Subgroups — C₁₀₁×#25881 #38808032

Order 25856.

1766 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄²×C₁₀₁	C₂	1	1	yes	maximal, characteristic
2	C₂×#486×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#476×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₀₁×#2563	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₀₁×#2034	C₂	1	4	yes	maximal, complemented
6	C₁₀₁×#1982	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₀₁×#1954	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₀₁×#1786	C₂	1	4	yes	maximal, complemented
9	C₄×#102×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×D₄×C₁₀₁	—	2	1	no	—
11	C₂³×D₄×C₁₀₁	C₂²	1	2	yes	—
12	D₄²×C₁₀₁	—	2	4	no	—
13	D₄²×C₁₀₁	—	2	4	no	—
14	C₂×C₄⋊Q₈×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
15	C₂×#127×C₁₀₁	C₂²	1	1	yes	characteristic
16	C₂×#121×C₁₀₁	—	2	1	no	—
17	C₂×#121×C₁₀₁	C₂²	1	2	yes	—
18	C₂×#120×C₁₀₁	—	2	2	no	—
19	C₂×C₄×D₄×C₁₀₁	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₁₀₁	C₂²	1	1	yes	characteristic
21	#486×C₁₀₁	—	2	4	no	—
22	#476×C₁₀₁	—	2	4	no	—
23	C₂×#106×C₁₀₁	C₂²	1	2	yes	complemented
24	C₂×C₄⋊C₈×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
25	C₂×#102×C₁₀₁	C₂²	1	2	yes	—
26	C₂×#102×C₁₀₁	C₂²	1	2	yes	—
27	C₂×#102×C₁₀₁	C₂²	1	4	yes	complemented
28	C₂×#102×C₁₀₁	C₂²	1	4	yes	complemented
29	C₂×C₂²⋊C₈×C₁₀₁	C₂²	1	4	yes	complemented
30	C₂×C₄×C₈×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
31	#393×C₁₀₁	—	2	2	no	—
32	#390×C₁₀₁	—	2	1	no	—
33	#382×C₁₀₁	—	2	1	no	—
34	#380×C₁₀₁	C₂²	1	4	yes	complemented
35	C₄×C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
36	#340×C₁₀₁	C₂²	1	2	yes	complemented
37	C₂⁵×C₁₀₁	—	2	2	no	—
38	C₂²×Q₈×C₁₀₁	—	2	1	no	—
39	C₂²×D₄×C₁₀₁	—	2	8	no	—
40	C₂²×D₄×C₁₀₁	—	2	2	no	—
41	C₂²×D₄×C₁₀₁	—	2	4	no	—
42	C₂²×D₄×C₁₀₁	—	2	4	no	—
43	C₂²×D₄×C₁₀₁	—	2	8	no	—
44	C₂²×D₄×C₁₀₁	—	2	2	no	—
45	C₂²×D₄×C₁₀₁	—	2	1	no	—
46	C₂²×D₄×C₁₀₁	—	2	1	no	—
47	C₂²×D₄×C₁₀₁	—	4	4	no	—
48	C₂²×D₄×C₁₀₁	—	4	4	no	—
49	C₂²×D₄×C₁₀₁	—	4	4	no	—
50	C₂²×D₄×C₁₀₁	D₄	1	1	yes	characteristic
51	C₂²×D₄×C₁₀₁	C₂³	1	2	yes	—
52	C₂²×D₄×C₁₀₁	C₂³	1	1	yes	characteristic
