Subgroups — C₁₀₁×#23887 #38806038

Order 25856.

1656 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	C₂×#577×C₁₀₁	C₂	1	2	yes	maximal, complemented
2	C₂×#456×C₁₀₁	C₂	1	2	yes	maximal, complemented
3	C₁₀₁×#3013	C₂	1	2	yes	maximal, complemented
4	C₁₀₁×#2019	C₂	1	2	yes	maximal, complemented
5	C₁₀₁×#2013	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₀₁×#2006	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₀₁×#1908	C₂	1	2	yes	maximal, complemented
8	C₁₀₁×#1876	C₂	1	2	yes	maximal, complemented
9	C₁₀₁×#1792	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×2₋¹⁺⁴×C₁₀₁	C₂²	1	2	yes	—
11	C₂×H(5,𝔽₂)×C₁₀₁	C₂²	1	1	yes	characteristic
12	#577×C₁₀₁	—	2	8	no	—
13	#577×C₁₀₁	—	2	8	no	—
14	C₂×#137×C₁₀₁	—	2	2	no	—
15	C₂×#137×C₁₀₁	C₂²	1	2	yes	—
16	C₂×#137×C₁₀₁	C₂²	1	2	yes	complemented
17	C₂×AGL(1,ℤ/8)×C₁₀₁	—	2	2	no	—
18	C₂×AGL(1,ℤ/8)×C₁₀₁	C₂²	1	2	yes	—
19	C₂×#135×C₁₀₁	—	2	2	no	—
20	C₂×#135×C₁₀₁	C₂²	1	2	yes	—
21	C₂²×SD₁₆×C₁₀₁	—	2	2	no	—
22	C₂²×SD₁₆×C₁₀₁	C₂²	1	2	yes	—
23	C₂×#131×C₁₀₁	C₂²	1	2	yes	—
24	#537×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₄⋊Q₈×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
26	#456×C₁₀₁	—	2	8	no	—
27	#452×C₁₀₁	—	2	2	no	—
28	#451×C₁₀₁	—	2	2	no	—
29	#449×C₁₀₁	—	2	2	no	—
30	#448×C₁₀₁	—	2	2	no	—
31	C₂×#104×C₁₀₁	C₂²	1	2	yes	—
32	C₂×#104×C₁₀₁	C₂²	1	2	yes	complemented
33	#417×C₁₀₁	C₂²	1	2	yes	—
34	C₂×#103×C₁₀₁	C₂²	1	2	yes	complemented
35	C₂×#101×C₁₀₁	C₂²	1	2	yes	complemented
36	C₂×#100×C₁₀₁	C₂²	1	1	yes	characteristic
37	#408×C₁₀₁	C₂²	1	2	yes	complemented
38	#390×C₁₀₁	C₂²	1	1	yes	characteristic
39	#343×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
40	#341×C₁₀₁	C₂²	1	2	yes	complemented
41	#336×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
42	2₋¹⁺⁴×C₁₀₁	—	2	4	no	—
43	2₋¹⁺⁴×C₁₀₁	—	2	4	no	—
44	2₋¹⁺⁴×C₁₀₁	—	2	4	no	—
45	2₋¹⁺⁴×C₁₀₁	—	4	2	no	—
46	H(5,𝔽₂)×C₁₀₁	—	2	4	no	—
47	H(5,𝔽₂)×C₁₀₁	—	4	1	no	—
48	H(5,𝔽₂)×C₁₀₁	D₄	1	4	yes	complemented
49	C₂×#41×C₁₀₁	—	2	2	no	—
50	C₂×#41×C₁₀₁	—	2	2	no	—
51	C₂×#41×C₁₀₁	—	2	2	no	—
52	C₂×#41×C₁₀₁	—	4	2	no	—
53	C₂×#41×C₁₀₁	C₂³	1	2	yes	—
54	C₂×#41×C₁₀₁	C₂³	1	2	yes	—
55	C₂²×Q₈×C₁₀₁	—	2	2	no	—
56	C₂²×Q₈×C₁₀₁	—	2	2	no	—
57	C₂²×Q₈×C₁₀₁	C₂³	1	2	yes	—
