Subgroups — C₁₀₁×#25855 #38808006

Order 25856.

2026 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#127×C₁₀₁	C₂	1	1	yes	maximal, characteristic
2	C₂×#486×C₁₀₁	C₂	1	2	yes	maximal, complemented
3	C₁₀₁×#2857	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₀₁×#2041	C₂	1	4	yes	maximal, complemented
5	C₁₀₁×#1957	C₂	1	2	yes	maximal, complemented
6	C₁₀₁×#1786	C₂	1	4	yes	maximal, complemented
7	C₄×C₂²⋊C₈×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂³×D₄×C₁₀₁	—	2	1	no	—
9	C₂³×D₄×C₁₀₁	—	2	1	no	—
10	C₂³×D₄×C₁₀₁	C₂²	1	2	yes	—
11	C₂×C₄⋊Q₈×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
12	C₂×#127×C₁₀₁	—	2	8	no	—
13	C₂×#127×C₁₀₁	—	2	1	no	—
14	C₂×#127×C₁₀₁	—	2	1	no	—
15	C₂×#127×C₁₀₁	C₂²	1	2	yes	—
16	C₂×#127×C₁₀₁	C₂²	1	2	yes	—
17	C₂×C₂²⋊Q₈×C₁₀₁	—	2	1	no	—
18	C₂²×C₄²×C₁₀₁	C₂²	1	1	yes	characteristic
19	#486×C₁₀₁	—	2	8	no	—
20	C₂×#102×C₁₀₁	C₂²	1	8	yes	complemented
21	C₂×#102×C₁₀₁	C₂²	1	8	yes	complemented
22	C₂×C₂²⋊C₈×C₁₀₁	C₂²	1	2	yes	—
23	C₂×C₄×C₈×C₁₀₁	C₂²	1	2	yes	complemented
24	#391×C₁₀₁	—	2	1	no	—
25	#389×C₁₀₁	—	2	1	no	—
26	#389×C₁₀₁	C₂²	1	2	yes	complemented
27	#384×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
28	#380×C₁₀₁	—	2	1	no	—
29	#380×C₁₀₁	C₂²	1	2	yes	—
30	#336×C₁₀₁	C₂²	1	2	yes	complemented
31	C₂⁵×C₁₀₁	—	2	2	no	—
32	C₂²×Q₈×C₁₀₁	—	2	1	no	—
33	C₂²×D₄×C₁₀₁	—	2	8	no	—
34	C₂²×D₄×C₁₀₁	—	2	8	no	—
35	C₂²×D₄×C₁₀₁	—	2	8	no	—
36	C₂²×D₄×C₁₀₁	—	2	2	no	—
37	C₂²×D₄×C₁₀₁	—	2	2	no	—
38	C₂²×D₄×C₁₀₁	—	2	2	no	—
39	C₂²×D₄×C₁₀₁	—	2	2	no	—
40	C₂²×D₄×C₁₀₁	—	2	2	no	—
41	C₂²×D₄×C₁₀₁	—	2	8	no	—
42	C₂²×D₄×C₁₀₁	—	4	4	no	—
43	C₂²×D₄×C₁₀₁	—	4	4	no	—
44	C₂²×D₄×C₁₀₁	—	4	4	no	—
45	C₂²×D₄×C₁₀₁	—	4	4	no	—
46	C₂²×D₄×C₁₀₁	—	4	4	no	—
47	C₂²×D₄×C₁₀₁	C₂³	1	4	yes	—
48	C₂³×C₄×C₁₀₁	D₄	1	1	yes	characteristic
49	C₂³×C₄×C₁₀₁	D₄	1	1	yes	characteristic
50	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₁₀₁	C₂³	1	4	yes	—
52	C₄⋊Q₈×C₁₀₁	—	2	4	no	—
53	#127×C₁₀₁	—	2	8	no	—
54	#127×C₁₀₁	—	2	8	no	—
55	#127×C₁₀₁	—	2	8	no	—
56	#127×C₁₀₁	—	2	4	no	—
57	#127×C₁₀₁	D₄	1	8	yes	—
58	C₂²⋊Q₈×C₁₀₁	—	4	4	no	—
59	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
60	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
