Subgroups — C₁₀₁×#22890 #38805041

Order 25856.

1020 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#455×C₁₀₁	C₂	1	1	yes	maximal, characteristic
2	C₁₀₁×#2947	C₂	1	2	yes	maximal, complemented
3	C₁₀₁×#2897	C₂	1	2	yes	maximal
4	C₁₀₁×#1959	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₀₁×#1931	C₂	1	2	yes	maximal, complemented
6	C₁₀₁×#1908	C₂	1	2	yes	maximal, complemented
7	C₁₀₁×#1888	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₀₁×#1859	C₂	1	2	yes	maximal, complemented
9	C₁₀₁×#1765	C₂	1	2	yes	maximal, complemented
10	C₂×H(5,𝔽₂)×C₁₀₁	C₂²	1	1	yes	characteristic
11	C₂×#137×C₁₀₁	C₂²	1	2	yes	—
12	C₂×#131×C₁₀₁	C₂²	1	2	yes	—
13	C₂×#124×C₁₀₁	C₂²	1	1	yes	characteristic
14	#520×C₁₀₁	C₂²	1	2	yes	—
15	#519×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
16	#455×C₁₀₁	C₄	1	8	yes	complemented
17	#441×C₁₀₁	—	2	2	no	—
18	#440×C₁₀₁	—	2	2	no	—
19	C₄×Q₁₆×C₁₀₁	—	2	2	no	—
20	C₄×SD₁₆×C₁₀₁	—	2	2	no	—
21	#428×C₁₀₁	C₂²	1	2	yes	complemented
22	C₂×#104×C₁₀₁	C₂²	1	2	yes	—
23	#418×C₁₀₁	—	2	2	no	—
24	#418×C₁₀₁	C₂²	1	2	yes	—
25	#417×C₁₀₁	—	2	2	no	—
26	#417×C₁₀₁	C₂²	1	2	yes	—
27	#416×C₁₀₁	—	2	2	no	—
28	#416×C₁₀₁	C₂²	1	2	yes	—
29	C₂×#103×C₁₀₁	C₂²	1	2	yes	complemented
30	C₂×#102×C₁₀₁	—	2	2	no	—
31	C₂×#102×C₁₀₁	C₂²	1	2	yes	—
32	C₂×#101×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
33	C₂×#100×C₁₀₁	C₂²	1	1	yes	characteristic
34	#405×C₁₀₁	C₂²	1	2	yes	complemented
35	C₂×#97×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
36	#384×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
37	#343×C₁₀₁	C₂²	1	2	yes	complemented
38	#341×C₁₀₁	C₂²	1	2	yes	complemented
39	#339×C₁₀₁	C₂²	1	2	yes	complemented
40	H(5,𝔽₂)×C₁₀₁	—	2	4	no	—
41	H(5,𝔽₂)×C₁₀₁	—	4	1	no	—
42	H(5,𝔽₂)×C₁₀₁	C₂×C₄	1	4	yes	—
43	C₂×#41×C₁₀₁	—	2	2	no	—
44	C₂×#41×C₁₀₁	C₂³	1	2	yes	—
45	C₂²×Q₈×C₁₀₁	C₂³	1	1	yes	characteristic
46	C₂²×D₄×C₁₀₁	—	2	2	no	—