58	C₂²×D₄×C₁₀₁	—	2	2	no	—
59	C₂²×D₄×C₁₀₁	—	4	1	no	—
60	C₂²×D₄×C₁₀₁	C₂³	1	1	yes	characteristic
61	#137×C₁₀₁	—	2	16	no	—
62	#137×C₁₀₁	—	2	4	no	—
63	#137×C₁₀₁	—	2	4	no	—
64	#137×C₁₀₁	—	4	2	no	—
65	#137×C₁₀₁	D₄	1	8	yes	complemented
66	AGL(1,ℤ/8)×C₁₀₁	—	2	16	no	—
67	AGL(1,ℤ/8)×C₁₀₁	—	2	4	no	—
68	AGL(1,ℤ/8)×C₁₀₁	—	2	4	no	—
69	#135×C₁₀₁	—	2	16	no	—
70	#135×C₁₀₁	—	2	4	no	—
71	#135×C₁₀₁	—	2	4	no	—
72	C₂×Q₁₆×C₁₀₁	—	2	2	no	—
73	C₂×Q₁₆×C₁₀₁	—	2	2	no	—
74	C₂×Q₁₆×C₁₀₁	D₄	1	2	yes	—
75	C₂×SD₁₆×C₁₀₁	—	2	16	no	—
76	C₂×SD₁₆×C₁₀₁	—	2	2	no	—
77	C₂×SD₁₆×C₁₀₁	—	2	4	no	—
78	C₂×SD₁₆×C₁₀₁	—	2	2	no	—
79	C₂×SD₁₆×C₁₀₁	—	2	4	no	—
80	C₂×SD₁₆×C₁₀₁	—	2	2	no	—
81	C₂×SD₁₆×C₁₀₁	—	2	2	no	—
82	C₂×SD₁₆×C₁₀₁	—	2	2	no	—
83	C₂×SD₁₆×C₁₀₁	D₄	1	2	yes	—
84	C₂×SD₁₆×C₁₀₁	D₄	1	2	yes	—
85	C₂×D₈×C₁₀₁	—	2	2	no	—
86	C₂×D₈×C₁₀₁	D₄	1	2	yes	—
87	#131×C₁₀₁	—	2	4	no	—
88	#131×C₁₀₁	—	2	4	no	—
89	C₂×M₁₆×C₁₀₁	—	2	2	no	—
90	C₂×M₁₆×C₁₀₁	C₂³	1	2	yes	—
91	C₂×M₁₆×C₁₀₁	C₂³	1	2	yes	—
92	C₂²×C₈×C₁₀₁	—	2	2	no	—
93	C₂²×C₈×C₁₀₁	C₂³	1	2	yes	—
94	C₄⋊Q₈×C₁₀₁	—	2	4	no	—
95	C₂²⋊Q₈×C₁₀₁	—	2	2	no	—
96	#121×C₁₀₁	—	2	2	no	—
97	#121×C₁₀₁	—	4	1	no	—
98	C₂×C₄⋊C₄×C₁₀₁	—	4	1	no	—
99	C₂×C₄⋊C₄×C₁₀₁	C₂³	1	1	yes	characteristic
100	C₂×C₂²⋊C₄×C₁₀₁	—	4	1	no	—
101	C₂×C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
102	#104×C₁₀₁	—	2	4	no	—
103	#104×C₁₀₁	—	2	4	no	—
104	#103×C₁₀₁	—	2	2	no	—
105	#103×C₁₀₁	—	2	2	no	—
106	#103×C₁₀₁	—	2	2	no	—
107	#102×C₁₀₁	—	2	2	no	—
108	#101×C₁₀₁	—	2	4	no	—
109	#100×C₁₀₁	—	4	1	no	—
110	C₂²⋊C₈×C₁₀₁	—	2	2	no	—
111	C₂²⋊C₈×C₁₀₁	—	2	2	no	—
112	C₂⁴×C₁₀₁	—	2	1	no	—
113	C₂⁴×C₁₀₁	—	4	1	no	—
114	#41×C₁₀₁	—	2	2	no	—
115	#41×C₁₀₁	—	2	2	no	—
116	#41×C₁₀₁	—	2	8	no	—
117	#41×C₁₀₁	—	2	8	no	—
118	#41×C₁₀₁	—	2	2	no	—
119	#41×C₁₀₁	—	2	2	no	—
120	#41×C₁₀₁	—	2	2	no	—
121	#41×C₁₀₁	—	2	2	no	—
122	#41×C₁₀₁	—	4	4	no	—
123	#41×C₁₀₁	—	4	8	no	—
124	#41×C₁₀₁	—	4	4	no	—
125	#41×C₁₀₁	—	4	4	no	—
126	#41×C₁₀₁	—	4	8	no	—
127	#41×C₁₀₁	—	4	4	no	—
128	#41×C₁₀₁	C₂×D₄	1	4	yes	—
129	#41×C₁₀₁	C₂×D₄	1	4	yes	—
130	C₂×Q₈×C₁₀₁	—	2	2	no	—
131	C₂×Q₈×C₁₀₁	—	2	8	no	—
132	C₂×Q₈×C₁₀₁	—	2	2	no	—
133	C₂×Q₈×C₁₀₁	—	2	2	no	—
134	C₂×Q₈×C₁₀₁	—	2	2	no	—
135	C₂×Q₈×C₁₀₁	—	2	2	no	—
136	C₂×Q₈×C₁₀₁	—	4	2	no	—
137	C₂×Q₈×C₁₀₁	—	4	4	no	—
138	C₂×Q₈×C₁₀₁	—	4	4	no	—
