Subgroups — C₂×C₁₀₁×#1717 #38801760

Order 25856.

966 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#493×C₁₀₁	C₂	1	1	yes	maximal, characteristic
2	C₂×#492×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#487×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#486×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#486×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#486×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₀₁×#1717	C₂	1	8	yes	maximal, direct product factor
8	C₂×#322×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×SD₁₆×C₁₀₁	—	2	2	no	—
10	C₂²×D₈×C₁₀₁	—	2	2	no	—
11	C₂×C₄⋊Q₈×C₁₀₁	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊Q₈×C₁₀₁	C₂²	1	1	yes	characteristic
13	C₂×#127×C₁₀₁	C₂²	1	1	yes	characteristic
14	C₂×#127×C₁₀₁	C₂²	1	1	yes	characteristic
15	#493×C₁₀₁	—	2	2	no	—
16	#493×C₁₀₁	C₂²	1	4	yes	—
17	#492×C₁₀₁	—	2	2	no	—
18	#492×C₁₀₁	C₂²	1	4	yes	complemented
19	#487×C₁₀₁	—	2	2	no	—
20	#487×C₁₀₁	C₂²	1	4	yes	complemented
21	#486×C₁₀₁	—	2	2	no	—
22	#486×C₁₀₁	—	2	2	no	—
23	#486×C₁₀₁	—	2	2	no	—
24	#486×C₁₀₁	C₂²	1	4	yes	complemented
25	#486×C₁₀₁	C₂²	1	4	yes	complemented
26	#486×C₁₀₁	C₂²	1	4	yes	complemented
27	C₂×#103×C₁₀₁	—	2	2	no	—
28	C₂×#102×C₁₀₁	—	2	2	no	—
29	C₂×#102×C₁₀₁	—	2	2	no	—
30	C₂×#102×C₁₀₁	—	2	2	no	—
31	C₂×C₄×C₈×C₁₀₁	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₈×C₁₀₁	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₈×C₁₀₁	C₂²	1	1	yes	characteristic
34	#322×C₁₀₁	C₂²	1	4	yes	complemented
35	C₂²×Q₈×C₁₀₁	—	2	1	no	—
36	C₂²×Q₈×C₁₀₁	—	2	1	no	—
37	C₂²×D₄×C₁₀₁	—	2	1	no	—
38	C₂²×D₄×C₁₀₁	—	2	1	no	—
39	C₂²×D₄×C₁₀₁	—	2	1	no	—
40	C₂²×D₄×C₁₀₁	—	2	1	no	—
41	C₂²×D₄×C₁₀₁	—	2	1	no	—
42	C₂²×D₄×C₁₀₁	—	2	1	no	—
43	C₂×SD₁₆×C₁₀₁	—	2	8	no	—
44	C₂×SD₁₆×C₁₀₁	—	4	8	no	—
45	C₂×D₈×C₁₀₁	—	2	8	no	—
46	C₂×D₈×C₁₀₁	—	4	8	no	—
47	C₂²×C₈×C₁₀₁	D₄	1	2	yes	—
48	C₂²×C₈×C₁₀₁	D₄	1	2	yes	—
49	C₂²×C₈×C₁₀₁	D₄	1	2	yes	—
50	C₄⋊Q₈×C₁₀₁	—	2	1	no	—
51	C₄⋊Q₈×C₁₀₁	—	2	1	no	—
52	C₄⋊Q₈×C₁₀₁	—	2	1	no	—
53	C₄⋊Q₈×C₁₀₁	—	2	1	no	—
54	C₄⋊Q₈×C₁₀₁	—	2	1	no	—
55	C₄⋊Q₈×C₁₀₁	—	2	1	no	—
56	C₄⋊Q₈×C₁₀₁	C₂³	1	2	yes	—
57	C₄⋊Q₈×C₁₀₁	C₂³	1	2	yes	—
58	#127×C₁₀₁	—	2	1	no	—
59	#127×C₁₀₁	—	2	1	no	—
60	#127×C₁₀₁	—	2	1	no	—
61	#127×C₁₀₁	—	2	1	no	—
62	#127×C₁₀₁	—	2	1	no	—