47	C₂²×D₄×C₁₀₁	—	4	1	no	—
48	C₂²×D₄×C₁₀₁	C₂³	1	1	yes	characteristic
49	#137×C₁₀₁	—	2	4	no	—
50	#137×C₁₀₁	C₂×C₄	1	8	yes	complemented
51	C₂×Q₁₆×C₁₀₁	—	2	2	no	—
52	C₂×SD₁₆×C₁₀₁	—	2	2	no	—
53	#131×C₁₀₁	—	2	4	no	—
54	#131×C₁₀₁	—	4	2	no	—
55	C₂×M₁₆×C₁₀₁	—	2	2	no	—
56	C₂×M₁₆×C₁₀₁	C₂³	1	2	yes	—
57	C₂×M₁₆×C₁₀₁	C₂³	1	2	yes	—
58	C₂²×C₈×C₁₀₁	—	2	2	no	—
59	C₂²×C₈×C₁₀₁	C₂³	1	2	yes	—
60	#124×C₁₀₁	—	4	1	no	—
61	#124×C₁₀₁	C₂×C₄	1	4	yes	complemented
62	C₄×Q₈×C₁₀₁	—	2	2	no	—
63	C₄×Q₈×C₁₀₁	—	2	2	no	—
64	C₄×Q₈×C₁₀₁	—	2	2	no	—
65	C₄×D₄×C₁₀₁	—	2	2	no	—
66	C₄×D₄×C₁₀₁	—	4	2	no	—
67	#117×C₁₀₁	—	2	2	no	—
68	#117×C₁₀₁	—	4	1	no	—
69	#117×C₁₀₁	C₂³	1	2	yes	—
70	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
71	C₂×C₄⋊C₄×C₁₀₁	—	4	1	no	—
72	C₂×C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
73	C₂×C₂²⋊C₄×C₁₀₁	—	4	1	no	—
74	C₂×C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
75	#107×C₁₀₁	—	2	2	no	—
76	#106×C₁₀₁	—	2	2	no	—
77	#104×C₁₀₁	C₂×C₄	1	8	yes	complemented
78	#103×C₁₀₁	—	2	2	no	—
79	#103×C₁₀₁	—	2	2	no	—
80	#103×C₁₀₁	—	2	2	no	—
81	#103×C₁₀₁	D₄	1	2	yes	—
82	#103×C₁₀₁	D₄	1	2	yes	—
83	#102×C₁₀₁	—	2	2	no	—
84	#102×C₁₀₁	—	2	2	no	—
85	#102×C₁₀₁	—	2	2	no	—
86	#102×C₁₀₁	—	2	2	no	—
87	#102×C₁₀₁	—	2	2	no	—
88	#102×C₁₀₁	D₄	1	2	yes	—
89	#102×C₁₀₁	D₄	1	2	yes	—
90	#101×C₁₀₁	—	4	1	no	—
91	#100×C₁₀₁	C₂×C₄	1	4	yes	complemented
92	#97×C₁₀₁	—	2	2	no	—
93	#97×C₁₀₁	—	4	1	no	—
94	C₄×C₈×C₁₀₁	—	2	2	no	—
95	C₂⁴×C₁₀₁	—	2	1	no	—
96	C₂⁴×C₁₀₁	—	4	1	no	—
97	#41×C₁₀₁	—	2	2	no	—
98	#41×C₁₀₁	—	2	2	no	—
99	#41×C₁₀₁	—	2	8	no	—
100	#41×C₁₀₁	—	4	4	no	—
101	#41×C₁₀₁	C₂²×C₄	1	4	yes	—
102	#41×C₁₀₁	#41	1	4	yes	—
103	C₂×Q₈×C₁₀₁	—	2	1	no	—
104	C₂×Q₈×C₁₀₁	—	2	2	no	—
105	C₂×Q₈×C₁₀₁	—	2	2	no	—
106	C₂×Q₈×C₁₀₁	C₂²×C₄	1	2	yes	—
107	C₂×Q₈×C₁₀₁	C₂×D₄	1	2	yes	—
108	C₂×D₄×C₁₀₁	—	2	2	no	—
109	C₂×D₄×C₁₀₁	—	2	8	no	—
110	C₂×D₄×C₁₀₁	—	2	2	no	—
111	C₂×D₄×C₁₀₁	—	2	2	no	—