139	C₂×Q₈×C₁₀₁	—	4	4	no	—
140	C₂×Q₈×C₁₀₁	C₂×D₄	1	2	yes	—
141	C₂×Q₈×C₁₀₁	C₂×D₄	1	4	yes	—
142	C₂×Q₈×C₁₀₁	C₂×D₄	1	2	yes	—
143	C₂×D₄×C₁₀₁	—	2	2	no	—
144	C₂×D₄×C₁₀₁	—	2	8	no	—
145	C₂×D₄×C₁₀₁	—	2	2	no	—
146	C₂×D₄×C₁₀₁	—	2	2	no	—
147	C₂×D₄×C₁₀₁	—	2	2	no	—
148	C₂×D₄×C₁₀₁	—	2	1	no	—
149	C₂×D₄×C₁₀₁	—	4	4	no	—
150	C₂×D₄×C₁₀₁	—	4	2	no	—
151	C₂×D₄×C₁₀₁	—	4	4	no	—
152	C₂×D₄×C₁₀₁	—	4	4	no	—
153	C₂×D₄×C₁₀₁	—	4	2	no	—
154	C₂×D₄×C₁₀₁	—	4	1	no	—
155	C₂×D₄×C₁₀₁	C₂×D₄	1	2	yes	—
156	C₂×D₄×C₁₀₁	C₂×D₄	1	2	yes	—
157	C₂×D₄×C₁₀₁	C₂×D₄	1	2	yes	—
158	C₂²×C₄×C₁₀₁	—	2	2	no	—
159	C₂²×C₄×C₁₀₁	—	2	1	no	—
160	C₂²×C₄×C₁₀₁	—	2	2	no	—
161	C₂²×C₄×C₁₀₁	—	2	2	no	—
162	C₂²×C₄×C₁₀₁	—	2	1	no	—
163	C₂²×C₄×C₁₀₁	—	4	1	no	—
164	C₂²×C₄×C₁₀₁	—	4	2	no	—
165	C₂²×C₄×C₁₀₁	—	4	2	no	—
166	C₂²×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
167	Q₁₆×C₁₀₁	—	2	8	no	—
168	Q₁₆×C₁₀₁	—	2	4	no	—
169	Q₁₆×C₁₀₁	—	4	4	no	—
170	SD₁₆×C₁₀₁	—	2	8	no	—
171	SD₁₆×C₁₀₁	—	2	8	no	—
172	SD₁₆×C₁₀₁	—	2	8	no	—
173	SD₁₆×C₁₀₁	—	2	4	no	—
174	SD₁₆×C₁₀₁	—	2	4	no	—
175	SD₁₆×C₁₀₁	—	2	8	no	—
176	SD₁₆×C₁₀₁	—	4	4	no	—
177	D₈×C₁₀₁	—	2	8	no	—
178	D₈×C₁₀₁	—	2	4	no	—
179	M₁₆×C₁₀₁	—	2	8	no	—
180	M₁₆×C₁₀₁	—	2	2	no	—
181	M₁₆×C₁₀₁	—	2	2	no	—
182	M₁₆×C₁₀₁	—	2	2	no	—
183	M₁₆×C₁₀₁	C₂×D₄	1	4	yes	—
184	C₂×C₈×C₁₀₁	—	2	8	no	—
185	C₂×C₈×C₁₀₁	—	2	2	no	—
186	C₂×C₈×C₁₀₁	—	2	2	no	—
187	C₂×C₈×C₁₀₁	—	2	2	no	—
188	C₂×C₈×C₁₀₁	—	2	2	no	—
189	C₂×C₈×C₁₀₁	C₂×D₄	1	2	yes	—
190	C₂×C₈×C₁₀₁	C₂×D₄	1	2	yes	—
191	C₄⋊C₄×C₁₀₁	—	2	2	no	—
192	C₄⋊C₄×C₁₀₁	—	4	4	no	—
193	C₄⋊C₄×C₁₀₁	—	4	1	no	—
194	C₂²⋊C₄×C₁₀₁	—	4	2	no	—
195	C₂²⋊C₄×C₁₀₁	—	8	2	no	—
196	C₄²×C₁₀₁	—	2	2	no	—
197	C₂³×C₁₀₁	—	2	2	no	—
198	C₂³×C₁₀₁	—	2	2	no	—
199	C₂³×C₁₀₁	—	2	2	no	—
200	C₂³×C₁₀₁	—	4	4	no	—
201	C₂³×C₁₀₁	—	4	1	no	—
202	C₂³×C₁₀₁	—	4	1	no	—
203	C₂³×C₁₀₁	—	8	1	no	—
204	C₂³×C₁₀₁	—	8	1	no	—
205	C₂³×C₁₀₁	—	16	1	no	—
206	C₂³×C₁₀₁	—	16	1	no	—
207	C₂³×C₁₀₁	H(5,𝔽₂)	1	1	yes	characteristic
208	Q₈×C₁₀₁	—	2	2	no	—
209	Q₈×C₁₀₁	—	2	4	no	—
210	Q₈×C₁₀₁	—	2	2	no	—
211	Q₈×C₁₀₁	—	2	4	no	—
212	Q₈×C₁₀₁	—	2	2	no	—
213	Q₈×C₁₀₁	—	4	8	no	—
214	Q₈×C₁₀₁	—	4	2	no	—
215	Q₈×C₁₀₁	—	4	2	no	—
216	Q₈×C₁₀₁	#120	1	4	yes	—
217	D₄×C₁₀₁	—	2	4	no	—
218	D₄×C₁₀₁	—	2	4	no	—
219	D₄×C₁₀₁	—	2	2	no	—
220	D₄×C₁₀₁	—	2	4	no	—
