Subgroups — C₁₀₁×#25870 #38808021

Order 25856.

1370 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	C₁₀₁×#3496	C₂	1	1	yes	maximal, characteristic
2	C₁₀₁×#3141	C₂	1	2	yes	maximal, complemented
3	C₁₀₁×#2542	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₀₁×#2039	C₂	1	4	yes	maximal, complemented
5	C₁₀₁×#1980	C₂	1	2	yes	maximal, complemented
6	C₁₀₁×#1792	C₂	1	4	yes	maximal, complemented
7	C₄×#100×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×H(5,𝔽₂)×C₁₀₁	C₂²	1	2	yes	—
9	#547×C₁₀₁	—	2	2	no	—
10	#546×C₁₀₁	—	2	4	no	—
11	D₄²×C₁₀₁	—	2	2	no	—
12	#537×C₁₀₁	C₂²	1	2	yes	—
13	#534×C₁₀₁	—	2	2	no	—
14	#532×C₁₀₁	C₂²	1	2	yes	—
15	C₂×C₄⋊Q₈×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
16	C₂×C₂²⋊Q₈×C₁₀₁	—	2	2	no	—
17	C₂×#121×C₁₀₁	—	2	2	no	—
18	C₂×C₄×D₄×C₁₀₁	C₂²	1	1	yes	characteristic
19	#489×C₁₀₁	—	2	4	no	—
20	#487×C₁₀₁	—	2	2	no	—
21	#486×C₁₀₁	—	2	2	no	—
22	C₂×#104×C₁₀₁	C₂²	1	8	yes	complemented
23	#417×C₁₀₁	C₂²	1	8	yes	complemented
24	C₂×#100×C₁₀₁	C₂²	1	2	yes	—
25	C₄×M₁₆×C₁₀₁	C₂²	1	2	yes	complemented
26	#399×C₁₀₁	—	2	2	no	—
27	#390×C₁₀₁	C₂²	1	2	yes	—
28	#384×C₁₀₁	C₂²	1	2	yes	complemented
29	C₄×C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
30	#343×C₁₀₁	C₂²	1	2	yes	complemented
31	H(5,𝔽₂)×C₁₀₁	—	2	8	no	—
32	H(5,𝔽₂)×C₁₀₁	—	4	4	no	—
33	C₂×#41×C₁₀₁	—	2	4	no	—
34	C₂×#41×C₁₀₁	C₂³	1	4	yes	—
35	C₂²×Q₈×C₁₀₁	—	2	1	no	—
36	C₂²×D₄×C₁₀₁	—	2	4	no	—
37	C₂²×D₄×C₁₀₁	—	2	2	no	—
38	C₂²×D₄×C₁₀₁	—	2	4	no	—
39	C₂²×D₄×C₁₀₁	C₂³	1	1	yes	characteristic
40	C₂³×C₄×C₁₀₁	D₄	1	2	yes	—
41	C₂×M₁₆×C₁₀₁	C₂³	1	4	yes	—
42	C₄⋊Q₈×C₁₀₁	—	2	2	no	—
43	C₄⋊Q₈×C₁₀₁	—	2	2	no	—
44	C₄⋊Q₈×C₁₀₁	D₄	1	2	yes	—
45	#127×C₁₀₁	D₄	1	2	yes	—
46	#124×C₁₀₁	D₄	1	4	yes	—
47	#123×C₁₀₁	—	2	8	no	—
48	C₂²⋊Q₈×C₁₀₁	—	2	4	no	—
49	C₂²⋊Q₈×C₁₀₁	—	4	8	no	—
50	#121×C₁₀₁	—	2	4	no	—
51	#121×C₁₀₁	—	2	4	no	—
52	#121×C₁₀₁	—	2	4	no	—
53	#121×C₁₀₁	—	2	2	no	—
54	#121×C₁₀₁	—	2	4	no	—
55	#121×C₁₀₁	—	2	2	no	—
56	#120×C₁₀₁	—	2	8	no	—
57	C₄×D₄×C₁₀₁	—	2	2	no	—
58	C₄×D₄×C₁₀₁	—	2	2	no	—
59	C₄×D₄×C₁₀₁	—	2	2	no	—
60	C₄×D₄×C₁₀₁	—	2	2	no	—
61	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
62	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
