Subgroups — C₁₀₁×#17611 #38799762

Order 25856.

1338 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₀₁×#3488	C₂	1	1	yes	maximal, characteristic
2	C₁₀₁×#2880	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₀₁×#2341	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₀₁×#1519	C₂	1	3	yes	maximal, complemented
5	C₁₀₁×#1513	C₂	1	3	yes	maximal, complemented
6	C₁₀₁×#1507	C₂	1	3	yes	maximal, complemented
7	C₁₀₁×#1501	C₂	1	3	yes	maximal, complemented
8	C₂×H(5,𝔽₂)×C₁₀₁	C₄	1	1	yes	characteristic, complemented
9	C₂²×#41×C₁₀₁	C₂²	1	1	yes	characteristic
10	C₂×#131×C₁₀₁	—	2	1	no	—
11	#550×C₁₀₁	—	2	1	no	—
12	#548×C₁₀₁	—	2	1	no	—
13	#546×C₁₀₁	—	2	3	no	—
14	D₄²×C₁₀₁	—	2	3	no	—
15	#537×C₁₀₁	C₄	1	3	yes	complemented
16	#535×C₁₀₁	C₄	1	3	yes	complemented
17	#525×C₁₀₁	C₂²	1	3	yes	—
18	C₂×#121×C₁₀₁	C₂²	1	3	yes	—
19	#520×C₁₀₁	C₄	1	1	yes	characteristic, complemented
20	C₂×C₄×Q₈×C₁₀₁	—	2	1	no	—
21	#408×C₁₀₁	—	2	3	no	—
22	#407×C₁₀₁	C₂²	1	3	yes	complemented
23	C₂×C₂²⋊C₈×C₁₀₁	C₂²	1	3	yes	complemented
24	#390×C₁₀₁	—	2	3	no	—
25	#380×C₁₀₁	C₂²	1	3	yes	complemented
26	C₄×C₂²⋊C₄×C₁₀₁	C₂²	1	3	yes	complemented
27	#328×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
28	#328×C₁₀₁	C₂²	1	3	yes	complemented
29	#327×C₁₀₁	C₂²	1	3	yes	complemented
30	#327×C₁₀₁	C₂²	1	3	yes	complemented
31	#327×C₁₀₁	C₂²	1	6	yes	complemented
32	H(5,𝔽₂)×C₁₀₁	—	4	4	no	—
33	C₂×#41×C₁₀₁	—	2	1	no	—
34	C₂×#41×C₁₀₁	—	4	4	no	—
35	C₂×#41×C₁₀₁	C₂×C₄	1	3	yes	—
36	C₂×#41×C₁₀₁	C₂×C₄	1	1	yes	characteristic
37	C₂×#41×C₁₀₁	C₂×C₄	1	3	yes	—
38	C₂×#41×C₁₀₁	D₄	1	1	yes	characteristic
39	C₂×#41×C₁₀₁	D₄	1	3	yes	—
40	C₂²×Q₈×C₁₀₁	D₄	1	1	yes	characteristic
41	C₂²×D₄×C₁₀₁	—	2	3	no	—
42	C₂²×D₄×C₁₀₁	—	2	3	no	—
43	C₂²×D₄×C₁₀₁	C₂×C₄	1	3	yes	—
44	C₂²×D₄×C₁₀₁	D₄	1	3	yes	—
45	C₂³×C₄×C₁₀₁	C₂³	1	3	yes	—
46	#131×C₁₀₁	—	4	4	no	—
47	C₂×M₁₆×C₁₀₁	—	2	3	no	—
48	C₂²×C₈×C₁₀₁	—	2	3	no	—
49	#127×C₁₀₁	—	2	3	no	—
50	#124×C₁₀₁	—	2	3	no	—
51	#123×C₁₀₁	—	2	3	no	—
52	C₂²⋊Q₈×C₁₀₁	—	2	3	no	—
53	C₂²⋊Q₈×C₁₀₁	C₂×C₄	1	3	yes	—
54	C₂²⋊Q₈×C₁₀₁	C₂³	1	1	yes	characteristic
55	#121×C₁₀₁	—	2	6	no	—
56	#121×C₁₀₁	—	2	3	no	—
57	#121×C₁₀₁	—	2	3	no	—
