Subgroups — C₁₀₁×#15510 #38797661

Order 25856.

1478 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#395×C₁₀₁	C₂	1	2	yes	maximal
2	C₂×#391×C₁₀₁	C₂	1	2	yes	maximal
3	C₁₀₁×#1446	C₂	1	1	yes	maximal, characteristic
4	C₁₀₁×#1446	C₂	1	1	yes	maximal, characteristic
5	C₁₀₁×#1444	C₂	1	1	yes	maximal, characteristic
6	C₁₀₁×#1444	C₂	1	2	yes	maximal
7	C₁₀₁×#1441	C₂	1	2	yes	maximal
8	C₁₀₁×#1436	C₂	1	2	yes	maximal
9	C₁₀₁×C₄⋊#95	C₂	1	2	yes	maximal
10	C₂³×Q₈×C₁₀₁	C₂²	1	1	yes	characteristic
11	C₂³×Q₈×C₁₀₁	C₂²	1	1	yes	characteristic
12	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	2	yes	—
13	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	2	yes	—
14	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	2	yes	—
15	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
16	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	2	yes	—
17	C₂²×C₄²×C₁₀₁	C₂²	1	2	yes	—
18	#395×C₁₀₁	—	2	8	no	—
19	#391×C₁₀₁	—	2	8	no	—
20	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
21	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
22	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
23	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
24	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
25	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
26	C₂×#95×C₁₀₁	C₂²	1	1	yes	characteristic
27	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
28	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
29	C₂×#95×C₁₀₁	C₂²	1	1	yes	characteristic
30	C₂×#95×C₁₀₁	C₂²	1	1	yes	characteristic
31	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
32	C₂×#95×C₁₀₁	C₂²	1	1	yes	characteristic
33	C₂²×Q₈×C₁₀₁	—	2	4	no	—
34	C₂²×Q₈×C₁₀₁	—	2	4	no	—
35	C₂²×Q₈×C₁₀₁	—	2	4	no	—
36	C₂²×Q₈×C₁₀₁	—	2	2	no	—
37	C₂²×Q₈×C₁₀₁	—	4	1	no	—
38	C₂²×Q₈×C₁₀₁	—	4	1	no	—
39	C₂²×Q₈×C₁₀₁	—	4	1	no	—
40	C₂²×Q₈×C₁₀₁	—	4	2	no	—
41	C₂²×Q₈×C₁₀₁	—	4	1	no	—
42	C₂²×Q₈×C₁₀₁	Q₈	1	4	yes	complemented
43	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
44	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
45	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
46	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