61	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
62	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
63	C₂×C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
64	C₂×C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
65	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
66	C₂×C₄²×C₁₀₁	—	2	4	no	—
67	C₂×C₄²×C₁₀₁	D₄	1	1	yes	characteristic
68	C₂×C₄²×C₁₀₁	D₄	1	1	yes	characteristic
69	C₂×C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
71	#102×C₁₀₁	—	2	16	no	—
72	#102×C₁₀₁	—	4	8	no	—
73	C₂²⋊C₈×C₁₀₁	—	2	4	no	—
74	C₄×C₈×C₁₀₁	—	2	4	no	—
75	#95×C₁₀₁	—	2	2	no	—
76	#95×C₁₀₁	—	2	2	no	—
77	C₂⁴×C₁₀₁	—	2	8	no	—
78	C₂⁴×C₁₀₁	—	2	4	no	—
79	C₂⁴×C₁₀₁	—	4	4	no	—
80	C₂⁴×C₁₀₁	—	4	4	no	—
81	C₂⁴×C₁₀₁	—	4	4	no	—
82	C₂⁴×C₁₀₁	—	4	4	no	—
83	C₂⁴×C₁₀₁	—	4	4	no	—
84	C₂⁴×C₁₀₁	—	4	4	no	—
85	C₂⁴×C₁₀₁	C₂×D₄	1	1	yes	characteristic
86	C₂×Q₈×C₁₀₁	—	4	2	no	—
87	C₂×Q₈×C₁₀₁	—	4	2	no	—
88	C₂×Q₈×C₁₀₁	—	4	2	no	—
89	C₂×D₄×C₁₀₁	—	2	8	no	—
90	C₂×D₄×C₁₀₁	—	2	8	no	—
91	C₂×D₄×C₁₀₁	—	2	8	no	—
92	C₂×D₄×C₁₀₁	—	2	8	no	—
93	C₂×D₄×C₁₀₁	—	2	8	no	—
94	C₂×D₄×C₁₀₁	—	2	4	no	—
95	C₂×D₄×C₁₀₁	—	2	8	no	—
96	C₂×D₄×C₁₀₁	—	2	8	no	—
97	C₂×D₄×C₁₀₁	—	4	32	no	—
98	C₂×D₄×C₁₀₁	—	4	4	no	—
99	C₂×D₄×C₁₀₁	—	4	4	no	—
100	C₂×D₄×C₁₀₁	—	4	4	no	—
101	C₂×D₄×C₁₀₁	—	4	32	no	—
102	C₂×D₄×C₁₀₁	—	4	32	no	—
103	C₂×D₄×C₁₀₁	—	4	4	no	—
104	C₂×D₄×C₁₀₁	—	4	4	no	—
105	C₂×D₄×C₁₀₁	—	4	4	no	—
106	C₂×D₄×C₁₀₁	—	4	4	no	—
107	C₂×D₄×C₁₀₁	—	4	4	no	—
108	C₂×D₄×C₁₀₁	—	4	4	no	—
109	C₂×D₄×C₁₀₁	—	4	4	no	—
110	C₂×D₄×C₁₀₁	C₂×D₄	1	8	yes	—
111	C₂²×C₄×C₁₀₁	—	2	2	no	—
112	C₂²×C₄×C₁₀₁	—	2	2	no	—
113	C₂²×C₄×C₁₀₁	—	2	2	no	—
114	C₂²×C₄×C₁₀₁	—	2	2	no	—
115	C₂²×C₄×C₁₀₁	—	2	2	no	—
116	C₂²×C₄×C₁₀₁	—	2	2	no	—
117	C₂²×C₄×C₁₀₁	—	2	2	no	—
118	C₂²×C₄×C₁₀₁	—	2	2	no	—
119	C₂²×C₄×C₁₀₁	D₈	1	4	yes	—
120	C₂²×C₄×C₁₀₁	SD₁₆	1	4	yes	—
121	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₀₁	#41	1	4	yes	—
127	C₂²×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
128	C₂×C₈×C₁₀₁	—	2	4	no	—
129	C₂×C₈×C₁₀₁	—	2	4	no	—
130	C₂×C₈×C₁₀₁	—	2	4	no	—
131	C₄⋊C₄×C₁₀₁	—	2	4	no	—
132	C₄⋊C₄×C₁₀₁	—	2	4	no	—
133	C₄⋊C₄×C₁₀₁	—	4	2	no	—
134	C₄⋊C₄×C₁₀₁	—	4	2	no	—
135	C₄⋊C₄×C₁₀₁	—	4	4	no	—
136	C₄⋊C₄×C₁₀₁	—	4	2	no	—
