	no	—
305	C₂²×Q₁₆	C₂²×C₁₀₁	1	2	yes	—
306	C₂²×SD₁₆	C₂²×C₁₀₁	1	2	yes	—
307	C₂²×SD₁₆	C₂²×C₁₀₁	1	2	yes	—
308	C₂²×D₈	C₂²×C₁₀₁	1	2	yes	—
309	C₂³×C₈	C₂²×C₁₀₁	1	2	yes	—
310	#532	—	2	8	no	—
311	C₂×C₄⋊Q₈	C₂²×C₁₀₁	1	1	yes	characteristic
312	C₂×#127	C₂²×C₁₀₁	1	1	yes	characteristic
313	C₂×#124	C₂²×C₁₀₁	1	2	yes	—
314	C₂×#121	—	2	2	no	—
315	C₂×C₄×D₄	—	2	2	no	—
316	C₂×#117	C₂²×C₁₀₁	1	1	yes	characteristic
317	C₂²×C₄²	C₂²×C₁₀₁	1	1	yes	characteristic
318	#416	—	2	8	no	—
319	C₂×#103	C₂²×C₁₀₁	1	2	yes	—
320	C₂×#103	C₂²×C₁₀₁	1	2	yes	—
321	C₂×#102	C₂²×C₁₀₁	1	2	yes	—
322	C₂×#102	C₂²×C₁₀₁	1	2	yes	—
323	#391	C₂²×C₁₀₁	1	1	yes	characteristic
324	#391	C₂²×C₁₀₁	1	1	yes	characteristic
325	#390	C₂²×C₁₀₁	1	1	yes	characteristic
326	#390	C₂²×C₁₀₁	1	1	yes	characteristic
327	#386	—	2	2	no	—
328	C₄×C₂²⋊C₄	—	2	2	no	—
329	#336	C₂²×C₁₀₁	1	1	yes	characteristic
330	#336	C₂²×C₁₀₁	1	2	yes	—
331	#336	C₂²×C₁₀₁	1	1	yes	characteristic
332	C₂×#41	—	2	4	no	—
333	C₂×#41	—	2	2	no	—
334	C₂×#41	—	2	4	no	—
335	C₂×#41	—	2	4	no	—
336	C₂×#41	—	2	4	no	—
337	C₂×#41	—	2	4	no	—
338	C₂×#41	—	2	4	no	—
339	C₂×#41	—	2	4	no	—
340	C₂×#41	D₄×C₁₀₁	1	8	yes	—
341	C₂×#41	D₄×C₁₀₁	1	4	yes	complemented
342	C₂²×Q₈	C₂³×C₁₀₁	1	2	yes	—
343	C₂²×Q₈	C₂³×C₁₀₁	1	1	yes	characteristic
344	C₂²×D₄	—	2	2	no	—
345	C₂²×D₄	—	2	1	no	—
346	C₂²×D₄	—	2	2	no	—
347	C₂²×D₄	C₂³×C₁₀₁	1	2	yes	—
348	C₂²×D₄	C₂³×C₁₀₁	1	1	yes	characteristic
349	C₂³×C₄	—	2	2	no	—
350	C₂³×C₄	—	2	1	no	—
351	C₂³×C₄	D₄×C₁₀₁	1	2	yes	—
352	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
353	#135	—	2	64	no	—
354	C₂×Q₁₆	—	2	4	no	—
355	C₂×Q₁₆	—	2	4	no	—
356	C₂×Q₁₆	—	2	4	no	—
357	C₂×SD₁₆	—	2	4	no	—
358	C₂×SD₁₆	—	2	4	no	—
359	C₂×SD₁₆	—	2	4	no	—
360	C₂×SD₁₆	—	2	4	no	—
361	C₂×SD₁₆	—	2	4	no	—
362	C₂×SD₁₆	—	2	4	no	—
363	C₂×D₈	—	2	4	no	—
364	C₂×D₈	—	2	4	no	—
365	C₂×D₈	—	2	4	no	—
366	C₂²×C₈	—	2	4	no	—
367	C₂²×C₈	—	2	4	no	—
368	C₂²×C₈	D₄×C₁₀₁	1	8	yes	complemented
369	C₂²×C₈	C₂³×C₁₀₁	1	2	yes	—
370	C₂²×C₈	C₂³×C₁₀₁	1	2	yes	—
371	C₄⋊Q₈	—	2	4	no	—
372	#127	—	2	4	no	—
373	#124	—	2	4	no	—
374	#124	—	2	4	no	—
375	#121	—	2	16	no	—
376	C₄×D₄	—	2	16	no	—
377	#117	—	2	4	no	—
378	C₂×C₄⋊C₄	—	2	2	no	—
