Subgroups — C₁₀₁×#25567 #38807718

Order 25856.

1522 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#547×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#486×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#459×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₀₁×#2541	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₀₁×#1999	C₂	1	4	yes	maximal, complemented
6	C₁₀₁×#1988	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₀₁×#1954	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₀₁×#1874	C₂	1	4	yes	maximal, complemented
9	C₄×#102×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₁₀₁	—	2	1	no	—
11	C₂²×D₈×C₁₀₁	C₂²	1	2	yes	—
12	#547×C₁₀₁	—	2	4	no	—
13	#547×C₁₀₁	—	2	4	no	—
14	C₂×C₄⋊Q₈×C₁₀₁	C₂²	1	1	yes	characteristic
15	C₂×#127×C₁₀₁	—	2	1	no	—
16	C₂×#127×C₁₀₁	C₂²	1	1	yes	characteristic
17	C₂×#123×C₁₀₁	—	2	2	no	—
18	C₂×C₂²⋊Q₈×C₁₀₁	—	2	1	no	—
19	C₂×#121×C₁₀₁	C₂²	1	2	yes	—
20	C₂×#121×C₁₀₁	C₂²	1	4	yes	—
21	C₂×C₄×D₄×C₁₀₁	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₁₀₁	C₂²	1	1	yes	characteristic
23	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	2	yes	—
24	#486×C₁₀₁	—	2	4	no	—
25	#459×C₁₀₁	—	2	4	no	—
26	C₂×C₄⋊C₈×C₁₀₁	C₂²	1	1	yes	characteristic
27	C₂×#102×C₁₀₁	C₂²	1	2	yes	—
28	C₂×#102×C₁₀₁	C₂²	1	4	yes	—
29	C₂×#102×C₁₀₁	C₂²	1	2	yes	—
30	C₂×C₂²⋊C₈×C₁₀₁	C₂²	1	4	yes	—
31	C₂×C₄×C₈×C₁₀₁	C₂²	1	1	yes	characteristic
32	#392×C₁₀₁	—	2	2	no	—
33	#390×C₁₀₁	—	2	1	no	—
34	C₄×C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
35	#340×C₁₀₁	C₂²	1	4	yes	—
36	#340×C₁₀₁	C₂²	1	2	yes	—
37	C₂×#41×C₁₀₁	—	2	8	no	—
38	C₂×#41×C₁₀₁	—	4	4	no	—
39	C₂×#41×C₁₀₁	—	4	4	no	—
40	C₂²×Q₈×C₁₀₁	—	2	1	no	—
41	C₂²×D₄×C₁₀₁	—	2	2	no	—
42	C₂²×D₄×C₁₀₁	—	2	4	no	—
43	C₂²×D₄×C₁₀₁	—	2	1	no	—
44	C₂²×D₄×C₁₀₁	—	2	1	no	—
45	C₂²×D₄×C₁₀₁	D₄	1	1	yes	characteristic
46	C₂²×D₄×C₁₀₁	C₂³	1	2	yes	—
47	C₂²×D₄×C₁₀₁	C₂³	1	1	yes	characteristic
48	C₂³×C₄×C₁₀₁	—	2	2	no	—
49	C₂³×C₄×C₁₀₁	—	2	1	no	—
50	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
51	C₂×D₈×C₁₀₁	—	2	4	no	—
52	C₂×D₈×C₁₀₁	—	4	4	no	—
53	C₂²×C₈×C₁₀₁	C₂³	1	2	yes	—
54	C₂²×C₈×C₁₀₁	C₂³	1	2	yes	—
55	C₄⋊Q₈×C₁₀₁	—	2	2	no	—
56	C₄⋊Q₈×C₁₀₁	D₄	1	4	yes	complemented
57	#127×C₁₀₁	—	2	2	no	—
58	#127×C₁₀₁	—	2	2	no	—
59	#127×C₁₀₁	—	4	4	no	—
60	#123×C₁₀₁	—	2	16	no	—