137	C₂²⋊C₄×C₁₀₁	—	4	4	no	—
138	C₄²×C₁₀₁	—	2	2	no	—
139	C₄²×C₁₀₁	—	2	2	no	—
140	C₄²×C₁₀₁	—	2	2	no	—
141	C₄²×C₁₀₁	C₂×D₄	1	4	yes	—
142	C₂³×C₁₀₁	—	2	1	no	—
143	C₂³×C₁₀₁	—	2	1	no	—
144	C₂³×C₁₀₁	—	2	1	no	—
145	C₂³×C₁₀₁	—	2	1	no	—
146	C₂³×C₁₀₁	—	2	8	no	—
147	C₂³×C₁₀₁	—	4	16	no	—
148	C₂³×C₁₀₁	—	4	16	no	—
149	C₂³×C₁₀₁	—	4	16	no	—
150	C₂³×C₁₀₁	—	4	4	no	—
151	C₂³×C₁₀₁	—	4	4	no	—
152	C₂³×C₁₀₁	—	4	4	no	—
153	C₂³×C₁₀₁	—	4	4	no	—
154	C₂³×C₁₀₁	—	4	4	no	—
155	C₂³×C₁₀₁	—	4	4	no	—
156	C₂³×C₁₀₁	—	8	8	no	—
157	C₂³×C₁₀₁	—	8	8	no	—
158	C₂³×C₁₀₁	—	8	8	no	—
159	C₂³×C₁₀₁	—	8	8	no	—
160	C₂³×C₁₀₁	#124	1	2	yes	—
161	C₂³×C₁₀₁	C₂×D₈	1	2	yes	—
162	C₂³×C₁₀₁	C₂×SD₁₆	1	2	yes	—
163	C₂³×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
164	Q₈×C₁₀₁	—	8	4	no	—
165	D₄×C₁₀₁	—	2	16	no	—
166	D₄×C₁₀₁	—	4	16	no	—
167	D₄×C₁₀₁	—	4	16	no	—
168	D₄×C₁₀₁	—	4	16	no	—
169	D₄×C₁₀₁	—	4	8	no	—
170	D₄×C₁₀₁	—	4	16	no	—
171	D₄×C₁₀₁	—	4	16	no	—
172	C₂×C₄×C₁₀₁	—	2	1	no	—
173	C₂×C₄×C₁₀₁	—	2	1	no	—
174	C₂×C₄×C₁₀₁	—	2	1	no	—
175	C₂×C₄×C₁₀₁	—	2	1	no	—
176	C₂×C₄×C₁₀₁	—	2	1	no	—
177	C₂×C₄×C₁₀₁	—	2	1	no	—
178	C₂×C₄×C₁₀₁	—	2	8	no	—
179	C₂×C₄×C₁₀₁	—	2	8	no	—
180	C₂×C₄×C₁₀₁	—	2	8	no	—
181	C₂×C₄×C₁₀₁	—	4	2	no	—
182	C₂×C₄×C₁₀₁	—	4	2	no	—
183	C₂×C₄×C₁₀₁	—	4	2	no	—
184	C₂×C₄×C₁₀₁	—	4	2	no	—
185	C₂×C₄×C₁₀₁	—	4	2	no	—
186	C₂×C₄×C₁₀₁	—	4	2	no	—
187	C₂×C₄×C₁₀₁	#120	1	2	yes	—
188	C₂×C₄×C₁₀₁	#120	1	2	yes	—
189	C₂×C₄×C₁₀₁	#124	1	2	yes	—
190	C₂×C₄×C₁₀₁	C₂×D₈	1	2	yes	—
191	C₂×C₄×C₁₀₁	C₂×D₈	1	2	yes	—
192	C₂×C₄×C₁₀₁	C₂×SD₁₆	1	2	yes	—
193	C₂×C₄×C₁₀₁	C₂×SD₁₆	1	2	yes	—
194	C₂×C₄×C₁₀₁	AGL(1,ℤ/8)	1	2	yes	—
195	C₂×C₄×C₁₀₁	AGL(1,ℤ/8)	1	2	yes	—
196	C₂×C₄×C₁₀₁	C₂²×D₄	1	2	yes	—
197	C₂×C₄×C₁₀₁	C₂×#41	1	2	yes	—
198	C₂×C₄×C₁₀₁	H(5,𝔽₂)	1	2	yes	—
199	C₈×C₁₀₁	—	4	4	no	—
200	C₂²×C₁₀₁	—	2	2	no	—
201	C₂²×C₁₀₁	—	2	2	no	—
202	C₂²×C₁₀₁	—	2	2	no	—
203	C₂²×C₁₀₁	—	2	2	no	—
204	C₂²×C₁₀₁	—	2	2	no	—
205	C₂²×C₁₀₁	—	2	2	no	—
206	C₂²×C₁₀₁	—	4	8	no	—
207	C₂²×C₁₀₁	—	4	8	no	—
208	C₂²×C₁₀₁	—	4	8	no	—
209	C₂²×C₁₀₁	—	8	32	no	—
210	C₂²×C₁₀₁	—	8	4	no	—
211	C₂²×C₁₀₁	—	8	4	no	—
212	C₂²×C₁₀₁	—	8	4	no	—
213	C₂²×C₁₀₁	—	8	4	no	—
214	C₂²×C₁₀₁	#486	1	4	yes	complemented
215	C₂²×C₁₀₁	C₂×#120	1	1	yes	characteristic
