Subgroups — C₂×C₁₀₁×#2039 #38805647

Order 25856.

1586 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#537×C₁₀₁	C₂	1	1	yes	maximal, characteristic
2	C₂²×#104×C₁₀₁	C₂	1	2	yes	maximal, complemented
3	C₂×#417×C₁₀₁	C₂	1	2	yes	maximal, complemented
4	C₂×#384×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₀₁×#2039	C₂	1	8	yes	maximal, direct product factor
6	C₂×#343×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#41×C₁₀₁	C₂²	1	2	yes	—
8	C₂²×M₁₆×C₁₀₁	C₂²	1	2	yes	—
9	#537×C₁₀₁	—	2	4	no	—
10	#537×C₁₀₁	—	2	2	no	—
11	#537×C₁₀₁	C₂²	1	4	yes	—
12	C₂×C₂²⋊Q₈×C₁₀₁	—	2	2	no	—
13	C₂×#121×C₁₀₁	—	2	2	no	—
14	C₂×#121×C₁₀₁	—	2	2	no	—
15	C₂²×C₄⋊C₄×C₁₀₁	—	2	2	no	—
16	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
17	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
18	C₂²×C₄²×C₁₀₁	C₂²	1	1	yes	characteristic
19	C₂×#104×C₁₀₁	—	2	8	no	—
20	C₂×#104×C₁₀₁	C₂²	1	8	yes	complemented
21	#417×C₁₀₁	—	2	4	no	—
22	#417×C₁₀₁	C₂²	1	8	yes	complemented
23	C₂×#103×C₁₀₁	—	2	2	no	—
24	C₂×#102×C₁₀₁	—	2	2	no	—
25	#384×C₁₀₁	—	2	2	no	—
26	#384×C₁₀₁	C₂²	1	4	yes	complemented
27	#343×C₁₀₁	C₂²	1	4	yes	complemented
28	C₂×#41×C₁₀₁	—	2	2	no	—
29	C₂×#41×C₁₀₁	—	2	2	no	—
30	C₂×#41×C₁₀₁	—	2	4	no	—
31	C₂×#41×C₁₀₁	—	2	4	no	—
32	C₂×#41×C₁₀₁	—	2	4	no	—
33	C₂×#41×C₁₀₁	—	2	4	no	—
34	C₂×#41×C₁₀₁	D₄	1	4	yes	—
35	C₂×#41×C₁₀₁	C₂³	1	4	yes	—
36	C₂²×Q₈×C₁₀₁	D₄	1	2	yes	—
37	C₂²×D₄×C₁₀₁	—	2	2	no	—
38	C₂²×D₄×C₁₀₁	—	2	2	no	—
39	C₂²×D₄×C₁₀₁	D₄	1	2	yes	—
40	C₂³×C₄×C₁₀₁	—	2	1	no	—
41	C₂³×C₄×C₁₀₁	—	2	2	no	—
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	C₂×M₁₆×C₁₀₁	—	2	2	no	—
46	C₂×M₁₆×C₁₀₁	—	2	4	no	—
47	C₂×M₁₆×C₁₀₁	—	2	4	no	—
48	C₂×M₁₆×C₁₀₁	C₂³	1	4	yes	—
49	C₂²×C₈×C₁₀₁	—	2	2	no	—
50	C₂²⋊Q₈×C₁₀₁	—	2	8	no	—
51	C₂²⋊Q₈×C₁₀₁	—	2	8	no	—
52	#121×C₁₀₁	—	2	8	no	—
53	#121×C₁₀₁	—	2	8	no	—
54	#121×C₁₀₁	—	2	8	no	—
55	#121×C₁₀₁	—	2	8	no	—
56	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
