Subgroups — C₁₀₁×#13976 #38796127

Order 25856.

1838 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×Q₈×C₁₀₁	C₂	1	1	yes	maximal, characteristic
2	C₂×#391×C₁₀₁	C₂	1	1	yes	maximal, characteristic
3	C₂×#391×C₁₀₁	C₂	1	1	yes	maximal, characteristic
4	C₂×#389×C₁₀₁	C₂	1	1	yes	maximal, characteristic
5	C₂×#384×C₁₀₁	C₂	1	1	yes	maximal, characteristic
6	C₁₀₁×#1444	C₂	1	4	yes	maximal
7	C₁₀₁×#1436	C₂	1	4	yes	maximal
8	C₁₀₁×C₄⋊#95	C₂	1	1	yes	maximal, characteristic
9	C₄×#95×C₁₀₁	C₂	1	1	yes	maximal, characteristic
10	C₂³×Q₈×C₁₀₁	C₂²	1	1	yes	characteristic
11	C₂×C₄×Q₈×C₁₀₁	—	2	4	no	—
12	C₂×C₄×Q₈×C₁₀₁	—	2	4	no	—
13	C₂×C₄×Q₈×C₁₀₁	—	2	4	no	—
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	4	yes	—
17	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
18	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
19	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	2	yes	—
20	C₂²×C₄²×C₁₀₁	C₂²	1	2	yes	—
21	C₂²×C₄²×C₁₀₁	C₂²	1	1	yes	characteristic
22	C₂²×C₄²×C₁₀₁	C₂²	1	1	yes	characteristic
23	C₂²×C₄²×C₁₀₁	C₂²	1	1	yes	characteristic
24	#391×C₁₀₁	—	2	4	no	—
25	#391×C₁₀₁	C₄	1	8	yes	complemented
26	#389×C₁₀₁	—	2	4	no	—
27	#384×C₁₀₁	—	2	4	no	—
28	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
29	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
30	C₂×#95×C₁₀₁	C₂²	1	4	yes	—
31	C₂×#95×C₁₀₁	C₂²	1	4	yes	—
32	C₂×#95×C₁₀₁	C₂²	1	4	yes	—
33	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
34	C₂²×Q₈×C₁₀₁	—	2	2	no	—
35	C₂²×Q₈×C₁₀₁	—	2	2	no	—
36	C₂²×Q₈×C₁₀₁	—	2	2	no	—
37	C₂²×Q₈×C₁₀₁	—	2	2	no	—
38	C₂²×Q₈×C₁₀₁	C₂×C₄	1	4	yes	—
39	C₂²×Q₈×C₁₀₁	D₄	1	4	yes	—
40	C₂²×Q₈×C₁₀₁	Q₈	1	4	yes	—
41	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
42	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
43	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
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	2	yes	—
48	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
49	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
50	C₄×Q₈×C₁₀₁	—	2	32	no	—
51	C₂×C₄⋊C₄×C₁₀₁	—	2	4	no	—
52	C₂×C₄⋊C₄×C₁₀₁	—	2	4	no	—
53	C₂×C₄⋊C₄×C₁₀₁	—	2	4	no	—
54	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
55	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
56	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
57	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
58	C₂×C₄⋊C₄×C₁₀₁	—	2	8	no	—