61	C₂²⋊Q₈×C₁₀₁	—	2	8	no	—
62	#121×C₁₀₁	—	2	4	no	—
63	#121×C₁₀₁	—	2	4	no	—
64	#121×C₁₀₁	—	2	8	no	—
65	#121×C₁₀₁	—	4	4	no	—
66	C₄×D₄×C₁₀₁	—	2	2	no	—
67	C₄×D₄×C₁₀₁	—	2	2	no	—
68	C₄×D₄×C₁₀₁	—	2	2	no	—
69	C₄×D₄×C₁₀₁	D₄	1	4	yes	complemented
70	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
71	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
72	C₂×C₄⋊C₄×C₁₀₁	—	2	4	no	—
73	C₂×C₄⋊C₄×C₁₀₁	—	2	4	no	—
74	C₂×C₄⋊C₄×C₁₀₁	D₄	1	1	yes	characteristic
75	C₂×C₄⋊C₄×C₁₀₁	C₂³	1	1	yes	characteristic
76	C₂×C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
77	C₂×C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
78	C₂×C₂²⋊C₄×C₁₀₁	—	2	1	no	—
79	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
80	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
81	C₂×C₂²⋊C₄×C₁₀₁	D₄	1	2	yes	—
82	C₂×C₄²×C₁₀₁	—	2	1	no	—
83	C₂×C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
84	C₄⋊C₈×C₁₀₁	—	2	2	no	—
85	#102×C₁₀₁	—	2	4	no	—
86	#102×C₁₀₁	—	2	8	no	—
87	#102×C₁₀₁	—	2	4	no	—
88	C₂²⋊C₈×C₁₀₁	—	4	4	no	—
89	C₄×C₈×C₁₀₁	—	2	2	no	—
90	#95×C₁₀₁	—	2	1	no	—
91	C₂⁴×C₁₀₁	—	2	1	no	—
92	C₂⁴×C₁₀₁	—	2	2	no	—
93	C₂⁴×C₁₀₁	C₂×D₄	1	2	yes	—
94	#41×C₁₀₁	—	4	32	no	—
95	C₂×Q₈×C₁₀₁	—	2	4	no	—
96	C₂×Q₈×C₁₀₁	—	4	2	no	—
97	C₂×Q₈×C₁₀₁	—	4	2	no	—
98	C₂×D₄×C₁₀₁	—	2	8	no	—
99	C₂×D₄×C₁₀₁	—	2	2	no	—
100	C₂×D₄×C₁₀₁	—	2	2	no	—
101	C₂×D₄×C₁₀₁	—	2	1	no	—
102	C₂×D₄×C₁₀₁	—	2	2	no	—
103	C₂×D₄×C₁₀₁	—	2	2	no	—
104	C₂×D₄×C₁₀₁	—	2	2	no	—
105	C₂×D₄×C₁₀₁	—	2	4	no	—
106	C₂×D₄×C₁₀₁	—	2	2	no	—
107	C₂×D₄×C₁₀₁	—	2	4	no	—
108	C₂×D₄×C₁₀₁	—	4	8	no	—
109	C₂×D₄×C₁₀₁	—	4	4	no	—
110	C₂×D₄×C₁₀₁	—	4	4	no	—
111	C₂×D₄×C₁₀₁	—	4	8	no	—
112	C₂×D₄×C₁₀₁	—	4	2	no	—
113	C₂×D₄×C₁₀₁	—	4	2	no	—
114	C₂×D₄×C₁₀₁	—	4	2	no	—
115	C₂×D₄×C₁₀₁	—	4	2	no	—
116	C₂×D₄×C₁₀₁	—	8	2	no	—
117	C₂×D₄×C₁₀₁	—	8	4	no	—
118	C₂×D₄×C₁₀₁	D₈	1	4	yes	complemented
119	C₂×D₄×C₁₀₁	C₂×D₄	1	2	yes	—
120	C₂²×C₄×C₁₀₁	—	2	8	no	—
121	C₂²×C₄×C₁₀₁	—	2	2	no	—
122	C₂²×C₄×C₁₀₁	—	2	1	no	—
123	C₂²×C₄×C₁₀₁	—	2	2	no	—
124	C₂²×C₄×C₁₀₁	—	2	4	no	—
125	C₂²×C₄×C₁₀₁	—	2	2	no	—
126	C₂²×C₄×C₁₀₁	—	2	2	no	—
127	C₂²×C₄×C₁₀₁	—	2	4	no	—
128	C₂²×C₄×C₁₀₁	—	2	4	no	—
129	C₂²×C₄×C₁₀₁	—	4	4	no	—
130	C₂²×C₄×C₁₀₁	—	4	4	no	—
131	C₂²×C₄×C₁₀₁	—	4	2	no	—
132	C₂²×C₄×C₁₀₁	—	4	2	no	—
133	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
