Subgroups — C₁₀₁×#24420 #38806571

Order 25856.

1326 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₀₁×#3585	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₀₁×#3068	C₂	1	2	yes	maximal, complemented
3	C₁₀₁×#3021	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₀₁×#3008	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₀₁×#2888	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₀₁×#2048	C₂	1	2	yes	maximal, complemented
7	C₁₀₁×#2018	C₂	1	2	yes	maximal, complemented
8	C₁₀₁×#1914	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₀₁×#1881	C₂	1	2	yes	maximal, complemented
10	C₁₀₁×#1858	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₀₁×#1791	C₂	1	1	yes	maximal, characteristic, complemented
12	#585×C₁₀₁	C₂²	1	1	yes	characteristic
13	C₂×H(5,𝔽₂)×C₁₀₁	C₂²	1	1	yes	characteristic
14	#577×C₁₀₁	—	2	4	no	—
15	#576×C₁₀₁	—	2	4	no	—
16	#575×C₁₀₁	—	2	2	no	—
17	#575×C₁₀₁	C₂²	1	2	yes	—
18	C₂×AGL(1,ℤ/8)×C₁₀₁	—	2	2	no	—
19	C₂×AGL(1,ℤ/8)×C₁₀₁	C₂²	1	2	yes	—
20	C₂×AGL(1,ℤ/8)×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
21	C₂×AGL(1,ℤ/8)×C₁₀₁	C₂²	1	2	yes	complemented
22	C₂²×D₈×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
23	#568×C₁₀₁	C₂²	1	1	yes	characteristic
24	#568×C₁₀₁	C₂²	1	2	yes	complemented
25	#535×C₁₀₁	C₂²	1	1	yes	characteristic
26	#472×C₁₀₁	—	2	4	no	—
27	#471×C₁₀₁	—	2	4	no	—
28	#454×C₁₀₁	—	2	2	no	—
29	#453×C₁₀₁	—	2	2	no	—
30	#449×C₁₀₁	—	2	2	no	—
31	#447×C₁₀₁	—	2	2	no	—
32	#430×C₁₀₁	C₂²	1	2	yes	complemented
33	#421×C₁₀₁	C₂²	1	2	yes	complemented
34	#418×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
35	#416×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
36	#413×C₁₀₁	—	2	2	no	—
37	#413×C₁₀₁	C₂²	1	1	yes	characteristic
38	#413×C₁₀₁	C₂²	1	1	yes	characteristic
39	#413×C₁₀₁	C₂²	1	2	yes	complemented
40	C₂×#100×C₁₀₁	—	2	2	no	—
41	C₂×#100×C₁₀₁	C₂²	1	2	yes	complemented
42	C₂×#100×C₁₀₁	C₂²	1	2	yes	complemented
43	#408×C₁₀₁	C₂²	1	1	yes	characteristic
44	#408×C₁₀₁	C₂²	1	2	yes	complemented
45	#344×C₁₀₁	C₂²	1	2	yes	complemented
46	#341×C₁₀₁	C₂²	1	2	yes	complemented
47	2₋¹⁺⁴×C₁₀₁	—	2	2	no	—
48	2₋¹⁺⁴×C₁₀₁	—	2	1	no	—
49	H(5,𝔽₂)×C₁₀₁	—	2	4	no	—
50	H(5,𝔽₂)×C₁₀₁	—	2	2	no	—
51	H(5,𝔽₂)×C₁₀₁	—	2	2	no	—
52	H(5,𝔽₂)×C₁₀₁	—	2	1	no	—
53	H(5,𝔽₂)×C₁₀₁	—	4	2	no	—
54	C₂×#41×C₁₀₁	—	2	1	no	—
55	C₂×#41×C₁₀₁	—	2	2	no	—
56	C₂×#41×C₁₀₁	—	4	2	no	—
57	C₂×#41×C₁₀₁	D₄	1	2	yes	—
58	C₂×#41×C₁₀₁	C₂³	1	2	yes	—
59	C₂×#41×C₁₀₁	C₂³	1	1	yes	characteristic
