Subgroups — C₁₀₁×#25859 #38808010

Order 25856.

1422 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#124×C₁₀₁	C₂	1	1	yes	maximal, characteristic
2	C₂×#488×C₁₀₁	C₂	1	2	yes	maximal, complemented
3	C₁₀₁×#2851	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₀₁×#2042	C₂	1	4	yes	maximal, complemented
5	C₁₀₁×#1958	C₂	1	2	yes	maximal, complemented
6	C₁₀₁×#1787	C₂	1	2	yes	maximal, complemented
7	C₁₀₁×#1786	C₂	1	2	yes	maximal
8	C₄×C₂²⋊C₈×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×Q₈×C₁₀₁	C₂²	1	1	yes	characteristic
10	C₂³×D₄×C₁₀₁	C₂²	1	1	yes	characteristic
11	C₂×#125×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
12	C₂×#124×C₁₀₁	—	2	8	no	—
13	C₂×#124×C₁₀₁	—	2	2	no	—
14	C₂×#124×C₁₀₁	C₂²	1	2	yes	—
15	C₂×#124×C₁₀₁	C₂²	1	2	yes	—
16	C₂²×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
17	C₂²×C₄²×C₁₀₁	C₂²	1	1	yes	characteristic
18	#488×C₁₀₁	—	2	8	no	—
19	C₂×#103×C₁₀₁	C₂²	1	4	yes	complemented
20	C₂×#103×C₁₀₁	C₂²	1	4	yes	complemented
21	C₂×#102×C₁₀₁	C₂²	1	4	yes	—
22	C₂×#102×C₁₀₁	C₂²	1	4	yes	—
23	C₂×C₂²⋊C₈×C₁₀₁	C₂²	1	2	yes	—
24	C₂×C₄×C₈×C₁₀₁	C₂²	1	2	yes	complemented
25	#389×C₁₀₁	C₂²	1	2	yes	complemented
26	#387×C₁₀₁	—	2	2	no	—
27	#385×C₁₀₁	—	2	2	no	—
28	#382×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
29	#380×C₁₀₁	C₂²	1	2	yes	—
30	#336×C₁₀₁	C₂²	1	2	yes	complemented
31	C₂⁵×C₁₀₁	—	2	1	no	—
32	C₂²×Q₈×C₁₀₁	—	2	4	no	—
33	C₂²×Q₈×C₁₀₁	—	2	1	no	—
34	C₂²×Q₈×C₁₀₁	—	2	4	no	—
35	C₂²×Q₈×C₁₀₁	—	4	2	no	—
36	C₂²×Q₈×C₁₀₁	C₂³	1	2	yes	—
37	C₂²×D₄×C₁₀₁	—	2	4	no	—
38	C₂²×D₄×C₁₀₁	—	2	1	no	—
39	C₂²×D₄×C₁₀₁	—	2	4	no	—
40	C₂²×D₄×C₁₀₁	—	4	2	no	—
41	C₂²×D₄×C₁₀₁	C₂³	1	2	yes	—
42	C₂³×C₄×C₁₀₁	—	2	1	no	—
43	C₂³×C₄×C₁₀₁	D₄	1	2	yes	—
44	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₁₀₁	C₂³	1	4	yes	—
46	#125×C₁₀₁	—	2	4	no	—
47	#124×C₁₀₁	—	2	16	no	—
48	#124×C₁₀₁	—	2	4	no	—
49	#124×C₁₀₁	—	2	4	no	—
50	#124×C₁₀₁	—	2	4	no	—
51	#124×C₁₀₁	D₄	1	8	yes	—
52	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
53	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
54	C₂×C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
55	C₂×C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
56	C₂×C₂²⋊C₄×C₁₀₁	—	2	16	no	—