53	C₂³×C₄×C₁₀₁	—	2	1	no	—
54	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
55	C₂²×C₈×C₁₀₁	C₂³	1	2	yes	—
56	C₂²×C₈×C₁₀₁	C₂³	1	2	yes	—
57	C₄⋊Q₈×C₁₀₁	—	2	2	no	—
58	C₄⋊Q₈×C₁₀₁	—	2	2	no	—
59	#127×C₁₀₁	—	2	2	no	—
60	#127×C₁₀₁	D₄	1	4	yes	—
61	#121×C₁₀₁	—	2	8	no	—
62	#121×C₁₀₁	—	2	4	no	—
63	#121×C₁₀₁	—	2	4	no	—
64	#120×C₁₀₁	—	2	16	no	—
65	C₄×D₄×C₁₀₁	—	2	2	no	—
66	C₄×D₄×C₁₀₁	—	2	2	no	—
67	C₄×D₄×C₁₀₁	—	2	2	no	—
68	C₄×D₄×C₁₀₁	D₄	1	4	yes	—
69	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
70	C₂×C₄⋊C₄×C₁₀₁	D₄	1	1	yes	characteristic
71	C₂×C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
72	C₂×C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
73	C₂×C₄⋊C₄×C₁₀₁	C₂³	1	1	yes	characteristic
74	C₂×C₂²⋊C₄×C₁₀₁	—	2	1	no	—
75	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
76	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
77	C₂×C₂²⋊C₄×C₁₀₁	D₄	1	2	yes	—
78	C₂×C₄²×C₁₀₁	—	2	1	no	—
79	C₂×C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
80	#106×C₁₀₁	—	2	4	no	—
81	C₄⋊C₈×C₁₀₁	—	2	2	no	—
82	#102×C₁₀₁	—	2	4	no	—
83	#102×C₁₀₁	—	2	8	no	—
84	#102×C₁₀₁	—	2	4	no	—
85	#102×C₁₀₁	—	4	4	no	—
86	C₂²⋊C₈×C₁₀₁	—	4	4	no	—
87	C₄×C₈×C₁₀₁	—	2	2	no	—
88	#95×C₁₀₁	—	2	1	no	—
89	#95×C₁₀₁	—	2	4	no	—
90	C₂⁴×C₁₀₁	—	2	1	no	—
91	C₂⁴×C₁₀₁	—	2	8	no	—
92	C₂⁴×C₁₀₁	—	2	2	no	—
93	C₂⁴×C₁₀₁	—	4	8	no	—
94	C₂⁴×C₁₀₁	—	4	4	no	—
95	C₂⁴×C₁₀₁	—	4	4	no	—
96	C₂⁴×C₁₀₁	—	8	4	no	—
97	C₂⁴×C₁₀₁	C₂×D₄	1	2	yes	—
98	C₂×Q₈×C₁₀₁	—	4	2	no	—
99	C₂×Q₈×C₁₀₁	—	8	2	no	—
100	C₂×D₄×C₁₀₁	—	2	8	no	—
101	C₂×D₄×C₁₀₁	—	2	8	no	—
102	C₂×D₄×C₁₀₁	—	2	2	no	—
103	C₂×D₄×C₁₀₁	—	2	4	no	—
104	C₂×D₄×C₁₀₁	—	2	4	no	—
105	C₂×D₄×C₁₀₁	—	2	2	no	—
106	C₂×D₄×C₁₀₁	—	2	1	no	—
107	C₂×D₄×C₁₀₁	—	2	2	no	—
108	C₂×D₄×C₁₀₁	—	2	4	no	—
109	C₂×D₄×C₁₀₁	—	2	2	no	—
110	C₂×D₄×C₁₀₁	—	2	4	no	—
111	C₂×D₄×C₁₀₁	—	4	8	no	—
112	C₂×D₄×C₁₀₁	—	4	16	no	—
113	C₂×D₄×C₁₀₁	—	4	8	no	—
114	C₂×D₄×C₁₀₁	—	4	32	no	—
115	C₂×D₄×C₁₀₁	—	4	4	no	—
116	C₂×D₄×C₁₀₁	—	4	4	no	—
117	C₂×D₄×C₁₀₁	—	4	8	no	—
118	C₂×D₄×C₁₀₁	—	4	2	no	—
119	C₂×D₄×C₁₀₁	—	4	2	no	—
120	C₂×D₄×C₁₀₁	—	8	2	no	—
121	C₂×D₄×C₁₀₁	SD₁₆	1	4	yes	—
122	C₂×D₄×C₁₀₁	C₂×D₄	1	4	yes	—
123	C₂×D₄×C₁₀₁	C₂×D₄	1	2	yes	—