60	C₂×#41×C₁₀₁	C₂³	1	1	yes	characteristic
61	C₂²×D₄×C₁₀₁	—	2	1	no	—
62	C₂²×D₄×C₁₀₁	—	2	2	no	—
63	C₂²×D₄×C₁₀₁	D₄	1	2	yes	—
64	C₂²×D₄×C₁₀₁	C₂³	1	1	yes	characteristic
65	C₂²×D₄×C₁₀₁	C₂³	1	1	yes	characteristic
66	#137×C₁₀₁	—	2	4	no	—
67	#137×C₁₀₁	—	2	2	no	—
68	#137×C₁₀₁	D₄	1	4	yes	complemented
69	AGL(1,ℤ/8)×C₁₀₁	—	2	8	no	—
70	AGL(1,ℤ/8)×C₁₀₁	—	2	4	no	—
71	AGL(1,ℤ/8)×C₁₀₁	—	2	2	no	—
72	AGL(1,ℤ/8)×C₁₀₁	—	2	4	no	—
73	AGL(1,ℤ/8)×C₁₀₁	—	2	4	no	—
74	AGL(1,ℤ/8)×C₁₀₁	—	2	4	no	—
75	AGL(1,ℤ/8)×C₁₀₁	—	2	4	no	—
76	AGL(1,ℤ/8)×C₁₀₁	—	4	2	no	—
77	AGL(1,ℤ/8)×C₁₀₁	D₄	1	4	yes	complemented
78	#135×C₁₀₁	—	2	8	no	—
79	#135×C₁₀₁	—	2	4	no	—
80	C₂×SD₁₆×C₁₀₁	—	2	4	no	—
81	C₂×SD₁₆×C₁₀₁	—	2	2	no	—
82	C₂×SD₁₆×C₁₀₁	—	2	1	no	—
83	C₂×SD₁₆×C₁₀₁	—	2	2	no	—
84	C₂×D₈×C₁₀₁	—	2	4	no	—
85	C₂×D₈×C₁₀₁	—	2	2	no	—
86	C₂×D₈×C₁₀₁	—	2	1	no	—
87	C₂×D₈×C₁₀₁	—	2	2	no	—
88	C₂×D₈×C₁₀₁	—	2	2	no	—
89	C₂×D₈×C₁₀₁	—	4	2	no	—
90	#131×C₁₀₁	—	2	4	no	—
91	#131×C₁₀₁	—	2	4	no	—
92	#131×C₁₀₁	—	4	2	no	—
93	C₂×M₁₆×C₁₀₁	—	2	2	no	—
94	C₂×M₁₆×C₁₀₁	—	2	4	no	—
95	C₂×M₁₆×C₁₀₁	C₂³	1	1	yes	characteristic
96	C₂×M₁₆×C₁₀₁	C₂³	1	2	yes	—
97	C₂×M₁₆×C₁₀₁	C₂³	1	2	yes	—
98	C₂×M₁₆×C₁₀₁	C₂³	1	2	yes	—
99	C₂²×C₈×C₁₀₁	C₂³	1	1	yes	characteristic
100	#127×C₁₀₁	—	2	1	no	—
101	#124×C₁₀₁	—	2	1	no	—
102	#121×C₁₀₁	—	2	2	no	—
103	#120×C₁₀₁	—	2	2	no	—
104	#117×C₁₀₁	C₂³	1	1	yes	characteristic
105	#108×C₁₀₁	—	2	4	no	—
106	#104×C₁₀₁	—	2	4	no	—
107	#103×C₁₀₁	—	2	1	no	—
108	#102×C₁₀₁	—	2	1	no	—
109	#102×C₁₀₁	—	2	2	no	—
110	#101×C₁₀₁	—	2	1	no	—
111	#101×C₁₀₁	—	2	2	no	—
112	#101×C₁₀₁	D₄	1	2	yes	—
113	#100×C₁₀₁	—	2	1	no	—
114	#100×C₁₀₁	—	2	2	no	—
115	#100×C₁₀₁	—	2	4	no	—
116	#100×C₁₀₁	—	2	4	no	—
117	#100×C₁₀₁	D₄	1	2	yes	—
118	C₂²⋊C₈×C₁₀₁	—	2	2	no	—
119	C₂²⋊C₈×C₁₀₁	—	4	2	no	—
120	C₂⁴×C₁₀₁	—	2	2	no	—
121	C₂⁴×C₁₀₁	—	2	1	no	—
122	C₂⁴×C₁₀₁	—	2	1	no	—
123	#41×C₁₀₁	—	2	2	no	—
124	#41×C₁₀₁	—	2	2	no	—
125	#41×C₁₀₁	—	2	2	no	—
126	#41×C₁₀₁	—	2	4	no	—
127	#41×C₁₀₁	—	2	4	no	—
128	#41×C₁₀₁	—	2	2	no	—
129	#41×C₁₀₁	—	2	2	no	—
130	#41×C₁₀₁	—	2	2	no	—
131	#41×C₁₀₁	—	2	2	no	—
132	#41×C₁₀₁	—	4	2	no	—
133	#41×C₁₀₁	—	4	4	no	—
134	#41×C₁₀₁	—	4	4	no	—
135	#41×C₁₀₁	—	4	2	no	—
136	#41×C₁₀₁	—	4	2	no	—
137	#41×C₁₀₁	—	4	2	no	—
138	#41×C₁₀₁	—	4	2	no	—
139	#41×C₁₀₁	C₂×D₄	1	4	yes	—
140	C₂×Q₈×C₁₀₁	—	2	2	no	—
141	C₂×Q₈×C₁₀₁	—	4	2	no	—
142	C₂×Q₈×C₁₀₁	C₂×D₄	1	2	yes	—
143	C₂×Q₈×C₁₀₁	C₂×D₄	1	1	yes	characteristic
144	C₂×Q₈×C₁₀₁	C₂×D₄	1	1	yes	characteristic
