Subgroups — C₁₀₁×#20985 #38803136

Order 25856.

2030 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#535×C₁₀₁	C₂	1	1	yes	maximal, characteristic
2	C₂×#518×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#410×C₁₀₁	C₂	1	2	yes	maximal, complemented
4	C₁₀₁×#2309	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₀₁×#1898	C₂	1	8	yes	maximal, complemented
6	C₁₀₁×#1740	C₂	1	2	yes	maximal, complemented
7	C₂²×#41×C₁₀₁	C₂²	1	1	yes	characteristic
8	C₂³×D₄×C₁₀₁	C₂²	1	1	yes	characteristic
9	#535×C₁₀₁	—	2	4	no	—
10	#535×C₁₀₁	—	2	4	no	—
11	C₂×#127×C₁₀₁	C₄	1	2	yes	complemented
12	C₂×#124×C₁₀₁	C₄	1	2	yes	complemented
13	C₂×#121×C₁₀₁	C₄	1	4	yes	complemented
14	C₂×#120×C₁₀₁	C₂²	1	4	yes	—
15	#518×C₁₀₁	—	2	8	no	—
16	C₂×C₄×D₄×C₁₀₁	—	2	4	no	—
17	C₂×#117×C₁₀₁	C₂²	1	2	yes	—
18	C₂×#117×C₁₀₁	C₂²	1	2	yes	—
19	C₂×#117×C₁₀₁	C₂²	1	1	yes	characteristic
20	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	4	yes	—
21	#410×C₁₀₁	—	2	8	no	—
22	C₂×#99×C₁₀₁	C₂²	1	8	yes	—
23	#390×C₁₀₁	—	2	4	no	—
24	#379×C₁₀₁	C₂²	1	4	yes	—
25	#342×C₁₀₁	C₂²	1	8	yes	—
26	C₂⁵×C₁₀₁	C₂³	1	2	yes	—
27	C₂×#41×C₁₀₁	—	2	4	no	—
28	C₂×#41×C₁₀₁	—	2	2	no	—
29	C₂×#41×C₁₀₁	—	2	2	no	—
30	C₂×#41×C₁₀₁	—	2	4	no	—
31	C₂²×Q₈×C₁₀₁	C₂×C₄	1	1	yes	characteristic, complemented
32	C₂²×D₄×C₁₀₁	—	2	4	no	—
33	C₂²×D₄×C₁₀₁	—	2	4	no	—
34	C₂²×D₄×C₁₀₁	C₂×C₄	1	2	yes	—
35	C₂²×D₄×C₁₀₁	C₂×C₄	1	2	yes	—
36	C₂²×D₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic, complemented
37	C₂²×D₄×C₁₀₁	C₂×C₄	1	8	yes	complemented
38	C₂²×D₄×C₁₀₁	D₄	1	4	yes	—
39	C₂²×D₄×C₁₀₁	D₄	1	4	yes	—
40	C₂²×D₄×C₁₀₁	C₂³	1	2	yes	—
41	C₂³×C₄×C₁₀₁	—	2	4	no	—
42	C₂³×C₄×C₁₀₁	C₂×C₄	1	2	yes	complemented
43	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
44	#127×C₁₀₁	—	2	8	no	—
45	#124×C₁₀₁	—	2	8	no	—
46	#121×C₁₀₁	—	2	16	no	—
47	#120×C₁₀₁	—	2	8	no	—
48	#120×C₁₀₁	—	2	8	no	—
49	C₄×D₄×C₁₀₁	—	2	32	no	—
50	#117×C₁₀₁	—	2	4	no	—
51	#117×C₁₀₁	—	2	2	no	—
52	#117×C₁₀₁	—	2	2	no	—
53	#117×C₁₀₁	—	2	4	no	—
54	#117×C₁₀₁	—	2	4	no	—
55	#117×C₁₀₁	D₄	1	8	yes	complemented