47	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
48	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
49	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
51	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
52	C₂×C₄⋊C₄×C₁₀₁	—	2	4	no	—
53	C₂×C₄⋊C₄×C₁₀₁	—	2	4	no	—
54	C₂×C₄⋊C₄×C₁₀₁	—	2	4	no	—
55	C₂×C₄⋊C₄×C₁₀₁	—	2	4	no	—
56	C₂×C₄⋊C₄×C₁₀₁	—	2	4	no	—
57	C₂×C₄⋊C₄×C₁₀₁	—	4	2	no	—
58	C₂×C₄⋊C₄×C₁₀₁	—	4	2	no	—
59	C₂×C₄⋊C₄×C₁₀₁	—	4	2	no	—
60	C₂×C₄⋊C₄×C₁₀₁	—	4	2	no	—
61	C₂×C₄⋊C₄×C₁₀₁	—	4	2	no	—
62	C₂×C₄⋊C₄×C₁₀₁	—	4	2	no	—
63	C₂×C₄⋊C₄×C₁₀₁	—	4	1	no	—
64	C₂×C₄⋊C₄×C₁₀₁	—	4	2	no	—
65	C₂×C₄⋊C₄×C₁₀₁	Q₈	1	8	yes	complemented
66	C₂×C₄²×C₁₀₁	—	2	4	no	—
67	C₂×C₄²×C₁₀₁	—	2	4	no	—
68	C₂×C₄²×C₁₀₁	—	4	2	no	—
69	#95×C₁₀₁	—	2	4	no	—
70	#95×C₁₀₁	—	2	4	no	—
71	#95×C₁₀₁	—	2	4	no	—
72	#95×C₁₀₁	—	2	4	no	—
73	#95×C₁₀₁	—	2	4	no	—
74	#95×C₁₀₁	—	2	4	no	—
75	#95×C₁₀₁	—	4	1	no	—
76	#95×C₁₀₁	—	4	2	no	—
77	#95×C₁₀₁	—	4	2	no	—
78	#95×C₁₀₁	—	4	1	no	—
79	#95×C₁₀₁	—	4	1	no	—
80	#95×C₁₀₁	D₄	1	8	yes	—
81	#95×C₁₀₁	Q₈	1	4	yes	complemented
82	C₂⁴×C₁₀₁	C₂⁴	1	1	yes	characteristic
83	C₂×Q₈×C₁₀₁	—	2	16	no	—
84	C₂×Q₈×C₁₀₁	—	4	4	no	—
85	C₂×Q₈×C₁₀₁	—	4	4	no	—
86	C₂×Q₈×C₁₀₁	—	4	8	no	—
87	C₂×Q₈×C₁₀₁	—	4	4	no	—
88	C₂×Q₈×C₁₀₁	—	4	4	no	—
89	C₂×Q₈×C₁₀₁	—	4	8	no	—
90	C₂×Q₈×C₁₀₁	—	4	8	no	—
91	C₂×Q₈×C₁₀₁	—	4	4	no	—
92	C₂×Q₈×C₁₀₁	—	4	4	no	—
93	C₂²×C₄×C₁₀₁	—	2	2	no	—
94	C₂²×C₄×C₁₀₁	—	2	2	no	—
95	C₂²×C₄×C₁₀₁	—	2	2	no	—
96	C₂²×C₄×C₁₀₁	—	2	2	no	—
97	C₂²×C₄×C₁₀₁	—	2	2	no	—
98	C₂²×C₄×C₁₀₁	—	2	2	no	—
99	C₂²×C₄×C₁₀₁	—	2	2	no	—
100	C₂²×C₄×C₁₀₁	—	2	2	no	—
101	C₂²×C₄×C₁₀₁	—	2	2	no	—
102	C₂²×C₄×C₁₀₁	—	2	2	no	—
103	C₂²×C₄×C₁₀₁	—	2	2	no	—
104	C₂²×C₄×C₁₀₁	—	2	2	no	—
105	C₂²×C₄×C₁₀₁	—	2	2	no	—
106	C₂²×C₄×C₁₀₁	—	2	2	no	—
107	C₂²×C₄×C₁₀₁	—	2	2	no	—
108	C₂²×C₄×C₁₀₁	—	2	2	no	—
109	C₂²×C₄×C₁₀₁	—	2	2	no	—
110	C₂²×C₄×C₁₀₁	—	2	2	no	—
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	1	no	—
115	C₂²×C₄×C₁₀₁	—	2	2	no	—
116	C₂²×C₄×C₁₀₁	—	2	2	no	—
117	C₂²×C₄×C₁₀₁	—	2	1	no	—
118	C₂²×C₄×C₁₀₁	—	2	1	no	—
119	C₂²×C₄×C₁₀₁	—	2	1	no	—
120	C₂²×C₄×C₁₀₁	—	2	1	no	—
121	C₂²×C₄×C₁₀₁	—	2	2	no	—
122	C₂²×C₄×C₁₀₁	—	2	2	no	—