112	C₂×D₄×C₁₀₁	—	2	1	no	—
113	C₂×D₄×C₁₀₁	—	4	4	no	—
114	C₂×D₄×C₁₀₁	—	4	2	no	—
115	C₂×D₄×C₁₀₁	—	4	4	no	—
116	C₂×D₄×C₁₀₁	—	4	4	no	—
117	C₂×D₄×C₁₀₁	C₂²×C₄	1	2	yes	—
118	C₂×D₄×C₁₀₁	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₁₀₁	—	2	2	no	—
120	C₂²×C₄×C₁₀₁	—	2	1	no	—
121	C₂²×C₄×C₁₀₁	—	2	1	no	—
122	C₂²×C₄×C₁₀₁	—	2	2	no	—
123	C₂²×C₄×C₁₀₁	—	4	1	no	—
124	C₂²×C₄×C₁₀₁	—	4	2	no	—
125	C₂²×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
126	Q₁₆×C₁₀₁	—	2	8	no	—
127	SD₁₆×C₁₀₁	—	2	8	no	—
128	M₁₆×C₁₀₁	—	2	2	no	—
129	M₁₆×C₁₀₁	—	2	2	no	—
130	M₁₆×C₁₀₁	—	2	2	no	—
131	M₁₆×C₁₀₁	—	4	4	no	—
132	M₁₆×C₁₀₁	C₂²×C₄	1	4	yes	—
133	C₂×C₈×C₁₀₁	—	2	2	no	—
134	C₂×C₈×C₁₀₁	—	2	2	no	—
135	C₂×C₈×C₁₀₁	—	2	2	no	—
136	C₂×C₈×C₁₀₁	—	2	2	no	—
137	C₂×C₈×C₁₀₁	—	4	4	no	—
138	C₂×C₈×C₁₀₁	C₂×D₄	1	2	yes	—
139	C₂×C₈×C₁₀₁	C₂×D₄	1	2	yes	—
140	C₄⋊C₄×C₁₀₁	—	2	2	no	—
141	C₄⋊C₄×C₁₀₁	—	2	2	no	—
142	C₄⋊C₄×C₁₀₁	—	4	2	no	—
143	C₄⋊C₄×C₁₀₁	—	4	1	no	—
144	C₄⋊C₄×C₁₀₁	—	4	1	no	—
145	C₄⋊C₄×C₁₀₁	—	8	2	no	—
146	C₄⋊C₄×C₁₀₁	C₂×D₄	1	2	yes	—
147	C₄⋊C₄×C₁₀₁	C₂×D₄	1	2	yes	—
148	C₂²⋊C₄×C₁₀₁	—	2	2	no	—
149	C₂²⋊C₄×C₁₀₁	—	4	4	no	—
150	C₂²⋊C₄×C₁₀₁	—	4	2	no	—
151	C₄²×C₁₀₁	—	2	2	no	—
152	C₄²×C₁₀₁	—	2	1	no	—
153	C₄²×C₁₀₁	—	4	2	no	—
154	C₄²×C₁₀₁	—	4	2	no	—
155	C₄²×C₁₀₁	C₂²×C₄	1	2	yes	—
156	C₂³×C₁₀₁	—	2	2	no	—
157	C₂³×C₁₀₁	—	2	2	no	—
158	C₂³×C₁₀₁	—	4	4	no	—
159	C₂³×C₁₀₁	—	4	1	no	—
160	C₂³×C₁₀₁	—	4	1	no	—
161	C₂³×C₁₀₁	—	8	1	no	—
162	C₂³×C₁₀₁	—	8	1	no	—
163	C₂³×C₁₀₁	—	16	1	no	—
164	C₂³×C₁₀₁	—	16	1	no	—
165	C₂³×C₁₀₁	H(5,𝔽₂)	1	1	yes	characteristic
166	Q₈×C₁₀₁	—	2	2	no	—
167	Q₈×C₁₀₁	—	2	4	no	—
168	Q₈×C₁₀₁	—	4	2	no	—
169	Q₈×C₁₀₁	C₄×D₄	1	4	yes	—
170	D₄×C₁₀₁	—	2	4	no	—
171	D₄×C₁₀₁	—	2	4	no	—
172	D₄×C₁₀₁	—	2	4	no	—
173	D₄×C₁₀₁	—	2	2	no	—
174	D₄×C₁₀₁	—	4	8	no	—
175	D₄×C₁₀₁	—	4	2	no	—
176	D₄×C₁₀₁	C₄×D₄	1	4	yes	—
177	C₂×C₄×C₁₀₁	—	2	2	no	—
178	C₂×C₄×C₁₀₁	—	2	4	no	—
179	C₂×C₄×C₁₀₁	—	2	4	no	—