56	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
57	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
58	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	2	yes	complemented
59	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
60	C₂×C₂²⋊C₄×C₁₀₁	—	2	16	no	—
61	C₂×C₂²⋊C₄×C₁₀₁	—	2	8	no	—
62	C₂×C₂²⋊C₄×C₁₀₁	C₂×C₄	1	8	yes	complemented
63	C₂×C₂²⋊C₄×C₁₀₁	C₂³	1	4	yes	—
64	C₂×C₂²⋊C₄×C₁₀₁	C₂³	1	2	yes	—
65	C₂×C₂²⋊C₄×C₁₀₁	C₂³	1	4	yes	—
66	C₂×C₄²×C₁₀₁	—	2	2	no	—
67	C₂×C₄²×C₁₀₁	—	2	2	no	—
68	C₂×C₄²×C₁₀₁	C₂×C₄	1	2	yes	complemented
69	#99×C₁₀₁	—	2	16	no	—
70	C₂⁴×C₁₀₁	—	2	4	no	—
71	C₂⁴×C₁₀₁	—	2	4	no	—
72	C₂⁴×C₁₀₁	—	8	4	no	—
73	C₂⁴×C₁₀₁	C₂²×C₄	1	2	yes	—
74	C₂⁴×C₁₀₁	C₂²×C₄	1	4	yes	—
75	C₂⁴×C₁₀₁	C₂×D₄	1	4	yes	—
76	C₂⁴×C₁₀₁	C₂×D₄	1	4	yes	—
77	C₂⁴×C₁₀₁	C₂⁴	1	1	yes	characteristic
78	#41×C₁₀₁	—	4	4	no	—
79	#41×C₁₀₁	—	4	4	no	—
80	#41×C₁₀₁	—	4	4	no	—
81	#41×C₁₀₁	—	4	4	no	—
82	C₂×Q₈×C₁₀₁	—	2	2	no	—
83	C₂×Q₈×C₁₀₁	—	2	4	no	—
84	C₂×D₄×C₁₀₁	—	2	4	no	—
85	C₂×D₄×C₁₀₁	—	2	2	no	—
86	C₂×D₄×C₁₀₁	—	2	2	no	—
87	C₂×D₄×C₁₀₁	—	2	4	no	—
88	C₂×D₄×C₁₀₁	—	2	16	no	—
89	C₂×D₄×C₁₀₁	—	2	2	no	—
90	C₂×D₄×C₁₀₁	—	2	8	no	—
91	C₂×D₄×C₁₀₁	—	2	8	no	—
92	C₂×D₄×C₁₀₁	—	2	4	no	—
93	C₂×D₄×C₁₀₁	—	2	8	no	—
94	C₂×D₄×C₁₀₁	—	2	8	no	—
95	C₂×D₄×C₁₀₁	—	2	8	no	—
96	C₂×D₄×C₁₀₁	—	2	8	no	—
97	C₂×D₄×C₁₀₁	—	8	8	no	—
98	C₂×D₄×C₁₀₁	C₂²⋊C₄	1	8	yes	—
99	C₂×D₄×C₁₀₁	C₂²⋊C₄	1	8	yes	—
100	C₂²×C₄×C₁₀₁	—	2	4	no	—
101	C₂²×C₄×C₁₀₁	—	2	16	no	—
102	C₂²×C₄×C₁₀₁	—	2	4	no	—
103	C₂²×C₄×C₁₀₁	—	2	8	no	—
104	C₂²×C₄×C₁₀₁	—	2	4	no	—
105	C₂²×C₄×C₁₀₁	—	8	8	no	—
106	C₂²×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
107	C₂²×C₄×C₁₀₁	C₂²×C₄	1	4	yes	—
108	C₂²×C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₁₀₁	C₂×D₄	1	4	yes	—
113	C₂²×C₄×C₁₀₁	#41	1	4	yes	—
114	C₄⋊C₄×C₁₀₁	—	2	4	no	—
115	C₄⋊C₄×C₁₀₁	—	2	8	no	—
116	C₄⋊C₄×C₁₀₁	—	4	4	no	—
117	C₂²⋊C₄×C₁₀₁	—	2	16	no	—
118	C₂²⋊C₄×C₁₀₁	—	2	16	no	—
119	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
120	C₂²⋊C₄×C₁₀₁	—	2	2	no	—
121	C₂²⋊C₄×C₁₀₁	—	2	2	no	—
122	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