123	C₂²×C₄×C₁₀₁	—	2	2	no	—
124	C₂²×C₄×C₁₀₁	—	2	2	no	—
125	C₂²×C₄×C₁₀₁	—	2	2	no	—
126	C₂²×C₄×C₁₀₁	—	2	2	no	—
127	C₂²×C₄×C₁₀₁	—	2	2	no	—
128	C₂²×C₄×C₁₀₁	—	2	1	no	—
129	C₂²×C₄×C₁₀₁	—	2	2	no	—
130	C₂²×C₄×C₁₀₁	—	2	2	no	—
131	C₂²×C₄×C₁₀₁	—	2	2	no	—
132	C₂²×C₄×C₁₀₁	—	2	2	no	—
133	C₂²×C₄×C₁₀₁	—	2	2	no	—
134	C₂²×C₄×C₁₀₁	—	2	2	no	—
135	C₂²×C₄×C₁₀₁	—	2	2	no	—
136	C₂²×C₄×C₁₀₁	—	2	2	no	—
137	C₂²×C₄×C₁₀₁	—	2	2	no	—
138	C₂²×C₄×C₁₀₁	C₂×D₄	1	4	yes	—
139	C₂²×C₄×C₁₀₁	C₂×D₄	1	4	yes	—
140	C₂²×C₄×C₁₀₁	C₂×D₄	1	4	yes	—
141	C₂²×C₄×C₁₀₁	C₂×Q₈	1	2	yes	—
142	C₂²×C₄×C₁₀₁	C₂×Q₈	1	4	yes	—
143	C₂²×C₄×C₁₀₁	C₂×Q₈	1	4	yes	—
144	C₂²×C₄×C₁₀₁	C₂×Q₈	1	2	yes	—
145	C₂²×C₄×C₁₀₁	C₂×Q₈	1	4	yes	—
146	C₂²×C₄×C₁₀₁	C₂×Q₈	1	4	yes	—
147	C₂²×C₄×C₁₀₁	C₂×Q₈	1	4	yes	—
148	C₂²×C₄×C₁₀₁	#41	1	2	yes	—
149	C₂²×C₄×C₁₀₁	#41	1	4	yes	—
150	C₄⋊C₄×C₁₀₁	—	4	8	no	—
151	C₄⋊C₄×C₁₀₁	—	4	8	no	—
152	C₄⋊C₄×C₁₀₁	—	4	8	no	—
153	C₄⋊C₄×C₁₀₁	—	4	8	no	—
154	C₄⋊C₄×C₁₀₁	—	4	4	no	—
155	C₄²×C₁₀₁	—	4	8	no	—
156	C₂³×C₁₀₁	C₂²×D₄	1	2	yes	—
157	C₂³×C₁₀₁	C₂²×Q₈	1	1	yes	characteristic
158	C₂³×C₁₀₁	C₂²×Q₈	1	1	yes	characteristic
159	C₂³×C₁₀₁	C₂²×Q₈	1	2	yes	—
160	C₂³×C₁₀₁	C₂×#41	1	2	yes	—
161	C₂³×C₁₀₁	C₂×#41	1	1	yes	characteristic
162	C₂³×C₁₀₁	H(5,𝔽₂)	1	1	yes	characteristic
163	C₂³×C₁₀₁	H(5,𝔽₂)	1	2	yes	—
164	C₂³×C₁₀₁	H(5,𝔽₂)	1	1	yes	characteristic
165	C₂³×C₁₀₁	H(5,𝔽₂)	1	1	yes	characteristic
166	C₂³×C₁₀₁	2₋¹⁺⁴	1	1	yes	characteristic
167	Q₈×C₁₀₁	—	4	16	no	—
168	Q₈×C₁₀₁	—	4	16	no	—
169	C₂×C₄×C₁₀₁	—	2	4	no	—
170	C₂×C₄×C₁₀₁	—	2	4	no	—
171	C₂×C₄×C₁₀₁	—	2	4	no	—
172	C₂×C₄×C₁₀₁	—	2	4	no	—
173	C₂×C₄×C₁₀₁	—	2	4	no	—
174	C₂×C₄×C₁₀₁	—	2	4	no	—
175	C₂×C₄×C₁₀₁	—	2	4	no	—
176	C₂×C₄×C₁₀₁	—	2	4	no	—
177	C₂×C₄×C₁₀₁	—	2	4	no	—
178	C₂×C₄×C₁₀₁	—	2	4	no	—
179	C₂×C₄×C₁₀₁	—	2	4	no	—
180	C₂×C₄×C₁₀₁	—	2	4	no	—
181	C₂×C₄×C₁₀₁	—	2	4	no	—
182	C₂×C₄×C₁₀₁	—	2	4	no	—
183	C₂×C₄×C₁₀₁	—	2	2	no	—
184	C₂×C₄×C₁₀₁	—	2	4	no	—
185	C₂×C₄×C₁₀₁	—	2	4	no	—
186	C₂×C₄×C₁₀₁	—	2	2	no	—
187	C₂×C₄×C₁₀₁	—	2	2	no	—
188	C₂×C₄×C₁₀₁	—	2	4	no	—
189	C₂×C₄×C₁₀₁	—	2	4	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	—	2	4	no	—
194	C₂×C₄×C₁₀₁	—	2	4	no	—
195	C₂×C₄×C₁₀₁	—	2	4	no	—