221	D₄×C₁₀₁	—	2	2	no	—
222	D₄×C₁₀₁	—	2	2	no	—
223	D₄×C₁₀₁	—	4	8	no	—
224	D₄×C₁₀₁	—	4	8	no	—
225	D₄×C₁₀₁	—	4	2	no	—
226	D₄×C₁₀₁	—	4	2	no	—
227	D₄×C₁₀₁	—	4	2	no	—
228	D₄×C₁₀₁	—	16	1	no	—
229	D₄×C₁₀₁	#120	1	4	yes	—
230	C₂×C₄×C₁₀₁	—	2	2	no	—
231	C₂×C₄×C₁₀₁	—	2	4	no	—
232	C₂×C₄×C₁₀₁	—	2	4	no	—
233	C₂×C₄×C₁₀₁	—	2	2	no	—
234	C₂×C₄×C₁₀₁	—	2	4	no	—
235	C₂×C₄×C₁₀₁	—	2	2	no	—
236	C₂×C₄×C₁₀₁	—	4	4	no	—
237	C₂×C₄×C₁₀₁	—	4	8	no	—
238	C₂×C₄×C₁₀₁	—	4	1	no	—
239	C₂×C₄×C₁₀₁	—	4	8	no	—
240	C₂×C₄×C₁₀₁	—	4	2	no	—
241	C₂×C₄×C₁₀₁	—	4	1	no	—
242	C₂×C₄×C₁₀₁	—	4	2	no	—
243	C₂×C₄×C₁₀₁	—	4	2	no	—
244	C₂×C₄×C₁₀₁	—	4	2	no	—
245	C₂×C₄×C₁₀₁	—	4	1	no	—
246	C₂×C₄×C₁₀₁	—	8	1	no	—
247	C₂×C₄×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
248	C₂×C₄×C₁₀₁	C₂²×D₄	1	2	yes	—
249	C₂×C₄×C₁₀₁	C₂²×D₄	1	2	yes	—
250	C₂×C₄×C₁₀₁	H(5,𝔽₂)	1	1	yes	characteristic
251	C₈×C₁₀₁	—	2	2	no	—
252	C₈×C₁₀₁	—	2	4	no	—
253	C₈×C₁₀₁	—	2	2	no	—
254	C₈×C₁₀₁	—	4	2	no	—
255	C₂²×C₁₀₁	—	2	1	no	—
256	C₂²×C₁₀₁	—	2	1	no	—
257	C₂²×C₁₀₁	—	2	4	no	—
258	C₂²×C₁₀₁	—	4	2	no	—
259	C₂²×C₁₀₁	—	4	2	no	—
260	C₂²×C₁₀₁	—	4	2	no	—
261	C₂²×C₁₀₁	—	4	2	no	—
262	C₂²×C₁₀₁	—	4	2	no	—
263	C₂²×C₁₀₁	—	4	2	no	—
264	C₂²×C₁₀₁	—	8	2	no	—
265	C₂²×C₁₀₁	—	8	1	no	—
266	C₂²×C₁₀₁	—	8	1	no	—
267	C₂²×C₁₀₁	—	16	1	no	—
268	C₂²×C₁₀₁	—	16	4	no	—
269	C₂²×C₁₀₁	#534	1	1	yes	characteristic
270	C₂²×C₁₀₁	D₄²	1	1	yes	characteristic
271	C₂²×C₁₀₁	D₄²	1	1	yes	characteristic
272	C₄×C₁₀₁	—	2	4	no	—
273	C₄×C₁₀₁	—	4	2	no	—
274	C₄×C₁₀₁	—	4	4	no	—
275	C₄×C₁₀₁	—	4	2	no	—
276	C₄×C₁₀₁	—	8	1	no	—
277	C₄×C₁₀₁	C₂×#120	1	2	yes	—
278	C₄×C₁₀₁	D₄²	1	2	yes	—
279	#23887	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
280	C₂×C₁₀₁	—	2	1	no	—
281	C₂×C₁₀₁	—	2	1	no	—
282	C₂×C₁₀₁	—	4	4	no	—
283	C₂×C₁₀₁	—	8	2	no	—
284	C₂×C₁₀₁	—	8	2	no	—
285	C₂×C₁₀₁	#2403	1	1	yes	characteristic
286	C₂×C₁₀₁	#3289	1	1	yes	characteristic
287	C₂×C₁₀₁	#3291	1	1	yes	characteristic
288	C₂×#577	C₂×C₁₀₁	1	2	yes	complemented
289	C₂×#456	C₂×C₁₀₁	1	2	yes	complemented
290	#3013	C₂×C₁₀₁	1	2	yes	complemented
291	#2019	C₂×C₁₀₁	1	2	yes	complemented
292	#2013	C₂×C₁₀₁	1	1	yes	characteristic, complemented
293	#2006	C₂×C₁₀₁	1	1	yes	characteristic, complemented
294	#1908	C₂×C₁₀₁	1	2	yes	complemented