123	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
124	C₂²⋊C₄×C₁₀₁	—	8	8	no	—
125	C₂²⋊C₄×C₁₀₁	C₂×D₄	1	8	yes	—
126	C₄²×C₁₀₁	—	2	4	no	—
127	C₄²×C₁₀₁	—	2	8	no	—
128	C₄²×C₁₀₁	—	4	4	no	—
129	C₂³×C₁₀₁	—	2	4	no	—
130	C₂³×C₁₀₁	—	2	4	no	—
131	C₂³×C₁₀₁	—	2	8	no	—
132	C₂³×C₁₀₁	—	2	8	no	—
133	C₂³×C₁₀₁	—	2	2	no	—
134	C₂³×C₁₀₁	—	2	4	no	—
135	C₂³×C₁₀₁	—	4	8	no	—
136	C₂³×C₁₀₁	—	4	2	no	—
137	C₂³×C₁₀₁	—	4	8	no	—
138	C₂³×C₁₀₁	—	4	8	no	—
139	C₂³×C₁₀₁	—	4	4	no	—
140	C₂³×C₁₀₁	—	8	8	no	—
141	C₂³×C₁₀₁	—	8	8	no	—
142	C₂³×C₁₀₁	C₂×C₂²⋊C₄	1	8	yes	—
143	C₂³×C₁₀₁	C₂³×C₄	1	1	yes	characteristic
144	C₂³×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
145	C₂³×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
146	C₂³×C₁₀₁	C₂²×D₄	1	2	yes	—
147	C₂³×C₁₀₁	C₂×#41	1	2	yes	—
148	Q₈×C₁₀₁	—	4	4	no	—
149	D₄×C₁₀₁	—	2	16	no	—
150	D₄×C₁₀₁	—	2	16	no	—
151	D₄×C₁₀₁	—	4	2	no	—
152	D₄×C₁₀₁	—	4	4	no	—
153	D₄×C₁₀₁	—	4	2	no	—
154	D₄×C₁₀₁	—	4	4	no	—
155	D₄×C₁₀₁	—	8	16	no	—
156	C₂×C₄×C₁₀₁	—	2	4	no	—
157	C₂×C₄×C₁₀₁	—	2	2	no	—
158	C₂×C₄×C₁₀₁	—	2	4	no	—
159	C₂×C₄×C₁₀₁	—	2	8	no	—
160	C₂×C₄×C₁₀₁	—	4	8	no	—
161	C₂×C₄×C₁₀₁	—	4	8	no	—
162	C₂×C₄×C₁₀₁	—	4	4	no	—
163	C₂×C₄×C₁₀₁	—	4	8	no	—
164	C₂×C₄×C₁₀₁	—	4	4	no	—
165	C₂×C₄×C₁₀₁	—	8	16	no	—
166	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	2	yes	—
167	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	2	yes	—
168	C₂×C₄×C₁₀₁	C₄×D₄	1	4	yes	—
169	C₂×C₄×C₁₀₁	C₄×D₄	1	4	yes	—
170	C₂×C₄×C₁₀₁	#120	1	4	yes	—
171	C₂×C₄×C₁₀₁	#121	1	4	yes	—
172	C₂×C₄×C₁₀₁	#121	1	4	yes	—
173	C₂×C₄×C₁₀₁	#123	1	4	yes	—
174	C₂²×C₁₀₁	—	2	2	no	—
175	C₂²×C₁₀₁	—	2	2	no	—
176	C₂²×C₁₀₁	—	2	2	no	—
177	C₂²×C₁₀₁	—	2	16	no	—
178	C₂²×C₁₀₁	—	2	8	no	—
179	C₂²×C₁₀₁	—	4	2	no	—
180	C₂²×C₁₀₁	—	4	2	no	—
181	C₂²×C₁₀₁	—	4	8	no	—
182	C₂²×C₁₀₁	—	4	8	no	—
183	C₂²×C₁₀₁	—	4	4	no	—
184	C₂²×C₁₀₁	—	4	2	no	—
185	C₂²×C₁₀₁	—	8	8	no	—
186	C₂²×C₁₀₁	—	8	8	no	—
187	C₂²×C₁₀₁	—	8	4	no	—
188	C₂²×C₁₀₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
189	C₂²×C₁₀₁	C₂×C₄×D₄	1	2	yes	—
190	C₂²×C₁₀₁	C₂×#120	1	1	yes	characteristic