58	#121×C₁₀₁	—	2	3	no	—
59	#121×C₁₀₁	C₂×C₄	1	6	yes	—
60	#121×C₁₀₁	C₂×C₄	1	3	yes	—
61	#121×C₁₀₁	C₂³	1	3	yes	—
62	#120×C₁₀₁	—	2	3	no	—
63	#120×C₁₀₁	—	2	6	no	—
64	C₄×Q₈×C₁₀₁	—	2	1	no	—
65	C₄×Q₈×C₁₀₁	—	4	4	no	—
66	C₄×D₄×C₁₀₁	—	2	3	no	—
67	C₄×D₄×C₁₀₁	—	2	3	no	—
68	C₄×D₄×C₁₀₁	—	2	3	no	—
69	#117×C₁₀₁	C₂×C₄	1	3	yes	—
70	C₂×C₄⋊C₄×C₁₀₁	—	2	3	no	—
71	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	3	yes	—
72	C₂×C₂²⋊C₄×C₁₀₁	—	2	3	no	—
73	C₂×C₂²⋊C₄×C₁₀₁	—	2	3	no	—
74	C₂×C₂²⋊C₄×C₁₀₁	—	2	3	no	—
75	C₂×C₄²×C₁₀₁	—	2	3	no	—
76	C₂²⋊C₈×C₁₀₁	—	2	3	no	—
77	C₂²⋊C₈×C₁₀₁	—	2	3	no	—
78	C₂²⋊C₈×C₁₀₁	C₂³	1	1	yes	characteristic
79	C₂²⋊C₈×C₁₀₁	C₂³	1	3	yes	—
80	#95×C₁₀₁	C₂³	1	1	yes	characteristic
81	#95×C₁₀₁	C₂³	1	3	yes	—
82	C₂⁴×C₁₀₁	—	2	3	no	—
83	C₂⁴×C₁₀₁	C₂×D₄	1	3	yes	—
84	#41×C₁₀₁	—	2	4	no	—
85	#41×C₁₀₁	—	2	4	no	—
86	#41×C₁₀₁	—	4	6	no	—
87	#41×C₁₀₁	—	4	6	no	—
88	#41×C₁₀₁	—	4	6	no	—
89	#41×C₁₀₁	—	4	4	no	—
90	C₂×Q₈×C₁₀₁	—	2	4	no	—
91	C₂×Q₈×C₁₀₁	C₂²⋊C₄	1	3	yes	—
92	C₂×Q₈×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
93	C₂×Q₈×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
94	C₂×D₄×C₁₀₁	—	2	3	no	—
95	C₂×D₄×C₁₀₁	—	2	3	no	—
96	C₂×D₄×C₁₀₁	—	2	3	no	—
97	C₂×D₄×C₁₀₁	—	2	6	no	—
98	C₂×D₄×C₁₀₁	—	2	3	no	—
99	C₂×D₄×C₁₀₁	—	4	6	no	—
100	C₂×D₄×C₁₀₁	—	4	6	no	—
101	C₂×D₄×C₁₀₁	—	4	12	no	—
102	C₂×D₄×C₁₀₁	—	8	3	no	—
103	C₂×D₄×C₁₀₁	—	8	3	no	—
104	C₂×D₄×C₁₀₁	C₂²⋊C₄	1	3	yes	—
105	C₂×D₄×C₁₀₁	C₂²⋊C₄	1	3	yes	—
106	C₂×D₄×C₁₀₁	C₂²⋊C₄	1	6	yes	—
107	C₂×D₄×C₁₀₁	C₂²×C₄	1	3	yes	—
108	C₂²×C₄×C₁₀₁	—	2	1	no	—
109	C₂²×C₄×C₁₀₁	—	2	3	no	—
110	C₂²×C₄×C₁₀₁	—	2	3	no	—
111	C₂²×C₄×C₁₀₁	—	2	3	no	—
112	C₂²×C₄×C₁₀₁	—	4	6	no	—
113	C₂²×C₄×C₁₀₁	C₂²×C₄	1	3	yes	—
114	C₂²×C₄×C₁₀₁	C₂²×C₄	1	3	yes	—
115	C₂²×C₄×C₁₀₁	C₂×D₄	1	3	yes	—
116	C₂²×C₄×C₁₀₁	C₂×D₄	1	3	yes	—
117	C₂²×C₄×C₁₀₁	C₂×D₄	1	3	yes	—
118	C₂²×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
119	M₁₆×C₁₀₁	—	4	6	no	—
120	C₂×C₈×C₁₀₁	—	2	1	no	—
121	C₂×C₈×C₁₀₁	—	2	3	no	—
122	C₂×C₈×C₁₀₁	—	4	6	no	—
123	C₄⋊C₄×C₁₀₁	—	2	3	no	—
124	C₄⋊C₄×C₁₀₁	—	2	3	no	—
125	C₄⋊C₄×C₁₀₁	—	2	1	no	—
126	C₄⋊C₄×C₁₀₁	—	4	6	no	—
127	C₄⋊C₄×C₁₀₁	C₂²×C₄	1	3	yes	—