295	#1876	C₂×C₁₀₁	1	2	yes	complemented
296	#1792	C₂×C₁₀₁	1	1	yes	characteristic, complemented
297	C₁₀₁	#23887	1	1	yes	characteristic, direct product factor, Sylow
298	C₂×2₋¹⁺⁴	C₂²×C₁₀₁	1	2	yes	—
299	C₂×H(5,𝔽₂)	C₂²×C₁₀₁	1	1	yes	characteristic
300	#577	—	2	8	no	—
301	#577	—	2	8	no	—
302	C₂×#137	—	2	2	no	—
303	C₂×#137	C₂²×C₁₀₁	1	2	yes	—
304	C₂×#137	C₂²×C₁₀₁	1	2	yes	complemented
305	C₂×AGL(1,ℤ/8)	—	2	2	no	—
306	C₂×AGL(1,ℤ/8)	C₂²×C₁₀₁	1	2	yes	—
307	C₂×#135	—	2	2	no	—
308	C₂×#135	C₂²×C₁₀₁	1	2	yes	—
309	C₂²×SD₁₆	—	2	2	no	—
310	C₂²×SD₁₆	C₂²×C₁₀₁	1	2	yes	—
311	C₂×#131	C₂²×C₁₀₁	1	2	yes	—
312	#537	C₂²×C₁₀₁	1	1	yes	characteristic, complemented
313	C₂×C₄⋊Q₈	C₂²×C₁₀₁	1	1	yes	characteristic, complemented
314	#456	—	2	8	no	—
315	#452	—	2	2	no	—
316	#451	—	2	2	no	—
317	#449	—	2	2	no	—
318	#448	—	2	2	no	—
319	C₂×#104	C₂²×C₁₀₁	1	2	yes	—
320	C₂×#104	C₂²×C₁₀₁	1	2	yes	complemented
321	#417	C₂²×C₁₀₁	1	2	yes	—
322	C₂×#103	C₂²×C₁₀₁	1	2	yes	complemented
323	C₂×#101	C₂²×C₁₀₁	1	2	yes	complemented
324	C₂×#100	C₂²×C₁₀₁	1	1	yes	characteristic
325	#408	C₂²×C₁₀₁	1	2	yes	complemented
326	#390	C₂²×C₁₀₁	1	1	yes	characteristic
327	#343	C₂²×C₁₀₁	1	1	yes	characteristic, complemented
328	#341	C₂²×C₁₀₁	1	2	yes	complemented
329	#336	C₂²×C₁₀₁	1	1	yes	characteristic, complemented
330	2₋¹⁺⁴	—	2	4	no	—
331	2₋¹⁺⁴	—	2	4	no	—
332	2₋¹⁺⁴	—	2	4	no	—
333	2₋¹⁺⁴	—	4	2	no	—
334	H(5,𝔽₂)	—	2	4	no	—
335	H(5,𝔽₂)	—	4	1	no	—
336	H(5,𝔽₂)	D₄×C₁₀₁	1	4	yes	complemented
337	C₂×#41	—	2	2	no	—
338	C₂×#41	—	2	2	no	—
339	C₂×#41	—	2	2	no	—
340	C₂×#41	—	4	2	no	—
341	C₂×#41	C₂³×C₁₀₁	1	2	yes	—
342	C₂×#41	C₂³×C₁₀₁	1	2	yes	—
343	C₂²×Q₈	—	2	2	no	—
344	C₂²×Q₈	—	2	2	no	—
345	C₂²×Q₈	C₂³×C₁₀₁	1	2	yes	—
346	C₂²×D₄	—	2	2	no	—
347	C₂²×D₄	—	4	1	no	—
348	C₂²×D₄	C₂³×C₁₀₁	1	1	yes	characteristic
349	#137	—	2	16	no	—
350	#137	—	2	4	no	—
351	#137	—	2	4	no	—
352	#137	—	4	2	no	—
353	#137	D₄×C₁₀₁	1	8	yes	complemented
354	AGL(1,ℤ/8)	—	2	16	no	—
355	AGL(1,ℤ/8)	—	2	4	no	—
356	AGL(1,ℤ/8)	—	2	4	no	—
357	#135	—	2	16	no	—
358	#135	—	2	4	no	—
359	#135	—	2	4	no	—
360	C₂×Q₁₆	—	2	2	no	—
361	C₂×Q₁₆	—	2	2	no	—
362	C₂×Q₁₆	D₄×C₁₀₁	1	2	yes	—
363	C₂×SD₁₆	—	2	16	no	—
364	C₂×SD₁₆	—	2	2	no	—
365	C₂×SD₁₆	—	2	4	no	—
366	C₂×SD₁₆	—	2	2	no	—