191	C₂²×C₁₀₁	C₂×#121	1	2	yes	—
192	C₂²×C₁₀₁	C₂×#123	1	1	yes	characteristic
193	C₄×C₁₀₁	—	4	8	no	—
194	C₄×C₁₀₁	—	4	4	no	—
195	C₄×C₁₀₁	—	4	2	no	—
196	C₄×C₁₀₁	—	8	4	no	—
197	C₄×C₁₀₁	#386	1	4	yes	—
198	C₄×C₁₀₁	#386	1	4	yes	—
199	#20985	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
200	C₂×C₁₀₁	—	2	1	no	—
201	C₂×C₁₀₁	—	2	2	no	—
202	C₂×C₁₀₁	—	2	1	no	—
203	C₂×C₁₀₁	—	2	2	no	—
204	C₂×C₁₀₁	—	4	8	no	—
205	C₂×C₁₀₁	—	8	2	no	—
206	C₂×C₁₀₁	C₂×#386	1	1	yes	characteristic
207	C₂×C₁₀₁	#2883	1	2	yes	—
208	C₂×#535	C₂×C₁₀₁	1	1	yes	characteristic
209	C₂×#518	C₂×C₁₀₁	1	1	yes	characteristic, complemented
210	C₂×#410	C₂×C₁₀₁	1	2	yes	complemented
211	#2309	C₂×C₁₀₁	1	1	yes	characteristic, complemented
212	#1898	C₂×C₁₀₁	1	8	yes	complemented
213	#1740	C₂×C₁₀₁	1	2	yes	complemented
214	C₁₀₁	#20985	1	1	yes	characteristic, direct product factor, Sylow
215	C₂²×#41	C₂²×C₁₀₁	1	1	yes	characteristic
216	C₂³×D₄	C₂²×C₁₀₁	1	1	yes	characteristic
217	#535	—	2	4	no	—
218	#535	—	2	4	no	—
219	C₂×#127	C₄×C₁₀₁	1	2	yes	complemented
220	C₂×#124	C₄×C₁₀₁	1	2	yes	complemented
221	C₂×#121	C₄×C₁₀₁	1	4	yes	complemented
222	C₂×#120	C₂²×C₁₀₁	1	4	yes	—
223	#518	—	2	8	no	—
224	C₂×C₄×D₄	—	2	4	no	—
225	C₂×#117	C₂²×C₁₀₁	1	2	yes	—
226	C₂×#117	C₂²×C₁₀₁	1	2	yes	—
227	C₂×#117	C₂²×C₁₀₁	1	1	yes	characteristic
228	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	4	yes	—
229	#410	—	2	8	no	—
230	C₂×#99	C₂²×C₁₀₁	1	8	yes	—
231	#390	—	2	4	no	—
232	#379	C₂²×C₁₀₁	1	4	yes	—
233	#342	C₂²×C₁₀₁	1	8	yes	—
234	C₂⁵	C₂³×C₁₀₁	1	2	yes	—
235	C₂×#41	—	2	2	no	—
236	C₂×#41	—	2	2	no	—
237	C₂×#41	—	2	4	no	—
238	C₂×#41	—	2	4	no	—
239	C₂²×Q₈	C₂×C₄×C₁₀₁	1	1	yes	characteristic, complemented
240	C₂²×D₄	—	2	4	no	—
241	C₂²×D₄	—	2	4	no	—
242	C₂²×D₄	C₂×C₄×C₁₀₁	1	2	yes	—
243	C₂²×D₄	C₂×C₄×C₁₀₁	1	2	yes	—
244	C₂²×D₄	C₂×C₄×C₁₀₁	1	1	yes	characteristic, complemented
245	C₂²×D₄	C₂×C₄×C₁₀₁	1	8	yes	complemented
246	C₂²×D₄	D₄×C₁₀₁	1	4	yes	—
247	C₂²×D₄	D₄×C₁₀₁	1	4	yes	—
248	C₂²×D₄	C₂³×C₁₀₁	1	2	yes	—
249	C₂³×C₄	—	2	4	no	—