128	C₄⋊C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
129	C₂²⋊C₄×C₁₀₁	—	2	3	no	—
130	C₂²⋊C₄×C₁₀₁	—	2	3	no	—
131	C₂²⋊C₄×C₁₀₁	—	2	1	no	—
132	C₂²⋊C₄×C₁₀₁	—	2	6	no	—
133	C₂²⋊C₄×C₁₀₁	—	2	3	no	—
134	C₂²⋊C₄×C₁₀₁	—	2	3	no	—
135	C₂²⋊C₄×C₁₀₁	—	4	6	no	—
136	C₂²⋊C₄×C₁₀₁	—	8	3	no	—
137	C₄²×C₁₀₁	—	2	3	no	—
138	C₄²×C₁₀₁	—	4	6	no	—
139	C₂³×C₁₀₁	—	2	3	no	—
140	C₂³×C₁₀₁	—	2	3	no	—
141	C₂³×C₁₀₁	—	2	3	no	—
142	C₂³×C₁₀₁	—	4	3	no	—
143	C₂³×C₁₀₁	—	4	3	no	—
144	C₂³×C₁₀₁	—	4	6	no	—
145	C₂³×C₁₀₁	—	8	3	no	—
146	C₂³×C₁₀₁	—	8	3	no	—
147	C₂³×C₁₀₁	C₂×C₂²⋊C₄	1	3	yes	—
148	C₂³×C₁₀₁	C₂×C₂²⋊C₄	1	3	yes	—
149	C₂³×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
150	Q₈×C₁₀₁	—	2	6	no	—
151	Q₈×C₁₀₁	—	4	1	no	—
152	Q₈×C₁₀₁	#99	1	4	yes	—
153	D₄×C₁₀₁	—	2	6	no	—
154	D₄×C₁₀₁	—	2	6	no	—
155	D₄×C₁₀₁	—	4	6	no	—
156	D₄×C₁₀₁	—	4	3	no	—
157	D₄×C₁₀₁	—	4	6	no	—
158	D₄×C₁₀₁	—	4	3	no	—
159	D₄×C₁₀₁	—	4	3	no	—
160	D₄×C₁₀₁	—	4	6	no	—
161	D₄×C₁₀₁	—	8	3	no	—
162	D₄×C₁₀₁	—	8	6	no	—
163	C₂×C₄×C₁₀₁	—	2	6	no	—
164	C₂×C₄×C₁₀₁	—	2	6	no	—
165	C₂×C₄×C₁₀₁	—	2	6	no	—
166	C₂×C₄×C₁₀₁	—	2	2	no	—
167	C₂×C₄×C₁₀₁	—	2	1	no	—
168	C₂×C₄×C₁₀₁	—	2	3	no	—
169	C₂×C₄×C₁₀₁	—	2	1	no	—
170	C₂×C₄×C₁₀₁	—	4	1	no	—
171	C₂×C₄×C₁₀₁	—	4	3	no	—
172	C₂×C₄×C₁₀₁	—	4	3	no	—
173	C₂×C₄×C₁₀₁	—	4	1	no	—
174	C₂×C₄×C₁₀₁	—	4	1	no	—
175	C₂×C₄×C₁₀₁	—	4	6	no	—
176	C₂×C₄×C₁₀₁	—	4	3	no	—
177	C₂×C₄×C₁₀₁	—	4	3	no	—
178	C₂×C₄×C₁₀₁	—	4	3	no	—
179	C₂×C₄×C₁₀₁	—	8	3	no	—
180	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	3	yes	—
181	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	3	yes	—
182	C₂×C₄×C₁₀₁	C₂³×C₄	1	1	yes	characteristic
183	C₂×C₄×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
184	C₈×C₁₀₁	—	4	1	no	—
185	C₈×C₁₀₁	—	4	3	no	—
186	C₂²×C₁₀₁	—	2	1	no	—
187	C₂²×C₁₀₁	—	2	1	no	—
188	C₂²×C₁₀₁	—	2	3	no	—
189	C₂²×C₁₀₁	—	2	3	no	—
190	C₂²×C₁₀₁	—	2	3	no	—
191	C₂²×C₁₀₁	—	2	3	no	—
192	C₂²×C₁₀₁	—	2	3	no	—
193	C₂²×C₁₀₁	—	2	3	no	—
194	C₂²×C₁₀₁	—	4	3	no	—
195	C₂²×C₁₀₁	—	4	3	no	—
196	C₂²×C₁₀₁	—	4	3	no	—
197	C₂²×C₁₀₁	—	8	3	no	—
198	C₂²×C₁₀₁	—	8	3	no	—
199	C₂²×C₁₀₁	—	16	6	no	—
200	C₂²×C₁₀₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
201	C₂²×C₁₀₁	#576	1	1	yes	characteristic