379	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	1	yes	characteristic
380	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	1	yes	characteristic
381	C₂×C₂²⋊C₄	—	2	4	no	—
382	C₂×C₂²⋊C₄	—	2	1	no	—
383	C₂×C₂²⋊C₄	—	2	2	no	—
384	C₂×C₂²⋊C₄	—	2	2	no	—
385	C₂×C₄²	—	2	4	no	—
386	C₂×C₄²	—	2	1	no	—
387	C₂×C₄²	D₄×C₁₀₁	1	2	yes	—
388	C₂×C₄²	C₂³×C₁₀₁	1	1	yes	characteristic
389	C₂×C₄²	C₂³×C₁₀₁	1	1	yes	characteristic
390	#103	—	2	4	no	—
391	#103	—	2	4	no	—
392	#102	—	2	4	no	—
393	#102	—	2	4	no	—
394	#95	—	2	2	no	—
395	#95	—	2	2	no	—
396	C₂⁴	—	2	1	no	—
397	C₂⁴	—	2	2	no	—
398	C₂⁴	C₂×D₄×C₁₀₁	1	1	yes	characteristic
399	#41	—	2	16	no	—
400	#41	—	2	16	no	—
401	#41	—	2	16	no	—
402	#41	—	4	8	no	—
403	#41	—	4	8	no	—
404	#41	—	4	8	no	—
405	C₂×Q₈	—	2	2	no	—
406	C₂×Q₈	—	2	1	no	—
407	C₂×Q₈	—	2	2	no	—
408	C₂×Q₈	—	2	2	no	—
409	C₂×Q₈	—	2	2	no	—
410	C₂×Q₈	—	2	2	no	—
411	C₂×Q₈	—	2	2	no	—
412	C₂×Q₈	—	2	2	no	—
413	C₂×Q₈	C₂×D₄×C₁₀₁	1	4	yes	—
414	C₂×Q₈	C₂×D₄×C₁₀₁	1	2	yes	—
415	C₂×D₄	—	2	8	no	—
416	C₂×D₄	—	2	8	no	—
417	C₂×D₄	—	2	4	no	—
418	C₂×D₄	—	2	2	no	—
419	C₂×D₄	—	2	2	no	—
420	C₂×D₄	—	2	2	no	—
421	C₂×D₄	—	2	2	no	—
422	C₂×D₄	—	2	2	no	—
423	C₂×D₄	—	2	2	no	—
424	C₂×D₄	—	2	2	no	—
425	C₂×D₄	—	2	1	no	—
426	C₂×D₄	—	4	4	no	—
427	C₂×D₄	—	4	2	no	—
428	C₂×D₄	—	4	4	no	—
429	C₂×D₄	—	4	4	no	—
430	C₂×D₄	—	4	2	no	—
431	C₂×D₄	—	4	4	no	—
432	C₂×D₄	C₂×D₄×C₁₀₁	1	4	yes	—
433	C₂×D₄	C₂×D₄×C₁₀₁	1	2	yes	—
434	C₂²×C₄	—	2	4	no	—
435	C₂²×C₄	—	2	1	no	—
436	C₂²×C₄	—	2	2	no	—
437	C₂²×C₄	—	2	8	no	—
438	C₂²×C₄	—	2	4	no	—
439	C₂²×C₄	—	2	4	no	—
440	C₂²×C₄	—	2	1	no	—
441	C₂²×C₄	—	2	1	no	—
442	C₂²×C₄	—	4	2	no	—
443	C₂²×C₄	—	4	2	no	—
444	C₂²×C₄	—	4	4	no	—
445	C₂²×C₄	—	4	4	no	—
446	C₂²×C₄	—	4	2	no	—
447	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
448	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
449	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
450	C₂²×C₄	C₂×D₄×C₁₀₁	1	4	yes	—
451	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
452	C₂²×C₄	C₂×D₄×C₁₀₁	1	4	yes	—
453	C₂²×C₄	#41×C₁₀₁	1	2	yes	—
454	C₂²×C₄	C₂⁴×C₁₀₁	1	1	yes	characteristic
455	Q₁₆	—	2	16	no	—
456	SD₁₆	—	2	16	no	—
