Subgroups — C₂×C₁₀₁×#1286 #38790106

Order 25856.

702 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#431×C₁₀₁	C₂	1	1	yes	maximal, characteristic
2	C₂×#423×C₁₀₁	C₂	1	1	yes	maximal, characteristic
3	C₂×#382×C₁₀₁	C₂	1	1	yes	maximal, characteristic
4	C₁₀₁×#1286	C₂	1	4	yes	maximal, direct product factor
5	C₂²×M₁₆×C₁₀₁	—	2	1	no	—
6	C₂²×C₄⋊C₄×C₁₀₁	—	2	1	no	—
7	C₂²×C₄²×C₁₀₁	C₂²	1	1	yes	characteristic
8	#431×C₁₀₁	—	2	1	no	—
9	#431×C₁₀₁	—	2	1	no	—
10	#431×C₁₀₁	C₄	1	2	yes	complemented
11	#431×C₁₀₁	C₂²	1	2	yes	—
12	#423×C₁₀₁	—	2	1	no	—
13	#423×C₁₀₁	—	2	1	no	—
14	#423×C₁₀₁	C₄	1	2	yes	complemented
15	#423×C₁₀₁	C₂²	1	2	yes	—
16	C₂×C₄⋊C₈×C₁₀₁	—	2	1	no	—
17	C₂×C₄⋊C₈×C₁₀₁	—	2	1	no	—
18	C₂×C₄⋊C₈×C₁₀₁	C₄	1	2	yes	complemented
19	C₂×C₂²⋊C₈×C₁₀₁	—	2	1	no	—
20	C₂×C₄×C₈×C₁₀₁	C₄	1	2	yes	complemented
21	#382×C₁₀₁	—	2	1	no	—
22	#382×C₁₀₁	—	2	1	no	—
23	#382×C₁₀₁	C₄	1	2	yes	—
24	#382×C₁₀₁	C₂²	1	2	yes	—
25	C₂×#95×C₁₀₁	—	2	1	no	—
26	C₂×#95×C₁₀₁	C₄	1	2	yes	—
27	C₂³×C₄×C₁₀₁	—	2	2	no	—
28	C₂³×C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
29	C₂³×C₄×C₁₀₁	D₄	1	1	yes	characteristic
30	C₂³×C₄×C₁₀₁	D₄	1	1	yes	characteristic
31	C₂×M₁₆×C₁₀₁	—	2	2	no	—
32	C₂×M₁₆×C₁₀₁	—	2	2	no	—
33	C₂×M₁₆×C₁₀₁	—	4	2	no	—
34	C₂×M₁₆×C₁₀₁	—	4	2	no	—
35	C₂²×C₈×C₁₀₁	—	2	2	no	—
36	C₂²×C₈×C₁₀₁	—	2	2	no	—
37	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
38	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
39	C₂×C₄⋊C₄×C₁₀₁	—	4	2	no	—
40	C₂×C₄⋊C₄×C₁₀₁	—	4	2	no	—
41	C₂×C₄²×C₁₀₁	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄²×C₁₀₁	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄²×C₁₀₁	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄²×C₁₀₁	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄²×C₁₀₁	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄²×C₁₀₁	D₄	1	1	yes	characteristic
47	C₂×C₄²×C₁₀₁	D₄	1	1	yes	characteristic
48	C₂×C₄²×C₁₀₁	D₄	1	1	yes	characteristic
49	C₂×C₄²×C₁₀₁	D₄	1	1	yes	characteristic
50	C₂×C₄²×C₁₀₁	Q₈	1	1	yes	characteristic
51	C₂×C₄²×C₁₀₁	Q₈	1	1	yes	characteristic
52	C₂×C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
53	C₄⋊C₈×C₁₀₁	—	2	2	no	—
54	C₄⋊C₈×C₁₀₁	—	2	2	no	—
55	C₄⋊C₈×C₁₀₁	—	2	2	no	—
56	C₄⋊C₈×C₁₀₁	—	2	2	no	—
57	C₄⋊C₈×C₁₀₁	—	2	2	no	—