59	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
60	C₂×C₄⋊C₄×C₁₀₁	—	2	4	no	—
61	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
62	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
63	C₂×C₄⋊C₄×C₁₀₁	—	2	8	no	—
64	C₂×C₄⋊C₄×C₁₀₁	—	4	4	no	—
65	C₂×C₄⋊C₄×C₁₀₁	—	4	4	no	—
66	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	4	yes	—
67	C₂×C₄⋊C₄×C₁₀₁	D₄	1	4	yes	—
68	C₂×C₄²×C₁₀₁	—	2	4	no	—
69	C₂×C₄²×C₁₀₁	—	2	4	no	—
70	C₂×C₄²×C₁₀₁	—	2	4	no	—
71	C₂×C₄²×C₁₀₁	—	2	2	no	—
72	C₂×C₄²×C₁₀₁	—	2	2	no	—
73	C₂×C₄²×C₁₀₁	—	2	2	no	—
74	C₂×C₄²×C₁₀₁	—	2	2	no	—
75	C₂×C₄²×C₁₀₁	—	2	2	no	—
76	C₂×C₄²×C₁₀₁	—	2	2	no	—
77	C₂×C₄²×C₁₀₁	—	2	2	no	—
78	C₂×C₄²×C₁₀₁	C₂×C₄	1	4	yes	—
79	C₂×C₄²×C₁₀₁	D₄	1	4	yes	—
80	#95×C₁₀₁	—	2	4	no	—
81	#95×C₁₀₁	—	2	8	no	—
82	#95×C₁₀₁	—	2	4	no	—
83	#95×C₁₀₁	—	4	4	no	—
84	#95×C₁₀₁	C₂×C₄	1	16	yes	—
85	#95×C₁₀₁	Q₈	1	8	yes	complemented
86	C₂⁴×C₁₀₁	C₂⁴	1	1	yes	characteristic
87	C₂×Q₈×C₁₀₁	—	2	8	no	—
88	C₂×Q₈×C₁₀₁	—	2	8	no	—
89	C₂×Q₈×C₁₀₁	—	2	8	no	—
90	C₂×Q₈×C₁₀₁	—	2	8	no	—
91	C₂×Q₈×C₁₀₁	—	2	8	no	—
92	C₂×Q₈×C₁₀₁	—	2	8	no	—
93	C₂×Q₈×C₁₀₁	C₄⋊C₄	1	16	yes	complemented
94	C₂²×C₄×C₁₀₁	—	2	1	no	—
95	C₂²×C₄×C₁₀₁	—	2	1	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	1	no	—
109	C₂²×C₄×C₁₀₁	—	2	2	no	—
110	C₂²×C₄×C₁₀₁	—	2	1	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	2	no	—
115	C₂²×C₄×C₁₀₁	—	2	2	no	—
116	C₂²×C₄×C₁₀₁	—	2	4	no	—
117	C₂²×C₄×C₁₀₁	—	2	2	no	—
118	C₂²×C₄×C₁₀₁	—	2	4	no	—
119	C₂²×C₄×C₁₀₁	—	2	4	no	—
120	C₂²×C₄×C₁₀₁	—	2	2	no	—
121	C₂²×C₄×C₁₀₁	—	2	4	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	4	no	—
127	C₂²×C₄×C₁₀₁	—	2	4	no	—
128	C₂²×C₄×C₁₀₁	C₂²×C₄	1	4	yes	—
129	C₂²×C₄×C₁₀₁	C₂²×C₄	1	4	yes	—
130	C₂²×C₄×C₁₀₁	C₂²×C₄	1	4	yes	—
131	C₂²×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
132	C₂²×C₄×C₁₀₁	C₂×D₄	1	4	yes	—
133	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
134	C₂²×C₄×C₁₀₁	C₂×D₄	1	4	yes	—
135	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
136	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
137	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
138	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
139	C₂²×C₄×C₁₀₁	C₂×Q₈	1	4	yes	—
140	C₂²×C₄×C₁₀₁	C₂×Q₈	1	4	yes	—
141	C₂²×C₄×C₁₀₁	C₂×Q₈	1	4	yes	—
142	C₂²×C₄×C₁₀₁	C₂×Q₈	1	4	yes	—
143	C₂²×C₄×C₁₀₁	C₂×Q₈	1	2	yes	—
144	C₂²×C₄×C₁₀₁	#41	1	4	yes	—
145	C₂²×C₄×C₁₀₁	#41	1	2	yes	—
146	C₂²×C₄×C₁₀₁	#41	1	2	yes	—