202	C₂²×C₁₀₁	#577	1	1	yes	characteristic
203	C₄×C₁₀₁	—	2	1	no	—
204	C₄×C₁₀₁	—	2	1	no	—
205	C₄×C₁₀₁	—	2	3	no	—
206	C₄×C₁₀₁	—	4	2	no	—
207	C₄×C₁₀₁	—	4	1	no	—
208	C₄×C₁₀₁	—	4	3	no	—
209	C₄×C₁₀₁	—	4	1	no	—
210	C₄×C₁₀₁	—	8	3	no	—
211	C₄×C₁₀₁	C₂×#99	1	6	yes	—
212	#17611	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
213	C₂×C₁₀₁	—	2	1	no	—
214	C₂×C₁₀₁	—	2	1	no	—
215	C₂×C₁₀₁	—	4	3	no	—
216	C₂×C₁₀₁	—	4	3	no	—
217	C₂×C₁₀₁	—	8	3	no	—
218	C₂×C₁₀₁	C₂²×#99	1	1	yes	characteristic
219	C₂×C₁₀₁	#2897	1	1	yes	characteristic
220	C₂×C₁₀₁	#2901	1	1	yes	characteristic
221	#3488	C₂×C₁₀₁	1	1	yes	characteristic
222	#2880	C₂×C₁₀₁	1	1	yes	characteristic, complemented
223	#2341	C₂×C₁₀₁	1	1	yes	characteristic, complemented
224	#1519	C₂×C₁₀₁	1	3	yes	complemented
225	#1513	C₂×C₁₀₁	1	3	yes	complemented
226	#1507	C₂×C₁₀₁	1	3	yes	complemented
227	#1501	C₂×C₁₀₁	1	3	yes	complemented
228	C₁₀₁	#17611	1	1	yes	characteristic, direct product factor, Sylow
229	C₂×H(5,𝔽₂)	C₄×C₁₀₁	1	1	yes	characteristic, complemented
230	C₂²×#41	C₂²×C₁₀₁	1	1	yes	characteristic
231	C₂×#131	—	2	1	no	—
232	#550	—	2	1	no	—
233	#548	—	2	1	no	—
234	#546	—	2	3	no	—
235	D₄²	—	2	3	no	—
236	#537	C₄×C₁₀₁	1	3	yes	complemented
237	#535	C₄×C₁₀₁	1	3	yes	complemented
238	#525	C₂²×C₁₀₁	1	3	yes	—
239	C₂×#121	C₂²×C₁₀₁	1	3	yes	—
240	#520	C₄×C₁₀₁	1	1	yes	characteristic, complemented
241	C₂×C₄×Q₈	—	2	1	no	—
242	#408	—	2	3	no	—
243	#407	C₂²×C₁₀₁	1	3	yes	complemented
244	C₂×C₂²⋊C₈	C₂²×C₁₀₁	1	3	yes	complemented
245	#390	—	2	3	no	—
246	#380	C₂²×C₁₀₁	1	3	yes	complemented
247	C₄×C₂²⋊C₄	C₂²×C₁₀₁	1	3	yes	complemented
248	#328	C₂²×C₁₀₁	1	1	yes	characteristic, complemented
249	#328	C₂²×C₁₀₁	1	3	yes	complemented
250	#327	C₂²×C₁₀₁	1	3	yes	complemented
251	#327	C₂²×C₁₀₁	1	3	yes	complemented
252	#327	C₂²×C₁₀₁	1	6	yes	complemented
253	H(5,𝔽₂)	—	4	4	no	—
254	C₂×#41	—	2	1	no	—
255	C₂×#41	—	4	4	no	—
256	C₂×#41	C₂×C₄×C₁₀₁	1	3	yes	—
257	C₂×#41	C₂×C₄×C₁₀₁	1	1	yes	characteristic
258	C₂×#41	C₂×C₄×C₁₀₁	1	3	yes	—
259	C₂×#41	D₄×C₁₀₁	1	1	yes	characteristic
260	C₂×#41	D₄×C₁₀₁	1	3	yes	—
261	C₂²×Q₈	D₄×C₁₀₁	1	1	yes	characteristic