57	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
58	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
59	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
60	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
61	C₂×C₄⋊C₄×C₁₀₁	—	2	8	no	—
62	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
63	C₂×C₄⋊C₄×C₁₀₁	—	4	8	no	—
64	C₂×C₄⋊C₄×C₁₀₁	D₄	1	2	yes	—
65	C₂×C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
66	C₂×C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
67	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
68	C₂×C₄²×C₁₀₁	—	2	1	no	—
69	C₂×C₄²×C₁₀₁	—	2	2	no	—
70	C₂×C₄²×C₁₀₁	D₄	1	4	yes	complemented
71	C₂×C₄²×C₁₀₁	C₂³	1	2	yes	—
72	#104×C₁₀₁	—	2	16	no	—
73	#103×C₁₀₁	—	2	8	no	—
74	#102×C₁₀₁	—	2	8	no	—
75	C₂⁴×C₁₀₁	—	2	2	no	—
76	C₂⁴×C₁₀₁	C₂×D₄	1	1	yes	characteristic
77	#41×C₁₀₁	—	2	8	no	—
78	#41×C₁₀₁	—	2	8	no	—
79	#41×C₁₀₁	—	2	4	no	—
80	#41×C₁₀₁	—	2	4	no	—
81	#41×C₁₀₁	—	2	4	no	—
82	#41×C₁₀₁	—	2	4	no	—
83	#41×C₁₀₁	—	4	4	no	—
84	#41×C₁₀₁	—	4	4	no	—
85	#41×C₁₀₁	—	4	4	no	—
86	#41×C₁₀₁	—	4	4	no	—
87	C₂×Q₈×C₁₀₁	—	2	2	no	—
88	C₂×Q₈×C₁₀₁	—	2	4	no	—
89	C₂×Q₈×C₁₀₁	—	2	4	no	—
90	C₂×Q₈×C₁₀₁	C₂×D₄	1	4	yes	—
91	C₂×D₄×C₁₀₁	—	2	4	no	—
92	C₂×D₄×C₁₀₁	—	2	4	no	—
93	C₂×D₄×C₁₀₁	—	2	8	no	—
94	C₂×D₄×C₁₀₁	—	2	2	no	—
95	C₂×D₄×C₁₀₁	—	2	4	no	—
96	C₂×D₄×C₁₀₁	—	2	4	no	—
97	C₂×D₄×C₁₀₁	—	4	4	no	—
98	C₂×D₄×C₁₀₁	—	4	4	no	—
99	C₂×D₄×C₁₀₁	—	8	4	no	—
100	C₂×D₄×C₁₀₁	C₂×D₄	1	4	yes	—
101	C₂²×C₄×C₁₀₁	—	2	4	no	—
102	C₂²×C₄×C₁₀₁	—	2	4	no	—
103	C₂²×C₄×C₁₀₁	—	2	4	no	—
104	C₂²×C₄×C₁₀₁	—	2	2	no	—
105	C₂²×C₄×C₁₀₁	—	2	2	no	—
106	C₂²×C₄×C₁₀₁	—	2	2	no	—
107	C₂²×C₄×C₁₀₁	—	2	2	no	—
108	C₂²×C₄×C₁₀₁	—	2	4	no	—
109	C₂²×C₄×C₁₀₁	—	2	4	no	—
110	C₂²×C₄×C₁₀₁	—	2	2	no	—
111	C₂²×C₄×C₁₀₁	—	4	4	no	—
112	C₂²×C₄×C₁₀₁	—	4	4	no	—
113	C₂²×C₄×C₁₀₁	—	4	4	no	—
114	C₂²×C₄×C₁₀₁	—	4	4	no	—
115	C₂²×C₄×C₁₀₁	—	4	1	no	—
116	C₂²×C₄×C₁₀₁	—	4	1	no	—