57	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
58	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
59	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
60	C₂×C₄²×C₁₀₁	—	2	4	no	—
61	C₂×C₄²×C₁₀₁	D₄	1	2	yes	—
62	C₂×C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
63	C₂×C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
64	#103×C₁₀₁	—	2	8	no	—
65	#103×C₁₀₁	—	4	4	no	—
66	#102×C₁₀₁	—	2	8	no	—
67	#102×C₁₀₁	—	4	4	no	—
68	C₂²⋊C₈×C₁₀₁	—	2	4	no	—
69	C₄×C₈×C₁₀₁	—	2	4	no	—
70	#95×C₁₀₁	—	2	2	no	—
71	#95×C₁₀₁	—	2	2	no	—
72	#95×C₁₀₁	—	2	2	no	—
73	C₂⁴×C₁₀₁	—	2	4	no	—
74	C₂⁴×C₁₀₁	—	2	2	no	—
75	C₂⁴×C₁₀₁	—	4	2	no	—
76	C₂⁴×C₁₀₁	—	4	4	no	—
77	C₂⁴×C₁₀₁	—	4	2	no	—
78	C₂⁴×C₁₀₁	—	4	4	no	—
79	C₂⁴×C₁₀₁	C₂×D₄	1	1	yes	characteristic
80	C₂×Q₈×C₁₀₁	—	2	4	no	—
81	C₂×Q₈×C₁₀₁	—	2	2	no	—
82	C₂×Q₈×C₁₀₁	—	2	4	no	—
83	C₂×Q₈×C₁₀₁	—	2	4	no	—
84	C₂×Q₈×C₁₀₁	—	4	16	no	—
85	C₂×Q₈×C₁₀₁	—	4	2	no	—
86	C₂×Q₈×C₁₀₁	—	4	2	no	—
87	C₂×Q₈×C₁₀₁	C₂×D₄	1	4	yes	—
88	C₂×D₄×C₁₀₁	—	2	4	no	—
89	C₂×D₄×C₁₀₁	—	2	2	no	—
90	C₂×D₄×C₁₀₁	—	2	4	no	—
91	C₂×D₄×C₁₀₁	—	2	4	no	—
92	C₂×D₄×C₁₀₁	—	4	16	no	—
93	C₂×D₄×C₁₀₁	—	4	2	no	—
94	C₂×D₄×C₁₀₁	—	4	2	no	—
95	C₂×D₄×C₁₀₁	C₂×D₄	1	4	yes	—
96	C₂²×C₄×C₁₀₁	—	2	2	no	—
97	C₂²×C₄×C₁₀₁	—	2	2	no	—
98	C₂²×C₄×C₁₀₁	—	2	4	no	—
99	C₂²×C₄×C₁₀₁	—	2	4	no	—
100	C₂²×C₄×C₁₀₁	—	2	2	no	—
101	C₂²×C₄×C₁₀₁	—	2	4	no	—
102	C₂²×C₄×C₁₀₁	—	2	2	no	—
103	C₂²×C₄×C₁₀₁	—	2	2	no	—
104	C₂²×C₄×C₁₀₁	—	4	2	no	—
105	C₂²×C₄×C₁₀₁	—	4	2	no	—
106	C₂²×C₄×C₁₀₁	—	4	2	no	—
107	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₀₁	#41	1	4	yes	—
111	C₂²×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
112	C₂×C₈×C₁₀₁	—	2	4	no	—
113	C₂×C₈×C₁₀₁	—	2	4	no	—
114	C₂×C₈×C₁₀₁	—	2	4	no	—
115	C₄⋊C₄×C₁₀₁	—	2	4	no	—
116	C₄⋊C₄×C₁₀₁	—	2	4	no	—
117	C₄⋊C₄×C₁₀₁	—	4	4	no	—
118	C₄⋊C₄×C₁₀₁	—	4	4	no	—
119	C₂²⋊C₄×C₁₀₁	—	2	16	no	—
120	C₂²⋊C₄×C₁₀₁	—	2	16	no	—
121	C₂²⋊C₄×C₁₀₁	—	4	4	no	—
122	C₄²×C₁₀₁	—	2	4	no	—
123	C₄²×C₁₀₁	—	2	2	no	—
124	C₄²×C₁₀₁	C₂×D₄	1	4	yes	—
125	C₂³×C₁₀₁	—	2	1	no	—
126	C₂³×C₁₀₁	—	2	1	no	—
127	C₂³×C₁₀₁	—	2	2	no	—
128	C₂³×C₁₀₁	—	2	4	no	—
129	C₂³×C₁₀₁	—	4	8	no	—
130	C₂³×C₁₀₁	—	4	16	no	—
131	C₂³×C₁₀₁	—	4	2	no	—
132	C₂³×C₁₀₁	—	4	2	no	—
133	C₂³×C₁₀₁	—	4	4	no	—