124	C₂×D₄×C₁₀₁	#41	1	4	yes	—
125	C₂²×C₄×C₁₀₁	—	2	1	no	—
126	C₂²×C₄×C₁₀₁	—	2	4	no	—
127	C₂²×C₄×C₁₀₁	—	2	2	no	—
128	C₂²×C₄×C₁₀₁	—	2	2	no	—
129	C₂²×C₄×C₁₀₁	—	2	4	no	—
130	C₂²×C₄×C₁₀₁	—	2	4	no	—
131	C₂²×C₄×C₁₀₁	—	2	2	no	—
132	C₂²×C₄×C₁₀₁	—	2	2	no	—
133	C₂²×C₄×C₁₀₁	—	4	2	no	—
134	C₂²×C₄×C₁₀₁	—	4	2	no	—
135	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
136	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
139	C₂×C₈×C₁₀₁	—	2	2	no	—
140	C₂×C₈×C₁₀₁	—	2	2	no	—
141	C₂×C₈×C₁₀₁	—	2	2	no	—
142	C₂×C₈×C₁₀₁	—	2	2	no	—
143	C₂×C₈×C₁₀₁	—	2	4	no	—
144	C₄⋊C₄×C₁₀₁	—	2	2	no	—
145	C₄⋊C₄×C₁₀₁	—	2	1	no	—
146	C₄⋊C₄×C₁₀₁	—	2	2	no	—
147	C₄⋊C₄×C₁₀₁	—	2	2	no	—
148	C₄⋊C₄×C₁₀₁	—	2	2	no	—
149	C₄⋊C₄×C₁₀₁	—	2	2	no	—
150	C₄⋊C₄×C₁₀₁	—	4	2	no	—
151	C₄⋊C₄×C₁₀₁	C₂×D₄	1	2	yes	—
152	C₂²⋊C₄×C₁₀₁	—	2	8	no	—
153	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
154	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
155	C₂²⋊C₄×C₁₀₁	—	8	4	no	—
156	C₄²×C₁₀₁	—	4	2	no	—
157	C₄²×C₁₀₁	C₂×D₄	1	2	yes	—
158	C₄²×C₁₀₁	C₂×D₄	1	2	yes	—
159	C₂³×C₁₀₁	—	2	2	no	—
160	C₂³×C₁₀₁	—	2	2	no	—
161	C₂³×C₁₀₁	—	2	4	no	—
162	C₂³×C₁₀₁	—	2	4	no	—
163	C₂³×C₁₀₁	—	2	2	no	—
164	C₂³×C₁₀₁	—	2	4	no	—
165	C₂³×C₁₀₁	—	2	4	no	—
166	C₂³×C₁₀₁	—	4	16	no	—
167	C₂³×C₁₀₁	—	4	16	no	—
168	C₂³×C₁₀₁	—	4	1	no	—
169	C₂³×C₁₀₁	—	4	1	no	—
170	C₂³×C₁₀₁	—	4	2	no	—
171	C₂³×C₁₀₁	—	4	4	no	—
172	C₂³×C₁₀₁	—	4	2	no	—
173	C₂³×C₁₀₁	—	4	2	no	—
174	C₂³×C₁₀₁	—	4	4	no	—
175	C₂³×C₁₀₁	—	8	16	no	—
176	C₂³×C₁₀₁	—	8	8	no	—
177	C₂³×C₁₀₁	—	8	16	no	—
178	C₂³×C₁₀₁	C₂×SD₁₆	1	4	yes	—
179	C₂³×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
180	Q₈×C₁₀₁	—	8	4	no	—
181	D₄×C₁₀₁	—	2	2	no	—
182	D₄×C₁₀₁	—	2	4	no	—
183	D₄×C₁₀₁	—	2	8	no	—
184	D₄×C₁₀₁	—	2	8	no	—
185	D₄×C₁₀₁	—	4	16	no	—
186	D₄×C₁₀₁	—	4	16	no	—
187	D₄×C₁₀₁	—	4	2	no	—
188	D₄×C₁₀₁	—	4	2	no	—
189	D₄×C₁₀₁	—	4	8	no	—
190	D₄×C₁₀₁	—	8	4	no	—
191	D₄×C₁₀₁	#124	1	4	yes	—
192	C₂×C₄×C₁₀₁	—	2	2	no	—
193	C₂×C₄×C₁₀₁	—	2	2	no	—
194	C₂×C₄×C₁₀₁	—	2	2	no	—
195	C₂×C₄×C₁₀₁	—	2	4	no	—
196	C₂×C₄×C₁₀₁	—	4	1	no	—
197	C₂×C₄×C₁₀₁	—	4	1	no	—
198	C₂×C₄×C₁₀₁	—	4	2	no	—
199	C₂×C₄×C₁₀₁	—	4	2	no	—
