Subgroups — C₁₀₁×#24423 #38806574

Order 25856.

1284 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₀₁×#3586	C₂	1	1	yes	maximal, characteristic
2	C₁₀₁×#3069	C₂	1	2	yes	maximal, complemented
3	C₁₀₁×#3022	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₀₁×#3011	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₀₁×#2889	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₀₁×#2049	C₂	1	2	yes	maximal, complemented
7	C₁₀₁×#2020	C₂	1	2	yes	maximal, complemented
8	C₁₀₁×#1915	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	C₂×2₋¹⁺⁴×C₁₀₁	C₂²	1	1	yes	characteristic
14	#578×C₁₀₁	—	2	4	no	—
15	#577×C₁₀₁	—	2	4	no	—
16	#575×C₁₀₁	—	2	2	no	—
17	#575×C₁₀₁	C₂²	1	2	yes	—
18	C₂×#137×C₁₀₁	—	2	2	no	—
19	C₂×#137×C₁₀₁	C₂²	1	2	yes	—
20	C₂×#137×C₁₀₁	C₂²	1	2	yes	—
21	C₂×#137×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
22	C₂²×Q₁₆×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
23	#568×C₁₀₁	C₂²	1	1	yes	characteristic
24	#568×C₁₀₁	C₂²	1	2	yes	complemented
25	#536×C₁₀₁	C₂²	1	1	yes	characteristic
26	#473×C₁₀₁	—	2	4	no	—
27	#471×C₁₀₁	—	2	4	no	—
28	#456×C₁₀₁	—	2	2	no	—
29	#455×C₁₀₁	—	2	2	no	—
30	#452×C₁₀₁	—	2	2	no	—
31	#451×C₁₀₁	—	2	2	no	—
32	#430×C₁₀₁	C₂²	1	2	yes	complemented
33	#421×C₁₀₁	C₂²	1	2	yes	—
34	#419×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	2	yes	—
39	#413×C₁₀₁	C₂²	1	1	yes	characteristic
40	C₂×#101×C₁₀₁	—	2	2	no	—
41	C₂×#101×C₁₀₁	C₂²	1	2	yes	complemented
42	C₂×#101×C₁₀₁	C₂²	1	2	yes	complemented
43	#408×C₁₀₁	C₂²	1	1	yes	characteristic
44	#408×C₁₀₁	C₂²	1	2	yes	—
45	#344×C₁₀₁	C₂²	1	2	yes	complemented
46	#341×C₁₀₁	C₂²	1	2	yes	complemented
47	2₋¹⁺⁴×C₁₀₁	—	2	4	no	—
48	2₋¹⁺⁴×C₁₀₁	—	2	2	no	—
49	2₋¹⁺⁴×C₁₀₁	—	2	1	no	—
50	2₋¹⁺⁴×C₁₀₁	—	4	2	no	—
51	H(5,𝔽₂)×C₁₀₁	—	2	2	no	—
52	H(5,𝔽₂)×C₁₀₁	—	2	2	no	—
53	H(5,𝔽₂)×C₁₀₁	—	2	1	no	—
54	C₂×#41×C₁₀₁	—	2	1	no	—
55	C₂×#41×C₁₀₁	—	2	2	no	—
56	C₂×#41×C₁₀₁	—	2	2	no	—
57	C₂×#41×C₁₀₁	—	4	2	no	—
58	C₂×#41×C₁₀₁	D₄	1	2	yes	—
59	C₂×#41×C₁₀₁	C₂³	1	2	yes	—
60	C₂×#41×C₁₀₁	C₂³	1	1	yes	characteristic
61	C₂×#41×C₁₀₁	C₂³	1	1	yes	characteristic
62	C₂²×Q₈×C₁₀₁	—	2	1	no	—
63	C₂²×Q₈×C₁₀₁	D₄	1	2	yes	—
64	C₂²×Q₈×C₁₀₁	C₂³	1	1	yes	characteristic