180	C₂×C₄×C₁₀₁	—	2	2	no	—
181	C₂×C₄×C₁₀₁	—	2	2	no	—
182	C₂×C₄×C₁₀₁	—	2	2	no	—
183	C₂×C₄×C₁₀₁	—	2	2	no	—
184	C₂×C₄×C₁₀₁	—	4	4	no	—
185	C₂×C₄×C₁₀₁	—	4	1	no	—
186	C₂×C₄×C₁₀₁	—	4	1	no	—
187	C₂×C₄×C₁₀₁	—	4	1	no	—
188	C₂×C₄×C₁₀₁	—	4	1	no	—
189	C₂×C₄×C₁₀₁	—	4	2	no	—
190	C₂×C₄×C₁₀₁	—	8	2	no	—
191	C₂×C₄×C₁₀₁	—	16	2	no	—
192	C₂×C₄×C₁₀₁	C₂³×C₄	1	1	yes	characteristic
193	C₂×C₄×C₁₀₁	C₂²×D₄	1	2	yes	—
194	C₂×C₄×C₁₀₁	C₂×#41	1	2	yes	—
195	C₂×C₄×C₁₀₁	H(5,𝔽₂)	1	1	yes	characteristic
196	C₈×C₁₀₁	—	2	4	no	—
197	C₈×C₁₀₁	—	2	2	no	—
198	C₈×C₁₀₁	—	2	2	no	—
199	C₈×C₁₀₁	—	4	2	no	—
200	C₂²×C₁₀₁	—	2	1	no	—
201	C₂²×C₁₀₁	—	2	1	no	—
202	C₂²×C₁₀₁	—	2	4	no	—
203	C₂²×C₁₀₁	—	4	2	no	—
204	C₂²×C₁₀₁	—	4	2	no	—
205	C₂²×C₁₀₁	—	4	2	no	—
206	C₂²×C₁₀₁	—	8	2	no	—
207	C₂²×C₁₀₁	—	8	1	no	—
208	C₂²×C₁₀₁	—	8	1	no	—
209	C₂²×C₁₀₁	—	16	1	no	—
210	C₂²×C₁₀₁	—	16	4	no	—
211	C₂²×C₁₀₁	#518	1	1	yes	characteristic
212	C₂²×C₁₀₁	D₄²	1	1	yes	characteristic
213	C₂²×C₁₀₁	#551	1	1	yes	characteristic
214	C₄×C₁₀₁	—	2	4	no	—
215	C₄×C₁₀₁	—	4	2	no	—
216	C₄×C₁₀₁	—	4	2	no	—
217	C₄×C₁₀₁	—	4	2	no	—
218	C₄×C₁₀₁	—	4	2	no	—
219	C₄×C₁₀₁	—	8	2	no	—
220	C₄×C₁₀₁	C₂×C₄×D₄	1	2	yes	—
221	C₄×C₁₀₁	#546	1	2	yes	—
222	#22890	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
223	C₂×C₁₀₁	—	2	1	no	—
224	C₂×C₁₀₁	—	2	1	no	—
225	C₂×C₁₀₁	—	4	4	no	—
226	C₂×C₁₀₁	—	8	2	no	—
227	C₂×C₁₀₁	#2358	1	1	yes	characteristic
228	C₂×C₁₀₁	#3288	1	1	yes	characteristic
229	C₂×C₁₀₁	#3289	1	1	yes	characteristic
230	C₂×#455	C₂×C₁₀₁	1	1	yes	characteristic
231	#2947	C₂×C₁₀₁	1	2	yes	complemented
232	#2897	C₂×C₁₀₁	1	2	yes	—
233	#1959	C₂×C₁₀₁	1	1	yes	characteristic, complemented
234	#1931	C₂×C₁₀₁	1	2	yes	complemented
235	#1908	C₂×C₁₀₁	1	2	yes	complemented
236	#1888	C₂×C₁₀₁	1	1	yes	characteristic, complemented
237	#1859	C₂×C₁₀₁	1	2	yes	complemented
238	#1765	C₂×C₁₀₁	1	2	yes	complemented
239	C₁₀₁	#22890	1	1	yes	characteristic, direct product factor, Sylow