200	C₂×C₄×C₁₀₁	—	4	4	no	—
201	C₂×C₄×C₁₀₁	—	4	8	no	—
202	C₂×C₄×C₁₀₁	—	4	2	no	—
203	C₂×C₄×C₁₀₁	—	4	2	no	—
204	C₂×C₄×C₁₀₁	—	4	2	no	—
205	C₂×C₄×C₁₀₁	—	4	2	no	—
206	C₂×C₄×C₁₀₁	—	4	4	no	—
207	C₂×C₄×C₁₀₁	#120	1	2	yes	—
208	C₂×C₄×C₁₀₁	#120	1	2	yes	—
209	C₂×C₄×C₁₀₁	C₂×SD₁₆	1	2	yes	—
210	C₂×C₄×C₁₀₁	AGL(1,ℤ/8)	1	2	yes	—
211	C₂×C₄×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
212	C₂×C₄×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
213	C₂×C₄×C₁₀₁	C₂×#41	1	2	yes	—
214	C₂×C₄×C₁₀₁	H(5,𝔽₂)	1	2	yes	—
215	C₈×C₁₀₁	—	4	2	no	—
216	C₈×C₁₀₁	—	4	2	no	—
217	C₂²×C₁₀₁	—	2	4	no	—
218	C₂²×C₁₀₁	—	2	4	no	—
219	C₂²×C₁₀₁	—	2	8	no	—
220	C₂²×C₁₀₁	—	4	2	no	—
221	C₂²×C₁₀₁	—	4	2	no	—
222	C₂²×C₁₀₁	—	4	2	no	—
223	C₂²×C₁₀₁	—	4	2	no	—
224	C₂²×C₁₀₁	—	4	4	no	—
225	C₂²×C₁₀₁	—	4	4	no	—
226	C₂²×C₁₀₁	—	4	4	no	—
227	C₂²×C₁₀₁	—	4	4	no	—
228	C₂²×C₁₀₁	—	4	4	no	—
229	C₂²×C₁₀₁	—	4	4	no	—
230	C₂²×C₁₀₁	—	8	32	no	—
231	C₂²×C₁₀₁	—	8	4	no	—
232	C₂²×C₁₀₁	—	8	4	no	—
233	C₂²×C₁₀₁	C₂×#120	1	1	yes	characteristic
234	C₂²×C₁₀₁	#546	1	2	yes	—
235	C₂²×C₁₀₁	C₂²×SD₁₆	1	1	yes	characteristic
236	C₂²×C₁₀₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
237	C₂²×C₁₀₁	#576	1	2	yes	—
238	C₄×C₁₀₁	—	2	2	no	—
239	C₄×C₁₀₁	—	4	2	no	—
240	C₄×C₁₀₁	—	4	2	no	—
241	C₄×C₁₀₁	—	8	2	no	—
242	C₄×C₁₀₁	—	8	2	no	—
243	C₄×C₁₀₁	#450	1	4	yes	—
244	C₄×C₁₀₁	C₂×#124	1	1	yes	characteristic
245	C₄×C₁₀₁	#535	1	1	yes	characteristic
246	C₄×C₁₀₁	#546	1	2	yes	—
247	#25881	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
248	C₂×C₁₀₁	—	4	4	no	—
249	C₂×C₁₀₁	—	4	4	no	—
250	C₂×C₁₀₁	—	8	4	no	—
251	C₂×C₁₀₁	#2435	1	1	yes	characteristic
252	C₂×C₁₀₁	C₂×#450	1	1	yes	characteristic
253	C₂×C₁₀₁	#3008	1	1	yes	characteristic
254	C₂×C₁₀₁	#3295	1	2	yes	—
255	C₂×C₁₀₁	#3325	1	2	yes	—
256	C₂×D₄²	C₂×C₁₀₁	1	1	yes	characteristic
257	C₂×#486	C₂×C₁₀₁	1	1	yes	characteristic, complemented
258	C₂×#476	C₂×C₁₀₁	1	1	yes	characteristic, complemented
259	#2563	C₂×C₁₀₁	1	1	yes	characteristic, complemented
260	#2034	C₂×C₁₀₁	1	4	yes	complemented
261	#1982	C₂×C₁₀₁	1	1	yes	characteristic, complemented
262	#1954	C₂×C₁₀₁	1	1	yes	characteristic, complemented