367	C₂×SD₁₆	—	2	4	no	—
368	C₂×SD₁₆	—	2	2	no	—
369	C₂×SD₁₆	—	2	2	no	—
370	C₂×SD₁₆	—	2	2	no	—
371	C₂×SD₁₆	D₄×C₁₀₁	1	2	yes	—
372	C₂×SD₁₆	D₄×C₁₀₁	1	2	yes	—
373	C₂×D₈	—	2	2	no	—
374	C₂×D₈	D₄×C₁₀₁	1	2	yes	—
375	#131	—	2	4	no	—
376	#131	—	2	4	no	—
377	C₂×M₁₆	—	2	2	no	—
378	C₂×M₁₆	C₂³×C₁₀₁	1	2	yes	—
379	C₂×M₁₆	C₂³×C₁₀₁	1	2	yes	—
380	C₂²×C₈	—	2	2	no	—
381	C₂²×C₈	C₂³×C₁₀₁	1	2	yes	—
382	C₄⋊Q₈	—	2	4	no	—
383	C₂²⋊Q₈	—	2	2	no	—
384	#121	—	2	2	no	—
385	#121	—	4	1	no	—
386	C₂×C₄⋊C₄	—	4	1	no	—
387	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	1	yes	characteristic
388	C₂×C₂²⋊C₄	—	4	1	no	—
389	C₂×C₄²	C₂³×C₁₀₁	1	1	yes	characteristic
390	#104	—	2	4	no	—
391	#104	—	2	4	no	—
392	#103	—	2	2	no	—
393	#103	—	2	2	no	—
394	#103	—	2	2	no	—
395	#102	—	2	2	no	—
396	#101	—	2	4	no	—
397	#100	—	4	1	no	—
398	C₂²⋊C₈	—	2	2	no	—
399	C₂²⋊C₈	—	2	2	no	—
400	C₂⁴	—	2	1	no	—
401	C₂⁴	—	4	1	no	—
402	#41	—	2	2	no	—
403	#41	—	2	2	no	—
404	#41	—	2	8	no	—
405	#41	—	2	8	no	—
406	#41	—	2	2	no	—
407	#41	—	2	2	no	—
408	#41	—	2	2	no	—
409	#41	—	2	2	no	—
410	#41	—	4	4	no	—
411	#41	—	4	8	no	—
412	#41	—	4	4	no	—
413	#41	—	4	4	no	—
414	#41	—	4	8	no	—
415	#41	—	4	4	no	—
416	#41	C₂×D₄×C₁₀₁	1	4	yes	—
417	#41	C₂×D₄×C₁₀₁	1	4	yes	—
418	C₂×Q₈	—	2	2	no	—
419	C₂×Q₈	—	2	8	no	—
420	C₂×Q₈	—	2	2	no	—
421	C₂×Q₈	—	2	2	no	—
422	C₂×Q₈	—	2	2	no	—
423	C₂×Q₈	—	2	2	no	—
424	C₂×Q₈	—	4	2	no	—
425	C₂×Q₈	—	4	4	no	—
426	C₂×Q₈	—	4	4	no	—
427	C₂×Q₈	—	4	4	no	—
428	C₂×Q₈	C₂×D₄×C₁₀₁	1	2	yes	—
429	C₂×Q₈	C₂×D₄×C₁₀₁	1	4	yes	—
430	C₂×Q₈	C₂×D₄×C₁₀₁	1	2	yes	—
431	C₂×D₄	—	2	2	no	—
432	C₂×D₄	—	2	8	no	—
433	C₂×D₄	—	2	2	no	—
434	C₂×D₄	—	2	2	no	—
435	C₂×D₄	—	2	2	no	—
436	C₂×D₄	—	2	1	no	—
437	C₂×D₄	—	4	4	no	—
438	C₂×D₄	—	4	2	no	—
439	C₂×D₄	—	4	4	no	—
440	C₂×D₄	—	4	4	no	—
441	C₂×D₄	—	4	2	no	—
442	C₂×D₄	—	4	1	no	—
443	C₂×D₄	C₂×D₄×C₁₀₁	1	2	yes	—
444	C₂×D₄	C₂×D₄×C₁₀₁	1	2	yes	—
445	C₂×D₄	C₂×D₄×C₁₀₁	1	2	yes	—
446	C₂²×C₄	—	2	2	no	—
447	C₂²×C₄	—	2	1	no	—
448	C₂²×C₄	—	2	2	no	—
449	C₂²×C₄	—	2	2	no	—
450	C₂²×C₄	—	2	1	no	—
451	C₂²×C₄	—	4	1	no	—
452	C₂²×C₄	—	4	2	no	—
453	C₂²×C₄	—	4	2	no	—
454	C₂²×C₄	C₂⁴×C₁₀₁	1	1	yes	characteristic
455	Q₁₆	—	2	8	no	—
456	Q₁₆	—	2	4	no	—
457	Q₁₆	—	4	4	no	—
458	SD₁₆	—	2	8	no	—
459	SD₁₆	—	2	8	no	—