134	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
137	D₈×C₁₀₁	—	4	8	no	—
138	C₂×C₈×C₁₀₁	—	2	2	no	—
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	4	no	—
143	C₄⋊C₄×C₁₀₁	—	2	8	no	—
144	C₄⋊C₄×C₁₀₁	—	2	4	no	—
145	C₄⋊C₄×C₁₀₁	—	2	2	no	—
146	C₄⋊C₄×C₁₀₁	—	2	1	no	—
147	C₄⋊C₄×C₁₀₁	—	2	2	no	—
148	C₄⋊C₄×C₁₀₁	—	2	2	no	—
149	C₄⋊C₄×C₁₀₁	C₂×D₄	1	2	yes	—
150	C₄⋊C₄×C₁₀₁	C₂×D₄	1	4	yes	—
151	C₄⋊C₄×C₁₀₁	#41	1	4	yes	complemented
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	—	4	8	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	4	no	—
161	C₂³×C₁₀₁	—	2	2	no	—
162	C₂³×C₁₀₁	—	2	4	no	—
163	C₂³×C₁₀₁	—	2	2	no	—
164	C₂³×C₁₀₁	—	4	2	no	—
165	C₂³×C₁₀₁	—	4	1	no	—
166	C₂³×C₁₀₁	—	4	1	no	—
167	C₂³×C₁₀₁	—	4	2	no	—
168	C₂³×C₁₀₁	—	4	2	no	—
169	C₂³×C₁₀₁	—	4	4	no	—
170	C₂³×C₁₀₁	—	4	2	no	—
171	C₂³×C₁₀₁	—	4	2	no	—
172	C₂³×C₁₀₁	—	4	4	no	—
173	C₂³×C₁₀₁	C₂×D₈	1	4	yes	—
174	C₂³×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
175	Q₈×C₁₀₁	—	4	8	no	—
176	D₄×C₁₀₁	—	2	2	no	—
177	D₄×C₁₀₁	—	2	2	no	—
178	D₄×C₁₀₁	—	2	8	no	—
179	D₄×C₁₀₁	—	4	16	no	—
180	D₄×C₁₀₁	—	4	2	no	—
181	D₄×C₁₀₁	—	4	2	no	—
182	D₄×C₁₀₁	—	4	2	no	—
183	D₄×C₁₀₁	—	4	4	no	—
184	D₄×C₁₀₁	—	8	4	no	—
185	D₄×C₁₀₁	—	8	16	no	—
186	D₄×C₁₀₁	—	8	4	no	—
187	C₂×C₄×C₁₀₁	—	2	2	no	—
188	C₂×C₄×C₁₀₁	—	2	2	no	—
189	C₂×C₄×C₁₀₁	—	2	2	no	—
190	C₂×C₄×C₁₀₁	—	2	4	no	—
191	C₂×C₄×C₁₀₁	—	2	4	no	—
192	C₂×C₄×C₁₀₁	—	2	4	no	—
193	C₂×C₄×C₁₀₁	—	4	16	no	—
194	C₂×C₄×C₁₀₁	—	4	2	no	—
195	C₂×C₄×C₁₀₁	—	4	1	no	—
196	C₂×C₄×C₁₀₁	—	4	2	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	2	no	—
201	C₂×C₄×C₁₀₁	—	4	2	no	—
202	C₂×C₄×C₁₀₁	—	4	4	no	—
203	C₂×C₄×C₁₀₁	—	4	8	no	—
204	C₂×C₄×C₁₀₁	#120	1	2	yes	—
205	C₂×C₄×C₁₀₁	#120	1	2	yes	—
206	C₂×C₄×C₁₀₁	C₂×D₈	1	2	yes	—
207	C₂×C₄×C₁₀₁	AGL(1,ℤ/8)	1	2	yes	—
208	C₂×C₄×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
209	C₂×C₄×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
210	C₂×C₄×C₁₀₁	C₂×#41	1	2	yes	—
211	C₂×C₄×C₁₀₁	H(5,𝔽₂)	1	2	yes	—
212	C₈×C₁₀₁	—	4	2	no	—
213	C₈×C₁₀₁	—	4	2	no	—
214	C₂²×C₁₀₁	—	2	4	no	—
215	C₂²×C₁₀₁	—	2	8	no	—
216	C₂²×C₁₀₁	—	4	4	no	—
217	C₂²×C₁₀₁	—	4	2	no	—
218	C₂²×C₁₀₁	—	4	2	no	—
219	C₂²×C₁₀₁	—	4	2	no	—
220	C₂²×C₁₀₁	—	4	2	no	—
221	C₂²×C₁₀₁	—	4	2	no	—
222	C₂²×C₁₀₁	—	8	2	no	—
223	C₂²×C₁₀₁	—	8	2	no	—