65	C₂²×Q₈×C₁₀₁	C₂³	1	1	yes	characteristic
66	#137×C₁₀₁	—	2	8	no	—
67	#137×C₁₀₁	—	2	4	no	—
68	#137×C₁₀₁	—	2	2	no	—
69	#137×C₁₀₁	—	2	4	no	—
70	#137×C₁₀₁	—	2	4	no	—
71	#137×C₁₀₁	—	2	4	no	—
72	#137×C₁₀₁	—	2	4	no	—
73	#137×C₁₀₁	—	4	2	no	—
74	#137×C₁₀₁	D₄	1	4	yes	—
75	AGL(1,ℤ/8)×C₁₀₁	—	2	4	no	—
76	AGL(1,ℤ/8)×C₁₀₁	—	2	2	no	—
77	AGL(1,ℤ/8)×C₁₀₁	D₄	1	4	yes	—
78	#135×C₁₀₁	—	2	8	no	—
79	#135×C₁₀₁	—	2	4	no	—
80	C₂×Q₁₆×C₁₀₁	—	2	4	no	—
81	C₂×Q₁₆×C₁₀₁	—	2	2	no	—
82	C₂×Q₁₆×C₁₀₁	—	2	1	no	—
83	C₂×Q₁₆×C₁₀₁	—	2	2	no	—
84	C₂×Q₁₆×C₁₀₁	—	2	2	no	—
85	C₂×Q₁₆×C₁₀₁	—	4	2	no	—
86	C₂×SD₁₆×C₁₀₁	—	2	4	no	—
87	C₂×SD₁₆×C₁₀₁	—	2	2	no	—
88	C₂×SD₁₆×C₁₀₁	—	2	1	no	—
89	C₂×SD₁₆×C₁₀₁	—	2	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	2	yes	—
96	C₂×M₁₆×C₁₀₁	C₂³	1	1	yes	characteristic
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	C₄⋊Q₈×C₁₀₁	—	2	1	no	—
101	#124×C₁₀₁	—	2	1	no	—
102	#123×C₁₀₁	—	2	2	no	—
103	C₂²⋊Q₈×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	#103×C₁₀₁	—	2	2	no	—
109	#102×C₁₀₁	—	2	1	no	—
110	#101×C₁₀₁	—	2	1	no	—
111	#101×C₁₀₁	—	2	2	no	—
112	#101×C₁₀₁	—	2	4	no	—
113	#101×C₁₀₁	—	2	4	no	—
114	#101×C₁₀₁	D₄	1	2	yes	—
115	#100×C₁₀₁	—	2	1	no	—
116	#100×C₁₀₁	—	2	2	no	—
117	#100×C₁₀₁	D₄	1	2	yes	—
118	C₂²⋊C₈×C₁₀₁	—	2	2	no	—
119	C₂²⋊C₈×C₁₀₁	—	4	2	no	—
120	#41×C₁₀₁	—	2	2	no	—
121	#41×C₁₀₁	—	2	2	no	—
122	#41×C₁₀₁	—	2	2	no	—
123	#41×C₁₀₁	—	2	4	no	—
124	#41×C₁₀₁	—	2	4	no	—
125	#41×C₁₀₁	—	2	2	no	—
126	#41×C₁₀₁	—	2	2	no	—
127	#41×C₁₀₁	—	2	2	no	—
128	#41×C₁₀₁	—	2	2	no	—
129	#41×C₁₀₁	—	4	2	no	—
130	#41×C₁₀₁	—	4	4	no	—
131	#41×C₁₀₁	—	4	4	no	—
132	#41×C₁₀₁	—	4	2	no	—
133	#41×C₁₀₁	—	4	8	no	—
134	#41×C₁₀₁	—	4	2	no	—
135	#41×C₁₀₁	—	4	2	no	—
136	#41×C₁₀₁	—	4	2	no	—
137	#41×C₁₀₁	C₂×D₄	1	4	yes	—
138	C₂×Q₈×C₁₀₁	—	2	2	no	—
139	C₂×Q₈×C₁₀₁	—	2	1	no	—
140	C₂×Q₈×C₁₀₁	—	2	2	no	—
141	C₂×Q₈×C₁₀₁	—	2	4	no	—
142	C₂×Q₈×C₁₀₁	—	2	2	no	—
143	C₂×Q₈×C₁₀₁	—	2	2	no	—
144	C₂×Q₈×C₁₀₁	—	2	1	no	—
145	C₂×Q₈×C₁₀₁	—	2	1	no	—
146	C₂×Q₈×C₁₀₁	—	2	2	no	—
147	C₂×Q₈×C₁₀₁	—	2	2	no	—
148	C₂×Q₈×C₁₀₁	—	4	2	no	—
149	C₂×Q₈×C₁₀₁	—	4	4	no	—
150	C₂×Q₈×C₁₀₁	—	4	2	no	—
151	C₂×Q₈×C₁₀₁	C₂×D₄	1	2	yes	—
152	C₂×Q₈×C₁₀₁	C₂×D₄	1	2	yes	—
153	C₂×Q₈×C₁₀₁	C₂×D₄	1	1	yes	characteristic