117	C₂²×C₄×C₁₀₁	C₂×D₄	1	4	yes	—
118	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
120	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
121	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
122	C₂²×C₄×C₁₀₁	#41	1	4	yes	—
123	C₂²×C₄×C₁₀₁	#41	1	2	yes	—
124	C₂²×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
125	M₁₆×C₁₀₁	—	2	4	no	—
126	M₁₆×C₁₀₁	—	2	4	no	—
127	M₁₆×C₁₀₁	—	4	4	no	—
128	C₂×C₈×C₁₀₁	—	2	4	no	—
129	C₂×C₈×C₁₀₁	—	4	4	no	—
130	C₄⋊C₄×C₁₀₁	—	2	8	no	—
131	C₄⋊C₄×C₁₀₁	—	2	4	no	—
132	C₄⋊C₄×C₁₀₁	—	2	4	no	—
133	C₄⋊C₄×C₁₀₁	—	2	4	no	—
134	C₄⋊C₄×C₁₀₁	—	4	16	no	—
135	C₄⋊C₄×C₁₀₁	—	4	2	no	—
136	C₂²⋊C₄×C₁₀₁	—	2	16	no	—
137	C₄²×C₁₀₁	—	2	4	no	—
138	C₄²×C₁₀₁	—	2	2	no	—
139	C₄²×C₁₀₁	C₂×D₄	1	4	yes	complemented
140	C₂³×C₁₀₁	—	2	2	no	—
141	C₂³×C₁₀₁	—	2	2	no	—
142	C₂³×C₁₀₁	—	2	4	no	—
143	C₂³×C₁₀₁	—	4	4	no	—
144	C₂³×C₁₀₁	—	4	4	no	—
145	C₂³×C₁₀₁	—	4	4	no	—
146	C₂³×C₁₀₁	#120	1	1	yes	characteristic
147	C₂³×C₁₀₁	#120	1	1	yes	characteristic
148	C₂³×C₁₀₁	#121	1	2	yes	—
149	C₂³×C₁₀₁	#124	1	2	yes	—
150	C₂³×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
151	Q₈×C₁₀₁	—	2	4	no	—
152	Q₈×C₁₀₁	—	2	4	no	—
153	Q₈×C₁₀₁	—	4	4	no	—
154	D₄×C₁₀₁	—	2	4	no	—
155	D₄×C₁₀₁	—	2	4	no	—
156	D₄×C₁₀₁	—	4	4	no	—
157	D₄×C₁₀₁	—	4	4	no	—
158	D₄×C₁₀₁	—	4	8	no	—
159	D₄×C₁₀₁	—	4	4	no	—
160	D₄×C₁₀₁	—	8	8	no	—
161	C₂×C₄×C₁₀₁	—	2	4	no	—
162	C₂×C₄×C₁₀₁	—	2	4	no	—
163	C₂×C₄×C₁₀₁	—	2	16	no	—
164	C₂×C₄×C₁₀₁	—	2	4	no	—
165	C₂×C₄×C₁₀₁	—	2	4	no	—
166	C₂×C₄×C₁₀₁	—	2	4	no	—
167	C₂×C₄×C₁₀₁	—	4	4	no	—
168	C₂×C₄×C₁₀₁	—	4	4	no	—
169	C₂×C₄×C₁₀₁	—	4	4	no	—
170	C₂×C₄×C₁₀₁	—	4	4	no	—
171	C₂×C₄×C₁₀₁	—	4	8	no	—
172	C₂×C₄×C₁₀₁	—	4	4	no	—
173	C₂×C₄×C₁₀₁	—	4	4	no	—
174	C₂×C₄×C₁₀₁	—	4	2	no	—
175	C₂×C₄×C₁₀₁	—	8	2	no	—
176	C₂×C₄×C₁₀₁	—	8	2	no	—
177	C₂×C₄×C₁₀₁	—	8	2	no	—
178	C₂×C₄×C₁₀₁	#120	1	2	yes	—
179	C₂×C₄×C₁₀₁	#121	1	4	yes	—
180	C₂×C₄×C₁₀₁	#121	1	4	yes	—
181	C₂×C₄×C₁₀₁	#121	1	2	yes	—