263	#1786	C₂×C₁₀₁	1	4	yes	complemented
264	C₄×#102	C₂×C₁₀₁	1	1	yes	characteristic, complemented
265	C₁₀₁	#25881	1	1	yes	characteristic, direct product factor, Sylow
266	C₂³×D₄	—	2	1	no	—
267	C₂³×D₄	C₂²×C₁₀₁	1	2	yes	—
268	D₄²	—	2	4	no	—
269	D₄²	—	2	4	no	—
270	C₂×C₄⋊Q₈	C₂²×C₁₀₁	1	1	yes	characteristic, complemented
271	C₂×#127	C₂²×C₁₀₁	1	1	yes	characteristic
272	C₂×#121	—	2	1	no	—
273	C₂×#121	C₂²×C₁₀₁	1	2	yes	—
274	C₂×#120	—	2	2	no	—
275	C₂×C₄×D₄	C₂²×C₁₀₁	1	1	yes	characteristic
276	C₂×C₄×D₄	C₂²×C₁₀₁	1	1	yes	characteristic
277	#486	—	2	4	no	—
278	#476	—	2	4	no	—
279	C₂×#106	C₂²×C₁₀₁	1	2	yes	complemented
280	C₂×C₄⋊C₈	C₂²×C₁₀₁	1	1	yes	characteristic, complemented
281	C₂×#102	C₂²×C₁₀₁	1	2	yes	—
282	C₂×#102	C₂²×C₁₀₁	1	2	yes	—
283	C₂×#102	C₂²×C₁₀₁	1	4	yes	complemented
284	C₂×#102	C₂²×C₁₀₁	1	4	yes	complemented
285	C₂×C₂²⋊C₈	C₂²×C₁₀₁	1	4	yes	complemented
286	C₂×C₄×C₈	C₂²×C₁₀₁	1	1	yes	characteristic, complemented
287	#393	—	2	2	no	—
288	#390	—	2	1	no	—
289	#382	—	2	1	no	—
290	#380	C₂²×C₁₀₁	1	4	yes	complemented
291	C₄×C₄⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic, complemented
292	#340	C₂²×C₁₀₁	1	2	yes	complemented
293	C₂⁵	—	2	2	no	—
294	C₂²×Q₈	—	2	1	no	—
295	C₂²×D₄	—	2	8	no	—
296	C₂²×D₄	—	2	2	no	—
297	C₂²×D₄	—	2	4	no	—
298	C₂²×D₄	—	2	4	no	—
299	C₂²×D₄	—	2	8	no	—
300	C₂²×D₄	—	2	2	no	—
301	C₂²×D₄	—	2	1	no	—
302	C₂²×D₄	—	2	1	no	—
303	C₂²×D₄	—	4	4	no	—
304	C₂²×D₄	—	4	4	no	—
305	C₂²×D₄	—	4	4	no	—
306	C₂²×D₄	D₄×C₁₀₁	1	1	yes	characteristic
307	C₂²×D₄	C₂³×C₁₀₁	1	2	yes	—
308	C₂²×D₄	C₂³×C₁₀₁	1	1	yes	characteristic
309	C₂³×C₄	—	2	1	no	—
310	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
311	C₂²×C₈	C₂³×C₁₀₁	1	2	yes	—
312	C₂²×C₈	C₂³×C₁₀₁	1	2	yes	—
313	C₄⋊Q₈	—	2	2	no	—
314	C₄⋊Q₈	—	2	2	no	—
315	#127	—	2	2	no	—
316	#127	D₄×C₁₀₁	1	4	yes	—
317	#121	—	2	8	no	—
318	#121	—	2	4	no	—
319	#121	—	2	4	no	—
320	#120	—	2	16	no	—
321	C₄×D₄	—	2	2	no	—
322	C₄×D₄	—	2	2	no	—
323	C₄×D₄	—	2	2	no	—
324	C₄×D₄	D₄×C₁₀₁	1	4	yes	—
325	C₂×C₄⋊C₄	—	2	1	no	—
326	C₂×C₄⋊C₄	D₄×C₁₀₁	1	1	yes	characteristic
327	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	2	yes	—