196	C₂×C₄×C₁₀₁	—	4	2	no	—
197	C₂×C₄×C₁₀₁	—	4	2	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	2	no	—
203	C₂×C₄×C₁₀₁	—	4	2	no	—
204	C₂×C₄×C₁₀₁	—	4	1	no	—
205	C₂×C₄×C₁₀₁	—	4	1	no	—
206	C₂×C₄×C₁₀₁	—	4	2	no	—
207	C₂×C₄×C₁₀₁	—	4	2	no	—
208	C₂×C₄×C₁₀₁	—	4	2	no	—
209	C₂×C₄×C₁₀₁	—	4	2	no	—
210	C₂×C₄×C₁₀₁	—	4	1	no	—
211	C₂×C₄×C₁₀₁	—	4	1	no	—
212	C₂×C₄×C₁₀₁	—	4	1	no	—
213	C₂×C₄×C₁₀₁	—	4	2	no	—
214	C₂×C₄×C₁₀₁	—	4	1	no	—
215	C₂×C₄×C₁₀₁	—	4	2	no	—
216	C₂×C₄×C₁₀₁	—	4	2	no	—
217	C₂×C₄×C₁₀₁	—	4	2	no	—
218	C₂×C₄×C₁₀₁	—	4	2	no	—
219	C₂×C₄×C₁₀₁	—	4	2	no	—
220	C₂×C₄×C₁₀₁	—	4	2	no	—
221	C₂×C₄×C₁₀₁	—	4	2	no	—
222	C₂×C₄×C₁₀₁	—	4	2	no	—
223	C₂×C₄×C₁₀₁	—	4	2	no	—
224	C₂×C₄×C₁₀₁	C₂²⋊Q₈	1	8	yes	—
225	C₂×C₄×C₁₀₁	C₄⋊Q₈	1	8	yes	—
226	C₂²×C₁₀₁	C₂×C₂²⋊Q₈	1	2	yes	—
227	C₂²×C₁₀₁	C₂×C₄⋊Q₈	1	2	yes	—
228	C₂²×C₁₀₁	#533	1	2	yes	—
229	C₂²×C₁₀₁	#535	1	2	yes	—
230	C₂²×C₁₀₁	#538	1	1	yes	characteristic
231	C₂²×C₁₀₁	#542	1	2	yes	—
232	C₂²×C₁₀₁	#543	1	2	yes	—
233	C₂²×C₁₀₁	#543	1	1	yes	characteristic
234	C₂²×C₁₀₁	#544	1	1	yes	characteristic
235	C₂²×C₁₀₁	D₄²	1	1	yes	characteristic
236	C₂²×C₁₀₁	#546	1	2	yes	—
237	C₂²×C₁₀₁	#546	1	2	yes	—
238	C₂²×C₁₀₁	D₄×Q₈	1	2	yes	—
239	C₂²×C₁₀₁	#551	1	1	yes	characteristic
240	C₂²×C₁₀₁	#554	1	2	yes	—
241	C₂²×C₁₀₁	#554	1	2	yes	—
242	C₂²×C₁₀₁	#554	1	1	yes	characteristic
243	C₂²×C₁₀₁	#557	1	1	yes	characteristic
244	C₂²×C₁₀₁	Q₈²	1	1	yes	characteristic
245	C₂²×C₁₀₁	Q₈²	1	2	yes	—
246	C₂²×C₁₀₁	Q₈²	1	1	yes	characteristic
247	C₂²×C₁₀₁	H(3,𝔽₄)	1	1	yes	characteristic
248	C₂²×C₁₀₁	#562	1	1	yes	characteristic
249	C₄×C₁₀₁	—	2	8	no	—
250	C₄×C₁₀₁	—	2	8	no	—
251	C₄×C₁₀₁	—	4	4	no	—
252	C₄×C₁₀₁	—	4	2	no	—
253	C₄×C₁₀₁	—	4	4	no	—
254	C₄×C₁₀₁	—	4	4	no	—
255	C₄×C₁₀₁	—	4	2	no	—
256	C₄×C₁₀₁	—	4	2	no	—
257	C₄×C₁₀₁	—	8	2	no	—
258	#15510	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
259	C₂×C₁₀₁	#2437	1	1	yes	characteristic
260	C₂×C₁₀₁	#2451	1	2	yes	—
261	C₂×C₁₀₁	#2549	1	2	yes	—
262	C₂×C₁₀₁	#2551	1	1	yes	characteristic
263	C₂×C₁₀₁	#2567	1	2	yes	—
264	C₂×C₁₀₁	#2586	1	1	yes	characteristic
265	C₂×C₁₀₁	#2670	1	1	yes	characteristic
266	C₂×C₁₀₁	#2692	1	2	yes	—
267	C₂×C₁₀₁	#2763	1	1	yes	characteristic