216	C₂²×C₁₀₁	C₂×#124	1	1	yes	characteristic
217	C₂²×C₁₀₁	#535	1	1	yes	characteristic
218	C₂²×C₁₀₁	C₂²×D₈	1	1	yes	characteristic
219	C₂²×C₁₀₁	C₂²×SD₁₆	1	1	yes	characteristic
220	C₂²×C₁₀₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
221	C₂²×C₁₀₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
222	C₄×C₁₀₁	—	2	2	no	—
223	C₄×C₁₀₁	—	2	2	no	—
224	C₄×C₁₀₁	—	2	2	no	—
225	C₄×C₁₀₁	—	8	2	no	—
226	C₄×C₁₀₁	—	8	2	no	—
227	C₄×C₁₀₁	#447	1	4	yes	—
228	C₄×C₁₀₁	#450	1	4	yes	—
229	C₄×C₁₀₁	#546	1	4	yes	—
230	#25855	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
231	C₂×C₁₀₁	—	2	4	no	—
232	C₂×C₁₀₁	—	8	8	no	—
233	C₂×C₁₀₁	#2435	1	1	yes	characteristic
234	C₂×C₁₀₁	C₂×#447	1	1	yes	characteristic
235	C₂×C₁₀₁	C₂×#450	1	1	yes	characteristic
236	C₂×C₁₀₁	C₂×#486	1	1	yes	characteristic
237	C₂×C₁₀₁	#3138	1	1	yes	characteristic
238	C₂×C₁₀₁	#3205	1	1	yes	characteristic
239	C₂×C₁₀₁	#3208	1	1	yes	characteristic
240	C₂²×#127	C₂×C₁₀₁	1	1	yes	characteristic
241	C₂×#486	C₂×C₁₀₁	1	2	yes	complemented
242	#2857	C₂×C₁₀₁	1	1	yes	characteristic, complemented
243	#2041	C₂×C₁₀₁	1	4	yes	complemented
244	#1957	C₂×C₁₀₁	1	2	yes	complemented
245	#1786	C₂×C₁₀₁	1	4	yes	complemented
246	C₄×C₂²⋊C₈	C₂×C₁₀₁	1	1	yes	characteristic, complemented
247	C₁₀₁	#25855	1	1	yes	characteristic, direct product factor, Sylow
248	C₂³×D₄	—	2	1	no	—
249	C₂³×D₄	—	2	1	no	—
250	C₂³×D₄	C₂²×C₁₀₁	1	2	yes	—
251	C₂×C₄⋊Q₈	C₂²×C₁₀₁	1	1	yes	characteristic, complemented
252	C₂×#127	—	2	8	no	—
253	C₂×#127	—	2	1	no	—
254	C₂×#127	—	2	1	no	—
255	C₂×#127	C₂²×C₁₀₁	1	2	yes	—
256	C₂×#127	C₂²×C₁₀₁	1	2	yes	—
257	C₂×C₂²⋊Q₈	—	2	1	no	—
258	C₂²×C₄²	C₂²×C₁₀₁	1	1	yes	characteristic
259	#486	—	2	8	no	—
260	C₂×#102	C₂²×C₁₀₁	1	8	yes	complemented
261	C₂×#102	C₂²×C₁₀₁	1	8	yes	complemented
262	C₂×C₂²⋊C₈	C₂²×C₁₀₁	1	2	yes	—
263	C₂×C₄×C₈	C₂²×C₁₀₁	1	2	yes	complemented
264	#391	—	2	1	no	—
265	#389	—	2	1	no	—
266	#389	C₂²×C₁₀₁	1	2	yes	complemented
267	#384	C₂²×C₁₀₁	1	1	yes	characteristic, complemented
268	#380	—	2	1	no	—
269	#380	C₂²×C₁₀₁	1	2	yes	—
270	#336	C₂²×C₁₀₁	1	2	yes	complemented
271	C₂⁵	—	2	2	no	—
272	C₂²×Q₈	—	2	1	no	—
273	C₂²×D₄	—	2	8	no	—
274	C₂²×D₄	—	2	8	no	—