154	C₂×Q₈×C₁₀₁	C₂×D₄	1	1	yes	characteristic
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	—	2	2	no	—
159	C₂×D₄×C₁₀₁	—	4	2	no	—
160	C₂×D₄×C₁₀₁	—	4	4	no	—
161	C₂×D₄×C₁₀₁	—	4	2	no	—
162	C₂×D₄×C₁₀₁	C₂×D₄	1	2	yes	—
163	C₂×D₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
164	C₂×D₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
165	C₂×D₄×C₁₀₁	#41	1	2	yes	—
166	C₂²×C₄×C₁₀₁	—	2	1	no	—
167	C₂²×C₄×C₁₀₁	—	2	2	no	—
168	C₂²×C₄×C₁₀₁	—	2	1	no	—
169	C₂²×C₄×C₁₀₁	—	2	2	no	—
170	C₂²×C₄×C₁₀₁	—	2	2	no	—
171	C₂²×C₄×C₁₀₁	—	2	1	no	—
172	C₂²×C₄×C₁₀₁	—	4	2	no	—
173	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
174	C₂²×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
175	Q₁₆×C₁₀₁	—	2	8	no	—
176	Q₁₆×C₁₀₁	—	2	4	no	—
177	Q₁₆×C₁₀₁	—	4	4	no	—
178	Q₁₆×C₁₀₁	—	4	4	no	—
179	Q₁₆×C₁₀₁	—	4	2	no	—
180	SD₁₆×C₁₀₁	—	2	8	no	—
181	SD₁₆×C₁₀₁	—	2	4	no	—
182	SD₁₆×C₁₀₁	—	2	4	no	—
183	SD₁₆×C₁₀₁	—	4	4	no	—
184	SD₁₆×C₁₀₁	—	4	2	no	—
185	D₈×C₁₀₁	—	2	4	no	—
186	M₁₆×C₁₀₁	—	2	4	no	—
187	M₁₆×C₁₀₁	—	2	2	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	—	4	4	no	—
193	M₁₆×C₁₀₁	C₂×D₄	1	4	yes	—
194	M₁₆×C₁₀₁	C₂×D₄	1	4	yes	—
195	C₂×C₈×C₁₀₁	—	2	4	no	—
196	C₂×C₈×C₁₀₁	—	2	2	no	—
197	C₂×C₈×C₁₀₁	—	2	2	no	—
198	C₂×C₈×C₁₀₁	—	2	1	no	—
199	C₂×C₈×C₁₀₁	—	2	1	no	—
200	C₂×C₈×C₁₀₁	—	2	2	no	—
201	C₂×C₈×C₁₀₁	—	2	2	no	—
202	C₂×C₈×C₁₀₁	—	4	4	no	—
203	C₄⋊C₄×C₁₀₁	—	2	1	no	—
204	C₄⋊C₄×C₁₀₁	—	4	2	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	—	4	2	no	—
211	C₂³×C₁₀₁	#121	1	2	yes	—
212	C₂³×C₁₀₁	C₂×#41	1	1	yes	characteristic
213	Q₈×C₁₀₁	—	2	1	no	—
214	Q₈×C₁₀₁	—	2	2	no	—
215	Q₈×C₁₀₁	—	2	2	no	—
216	Q₈×C₁₀₁	—	2	2	no	—
217	Q₈×C₁₀₁	—	2	2	no	—
218	Q₈×C₁₀₁	—	2	2	no	—
219	Q₈×C₁₀₁	—	4	4	no	—
220	Q₈×C₁₀₁	—	4	2	no	—
221	Q₈×C₁₀₁	—	4	2	no	—
222	Q₈×C₁₀₁	—	4	1	no	—
223	Q₈×C₁₀₁	—	4	1	no	—
224	Q₈×C₁₀₁	—	4	2	no	—
225	Q₈×C₁₀₁	#120	1	2	yes	—
226	D₄×C₁₀₁	—	2	4	no	—
227	D₄×C₁₀₁	—	2	4	no	—
228	D₄×C₁₀₁	—	2	2	no	—
229	D₄×C₁₀₁	—	2	1	no	—
230	D₄×C₁₀₁	—	2	2	no	—
231	D₄×C₁₀₁	—	2	2	no	—
232	D₄×C₁₀₁	—	4	2	no	—
233	D₄×C₁₀₁	—	4	4	no	—
234	D₄×C₁₀₁	—	4	4	no	—
235	D₄×C₁₀₁	—	4	2	no	—
236	D₄×C₁₀₁	—	4	2	no	—
237	D₄×C₁₀₁	#120	1	2	yes	—
238	C₂×C₄×C₁₀₁	—	2	1	no	—