262	C₂²×D₄	—	2	3	no	—
263	C₂²×D₄	—	2	3	no	—
264	C₂²×D₄	C₂×C₄×C₁₀₁	1	3	yes	—
265	C₂²×D₄	D₄×C₁₀₁	1	3	yes	—
266	C₂³×C₄	C₂³×C₁₀₁	1	3	yes	—
267	#131	—	4	4	no	—
268	C₂×M₁₆	—	2	3	no	—
269	C₂²×C₈	—	2	3	no	—
270	#127	—	2	3	no	—
271	#124	—	2	3	no	—
272	#123	—	2	3	no	—
273	C₂²⋊Q₈	—	2	3	no	—
274	C₂²⋊Q₈	C₂×C₄×C₁₀₁	1	3	yes	—
275	C₂²⋊Q₈	C₂³×C₁₀₁	1	1	yes	characteristic
276	#121	—	2	6	no	—
277	#121	—	2	3	no	—
278	#121	—	2	3	no	—
279	#121	—	2	3	no	—
280	#121	C₂×C₄×C₁₀₁	1	6	yes	—
281	#121	C₂×C₄×C₁₀₁	1	3	yes	—
282	#121	C₂³×C₁₀₁	1	3	yes	—
283	#120	—	2	3	no	—
284	#120	—	2	6	no	—
285	C₄×Q₈	—	2	1	no	—
286	C₄×Q₈	—	4	4	no	—
287	C₄×D₄	—	2	3	no	—
288	C₄×D₄	—	2	3	no	—
289	C₄×D₄	—	2	3	no	—
290	#117	C₂×C₄×C₁₀₁	1	3	yes	—
291	C₂×C₄⋊C₄	—	2	3	no	—
292	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	3	yes	—
293	C₂×C₂²⋊C₄	—	2	3	no	—
294	C₂×C₂²⋊C₄	—	2	3	no	—
295	C₂×C₂²⋊C₄	—	2	3	no	—
296	C₂×C₄²	—	2	3	no	—
297	C₂²⋊C₈	—	2	3	no	—
298	C₂²⋊C₈	—	2	3	no	—
299	C₂²⋊C₈	C₂³×C₁₀₁	1	1	yes	characteristic
300	C₂²⋊C₈	C₂³×C₁₀₁	1	3	yes	—
301	#95	C₂³×C₁₀₁	1	1	yes	characteristic
302	#95	C₂³×C₁₀₁	1	3	yes	—
303	C₂⁴	—	2	3	no	—
304	C₂⁴	C₂×D₄×C₁₀₁	1	3	yes	—
305	#41	—	2	4	no	—
306	#41	—	2	4	no	—
307	#41	—	4	6	no	—
308	#41	—	4	6	no	—
309	#41	—	4	6	no	—
310	#41	—	4	4	no	—
311	C₂×Q₈	—	2	4	no	—
312	C₂×Q₈	C₂²⋊C₄×C₁₀₁	1	3	yes	—
313	C₂×Q₈	C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
314	C₂×Q₈	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
315	C₂×D₄	—	2	3	no	—
316	C₂×D₄	—	2	3	no	—
317	C₂×D₄	—	2	3	no	—
318	C₂×D₄	—	2	6	no	—
319	C₂×D₄	—	2	3	no	—
320	C₂×D₄	—	4	6	no	—
321	C₂×D₄	—	4	6	no	—
322	C₂×D₄	—	4	12	no	—
323	C₂×D₄	—	8	3	no	—
324	C₂×D₄	—	8	3	no	—
325	C₂×D₄	C₂²⋊C₄×C₁₀₁	1	3	yes	—
326	C₂×D₄	C₂²⋊C₄×C₁₀₁	1	3	yes	—
327	C₂×D₄	C₂²⋊C₄×C₁₀₁	1	6	yes	—
328	C₂×D₄	C₂²×C₄×C₁₀₁	1	3	yes	—
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	2	3	no	—
331	C₂²×C₄	—	2	3	no	—
332	C₂²×C₄	—	2	3	no	—
333	C₂²×C₄	—	4	6	no	—
334	C₂²×C₄	C₂²×C₄×C₁₀₁	1	3	yes	—
335	C₂²×C₄	C₂²×C₄×C₁₀₁	1	3	yes	—
336	C₂²×C₄	C₂×D₄×C₁₀₁	1	3	yes	—
337	C₂²×C₄	C₂×D₄×C₁₀₁	1	3	yes	—
338	C₂²×C₄	C₂×D₄×C₁₀₁	1	3	yes	—
339	C₂²×C₄	C₂⁴×C₁₀₁	1	1	yes	characteristic