63	#127×C₁₀₁	—	2	1	no	—
64	#127×C₁₀₁	C₂³	1	2	yes	—
65	#127×C₁₀₁	C₂³	1	2	yes	—
66	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
67	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
68	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
69	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
70	C₂×C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
71	#103×C₁₀₁	—	2	8	no	—
72	#102×C₁₀₁	—	2	8	no	—
73	#102×C₁₀₁	—	2	8	no	—
74	#102×C₁₀₁	—	2	8	no	—
75	C₄×C₈×C₁₀₁	D₄	1	2	yes	—
76	C₄×C₈×C₁₀₁	D₄	1	2	yes	—
77	C₄×C₈×C₁₀₁	D₄	1	2	yes	—
78	C₄×C₈×C₁₀₁	C₂³	1	2	yes	—
79	C₄×C₈×C₁₀₁	C₂³	1	2	yes	—
80	C₄×C₈×C₁₀₁	C₂³	1	2	yes	—
81	C₂⁴×C₁₀₁	—	4	1	no	—
82	C₂⁴×C₁₀₁	—	4	1	no	—
83	C₂×Q₈×C₁₀₁	—	2	2	no	—
84	C₂×Q₈×C₁₀₁	—	2	2	no	—
85	C₂×Q₈×C₁₀₁	—	4	1	no	—
86	C₂×Q₈×C₁₀₁	—	4	1	no	—
87	C₂×Q₈×C₁₀₁	—	4	4	no	—
88	C₂×Q₈×C₁₀₁	—	4	4	no	—
89	C₂×D₄×C₁₀₁	—	2	2	no	—
90	C₂×D₄×C₁₀₁	—	2	2	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	1	no	—
96	C₂×D₄×C₁₀₁	—	4	1	no	—
97	C₂×D₄×C₁₀₁	—	4	1	no	—
98	C₂×D₄×C₁₀₁	—	4	1	no	—
99	C₂×D₄×C₁₀₁	—	4	1	no	—
100	C₂×D₄×C₁₀₁	—	4	1	no	—
101	C₂×D₄×C₁₀₁	—	4	4	no	—
102	C₂×D₄×C₁₀₁	—	4	4	no	—
103	C₂×D₄×C₁₀₁	—	4	4	no	—
104	C₂×D₄×C₁₀₁	—	4	4	no	—
105	C₂×D₄×C₁₀₁	—	4	4	no	—
106	C₂×D₄×C₁₀₁	—	4	4	no	—
107	C₂²×C₄×C₁₀₁	—	4	1	no	—
108	C₂²×C₄×C₁₀₁	—	4	1	no	—
109	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
112	SD₁₆×C₁₀₁	—	4	16	no	—
113	D₈×C₁₀₁	—	4	16	no	—
114	C₂×C₈×C₁₀₁	—	2	4	no	—
115	C₂×C₈×C₁₀₁	—	2	4	no	—
116	C₂×C₈×C₁₀₁	—	2	4	no	—
117	C₂×C₈×C₁₀₁	C₂×D₄	1	4	yes	—
118	C₂×C₈×C₁₀₁	C₂×D₄	1	4	yes	—
119	C₂×C₈×C₁₀₁	C₂×D₄	1	4	yes	—
120	C₄⋊C₄×C₁₀₁	—	2	2	no	—
121	C₄⋊C₄×C₁₀₁	—	2	2	no	—
122	C₄⋊C₄×C₁₀₁	—	2	2	no	—
123	C₄⋊C₄×C₁₀₁	—	2	2	no	—
124	C₄⋊C₄×C₁₀₁	—	4	1	no	—
125	C₄⋊C₄×C₁₀₁	—	4	1	no	—
126	C₄⋊C₄×C₁₀₁	—	4	1	no	—
127	C₄⋊C₄×C₁₀₁	—	4	1	no	—
128	C₄²×C₁₀₁	C₂×D₄	1	1	yes	characteristic
129	C₄²×C₁₀₁	C₂×D₄	1	1	yes	characteristic
130	C₄²×C₁₀₁	C₂×D₄	1	1	yes	characteristic
131	C₄²×C₁₀₁	C₂⁴	1	1	yes	characteristic
132	C₂³×C₁₀₁	—	4	2	no	—
133	C₂³×C₁₀₁	—	4	2	no	—
134	C₂³×C₁₀₁	—	8	2	no	—
135	C₂³×C₁₀₁	—	8	2	no	—
136	C₂³×C₁₀₁	—	8	2	no	—
137	C₂³×C₁₀₁	—	8	2	no	—
138	C₂³×C₁₀₁	—	8	2	no	—
139	C₂³×C₁₀₁	—	8	2	no	—
140	C₂³×C₁₀₁	#127	1	1	yes	characteristic
141	Q₈×C₁₀₁	—	4	4	no	—