460	SD₁₆	—	2	8	no	—
461	SD₁₆	—	2	4	no	—
462	SD₁₆	—	2	4	no	—
463	SD₁₆	—	2	8	no	—
464	SD₁₆	—	4	4	no	—
465	D₈	—	2	8	no	—
466	D₈	—	2	4	no	—
467	M₁₆	—	2	8	no	—
468	M₁₆	—	2	2	no	—
469	M₁₆	—	2	2	no	—
470	M₁₆	—	2	2	no	—
471	M₁₆	C₂×D₄×C₁₀₁	1	4	yes	—
472	C₂×C₈	—	2	8	no	—
473	C₂×C₈	—	2	2	no	—
474	C₂×C₈	—	2	2	no	—
475	C₂×C₈	—	2	2	no	—
476	C₂×C₈	—	2	2	no	—
477	C₂×C₈	C₂×D₄×C₁₀₁	1	2	yes	—
478	C₂×C₈	C₂×D₄×C₁₀₁	1	2	yes	—
479	C₄⋊C₄	—	2	2	no	—
480	C₄⋊C₄	—	4	4	no	—
481	C₄⋊C₄	—	4	1	no	—
482	C₂²⋊C₄	—	4	2	no	—
483	C₂²⋊C₄	—	8	2	no	—
484	C₄²	—	2	2	no	—
485	C₂³	—	2	2	no	—
486	C₂³	—	2	2	no	—
487	C₂³	—	2	2	no	—
488	C₂³	—	4	4	no	—
489	C₂³	—	4	1	no	—
490	C₂³	—	4	1	no	—
491	C₂³	—	8	1	no	—
492	C₂³	—	8	1	no	—
493	C₂³	—	16	1	no	—
494	C₂³	—	16	1	no	—
495	C₂³	H(5,𝔽₂)×C₁₀₁	1	1	yes	characteristic
496	Q₈	—	2	2	no	—
497	Q₈	—	2	4	no	—
498	Q₈	—	2	2	no	—
499	Q₈	—	2	4	no	—
500	Q₈	—	2	2	no	—
501	Q₈	—	4	8	no	—
502	Q₈	—	4	2	no	—
503	Q₈	—	4	2	no	—
504	Q₈	#120×C₁₀₁	1	4	yes	—
505	D₄	—	2	4	no	—
506	D₄	—	2	4	no	—
507	D₄	—	2	2	no	—
508	D₄	—	2	4	no	—
509	D₄	—	2	2	no	—
510	D₄	—	2	2	no	—
511	D₄	—	4	8	no	—
512	D₄	—	4	8	no	—
513	D₄	—	4	2	no	—
514	D₄	—	4	2	no	—
515	D₄	—	4	2	no	—
516	D₄	—	16	1	no	—
517	D₄	#120×C₁₀₁	1	4	yes	—
518	C₂×C₄	—	2	2	no	—
519	C₂×C₄	—	2	4	no	—
520	C₂×C₄	—	2	4	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	2	4	no	—
524	C₂×C₄	—	4	4	no	—
525	C₂×C₄	—	4	8	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	4	8	no	—
528	C₂×C₄	—	4	2	no	—
529	C₂×C₄	—	4	1	no	—
530	C₂×C₄	—	4	2	no	—
531	C₂×C₄	—	4	2	no	—
532	C₂×C₄	—	4	2	no	—
533	C₂×C₄	—	4	1	no	—
534	C₂×C₄	—	8	1	no	—
535	C₂×C₄	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
536	C₂×C₄	C₂²×D₄×C₁₀₁	1	2	yes	—
537	C₂×C₄	C₂²×D₄×C₁₀₁	1	2	yes	—
538	C₂×C₄	H(5,𝔽₂)×C₁₀₁	1	1	yes	characteristic
539	C₈	—	2	2	no	—
540	C₈	—	2	4	no	—
541	C₈	—	2	2	no	—
542	C₈	—	4	2	no	—
543	C₂²	—	2	1	no	—
544	C₂²	—	2	1	no	—
545	C₂²	—	2	4	no	—
546	C₂²	—	4	2	no	—
547	C₂²	—	4	2	no	—
548	C₂²	—	4	2	no	—
549	C₂²	—	4	2	no	—
550	C₂²	—	4	2	no	—
551	C₂²	—	4	2	no	—
552	C₂²	—	8	2	no	—
553	C₂²	—	8	1	no	—
554	C₂²	—	8	1	no	—
555	C₂²	—	16	1	no	—
556	C₂²	—	16	4	no	—
557	C₂²	#534×C₁₀₁	1	1	yes	characteristic
558	C₂²	D₄²×C₁₀₁	1	1	yes	characteristic