240	C₂×H(5,𝔽₂)	C₂²×C₁₀₁	1	1	yes	characteristic
241	C₂×#137	C₂²×C₁₀₁	1	2	yes	—
242	C₂×#131	C₂²×C₁₀₁	1	2	yes	—
243	C₂×#124	C₂²×C₁₀₁	1	1	yes	characteristic
244	#520	C₂²×C₁₀₁	1	2	yes	—
245	#519	C₂²×C₁₀₁	1	1	yes	characteristic, complemented
246	#455	C₄×C₁₀₁	1	8	yes	complemented
247	#441	—	2	2	no	—
248	#440	—	2	2	no	—
249	C₄×Q₁₆	—	2	2	no	—
250	C₄×SD₁₆	—	2	2	no	—
251	#428	C₂²×C₁₀₁	1	2	yes	complemented
252	C₂×#104	C₂²×C₁₀₁	1	2	yes	—
253	#418	—	2	2	no	—
254	#418	C₂²×C₁₀₁	1	2	yes	—
255	#417	—	2	2	no	—
256	#417	C₂²×C₁₀₁	1	2	yes	—
257	#416	—	2	2	no	—
258	#416	C₂²×C₁₀₁	1	2	yes	—
259	C₂×#103	C₂²×C₁₀₁	1	2	yes	complemented
260	C₂×#102	—	2	2	no	—
261	C₂×#102	C₂²×C₁₀₁	1	2	yes	—
262	C₂×#101	C₂²×C₁₀₁	1	1	yes	characteristic, complemented
263	C₂×#100	C₂²×C₁₀₁	1	1	yes	characteristic
264	#405	C₂²×C₁₀₁	1	2	yes	complemented
265	C₂×#97	C₂²×C₁₀₁	1	1	yes	characteristic, complemented
266	#384	C₂²×C₁₀₁	1	1	yes	characteristic, complemented
267	#343	C₂²×C₁₀₁	1	2	yes	complemented
268	#341	C₂²×C₁₀₁	1	2	yes	complemented
269	#339	C₂²×C₁₀₁	1	2	yes	complemented
270	H(5,𝔽₂)	—	2	4	no	—
271	H(5,𝔽₂)	—	4	1	no	—
272	H(5,𝔽₂)	C₂×C₄×C₁₀₁	1	4	yes	—
273	C₂×#41	—	2	2	no	—
274	C₂×#41	C₂³×C₁₀₁	1	2	yes	—
275	C₂²×Q₈	C₂³×C₁₀₁	1	1	yes	characteristic
276	C₂²×D₄	—	2	2	no	—
277	C₂²×D₄	—	4	1	no	—
278	C₂²×D₄	C₂³×C₁₀₁	1	1	yes	characteristic
279	#137	—	2	4	no	—
280	#137	C₂×C₄×C₁₀₁	1	8	yes	complemented
281	C₂×Q₁₆	—	2	2	no	—
282	C₂×SD₁₆	—	2	2	no	—
283	#131	—	2	4	no	—
284	#131	—	4	2	no	—
285	C₂×M₁₆	—	2	2	no	—
286	C₂×M₁₆	C₂³×C₁₀₁	1	2	yes	—
287	C₂×M₁₆	C₂³×C₁₀₁	1	2	yes	—
288	C₂²×C₈	—	2	2	no	—
289	C₂²×C₈	C₂³×C₁₀₁	1	2	yes	—
290	#124	—	4	1	no	—
291	#124	C₂×C₄×C₁₀₁	1	4	yes	complemented
292	C₄×Q₈	—	2	2	no	—
293	C₄×Q₈	—	2	2	no	—
294	C₄×Q₈	—	2	2	no	—
295	C₄×D₄	—	2	2	no	—
296	C₄×D₄	—	4	2	no	—
297	#117	—	2	2	no	—
298	#117	—	4	1	no	—
299	#117	C₂³×C₁₀₁	1	2	yes	—