142	Q₈×C₁₀₁	—	4	4	no	—
143	Q₈×C₁₀₁	—	8	2	no	—
144	Q₈×C₁₀₁	—	8	2	no	—
145	D₄×C₁₀₁	—	4	4	no	—
146	D₄×C₁₀₁	—	4	4	no	—
147	D₄×C₁₀₁	—	4	4	no	—
148	D₄×C₁₀₁	—	4	4	no	—
149	D₄×C₁₀₁	—	4	4	no	—
150	D₄×C₁₀₁	—	4	4	no	—
151	D₄×C₁₀₁	—	8	2	no	—
152	D₄×C₁₀₁	—	8	2	no	—
153	D₄×C₁₀₁	—	8	2	no	—
154	D₄×C₁₀₁	—	8	2	no	—
155	D₄×C₁₀₁	—	8	2	no	—
156	D₄×C₁₀₁	—	8	2	no	—
157	C₂×C₄×C₁₀₁	—	4	2	no	—
158	C₂×C₄×C₁₀₁	—	4	2	no	—
159	C₂×C₄×C₁₀₁	—	8	2	no	—
160	C₂×C₄×C₁₀₁	—	8	2	no	—
161	C₂×C₄×C₁₀₁	#127	1	1	yes	characteristic
162	C₂×C₄×C₁₀₁	#127	1	1	yes	characteristic
163	C₂×C₄×C₁₀₁	#127	1	1	yes	characteristic
164	C₂×C₄×C₁₀₁	#135	1	4	yes	—
165	C₂×C₄×C₁₀₁	AGL(1,ℤ/8)	1	4	yes	—
166	C₂×C₄×C₁₀₁	AGL(1,ℤ/8)	1	4	yes	—
167	C₂×C₄×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
168	C₂×C₄×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
170	C₈×C₁₀₁	—	2	4	no	—
171	C₈×C₁₀₁	—	2	4	no	—
172	C₈×C₁₀₁	—	2	4	no	—
173	C₂²×C₁₀₁	—	8	2	no	—
174	C₂²×C₁₀₁	—	8	2	no	—
175	C₂²×C₁₀₁	—	8	2	no	—
176	C₂²×C₁₀₁	—	8	2	no	—
177	C₂²×C₁₀₁	—	8	2	no	—
178	C₂²×C₁₀₁	—	8	2	no	—
179	C₂²×C₁₀₁	—	16	4	no	—
180	C₂²×C₁₀₁	—	16	4	no	—
181	C₂²×C₁₀₁	#495	1	2	yes	—
182	C₂²×C₁₀₁	#496	1	2	yes	—
183	C₂²×C₁₀₁	#496	1	2	yes	—
184	C₂²×C₁₀₁	C₂×#127	1	1	yes	characteristic
185	C₄×C₁₀₁	—	8	2	no	—
186	C₄×C₁₀₁	—	8	2	no	—
187	C₄×C₁₀₁	#495	1	2	yes	—
188	C₄×C₁₀₁	#496	1	2	yes	—
189	C₄×C₁₀₁	#496	1	2	yes	—
190	C₄×C₁₀₁	C₂×#135	1	2	yes	—
191	C₄×C₁₀₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
192	C₄×C₁₀₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
193	C₂×#1717	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
194	C₂×C₁₀₁	—	16	2	no	—
195	C₂×C₁₀₁	—	16	2	no	—
196	C₂×C₁₀₁	#1717	1	4	yes	direct product factor
197	C₂×C₁₀₁	C₂×#495	1	1	yes	characteristic
198	C₂×C₁₀₁	C₂×#496	1	1	yes	characteristic
199	C₂×C₁₀₁	C₂×#496	1	1	yes	characteristic
200	C₂×#493	C₂×C₁₀₁	1	1	yes	characteristic
201	C₂×#492	C₂×C₁₀₁	1	1	yes	characteristic, complemented
202	C₂×#487	C₂×C₁₀₁	1	1	yes	characteristic, complemented
203	C₂×#486	C₂×C₁₀₁	1	1	yes	characteristic, complemented
204	C₂×#486	C₂×C₁₀₁	1	1	yes	characteristic, complemented
205	C₂×#486	C₂×C₁₀₁	1	1	yes	characteristic, complemented
206	#1717	C₂×C₁₀₁	1	8	yes	direct product factor