134	C₂³×C₁₀₁	—	4	4	no	—
135	C₂³×C₁₀₁	—	8	4	no	—
136	C₂³×C₁₀₁	—	8	8	no	—
137	C₂³×C₁₀₁	—	8	4	no	—
138	C₂³×C₁₀₁	#124	1	2	yes	—
139	C₂³×C₁₀₁	#135	1	4	yes	—
140	C₂³×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
141	Q₈×C₁₀₁	—	2	8	no	—
142	Q₈×C₁₀₁	—	4	8	no	—
143	Q₈×C₁₀₁	—	4	4	no	—
144	D₄×C₁₀₁	—	2	8	no	—
145	D₄×C₁₀₁	—	4	8	no	—
146	D₄×C₁₀₁	—	4	4	no	—
147	C₂×C₄×C₁₀₁	—	2	1	no	—
148	C₂×C₄×C₁₀₁	—	2	1	no	—
149	C₂×C₄×C₁₀₁	—	2	2	no	—
150	C₂×C₄×C₁₀₁	—	2	2	no	—
151	C₂×C₄×C₁₀₁	—	2	8	no	—
152	C₂×C₄×C₁₀₁	—	2	2	no	—
153	C₂×C₄×C₁₀₁	—	2	4	no	—
154	C₂×C₄×C₁₀₁	—	2	2	no	—
155	C₂×C₄×C₁₀₁	—	2	2	no	—
156	C₂×C₄×C₁₀₁	—	4	8	no	—
157	C₂×C₄×C₁₀₁	—	4	8	no	—
158	C₂×C₄×C₁₀₁	—	4	2	no	—
159	C₂×C₄×C₁₀₁	—	4	2	no	—
160	C₂×C₄×C₁₀₁	—	4	2	no	—
161	C₂×C₄×C₁₀₁	—	4	2	no	—
162	C₂×C₄×C₁₀₁	—	4	2	no	—
163	C₂×C₄×C₁₀₁	—	4	2	no	—
164	C₂×C₄×C₁₀₁	—	4	2	no	—
165	C₂×C₄×C₁₀₁	—	4	2	no	—
166	C₂×C₄×C₁₀₁	#120	1	4	yes	—
167	C₂×C₄×C₁₀₁	#124	1	2	yes	—
168	C₂×C₄×C₁₀₁	C₂²×D₄	1	2	yes	—
169	C₂×C₄×C₁₀₁	C₂×#41	1	2	yes	—
170	C₂×C₄×C₁₀₁	H(5,𝔽₂)	1	2	yes	—
171	C₈×C₁₀₁	—	4	4	no	—
172	C₂²×C₁₀₁	—	2	2	no	—
173	C₂²×C₁₀₁	—	2	2	no	—
174	C₂²×C₁₀₁	—	2	4	no	—
175	C₂²×C₁₀₁	—	2	4	no	—
176	C₂²×C₁₀₁	—	4	4	no	—
177	C₂²×C₁₀₁	—	4	8	no	—
178	C₂²×C₁₀₁	—	8	16	no	—
179	C₂²×C₁₀₁	—	8	2	no	—
180	C₂²×C₁₀₁	—	8	2	no	—
181	C₂²×C₁₀₁	—	8	4	no	—
182	C₂²×C₁₀₁	#488	1	4	yes	complemented
183	C₂²×C₁₀₁	C₂×#120	1	1	yes	characteristic
184	C₂²×C₁₀₁	C₂×#124	1	1	yes	characteristic
185	C₂²×C₁₀₁	#535	1	1	yes	characteristic
186	C₂²×C₁₀₁	C₂×#135	1	2	yes	—
187	C₂²×C₁₀₁	#575	1	2	yes	—
188	C₄×C₁₀₁	—	2	2	no	—
189	C₄×C₁₀₁	—	2	4	no	—
190	C₄×C₁₀₁	—	4	4	no	—
191	C₄×C₁₀₁	—	4	2	no	—
192	C₄×C₁₀₁	—	8	2	no	—
193	C₄×C₁₀₁	—	8	2	no	—
194	C₄×C₁₀₁	#546	1	4	yes	—
195	#25859	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
196	C₂×C₁₀₁	—	2	4	no	—
197	C₂×C₁₀₁	—	8	4	no	—
198	C₂×C₁₀₁	#2435	1	1	yes	characteristic
199	C₂×C₁₀₁	#3002	1	2	yes	—
200	C₂×C₁₀₁	C₂×#488	1	1	yes	characteristic
201	C₂×C₁₀₁	#3140	1	1	yes	characteristic
202	C₂×C₁₀₁	#3211	1	2	yes	—
203	C₂²×#124	C₂×C₁₀₁	1	1	yes	characteristic
204	C₂×#488	C₂×C₁₀₁	1	2	yes	complemented
205	#2851	C₂×C₁₀₁	1	1	yes	characteristic, complemented
206	#2042	C₂×C₁₀₁	1	4	yes	complemented