239	C₂×C₄×C₁₀₁	—	2	2	no	—
240	C₂×C₄×C₁₀₁	—	2	2	no	—
241	C₂×C₄×C₁₀₁	—	2	4	no	—
242	C₂×C₄×C₁₀₁	—	2	2	no	—
243	C₂×C₄×C₁₀₁	—	2	2	no	—
244	C₂×C₄×C₁₀₁	—	4	4	no	—
245	C₂×C₄×C₁₀₁	—	4	4	no	—
246	C₂×C₄×C₁₀₁	—	4	4	no	—
247	C₂×C₄×C₁₀₁	—	4	2	no	—
248	C₂×C₄×C₁₀₁	—	4	2	no	—
249	C₂×C₄×C₁₀₁	—	4	2	no	—
250	C₂×C₄×C₁₀₁	—	4	2	no	—
251	C₂×C₄×C₁₀₁	—	4	1	no	—
252	C₂×C₄×C₁₀₁	—	4	1	no	—
253	C₂×C₄×C₁₀₁	—	4	2	no	—
254	C₂×C₄×C₁₀₁	#121	1	2	yes	—
255	C₂×C₄×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
256	C₂×C₄×C₁₀₁	C₂²×D₄	1	2	yes	—
257	C₂×C₄×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
258	C₂×C₄×C₁₀₁	H(5,𝔽₂)	1	2	yes	—
259	C₈×C₁₀₁	—	2	4	no	—
260	C₈×C₁₀₁	—	2	4	no	—
261	C₈×C₁₀₁	—	4	1	no	—
262	C₈×C₁₀₁	—	4	1	no	—
263	C₈×C₁₀₁	—	4	2	no	—
264	C₂²×C₁₀₁	—	2	2	no	—
265	C₂²×C₁₀₁	—	2	2	no	—
266	C₂²×C₁₀₁	—	4	1	no	—
267	C₂²×C₁₀₁	—	4	2	no	—
268	C₂²×C₁₀₁	—	4	2	no	—
269	C₂²×C₁₀₁	—	8	1	no	—
270	C₂²×C₁₀₁	—	8	2	no	—
271	C₂²×C₁₀₁	—	16	2	no	—
272	C₂²×C₁₀₁	C₂×#121	1	1	yes	characteristic
273	C₂²×C₁₀₁	#546	1	2	yes	—
274	C₄×C₁₀₁	—	2	2	no	—
275	C₄×C₁₀₁	—	2	2	no	—
276	C₄×C₁₀₁	—	4	2	no	—
277	C₄×C₁₀₁	—	4	2	no	—
278	C₄×C₁₀₁	—	8	1	no	—
279	C₄×C₁₀₁	—	8	1	no	—
280	C₄×C₁₀₁	C₂×#120	1	1	yes	characteristic
281	C₄×C₁₀₁	#534	1	1	yes	characteristic
282	C₄×C₁₀₁	D₄²	1	2	yes	—
283	#24423	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
284	C₂×C₁₀₁	—	2	1	no	—
285	C₂×C₁₀₁	—	2	2	no	—
286	C₂×C₁₀₁	—	4	2	no	—
287	C₂×C₁₀₁	—	4	2	no	—
288	C₂×C₁₀₁	—	8	2	no	—
289	C₂×C₁₀₁	#2410	1	1	yes	characteristic
290	#3586	C₂×C₁₀₁	1	1	yes	characteristic
291	#3069	C₂×C₁₀₁	1	2	yes	complemented
292	#3022	C₂×C₁₀₁	1	1	yes	characteristic, complemented
293	#3011	C₂×C₁₀₁	1	1	yes	characteristic, complemented
294	#2889	C₂×C₁₀₁	1	1	yes	characteristic, complemented
295	#2049	C₂×C₁₀₁	1	2	yes	complemented
296	#2020	C₂×C₁₀₁	1	2	yes	complemented
297	#1915	C₂×C₁₀₁	1	1	yes	characteristic, complemented
298	#1881	C₂×C₁₀₁	1	2	yes	complemented
299	#1858	C₂×C₁₀₁	1	1	yes	characteristic, complemented
300	#1791	C₂×C₁₀₁	1	1	yes	characteristic, complemented
301	C₁₀₁	#24423	1	1	yes	characteristic, direct product factor, Sylow
302	#585	C₂²×C₁₀₁	1	1	yes	characteristic
303	C₂×2₋¹⁺⁴	C₂²×C₁₀₁	1	1	yes	characteristic