207	C₂×#322	C₂×C₁₀₁	1	1	yes	characteristic, complemented
208	C₁₀₁	C₂×#1717	1	1	yes	characteristic, direct product factor, Sylow
209	C₂²×SD₁₆	—	2	2	no	—
210	C₂²×D₈	—	2	2	no	—
211	C₂×C₄⋊Q₈	C₂²×C₁₀₁	1	1	yes	characteristic
212	C₂×C₄⋊Q₈	C₂²×C₁₀₁	1	1	yes	characteristic
213	C₂×#127	C₂²×C₁₀₁	1	1	yes	characteristic
214	C₂×#127	C₂²×C₁₀₁	1	1	yes	characteristic
215	#493	—	2	2	no	—
216	#493	C₂²×C₁₀₁	1	4	yes	—
217	#492	—	2	2	no	—
218	#492	C₂²×C₁₀₁	1	4	yes	complemented
219	#487	—	2	2	no	—
220	#487	C₂²×C₁₀₁	1	4	yes	complemented
221	#486	—	2	2	no	—
222	#486	—	2	2	no	—
223	#486	—	2	2	no	—
224	#486	C₂²×C₁₀₁	1	4	yes	complemented
225	#486	C₂²×C₁₀₁	1	4	yes	complemented
226	#486	C₂²×C₁₀₁	1	4	yes	complemented
227	C₂×#103	—	2	2	no	—
228	C₂×#102	—	2	2	no	—
229	C₂×#102	—	2	2	no	—
230	C₂×#102	—	2	2	no	—
231	C₂×C₄×C₈	C₂²×C₁₀₁	1	1	yes	characteristic
232	C₂×C₄×C₈	C₂²×C₁₀₁	1	1	yes	characteristic
233	C₂×C₄×C₈	C₂²×C₁₀₁	1	1	yes	characteristic
234	#322	C₂²×C₁₀₁	1	4	yes	complemented
235	C₂²×Q₈	—	2	1	no	—
236	C₂²×Q₈	—	2	1	no	—
237	C₂²×D₄	—	2	1	no	—
238	C₂²×D₄	—	2	1	no	—
239	C₂²×D₄	—	2	1	no	—
240	C₂²×D₄	—	2	1	no	—
241	C₂²×D₄	—	2	1	no	—
242	C₂²×D₄	—	2	1	no	—
243	C₂×SD₁₆	—	2	8	no	—
244	C₂×SD₁₆	—	4	8	no	—
245	C₂×D₈	—	2	8	no	—
246	C₂×D₈	—	4	8	no	—
247	C₂²×C₈	D₄×C₁₀₁	1	2	yes	—
248	C₂²×C₈	D₄×C₁₀₁	1	2	yes	—
249	C₂²×C₈	D₄×C₁₀₁	1	2	yes	—
250	C₄⋊Q₈	—	2	1	no	—
251	C₄⋊Q₈	—	2	1	no	—
252	C₄⋊Q₈	—	2	1	no	—
253	C₄⋊Q₈	—	2	1	no	—
254	C₄⋊Q₈	—	2	1	no	—
255	C₄⋊Q₈	—	2	1	no	—
256	C₄⋊Q₈	C₂³×C₁₀₁	1	2	yes	—
257	C₄⋊Q₈	C₂³×C₁₀₁	1	2	yes	—
258	#127	—	2	1	no	—
259	#127	—	2	1	no	—
260	#127	—	2	1	no	—
261	#127	—	2	1	no	—
262	#127	—	2	1	no	—
263	#127	—	2	1	no	—
264	#127	C₂³×C₁₀₁	1	2	yes	—
265	#127	C₂³×C₁₀₁	1	2	yes	—
266	C₂×C₄⋊C₄	—	2	1	no	—
267	C₂×C₄⋊C₄	—	2	1	no	—
268	C₂×C₄⋊C₄	—	2	1	no	—
269	C₂×C₄⋊C₄	—	2	1	no	—
270	C₂×C₄²	C₂³×C₁₀₁	1	1	yes	characteristic
271	#103	—	2	8	no	—
272	#102	—	2	8	no	—
273	#102	—	2	8	no	—
274	#102	—	2	8	no	—
275	C₄×C₈	D₄×C₁₀₁	1	2	yes	—
276	C₄×C₈	D₄×C₁₀₁	1	2	yes	—
277	C₄×C₈	D₄×C₁₀₁	1	2	yes	—
278	C₄×C₈	C₂³×C₁₀₁	1	2	yes	—
279	C₄×C₈	C₂³×C₁₀₁	1	2	yes	—
280	C₄×C₈	C₂³×C₁₀₁	1	2	yes	—
281	C₂⁴	—	4	1	no	—
282	C₂⁴	—	4	1	no	—
283	C₂×Q₈	—	2	2	no	—
284	C₂×Q₈	—	2	2	no	—
285	C₂×Q₈	—	4	1	no	—
286	C₂×Q₈	—	4	1	no	—
287	C₂×Q₈	—	4	4	no	—