250	C₂³×C₄	C₂×C₄×C₁₀₁	1	2	yes	complemented
251	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
252	#127	—	2	8	no	—
253	#124	—	2	8	no	—
254	#121	—	2	16	no	—
255	#120	—	2	8	no	—
256	#120	—	2	8	no	—
257	C₄×D₄	—	2	32	no	—
258	#117	—	2	4	no	—
259	#117	—	2	2	no	—
260	#117	—	2	2	no	—
261	#117	—	2	4	no	—
262	#117	—	2	4	no	—
263	#117	D₄×C₁₀₁	1	8	yes	complemented
264	C₂×C₄⋊C₄	—	2	2	no	—
265	C₂×C₄⋊C₄	—	2	2	no	—
266	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	2	yes	complemented
267	C₂×C₂²⋊C₄	—	2	4	no	—
268	C₂×C₂²⋊C₄	—	2	16	no	—
269	C₂×C₂²⋊C₄	—	2	8	no	—
270	C₂×C₂²⋊C₄	C₂×C₄×C₁₀₁	1	8	yes	complemented
271	C₂×C₂²⋊C₄	C₂³×C₁₀₁	1	4	yes	—
272	C₂×C₂²⋊C₄	C₂³×C₁₀₁	1	2	yes	—
273	C₂×C₂²⋊C₄	C₂³×C₁₀₁	1	4	yes	—
274	C₂×C₄²	—	2	2	no	—
275	C₂×C₄²	—	2	2	no	—
276	C₂×C₄²	C₂×C₄×C₁₀₁	1	2	yes	complemented
277	#99	—	2	16	no	—
278	C₂⁴	—	2	4	no	—
279	C₂⁴	—	2	4	no	—
280	C₂⁴	—	8	4	no	—
281	C₂⁴	C₂²×C₄×C₁₀₁	1	2	yes	—
282	C₂⁴	C₂²×C₄×C₁₀₁	1	4	yes	—
283	C₂⁴	C₂×D₄×C₁₀₁	1	4	yes	—
284	C₂⁴	C₂×D₄×C₁₀₁	1	4	yes	—
285	C₂⁴	C₂⁴×C₁₀₁	1	1	yes	characteristic
286	#41	—	4	4	no	—
287	#41	—	4	4	no	—
288	#41	—	4	4	no	—
289	#41	—	4	4	no	—
290	C₂×Q₈	—	2	2	no	—
291	C₂×Q₈	—	2	4	no	—
292	C₂×D₄	—	2	4	no	—
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	—	2	2	no	—
295	C₂×D₄	—	2	4	no	—
296	C₂×D₄	—	2	16	no	—
297	C₂×D₄	—	2	2	no	—
298	C₂×D₄	—	2	8	no	—
299	C₂×D₄	—	2	8	no	—
300	C₂×D₄	—	2	4	no	—
301	C₂×D₄	—	2	8	no	—
302	C₂×D₄	—	2	8	no	—
303	C₂×D₄	—	2	8	no	—
304	C₂×D₄	—	2	8	no	—
305	C₂×D₄	—	8	8	no	—
306	C₂×D₄	C₂²⋊C₄×C₁₀₁	1	8	yes	—
307	C₂×D₄	C₂²⋊C₄×C₁₀₁	1	8	yes	—
308	C₂²×C₄	—	2	4	no	—
309	C₂²×C₄	—	2	16	no	—
310	C₂²×C₄	—	2	4	no	—
311	C₂²×C₄	—	2	8	no	—
312	C₂²×C₄	—	2	4	no	—
313	C₂²×C₄	—	8	8	no	—
314	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
315	C₂²×C₄	C₂²×C₄×C₁₀₁	1	4	yes	—
316	C₂²×C₄	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
317	C₂²×C₄	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
318	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
319	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