300	C₂×C₄⋊C₄	—	2	2	no	—
301	C₂×C₄⋊C₄	—	4	1	no	—
302	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	2	yes	—
303	C₂×C₂²⋊C₄	—	4	1	no	—
304	C₂×C₄²	C₂³×C₁₀₁	1	1	yes	characteristic
305	#107	—	2	2	no	—
306	#106	—	2	2	no	—
307	#104	C₂×C₄×C₁₀₁	1	8	yes	complemented
308	#103	—	2	2	no	—
309	#103	—	2	2	no	—
310	#103	—	2	2	no	—
311	#103	D₄×C₁₀₁	1	2	yes	—
312	#103	D₄×C₁₀₁	1	2	yes	—
313	#102	—	2	2	no	—
314	#102	—	2	2	no	—
315	#102	—	2	2	no	—
316	#102	—	2	2	no	—
317	#102	—	2	2	no	—
318	#102	D₄×C₁₀₁	1	2	yes	—
319	#102	D₄×C₁₀₁	1	2	yes	—
320	#101	—	4	1	no	—
321	#100	C₂×C₄×C₁₀₁	1	4	yes	complemented
322	#97	—	2	2	no	—
323	#97	—	4	1	no	—
324	C₄×C₈	—	2	2	no	—
325	C₂⁴	—	2	1	no	—
326	C₂⁴	—	4	1	no	—
327	#41	—	2	2	no	—
328	#41	—	2	2	no	—
329	#41	—	2	8	no	—
330	#41	—	4	4	no	—
331	#41	C₂²×C₄×C₁₀₁	1	4	yes	—
332	#41	#41×C₁₀₁	1	4	yes	—
333	C₂×Q₈	—	2	1	no	—
334	C₂×Q₈	—	2	2	no	—
335	C₂×Q₈	—	2	2	no	—
336	C₂×Q₈	C₂²×C₄×C₁₀₁	1	2	yes	—
337	C₂×Q₈	C₂×D₄×C₁₀₁	1	2	yes	—
338	C₂×D₄	—	2	2	no	—
339	C₂×D₄	—	2	8	no	—
340	C₂×D₄	—	2	2	no	—
341	C₂×D₄	—	2	2	no	—
342	C₂×D₄	—	2	1	no	—
343	C₂×D₄	—	4	4	no	—
344	C₂×D₄	—	4	2	no	—
345	C₂×D₄	—	4	4	no	—
346	C₂×D₄	—	4	4	no	—
347	C₂×D₄	C₂²×C₄×C₁₀₁	1	2	yes	—
348	C₂×D₄	C₂×D₄×C₁₀₁	1	2	yes	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	1	no	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	4	1	no	—
354	C₂²×C₄	—	4	2	no	—
355	C₂²×C₄	C₂⁴×C₁₀₁	1	1	yes	characteristic
356	Q₁₆	—	2	8	no	—
357	SD₁₆	—	2	8	no	—
358	M₁₆	—	2	2	no	—
359	M₁₆	—	2	2	no	—
360	M₁₆	—	2	2	no	—
361	M₁₆	—	4	4	no	—
362	M₁₆	C₂²×C₄×C₁₀₁	1	4	yes	—
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	4	4	no	—
368	C₂×C₈	C₂×D₄×C₁₀₁	1	2	yes	—
369	C₂×C₈	C₂×D₄×C₁₀₁	1	2	yes	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	4	2	no	—
373	C₄⋊C₄	—	4	1	no	—
374	C₄⋊C₄	—	4	1	no	—
375	C₄⋊C₄	—	8	2	no	—
376	C₄⋊C₄	C₂×D₄×C₁₀₁	1	2	yes	—
377	C₄⋊C₄	C₂×D₄×C₁₀₁	1	2	yes	—