457	SD₁₆	—	2	16	no	—
458	D₈	—	2	16	no	—
459	C₂×C₈	—	2	16	no	—
460	C₂×C₈	—	2	2	no	—
461	C₂×C₈	—	2	2	no	—
462	C₂×C₈	—	2	2	no	—
463	C₂×C₈	—	2	2	no	—
464	C₂×C₈	C₂×D₄×C₁₀₁	1	4	yes	—
465	C₂×C₈	C₂×D₄×C₁₀₁	1	4	yes	—
466	C₄⋊C₄	—	2	8	no	—
467	C₄⋊C₄	—	2	2	no	—
468	C₄⋊C₄	—	2	2	no	—
469	C₂²⋊C₄	—	2	16	no	—
470	C₂²⋊C₄	—	4	4	no	—
471	C₂²⋊C₄	—	4	2	no	—
472	C₂²⋊C₄	—	4	4	no	—
473	C₄²	—	2	4	no	—
474	C₄²	—	2	2	no	—
475	C₄²	—	2	2	no	—
476	C₄²	—	4	2	no	—
477	C₂³	—	2	2	no	—
478	C₂³	—	2	2	no	—
479	C₂³	—	2	4	no	—
480	C₂³	—	2	2	no	—
481	C₂³	—	4	1	no	—
482	C₂³	—	4	2	no	—
483	C₂³	—	4	2	no	—
484	C₂³	—	4	1	no	—
485	C₂³	—	4	2	no	—
486	C₂³	—	4	4	no	—
487	C₂³	—	4	2	no	—
488	C₂³	—	4	4	no	—
489	C₂³	#120×C₁₀₁	1	2	yes	—
490	C₂³	#121×C₁₀₁	1	2	yes	—
491	C₂³	#127×C₁₀₁	1	2	yes	—
492	C₂³	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
493	Q₈	—	2	4	no	—
494	Q₈	—	2	4	no	—
495	Q₈	—	2	4	no	—
496	Q₈	—	4	2	no	—
497	Q₈	—	4	2	no	—
498	Q₈	—	4	2	no	—
499	D₄	—	2	4	no	—
500	D₄	—	2	4	no	—
501	D₄	—	2	4	no	—
502	D₄	—	4	16	no	—
503	D₄	—	4	16	no	—
504	D₄	—	4	8	no	—
505	D₄	—	4	2	no	—
506	D₄	—	4	2	no	—
507	D₄	—	4	2	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	2	4	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	2	no	—
515	C₂×C₄	—	4	8	no	—
516	C₂×C₄	—	4	1	no	—
517	C₂×C₄	—	4	2	no	—
518	C₂×C₄	—	4	1	no	—
519	C₂×C₄	—	4	2	no	—
520	C₂×C₄	—	4	16	no	—
521	C₂×C₄	—	4	8	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	4	2	no	—
525	C₂×C₄	—	4	2	no	—
526	C₂×C₄	#120×C₁₀₁	1	8	yes	—
527	C₂×C₄	#120×C₁₀₁	1	2	yes	—
528	C₂×C₄	#121×C₁₀₁	1	8	yes	—
529	C₂×C₄	#121×C₁₀₁	1	2	yes	—
530	C₂×C₄	#127×C₁₀₁	1	2	yes	—
531	C₂×C₄	#135×C₁₀₁	1	4	yes	complemented
532	C₂×C₄	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
533	C₂×C₄	C₂²×D₄×C₁₀₁	1	2	yes	—
534	C₂×C₄	C₂²×D₄×C₁₀₁	1	2	yes	—
535	C₂×C₄	C₂×#41×C₁₀₁	1	1	yes	characteristic
536	C₈	—	2	4	no	—
537	C₈	—	2	4	no	—
538	C₂²	—	2	4	no	—
539	C₂²	—	2	4	no	—
540	C₂²	—	2	2	no	—
541	C₂²	—	2	2	no	—
542	C₂²	—	4	8	no	—
543	C₂²	—	4	4	no	—
544	C₂²	—	4	2	no	—
545	C₂²	—	4	4	no	—
546	C₂²	—	8	2	no	—
547	C₂²	—	8	4	no	—
548	C₂²	—	8	1	no	—
549	C₂²	—	8	2	no	—
550	C₂²	—	8	1	no	—
551	C₂²	—	8	2	no	—