288	C₂×Q₈	—	4	4	no	—
289	C₂×D₄	—	2	2	no	—
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	—	2	2	no	—
292	C₂×D₄	—	2	2	no	—
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	—	2	2	no	—
295	C₂×D₄	—	4	1	no	—
296	C₂×D₄	—	4	1	no	—
297	C₂×D₄	—	4	1	no	—
298	C₂×D₄	—	4	1	no	—
299	C₂×D₄	—	4	1	no	—
300	C₂×D₄	—	4	1	no	—
301	C₂×D₄	—	4	4	no	—
302	C₂×D₄	—	4	4	no	—
303	C₂×D₄	—	4	4	no	—
304	C₂×D₄	—	4	4	no	—
305	C₂×D₄	—	4	4	no	—
306	C₂×D₄	—	4	4	no	—
307	C₂²×C₄	—	4	1	no	—
308	C₂²×C₄	—	4	1	no	—
309	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
310	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
311	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
312	SD₁₆	—	4	16	no	—
313	D₈	—	4	16	no	—
314	C₂×C₈	—	2	4	no	—
315	C₂×C₈	—	2	4	no	—
316	C₂×C₈	—	2	4	no	—
317	C₂×C₈	C₂×D₄×C₁₀₁	1	4	yes	—
318	C₂×C₈	C₂×D₄×C₁₀₁	1	4	yes	—
319	C₂×C₈	C₂×D₄×C₁₀₁	1	4	yes	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	2	2	no	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	4	1	no	—
325	C₄⋊C₄	—	4	1	no	—
326	C₄⋊C₄	—	4	1	no	—
327	C₄⋊C₄	—	4	1	no	—
328	C₄²	C₂×D₄×C₁₀₁	1	1	yes	characteristic
329	C₄²	C₂×D₄×C₁₀₁	1	1	yes	characteristic
330	C₄²	C₂×D₄×C₁₀₁	1	1	yes	characteristic
331	C₄²	C₂⁴×C₁₀₁	1	1	yes	characteristic
332	C₂³	—	4	2	no	—
333	C₂³	—	4	2	no	—
334	C₂³	—	8	2	no	—
335	C₂³	—	8	2	no	—
336	C₂³	—	8	2	no	—
337	C₂³	—	8	2	no	—
338	C₂³	—	8	2	no	—
339	C₂³	—	8	2	no	—
340	C₂³	#127×C₁₀₁	1	1	yes	characteristic
341	Q₈	—	4	4	no	—
342	Q₈	—	4	4	no	—
343	Q₈	—	8	2	no	—
344	Q₈	—	8	2	no	—
345	D₄	—	4	4	no	—
346	D₄	—	4	4	no	—
347	D₄	—	4	4	no	—
348	D₄	—	4	4	no	—
349	D₄	—	4	4	no	—
350	D₄	—	4	4	no	—
351	D₄	—	8	2	no	—
352	D₄	—	8	2	no	—
353	D₄	—	8	2	no	—
354	D₄	—	8	2	no	—
355	D₄	—	8	2	no	—
356	D₄	—	8	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	8	2	no	—
360	C₂×C₄	—	8	2	no	—
361	C₂×C₄	#127×C₁₀₁	1	1	yes	characteristic
362	C₂×C₄	#127×C₁₀₁	1	1	yes	characteristic
363	C₂×C₄	#127×C₁₀₁	1	1	yes	characteristic
364	C₂×C₄	#135×C₁₀₁	1	4	yes	—
365	C₂×C₄	AGL(1,ℤ/8)×C₁₀₁	1	4	yes	—
366	C₂×C₄	AGL(1,ℤ/8)×C₁₀₁	1	4	yes	—
367	C₂×C₄	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
368	C₂×C₄	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
369	C₂×C₄	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