58	C₄⋊C₈×C₁₀₁	C₂×C₄	1	4	yes	complemented
59	C₂²⋊C₈×C₁₀₁	—	2	2	no	—
60	C₂²⋊C₈×C₁₀₁	—	2	2	no	—
61	C₄×C₈×C₁₀₁	—	2	2	no	—
62	C₄×C₈×C₁₀₁	C₂×C₄	1	4	yes	complemented
63	#95×C₁₀₁	—	2	2	no	—
64	#95×C₁₀₁	—	2	2	no	—
65	#95×C₁₀₁	—	2	2	no	—
66	#95×C₁₀₁	C₂×C₄	1	4	yes	—
67	C₂⁴×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
68	C₂²×C₄×C₁₀₁	—	2	4	no	—
69	C₂²×C₄×C₁₀₁	—	4	2	no	—
70	C₂²×C₄×C₁₀₁	—	4	2	no	—
71	C₂²×C₄×C₁₀₁	—	4	4	no	—
72	C₂²×C₄×C₁₀₁	—	4	4	no	—
73	C₂²×C₄×C₁₀₁	—	4	4	no	—
74	C₂²×C₄×C₁₀₁	C₄²	1	1	yes	characteristic
75	C₂²×C₄×C₁₀₁	C₄²	1	1	yes	characteristic
76	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
77	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₀₁	C₄⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₀₁	C₄⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₀₁	C₄⋊C₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₀₁	C₄⋊C₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₀₁	C₄⋊C₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₀₁	C₄⋊C₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₀₁	D₈	1	2	yes	—
90	C₂²×C₄×C₁₀₁	SD₁₆	1	2	yes	—
91	C₂²×C₄×C₁₀₁	SD₁₆	1	2	yes	—
92	C₂²×C₄×C₁₀₁	Q₁₆	1	2	yes	—
93	C₂²×C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
96	M₁₆×C₁₀₁	—	4	4	no	—
97	M₁₆×C₁₀₁	—	4	2	no	—
98	M₁₆×C₁₀₁	—	4	2	no	—
99	C₂×C₈×C₁₀₁	—	2	4	no	—
100	C₂×C₈×C₁₀₁	—	2	4	no	—
101	C₂×C₈×C₁₀₁	—	4	4	no	—
102	C₂×C₈×C₁₀₁	—	4	4	no	—
103	C₄⋊C₄×C₁₀₁	—	4	4	no	—
104	C₄⋊C₄×C₁₀₁	—	4	2	no	—
105	C₄⋊C₄×C₁₀₁	—	4	2	no	—
106	C₄²×C₁₀₁	C₄²	1	1	yes	characteristic
107	C₄²×C₁₀₁	C₄²	1	1	yes	characteristic
108	C₄²×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
109	C₄²×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
110	C₄²×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
111	C₄²×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
112	C₄²×C₁₀₁	C₄⋊C₄	1	1	yes	characteristic
113	C₄²×C₁₀₁	C₄⋊C₄	1	1	yes	characteristic
114	C₄²×C₁₀₁	C₄⋊C₄	1	1	yes	characteristic
115	C₄²×C₁₀₁	C₄⋊C₄	1	1	yes	characteristic
116	C₄²×C₁₀₁	C₄⋊C₄	1	1	yes	characteristic
117	C₄²×C₁₀₁	C₄⋊C₄	1	1	yes	characteristic
118	C₄²×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
119	C₄²×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