207	#1958	C₂×C₁₀₁	1	2	yes	complemented
208	#1787	C₂×C₁₀₁	1	2	yes	complemented
209	#1786	C₂×C₁₀₁	1	2	yes	—
210	C₄×C₂²⋊C₈	C₂×C₁₀₁	1	1	yes	characteristic, complemented
211	C₁₀₁	#25859	1	1	yes	characteristic, direct product factor, Sylow
212	C₂³×Q₈	C₂²×C₁₀₁	1	1	yes	characteristic
213	C₂³×D₄	C₂²×C₁₀₁	1	1	yes	characteristic
214	C₂×#125	C₂²×C₁₀₁	1	1	yes	characteristic, complemented
215	C₂×#124	—	2	8	no	—
216	C₂×#124	—	2	2	no	—
217	C₂×#124	C₂²×C₁₀₁	1	2	yes	—
218	C₂×#124	C₂²×C₁₀₁	1	2	yes	—
219	C₂²×C₂²⋊C₄	—	2	2	no	—
220	C₂²×C₄²	C₂²×C₁₀₁	1	1	yes	characteristic
221	#488	—	2	8	no	—
222	C₂×#103	C₂²×C₁₀₁	1	4	yes	complemented
223	C₂×#103	C₂²×C₁₀₁	1	4	yes	complemented
224	C₂×#102	C₂²×C₁₀₁	1	4	yes	—
225	C₂×#102	C₂²×C₁₀₁	1	4	yes	—
226	C₂×C₂²⋊C₈	C₂²×C₁₀₁	1	2	yes	—
227	C₂×C₄×C₈	C₂²×C₁₀₁	1	2	yes	complemented
228	#389	C₂²×C₁₀₁	1	2	yes	complemented
229	#387	—	2	2	no	—
230	#385	—	2	2	no	—
231	#382	C₂²×C₁₀₁	1	1	yes	characteristic, complemented
232	#380	C₂²×C₁₀₁	1	2	yes	—
233	#336	C₂²×C₁₀₁	1	2	yes	complemented
234	C₂⁵	—	2	1	no	—
235	C₂²×Q₈	—	2	4	no	—
236	C₂²×Q₈	—	2	1	no	—
237	C₂²×Q₈	—	2	4	no	—
238	C₂²×Q₈	—	4	2	no	—
239	C₂²×Q₈	C₂³×C₁₀₁	1	2	yes	—
240	C₂²×D₄	—	2	4	no	—
241	C₂²×D₄	—	2	1	no	—
242	C₂²×D₄	—	2	4	no	—
243	C₂²×D₄	—	4	2	no	—
244	C₂²×D₄	C₂³×C₁₀₁	1	2	yes	—
245	C₂³×C₄	—	2	1	no	—
246	C₂³×C₄	D₄×C₁₀₁	1	2	yes	—
247	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
248	C₂²×C₈	C₂³×C₁₀₁	1	4	yes	—
249	#125	—	2	4	no	—
250	#124	—	2	16	no	—
251	#124	—	2	4	no	—
252	#124	—	2	4	no	—
253	#124	—	2	4	no	—
254	#124	D₄×C₁₀₁	1	8	yes	—
255	C₂×C₄⋊C₄	—	2	2	no	—
256	C₂×C₄⋊C₄	—	2	2	no	—
257	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	2	yes	—
258	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	2	yes	—
259	C₂×C₂²⋊C₄	—	2	16	no	—
260	C₂×C₂²⋊C₄	—	2	4	no	—
261	C₂×C₂²⋊C₄	—	2	4	no	—
262	C₂×C₂²⋊C₄	—	2	2	no	—
263	C₂×C₄²	—	2	4	no	—
264	C₂×C₄²	D₄×C₁₀₁	1	2	yes	—
265	C₂×C₄²	C₂³×C₁₀₁	1	1	yes	characteristic
266	C₂×C₄²	C₂³×C₁₀₁	1	1	yes	characteristic
267	#103	—	2	8	no	—
268	#103	—	4	4	no	—
269	#102	—	2	8	no	—
270	#102	—	4	4	no	—
271	C₂²⋊C₈	—	2	4	no	—
272	C₄×C₈	—	2	4	no	—
273	#95	—	2	2	no	—
274	#95	—	2	2	no	—
275	#95	—	2	2	no	—
276	C₂⁴	—	2	4	no	—
277	C₂⁴	—	2	2	no	—