145	C₂×D₄×C₁₀₁	—	2	1	no	—
146	C₂×D₄×C₁₀₁	—	2	2	no	—
147	C₂×D₄×C₁₀₁	—	2	4	no	—
148	C₂×D₄×C₁₀₁	—	2	2	no	—
149	C₂×D₄×C₁₀₁	—	2	2	no	—
150	C₂×D₄×C₁₀₁	—	2	2	no	—
151	C₂×D₄×C₁₀₁	—	2	2	no	—
152	C₂×D₄×C₁₀₁	—	2	1	no	—
153	C₂×D₄×C₁₀₁	—	2	2	no	—
154	C₂×D₄×C₁₀₁	—	2	1	no	—
155	C₂×D₄×C₁₀₁	—	2	1	no	—
156	C₂×D₄×C₁₀₁	—	2	2	no	—
157	C₂×D₄×C₁₀₁	—	2	2	no	—
158	C₂×D₄×C₁₀₁	—	4	2	no	—
159	C₂×D₄×C₁₀₁	—	4	4	no	—
160	C₂×D₄×C₁₀₁	—	4	8	no	—
161	C₂×D₄×C₁₀₁	—	4	2	no	—
162	C₂×D₄×C₁₀₁	—	4	4	no	—
163	C₂×D₄×C₁₀₁	—	4	2	no	—
164	C₂×D₄×C₁₀₁	—	4	2	no	—
165	C₂×D₄×C₁₀₁	C₂×D₄	1	2	yes	—
166	C₂×D₄×C₁₀₁	C₂×D₄	1	2	yes	—
167	C₂×D₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
168	C₂×D₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
169	C₂×D₄×C₁₀₁	#41	1	2	yes	—
170	C₂²×C₄×C₁₀₁	—	2	1	no	—
171	C₂²×C₄×C₁₀₁	—	2	2	no	—
172	C₂²×C₄×C₁₀₁	—	2	2	no	—
173	C₂²×C₄×C₁₀₁	—	4	2	no	—
174	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
175	C₂²×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
176	Q₁₆×C₁₀₁	—	2	4	no	—
177	SD₁₆×C₁₀₁	—	2	8	no	—
178	SD₁₆×C₁₀₁	—	2	4	no	—
179	SD₁₆×C₁₀₁	—	2	4	no	—
180	SD₁₆×C₁₀₁	—	4	4	no	—
181	SD₁₆×C₁₀₁	—	4	2	no	—
182	D₈×C₁₀₁	—	2	8	no	—
183	D₈×C₁₀₁	—	2	4	no	—
184	D₈×C₁₀₁	—	4	4	no	—
185	D₈×C₁₀₁	—	4	4	no	—
186	D₈×C₁₀₁	—	4	2	no	—
187	M₁₆×C₁₀₁	—	2	4	no	—
188	M₁₆×C₁₀₁	—	2	2	no	—
189	M₁₆×C₁₀₁	—	2	2	no	—
190	M₁₆×C₁₀₁	—	2	2	no	—
191	M₁₆×C₁₀₁	—	2	2	no	—
192	M₁₆×C₁₀₁	—	2	2	no	—
193	M₁₆×C₁₀₁	—	4	4	no	—
194	M₁₆×C₁₀₁	C₂×D₄	1	4	yes	—
195	M₁₆×C₁₀₁	C₂×D₄	1	4	yes	—
196	C₂×C₈×C₁₀₁	—	2	4	no	—
197	C₂×C₈×C₁₀₁	—	2	2	no	—
198	C₂×C₈×C₁₀₁	—	2	2	no	—
199	C₂×C₈×C₁₀₁	—	2	1	no	—
200	C₂×C₈×C₁₀₁	—	2	1	no	—
201	C₂×C₈×C₁₀₁	—	2	2	no	—
202	C₂×C₈×C₁₀₁	—	2	2	no	—
203	C₂×C₈×C₁₀₁	—	4	4	no	—
204	C₄⋊C₄×C₁₀₁	—	2	1	no	—
205	C₂²⋊C₄×C₁₀₁	—	2	1	no	—
206	C₂²⋊C₄×C₁₀₁	—	4	2	no	—
207	C₄²×C₁₀₁	—	2	1	no	—
208	C₂³×C₁₀₁	—	2	1	no	—
209	C₂³×C₁₀₁	—	2	2	no	—
210	C₂³×C₁₀₁	—	2	2	no	—
211	C₂³×C₁₀₁	—	4	4	no	—
212	C₂³×C₁₀₁	—	4	2	no	—
213	C₂³×C₁₀₁	—	4	2	no	—
214	C₂³×C₁₀₁	—	4	1	no	—
215	C₂³×C₁₀₁	—	4	2	no	—
216	C₂³×C₁₀₁	—	16	1	no	—
217	C₂³×C₁₀₁	—	16	1	no	—
218	C₂³×C₁₀₁	—	16	2	no	—
219	C₂³×C₁₀₁	#121	1	2	yes	—
220	C₂³×C₁₀₁	C₂×#41	1	1	yes	characteristic
221	Q₈×C₁₀₁	—	2	1	no	—
222	Q₈×C₁₀₁	—	2	2	no	—
223	Q₈×C₁₀₁	—	2	2	no	—
224	Q₈×C₁₀₁	—	2	2	no	—
225	Q₈×C₁₀₁	—	4	2	no	—
226	Q₈×C₁₀₁	#120	1	2	yes	—
227	D₄×C₁₀₁	—	2	4	no	—
228	D₄×C₁₀₁	—	2	4	no	—
229	D₄×C₁₀₁	—	2	2	no	—
230	D₄×C₁₀₁	—	2	2	no	—
231	D₄×C₁₀₁	—	2	1	no	—