120	C₄²×C₁₀₁	C₂×D₄	1	1	yes	characteristic
121	C₄²×C₁₀₁	C₂×Q₈	1	1	yes	characteristic
122	C₂³×C₁₀₁	—	2	2	no	—
123	C₂³×C₁₀₁	—	2	2	no	—
124	C₂³×C₁₀₁	#95	1	1	yes	characteristic
125	C₂³×C₁₀₁	#95	1	1	yes	characteristic
126	C₂³×C₁₀₁	#102	1	2	yes	—
127	C₂³×C₁₀₁	#103	1	2	yes	—
128	C₂³×C₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
129	C₂×C₄×C₁₀₁	—	2	2	no	—
130	C₂×C₄×C₁₀₁	—	2	2	no	—
131	C₂×C₄×C₁₀₁	—	2	2	no	—
132	C₂×C₄×C₁₀₁	—	2	2	no	—
133	C₂×C₄×C₁₀₁	—	4	1	no	—
134	C₂×C₄×C₁₀₁	—	4	1	no	—
135	C₂×C₄×C₁₀₁	—	4	1	no	—
136	C₂×C₄×C₁₀₁	—	4	1	no	—
137	C₂×C₄×C₁₀₁	—	4	1	no	—
138	C₂×C₄×C₁₀₁	—	4	1	no	—
139	C₂×C₄×C₁₀₁	—	4	1	no	—
140	C₂×C₄×C₁₀₁	—	4	1	no	—
141	C₂×C₄×C₁₀₁	—	4	4	no	—
142	C₂×C₄×C₁₀₁	—	4	4	no	—
143	C₂×C₄×C₁₀₁	—	4	4	no	—
144	C₂×C₄×C₁₀₁	—	8	8	no	—
145	C₂×C₄×C₁₀₁	#95	1	1	yes	characteristic
146	C₂×C₄×C₁₀₁	#95	1	1	yes	characteristic
147	C₂×C₄×C₁₀₁	#95	1	1	yes	characteristic
148	C₂×C₄×C₁₀₁	#95	1	1	yes	characteristic
149	C₂×C₄×C₁₀₁	#95	1	1	yes	characteristic
150	C₂×C₄×C₁₀₁	#95	1	1	yes	characteristic
151	C₂×C₄×C₁₀₁	#102	1	2	yes	—
152	C₂×C₄×C₁₀₁	#102	1	2	yes	—
153	C₂×C₄×C₁₀₁	#102	1	2	yes	—
154	C₂×C₄×C₁₀₁	#103	1	2	yes	—
155	C₂×C₄×C₁₀₁	#103	1	2	yes	—
156	C₂×C₄×C₁₀₁	#103	1	2	yes	—
157	C₂×C₄×C₁₀₁	#106	1	2	yes	—
158	C₂×C₄×C₁₀₁	#106	1	2	yes	—
159	C₂×C₄×C₁₀₁	#107	1	2	yes	—
160	C₂×C₄×C₁₀₁	#107	1	2	yes	—
161	C₂×C₄×C₁₀₁	C₂×C₄²	1	1	yes	characteristic
162	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
163	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
164	C₂×C₄×C₁₀₁	C₂×C₄⋊C₄	1	1	yes	characteristic
165	C₂×C₄×C₁₀₁	C₂×C₄⋊C₄	1	1	yes	characteristic
166	C₂×C₄×C₁₀₁	C₂×C₄⋊C₄	1	1	yes	characteristic
167	C₂×C₄×C₁₀₁	C₂×D₈	1	1	yes	characteristic
168	C₂×C₄×C₁₀₁	C₂×SD₁₆	1	1	yes	characteristic
169	C₂×C₄×C₁₀₁	C₂×SD₁₆	1	1	yes	characteristic
170	C₂×C₄×C₁₀₁	C₂×Q₁₆	1	1	yes	characteristic
171	C₈×C₁₀₁	—	4	4	no	—
172	C₈×C₁₀₁	—	4	4	no	—
173	C₂²×C₁₀₁	—	2	4	no	—
174	C₂²×C₁₀₁	—	2	4	no	—
175	C₂²×C₁₀₁	—	2	1	no	—
176	C₂²×C₁₀₁	—	2	1	no	—
177	C₂²×C₁₀₁	—	2	1	no	—
178	C₂²×C₁₀₁	—	2	1	no	—
179	C₂²×C₁₀₁	H(3,ℤ/4)	1	2	yes	—
180	C₂²×C₁₀₁	#340	1	2	yes	—
181	C₂²×C₁₀₁	#340	1	2	yes	—
182	C₂²×C₁₀₁	#344	1	2	yes	—
183	C₂²×C₁₀₁	C₂×#95	1	1	yes	characteristic
184	C₂²×C₁₀₁	C₂×#102	1	1	yes	characteristic