370	C₈	—	2	4	no	—
371	C₈	—	2	4	no	—
372	C₈	—	2	4	no	—
373	C₂²	—	8	2	no	—
374	C₂²	—	8	2	no	—
375	C₂²	—	8	2	no	—
376	C₂²	—	8	2	no	—
377	C₂²	—	8	2	no	—
378	C₂²	—	8	2	no	—
379	C₂²	—	16	4	no	—
380	C₂²	—	16	4	no	—
381	C₂²	#495×C₁₀₁	1	2	yes	—
382	C₂²	#496×C₁₀₁	1	2	yes	—
383	C₂²	#496×C₁₀₁	1	2	yes	—
384	C₂²	C₂×#127×C₁₀₁	1	1	yes	characteristic
385	C₄	—	8	2	no	—
386	C₄	—	8	2	no	—
387	C₄	#495×C₁₀₁	1	2	yes	—
388	C₄	#496×C₁₀₁	1	2	yes	—
389	C₄	#496×C₁₀₁	1	2	yes	—
390	C₄	C₂×#135×C₁₀₁	1	2	yes	—
391	C₄	C₂×AGL(1,ℤ/8)×C₁₀₁	1	2	yes	—
392	C₄	C₂×AGL(1,ℤ/8)×C₁₀₁	1	2	yes	—
393	C₂	—	16	2	no	—
394	C₂	—	16	2	no	—
395	C₂	C₁₀₁×#1717	1	4	yes	direct product factor
396	C₂	C₂×#495×C₁₀₁	1	1	yes	characteristic
397	C₂	C₂×#496×C₁₀₁	1	1	yes	characteristic
398	C₂	C₂×#496×C₁₀₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₀₁	#127
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₀₁
prime radical	C₂×#493×C₁₀₁	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₀₁ ◁ C₂×C₄²×C₁₀₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#492×C₁₀₁	C₂	semidirect
3. C₂×#487×C₁₀₁	C₂	semidirect
4. C₂×#486×C₁₀₁	C₂	semidirect
5. C₂×#486×C₁₀₁	C₂	semidirect
6. C₂×#486×C₁₀₁	C₂	semidirect
7. C₁₀₁×#1717	C₂	direct (N × H)
8. C₂×#322×C₁₀₁	C₂	semidirect
18. #492×C₁₀₁	C₂²	semidirect
20. #487×C₁₀₁	C₂²	semidirect
24. #486×C₁₀₁	C₂²	semidirect
25. #486×C₁₀₁	C₂²	semidirect
26. #486×C₁₀₁	C₂²	semidirect
34. #322×C₁₀₁	C₂²	semidirect
193. C₂×#1717	C₁₀₁	direct (N × H)
196. C₂×C₁₀₁	#1717	direct (N × H)
201. C₂×#492	C₂×C₁₀₁	semidirect
202. C₂×#487	C₂×C₁₀₁	semidirect
203. C₂×#486	C₂×C₁₀₁	semidirect
204. C₂×#486	C₂×C₁₀₁	semidirect
205. C₂×#486	C₂×C₁₀₁	semidirect
206. #1717	C₂×C₁₀₁	direct (N × H)
207. C₂×#322	C₂×C₁₀₁	semidirect
208. C₁₀₁	C₂×#1717	direct (N × H)
218. #492	C₂²×C₁₀₁	semidirect
220. #487	C₂²×C₁₀₁	semidirect
224. #486	C₂²×C₁₀₁	semidirect
225. #486	C₂²×C₁₀₁	semidirect
226. #486	C₂²×C₁₀₁	semidirect
234. #322	C₂²×C₁₀₁	semidirect
395. C₂	C₁₀₁×#1717	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×#493×C₁₀₁	2
C₂×#492×C₁₀₁	2
C₂×#487×C₁₀₁	2
C₂×#486×C₁₀₁	2
C₁₀₁×#1717	2
C₂×#322×C₁₀₁	2
C₂×#1717	101

Subgroups — C2×C101×#1717 #38801760

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₀₁×#1717 #38801760