232	D₄×C₁₀₁	—	2	2	no	—
233	D₄×C₁₀₁	—	2	2	no	—
234	D₄×C₁₀₁	—	2	2	no	—
235	D₄×C₁₀₁	—	4	4	no	—
236	D₄×C₁₀₁	—	4	4	no	—
237	D₄×C₁₀₁	—	4	2	no	—
238	D₄×C₁₀₁	—	4	4	no	—
239	D₄×C₁₀₁	—	4	2	no	—
240	D₄×C₁₀₁	—	4	2	no	—
241	D₄×C₁₀₁	—	4	1	no	—
242	D₄×C₁₀₁	—	4	1	no	—
243	D₄×C₁₀₁	—	4	2	no	—
244	D₄×C₁₀₁	—	4	2	no	—
245	D₄×C₁₀₁	—	16	2	no	—
246	D₄×C₁₀₁	#120	1	2	yes	—
247	C₂×C₄×C₁₀₁	—	2	1	no	—
248	C₂×C₄×C₁₀₁	—	2	2	no	—
249	C₂×C₄×C₁₀₁	—	2	2	no	—
250	C₂×C₄×C₁₀₁	—	2	4	no	—
251	C₂×C₄×C₁₀₁	—	2	2	no	—
252	C₂×C₄×C₁₀₁	—	4	4	no	—
253	C₂×C₄×C₁₀₁	—	4	4	no	—
254	C₂×C₄×C₁₀₁	—	4	2	no	—
255	C₂×C₄×C₁₀₁	—	4	2	no	—
256	C₂×C₄×C₁₀₁	—	4	2	no	—
257	C₂×C₄×C₁₀₁	—	4	1	no	—
258	C₂×C₄×C₁₀₁	#121	1	2	yes	—
259	C₂×C₄×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
260	C₂×C₄×C₁₀₁	C₂²×D₄	1	2	yes	—
261	C₂×C₄×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
262	C₂×C₄×C₁₀₁	H(5,𝔽₂)	1	2	yes	—
263	C₈×C₁₀₁	—	2	4	no	—
264	C₈×C₁₀₁	—	2	4	no	—
265	C₈×C₁₀₁	—	4	1	no	—
266	C₈×C₁₀₁	—	4	1	no	—
267	C₈×C₁₀₁	—	4	2	no	—
268	C₂²×C₁₀₁	—	2	2	no	—
269	C₂²×C₁₀₁	—	2	2	no	—
270	C₂²×C₁₀₁	—	4	1	no	—
271	C₂²×C₁₀₁	—	4	2	no	—
272	C₂²×C₁₀₁	—	4	2	no	—
273	C₂²×C₁₀₁	—	4	2	no	—
274	C₂²×C₁₀₁	—	8	1	no	—
275	C₂²×C₁₀₁	—	8	2	no	—
276	C₂²×C₁₀₁	—	8	2	no	—
277	C₂²×C₁₀₁	—	8	2	no	—
278	C₂²×C₁₀₁	—	8	1	no	—
279	C₂²×C₁₀₁	—	16	2	no	—
280	C₂²×C₁₀₁	—	16	2	no	—
281	C₂²×C₁₀₁	—	16	4	no	—
282	C₂²×C₁₀₁	—	16	2	no	—
283	C₂²×C₁₀₁	C₂×#121	1	1	yes	characteristic
284	C₂²×C₁₀₁	#546	1	2	yes	—
285	C₄×C₁₀₁	—	2	2	no	—
286	C₄×C₁₀₁	—	2	2	no	—
287	C₄×C₁₀₁	—	4	2	no	—
288	C₄×C₁₀₁	—	8	1	no	—
289	C₄×C₁₀₁	C₂×#120	1	1	yes	characteristic
290	C₄×C₁₀₁	#534	1	1	yes	characteristic
291	C₄×C₁₀₁	D₄²	1	2	yes	—
292	#24420	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
293	C₂×C₁₀₁	—	2	1	no	—
294	C₂×C₁₀₁	—	2	2	no	—
295	C₂×C₁₀₁	—	4	2	no	—
296	C₂×C₁₀₁	—	4	2	no	—
297	C₂×C₁₀₁	—	8	2	no	—
298	C₂×C₁₀₁	—	8	2	no	—
299	C₂×C₁₀₁	—	16	1	no	—
300	C₂×C₁₀₁	#2410	1	1	yes	characteristic
301	#3585	C₂×C₁₀₁	1	1	yes	characteristic, complemented
302	#3068	C₂×C₁₀₁	1	2	yes	complemented
303	#3021	C₂×C₁₀₁	1	1	yes	characteristic, complemented
304	#3008	C₂×C₁₀₁	1	1	yes	characteristic, complemented
305	#2888	C₂×C₁₀₁	1	1	yes	characteristic, complemented
306	#2048	C₂×C₁₀₁	1	2	yes	complemented
307	#2018	C₂×C₁₀₁	1	2	yes	complemented
308	#1914	C₂×C₁₀₁	1	1	yes	characteristic, complemented
309	#1881	C₂×C₁₀₁	1	2	yes	complemented
310	#1858	C₂×C₁₀₁	1	1	yes	characteristic, complemented