278	C₂⁴	—	4	2	no	—
279	C₂⁴	—	4	4	no	—
280	C₂⁴	—	4	2	no	—
281	C₂⁴	—	4	4	no	—
282	C₂⁴	C₂×D₄×C₁₀₁	1	1	yes	characteristic
283	C₂×Q₈	—	2	4	no	—
284	C₂×Q₈	—	2	2	no	—
285	C₂×Q₈	—	2	4	no	—
286	C₂×Q₈	—	2	4	no	—
287	C₂×Q₈	—	4	16	no	—
288	C₂×Q₈	—	4	2	no	—
289	C₂×Q₈	—	4	2	no	—
290	C₂×Q₈	C₂×D₄×C₁₀₁	1	4	yes	—
291	C₂×D₄	—	2	4	no	—
292	C₂×D₄	—	2	2	no	—
293	C₂×D₄	—	2	4	no	—
294	C₂×D₄	—	2	4	no	—
295	C₂×D₄	—	4	16	no	—
296	C₂×D₄	—	4	2	no	—
297	C₂×D₄	—	4	2	no	—
298	C₂×D₄	C₂×D₄×C₁₀₁	1	4	yes	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	4	no	—
302	C₂²×C₄	—	2	4	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	4	no	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	4	2	no	—
308	C₂²×C₄	—	4	2	no	—
309	C₂²×C₄	—	4	2	no	—
310	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
311	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
312	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
313	C₂²×C₄	#41×C₁₀₁	1	4	yes	—
314	C₂²×C₄	C₂⁴×C₁₀₁	1	1	yes	characteristic
315	C₂×C₈	—	2	4	no	—
316	C₂×C₈	—	2	4	no	—
317	C₂×C₈	—	2	4	no	—
318	C₄⋊C₄	—	2	4	no	—
319	C₄⋊C₄	—	2	4	no	—
320	C₄⋊C₄	—	4	4	no	—
321	C₄⋊C₄	—	4	4	no	—
322	C₂²⋊C₄	—	2	16	no	—
323	C₂²⋊C₄	—	2	16	no	—
324	C₂²⋊C₄	—	4	4	no	—
325	C₄²	—	2	4	no	—
326	C₄²	—	2	2	no	—
327	C₄²	C₂×D₄×C₁₀₁	1	4	yes	—
328	C₂³	—	2	1	no	—
329	C₂³	—	2	1	no	—
330	C₂³	—	2	2	no	—
331	C₂³	—	2	4	no	—
332	C₂³	—	4	8	no	—
333	C₂³	—	4	16	no	—
334	C₂³	—	4	2	no	—
335	C₂³	—	4	2	no	—
336	C₂³	—	4	4	no	—
337	C₂³	—	4	4	no	—
338	C₂³	—	8	8	no	—
339	C₂³	—	8	4	no	—
340	C₂³	—	8	4	no	—
341	C₂³	#124×C₁₀₁	1	2	yes	—
342	C₂³	#135×C₁₀₁	1	4	yes	—
343	C₂³	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
344	Q₈	—	2	8	no	—
345	Q₈	—	4	8	no	—
346	Q₈	—	4	4	no	—
347	D₄	—	2	8	no	—
348	D₄	—	4	8	no	—
349	D₄	—	4	4	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	8	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	4	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	4	8	no	—
360	C₂×C₄	—	4	8	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	#120×C₁₀₁	1	4	yes	—
370	C₂×C₄	#124×C₁₀₁	1	2	yes	—
371	C₂×C₄	C₂²×D₄×C₁₀₁	1	2	yes	—
372	C₂×C₄	C₂×#41×C₁₀₁	1	2	yes	—
373	C₂×C₄	H(5,𝔽₂)×C₁₀₁	1	2	yes	—
374	C₈	—	4	4	no	—
375	C₂²	—	2	2	no	—