328	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	2	yes	—
329	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	1	yes	characteristic
330	C₂×C₂²⋊C₄	—	2	1	no	—
331	C₂×C₂²⋊C₄	—	2	2	no	—
332	C₂×C₂²⋊C₄	—	2	4	no	—
333	C₂×C₂²⋊C₄	D₄×C₁₀₁	1	2	yes	—
334	C₂×C₄²	—	2	1	no	—
335	C₂×C₄²	C₂³×C₁₀₁	1	1	yes	characteristic
336	#106	—	2	4	no	—
337	C₄⋊C₈	—	2	2	no	—
338	#102	—	2	4	no	—
339	#102	—	2	8	no	—
340	#102	—	2	4	no	—
341	#102	—	4	4	no	—
342	C₂²⋊C₈	—	4	4	no	—
343	C₄×C₈	—	2	2	no	—
344	#95	—	2	1	no	—
345	#95	—	2	4	no	—
346	C₂⁴	—	2	1	no	—
347	C₂⁴	—	2	8	no	—
348	C₂⁴	—	2	2	no	—
349	C₂⁴	—	4	8	no	—
350	C₂⁴	—	4	4	no	—
351	C₂⁴	—	4	4	no	—
352	C₂⁴	—	8	4	no	—
353	C₂⁴	C₂×D₄×C₁₀₁	1	2	yes	—
354	C₂×Q₈	—	4	2	no	—
355	C₂×Q₈	—	8	2	no	—
356	C₂×D₄	—	2	8	no	—
357	C₂×D₄	—	2	8	no	—
358	C₂×D₄	—	2	2	no	—
359	C₂×D₄	—	2	4	no	—
360	C₂×D₄	—	2	4	no	—
361	C₂×D₄	—	2	2	no	—
362	C₂×D₄	—	2	1	no	—
363	C₂×D₄	—	2	2	no	—
364	C₂×D₄	—	2	4	no	—
365	C₂×D₄	—	2	2	no	—
366	C₂×D₄	—	2	4	no	—
367	C₂×D₄	—	4	8	no	—
368	C₂×D₄	—	4	16	no	—
369	C₂×D₄	—	4	32	no	—
370	C₂×D₄	—	4	8	no	—
371	C₂×D₄	—	4	4	no	—
372	C₂×D₄	—	4	4	no	—
373	C₂×D₄	—	4	8	no	—
374	C₂×D₄	—	4	2	no	—
375	C₂×D₄	—	4	2	no	—
376	C₂×D₄	—	8	2	no	—
377	C₂×D₄	SD₁₆×C₁₀₁	1	4	yes	—
378	C₂×D₄	C₂×D₄×C₁₀₁	1	4	yes	—
379	C₂×D₄	C₂×D₄×C₁₀₁	1	2	yes	—
380	C₂×D₄	#41×C₁₀₁	1	4	yes	—
381	C₂²×C₄	—	2	1	no	—
382	C₂²×C₄	—	2	4	no	—
383	C₂²×C₄	—	2	2	no	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	2	4	no	—
386	C₂²×C₄	—	2	4	no	—
387	C₂²×C₄	—	2	2	no	—
388	C₂²×C₄	—	2	2	no	—
389	C₂²×C₄	—	4	2	no	—
390	C₂²×C₄	—	4	2	no	—
391	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
392	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
393	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
394	C₂²×C₄	C₂⁴×C₁₀₁	1	1	yes	characteristic
395	C₂×C₈	—	2	2	no	—
396	C₂×C₈	—	2	2	no	—
397	C₂×C₈	—	2	2	no	—
398	C₂×C₈	—	2	2	no	—
399	C₂×C₈	—	2	4	no	—
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	—	2	1	no	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	—	2	2	no	—
406	C₄⋊C₄	—	4	2	no	—
407	C₄⋊C₄	C₂×D₄×C₁₀₁	1	2	yes	—
408	C₂²⋊C₄	—	2	8	no	—