552	C₂²	#392×C₁₀₁	1	4	yes	—
553	C₂²	C₂×#120×C₁₀₁	1	1	yes	characteristic
554	C₂²	C₂×#121×C₁₀₁	1	1	yes	characteristic
555	C₂²	C₂×#127×C₁₀₁	1	1	yes	characteristic
556	C₂²	C₂×#135×C₁₀₁	1	2	yes	—
557	C₂²	#575×C₁₀₁	1	2	yes	—
558	C₄	—	2	4	no	—
559	C₄	—	4	2	no	—
560	C₄	—	4	4	no	—
561	C₄	—	4	2	no	—
562	C₄	—	8	1	no	—
563	C₄	—	8	1	no	—
564	C₄	#392×C₁₀₁	1	4	yes	—
565	C₄	C₂×#120×C₁₀₁	1	2	yes	—
566	C₄	C₂×#121×C₁₀₁	1	2	yes	—
567	C₂	—	2	4	no	—
568	C₂	—	8	4	no	—
569	C₂	—	8	2	no	—
570	C₂	C₂×#392×C₁₀₁	1	1	yes	characteristic
571	C₂	C₁₀₁×#3002	1	2	yes	—
572	C₂	C₁₀₁×#3035	1	2	yes	—
573	C₂	C₁₀₁×#3147	1	1	yes	characteristic
574	C₂	C₁₀₁×#3150	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₀₁	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₀₁
socle	C₂³×C₁₀₁	C₂²×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₀₁ ◁ C₂²×C₄²×C₁₀₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×#135×C₁₀₁	C₂	semidirect
2. C₂×#532×C₁₀₁	C₂	semidirect
3. C₂×#416×C₁₀₁	C₂	semidirect
4. C₁₀₁×#2297	C₂	semidirect
5. C₁₀₁×#2016	C₂	semidirect
6. C₁₀₁×#2015	C₂	semidirect
7. C₁₀₁×#2014	C₂	semidirect
8. C₁₀₁×#2013	C₂	semidirect
9. C₁₀₁×#2012	C₂	semidirect
10. C₁₀₁×#2011	C₂	semidirect
11. C₂×#336×C₁₀₁	C₂	semidirect
53. C₂×#41×C₁₀₁	D₄	semidirect
80. C₂²×C₈×C₁₀₁	D₄	semidirect
243. C₂×C₄×C₁₀₁	#135	semidirect
279. #23421	C₁₀₁	direct (N × H)
288. C₂²×#135	C₂×C₁₀₁	semidirect
289. C₂×#532	C₂×C₁₀₁	semidirect
290. C₂×#416	C₂×C₁₀₁	semidirect
291. #2297	C₂×C₁₀₁	semidirect
292. #2016	C₂×C₁₀₁	semidirect
293. #2015	C₂×C₁₀₁	semidirect
294. #2014	C₂×C₁₀₁	semidirect
295. #2013	C₂×C₁₀₁	semidirect
296. #2012	C₂×C₁₀₁	semidirect
297. #2011	C₂×C₁₀₁	semidirect
298. C₂×#336	C₂×C₁₀₁	semidirect
299. C₁₀₁	#23421	direct (N × H)
341. C₂×#41	D₄×C₁₀₁	semidirect
368. C₂²×C₈	D₄×C₁₀₁	semidirect
531. C₂×C₄	#135×C₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#135×C₁₀₁	2
C₂×#532×C₁₀₁	2
C₂×#416×C₁₀₁	2
C₁₀₁×#2297	2
C₁₀₁×#2016	2
C₁₀₁×#2015	2
C₁₀₁×#2014	2
C₁₀₁×#2013	2
C₁₀₁×#2012	2
C₁₀₁×#2011	2
C₂×#336×C₁₀₁	2
#23421	101

Subgroups — C101×#23421 #38805572

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#23421 #38805572