340	M₁₆	—	4	6	no	—
341	C₂×C₈	—	2	1	no	—
342	C₂×C₈	—	2	3	no	—
343	C₂×C₈	—	4	6	no	—
344	C₄⋊C₄	—	2	3	no	—
345	C₄⋊C₄	—	2	3	no	—
346	C₄⋊C₄	—	2	1	no	—
347	C₄⋊C₄	—	4	6	no	—
348	C₄⋊C₄	C₂²×C₄×C₁₀₁	1	3	yes	—
349	C₄⋊C₄	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
350	C₂²⋊C₄	—	2	3	no	—
351	C₂²⋊C₄	—	2	3	no	—
352	C₂²⋊C₄	—	2	1	no	—
353	C₂²⋊C₄	—	2	6	no	—
354	C₂²⋊C₄	—	2	3	no	—
355	C₂²⋊C₄	—	2	3	no	—
356	C₂²⋊C₄	—	4	6	no	—
357	C₂²⋊C₄	—	8	3	no	—
358	C₄²	—	2	3	no	—
359	C₄²	—	4	6	no	—
360	C₂³	—	2	3	no	—
361	C₂³	—	2	3	no	—
362	C₂³	—	2	3	no	—
363	C₂³	—	4	3	no	—
364	C₂³	—	4	3	no	—
365	C₂³	—	4	6	no	—
366	C₂³	—	8	3	no	—
367	C₂³	—	8	3	no	—
368	C₂³	C₂×C₂²⋊C₄×C₁₀₁	1	3	yes	—
369	C₂³	C₂×C₂²⋊C₄×C₁₀₁	1	3	yes	—
370	C₂³	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
371	Q₈	—	2	6	no	—
372	Q₈	—	4	1	no	—
373	Q₈	#99×C₁₀₁	1	4	yes	—
374	D₄	—	2	6	no	—
375	D₄	—	2	6	no	—
376	D₄	—	4	6	no	—
377	D₄	—	4	3	no	—
378	D₄	—	4	6	no	—
379	D₄	—	4	3	no	—
380	D₄	—	4	3	no	—
381	D₄	—	4	6	no	—
382	D₄	—	8	6	no	—
383	D₄	—	8	3	no	—
384	C₂×C₄	—	2	6	no	—
385	C₂×C₄	—	2	6	no	—
386	C₂×C₄	—	2	6	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	3	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	3	no	—
393	C₂×C₄	—	4	3	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	6	no	—
397	C₂×C₄	—	4	3	no	—
398	C₂×C₄	—	4	3	no	—
399	C₂×C₄	—	4	3	no	—
400	C₂×C₄	—	8	3	no	—
401	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	3	yes	—
402	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	3	yes	—
403	C₂×C₄	C₂³×C₄×C₁₀₁	1	1	yes	characteristic
404	C₂×C₄	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
405	C₈	—	4	1	no	—
406	C₈	—	4	3	no	—
407	C₂²	—	2	1	no	—
408	C₂²	—	2	1	no	—
409	C₂²	—	2	3	no	—
410	C₂²	—	2	3	no	—
411	C₂²	—	2	3	no	—
412	C₂²	—	2	3	no	—
413	C₂²	—	2	3	no	—
414	C₂²	—	2	3	no	—
415	C₂²	—	4	3	no	—
416	C₂²	—	4	3	no	—
417	C₂²	—	4	3	no	—
418	C₂²	—	8	3	no	—
419	C₂²	—	8	3	no	—
420	C₂²	—	16	6	no	—
421	C₂²	C₂²×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
422	C₂²	#576×C₁₀₁	1	1	yes	characteristic
423	C₂²	#577×C₁₀₁	1	1	yes	characteristic
424	C₄	—	2	1	no	—
425	C₄	—	2	1	no	—