304	#578	—	2	4	no	—
305	#577	—	2	4	no	—
306	#575	—	2	2	no	—
307	#575	C₂²×C₁₀₁	1	2	yes	—
308	C₂×#137	—	2	2	no	—
309	C₂×#137	C₂²×C₁₀₁	1	2	yes	—
310	C₂×#137	C₂²×C₁₀₁	1	2	yes	—
311	C₂×#137	C₂²×C₁₀₁	1	1	yes	characteristic, complemented
312	C₂²×Q₁₆	C₂²×C₁₀₁	1	1	yes	characteristic, complemented
313	#568	C₂²×C₁₀₁	1	1	yes	characteristic
314	#568	C₂²×C₁₀₁	1	2	yes	complemented
315	#536	C₂²×C₁₀₁	1	1	yes	characteristic
316	#473	—	2	4	no	—
317	#471	—	2	4	no	—
318	#456	—	2	2	no	—
319	#455	—	2	2	no	—
320	#452	—	2	2	no	—
321	#451	—	2	2	no	—
322	#430	C₂²×C₁₀₁	1	2	yes	complemented
323	#421	C₂²×C₁₀₁	1	2	yes	—
324	#419	C₂²×C₁₀₁	1	1	yes	characteristic, complemented
325	#416	C₂²×C₁₀₁	1	1	yes	characteristic, complemented
326	#413	—	2	2	no	—
327	#413	C₂²×C₁₀₁	1	2	yes	—
328	#413	C₂²×C₁₀₁	1	1	yes	characteristic
329	#413	C₂²×C₁₀₁	1	1	yes	characteristic
330	C₂×#101	—	2	2	no	—
331	C₂×#101	C₂²×C₁₀₁	1	2	yes	complemented
332	C₂×#101	C₂²×C₁₀₁	1	2	yes	complemented
333	#408	C₂²×C₁₀₁	1	1	yes	characteristic
334	#408	C₂²×C₁₀₁	1	2	yes	—
335	#344	C₂²×C₁₀₁	1	2	yes	complemented
336	#341	C₂²×C₁₀₁	1	2	yes	complemented
337	2₋¹⁺⁴	—	2	4	no	—
338	2₋¹⁺⁴	—	2	2	no	—
339	2₋¹⁺⁴	—	2	1	no	—
340	2₋¹⁺⁴	—	4	2	no	—
341	H(5,𝔽₂)	—	2	2	no	—
342	H(5,𝔽₂)	—	2	2	no	—
343	H(5,𝔽₂)	—	2	1	no	—
344	C₂×#41	—	2	1	no	—
345	C₂×#41	—	2	2	no	—
346	C₂×#41	—	2	2	no	—
347	C₂×#41	—	4	2	no	—
348	C₂×#41	D₄×C₁₀₁	1	2	yes	—
349	C₂×#41	C₂³×C₁₀₁	1	2	yes	—
350	C₂×#41	C₂³×C₁₀₁	1	1	yes	characteristic
351	C₂×#41	C₂³×C₁₀₁	1	1	yes	characteristic
352	C₂²×Q₈	—	2	1	no	—
353	C₂²×Q₈	D₄×C₁₀₁	1	2	yes	—
354	C₂²×Q₈	C₂³×C₁₀₁	1	1	yes	characteristic
355	C₂²×Q₈	C₂³×C₁₀₁	1	1	yes	characteristic
356	#137	—	2	8	no	—
357	#137	—	2	4	no	—
358	#137	—	2	2	no	—
359	#137	—	2	4	no	—
360	#137	—	2	4	no	—
361	#137	—	2	4	no	—
362	#137	—	2	4	no	—
363	#137	—	4	2	no	—
364	#137	D₄×C₁₀₁	1	4	yes	—
365	AGL(1,ℤ/8)	—	2	4	no	—
366	AGL(1,ℤ/8)	—	2	2	no	—
367	AGL(1,ℤ/8)	D₄×C₁₀₁	1	4	yes	—
368	#135	—	2	8	no	—
369	#135	—	2	4	no	—
370	C₂×Q₁₆	—	2	4	no	—
371	C₂×Q₁₆	—	2	2	no	—
372	C₂×Q₁₆	—	2	2	no	—
373	C₂×Q₁₆	—	2	2	no	—
374	C₂×Q₁₆	—	2	1	no	—
375	C₂×Q₁₆	—	4	2	no	—
376	C₂×SD₁₆	—	2	4	no	—
377	C₂×SD₁₆	—	2	2	no	—
378	C₂×SD₁₆	—	2	2	no	—