275	C₂²×D₄	—	2	8	no	—
276	C₂²×D₄	—	2	2	no	—
277	C₂²×D₄	—	2	2	no	—
278	C₂²×D₄	—	2	2	no	—
279	C₂²×D₄	—	2	2	no	—
280	C₂²×D₄	—	2	2	no	—
281	C₂²×D₄	—	2	8	no	—
282	C₂²×D₄	—	4	4	no	—
283	C₂²×D₄	—	4	4	no	—
284	C₂²×D₄	—	4	4	no	—
285	C₂²×D₄	—	4	4	no	—
286	C₂²×D₄	—	4	4	no	—
287	C₂²×D₄	C₂³×C₁₀₁	1	4	yes	—
288	C₂³×C₄	D₄×C₁₀₁	1	1	yes	characteristic
289	C₂³×C₄	D₄×C₁₀₁	1	1	yes	characteristic
290	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
291	C₂²×C₈	C₂³×C₁₀₁	1	4	yes	—
292	C₄⋊Q₈	—	2	4	no	—
293	#127	—	2	8	no	—
294	#127	—	2	8	no	—
295	#127	—	2	8	no	—
296	#127	—	2	4	no	—
297	#127	D₄×C₁₀₁	1	8	yes	—
298	C₂²⋊Q₈	—	4	4	no	—
299	C₂×C₄⋊C₄	—	2	1	no	—
300	C₂×C₄⋊C₄	—	2	2	no	—
301	C₂×C₄⋊C₄	—	2	1	no	—
302	C₂×C₄⋊C₄	—	2	1	no	—
303	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	2	yes	—
304	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	2	yes	—
305	C₂×C₂²⋊C₄	—	2	2	no	—
306	C₂×C₄²	—	2	4	no	—
307	C₂×C₄²	D₄×C₁₀₁	1	1	yes	characteristic
308	C₂×C₄²	D₄×C₁₀₁	1	1	yes	characteristic
309	C₂×C₄²	C₂³×C₁₀₁	1	1	yes	characteristic
310	C₂×C₄²	C₂³×C₁₀₁	1	1	yes	characteristic
311	#102	—	2	16	no	—
312	#102	—	4	8	no	—
313	C₂²⋊C₈	—	2	4	no	—
314	C₄×C₈	—	2	4	no	—
315	#95	—	2	2	no	—
316	#95	—	2	2	no	—
317	C₂⁴	—	2	8	no	—
318	C₂⁴	—	2	4	no	—
319	C₂⁴	—	4	4	no	—
320	C₂⁴	—	4	4	no	—
321	C₂⁴	—	4	4	no	—
322	C₂⁴	—	4	4	no	—
323	C₂⁴	—	4	4	no	—
324	C₂⁴	—	4	4	no	—
325	C₂⁴	C₂×D₄×C₁₀₁	1	1	yes	characteristic
326	C₂×Q₈	—	4	2	no	—
327	C₂×Q₈	—	4	2	no	—
328	C₂×Q₈	—	4	2	no	—
329	C₂×D₄	—	2	8	no	—
330	C₂×D₄	—	2	8	no	—
331	C₂×D₄	—	2	8	no	—
332	C₂×D₄	—	2	8	no	—
333	C₂×D₄	—	2	8	no	—
334	C₂×D₄	—	2	4	no	—
335	C₂×D₄	—	2	8	no	—
336	C₂×D₄	—	2	8	no	—
337	C₂×D₄	—	4	32	no	—
338	C₂×D₄	—	4	4	no	—
339	C₂×D₄	—	4	4	no	—
340	C₂×D₄	—	4	4	no	—
341	C₂×D₄	—	4	32	no	—
342	C₂×D₄	—	4	32	no	—
343	C₂×D₄	—	4	4	no	—
344	C₂×D₄	—	4	4	no	—
345	C₂×D₄	—	4	4	no	—
346	C₂×D₄	—	4	4	no	—
347	C₂×D₄	—	4	4	no	—
348	C₂×D₄	—	4	4	no	—
349	C₂×D₄	—	4	4	no	—
350	C₂×D₄	C₂×D₄×C₁₀₁	1	8	yes	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	D₈×C₁₀₁	1	4	yes	—
360	C₂²×C₄	SD₁₆×C₁₀₁	1	4	yes	—
361	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
362	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