147	C₄⋊C₄×C₁₀₁	—	2	16	no	—
148	C₄⋊C₄×C₁₀₁	—	2	8	no	—
149	C₄⋊C₄×C₁₀₁	—	2	8	no	—
150	C₄⋊C₄×C₁₀₁	—	4	16	no	—
151	C₄⋊C₄×C₁₀₁	—	4	8	no	—
152	C₄⋊C₄×C₁₀₁	—	4	4	no	—
153	C₄²×C₁₀₁	—	2	16	no	—
154	C₄²×C₁₀₁	—	2	8	no	—
155	C₄²×C₁₀₁	—	2	8	no	—
156	C₄²×C₁₀₁	—	4	4	no	—
157	C₂³×C₁₀₁	C₂³×C₄	1	1	yes	characteristic
158	C₂³×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
159	C₂³×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
160	C₂³×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
161	C₂³×C₁₀₁	C₂²×Q₈	1	1	yes	characteristic
162	C₂³×C₁₀₁	C₂²×Q₈	1	2	yes	—
163	C₂³×C₁₀₁	C₂×#41	1	1	yes	characteristic
164	C₂³×C₁₀₁	C₂×#41	1	1	yes	characteristic
165	C₂³×C₁₀₁	C₂×#41	1	2	yes	—
166	C₂³×C₁₀₁	H(5,𝔽₂)	1	2	yes	—
167	C₂³×C₁₀₁	2₋¹⁺⁴	1	2	yes	—
168	Q₈×C₁₀₁	—	2	32	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	2	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	2	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	4	no	—
184	C₂×C₄×C₁₀₁	—	2	4	no	—
185	C₂×C₄×C₁₀₁	—	2	4	no	—
186	C₂×C₄×C₁₀₁	—	2	8	no	—
187	C₂×C₄×C₁₀₁	—	2	4	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	2	no	—
192	C₂×C₄×C₁₀₁	—	2	8	no	—
193	C₂×C₄×C₁₀₁	—	2	4	no	—
194	C₂×C₄×C₁₀₁	—	2	4	no	—
195	C₂×C₄×C₁₀₁	—	4	2	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	4	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	2	no	—
205	C₂×C₄×C₁₀₁	—	4	4	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	4	no	—
211	C₂×C₄×C₁₀₁	—	4	4	no	—
212	C₂×C₄×C₁₀₁	C₂×C₄⋊C₄	1	8	yes	—
213	C₂×C₄×C₁₀₁	C₂×C₄⋊C₄	1	4	yes	—
214	C₂×C₄×C₁₀₁	C₄×D₄	1	4	yes	—
215	C₂×C₄×C₁₀₁	C₄×D₄	1	4	yes	—
216	C₂×C₄×C₁₀₁	C₄×Q₈	1	8	yes	complemented
217	C₂×C₄×C₁₀₁	#120	1	4	yes	—
218	C₂×C₄×C₁₀₁	C₂²⋊Q₈	1	4	yes	—
219	C₂×C₄×C₁₀₁	C₂²⋊Q₈	1	4	yes	—
220	C₂×C₄×C₁₀₁	#123	1	4	yes	—
221	C₂×C₄×C₁₀₁	C₄⋊Q₈	1	4	yes	—
222	C₂²×C₁₀₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
223	C₂²×C₁₀₁	C₂×C₄×D₄	1	1	yes	characteristic
224	C₂²×C₁₀₁	C₂×C₄×D₄	1	1	yes	characteristic
225	C₂²×C₁₀₁	C₂×C₄×Q₈	1	2	yes	—
226	C₂²×C₁₀₁	#520	1	2	yes	—
227	C₂²×C₁₀₁	C₂×#120	1	1	yes	characteristic
228	C₂²×C₁₀₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
229	C₂²×C₁₀₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
230	C₂²×C₁₀₁	C₂×#123	1	1	yes	characteristic
231	C₂²×C₁₀₁	C₂×C₄⋊Q₈	1	1	yes	characteristic
232	C₂²×C₁₀₁	#532	1	1	yes	characteristic
233	C₂²×C₁₀₁	#533	1	2	yes	—
234	C₂²×C₁₀₁	#535	1	1	yes	characteristic