224	C₂²×C₁₀₁	—	8	4	no	—
225	C₂²×C₁₀₁	—	8	2	no	—
226	C₂²×C₁₀₁	—	8	2	no	—
227	C₂²×C₁₀₁	—	8	2	no	—
228	C₂²×C₁₀₁	—	8	4	no	—
229	C₂²×C₁₀₁	C₂×#120	1	1	yes	characteristic
230	C₂²×C₁₀₁	#546	1	2	yes	—
231	C₂²×C₁₀₁	C₂²×D₈	1	1	yes	characteristic
232	C₂²×C₁₀₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
233	C₂²×C₁₀₁	#577	1	2	yes	—
234	C₄×C₁₀₁	—	2	2	no	—
235	C₄×C₁₀₁	—	4	2	no	—
236	C₄×C₁₀₁	—	4	2	no	—
237	C₄×C₁₀₁	—	4	4	no	—
238	C₄×C₁₀₁	—	4	4	no	—
239	C₄×C₁₀₁	#447	1	4	yes	—
240	C₄×C₁₀₁	#532	1	1	yes	characteristic
241	C₄×C₁₀₁	#535	1	1	yes	characteristic
242	C₄×C₁₀₁	#550	1	2	yes	—
243	#25567	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
244	C₂×C₁₀₁	—	4	4	no	—
245	C₂×C₁₀₁	—	8	2	no	—
246	C₂×C₁₀₁	—	16	2	no	—
247	C₂×C₁₀₁	#2431	1	1	yes	characteristic
248	C₂×C₁₀₁	C₂×#447	1	1	yes	characteristic
249	C₂×C₁₀₁	#3010	1	1	yes	characteristic
250	C₂×C₁₀₁	#3294	1	2	yes	—
251	C₂×C₁₀₁	#3332	1	2	yes	—
252	C₂×#547	C₂×C₁₀₁	1	1	yes	characteristic, complemented
253	C₂×#486	C₂×C₁₀₁	1	1	yes	characteristic, complemented
254	C₂×#459	C₂×C₁₀₁	1	1	yes	characteristic, complemented
255	#2541	C₂×C₁₀₁	1	1	yes	characteristic, complemented
256	#1999	C₂×C₁₀₁	1	4	yes	complemented
257	#1988	C₂×C₁₀₁	1	1	yes	characteristic, complemented
258	#1954	C₂×C₁₀₁	1	1	yes	characteristic, complemented
259	#1874	C₂×C₁₀₁	1	4	yes	complemented
260	C₄×#102	C₂×C₁₀₁	1	1	yes	characteristic, complemented
261	C₁₀₁	#25567	1	1	yes	characteristic, direct product factor, Sylow
262	C₂²×#41	—	2	1	no	—
263	C₂²×D₈	C₂²×C₁₀₁	1	2	yes	—
264	#547	—	2	4	no	—
265	#547	—	2	4	no	—
266	C₂×C₄⋊Q₈	C₂²×C₁₀₁	1	1	yes	characteristic
267	C₂×#127	—	2	1	no	—
268	C₂×#127	C₂²×C₁₀₁	1	1	yes	characteristic
269	C₂×#123	—	2	2	no	—
270	C₂×C₂²⋊Q₈	—	2	1	no	—
271	C₂×#121	C₂²×C₁₀₁	1	2	yes	—
272	C₂×#121	C₂²×C₁₀₁	1	4	yes	—
273	C₂×C₄×D₄	C₂²×C₁₀₁	1	1	yes	characteristic
274	C₂×C₄×D₄	C₂²×C₁₀₁	1	1	yes	characteristic
275	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	2	yes	—
276	#486	—	2	4	no	—
277	#459	—	2	4	no	—
278	C₂×C₄⋊C₈	C₂²×C₁₀₁	1	1	yes	characteristic
279	C₂×#102	C₂²×C₁₀₁	1	4	yes	—
280	C₂×#102	C₂²×C₁₀₁	1	2	yes	—
281	C₂×#102	C₂²×C₁₀₁	1	2	yes	—
282	C₂×C₂²⋊C₈	C₂²×C₁₀₁	1	4	yes	—
283	C₂×C₄×C₈	C₂²×C₁₀₁	1	1	yes	characteristic
284	#392	—	2	2	no	—
285	#390	—	2	1	no	—