409	C₂²⋊C₄	—	2	4	no	—
410	C₂²⋊C₄	—	2	4	no	—
411	C₂²⋊C₄	—	8	4	no	—
412	C₄²	—	4	2	no	—
413	C₄²	C₂×D₄×C₁₀₁	1	2	yes	—
414	C₄²	C₂×D₄×C₁₀₁	1	2	yes	—
415	C₂³	—	2	2	no	—
416	C₂³	—	2	2	no	—
417	C₂³	—	2	4	no	—
418	C₂³	—	2	4	no	—
419	C₂³	—	2	2	no	—
420	C₂³	—	2	4	no	—
421	C₂³	—	2	4	no	—
422	C₂³	—	4	16	no	—
423	C₂³	—	4	16	no	—
424	C₂³	—	4	1	no	—
425	C₂³	—	4	1	no	—
426	C₂³	—	4	2	no	—
427	C₂³	—	4	4	no	—
428	C₂³	—	4	2	no	—
429	C₂³	—	4	2	no	—
430	C₂³	—	4	4	no	—
431	C₂³	—	8	16	no	—
432	C₂³	—	8	8	no	—
433	C₂³	—	8	16	no	—
434	C₂³	C₂×SD₁₆×C₁₀₁	1	4	yes	—
435	C₂³	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
436	Q₈	—	8	4	no	—
437	D₄	—	2	8	no	—
438	D₄	—	2	2	no	—
439	D₄	—	2	4	no	—
440	D₄	—	2	8	no	—
441	D₄	—	4	16	no	—
442	D₄	—	4	16	no	—
443	D₄	—	4	8	no	—
444	D₄	—	4	2	no	—
445	D₄	—	4	2	no	—
446	D₄	—	8	4	no	—
447	D₄	#124×C₁₀₁	1	4	yes	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	4	no	—
452	C₂×C₄	—	4	1	no	—
453	C₂×C₄	—	4	1	no	—
454	C₂×C₄	—	4	8	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	4	4	no	—
458	C₂×C₄	—	4	2	no	—
459	C₂×C₄	—	4	2	no	—
460	C₂×C₄	—	4	2	no	—
461	C₂×C₄	—	4	2	no	—
462	C₂×C₄	—	4	4	no	—
463	C₂×C₄	#120×C₁₀₁	1	2	yes	—
464	C₂×C₄	#120×C₁₀₁	1	2	yes	—
465	C₂×C₄	C₂×SD₁₆×C₁₀₁	1	2	yes	—
466	C₂×C₄	AGL(1,ℤ/8)×C₁₀₁	1	2	yes	—
467	C₂×C₄	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
468	C₂×C₄	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
469	C₂×C₄	C₂×#41×C₁₀₁	1	2	yes	—
470	C₂×C₄	H(5,𝔽₂)×C₁₀₁	1	2	yes	—
471	C₈	—	4	2	no	—
472	C₈	—	4	2	no	—
473	C₂²	—	2	4	no	—
474	C₂²	—	2	4	no	—
475	C₂²	—	2	8	no	—
476	C₂²	—	4	2	no	—
477	C₂²	—	4	2	no	—
478	C₂²	—	4	2	no	—
479	C₂²	—	4	2	no	—
480	C₂²	—	4	4	no	—
481	C₂²	—	4	4	no	—
482	C₂²	—	4	4	no	—
483	C₂²	—	4	4	no	—
484	C₂²	—	4	4	no	—
485	C₂²	—	4	4	no	—
486	C₂²	—	8	32	no	—
487	C₂²	—	8	4	no	—
488	C₂²	—	8	4	no	—
489	C₂²	C₂×#120×C₁₀₁	1	1	yes	characteristic
490	C₂²	#546×C₁₀₁	1	2	yes	—
491	C₂²	C₂²×SD₁₆×C₁₀₁	1	1	yes	characteristic
492	C₂²	C₂×AGL(1,ℤ/8)×C₁₀₁	1	1	yes	characteristic
493	C₂²	#576×C₁₀₁	1	2	yes	—
494	C₄	—	2	2	no	—
495	C₄	—	4	2	no	—
496	C₄	—	4	2	no	—
497	C₄	—	8	2	no	—
498	C₄	—	8	2	no	—
499	C₄	#450×C₁₀₁	1	4	yes	—