559	C₂²	D₄²×C₁₀₁	1	1	yes	characteristic
560	C₄	—	2	4	no	—
561	C₄	—	4	2	no	—
562	C₄	—	4	2	no	—
563	C₄	—	4	4	no	—
564	C₄	—	8	1	no	—
565	C₄	C₂×#120×C₁₀₁	1	2	yes	—
566	C₄	D₄²×C₁₀₁	1	2	yes	—
567	C₂	—	2	1	no	—
568	C₂	—	2	1	no	—
569	C₂	—	4	4	no	—
570	C₂	—	8	2	no	—
571	C₂	—	8	2	no	—
572	C₂	C₁₀₁×#2403	1	1	yes	characteristic
573	C₂	C₁₀₁×#3289	1	1	yes	characteristic
574	C₂	C₁₀₁×#3291	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₀₁	D₄²
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₀₁
LCS	G ▷ C₂²×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
1. C₂×#577×C₁₀₁	C₂	semidirect
2. C₂×#456×C₁₀₁	C₂	semidirect
3. C₁₀₁×#3013	C₂	semidirect
4. C₁₀₁×#2019	C₂	semidirect
5. C₁₀₁×#2013	C₂	semidirect
6. C₁₀₁×#2006	C₂	semidirect
7. C₁₀₁×#1908	C₂	semidirect
8. C₁₀₁×#1876	C₂	semidirect
9. C₁₀₁×#1792	C₂	semidirect
16. C₂×#137×C₁₀₁	C₂²	semidirect
24. #537×C₁₀₁	C₂²	semidirect
25. C₂×C₄⋊Q₈×C₁₀₁	C₂²	semidirect
32. C₂×#104×C₁₀₁	C₂²	semidirect
34. C₂×#103×C₁₀₁	C₂²	semidirect
35. C₂×#101×C₁₀₁	C₂²	semidirect
37. #408×C₁₀₁	C₂²	semidirect
39. #343×C₁₀₁	C₂²	semidirect
40. #341×C₁₀₁	C₂²	semidirect
41. #336×C₁₀₁	C₂²	semidirect
48. H(5,𝔽₂)×C₁₀₁	D₄	semidirect
65. #137×C₁₀₁	D₄	semidirect
279. #23887	C₁₀₁	direct (N × H)
288. C₂×#577	C₂×C₁₀₁	semidirect
289. C₂×#456	C₂×C₁₀₁	semidirect
290. #3013	C₂×C₁₀₁	semidirect
291. #2019	C₂×C₁₀₁	semidirect
292. #2013	C₂×C₁₀₁	semidirect
293. #2006	C₂×C₁₀₁	semidirect
294. #1908	C₂×C₁₀₁	semidirect
295. #1876	C₂×C₁₀₁	semidirect
296. #1792	C₂×C₁₀₁	semidirect
297. C₁₀₁	#23887	direct (N × H)
304. C₂×#137	C₂²×C₁₀₁	semidirect
312. #537	C₂²×C₁₀₁	semidirect
313. C₂×C₄⋊Q₈	C₂²×C₁₀₁	semidirect
320. C₂×#104	C₂²×C₁₀₁	semidirect
322. C₂×#103	C₂²×C₁₀₁	semidirect
323. C₂×#101	C₂²×C₁₀₁	semidirect
325. #408	C₂²×C₁₀₁	semidirect
327. #343	C₂²×C₁₀₁	semidirect
328. #341	C₂²×C₁₀₁	semidirect
329. #336	C₂²×C₁₀₁	semidirect
336. H(5,𝔽₂)	D₄×C₁₀₁	semidirect
353. #137	D₄×C₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#577×C₁₀₁	2
C₂×#456×C₁₀₁	2
C₁₀₁×#3013	2
C₁₀₁×#2019	2
C₁₀₁×#2013	2
C₁₀₁×#2006	2
C₁₀₁×#1908	2
C₁₀₁×#1876	2
C₁₀₁×#1792	2
#23887	101

Subgroups — C101×#23887 #38806038

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#23887 #38806038