235	C₂²×C₁₀₁	#536	1	1	yes	characteristic
236	C₂²×C₁₀₁	#542	1	2	yes	—
237	C₂²×C₁₀₁	#546	1	2	yes	—
238	C₂²×C₁₀₁	D₄×Q₈	1	2	yes	—
239	C₂²×C₁₀₁	D₄×Q₈	1	2	yes	—
240	C₂²×C₁₀₁	#550	1	2	yes	—
241	C₂²×C₁₀₁	#552	1	2	yes	—
242	C₂²×C₁₀₁	#554	1	2	yes	—
243	C₂²×C₁₀₁	#557	1	2	yes	—
244	C₂²×C₁₀₁	Q₈²	1	2	yes	—
245	C₄×C₁₀₁	—	2	8	no	—
246	C₄×C₁₀₁	—	2	4	no	—
247	C₄×C₁₀₁	—	2	8	no	—
248	C₄×C₁₀₁	—	4	4	no	—
249	C₄×C₁₀₁	—	4	4	no	—
250	C₄×C₁₀₁	—	4	2	no	—
251	C₄×C₁₀₁	—	4	4	no	—
252	C₄×C₁₀₁	—	8	2	no	—
253	C₄×C₁₀₁	#385	1	8	yes	—
254	#13976	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
255	C₂×C₁₀₁	C₂×#385	1	1	yes	characteristic
256	C₂×C₁₀₁	C₄×C₄⋊Q₈	1	1	yes	characteristic
257	C₂×C₁₀₁	#2326	1	1	yes	characteristic
258	C₂×C₁₀₁	Q₈×C₄⋊C₄	1	2	yes	—
259	C₂×C₁₀₁	#2360	1	2	yes	—
260	C₂×C₁₀₁	#2423	1	2	yes	—
261	C₂×C₁₀₁	#2431	1	1	yes	characteristic
262	C₂×C₁₀₁	#2434	1	1	yes	characteristic
263	C₂×C₁₀₁	#2451	1	2	yes	—
264	C₂×C₁₀₁	#2565	1	1	yes	characteristic
265	C₂×C₁₀₁	#2567	1	1	yes	characteristic
266	C₂²×C₄×Q₈	C₂×C₁₀₁	1	1	yes	characteristic
267	C₂×#391	C₂×C₁₀₁	1	1	yes	characteristic
268	C₂×#391	C₂×C₁₀₁	1	1	yes	characteristic
269	C₂×#389	C₂×C₁₀₁	1	1	yes	characteristic
270	C₂×#384	C₂×C₁₀₁	1	1	yes	characteristic
271	#1444	C₂×C₁₀₁	1	4	yes	—
272	#1436	C₂×C₁₀₁	1	4	yes	—
273	C₄⋊#95	C₂×C₁₀₁	1	1	yes	characteristic
274	C₄×#95	C₂×C₁₀₁	1	1	yes	characteristic
275	C₁₀₁	#13976	1	1	yes	characteristic, direct product factor, Sylow
276	C₂³×Q₈	C₂²×C₁₀₁	1	1	yes	characteristic
277	C₂×C₄×Q₈	—	2	4	no	—
278	C₂×C₄×Q₈	—	2	4	no	—
279	C₂×C₄×Q₈	—	2	4	no	—
280	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	2	yes	—
281	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
282	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	4	yes	—
283	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
284	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
285	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	2	yes	—
286	C₂²×C₄²	C₂²×C₁₀₁	1	2	yes	—
287	C₂²×C₄²	C₂²×C₁₀₁	1	1	yes	characteristic
288	C₂²×C₄²	C₂²×C₁₀₁	1	1	yes	characteristic
289	C₂²×C₄²	C₂²×C₁₀₁	1	1	yes	characteristic
290	#391	—	2	4	no	—
291	#391	C₄×C₁₀₁	1	8	yes	complemented
292	#389	—	2	4	no	—
293	#384	—	2	4	no	—
294	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
295	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
296	C₂×#95	C₂²×C₁₀₁	1	4	yes	—