376	C₂²	—	2	4	no	—
377	C₂²	—	2	4	no	—
378	C₂²	—	2	2	no	—
379	C₂²	—	4	4	no	—
380	C₂²	—	4	8	no	—
381	C₂²	—	8	16	no	—
382	C₂²	—	8	4	no	—
383	C₂²	—	8	2	no	—
384	C₂²	—	8	2	no	—
385	C₂²	#488×C₁₀₁	1	4	yes	complemented
386	C₂²	C₂×#120×C₁₀₁	1	1	yes	characteristic
387	C₂²	C₂×#124×C₁₀₁	1	1	yes	characteristic
388	C₂²	#535×C₁₀₁	1	1	yes	characteristic
389	C₂²	C₂×#135×C₁₀₁	1	2	yes	—
390	C₂²	#575×C₁₀₁	1	2	yes	—
391	C₄	—	2	2	no	—
392	C₄	—	2	4	no	—
393	C₄	—	4	4	no	—
394	C₄	—	4	2	no	—
395	C₄	—	8	2	no	—
396	C₄	—	8	2	no	—
397	C₄	#546×C₁₀₁	1	4	yes	—
398	C₂	—	2	4	no	—
399	C₂	—	8	4	no	—
400	C₂	C₁₀₁×#2435	1	1	yes	characteristic
401	C₂	C₁₀₁×#3002	1	2	yes	—
402	C₂	C₂×#488×C₁₀₁	1	1	yes	characteristic
403	C₂	C₁₀₁×#3140	1	1	yes	characteristic
404	C₂	C₁₀₁×#3211	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₀₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₀₁
prime radical	C₂³×D₄×C₁₀₁	C₂²
LCS	G ▷ C₂²×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
2. C₂×#488×C₁₀₁	C₂	semidirect
3. C₁₀₁×#2851	C₂	semidirect
4. C₁₀₁×#2042	C₂	semidirect
5. C₁₀₁×#1958	C₂	semidirect
6. C₁₀₁×#1787	C₂	semidirect
8. C₄×C₂²⋊C₈×C₁₀₁	C₂	semidirect
11. C₂×#125×C₁₀₁	C₂²	semidirect
19. C₂×#103×C₁₀₁	C₂²	semidirect
20. C₂×#103×C₁₀₁	C₂²	semidirect
24. C₂×C₄×C₈×C₁₀₁	C₂²	semidirect
25. #389×C₁₀₁	C₂²	semidirect
28. #382×C₁₀₁	C₂²	semidirect
30. #336×C₁₀₁	C₂²	semidirect
182. C₂²×C₁₀₁	#488	semidirect
195. #25859	C₁₀₁	direct (N × H)
204. C₂×#488	C₂×C₁₀₁	semidirect
205. #2851	C₂×C₁₀₁	semidirect
206. #2042	C₂×C₁₀₁	semidirect
207. #1958	C₂×C₁₀₁	semidirect
208. #1787	C₂×C₁₀₁	semidirect
210. C₄×C₂²⋊C₈	C₂×C₁₀₁	semidirect
211. C₁₀₁	#25859	direct (N × H)
214. C₂×#125	C₂²×C₁₀₁	semidirect
222. C₂×#103	C₂²×C₁₀₁	semidirect
223. C₂×#103	C₂²×C₁₀₁	semidirect
227. C₂×C₄×C₈	C₂²×C₁₀₁	semidirect
228. #389	C₂²×C₁₀₁	semidirect
231. #382	C₂²×C₁₀₁	semidirect
233. #336	C₂²×C₁₀₁	semidirect
385. C₂²	#488×C₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#124×C₁₀₁	2
C₂×#488×C₁₀₁	2
C₁₀₁×#2851	2
C₁₀₁×#2042	2
C₁₀₁×#1958	2
C₁₀₁×#1787	2
C₁₀₁×#1786	2
C₄×C₂²⋊C₈×C₁₀₁	2
#25859	101

Subgroups — C101×#25859 #38808010

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#25859 #38808010