379	C₂×SD₁₆	—	2	1	no	—
380	#131	—	2	4	no	—
381	#131	—	2	4	no	—
382	#131	—	4	2	no	—
383	C₂×M₁₆	—	2	2	no	—
384	C₂×M₁₆	—	2	4	no	—
385	C₂×M₁₆	C₂³×C₁₀₁	1	2	yes	—
386	C₂×M₁₆	C₂³×C₁₀₁	1	1	yes	characteristic
387	C₂×M₁₆	C₂³×C₁₀₁	1	2	yes	—
388	C₂×M₁₆	C₂³×C₁₀₁	1	2	yes	—
389	C₂²×C₈	C₂³×C₁₀₁	1	1	yes	characteristic
390	C₄⋊Q₈	—	2	1	no	—
391	#124	—	2	1	no	—
392	#123	—	2	2	no	—
393	C₂²⋊Q₈	—	2	2	no	—
394	#117	C₂³×C₁₀₁	1	1	yes	characteristic
395	#108	—	2	4	no	—
396	#104	—	2	4	no	—
397	#103	—	2	1	no	—
398	#103	—	2	2	no	—
399	#102	—	2	1	no	—
400	#101	—	2	1	no	—
401	#101	—	2	2	no	—
402	#101	—	2	4	no	—
403	#101	—	2	4	no	—
404	#101	D₄×C₁₀₁	1	2	yes	—
405	#100	—	2	1	no	—
406	#100	—	2	2	no	—
407	#100	D₄×C₁₀₁	1	2	yes	—
408	C₂²⋊C₈	—	2	2	no	—
409	C₂²⋊C₈	—	4	2	no	—
410	#41	—	2	2	no	—
411	#41	—	2	2	no	—
412	#41	—	2	2	no	—
413	#41	—	2	4	no	—
414	#41	—	2	4	no	—
415	#41	—	2	2	no	—
416	#41	—	2	2	no	—
417	#41	—	2	2	no	—
418	#41	—	2	2	no	—
419	#41	—	4	2	no	—
420	#41	—	4	4	no	—
421	#41	—	4	4	no	—
422	#41	—	4	2	no	—
423	#41	—	4	8	no	—
424	#41	—	4	2	no	—
425	#41	—	4	2	no	—
426	#41	—	4	2	no	—
427	#41	C₂×D₄×C₁₀₁	1	4	yes	—
428	C₂×Q₈	—	2	2	no	—
429	C₂×Q₈	—	2	1	no	—
430	C₂×Q₈	—	2	2	no	—
431	C₂×Q₈	—	2	4	no	—
432	C₂×Q₈	—	2	2	no	—
433	C₂×Q₈	—	2	2	no	—
434	C₂×Q₈	—	2	1	no	—
435	C₂×Q₈	—	2	1	no	—
436	C₂×Q₈	—	2	2	no	—
437	C₂×Q₈	—	2	2	no	—
438	C₂×Q₈	—	4	2	no	—
439	C₂×Q₈	—	4	4	no	—
440	C₂×Q₈	—	4	2	no	—
441	C₂×Q₈	C₂×D₄×C₁₀₁	1	2	yes	—
442	C₂×Q₈	C₂×D₄×C₁₀₁	1	2	yes	—
443	C₂×Q₈	C₂×D₄×C₁₀₁	1	1	yes	characteristic
444	C₂×Q₈	C₂×D₄×C₁₀₁	1	1	yes	characteristic
445	C₂×D₄	—	2	1	no	—
446	C₂×D₄	—	2	2	no	—
447	C₂×D₄	—	2	2	no	—
448	C₂×D₄	—	2	2	no	—
449	C₂×D₄	—	4	2	no	—
450	C₂×D₄	—	4	4	no	—
451	C₂×D₄	—	4	2	no	—
452	C₂×D₄	C₂×D₄×C₁₀₁	1	2	yes	—
453	C₂×D₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
454	C₂×D₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
455	C₂×D₄	#41×C₁₀₁	1	2	yes	—
456	C₂²×C₄	—	2	1	no	—
457	C₂²×C₄	—	2	2	no	—
458	C₂²×C₄	—	2	1	no	—
459	C₂²×C₄	—	2	2	no	—
460	C₂²×C₄	—	2	2	no	—
461	C₂²×C₄	—	2	1	no	—
462	C₂²×C₄	—	4	2	no	—
463	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
464	C₂²×C₄	C₂⁴×C₁₀₁	1	1	yes	characteristic