378	C₂²⋊C₄	—	2	2	no	—
379	C₂²⋊C₄	—	4	4	no	—
380	C₂²⋊C₄	—	4	2	no	—
381	C₄²	—	2	2	no	—
382	C₄²	—	2	1	no	—
383	C₄²	—	4	2	no	—
384	C₄²	—	4	2	no	—
385	C₄²	C₂²×C₄×C₁₀₁	1	2	yes	—
386	C₂³	—	2	2	no	—
387	C₂³	—	2	2	no	—
388	C₂³	—	4	4	no	—
389	C₂³	—	4	1	no	—
390	C₂³	—	4	1	no	—
391	C₂³	—	8	1	no	—
392	C₂³	—	8	1	no	—
393	C₂³	—	16	1	no	—
394	C₂³	—	16	1	no	—
395	C₂³	H(5,𝔽₂)×C₁₀₁	1	1	yes	characteristic
396	Q₈	—	2	2	no	—
397	Q₈	—	2	4	no	—
398	Q₈	—	4	2	no	—
399	Q₈	C₄×D₄×C₁₀₁	1	4	yes	—
400	D₄	—	2	4	no	—
401	D₄	—	2	4	no	—
402	D₄	—	2	4	no	—
403	D₄	—	2	2	no	—
404	D₄	—	4	8	no	—
405	D₄	—	4	2	no	—
406	D₄	C₄×D₄×C₁₀₁	1	4	yes	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	4	4	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	4	1	no	—
418	C₂×C₄	—	4	1	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	8	2	no	—
421	C₂×C₄	—	16	2	no	—
422	C₂×C₄	C₂³×C₄×C₁₀₁	1	1	yes	characteristic
423	C₂×C₄	C₂²×D₄×C₁₀₁	1	2	yes	—
424	C₂×C₄	C₂×#41×C₁₀₁	1	2	yes	—
425	C₂×C₄	H(5,𝔽₂)×C₁₀₁	1	1	yes	characteristic
426	C₈	—	2	4	no	—
427	C₈	—	2	2	no	—
428	C₈	—	2	2	no	—
429	C₈	—	4	2	no	—
430	C₂²	—	2	1	no	—
431	C₂²	—	2	1	no	—
432	C₂²	—	2	4	no	—
433	C₂²	—	4	2	no	—
434	C₂²	—	4	2	no	—
435	C₂²	—	4	2	no	—
436	C₂²	—	8	2	no	—
437	C₂²	—	8	1	no	—
438	C₂²	—	8	1	no	—
439	C₂²	—	16	1	no	—
440	C₂²	—	16	4	no	—
441	C₂²	#518×C₁₀₁	1	1	yes	characteristic
442	C₂²	D₄²×C₁₀₁	1	1	yes	characteristic
443	C₂²	#551×C₁₀₁	1	1	yes	characteristic
444	C₄	—	2	4	no	—
445	C₄	—	4	2	no	—
446	C₄	—	4	2	no	—
447	C₄	—	4	2	no	—
448	C₄	—	4	2	no	—
449	C₄	—	8	2	no	—
450	C₄	C₂×C₄×D₄×C₁₀₁	1	2	yes	—
451	C₄	#546×C₁₀₁	1	2	yes	—
452	C₂	—	2	1	no	—
453	C₂	—	2	1	no	—
454	C₂	—	4	4	no	—
455	C₂	—	8	2	no	—
456	C₂	C₁₀₁×#2358	1	1	yes	characteristic
457	C₂	C₁₀₁×#3288	1	1	yes	characteristic
458	C₂	C₁₀₁×#3289	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₀₁	D₄²
commutator	C₂×C₄	C₂³×C₄×C₁₀₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₀₁