311	#1791	C₂×C₁₀₁	1	1	yes	characteristic, complemented
312	C₁₀₁	#24420	1	1	yes	characteristic, direct product factor, Sylow
313	#585	C₂²×C₁₀₁	1	1	yes	characteristic
314	C₂×H(5,𝔽₂)	C₂²×C₁₀₁	1	1	yes	characteristic
315	#577	—	2	4	no	—
316	#576	—	2	4	no	—
317	#575	—	2	2	no	—
318	#575	C₂²×C₁₀₁	1	2	yes	—
319	C₂×AGL(1,ℤ/8)	—	2	2	no	—
320	C₂×AGL(1,ℤ/8)	C₂²×C₁₀₁	1	2	yes	—
321	C₂×AGL(1,ℤ/8)	C₂²×C₁₀₁	1	1	yes	characteristic, complemented
322	C₂×AGL(1,ℤ/8)	C₂²×C₁₀₁	1	2	yes	complemented
323	C₂²×D₈	C₂²×C₁₀₁	1	1	yes	characteristic, complemented
324	#568	C₂²×C₁₀₁	1	1	yes	characteristic
325	#568	C₂²×C₁₀₁	1	2	yes	complemented
326	#535	C₂²×C₁₀₁	1	1	yes	characteristic
327	#472	—	2	4	no	—
328	#471	—	2	4	no	—
329	#454	—	2	2	no	—
330	#453	—	2	2	no	—
331	#449	—	2	2	no	—
332	#447	—	2	2	no	—
333	#430	C₂²×C₁₀₁	1	2	yes	complemented
334	#421	C₂²×C₁₀₁	1	2	yes	complemented
335	#418	C₂²×C₁₀₁	1	1	yes	characteristic, complemented
336	#416	C₂²×C₁₀₁	1	1	yes	characteristic, complemented
337	#413	—	2	2	no	—
338	#413	C₂²×C₁₀₁	1	1	yes	characteristic
339	#413	C₂²×C₁₀₁	1	1	yes	characteristic
340	#413	C₂²×C₁₀₁	1	2	yes	complemented
341	C₂×#100	—	2	2	no	—
342	C₂×#100	C₂²×C₁₀₁	1	2	yes	complemented
343	C₂×#100	C₂²×C₁₀₁	1	2	yes	complemented
344	#408	C₂²×C₁₀₁	1	1	yes	characteristic
345	#408	C₂²×C₁₀₁	1	2	yes	complemented
346	#344	C₂²×C₁₀₁	1	2	yes	complemented
347	#341	C₂²×C₁₀₁	1	2	yes	complemented
348	2₋¹⁺⁴	—	2	2	no	—
349	2₋¹⁺⁴	—	2	1	no	—
350	H(5,𝔽₂)	—	2	4	no	—
351	H(5,𝔽₂)	—	2	2	no	—
352	H(5,𝔽₂)	—	2	2	no	—
353	H(5,𝔽₂)	—	2	1	no	—
354	H(5,𝔽₂)	—	4	2	no	—
355	C₂×#41	—	2	1	no	—
356	C₂×#41	—	2	2	no	—
357	C₂×#41	—	4	2	no	—
358	C₂×#41	D₄×C₁₀₁	1	2	yes	—
359	C₂×#41	C₂³×C₁₀₁	1	2	yes	—
360	C₂×#41	C₂³×C₁₀₁	1	1	yes	characteristic
361	C₂×#41	C₂³×C₁₀₁	1	1	yes	characteristic
362	C₂²×D₄	—	2	1	no	—
363	C₂²×D₄	—	2	2	no	—
364	C₂²×D₄	D₄×C₁₀₁	1	2	yes	—
365	C₂²×D₄	C₂³×C₁₀₁	1	1	yes	characteristic
366	C₂²×D₄	C₂³×C₁₀₁	1	1	yes	characteristic
367	#137	—	2	4	no	—
368	#137	—	2	2	no	—
369	#137	D₄×C₁₀₁	1	4	yes	complemented
370	AGL(1,ℤ/8)	—	2	8	no	—
371	AGL(1,ℤ/8)	—	2	4	no	—
372	AGL(1,ℤ/8)	—	2	2	no	—
373	AGL(1,ℤ/8)	—	2	4	no	—
374	AGL(1,ℤ/8)	—	2	4	no	—
375	AGL(1,ℤ/8)	—	2	4	no	—
376	AGL(1,ℤ/8)	—	2	4	no	—
377	AGL(1,ℤ/8)	—	4	2	no	—
378	AGL(1,ℤ/8)	D₄×C₁₀₁	1	4	yes	complemented
379	#135	—	2	8	no	—
380	#135	—	2	4	no	—
381	C₂×SD₁₆	—	2	4	no	—
382	C₂×SD₁₆	—	2	2	no	—
383	C₂×SD₁₆	—	2	1	no	—
384	C₂×SD₁₆	—	2	2	no	—