63	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
64	C₂×C₄⋊C₄×C₁₀₁	—	2	4	no	—
65	C₂×C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
66	C₂×C₄⋊C₄×C₁₀₁	C₂³	1	1	yes	characteristic
67	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
68	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
69	C₂×C₂²⋊C₄×C₁₀₁	D₄	1	2	yes	—
70	C₂×C₄²×C₁₀₁	C₂³	1	2	yes	—
71	C₂×C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
72	#104×C₁₀₁	—	4	8	no	—
73	#103×C₁₀₁	—	2	8	no	—
74	#102×C₁₀₁	—	2	8	no	—
75	#100×C₁₀₁	—	2	4	no	—
76	#97×C₁₀₁	—	2	2	no	—
77	C₄×C₈×C₁₀₁	—	2	2	no	—
78	#95×C₁₀₁	—	2	1	no	—
79	C₂⁴×C₁₀₁	—	2	4	no	—
80	C₂⁴×C₁₀₁	C₂×D₄	1	2	yes	—
81	#41×C₁₀₁	—	2	8	no	—
82	#41×C₁₀₁	—	2	8	no	—
83	#41×C₁₀₁	—	4	16	no	—
84	C₂×Q₈×C₁₀₁	—	4	4	no	—
85	C₂×Q₈×C₁₀₁	—	4	1	no	—
86	C₂×Q₈×C₁₀₁	—	4	1	no	—
87	C₂×Q₈×C₁₀₁	C₂×D₄	1	4	yes	—
88	C₂×D₄×C₁₀₁	—	2	8	no	—
89	C₂×D₄×C₁₀₁	—	2	4	no	—
90	C₂×D₄×C₁₀₁	—	2	4	no	—
91	C₂×D₄×C₁₀₁	—	2	2	no	—
92	C₂×D₄×C₁₀₁	—	2	2	no	—
93	C₂×D₄×C₁₀₁	—	2	2	no	—
94	C₂×D₄×C₁₀₁	—	2	2	no	—
95	C₂×D₄×C₁₀₁	—	4	16	no	—
96	C₂×D₄×C₁₀₁	—	4	8	no	—
97	C₂×D₄×C₁₀₁	—	4	8	no	—
98	C₂×D₄×C₁₀₁	—	8	4	no	—
99	C₂×D₄×C₁₀₁	C₂×D₄	1	4	yes	—
100	C₂×D₄×C₁₀₁	#41	1	4	yes	—
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	—	2	4	no	—
105	C₂²×C₄×C₁₀₁	—	2	2	no	—
106	C₂²×C₄×C₁₀₁	—	2	2	no	—
107	C₂²×C₄×C₁₀₁	—	4	4	no	—
108	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
112	M₁₆×C₁₀₁	—	2	4	no	—
113	M₁₆×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	—	2	2	no	—
118	C₄⋊C₄×C₁₀₁	—	2	2	no	—
119	C₄⋊C₄×C₁₀₁	—	2	2	no	—
120	C₄⋊C₄×C₁₀₁	—	2	4	no	—
121	C₄⋊C₄×C₁₀₁	—	4	8	no	—
122	C₄⋊C₄×C₁₀₁	—	4	2	no	—
123	C₂²⋊C₄×C₁₀₁	—	2	8	no	—
124	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
125	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
126	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
127	C₂²⋊C₄×C₁₀₁	—	4	8	no	—
128	C₄²×C₁₀₁	—	2	4	no	—
129	C₄²×C₁₀₁	C₂×D₄	1	2	yes	—
130	C₄²×C₁₀₁	C₂×D₄	1	2	yes	—
131	C₂³×C₁₀₁	—	2	2	no	—
132	C₂³×C₁₀₁	—	2	2	no	—
133	C₂³×C₁₀₁	—	2	4	no	—
134	C₂³×C₁₀₁	—	4	2	no	—
135	C₂³×C₁₀₁	—	4	2	no	—
136	C₂³×C₁₀₁	—	4	8	no	—
137	C₂³×C₁₀₁	—	8	4	no	—
138	C₂³×C₁₀₁	—	8	4	no	—
139	C₂³×C₁₀₁	#124	1	4	yes	—