320	C₂²×C₄	C₂×D₄×C₁₀₁	1	4	yes	—
321	C₂²×C₄	#41×C₁₀₁	1	4	yes	—
322	C₄⋊C₄	—	2	4	no	—
323	C₄⋊C₄	—	2	8	no	—
324	C₄⋊C₄	—	4	4	no	—
325	C₂²⋊C₄	—	2	16	no	—
326	C₂²⋊C₄	—	2	16	no	—
327	C₂²⋊C₄	—	2	4	no	—
328	C₂²⋊C₄	—	2	2	no	—
329	C₂²⋊C₄	—	2	2	no	—
330	C₂²⋊C₄	—	2	4	no	—
331	C₂²⋊C₄	—	2	4	no	—
332	C₂²⋊C₄	—	8	8	no	—
333	C₂²⋊C₄	C₂×D₄×C₁₀₁	1	8	yes	—
334	C₄²	—	2	4	no	—
335	C₄²	—	2	8	no	—
336	C₄²	—	4	4	no	—
337	C₂³	—	2	4	no	—
338	C₂³	—	2	4	no	—
339	C₂³	—	2	8	no	—
340	C₂³	—	2	8	no	—
341	C₂³	—	2	2	no	—
342	C₂³	—	2	4	no	—
343	C₂³	—	4	8	no	—
344	C₂³	—	4	2	no	—
345	C₂³	—	4	8	no	—
346	C₂³	—	4	8	no	—
347	C₂³	—	4	4	no	—
348	C₂³	—	8	8	no	—
349	C₂³	—	8	8	no	—
350	C₂³	C₂×C₂²⋊C₄×C₁₀₁	1	8	yes	—
351	C₂³	C₂³×C₄×C₁₀₁	1	1	yes	characteristic
352	C₂³	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
353	C₂³	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
354	C₂³	C₂²×D₄×C₁₀₁	1	2	yes	—
355	C₂³	C₂×#41×C₁₀₁	1	2	yes	—
356	Q₈	—	4	4	no	—
357	D₄	—	2	16	no	—
358	D₄	—	2	16	no	—
359	D₄	—	4	2	no	—
360	D₄	—	4	4	no	—
361	D₄	—	4	2	no	—
362	D₄	—	4	4	no	—
363	D₄	—	8	16	no	—
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	2	8	no	—
368	C₂×C₄	—	4	8	no	—
369	C₂×C₄	—	4	8	no	—
370	C₂×C₄	—	4	4	no	—
371	C₂×C₄	—	4	8	no	—
372	C₂×C₄	—	4	4	no	—
373	C₂×C₄	—	8	16	no	—
374	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	2	yes	—
375	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	2	yes	—
376	C₂×C₄	C₄×D₄×C₁₀₁	1	4	yes	—
377	C₂×C₄	C₄×D₄×C₁₀₁	1	4	yes	—
378	C₂×C₄	#120×C₁₀₁	1	4	yes	—
379	C₂×C₄	#121×C₁₀₁	1	4	yes	—
380	C₂×C₄	#121×C₁₀₁	1	4	yes	—
381	C₂×C₄	#123×C₁₀₁	1	4	yes	—
382	C₂²	—	2	2	no	—
383	C₂²	—	2	2	no	—
384	C₂²	—	2	2	no	—
385	C₂²	—	2	8	no	—
386	C₂²	—	2	16	no	—
387	C₂²	—	4	2	no	—
388	C₂²	—	4	2	no	—
389	C₂²	—	4	8	no	—
390	C₂²	—	4	8	no	—
391	C₂²	—	4	2	no	—
392	C₂²	—	4	4	no	—
393	C₂²	—	8	8	no	—
394	C₂²	—	8	8	no	—
395	C₂²	—	8	4	no	—
396	C₂²	C₂²×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
397	C₂²	C₂×C₄×D₄×C₁₀₁	1	2	yes	—
398	C₂²	C₂×#120×C₁₀₁	1	1	yes	characteristic
399	C₂²	C₂×#121×C₁₀₁	1	2	yes	—