185	C₂²×C₁₀₁	C₂×#103	1	1	yes	characteristic
186	C₄×C₁₀₁	—	2	1	no	—
187	C₄×C₁₀₁	—	2	1	no	—
188	C₄×C₁₀₁	—	2	1	no	—
189	C₄×C₁₀₁	—	2	1	no	—
190	C₄×C₁₀₁	—	2	1	no	—
191	C₄×C₁₀₁	—	2	1	no	—
192	C₄×C₁₀₁	—	2	1	no	—
193	C₄×C₁₀₁	—	2	1	no	—
194	C₄×C₁₀₁	—	8	4	no	—
195	C₄×C₁₀₁	#340	1	2	yes	—
196	C₄×C₁₀₁	#340	1	2	yes	—
197	C₄×C₁₀₁	C₂×#102	1	1	yes	characteristic
198	C₄×C₁₀₁	C₂×#103	1	1	yes	characteristic
199	C₄×C₁₀₁	C₂×#106	1	1	yes	characteristic
200	C₄×C₁₀₁	C₂×#107	1	1	yes	characteristic
201	C₂×#1286	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
202	C₂×C₁₀₁	—	2	1	no	—
203	C₂×C₁₀₁	—	2	2	no	—
204	C₂×C₁₀₁	—	2	1	no	—
205	C₂×C₁₀₁	#1286	1	4	yes	direct product factor
206	C₂×C₁₀₁	C₂×H(3,ℤ/4)	1	1	yes	characteristic
207	C₂×C₁₀₁	C₂×#340	1	1	yes	characteristic
208	C₂×C₁₀₁	C₂×#344	1	1	yes	characteristic
209	C₂×#431	C₂×C₁₀₁	1	1	yes	characteristic
210	C₂×#423	C₂×C₁₀₁	1	1	yes	characteristic
211	C₂×#382	C₂×C₁₀₁	1	1	yes	characteristic
212	#1286	C₂×C₁₀₁	1	4	yes	direct product factor
213	C₁₀₁	C₂×#1286	1	1	yes	characteristic, direct product factor, Sylow
214	C₂²×M₁₆	—	2	1	no	—
215	C₂²×C₄⋊C₄	—	2	1	no	—
216	C₂²×C₄²	C₂²×C₁₀₁	1	1	yes	characteristic
217	#431	—	2	1	no	—
218	#431	—	2	1	no	—
219	#431	C₄×C₁₀₁	1	2	yes	complemented
220	#431	C₂²×C₁₀₁	1	2	yes	—
221	#423	—	2	1	no	—
222	#423	—	2	1	no	—
223	#423	C₄×C₁₀₁	1	2	yes	complemented
224	#423	C₂²×C₁₀₁	1	2	yes	—
225	C₂×C₄⋊C₈	—	2	1	no	—
226	C₂×C₄⋊C₈	—	2	1	no	—
227	C₂×C₄⋊C₈	C₄×C₁₀₁	1	2	yes	complemented
228	C₂×C₂²⋊C₈	—	2	1	no	—
229	C₂×C₄×C₈	C₄×C₁₀₁	1	2	yes	complemented
230	#382	—	2	1	no	—
231	#382	—	2	1	no	—
232	#382	C₄×C₁₀₁	1	2	yes	—
233	#382	C₂²×C₁₀₁	1	2	yes	—
234	C₂×#95	—	2	1	no	—
235	C₂×#95	C₄×C₁₀₁	1	2	yes	—
236	C₂³×C₄	—	2	2	no	—
237	C₂³×C₄	C₂×C₄×C₁₀₁	1	1	yes	characteristic
238	C₂³×C₄	D₄×C₁₀₁	1	1	yes	characteristic
239	C₂³×C₄	D₄×C₁₀₁	1	1	yes	characteristic
240	C₂×M₁₆	—	2	2	no	—
241	C₂×M₁₆	—	2	2	no	—
242	C₂×M₁₆	—	4	2	no	—
243	C₂×M₁₆	—	4	2	no	—
244	C₂²×C₈	—	2	2	no	—
245	C₂²×C₈	—	2	2	no	—
246	C₂×C₄⋊C₄	—	2	2	no	—
247	C₂×C₄⋊C₄	—	2	2	no	—
248	C₂×C₄⋊C₄	—	4	2	no	—
249	C₂×C₄⋊C₄	—	4	2	no	—
250	C₂×C₄²	C₂×C₄×C₁₀₁	1	1	yes	characteristic
251	C₂×C₄²	C₂×C₄×C₁₀₁	1	1	yes	characteristic
252	C₂×C₄²	C₂×C₄×C₁₀₁	1	1	yes	characteristic