140	C₂³×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
141	Q₈×C₁₀₁	—	2	8	no	—
142	Q₈×C₁₀₁	—	8	2	no	—
143	Q₈×C₁₀₁	—	8	2	no	—
144	D₄×C₁₀₁	—	2	8	no	—
145	D₄×C₁₀₁	—	2	8	no	—
146	D₄×C₁₀₁	—	4	16	no	—
147	D₄×C₁₀₁	—	4	4	no	—
148	D₄×C₁₀₁	—	4	4	no	—
149	D₄×C₁₀₁	—	4	4	no	—
150	D₄×C₁₀₁	—	8	2	no	—
151	D₄×C₁₀₁	—	8	4	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	4	no	—
156	C₂×C₄×C₁₀₁	—	4	1	no	—
157	C₂×C₄×C₁₀₁	—	4	2	no	—
158	C₂×C₄×C₁₀₁	—	4	8	no	—
159	C₂×C₄×C₁₀₁	—	4	2	no	—
160	C₂×C₄×C₁₀₁	—	4	8	no	—
161	C₂×C₄×C₁₀₁	—	4	4	no	—
162	C₂×C₄×C₁₀₁	—	4	2	no	—
163	C₂×C₄×C₁₀₁	—	4	4	no	—
164	C₂×C₄×C₁₀₁	—	4	2	no	—
165	C₂×C₄×C₁₀₁	—	8	2	no	—
166	C₂×C₄×C₁₀₁	#120	1	2	yes	—
167	C₂×C₄×C₁₀₁	#120	1	1	yes	characteristic
168	C₂×C₄×C₁₀₁	#120	1	1	yes	characteristic
169	C₂×C₄×C₁₀₁	C₂²×D₄	1	2	yes	—
170	C₂×C₄×C₁₀₁	C₂×#41	1	2	yes	—
171	C₂×C₄×C₁₀₁	H(5,𝔽₂)	1	2	yes	—
172	C₈×C₁₀₁	—	4	4	no	—
173	C₂²×C₁₀₁	—	2	1	no	—
174	C₂²×C₁₀₁	—	2	1	no	—
175	C₂²×C₁₀₁	—	2	4	no	—
176	C₂²×C₁₀₁	—	4	4	no	—
177	C₂²×C₁₀₁	—	4	2	no	—
178	C₂²×C₁₀₁	—	4	2	no	—
179	C₂²×C₁₀₁	—	4	4	no	—
180	C₂²×C₁₀₁	—	4	4	no	—
181	C₂²×C₁₀₁	—	4	4	no	—
182	C₂²×C₁₀₁	—	8	2	no	—
183	C₂²×C₁₀₁	—	16	8	no	—
184	C₂²×C₁₀₁	C₂×#120	1	1	yes	characteristic
185	C₂²×C₁₀₁	C₂×#124	1	1	yes	characteristic
186	C₂²×C₁₀₁	#535	1	1	yes	characteristic
187	C₄×C₁₀₁	—	2	1	no	—
188	C₄×C₁₀₁	—	2	2	no	—
189	C₄×C₁₀₁	—	4	4	no	—
190	C₄×C₁₀₁	—	4	4	no	—
191	C₄×C₁₀₁	—	4	2	no	—
192	C₄×C₁₀₁	—	8	2	no	—
193	C₄×C₁₀₁	#453	1	2	yes	—
194	C₄×C₁₀₁	#546	1	4	yes	—
195	#25870	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
196	C₂×C₁₀₁	—	2	1	no	—
197	C₂×C₁₀₁	—	2	1	no	—
198	C₂×C₁₀₁	—	4	4	no	—
199	C₂×C₁₀₁	—	8	4	no	—
200	C₂×C₁₀₁	#2435	1	1	yes	characteristic
201	C₂×C₁₀₁	C₂×#453	1	1	yes	characteristic
202	C₂×C₁₀₁	#3022	1	1	yes	characteristic
203	#3496	C₂×C₁₀₁	1	1	yes	characteristic
204	#3141	C₂×C₁₀₁	1	2	yes	complemented
205	#2542	C₂×C₁₀₁	1	1	yes	characteristic, complemented
206	#2039	C₂×C₁₀₁	1	4	yes	complemented
207	#1980	C₂×C₁₀₁	1	2	yes	complemented
208	#1792	C₂×C₁₀₁	1	4	yes	complemented
209	C₄×#100	C₂×C₁₀₁	1	1	yes	characteristic, complemented
210	C₁₀₁	#25870	1	1	yes	characteristic, direct product factor, Sylow