286	C₄×C₄⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
287	#340	C₂²×C₁₀₁	1	2	yes	—
288	#340	C₂²×C₁₀₁	1	4	yes	—
289	C₂×#41	—	2	8	no	—
290	C₂×#41	—	4	4	no	—
291	C₂×#41	—	4	4	no	—
292	C₂²×Q₈	—	2	1	no	—
293	C₂²×D₄	—	2	2	no	—
294	C₂²×D₄	—	2	4	no	—
295	C₂²×D₄	—	2	1	no	—
296	C₂²×D₄	—	2	1	no	—
297	C₂²×D₄	D₄×C₁₀₁	1	1	yes	characteristic
298	C₂²×D₄	C₂³×C₁₀₁	1	2	yes	—
299	C₂²×D₄	C₂³×C₁₀₁	1	1	yes	characteristic
300	C₂³×C₄	—	2	2	no	—
301	C₂³×C₄	—	2	1	no	—
302	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
303	C₂×D₈	—	2	4	no	—
304	C₂×D₈	—	4	4	no	—
305	C₂²×C₈	C₂³×C₁₀₁	1	2	yes	—
306	C₂²×C₈	C₂³×C₁₀₁	1	2	yes	—
307	C₄⋊Q₈	—	2	2	no	—
308	C₄⋊Q₈	D₄×C₁₀₁	1	4	yes	complemented
309	#127	—	2	2	no	—
310	#127	—	2	2	no	—
311	#127	—	4	4	no	—
312	#123	—	2	16	no	—
313	C₂²⋊Q₈	—	2	8	no	—
314	#121	—	2	4	no	—
315	#121	—	2	4	no	—
316	#121	—	2	8	no	—
317	#121	—	4	4	no	—
318	C₄×D₄	—	2	2	no	—
319	C₄×D₄	—	2	2	no	—
320	C₄×D₄	—	2	2	no	—
321	C₄×D₄	D₄×C₁₀₁	1	4	yes	complemented
322	C₂×C₄⋊C₄	—	2	2	no	—
323	C₂×C₄⋊C₄	—	2	1	no	—
324	C₂×C₄⋊C₄	—	2	4	no	—
325	C₂×C₄⋊C₄	—	2	4	no	—
326	C₂×C₄⋊C₄	D₄×C₁₀₁	1	1	yes	characteristic
327	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	1	yes	characteristic
328	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	2	yes	—
329	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	2	yes	—
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	C₄⋊C₈	—	2	2	no	—
337	#102	—	2	4	no	—
338	#102	—	2	8	no	—
339	#102	—	2	4	no	—
340	C₂²⋊C₈	—	4	4	no	—
341	C₄×C₈	—	2	2	no	—
342	#95	—	2	1	no	—
343	C₂⁴	—	2	1	no	—
344	C₂⁴	—	2	2	no	—
345	C₂⁴	C₂×D₄×C₁₀₁	1	2	yes	—
346	#41	—	4	32	no	—
347	C₂×Q₈	—	2	4	no	—
348	C₂×Q₈	—	4	2	no	—
349	C₂×Q₈	—	4	2	no	—
350	C₂×D₄	—	2	8	no	—
351	C₂×D₄	—	2	2	no	—
352	C₂×D₄	—	2	2	no	—
353	C₂×D₄	—	2	1	no	—
354	C₂×D₄	—	2	2	no	—
355	C₂×D₄	—	2	2	no	—
356	C₂×D₄	—	2	2	no	—
357	C₂×D₄	—	2	4	no	—
358	C₂×D₄	—	2	2	no	—
359	C₂×D₄	—	2	4	no	—
360	C₂×D₄	—	4	8	no	—
361	C₂×D₄	—	4	4	no	—
362	C₂×D₄	—	4	4	no	—
363	C₂×D₄	—	4	8	no	—
364	C₂×D₄	—	4	2	no	—
365	C₂×D₄	—	4	2	no	—
366	C₂×D₄	—	4	2	no	—
367	C₂×D₄	—	4	2	no	—
368	C₂×D₄	—	8	2	no	—
369	C₂×D₄	—	8	4	no	—
370	C₂×D₄	D₈×C₁₀₁	1	4	yes	complemented
371	C₂×D₄	C₂×D₄×C₁₀₁	1	2	yes	—
372	C₂²×C₄	—	2	8	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	2	4	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	2	4	no	—