253	C₂×C₄²	C₂×C₄×C₁₀₁	1	1	yes	characteristic
254	C₂×C₄²	C₂×C₄×C₁₀₁	1	1	yes	characteristic
255	C₂×C₄²	D₄×C₁₀₁	1	1	yes	characteristic
256	C₂×C₄²	D₄×C₁₀₁	1	1	yes	characteristic
257	C₂×C₄²	D₄×C₁₀₁	1	1	yes	characteristic
258	C₂×C₄²	D₄×C₁₀₁	1	1	yes	characteristic
259	C₂×C₄²	Q₈×C₁₀₁	1	1	yes	characteristic
260	C₂×C₄²	Q₈×C₁₀₁	1	1	yes	characteristic
261	C₂×C₄²	C₂³×C₁₀₁	1	1	yes	characteristic
262	C₄⋊C₈	—	2	2	no	—
263	C₄⋊C₈	—	2	2	no	—
264	C₄⋊C₈	—	2	2	no	—
265	C₄⋊C₈	—	2	2	no	—
266	C₄⋊C₈	—	2	2	no	—
267	C₄⋊C₈	C₂×C₄×C₁₀₁	1	4	yes	complemented
268	C₂²⋊C₈	—	2	2	no	—
269	C₂²⋊C₈	—	2	2	no	—
270	C₄×C₈	—	2	2	no	—
271	C₄×C₈	C₂×C₄×C₁₀₁	1	4	yes	complemented
272	#95	—	2	2	no	—
273	#95	—	2	2	no	—
274	#95	—	2	2	no	—
275	#95	C₂×C₄×C₁₀₁	1	4	yes	—
276	C₂⁴	C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
277	C₂²×C₄	—	2	4	no	—
278	C₂²×C₄	—	4	2	no	—
279	C₂²×C₄	—	4	2	no	—
280	C₂²×C₄	—	4	4	no	—
281	C₂²×C₄	—	4	4	no	—
282	C₂²×C₄	—	4	4	no	—
283	C₂²×C₄	C₄²×C₁₀₁	1	1	yes	characteristic
284	C₂²×C₄	C₄²×C₁₀₁	1	1	yes	characteristic
285	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
286	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
287	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
288	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
289	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
290	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
291	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
292	C₂²×C₄	C₄⋊C₄×C₁₀₁	1	1	yes	characteristic
293	C₂²×C₄	C₄⋊C₄×C₁₀₁	1	1	yes	characteristic
294	C₂²×C₄	C₄⋊C₄×C₁₀₁	1	1	yes	characteristic
295	C₂²×C₄	C₄⋊C₄×C₁₀₁	1	1	yes	characteristic
296	C₂²×C₄	C₄⋊C₄×C₁₀₁	1	1	yes	characteristic
297	C₂²×C₄	C₄⋊C₄×C₁₀₁	1	1	yes	characteristic
298	C₂²×C₄	D₈×C₁₀₁	1	2	yes	—
299	C₂²×C₄	SD₁₆×C₁₀₁	1	2	yes	—
300	C₂²×C₄	SD₁₆×C₁₀₁	1	2	yes	—
301	C₂²×C₄	Q₁₆×C₁₀₁	1	2	yes	—
302	C₂²×C₄	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
303	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
304	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
305	M₁₆	—	4	4	no	—
306	M₁₆	—	4	2	no	—
307	M₁₆	—	4	2	no	—
308	C₂×C₈	—	2	4	no	—
309	C₂×C₈	—	2	4	no	—
310	C₂×C₈	—	4	4	no	—
311	C₂×C₈	—	4	4	no	—
312	C₄⋊C₄	—	4	4	no	—
313	C₄⋊C₄	—	4	2	no	—
314	C₄⋊C₄	—	4	2	no	—