268	C₂×C₁₀₁	#2806	1	1	yes	characteristic
269	C₂×C₁₀₁	#2811	1	1	yes	characteristic
270	C₂×#395	C₂×C₁₀₁	1	2	yes	—
271	C₂×#391	C₂×C₁₀₁	1	2	yes	—
272	#1446	C₂×C₁₀₁	1	1	yes	characteristic
273	#1446	C₂×C₁₀₁	1	1	yes	characteristic
274	#1444	C₂×C₁₀₁	1	1	yes	characteristic
275	#1444	C₂×C₁₀₁	1	2	yes	—
276	#1441	C₂×C₁₀₁	1	2	yes	—
277	#1436	C₂×C₁₀₁	1	2	yes	—
278	C₄⋊#95	C₂×C₁₀₁	1	2	yes	—
279	C₁₀₁	#15510	1	1	yes	characteristic, direct product factor, Sylow
280	C₂³×Q₈	C₂²×C₁₀₁	1	1	yes	characteristic
281	C₂³×Q₈	C₂²×C₁₀₁	1	1	yes	characteristic
282	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	2	yes	—
283	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	2	yes	—
284	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	2	yes	—
285	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
286	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	2	yes	—
287	C₂²×C₄²	C₂²×C₁₀₁	1	2	yes	—
288	#395	—	2	8	no	—
289	#391	—	2	8	no	—
290	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
291	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
292	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
293	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
294	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
295	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
296	C₂×#95	C₂²×C₁₀₁	1	1	yes	characteristic
297	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
298	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
299	C₂×#95	C₂²×C₁₀₁	1	1	yes	characteristic
300	C₂×#95	C₂²×C₁₀₁	1	1	yes	characteristic
301	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
302	C₂×#95	C₂²×C₁₀₁	1	1	yes	characteristic
303	C₂²×Q₈	—	2	4	no	—
304	C₂²×Q₈	—	2	4	no	—
305	C₂²×Q₈	—	2	4	no	—
306	C₂²×Q₈	—	2	2	no	—
307	C₂²×Q₈	—	4	1	no	—
308	C₂²×Q₈	—	4	1	no	—
309	C₂²×Q₈	—	4	1	no	—
310	C₂²×Q₈	—	4	2	no	—
311	C₂²×Q₈	—	4	1	no	—
312	C₂²×Q₈	Q₈×C₁₀₁	1	4	yes	complemented
313	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
314	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
315	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
316	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