363	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
364	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
365	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
366	C₂²×C₄	#41×C₁₀₁	1	4	yes	—
367	C₂²×C₄	C₂⁴×C₁₀₁	1	1	yes	characteristic
368	C₂×C₈	—	2	4	no	—
369	C₂×C₈	—	2	4	no	—
370	C₂×C₈	—	2	4	no	—
371	C₄⋊C₄	—	2	4	no	—
372	C₄⋊C₄	—	2	4	no	—
373	C₄⋊C₄	—	4	2	no	—
374	C₄⋊C₄	—	4	2	no	—
375	C₄⋊C₄	—	4	4	no	—
376	C₄⋊C₄	—	4	2	no	—
377	C₂²⋊C₄	—	4	4	no	—
378	C₄²	—	2	2	no	—
379	C₄²	—	2	2	no	—
380	C₄²	—	2	2	no	—
381	C₄²	C₂×D₄×C₁₀₁	1	4	yes	—
382	C₂³	—	2	1	no	—
383	C₂³	—	2	1	no	—
384	C₂³	—	2	1	no	—
385	C₂³	—	2	1	no	—
386	C₂³	—	2	8	no	—
387	C₂³	—	4	16	no	—
388	C₂³	—	4	16	no	—
389	C₂³	—	4	16	no	—
390	C₂³	—	4	4	no	—
391	C₂³	—	4	4	no	—
392	C₂³	—	4	4	no	—
393	C₂³	—	4	4	no	—
394	C₂³	—	4	4	no	—
395	C₂³	—	4	4	no	—
396	C₂³	—	8	8	no	—
397	C₂³	—	8	8	no	—
398	C₂³	—	8	8	no	—
399	C₂³	—	8	8	no	—
400	C₂³	#124×C₁₀₁	1	2	yes	—
401	C₂³	C₂×D₈×C₁₀₁	1	2	yes	—
402	C₂³	C₂×SD₁₆×C₁₀₁	1	2	yes	—
403	C₂³	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
404	Q₈	—	8	4	no	—
405	D₄	—	2	16	no	—
406	D₄	—	4	16	no	—
407	D₄	—	4	16	no	—
408	D₄	—	4	16	no	—
409	D₄	—	4	16	no	—
410	D₄	—	4	16	no	—
411	D₄	—	4	8	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	8	no	—
419	C₂×C₄	—	2	8	no	—
420	C₂×C₄	—	2	8	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	#120×C₁₀₁	1	2	yes	—
428	C₂×C₄	#120×C₁₀₁	1	2	yes	—
429	C₂×C₄	#124×C₁₀₁	1	2	yes	—
430	C₂×C₄	C₂×D₈×C₁₀₁	1	2	yes	—
431	C₂×C₄	C₂×D₈×C₁₀₁	1	2	yes	—
432	C₂×C₄	C₂×SD₁₆×C₁₀₁	1	2	yes	—
433	C₂×C₄	C₂×SD₁₆×C₁₀₁	1	2	yes	—
434	C₂×C₄	AGL(1,ℤ/8)×C₁₀₁	1	2	yes	—
435	C₂×C₄	AGL(1,ℤ/8)×C₁₀₁	1	2	yes	—
436	C₂×C₄	C₂²×D₄×C₁₀₁	1	2	yes	—
437	C₂×C₄	C₂×#41×C₁₀₁	1	2	yes	—
438	C₂×C₄	H(5,𝔽₂)×C₁₀₁	1	2	yes	—
439	C₈	—	4	4	no	—
440	C₂²	—	2	2	no	—
441	C₂²	—	2	2	no	—
442	C₂²	—	2	2	no	—
443	C₂²	—	2	2	no	—
444	C₂²	—	2	2	no	—
445	C₂²	—	2	2	no	—
446	C₂²	—	4	8	no	—
447	C₂²	—	4	8	no	—
448	C₂²	—	4	8	no	—
449	C₂²	—	8	32	no	—
450	C₂²	—	8	4	no	—
451	C₂²	—	8	4	no	—
452	C₂²	—	8	4	no	—
453	C₂²	—	8	4	no	—
454	C₂²	#486×C₁₀₁	1	4	yes	complemented
455	C₂²	C₂×#120×C₁₀₁	1	1	yes	characteristic
456	C₂²	C₂×#124×C₁₀₁	1	1	yes	characteristic