211	C₂×H(5,𝔽₂)	C₂²×C₁₀₁	1	2	yes	—
212	#547	—	2	2	no	—
213	#546	—	2	4	no	—
214	D₄²	—	2	2	no	—
215	#537	C₂²×C₁₀₁	1	2	yes	—
216	#534	—	2	2	no	—
217	#532	C₂²×C₁₀₁	1	2	yes	—
218	C₂×C₄⋊Q₈	C₂²×C₁₀₁	1	1	yes	characteristic, complemented
219	C₂×C₂²⋊Q₈	—	2	2	no	—
220	C₂×#121	—	2	2	no	—
221	C₂×C₄×D₄	C₂²×C₁₀₁	1	1	yes	characteristic
222	#489	—	2	4	no	—
223	#487	—	2	2	no	—
224	#486	—	2	2	no	—
225	C₂×#104	C₂²×C₁₀₁	1	8	yes	complemented
226	#417	C₂²×C₁₀₁	1	8	yes	complemented
227	C₂×#100	C₂²×C₁₀₁	1	2	yes	—
228	C₄×M₁₆	C₂²×C₁₀₁	1	2	yes	complemented
229	#399	—	2	2	no	—
230	#390	C₂²×C₁₀₁	1	2	yes	—
231	#384	C₂²×C₁₀₁	1	2	yes	complemented
232	C₄×C₄⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic, complemented
233	#343	C₂²×C₁₀₁	1	2	yes	complemented
234	H(5,𝔽₂)	—	2	8	no	—
235	H(5,𝔽₂)	—	4	4	no	—
236	C₂×#41	—	2	4	no	—
237	C₂×#41	C₂³×C₁₀₁	1	4	yes	—
238	C₂²×Q₈	—	2	1	no	—
239	C₂²×D₄	—	2	4	no	—
240	C₂²×D₄	—	2	2	no	—
241	C₂²×D₄	—	2	4	no	—
242	C₂²×D₄	C₂³×C₁₀₁	1	1	yes	characteristic
243	C₂³×C₄	D₄×C₁₀₁	1	2	yes	—
244	C₂×M₁₆	C₂³×C₁₀₁	1	4	yes	—
245	C₄⋊Q₈	—	2	2	no	—
246	C₄⋊Q₈	—	2	2	no	—
247	C₄⋊Q₈	D₄×C₁₀₁	1	2	yes	—
248	#127	D₄×C₁₀₁	1	2	yes	—
249	#124	D₄×C₁₀₁	1	4	yes	—
250	#123	—	2	8	no	—
251	C₂²⋊Q₈	—	2	4	no	—
252	C₂²⋊Q₈	—	4	8	no	—
253	#121	—	2	4	no	—
254	#121	—	2	4	no	—
255	#121	—	2	4	no	—
256	#121	—	2	2	no	—
257	#121	—	2	4	no	—
258	#121	—	2	2	no	—
259	#120	—	2	8	no	—
260	C₄×D₄	—	2	2	no	—
261	C₄×D₄	—	2	2	no	—
262	C₄×D₄	—	2	2	no	—
263	C₄×D₄	—	2	2	no	—
264	C₂×C₄⋊C₄	—	2	2	no	—
265	C₂×C₄⋊C₄	—	2	1	no	—
266	C₂×C₄⋊C₄	—	2	4	no	—
267	C₂×C₄⋊C₄	—	2	1	no	—
268	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	2	yes	—
269	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	1	yes	characteristic
270	C₂×C₂²⋊C₄	—	2	4	no	—
271	C₂×C₂²⋊C₄	—	2	4	no	—
272	C₂×C₂²⋊C₄	D₄×C₁₀₁	1	2	yes	—
273	C₂×C₄²	C₂³×C₁₀₁	1	2	yes	—
274	C₂×C₄²	C₂³×C₁₀₁	1	1	yes	characteristic
275	#104	—	4	8	no	—
276	#103	—	2	8	no	—
277	#102	—	2	8	no	—
278	#100	—	2	4	no	—
279	#97	—	2	2	no	—
280	C₄×C₈	—	2	2	no	—
281	#95	—	2	1	no	—
282	C₂⁴	—	2	4	no	—
283	C₂⁴	C₂×D₄×C₁₀₁	1	2	yes	—
284	#41	—	2	8	no	—
285	#41	—	2	8	no	—
286	#41	—	4	16	no	—
287	C₂×Q₈	—	4	4	no	—
288	C₂×Q₈	—	4	1	no	—