317	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
318	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
319	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
320	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
321	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
322	C₂×C₄⋊C₄	—	2	4	no	—
323	C₂×C₄⋊C₄	—	2	4	no	—
324	C₂×C₄⋊C₄	—	2	4	no	—
325	C₂×C₄⋊C₄	—	2	4	no	—
326	C₂×C₄⋊C₄	—	2	4	no	—
327	C₂×C₄⋊C₄	—	4	2	no	—
328	C₂×C₄⋊C₄	—	4	2	no	—
329	C₂×C₄⋊C₄	—	4	2	no	—
330	C₂×C₄⋊C₄	—	4	2	no	—
331	C₂×C₄⋊C₄	—	4	2	no	—
332	C₂×C₄⋊C₄	—	4	2	no	—
333	C₂×C₄⋊C₄	—	4	1	no	—
334	C₂×C₄⋊C₄	—	4	2	no	—
335	C₂×C₄⋊C₄	Q₈×C₁₀₁	1	8	yes	complemented
336	C₂×C₄²	—	2	4	no	—
337	C₂×C₄²	—	2	4	no	—
338	C₂×C₄²	—	4	2	no	—
339	#95	—	2	4	no	—
340	#95	—	2	4	no	—
341	#95	—	2	4	no	—
342	#95	—	2	4	no	—
343	#95	—	2	4	no	—
344	#95	—	2	4	no	—
345	#95	—	4	1	no	—
346	#95	—	4	2	no	—
347	#95	—	4	2	no	—
348	#95	—	4	1	no	—
349	#95	—	4	1	no	—
350	#95	D₄×C₁₀₁	1	8	yes	—
351	#95	Q₈×C₁₀₁	1	4	yes	complemented
352	C₂⁴	C₂⁴×C₁₀₁	1	1	yes	characteristic
353	C₂×Q₈	—	2	16	no	—
354	C₂×Q₈	—	4	4	no	—
355	C₂×Q₈	—	4	4	no	—
356	C₂×Q₈	—	4	8	no	—
357	C₂×Q₈	—	4	4	no	—
358	C₂×Q₈	—	4	4	no	—
359	C₂×Q₈	—	4	8	no	—
360	C₂×Q₈	—	4	8	no	—
361	C₂×Q₈	—	4	4	no	—
362	C₂×Q₈	—	4	4	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	—	2	2	no	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	2	2	no	—
384	C₂²×C₄	—	2	1	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	2	2	no	—
387	C₂²×C₄	—	2	1	no	—
388	C₂²×C₄	—	2	1	no	—
389	C₂²×C₄	—	2	1	no	—
390	C₂²×C₄	—	2	1	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	2	2	no	—
394	C₂²×C₄	—	2	2	no	—
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	—	2	2	no	—
397	C₂²×C₄	—	2	2	no	—
398	C₂²×C₄	—	2	1	no	—
399	C₂²×C₄	—	2	2	no	—
400	C₂²×C₄	—	2	2	no	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	—	2	2	no	—
403	C₂²×C₄	—	2	2	no	—
404	C₂²×C₄	—	2	2	no	—
405	C₂²×C₄	—	2	2	no	—
406	C₂²×C₄	—	2	2	no	—
407	C₂²×C₄	—	2	2	no	—
408	C₂²×C₄	C₂×D₄×C₁₀₁	1	4	yes	—
409	C₂²×C₄	C₂×D₄×C₁₀₁	1	4	yes	—
410	C₂²×C₄	C₂×D₄×C₁₀₁	1	4	yes	—
411	C₂²×C₄	C₂×Q₈×C₁₀₁	1	2	yes	—