457	C₂²	#535×C₁₀₁	1	1	yes	characteristic
458	C₂²	C₂²×D₈×C₁₀₁	1	1	yes	characteristic
459	C₂²	C₂²×SD₁₆×C₁₀₁	1	1	yes	characteristic
460	C₂²	C₂×AGL(1,ℤ/8)×C₁₀₁	1	1	yes	characteristic
461	C₂²	C₂×AGL(1,ℤ/8)×C₁₀₁	1	1	yes	characteristic
462	C₄	—	2	2	no	—
463	C₄	—	2	2	no	—
464	C₄	—	2	2	no	—
465	C₄	—	8	2	no	—
466	C₄	—	8	2	no	—
467	C₄	#447×C₁₀₁	1	4	yes	—
468	C₄	#450×C₁₀₁	1	4	yes	—
469	C₄	#546×C₁₀₁	1	4	yes	—
470	C₂	—	2	4	no	—
471	C₂	—	8	8	no	—
472	C₂	C₁₀₁×#2435	1	1	yes	characteristic
473	C₂	C₂×#447×C₁₀₁	1	1	yes	characteristic
474	C₂	C₂×#450×C₁₀₁	1	1	yes	characteristic
475	C₂	C₂×#486×C₁₀₁	1	1	yes	characteristic
476	C₂	C₁₀₁×#3138	1	1	yes	characteristic
477	C₂	C₁₀₁×#3205	1	1	yes	characteristic
478	C₂	C₁₀₁×#3208	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₀₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₀₁
prime radical	C₂²×#127×C₁₀₁	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₀₁ ◁ C₂²×C₄²×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. C₁₀₁×#2857	C₂	semidirect
4. C₁₀₁×#2041	C₂	semidirect
5. C₁₀₁×#1957	C₂	semidirect
6. C₁₀₁×#1786	C₂	semidirect
7. C₄×C₂²⋊C₈×C₁₀₁	C₂	semidirect
11. C₂×C₄⋊Q₈×C₁₀₁	C₂²	semidirect
20. C₂×#102×C₁₀₁	C₂²	semidirect
21. C₂×#102×C₁₀₁	C₂²	semidirect
23. C₂×C₄×C₈×C₁₀₁	C₂²	semidirect
26. #389×C₁₀₁	C₂²	semidirect
27. #384×C₁₀₁	C₂²	semidirect
30. #336×C₁₀₁	C₂²	semidirect
214. C₂²×C₁₀₁	#486	semidirect
230. #25855	C₁₀₁	direct (N × H)
241. C₂×#486	C₂×C₁₀₁	semidirect
242. #2857	C₂×C₁₀₁	semidirect
243. #2041	C₂×C₁₀₁	semidirect
244. #1957	C₂×C₁₀₁	semidirect
245. #1786	C₂×C₁₀₁	semidirect
246. C₄×C₂²⋊C₈	C₂×C₁₀₁	semidirect
247. C₁₀₁	#25855	direct (N × H)
251. C₂×C₄⋊Q₈	C₂²×C₁₀₁	semidirect
260. C₂×#102	C₂²×C₁₀₁	semidirect
261. C₂×#102	C₂²×C₁₀₁	semidirect
263. C₂×C₄×C₈	C₂²×C₁₀₁	semidirect
266. #389	C₂²×C₁₀₁	semidirect
267. #384	C₂²×C₁₀₁	semidirect
270. #336	C₂²×C₁₀₁	semidirect
454. C₂²	#486×C₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#127×C₁₀₁	2
C₂×#486×C₁₀₁	2
C₁₀₁×#2857	2
C₁₀₁×#2041	2
C₁₀₁×#1957	2
C₁₀₁×#1786	2
C₄×C₂²⋊C₈×C₁₀₁	2
#25855	101

Subgroups — C101×#25855 #38808006

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#25855 #38808006