385	C₂×D₈	—	2	4	no	—
386	C₂×D₈	—	2	2	no	—
387	C₂×D₈	—	2	2	no	—
388	C₂×D₈	—	2	1	no	—
389	C₂×D₈	—	2	2	no	—
390	C₂×D₈	—	4	2	no	—
391	#131	—	2	4	no	—
392	#131	—	2	4	no	—
393	#131	—	4	2	no	—
394	C₂×M₁₆	—	2	2	no	—
395	C₂×M₁₆	—	2	4	no	—
396	C₂×M₁₆	C₂³×C₁₀₁	1	2	yes	—
397	C₂×M₁₆	C₂³×C₁₀₁	1	1	yes	characteristic
398	C₂×M₁₆	C₂³×C₁₀₁	1	2	yes	—
399	C₂×M₁₆	C₂³×C₁₀₁	1	2	yes	—
400	C₂²×C₈	C₂³×C₁₀₁	1	1	yes	characteristic
401	#127	—	2	1	no	—
402	#124	—	2	1	no	—
403	#121	—	2	2	no	—
404	#120	—	2	2	no	—
405	#117	C₂³×C₁₀₁	1	1	yes	characteristic
406	#108	—	2	4	no	—
407	#104	—	2	4	no	—
408	#103	—	2	1	no	—
409	#102	—	2	1	no	—
410	#102	—	2	2	no	—
411	#101	—	2	1	no	—
412	#101	—	2	2	no	—
413	#101	D₄×C₁₀₁	1	2	yes	—
414	#100	—	2	1	no	—
415	#100	—	2	2	no	—
416	#100	—	2	4	no	—
417	#100	—	2	4	no	—
418	#100	D₄×C₁₀₁	1	2	yes	—
419	C₂²⋊C₈	—	2	2	no	—
420	C₂²⋊C₈	—	4	2	no	—
421	C₂⁴	—	2	2	no	—
422	C₂⁴	—	2	1	no	—
423	C₂⁴	—	2	1	no	—
424	#41	—	2	2	no	—
425	#41	—	2	2	no	—
426	#41	—	2	2	no	—
427	#41	—	2	4	no	—
428	#41	—	2	4	no	—
429	#41	—	2	2	no	—
430	#41	—	2	2	no	—
431	#41	—	2	2	no	—
432	#41	—	2	2	no	—
433	#41	—	4	2	no	—
434	#41	—	4	4	no	—
435	#41	—	4	4	no	—
436	#41	—	4	2	no	—
437	#41	—	4	2	no	—
438	#41	—	4	2	no	—
439	#41	—	4	2	no	—
440	#41	C₂×D₄×C₁₀₁	1	4	yes	—
441	C₂×Q₈	—	2	2	no	—
442	C₂×Q₈	—	4	2	no	—
443	C₂×Q₈	C₂×D₄×C₁₀₁	1	2	yes	—
444	C₂×Q₈	C₂×D₄×C₁₀₁	1	1	yes	characteristic
445	C₂×Q₈	C₂×D₄×C₁₀₁	1	1	yes	characteristic
446	C₂×D₄	—	2	1	no	—
447	C₂×D₄	—	2	2	no	—
448	C₂×D₄	—	2	4	no	—
449	C₂×D₄	—	2	2	no	—
450	C₂×D₄	—	2	2	no	—
451	C₂×D₄	—	2	2	no	—
452	C₂×D₄	—	2	2	no	—
453	C₂×D₄	—	2	1	no	—
454	C₂×D₄	—	2	2	no	—
455	C₂×D₄	—	2	1	no	—
456	C₂×D₄	—	2	1	no	—
457	C₂×D₄	—	2	2	no	—
458	C₂×D₄	—	2	2	no	—
459	C₂×D₄	—	4	2	no	—
460	C₂×D₄	—	4	4	no	—
461	C₂×D₄	—	4	8	no	—
462	C₂×D₄	—	4	2	no	—
463	C₂×D₄	—	4	4	no	—
464	C₂×D₄	—	4	2	no	—
465	C₂×D₄	—	4	2	no	—
466	C₂×D₄	C₂×D₄×C₁₀₁	1	2	yes	—
467	C₂×D₄	C₂×D₄×C₁₀₁	1	2	yes	—
468	C₂×D₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
469	C₂×D₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
470	C₂×D₄	#41×C₁₀₁	1	2	yes	—
471	C₂²×C₄	—	2	1	no	—
472	C₂²×C₄	—	2	2	no	—
473	C₂²×C₄	—	2	2	no	—
474	C₂²×C₄	—	4	2	no	—
475	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
476	C₂²×C₄	C₂⁴×C₁₀₁	1	1	yes	characteristic
477	Q₁₆	—	2	4	no	—
478	SD₁₆	—	2	8	no	—
479	SD₁₆	—	2	4	no	—
480	SD₁₆	—	2	4	no	—
481	SD₁₆	—	4	4	no	—
482	SD₁₆	—	4	2	no	—
483	D₈	—	2	8	no	—
484	D₈	—	2	4	no	—