380	C₂²×C₄	—	2	4	no	—
381	C₂²×C₄	—	4	4	no	—
382	C₂²×C₄	—	4	4	no	—
383	C₂²×C₄	—	4	2	no	—
384	C₂²×C₄	—	4	2	no	—
385	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
386	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
387	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
388	C₂²×C₄	C₂⁴×C₁₀₁	1	1	yes	characteristic
389	D₈	—	4	8	no	—
390	C₂×C₈	—	2	2	no	—
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	2	2	no	—
393	C₂×C₈	—	2	2	no	—
394	C₂×C₈	—	2	4	no	—
395	C₄⋊C₄	—	2	8	no	—
396	C₄⋊C₄	—	2	4	no	—
397	C₄⋊C₄	—	2	2	no	—
398	C₄⋊C₄	—	2	1	no	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	C₂×D₄×C₁₀₁	1	2	yes	—
402	C₄⋊C₄	C₂×D₄×C₁₀₁	1	4	yes	—
403	C₄⋊C₄	#41×C₁₀₁	1	4	yes	complemented
404	C₂²⋊C₄	—	2	8	no	—
405	C₂²⋊C₄	—	2	4	no	—
406	C₂²⋊C₄	—	2	4	no	—
407	C₂²⋊C₄	—	4	8	no	—
408	C₄²	—	4	2	no	—
409	C₄²	C₂×D₄×C₁₀₁	1	2	yes	—
410	C₄²	C₂×D₄×C₁₀₁	1	2	yes	—
411	C₂³	—	2	2	no	—
412	C₂³	—	2	4	no	—
413	C₂³	—	2	2	no	—
414	C₂³	—	2	4	no	—
415	C₂³	—	2	2	no	—
416	C₂³	—	4	2	no	—
417	C₂³	—	4	1	no	—
418	C₂³	—	4	1	no	—
419	C₂³	—	4	2	no	—
420	C₂³	—	4	2	no	—
421	C₂³	—	4	4	no	—
422	C₂³	—	4	2	no	—
423	C₂³	—	4	2	no	—
424	C₂³	—	4	4	no	—
425	C₂³	C₂×D₈×C₁₀₁	1	4	yes	—
426	C₂³	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
427	Q₈	—	4	8	no	—
428	D₄	—	2	8	no	—
429	D₄	—	2	2	no	—
430	D₄	—	2	2	no	—
431	D₄	—	4	16	no	—
432	D₄	—	4	2	no	—
433	D₄	—	4	2	no	—
434	D₄	—	4	2	no	—
435	D₄	—	4	4	no	—
436	D₄	—	8	4	no	—
437	D₄	—	8	16	no	—
438	D₄	—	8	4	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	4	no	—
443	C₂×C₄	—	2	4	no	—
444	C₂×C₄	—	2	4	no	—
445	C₂×C₄	—	4	16	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	1	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	1	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	4	2	no	—
452	C₂×C₄	—	4	8	no	—
453	C₂×C₄	—	4	2	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	4	4	no	—
456	C₂×C₄	#120×C₁₀₁	1	2	yes	—
457	C₂×C₄	#120×C₁₀₁	1	2	yes	—
458	C₂×C₄	C₂×D₈×C₁₀₁	1	2	yes	—
459	C₂×C₄	AGL(1,ℤ/8)×C₁₀₁	1	2	yes	—
460	C₂×C₄	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
461	C₂×C₄	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
462	C₂×C₄	C₂×#41×C₁₀₁	1	2	yes	—
463	C₂×C₄	H(5,𝔽₂)×C₁₀₁	1	2	yes	—
464	C₈	—	4	2	no	—
465	C₈	—	4	2	no	—