315	C₄²	C₄²×C₁₀₁	1	1	yes	characteristic
316	C₄²	C₄²×C₁₀₁	1	1	yes	characteristic
317	C₄²	C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
318	C₄²	C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
319	C₄²	C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
320	C₄²	C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
321	C₄²	C₄⋊C₄×C₁₀₁	1	1	yes	characteristic
322	C₄²	C₄⋊C₄×C₁₀₁	1	1	yes	characteristic
323	C₄²	C₄⋊C₄×C₁₀₁	1	1	yes	characteristic
324	C₄²	C₄⋊C₄×C₁₀₁	1	1	yes	characteristic
325	C₄²	C₄⋊C₄×C₁₀₁	1	1	yes	characteristic
326	C₄²	C₄⋊C₄×C₁₀₁	1	1	yes	characteristic
327	C₄²	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
328	C₄²	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
329	C₄²	C₂×D₄×C₁₀₁	1	1	yes	characteristic
330	C₄²	C₂×Q₈×C₁₀₁	1	1	yes	characteristic
331	C₂³	—	2	2	no	—
332	C₂³	—	2	2	no	—
333	C₂³	#95×C₁₀₁	1	1	yes	characteristic
334	C₂³	#95×C₁₀₁	1	1	yes	characteristic
335	C₂³	#102×C₁₀₁	1	2	yes	—
336	C₂³	#103×C₁₀₁	1	2	yes	—
337	C₂³	C₂×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	4	1	no	—
343	C₂×C₄	—	4	1	no	—
344	C₂×C₄	—	4	1	no	—
345	C₂×C₄	—	4	1	no	—
346	C₂×C₄	—	4	1	no	—
347	C₂×C₄	—	4	1	no	—
348	C₂×C₄	—	4	1	no	—
349	C₂×C₄	—	4	1	no	—
350	C₂×C₄	—	4	4	no	—
351	C₂×C₄	—	4	4	no	—
352	C₂×C₄	—	4	4	no	—
353	C₂×C₄	—	8	8	no	—
354	C₂×C₄	#95×C₁₀₁	1	1	yes	characteristic
355	C₂×C₄	#95×C₁₀₁	1	1	yes	characteristic
356	C₂×C₄	#95×C₁₀₁	1	1	yes	characteristic
357	C₂×C₄	#95×C₁₀₁	1	1	yes	characteristic
358	C₂×C₄	#95×C₁₀₁	1	1	yes	characteristic
359	C₂×C₄	#95×C₁₀₁	1	1	yes	characteristic
360	C₂×C₄	#102×C₁₀₁	1	2	yes	—
361	C₂×C₄	#102×C₁₀₁	1	2	yes	—
362	C₂×C₄	#102×C₁₀₁	1	2	yes	—
363	C₂×C₄	#103×C₁₀₁	1	2	yes	—
364	C₂×C₄	#103×C₁₀₁	1	2	yes	—
365	C₂×C₄	#103×C₁₀₁	1	2	yes	—
366	C₂×C₄	#106×C₁₀₁	1	2	yes	—
367	C₂×C₄	#106×C₁₀₁	1	2	yes	—
368	C₂×C₄	#107×C₁₀₁	1	2	yes	—
369	C₂×C₄	#107×C₁₀₁	1	2	yes	—
370	C₂×C₄	C₂×C₄²×C₁₀₁	1	1	yes	characteristic
371	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
372	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
373	C₂×C₄	C₂×C₄⋊C₄×C₁₀₁	1	1	yes	characteristic
374	C₂×C₄	C₂×C₄⋊C₄×C₁₀₁	1	1	yes	characteristic
375	C₂×C₄	C₂×C₄⋊C₄×C₁₀₁	1	1	yes	characteristic
376	C₂×C₄	C₂×D₈×C₁₀₁	1	1	yes	characteristic