400	C₂²	C₂×#123×C₁₀₁	1	1	yes	characteristic
401	C₄	—	4	8	no	—
402	C₄	—	4	2	no	—
403	C₄	—	4	4	no	—
404	C₄	—	8	4	no	—
405	C₄	#386×C₁₀₁	1	4	yes	—
406	C₄	#386×C₁₀₁	1	4	yes	—
407	C₂	—	2	1	no	—
408	C₂	—	2	2	no	—
409	C₂	—	2	1	no	—
410	C₂	—	2	2	no	—
411	C₂	—	4	8	no	—
412	C₂	—	8	2	no	—
413	C₂	C₂×#386×C₁₀₁	1	1	yes	characteristic
414	C₂	C₁₀₁×#2883	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₀₁	C₂²×C₂²⋊C₄
commutator	C₂³	C₂³×C₄×C₁₀₁
Frattini, cosocle	C₂⁴	C₂⁴×C₁₀₁
prime radical	C₂×#535×C₁₀₁	C₂
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₁ ◁ C₂³×D₄×C₁₀₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#518×C₁₀₁	C₂	semidirect
3. C₂×#410×C₁₀₁	C₂	semidirect
4. C₁₀₁×#2309	C₂	semidirect
5. C₁₀₁×#1898	C₂	semidirect
6. C₁₀₁×#1740	C₂	semidirect
11. C₂×#127×C₁₀₁	C₄	semidirect
12. C₂×#124×C₁₀₁	C₄	semidirect
13. C₂×#121×C₁₀₁	C₄	semidirect
31. C₂²×Q₈×C₁₀₁	C₂×C₄	semidirect
36. C₂²×D₄×C₁₀₁	C₂×C₄	semidirect
37. C₂²×D₄×C₁₀₁	C₂×C₄	semidirect
42. C₂³×C₄×C₁₀₁	C₂×C₄	semidirect
55. #117×C₁₀₁	D₄	semidirect
58. C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	semidirect
62. C₂×C₂²⋊C₄×C₁₀₁	C₂×C₄	semidirect
68. C₂×C₄²×C₁₀₁	C₂×C₄	semidirect
199. #20985	C₁₀₁	direct (N × H)
209. C₂×#518	C₂×C₁₀₁	semidirect
210. C₂×#410	C₂×C₁₀₁	semidirect
211. #2309	C₂×C₁₀₁	semidirect
212. #1898	C₂×C₁₀₁	semidirect
213. #1740	C₂×C₁₀₁	semidirect
214. C₁₀₁	#20985	direct (N × H)
219. C₂×#127	C₄×C₁₀₁	semidirect
220. C₂×#124	C₄×C₁₀₁	semidirect
221. C₂×#121	C₄×C₁₀₁	semidirect
239. C₂²×Q₈	C₂×C₄×C₁₀₁	semidirect
244. C₂²×D₄	C₂×C₄×C₁₀₁	semidirect
245. C₂²×D₄	C₂×C₄×C₁₀₁	semidirect
250. C₂³×C₄	C₂×C₄×C₁₀₁	semidirect
263. #117	D₄×C₁₀₁	semidirect
266. C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	semidirect
270. C₂×C₂²⋊C₄	C₂×C₄×C₁₀₁	semidirect
276. C₂×C₄²	C₂×C₄×C₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#535×C₁₀₁	2
C₂×#518×C₁₀₁	2
C₂×#410×C₁₀₁	2
C₁₀₁×#2309	2
C₁₀₁×#1898	2
C₁₀₁×#1740	2
#20985	101

Subgroups — C101×#20985 #38803136

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#20985 #38803136