297	C₂×#95	C₂²×C₁₀₁	1	4	yes	—
298	C₂×#95	C₂²×C₁₀₁	1	4	yes	—
299	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
300	C₂²×Q₈	—	2	2	no	—
301	C₂²×Q₈	—	2	2	no	—
302	C₂²×Q₈	—	2	2	no	—
303	C₂²×Q₈	—	2	2	no	—
304	C₂²×Q₈	C₂×C₄×C₁₀₁	1	4	yes	—
305	C₂²×Q₈	D₄×C₁₀₁	1	4	yes	—
306	C₂²×Q₈	Q₈×C₁₀₁	1	4	yes	—
307	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
308	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
309	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
310	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
311	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
312	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
313	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
314	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
315	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
316	C₄×Q₈	—	2	32	no	—
317	C₂×C₄⋊C₄	—	2	4	no	—
318	C₂×C₄⋊C₄	—	2	4	no	—
319	C₂×C₄⋊C₄	—	2	4	no	—
320	C₂×C₄⋊C₄	—	2	2	no	—
321	C₂×C₄⋊C₄	—	2	2	no	—
322	C₂×C₄⋊C₄	—	2	2	no	—
323	C₂×C₄⋊C₄	—	2	2	no	—
324	C₂×C₄⋊C₄	—	2	8	no	—
325	C₂×C₄⋊C₄	—	2	2	no	—
326	C₂×C₄⋊C₄	—	2	4	no	—
327	C₂×C₄⋊C₄	—	2	2	no	—
328	C₂×C₄⋊C₄	—	2	2	no	—
329	C₂×C₄⋊C₄	—	2	8	no	—
330	C₂×C₄⋊C₄	—	4	4	no	—
331	C₂×C₄⋊C₄	—	4	4	no	—
332	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	4	yes	—
333	C₂×C₄⋊C₄	D₄×C₁₀₁	1	4	yes	—
334	C₂×C₄²	—	2	4	no	—
335	C₂×C₄²	—	2	4	no	—
336	C₂×C₄²	—	2	4	no	—
337	C₂×C₄²	—	2	2	no	—
338	C₂×C₄²	—	2	2	no	—
339	C₂×C₄²	—	2	2	no	—
340	C₂×C₄²	—	2	2	no	—
341	C₂×C₄²	—	2	2	no	—
342	C₂×C₄²	—	2	2	no	—
343	C₂×C₄²	—	2	2	no	—
344	C₂×C₄²	C₂×C₄×C₁₀₁	1	4	yes	—
345	C₂×C₄²	D₄×C₁₀₁	1	4	yes	—
346	#95	—	2	4	no	—
347	#95	—	2	8	no	—
348	#95	—	2	4	no	—
349	#95	—	4	4	no	—
350	#95	C₂×C₄×C₁₀₁	1	16	yes	—
351	#95	Q₈×C₁₀₁	1	8	yes	complemented
352	C₂⁴	C₂⁴×C₁₀₁	1	1	yes	characteristic
353	C₂×Q₈	—	2	8	no	—
354	C₂×Q₈	—	2	8	no	—
355	C₂×Q₈	—	2	8	no	—
356	C₂×Q₈	—	2	8	no	—
357	C₂×Q₈	—	2	8	no	—
358	C₂×Q₈	—	2	8	no	—
359	C₂×Q₈	C₄⋊C₄×C₁₀₁	1	16	yes	complemented
360	C₂²×C₄	—	2	1	no	—
361	C₂²×C₄	—	2	1	no	—
362	C₂²×C₄	—	2	2	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	1	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	2	1	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	4	no	—
383	C₂²×C₄	—	2	2	no	—
384	C₂²×C₄	—	2	4	no	—
385	C₂²×C₄	—	2	4	no	—
386	C₂²×C₄	—	2	2	no	—
387	C₂²×C₄	—	2	4	no	—