465	Q₁₆	—	2	8	no	—
466	Q₁₆	—	2	4	no	—
467	Q₁₆	—	4	4	no	—
468	Q₁₆	—	4	4	no	—
469	Q₁₆	—	4	2	no	—
470	SD₁₆	—	2	8	no	—
471	SD₁₆	—	2	4	no	—
472	SD₁₆	—	2	4	no	—
473	SD₁₆	—	4	4	no	—
474	SD₁₆	—	4	2	no	—
475	D₈	—	2	4	no	—
476	M₁₆	—	2	4	no	—
477	M₁₆	—	2	2	no	—
478	M₁₆	—	2	2	no	—
479	M₁₆	—	2	2	no	—
480	M₁₆	—	2	2	no	—
481	M₁₆	—	2	2	no	—
482	M₁₆	—	4	4	no	—
483	M₁₆	C₂×D₄×C₁₀₁	1	4	yes	—
484	M₁₆	C₂×D₄×C₁₀₁	1	4	yes	—
485	C₂×C₈	—	2	4	no	—
486	C₂×C₈	—	2	2	no	—
487	C₂×C₈	—	2	2	no	—
488	C₂×C₈	—	2	1	no	—
489	C₂×C₈	—	2	1	no	—
490	C₂×C₈	—	2	2	no	—
491	C₂×C₈	—	2	2	no	—
492	C₂×C₈	—	4	4	no	—
493	C₄⋊C₄	—	2	1	no	—
494	C₄⋊C₄	—	4	2	no	—
495	C₂²⋊C₄	—	2	1	no	—
496	C₂²⋊C₄	—	4	2	no	—
497	C₄²	—	2	1	no	—
498	C₂³	—	2	1	no	—
499	C₂³	—	2	2	no	—
500	C₂³	—	4	2	no	—
501	C₂³	#121×C₁₀₁	1	2	yes	—
502	C₂³	C₂×#41×C₁₀₁	1	1	yes	characteristic
503	Q₈	—	2	1	no	—
504	Q₈	—	2	2	no	—
505	Q₈	—	2	2	no	—
506	Q₈	—	2	2	no	—
507	Q₈	—	2	2	no	—
508	Q₈	—	2	2	no	—
509	Q₈	—	4	4	no	—
510	Q₈	—	4	2	no	—
511	Q₈	—	4	2	no	—
512	Q₈	—	4	1	no	—
513	Q₈	—	4	1	no	—
514	Q₈	—	4	2	no	—
515	Q₈	#120×C₁₀₁	1	2	yes	—
516	D₄	—	2	4	no	—
517	D₄	—	2	4	no	—
518	D₄	—	2	2	no	—
519	D₄	—	2	1	no	—
520	D₄	—	2	2	no	—
521	D₄	—	2	2	no	—
522	D₄	—	4	2	no	—
523	D₄	—	4	4	no	—
524	D₄	—	4	4	no	—
525	D₄	—	4	2	no	—
526	D₄	—	4	2	no	—
527	D₄	#120×C₁₀₁	1	2	yes	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	2	no	—
530	C₂×C₄	—	2	2	no	—
531	C₂×C₄	—	2	4	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	4	4	no	—
535	C₂×C₄	—	4	4	no	—
536	C₂×C₄	—	4	4	no	—
537	C₂×C₄	—	4	2	no	—
538	C₂×C₄	—	4	2	no	—
539	C₂×C₄	—	4	2	no	—
540	C₂×C₄	—	4	2	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	4	1	no	—
543	C₂×C₄	—	4	2	no	—
544	C₂×C₄	#121×C₁₀₁	1	2	yes	—
545	C₂×C₄	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
546	C₂×C₄	C₂²×D₄×C₁₀₁	1	2	yes	—
547	C₂×C₄	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
548	C₂×C₄	H(5,𝔽₂)×C₁₀₁	1	2	yes	—
549	C₈	—	2	4	no	—
550	C₈	—	2	4	no	—
551	C₈	—	4	1	no	—
552	C₈	—	4	1	no	—
553	C₈	—	4	2	no	—
554	C₂²	—	2	2	no	—
555	C₂²	—	2	2	no	—
556	C₂²	—	4	1	no	—
557	C₂²	—	4	2	no	—
558	C₂²	—	4	2	no	—
559	C₂²	—	8	1	no	—
560	C₂²	—	8	2	no	—
561	C₂²	—	16	2	no	—
562	C₂²	C₂×#121×C₁₀₁	1	1	yes	characteristic