485	D₈	—	4	4	no	—
486	D₈	—	4	4	no	—
487	D₈	—	4	2	no	—
488	M₁₆	—	2	4	no	—
489	M₁₆	—	2	2	no	—
490	M₁₆	—	2	2	no	—
491	M₁₆	—	2	2	no	—
492	M₁₆	—	2	2	no	—
493	M₁₆	—	2	2	no	—
494	M₁₆	—	4	4	no	—
495	M₁₆	C₂×D₄×C₁₀₁	1	4	yes	—
496	M₁₆	C₂×D₄×C₁₀₁	1	4	yes	—
497	C₂×C₈	—	2	4	no	—
498	C₂×C₈	—	2	2	no	—
499	C₂×C₈	—	2	2	no	—
500	C₂×C₈	—	2	1	no	—
501	C₂×C₈	—	2	1	no	—
502	C₂×C₈	—	2	2	no	—
503	C₂×C₈	—	2	2	no	—
504	C₂×C₈	—	4	4	no	—
505	C₄⋊C₄	—	2	1	no	—
506	C₂²⋊C₄	—	2	1	no	—
507	C₂²⋊C₄	—	4	2	no	—
508	C₄²	—	2	1	no	—
509	C₂³	—	2	1	no	—
510	C₂³	—	2	2	no	—
511	C₂³	—	2	2	no	—
512	C₂³	—	4	4	no	—
513	C₂³	—	4	2	no	—
514	C₂³	—	4	2	no	—
515	C₂³	—	4	1	no	—
516	C₂³	—	4	2	no	—
517	C₂³	—	16	1	no	—
518	C₂³	—	16	1	no	—
519	C₂³	—	16	2	no	—
520	C₂³	#121×C₁₀₁	1	2	yes	—
521	C₂³	C₂×#41×C₁₀₁	1	1	yes	characteristic
522	Q₈	—	2	1	no	—
523	Q₈	—	2	2	no	—
524	Q₈	—	2	2	no	—
525	Q₈	—	2	2	no	—
526	Q₈	—	4	2	no	—
527	Q₈	#120×C₁₀₁	1	2	yes	—
528	D₄	—	2	4	no	—
529	D₄	—	2	4	no	—
530	D₄	—	2	2	no	—
531	D₄	—	2	2	no	—
532	D₄	—	2	1	no	—
533	D₄	—	2	2	no	—
534	D₄	—	2	2	no	—
535	D₄	—	2	2	no	—
536	D₄	—	4	4	no	—
537	D₄	—	4	4	no	—
538	D₄	—	4	2	no	—
539	D₄	—	4	4	no	—
540	D₄	—	4	2	no	—
541	D₄	—	4	2	no	—
542	D₄	—	4	1	no	—
543	D₄	—	4	1	no	—
544	D₄	—	4	2	no	—
545	D₄	—	4	2	no	—
546	D₄	—	16	2	no	—
547	D₄	#120×C₁₀₁	1	2	yes	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	2	4	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	4	4	no	—
554	C₂×C₄	—	4	4	no	—
555	C₂×C₄	—	4	2	no	—
556	C₂×C₄	—	4	2	no	—
557	C₂×C₄	—	4	2	no	—
558	C₂×C₄	—	4	1	no	—
559	C₂×C₄	#121×C₁₀₁	1	2	yes	—
560	C₂×C₄	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
561	C₂×C₄	C₂²×D₄×C₁₀₁	1	2	yes	—
562	C₂×C₄	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
563	C₂×C₄	H(5,𝔽₂)×C₁₀₁	1	2	yes	—
564	C₈	—	2	4	no	—
565	C₈	—	2	4	no	—
566	C₈	—	4	1	no	—
567	C₈	—	4	1	no	—
568	C₈	—	4	2	no	—
569	C₂²	—	2	2	no	—
570	C₂²	—	2	2	no	—
571	C₂²	—	4	1	no	—
572	C₂²	—	4	2	no	—
573	C₂²	—	4	2	no	—
574	C₂²	—	4	2	no	—
575	C₂²	—	8	1	no	—
576	C₂²	—	8	2	no	—
577	C₂²	—	8	2	no	—
578	C₂²	—	8	2	no	—
579	C₂²	—	8	1	no	—
580	C₂²	—	16	2	no	—
581	C₂²	—	16	2	no	—
582	C₂²	—	16	4	no	—
583	C₂²	—	16	2	no	—
584	C₂²	C₂×#121×C₁₀₁	1	1	yes	characteristic
585	C₂²	#546×C₁₀₁	1	2	yes	—
586	C₄	—	2	2	no	—
587	C₄	—	2	2	no	—
588	C₄	—	4	2	no	—
589	C₄	—	8	1	no	—
590	C₄	C₂×#120×C₁₀₁	1	1	yes	characteristic
591	C₄	#534×C₁₀₁	1	1	yes	characteristic
592	C₄	D₄²×C₁₀₁	1	2	yes	—
593	C₂	—	2	1	no	—