388	C₂²×C₄	—	2	2	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	2	2	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	2	4	no	—
393	C₂²×C₄	—	2	4	no	—
394	C₂²×C₄	C₂²×C₄×C₁₀₁	1	4	yes	—
395	C₂²×C₄	C₂²×C₄×C₁₀₁	1	4	yes	—
396	C₂²×C₄	C₂²×C₄×C₁₀₁	1	4	yes	—
397	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
398	C₂²×C₄	C₂×D₄×C₁₀₁	1	4	yes	—
399	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
400	C₂²×C₄	C₂×D₄×C₁₀₁	1	4	yes	—
401	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
402	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
403	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
404	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
405	C₂²×C₄	C₂×Q₈×C₁₀₁	1	4	yes	—
406	C₂²×C₄	C₂×Q₈×C₁₀₁	1	4	yes	—
407	C₂²×C₄	C₂×Q₈×C₁₀₁	1	4	yes	—
408	C₂²×C₄	C₂×Q₈×C₁₀₁	1	4	yes	—
409	C₂²×C₄	C₂×Q₈×C₁₀₁	1	2	yes	—
410	C₂²×C₄	#41×C₁₀₁	1	4	yes	—
411	C₂²×C₄	#41×C₁₀₁	1	2	yes	—
412	C₂²×C₄	#41×C₁₀₁	1	2	yes	—
413	C₄⋊C₄	—	2	16	no	—
414	C₄⋊C₄	—	2	8	no	—
415	C₄⋊C₄	—	2	8	no	—
416	C₄⋊C₄	—	4	16	no	—
417	C₄⋊C₄	—	4	8	no	—
418	C₄⋊C₄	—	4	4	no	—
419	C₄²	—	2	16	no	—
420	C₄²	—	2	8	no	—
421	C₄²	—	2	8	no	—
422	C₄²	—	4	4	no	—
423	C₂³	C₂³×C₄×C₁₀₁	1	1	yes	characteristic
424	C₂³	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
425	C₂³	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
426	C₂³	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
427	C₂³	C₂²×Q₈×C₁₀₁	1	1	yes	characteristic
428	C₂³	C₂²×Q₈×C₁₀₁	1	2	yes	—
429	C₂³	C₂×#41×C₁₀₁	1	1	yes	characteristic
430	C₂³	C₂×#41×C₁₀₁	1	1	yes	characteristic
431	C₂³	C₂×#41×C₁₀₁	1	2	yes	—
432	C₂³	H(5,𝔽₂)×C₁₀₁	1	2	yes	—
433	C₂³	2₋¹⁺⁴×C₁₀₁	1	2	yes	—
434	Q₈	—	2	32	no	—
435	C₂×C₄	—	2	4	no	—
436	C₂×C₄	—	2	4	no	—
437	C₂×C₄	—	2	4	no	—
438	C₂×C₄	—	2	4	no	—
439	C₂×C₄	—	2	2	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	2	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	8	no	—
453	C₂×C₄	—	2	4	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	4	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	8	no	—
459	C₂×C₄	—	2	4	no	—
460	C₂×C₄	—	2	4	no	—
461	C₂×C₄	—	4	2	no	—
462	C₂×C₄	—	4	2	no	—
463	C₂×C₄	—	4	2	no	—
464	C₂×C₄	—	4	2	no	—
465	C₂×C₄	—	4	2	no	—
466	C₂×C₄	—	4	2	no	—
467	C₂×C₄	—	4	4	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	—	4	2	no	—
471	C₂×C₄	—	4	4	no	—
472	C₂×C₄	—	4	2	no	—
473	C₂×C₄	—	4	2	no	—
474	C₂×C₄	—	4	2	no	—
475	C₂×C₄	—	4	2	no	—
476	C₂×C₄	—	4	4	no	—
477	C₂×C₄	—	4	4	no	—