412	C₂²×C₄	C₂×Q₈×C₁₀₁	1	4	yes	—
413	C₂²×C₄	C₂×Q₈×C₁₀₁	1	4	yes	—
414	C₂²×C₄	C₂×Q₈×C₁₀₁	1	2	yes	—
415	C₂²×C₄	C₂×Q₈×C₁₀₁	1	4	yes	—
416	C₂²×C₄	C₂×Q₈×C₁₀₁	1	4	yes	—
417	C₂²×C₄	C₂×Q₈×C₁₀₁	1	4	yes	—
418	C₂²×C₄	#41×C₁₀₁	1	2	yes	—
419	C₂²×C₄	#41×C₁₀₁	1	4	yes	—
420	C₄⋊C₄	—	4	8	no	—
421	C₄⋊C₄	—	4	8	no	—
422	C₄⋊C₄	—	4	8	no	—
423	C₄⋊C₄	—	4	8	no	—
424	C₄⋊C₄	—	4	4	no	—
425	C₄²	—	4	8	no	—
426	C₂³	C₂²×D₄×C₁₀₁	1	2	yes	—
427	C₂³	C₂²×Q₈×C₁₀₁	1	1	yes	characteristic
428	C₂³	C₂²×Q₈×C₁₀₁	1	1	yes	characteristic
429	C₂³	C₂²×Q₈×C₁₀₁	1	2	yes	—
430	C₂³	C₂×#41×C₁₀₁	1	2	yes	—
431	C₂³	C₂×#41×C₁₀₁	1	1	yes	characteristic
432	C₂³	H(5,𝔽₂)×C₁₀₁	1	1	yes	characteristic
433	C₂³	H(5,𝔽₂)×C₁₀₁	1	2	yes	—
434	C₂³	H(5,𝔽₂)×C₁₀₁	1	1	yes	characteristic
435	C₂³	H(5,𝔽₂)×C₁₀₁	1	1	yes	characteristic
436	C₂³	2₋¹⁺⁴×C₁₀₁	1	1	yes	characteristic
437	Q₈	—	4	16	no	—
438	Q₈	—	4	16	no	—
439	C₂×C₄	—	2	4	no	—
440	C₂×C₄	—	2	4	no	—
441	C₂×C₄	—	2	4	no	—
442	C₂×C₄	—	2	4	no	—
443	C₂×C₄	—	2	4	no	—
444	C₂×C₄	—	2	4	no	—
445	C₂×C₄	—	2	4	no	—
446	C₂×C₄	—	2	4	no	—
447	C₂×C₄	—	2	4	no	—
448	C₂×C₄	—	2	4	no	—
449	C₂×C₄	—	2	4	no	—
450	C₂×C₄	—	2	4	no	—
451	C₂×C₄	—	2	4	no	—
452	C₂×C₄	—	2	4	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	4	no	—
455	C₂×C₄	—	2	4	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	4	no	—
459	C₂×C₄	—	2	4	no	—
460	C₂×C₄	—	2	4	no	—
461	C₂×C₄	—	2	4	no	—
462	C₂×C₄	—	2	4	no	—
463	C₂×C₄	—	2	4	no	—
464	C₂×C₄	—	2	4	no	—
465	C₂×C₄	—	2	4	no	—
466	C₂×C₄	—	4	2	no	—
467	C₂×C₄	—	4	2	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	—	4	2	no	—
471	C₂×C₄	—	4	2	no	—
472	C₂×C₄	—	4	2	no	—
473	C₂×C₄	—	4	2	no	—
474	C₂×C₄	—	4	1	no	—
475	C₂×C₄	—	4	1	no	—
476	C₂×C₄	—	4	2	no	—
477	C₂×C₄	—	4	2	no	—
478	C₂×C₄	—	4	2	no	—
479	C₂×C₄	—	4	2	no	—
480	C₂×C₄	—	4	1	no	—
481	C₂×C₄	—	4	1	no	—
482	C₂×C₄	—	4	1	no	—
483	C₂×C₄	—	4	2	no	—
484	C₂×C₄	—	4	1	no	—
485	C₂×C₄	—	4	2	no	—
486	C₂×C₄	—	4	2	no	—
487	C₂×C₄	—	4	2	no	—
488	C₂×C₄	—	4	2	no	—
489	C₂×C₄	—	4	2	no	—
490	C₂×C₄	—	4	2	no	—
491	C₂×C₄	—	4	2	no	—
492	C₂×C₄	—	4	2	no	—
493	C₂×C₄	—	4	2	no	—
494	C₂×C₄	C₂²⋊Q₈×C₁₀₁	1	8	yes	—
495	C₂×C₄	C₄⋊Q₈×C₁₀₁	1	8	yes	—
496	C₂²	C₂×C₂²⋊Q₈×C₁₀₁	1	2	yes	—