prime radical	C₂×H(5,𝔽₂)×C₁₀₁	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₁ ◁ C₂²×C₄×C₁₀₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₀₁×#2947	C₂	semidirect
4. C₁₀₁×#1959	C₂	semidirect
5. C₁₀₁×#1931	C₂	semidirect
6. C₁₀₁×#1908	C₂	semidirect
7. C₁₀₁×#1888	C₂	semidirect
8. C₁₀₁×#1859	C₂	semidirect
9. C₁₀₁×#1765	C₂	semidirect
15. #519×C₁₀₁	C₂²	semidirect
16. #455×C₁₀₁	C₄	semidirect
21. #428×C₁₀₁	C₂²	semidirect
29. C₂×#103×C₁₀₁	C₂²	semidirect
32. C₂×#101×C₁₀₁	C₂²	semidirect
34. #405×C₁₀₁	C₂²	semidirect
35. C₂×#97×C₁₀₁	C₂²	semidirect
36. #384×C₁₀₁	C₂²	semidirect
37. #343×C₁₀₁	C₂²	semidirect
38. #341×C₁₀₁	C₂²	semidirect
39. #339×C₁₀₁	C₂²	semidirect
50. #137×C₁₀₁	C₂×C₄	semidirect
61. #124×C₁₀₁	C₂×C₄	semidirect
77. #104×C₁₀₁	C₂×C₄	semidirect
91. #100×C₁₀₁	C₂×C₄	semidirect
222. #22890	C₁₀₁	direct (N × H)
231. #2947	C₂×C₁₀₁	semidirect
233. #1959	C₂×C₁₀₁	semidirect
234. #1931	C₂×C₁₀₁	semidirect
235. #1908	C₂×C₁₀₁	semidirect
236. #1888	C₂×C₁₀₁	semidirect
237. #1859	C₂×C₁₀₁	semidirect
238. #1765	C₂×C₁₀₁	semidirect
239. C₁₀₁	#22890	direct (N × H)
245. #519	C₂²×C₁₀₁	semidirect
246. #455	C₄×C₁₀₁	semidirect
251. #428	C₂²×C₁₀₁	semidirect
259. C₂×#103	C₂²×C₁₀₁	semidirect
262. C₂×#101	C₂²×C₁₀₁	semidirect
264. #405	C₂²×C₁₀₁	semidirect
265. C₂×#97	C₂²×C₁₀₁	semidirect
266. #384	C₂²×C₁₀₁	semidirect
267. #343	C₂²×C₁₀₁	semidirect
268. #341	C₂²×C₁₀₁	semidirect
269. #339	C₂²×C₁₀₁	semidirect
280. #137	C₂×C₄×C₁₀₁	semidirect
291. #124	C₂×C₄×C₁₀₁	semidirect
307. #104	C₂×C₄×C₁₀₁	semidirect
321. #100	C₂×C₄×C₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#455×C₁₀₁	2
C₁₀₁×#2947	2
C₁₀₁×#2897	2
C₁₀₁×#1959	2
C₁₀₁×#1931	2
C₁₀₁×#1908	2
C₁₀₁×#1888	2
C₁₀₁×#1859	2
C₁₀₁×#1765	2
#22890	101

Subgroups — C101×#22890 #38805041

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#22890 #38805041