289	C₂×Q₈	—	4	1	no	—
290	C₂×Q₈	C₂×D₄×C₁₀₁	1	4	yes	—
291	C₂×D₄	—	2	8	no	—
292	C₂×D₄	—	2	4	no	—
293	C₂×D₄	—	2	4	no	—
294	C₂×D₄	—	2	2	no	—
295	C₂×D₄	—	2	2	no	—
296	C₂×D₄	—	2	2	no	—
297	C₂×D₄	—	2	2	no	—
298	C₂×D₄	—	4	16	no	—
299	C₂×D₄	—	4	8	no	—
300	C₂×D₄	—	4	8	no	—
301	C₂×D₄	—	8	4	no	—
302	C₂×D₄	C₂×D₄×C₁₀₁	1	4	yes	—
303	C₂×D₄	#41×C₁₀₁	1	4	yes	—
304	C₂²×C₄	—	2	4	no	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	2	4	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	4	4	no	—
311	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
312	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
313	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
314	C₂²×C₄	C₂⁴×C₁₀₁	1	1	yes	characteristic
315	M₁₆	—	2	4	no	—
316	M₁₆	—	2	4	no	—
317	C₂×C₈	—	2	4	no	—
318	C₄⋊C₄	—	2	4	no	—
319	C₄⋊C₄	—	2	4	no	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	2	2	no	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	2	4	no	—
324	C₄⋊C₄	—	4	8	no	—
325	C₄⋊C₄	—	4	2	no	—
326	C₂²⋊C₄	—	2	8	no	—
327	C₂²⋊C₄	—	2	4	no	—
328	C₂²⋊C₄	—	2	4	no	—
329	C₂²⋊C₄	—	2	4	no	—
330	C₂²⋊C₄	—	4	8	no	—
331	C₄²	—	2	4	no	—
332	C₄²	C₂×D₄×C₁₀₁	1	2	yes	—
333	C₄²	C₂×D₄×C₁₀₁	1	2	yes	—
334	C₂³	—	2	2	no	—
335	C₂³	—	2	2	no	—
336	C₂³	—	2	4	no	—
337	C₂³	—	4	2	no	—
338	C₂³	—	4	2	no	—
339	C₂³	—	4	8	no	—
340	C₂³	—	8	4	no	—
341	C₂³	—	8	4	no	—
342	C₂³	#124×C₁₀₁	1	4	yes	—
343	C₂³	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
344	Q₈	—	2	8	no	—
345	Q₈	—	8	2	no	—
346	Q₈	—	8	2	no	—
347	D₄	—	2	8	no	—
348	D₄	—	2	8	no	—
349	D₄	—	4	16	no	—
350	D₄	—	4	4	no	—
351	D₄	—	4	4	no	—
352	D₄	—	4	4	no	—
353	D₄	—	8	2	no	—
354	D₄	—	8	4	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	4	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	4	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	4	8	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	4	no	—
364	C₂×C₄	—	4	8	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	4	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	8	2	no	—
369	C₂×C₄	#120×C₁₀₁	1	2	yes	—
370	C₂×C₄	#120×C₁₀₁	1	1	yes	characteristic
371	C₂×C₄	#120×C₁₀₁	1	1	yes	characteristic
372	C₂×C₄	C₂²×D₄×C₁₀₁	1	2	yes	—