377	C₂×C₄	C₂×SD₁₆×C₁₀₁	1	1	yes	characteristic
378	C₂×C₄	C₂×SD₁₆×C₁₀₁	1	1	yes	characteristic
379	C₂×C₄	C₂×Q₁₆×C₁₀₁	1	1	yes	characteristic
380	C₈	—	4	4	no	—
381	C₈	—	4	4	no	—
382	C₂²	—	2	1	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	2	1	no	—
385	C₂²	—	2	1	no	—
386	C₂²	—	2	4	no	—
387	C₂²	—	2	4	no	—
388	C₂²	H(3,ℤ/4)×C₁₀₁	1	2	yes	—
389	C₂²	#340×C₁₀₁	1	2	yes	—
390	C₂²	#340×C₁₀₁	1	2	yes	—
391	C₂²	#344×C₁₀₁	1	2	yes	—
392	C₂²	C₂×#95×C₁₀₁	1	1	yes	characteristic
393	C₂²	C₂×#102×C₁₀₁	1	1	yes	characteristic
394	C₂²	C₂×#103×C₁₀₁	1	1	yes	characteristic
395	C₄	—	2	1	no	—
396	C₄	—	2	1	no	—
397	C₄	—	2	1	no	—
398	C₄	—	2	1	no	—
399	C₄	—	2	1	no	—
400	C₄	—	2	1	no	—
401	C₄	—	2	1	no	—
402	C₄	—	2	1	no	—
403	C₄	—	8	4	no	—
404	C₄	#340×C₁₀₁	1	2	yes	—
405	C₄	#340×C₁₀₁	1	2	yes	—
406	C₄	C₂×#102×C₁₀₁	1	1	yes	characteristic
407	C₄	C₂×#103×C₁₀₁	1	1	yes	characteristic
408	C₄	C₂×#106×C₁₀₁	1	1	yes	characteristic
409	C₄	C₂×#107×C₁₀₁	1	1	yes	characteristic
410	C₂	—	2	1	no	—
411	C₂	—	2	1	no	—
412	C₂	—	2	2	no	—
413	C₂	C₁₀₁×#1286	1	4	yes	direct product factor
414	C₂	C₂×H(3,ℤ/4)×C₁₀₁	1	1	yes	characteristic
415	C₂	C₂×#340×C₁₀₁	1	1	yes	characteristic
416	C₂	C₂×#344×C₁₀₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₀₁	#95
commutator	C₂×C₄	C₂×C₄²×C₁₀₁
Frattini, cosocle	C₂×C₄²	C₂³×C₁₀₁
prime radical	C₂⁴×C₁₀₁	C₂²⋊C₄
LCS	G ▷ C₂×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
4. C₁₀₁×#1286	C₂	direct (N × H)
10. #431×C₁₀₁	C₄	semidirect
14. #423×C₁₀₁	C₄	semidirect
18. C₂×C₄⋊C₈×C₁₀₁	C₄	semidirect
20. C₂×C₄×C₈×C₁₀₁	C₄	semidirect
58. C₄⋊C₈×C₁₀₁	C₂×C₄	semidirect
62. C₄×C₈×C₁₀₁	C₂×C₄	semidirect
201. C₂×#1286	C₁₀₁	direct (N × H)
205. C₂×C₁₀₁	#1286	direct (N × H)
212. #1286	C₂×C₁₀₁	direct (N × H)
213. C₁₀₁	C₂×#1286	direct (N × H)
219. #431	C₄×C₁₀₁	semidirect
223. #423	C₄×C₁₀₁	semidirect
227. C₂×C₄⋊C₈	C₄×C₁₀₁	semidirect
229. C₂×C₄×C₈	C₄×C₁₀₁	semidirect
267. C₄⋊C₈	C₂×C₄×C₁₀₁	semidirect
271. C₄×C₈	C₂×C₄×C₁₀₁	semidirect
413. C₂	C₁₀₁×#1286	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#431×C₁₀₁	2
C₂×#423×C₁₀₁	2
C₂×#382×C₁₀₁	2
C₁₀₁×#1286	2
C₂×#1286	101

Subgroups — C2×C101×#1286 #38790106

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₀₁×#1286 #38790106