563	C₂²	#546×C₁₀₁	1	2	yes	—
564	C₄	—	2	2	no	—
565	C₄	—	2	2	no	—
566	C₄	—	4	2	no	—
567	C₄	—	4	2	no	—
568	C₄	—	8	1	no	—
569	C₄	—	8	1	no	—
570	C₄	C₂×#120×C₁₀₁	1	1	yes	characteristic
571	C₄	#534×C₁₀₁	1	1	yes	characteristic
572	C₄	D₄²×C₁₀₁	1	2	yes	—
573	C₂	—	2	1	no	—
574	C₂	—	2	2	no	—
575	C₂	—	4	2	no	—
576	C₂	—	4	2	no	—
577	C₂	—	8	2	no	—
578	C₂	C₁₀₁×#2410	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₀₁	#2410
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₀₁
prime radical	C₁₀₁×#3586	C₂
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
2. C₁₀₁×#3069	C₂	semidirect
3. C₁₀₁×#3022	C₂	semidirect
4. C₁₀₁×#3011	C₂	semidirect
5. C₁₀₁×#2889	C₂	semidirect
6. C₁₀₁×#2049	C₂	semidirect
7. C₁₀₁×#2020	C₂	semidirect
8. C₁₀₁×#1915	C₂	semidirect
9. C₁₀₁×#1881	C₂	semidirect
10. C₁₀₁×#1858	C₂	semidirect
11. C₁₀₁×#1791	C₂	semidirect
21. C₂×#137×C₁₀₁	C₂²	semidirect
22. C₂²×Q₁₆×C₁₀₁	C₂²	semidirect
24. #568×C₁₀₁	C₂²	semidirect
32. #430×C₁₀₁	C₂²	semidirect
34. #419×C₁₀₁	C₂²	semidirect
35. #416×C₁₀₁	C₂²	semidirect
41. C₂×#101×C₁₀₁	C₂²	semidirect
42. C₂×#101×C₁₀₁	C₂²	semidirect
45. #344×C₁₀₁	C₂²	semidirect
46. #341×C₁₀₁	C₂²	semidirect
283. #24423	C₁₀₁	direct (N × H)
291. #3069	C₂×C₁₀₁	semidirect
292. #3022	C₂×C₁₀₁	semidirect
293. #3011	C₂×C₁₀₁	semidirect
294. #2889	C₂×C₁₀₁	semidirect
295. #2049	C₂×C₁₀₁	semidirect
296. #2020	C₂×C₁₀₁	semidirect
297. #1915	C₂×C₁₀₁	semidirect
298. #1881	C₂×C₁₀₁	semidirect
299. #1858	C₂×C₁₀₁	semidirect
300. #1791	C₂×C₁₀₁	semidirect
301. C₁₀₁	#24423	direct (N × H)
311. C₂×#137	C₂²×C₁₀₁	semidirect
312. C₂²×Q₁₆	C₂²×C₁₀₁	semidirect
314. #568	C₂²×C₁₀₁	semidirect
322. #430	C₂²×C₁₀₁	semidirect
324. #419	C₂²×C₁₀₁	semidirect
325. #416	C₂²×C₁₀₁	semidirect
331. C₂×#101	C₂²×C₁₀₁	semidirect
332. C₂×#101	C₂²×C₁₀₁	semidirect
335. #344	C₂²×C₁₀₁	semidirect
336. #341	C₂²×C₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₁₀₁×#3586	2
C₁₀₁×#3069	2
C₁₀₁×#3022	2
C₁₀₁×#3011	2
C₁₀₁×#2889	2
C₁₀₁×#2049	2
C₁₀₁×#2020	2
C₁₀₁×#1915	2
C₁₀₁×#1881	2
C₁₀₁×#1858	2
C₁₀₁×#1791	2
#24423	101

Subgroups — C101×#24423 #38806574

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#24423 #38806574