373	C₂×C₄	C₂×#41×C₁₀₁	1	2	yes	—
374	C₂×C₄	H(5,𝔽₂)×C₁₀₁	1	2	yes	—
375	C₈	—	4	4	no	—
376	C₂²	—	2	1	no	—
377	C₂²	—	2	1	no	—
378	C₂²	—	2	4	no	—
379	C₂²	—	4	4	no	—
380	C₂²	—	4	2	no	—
381	C₂²	—	4	2	no	—
382	C₂²	—	4	4	no	—
383	C₂²	—	4	4	no	—
384	C₂²	—	4	4	no	—
385	C₂²	—	8	2	no	—
386	C₂²	—	16	8	no	—
387	C₂²	C₂×#120×C₁₀₁	1	1	yes	characteristic
388	C₂²	C₂×#124×C₁₀₁	1	1	yes	characteristic
389	C₂²	#535×C₁₀₁	1	1	yes	characteristic
390	C₄	—	2	1	no	—
391	C₄	—	2	2	no	—
392	C₄	—	4	4	no	—
393	C₄	—	4	4	no	—
394	C₄	—	4	2	no	—
395	C₄	—	8	2	no	—
396	C₄	#453×C₁₀₁	1	2	yes	—
397	C₄	#546×C₁₀₁	1	4	yes	—
398	C₂	—	2	1	no	—
399	C₂	—	2	1	no	—
400	C₂	—	4	4	no	—
401	C₂	—	8	4	no	—
402	C₂	C₁₀₁×#2435	1	1	yes	characteristic
403	C₂	C₂×#453×C₁₀₁	1	1	yes	characteristic
404	C₂	C₁₀₁×#3022	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₀₁	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₀₁
prime radical	C₁₀₁×#3496	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₁ ◁ C₂×C₄²×C₁₀₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₀₁×#3141	C₂	semidirect
3. C₁₀₁×#2542	C₂	semidirect
4. C₁₀₁×#2039	C₂	semidirect
5. C₁₀₁×#1980	C₂	semidirect
6. C₁₀₁×#1792	C₂	semidirect
7. C₄×#100×C₁₀₁	C₂	semidirect
15. C₂×C₄⋊Q₈×C₁₀₁	C₂²	semidirect
22. C₂×#104×C₁₀₁	C₂²	semidirect
23. #417×C₁₀₁	C₂²	semidirect
25. C₄×M₁₆×C₁₀₁	C₂²	semidirect
28. #384×C₁₀₁	C₂²	semidirect
29. C₄×C₄⋊C₄×C₁₀₁	C₂²	semidirect
30. #343×C₁₀₁	C₂²	semidirect
195. #25870	C₁₀₁	direct (N × H)
204. #3141	C₂×C₁₀₁	semidirect
205. #2542	C₂×C₁₀₁	semidirect
206. #2039	C₂×C₁₀₁	semidirect
207. #1980	C₂×C₁₀₁	semidirect
208. #1792	C₂×C₁₀₁	semidirect
209. C₄×#100	C₂×C₁₀₁	semidirect
210. C₁₀₁	#25870	direct (N × H)
218. C₂×C₄⋊Q₈	C₂²×C₁₀₁	semidirect
225. C₂×#104	C₂²×C₁₀₁	semidirect
226. #417	C₂²×C₁₀₁	semidirect
228. C₄×M₁₆	C₂²×C₁₀₁	semidirect
231. #384	C₂²×C₁₀₁	semidirect
232. C₄×C₄⋊C₄	C₂²×C₁₀₁	semidirect
233. #343	C₂²×C₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₁₀₁×#3496	2
C₁₀₁×#3141	2
C₁₀₁×#2542	2
C₁₀₁×#2039	2
C₁₀₁×#1980	2
C₁₀₁×#1792	2
C₄×#100×C₁₀₁	2
#25870	101

Subgroups — C101×#25870 #38808021

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#25870 #38808021