500	C₄	C₂×#124×C₁₀₁	1	1	yes	characteristic
501	C₄	#535×C₁₀₁	1	1	yes	characteristic
502	C₄	#546×C₁₀₁	1	2	yes	—
503	C₂	—	4	4	no	—
504	C₂	—	4	4	no	—
505	C₂	—	8	4	no	—
506	C₂	C₁₀₁×#2435	1	1	yes	characteristic
507	C₂	C₂×#450×C₁₀₁	1	1	yes	characteristic
508	C₂	C₁₀₁×#3008	1	1	yes	characteristic
509	C₂	C₁₀₁×#3295	1	2	yes	—
510	C₂	C₁₀₁×#3325	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₀₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₀₁
prime radical	C₂×D₄²×C₁₀₁	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₀₁ ◁ C₂×C₄×D₄×C₁₀₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#486×C₁₀₁	C₂	semidirect
3. C₂×#476×C₁₀₁	C₂	semidirect
4. C₁₀₁×#2563	C₂	semidirect
5. C₁₀₁×#2034	C₂	semidirect
6. C₁₀₁×#1982	C₂	semidirect
7. C₁₀₁×#1954	C₂	semidirect
8. C₁₀₁×#1786	C₂	semidirect
9. C₄×#102×C₁₀₁	C₂	semidirect
14. C₂×C₄⋊Q₈×C₁₀₁	C₂²	semidirect
23. C₂×#106×C₁₀₁	C₂²	semidirect
24. C₂×C₄⋊C₈×C₁₀₁	C₂²	semidirect
27. C₂×#102×C₁₀₁	C₂²	semidirect
28. C₂×#102×C₁₀₁	C₂²	semidirect
29. C₂×C₂²⋊C₈×C₁₀₁	C₂²	semidirect
30. C₂×C₄×C₈×C₁₀₁	C₂²	semidirect
34. #380×C₁₀₁	C₂²	semidirect
35. C₄×C₄⋊C₄×C₁₀₁	C₂²	semidirect
36. #340×C₁₀₁	C₂²	semidirect
247. #25881	C₁₀₁	direct (N × H)
257. C₂×#486	C₂×C₁₀₁	semidirect
258. C₂×#476	C₂×C₁₀₁	semidirect
259. #2563	C₂×C₁₀₁	semidirect
260. #2034	C₂×C₁₀₁	semidirect
261. #1982	C₂×C₁₀₁	semidirect
262. #1954	C₂×C₁₀₁	semidirect
263. #1786	C₂×C₁₀₁	semidirect
264. C₄×#102	C₂×C₁₀₁	semidirect
265. C₁₀₁	#25881	direct (N × H)
270. C₂×C₄⋊Q₈	C₂²×C₁₀₁	semidirect
279. C₂×#106	C₂²×C₁₀₁	semidirect
280. C₂×C₄⋊C₈	C₂²×C₁₀₁	semidirect
283. C₂×#102	C₂²×C₁₀₁	semidirect
284. C₂×#102	C₂²×C₁₀₁	semidirect
285. C₂×C₂²⋊C₈	C₂²×C₁₀₁	semidirect
286. C₂×C₄×C₈	C₂²×C₁₀₁	semidirect
290. #380	C₂²×C₁₀₁	semidirect
291. C₄×C₄⋊C₄	C₂²×C₁₀₁	semidirect
292. #340	C₂²×C₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄²×C₁₀₁	2
C₂×#486×C₁₀₁	2
C₂×#476×C₁₀₁	2
C₁₀₁×#2563	2
C₁₀₁×#2034	2
C₁₀₁×#1982	2
C₁₀₁×#1954	2
C₁₀₁×#1786	2
C₄×#102×C₁₀₁	2
#25881	101

Subgroups — C101×#25881 #38808032

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#25881 #38808032