466	C₂²	—	2	4	no	—
467	C₂²	—	2	8	no	—
468	C₂²	—	4	2	no	—
469	C₂²	—	4	2	no	—
470	C₂²	—	4	4	no	—
471	C₂²	—	4	2	no	—
472	C₂²	—	4	2	no	—
473	C₂²	—	4	2	no	—
474	C₂²	—	8	2	no	—
475	C₂²	—	8	2	no	—
476	C₂²	—	8	2	no	—
477	C₂²	—	8	2	no	—
478	C₂²	—	8	2	no	—
479	C₂²	—	8	4	no	—
480	C₂²	—	8	4	no	—
481	C₂²	C₂×#120×C₁₀₁	1	1	yes	characteristic
482	C₂²	#546×C₁₀₁	1	2	yes	—
483	C₂²	C₂²×D₈×C₁₀₁	1	1	yes	characteristic
484	C₂²	C₂×AGL(1,ℤ/8)×C₁₀₁	1	1	yes	characteristic
485	C₂²	#577×C₁₀₁	1	2	yes	—
486	C₄	—	2	2	no	—
487	C₄	—	4	2	no	—
488	C₄	—	4	2	no	—
489	C₄	—	4	4	no	—
490	C₄	—	4	4	no	—
491	C₄	#447×C₁₀₁	1	4	yes	—
492	C₄	#532×C₁₀₁	1	1	yes	characteristic
493	C₄	#535×C₁₀₁	1	1	yes	characteristic
494	C₄	#550×C₁₀₁	1	2	yes	—
495	C₂	—	4	4	no	—
496	C₂	—	8	2	no	—
497	C₂	—	16	2	no	—
498	C₂	C₁₀₁×#2431	1	1	yes	characteristic
499	C₂	C₂×#447×C₁₀₁	1	1	yes	characteristic
500	C₂	C₁₀₁×#3010	1	1	yes	characteristic
501	C₂	C₁₀₁×#3294	1	2	yes	—
502	C₂	C₁₀₁×#3332	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₀₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₀₁
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
1. C₂×#547×C₁₀₁	C₂	semidirect
2. C₂×#486×C₁₀₁	C₂	semidirect
3. C₂×#459×C₁₀₁	C₂	semidirect
4. C₁₀₁×#2541	C₂	semidirect
5. C₁₀₁×#1999	C₂	semidirect
6. C₁₀₁×#1988	C₂	semidirect
7. C₁₀₁×#1954	C₂	semidirect
8. C₁₀₁×#1874	C₂	semidirect
9. C₄×#102×C₁₀₁	C₂	semidirect
56. C₄⋊Q₈×C₁₀₁	D₄	semidirect
69. C₄×D₄×C₁₀₁	D₄	semidirect
118. C₂×D₄×C₁₀₁	D₈	semidirect
151. C₄⋊C₄×C₁₀₁	#41	semidirect
243. #25567	C₁₀₁	direct (N × H)
252. C₂×#547	C₂×C₁₀₁	semidirect
253. C₂×#486	C₂×C₁₀₁	semidirect
254. C₂×#459	C₂×C₁₀₁	semidirect
255. #2541	C₂×C₁₀₁	semidirect
256. #1999	C₂×C₁₀₁	semidirect
257. #1988	C₂×C₁₀₁	semidirect
258. #1954	C₂×C₁₀₁	semidirect
259. #1874	C₂×C₁₀₁	semidirect
260. C₄×#102	C₂×C₁₀₁	semidirect
261. C₁₀₁	#25567	direct (N × H)
308. C₄⋊Q₈	D₄×C₁₀₁	semidirect
321. C₄×D₄	D₄×C₁₀₁	semidirect
370. C₂×D₄	D₈×C₁₀₁	semidirect
403. C₄⋊C₄	#41×C₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#547×C₁₀₁	2
C₂×#486×C₁₀₁	2
C₂×#459×C₁₀₁	2
C₁₀₁×#2541	2
C₁₀₁×#1999	2
C₁₀₁×#1988	2
C₁₀₁×#1954	2
C₁₀₁×#1874	2
C₄×#102×C₁₀₁	2
#25567	101

Subgroups — C101×#25567 #38807718

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#25567 #38807718