426	C₄	—	2	3	no	—
427	C₄	—	4	2	no	—
428	C₄	—	4	1	no	—
429	C₄	—	4	3	no	—
430	C₄	—	4	1	no	—
431	C₄	—	8	3	no	—
432	C₄	C₂×#99×C₁₀₁	1	6	yes	—
433	C₂	—	2	1	no	—
434	C₂	—	2	1	no	—
435	C₂	—	4	3	no	—
436	C₂	—	4	3	no	—
437	C₂	—	8	3	no	—
438	C₂	C₂²×#99×C₁₀₁	1	1	yes	characteristic
439	C₂	C₁₀₁×#2897	1	1	yes	characteristic
440	C₂	C₁₀₁×#2901	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₀₁	C₂²×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₁₀₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₀₁
prime radical	C₁₀₁×#3488	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₁ ◁ C₂²×#41×C₁₀₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₀₁×#2880	C₂	semidirect
3. C₁₀₁×#2341	C₂	semidirect
4. C₁₀₁×#1519	C₂	semidirect
5. C₁₀₁×#1513	C₂	semidirect
6. C₁₀₁×#1507	C₂	semidirect
7. C₁₀₁×#1501	C₂	semidirect
8. C₂×H(5,𝔽₂)×C₁₀₁	C₄	semidirect
15. #537×C₁₀₁	C₄	semidirect
16. #535×C₁₀₁	C₄	semidirect
19. #520×C₁₀₁	C₄	semidirect
22. #407×C₁₀₁	C₂²	semidirect
23. C₂×C₂²⋊C₈×C₁₀₁	C₂²	semidirect
25. #380×C₁₀₁	C₂²	semidirect
26. C₄×C₂²⋊C₄×C₁₀₁	C₂²	semidirect
27. #328×C₁₀₁	C₂²	semidirect
28. #328×C₁₀₁	C₂²	semidirect
29. #327×C₁₀₁	C₂²	semidirect
30. #327×C₁₀₁	C₂²	semidirect
31. #327×C₁₀₁	C₂²	semidirect
212. #17611	C₁₀₁	direct (N × H)
222. #2880	C₂×C₁₀₁	semidirect
223. #2341	C₂×C₁₀₁	semidirect
224. #1519	C₂×C₁₀₁	semidirect
225. #1513	C₂×C₁₀₁	semidirect
226. #1507	C₂×C₁₀₁	semidirect
227. #1501	C₂×C₁₀₁	semidirect
228. C₁₀₁	#17611	direct (N × H)
229. C₂×H(5,𝔽₂)	C₄×C₁₀₁	semidirect
236. #537	C₄×C₁₀₁	semidirect
237. #535	C₄×C₁₀₁	semidirect
240. #520	C₄×C₁₀₁	semidirect
243. #407	C₂²×C₁₀₁	semidirect
244. C₂×C₂²⋊C₈	C₂²×C₁₀₁	semidirect
246. #380	C₂²×C₁₀₁	semidirect
247. C₄×C₂²⋊C₄	C₂²×C₁₀₁	semidirect
248. #328	C₂²×C₁₀₁	semidirect
249. #328	C₂²×C₁₀₁	semidirect
250. #327	C₂²×C₁₀₁	semidirect
251. #327	C₂²×C₁₀₁	semidirect
252. #327	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×#3488	2
C₁₀₁×#2880	2
C₁₀₁×#2341	2
C₁₀₁×#1519	2
C₁₀₁×#1513	2
C₁₀₁×#1507	2
C₁₀₁×#1501	2
#17611	101

Subgroups — C101×#17611 #38799762

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#17611 #38799762