594	C₂	—	2	2	no	—
595	C₂	—	4	2	no	—
596	C₂	—	4	2	no	—
597	C₂	—	8	2	no	—
598	C₂	—	8	2	no	—
599	C₂	—	16	1	no	—
600	C₂	C₁₀₁×#2410	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₀₁	#2410
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₀₁
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₀₁ ◁ C₂²×C₄×C₁₀₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₀₁×#3585	C₂	semidirect
2. C₁₀₁×#3068	C₂	semidirect
3. C₁₀₁×#3021	C₂	semidirect
4. C₁₀₁×#3008	C₂	semidirect
5. C₁₀₁×#2888	C₂	semidirect
6. C₁₀₁×#2048	C₂	semidirect
7. C₁₀₁×#2018	C₂	semidirect
8. C₁₀₁×#1914	C₂	semidirect
9. C₁₀₁×#1881	C₂	semidirect
10. C₁₀₁×#1858	C₂	semidirect
11. C₁₀₁×#1791	C₂	semidirect
20. C₂×AGL(1,ℤ/8)×C₁₀₁	C₂²	semidirect
21. C₂×AGL(1,ℤ/8)×C₁₀₁	C₂²	semidirect
22. C₂²×D₈×C₁₀₁	C₂²	semidirect
24. #568×C₁₀₁	C₂²	semidirect
32. #430×C₁₀₁	C₂²	semidirect
33. #421×C₁₀₁	C₂²	semidirect
34. #418×C₁₀₁	C₂²	semidirect
35. #416×C₁₀₁	C₂²	semidirect
39. #413×C₁₀₁	C₂²	semidirect
41. C₂×#100×C₁₀₁	C₂²	semidirect
42. C₂×#100×C₁₀₁	C₂²	semidirect
44. #408×C₁₀₁	C₂²	semidirect
45. #344×C₁₀₁	C₂²	semidirect
46. #341×C₁₀₁	C₂²	semidirect
68. #137×C₁₀₁	D₄	semidirect
77. AGL(1,ℤ/8)×C₁₀₁	D₄	semidirect
292. #24420	C₁₀₁	direct (N × H)
301. #3585	C₂×C₁₀₁	semidirect
302. #3068	C₂×C₁₀₁	semidirect
303. #3021	C₂×C₁₀₁	semidirect
304. #3008	C₂×C₁₀₁	semidirect
305. #2888	C₂×C₁₀₁	semidirect
306. #2048	C₂×C₁₀₁	semidirect
307. #2018	C₂×C₁₀₁	semidirect
308. #1914	C₂×C₁₀₁	semidirect
309. #1881	C₂×C₁₀₁	semidirect
310. #1858	C₂×C₁₀₁	semidirect
311. #1791	C₂×C₁₀₁	semidirect
312. C₁₀₁	#24420	direct (N × H)
321. C₂×AGL(1,ℤ/8)	C₂²×C₁₀₁	semidirect
322. C₂×AGL(1,ℤ/8)	C₂²×C₁₀₁	semidirect
323. C₂²×D₈	C₂²×C₁₀₁	semidirect
325. #568	C₂²×C₁₀₁	semidirect
333. #430	C₂²×C₁₀₁	semidirect
334. #421	C₂²×C₁₀₁	semidirect
335. #418	C₂²×C₁₀₁	semidirect
336. #416	C₂²×C₁₀₁	semidirect
340. #413	C₂²×C₁₀₁	semidirect
342. C₂×#100	C₂²×C₁₀₁	semidirect
343. C₂×#100	C₂²×C₁₀₁	semidirect
345. #408	C₂²×C₁₀₁	semidirect
346. #344	C₂²×C₁₀₁	semidirect
347. #341	C₂²×C₁₀₁	semidirect
369. #137	D₄×C₁₀₁	semidirect
378. AGL(1,ℤ/8)	D₄×C₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₁₀₁×#3585	2
C₁₀₁×#3068	2
C₁₀₁×#3021	2
C₁₀₁×#3008	2
C₁₀₁×#2888	2
C₁₀₁×#2048	2
C₁₀₁×#2018	2
C₁₀₁×#1914	2
C₁₀₁×#1881	2
C₁₀₁×#1858	2
C₁₀₁×#1791	2
#24420	101

Subgroups — C101×#24420 #38806571

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#24420 #38806571