497	C₂²	C₂×C₄⋊Q₈×C₁₀₁	1	2	yes	—
498	C₂²	#533×C₁₀₁	1	2	yes	—
499	C₂²	#535×C₁₀₁	1	2	yes	—
500	C₂²	#538×C₁₀₁	1	1	yes	characteristic
501	C₂²	#542×C₁₀₁	1	2	yes	—
502	C₂²	#543×C₁₀₁	1	2	yes	—
503	C₂²	#543×C₁₀₁	1	1	yes	characteristic
504	C₂²	#544×C₁₀₁	1	1	yes	characteristic
505	C₂²	D₄²×C₁₀₁	1	1	yes	characteristic
506	C₂²	#546×C₁₀₁	1	2	yes	—
507	C₂²	#546×C₁₀₁	1	2	yes	—
508	C₂²	D₄×Q₈×C₁₀₁	1	2	yes	—
509	C₂²	#551×C₁₀₁	1	1	yes	characteristic
510	C₂²	#554×C₁₀₁	1	2	yes	—
511	C₂²	#554×C₁₀₁	1	2	yes	—
512	C₂²	#554×C₁₀₁	1	1	yes	characteristic
513	C₂²	#557×C₁₀₁	1	1	yes	characteristic
514	C₂²	Q₈²×C₁₀₁	1	2	yes	—
515	C₂²	Q₈²×C₁₀₁	1	1	yes	characteristic
516	C₂²	Q₈²×C₁₀₁	1	1	yes	characteristic
517	C₂²	H(3,𝔽₄)×C₁₀₁	1	1	yes	characteristic
518	C₂²	#562×C₁₀₁	1	1	yes	characteristic
519	C₄	—	2	8	no	—
520	C₄	—	2	8	no	—
521	C₄	—	4	4	no	—
522	C₄	—	4	2	no	—
523	C₄	—	4	4	no	—
524	C₄	—	4	4	no	—
525	C₄	—	4	2	no	—
526	C₄	—	4	2	no	—
527	C₄	—	8	2	no	—
528	C₂	C₁₀₁×#2437	1	1	yes	characteristic
529	C₂	C₁₀₁×#2451	1	2	yes	—
530	C₂	C₁₀₁×#2549	1	2	yes	—
531	C₂	C₁₀₁×#2551	1	1	yes	characteristic
532	C₂	C₁₀₁×#2567	1	2	yes	—
533	C₂	C₁₀₁×#2586	1	1	yes	characteristic
534	C₂	C₁₀₁×#2670	1	1	yes	characteristic
535	C₂	C₁₀₁×#2692	1	2	yes	—
536	C₂	C₁₀₁×#2763	1	1	yes	characteristic
537	C₂	C₁₀₁×#2806	1	1	yes	characteristic
538	C₂	C₁₀₁×#2811	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₁₀₁	C₂⁴
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₁₀₁
LCS	G ▷ C₂⁴ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₀₁ ◁ G

Complements

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

N	H ≅ G/N	type
42. C₂²×Q₈×C₁₀₁	Q₈	semidirect
65. C₂×C₄⋊C₄×C₁₀₁	Q₈	semidirect
81. #95×C₁₀₁	Q₈	semidirect
258. #15510	C₁₀₁	direct (N × H)
279. C₁₀₁	#15510	direct (N × H)
312. C₂²×Q₈	Q₈×C₁₀₁	semidirect
335. C₂×C₄⋊C₄	Q₈×C₁₀₁	semidirect
351. #95	Q₈×C₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#395×C₁₀₁	2
C₂×#391×C₁₀₁	2
C₁₀₁×#1446	2
C₁₀₁×#1444	2
C₁₀₁×#1441	2
C₁₀₁×#1436	2
C₁₀₁×C₄⋊#95	2
#15510	101

Subgroups — C101×#15510 #38797661

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#15510 #38797661