478	C₂×C₄	C₂×C₄⋊C₄×C₁₀₁	1	8	yes	—
479	C₂×C₄	C₂×C₄⋊C₄×C₁₀₁	1	4	yes	—
480	C₂×C₄	C₄×D₄×C₁₀₁	1	4	yes	—
481	C₂×C₄	C₄×D₄×C₁₀₁	1	4	yes	—
482	C₂×C₄	C₄×Q₈×C₁₀₁	1	8	yes	complemented
483	C₂×C₄	#120×C₁₀₁	1	4	yes	—
484	C₂×C₄	C₂²⋊Q₈×C₁₀₁	1	4	yes	—
485	C₂×C₄	C₂²⋊Q₈×C₁₀₁	1	4	yes	—
486	C₂×C₄	#123×C₁₀₁	1	4	yes	—
487	C₂×C₄	C₄⋊Q₈×C₁₀₁	1	4	yes	—
488	C₂²	C₂²×C₄⋊C₄×C₁₀₁	1	1	yes	characteristic
489	C₂²	C₂×C₄×D₄×C₁₀₁	1	1	yes	characteristic
490	C₂²	C₂×C₄×D₄×C₁₀₁	1	1	yes	characteristic
491	C₂²	C₂×C₄×Q₈×C₁₀₁	1	2	yes	—
492	C₂²	#520×C₁₀₁	1	2	yes	—
493	C₂²	C₂×#120×C₁₀₁	1	1	yes	characteristic
494	C₂²	C₂×C₂²⋊Q₈×C₁₀₁	1	1	yes	characteristic
495	C₂²	C₂×C₂²⋊Q₈×C₁₀₁	1	1	yes	characteristic
496	C₂²	C₂×#123×C₁₀₁	1	1	yes	characteristic
497	C₂²	C₂×C₄⋊Q₈×C₁₀₁	1	1	yes	characteristic
498	C₂²	#532×C₁₀₁	1	1	yes	characteristic
499	C₂²	#533×C₁₀₁	1	2	yes	—
500	C₂²	#535×C₁₀₁	1	1	yes	characteristic
501	C₂²	#536×C₁₀₁	1	1	yes	characteristic
502	C₂²	#542×C₁₀₁	1	2	yes	—
503	C₂²	#546×C₁₀₁	1	2	yes	—
504	C₂²	D₄×Q₈×C₁₀₁	1	2	yes	—
505	C₂²	D₄×Q₈×C₁₀₁	1	2	yes	—
506	C₂²	#550×C₁₀₁	1	2	yes	—
507	C₂²	#552×C₁₀₁	1	2	yes	—
508	C₂²	#554×C₁₀₁	1	2	yes	—
509	C₂²	#557×C₁₀₁	1	2	yes	—
510	C₂²	Q₈²×C₁₀₁	1	2	yes	—
511	C₄	—	2	4	no	—
512	C₄	—	2	8	no	—
513	C₄	—	2	8	no	—
514	C₄	—	4	4	no	—
515	C₄	—	4	2	no	—
516	C₄	—	4	4	no	—
517	C₄	—	4	4	no	—
518	C₄	—	8	2	no	—
519	C₄	#385×C₁₀₁	1	8	yes	—
520	C₂	C₂×#385×C₁₀₁	1	1	yes	characteristic
521	C₂	C₄×C₄⋊Q₈×C₁₀₁	1	1	yes	characteristic
522	C₂	C₁₀₁×#2326	1	1	yes	characteristic
523	C₂	Q₈×C₄⋊C₄×C₁₀₁	1	2	yes	—
524	C₂	C₁₀₁×#2360	1	2	yes	—
525	C₂	C₁₀₁×#2423	1	2	yes	—
526	C₂	C₁₀₁×#2431	1	1	yes	characteristic
527	C₂	C₁₀₁×#2434	1	1	yes	characteristic
528	C₂	C₁₀₁×#2451	1	2	yes	—
529	C₂	C₁₀₁×#2565	1	1	yes	characteristic
530	C₂	C₁₀₁×#2567	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
25. #391×C₁₀₁	C₄	semidirect
85. #95×C₁₀₁	Q₈	semidirect
93. C₂×Q₈×C₁₀₁	C₄⋊C₄	semidirect
216. C₂×C₄×C₁₀₁	C₄×Q₈	semidirect
254. #13976	C₁₀₁	direct (N × H)
275. C₁₀₁	#13976	direct (N × H)
291. #391	C₄×C₁₀₁	semidirect
351. #95	Q₈×C₁₀₁	semidirect
359. C₂×Q₈	C₄⋊C₄×C₁₀₁	semidirect
482. C₂×C₄	C₄×Q₈×C₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄×Q₈×C₁₀₁	2
C₂×#391×C₁₀₁	2
C₂×#389×C₁₀₁	2
C₂×#384×C₁₀₁	2
C₁₀₁×#1444	2
C₁₀₁×#1436	2
C₁₀₁×C₄⋊#95	2
C₄×#95×C₁₀₁	2
#13976	101

Subgroups — C101×#13976 #38796127

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#13976 #38796127