182	C₂×C₄×C₁₀₁	#123	1	4	yes	—
183	C₂×C₄×C₁₀₁	#123	1	4	yes	—
184	C₂×C₄×C₁₀₁	#124	1	2	yes	—
185	C₂×C₄×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₄×C₁₀₁	C₂²×D₄	1	2	yes	—
187	C₂×C₄×C₁₀₁	C₂×#41	1	2	yes	—
188	C₂×C₄×C₁₀₁	C₂×#41	1	1	yes	characteristic
189	C₈×C₁₀₁	—	4	4	no	—
190	C₂²×C₁₀₁	—	2	1	no	—
191	C₂²×C₁₀₁	—	2	1	no	—
192	C₂²×C₁₀₁	—	2	1	no	—
193	C₂²×C₁₀₁	—	2	1	no	—
194	C₂²×C₁₀₁	—	2	4	no	—
195	C₂²×C₁₀₁	—	2	4	no	—
196	C₂²×C₁₀₁	—	4	4	no	—
197	C₂²×C₁₀₁	—	4	4	no	—
198	C₂²×C₁₀₁	—	4	4	no	—
199	C₂²×C₁₀₁	—	8	8	no	—
200	C₂²×C₁₀₁	#394	1	2	yes	—
201	C₂²×C₁₀₁	#394	1	2	yes	—
202	C₂²×C₁₀₁	#453	1	2	yes	—
203	C₂²×C₁₀₁	#456	1	2	yes	—
204	C₂²×C₁₀₁	C₂×#120	1	1	yes	characteristic
205	C₂²×C₁₀₁	C₂×#121	1	1	yes	characteristic
206	C₂²×C₁₀₁	C₂×#124	1	1	yes	characteristic
207	C₄×C₁₀₁	—	2	8	no	—
208	C₄×C₁₀₁	—	4	4	no	—
209	C₄×C₁₀₁	—	4	4	no	—
210	C₄×C₁₀₁	—	8	2	no	—
211	C₄×C₁₀₁	#394	1	4	yes	—
212	C₄×C₁₀₁	C₂×#121	1	2	yes	—
213	C₄×C₁₀₁	C₂×#123	1	2	yes	—
214	C₂×#2039	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
215	C₂×C₁₀₁	—	2	1	no	—
216	C₂×C₁₀₁	—	2	1	no	—
217	C₂×C₁₀₁	—	2	2	no	—
218	C₂×C₁₀₁	—	8	4	no	—
219	C₂×C₁₀₁	#2039	1	4	yes	direct product factor
220	C₂×C₁₀₁	C₂×#394	1	1	yes	characteristic
221	C₂×C₁₀₁	C₂×#453	1	1	yes	characteristic
222	C₂×C₁₀₁	C₂×#456	1	1	yes	characteristic
223	C₂×#537	C₂×C₁₀₁	1	1	yes	characteristic
224	C₂²×#104	C₂×C₁₀₁	1	2	yes	complemented
225	C₂×#417	C₂×C₁₀₁	1	2	yes	complemented
226	C₂×#384	C₂×C₁₀₁	1	1	yes	characteristic, complemented
227	#2039	C₂×C₁₀₁	1	8	yes	direct product factor
228	C₂×#343	C₂×C₁₀₁	1	1	yes	characteristic, complemented
229	C₁₀₁	C₂×#2039	1	1	yes	characteristic, direct product factor, Sylow
230	C₂²×#41	C₂²×C₁₀₁	1	2	yes	—
231	C₂²×M₁₆	C₂²×C₁₀₁	1	2	yes	—
232	#537	—	2	4	no	—
233	#537	—	2	2	no	—
234	#537	C₂²×C₁₀₁	1	4	yes	—
235	C₂×C₂²⋊Q₈	—	2	2	no	—
236	C₂×#121	—	2	2	no	—
237	C₂×#121	—	2	2	no	—
238	C₂²×C₄⋊C₄	—	2	2	no	—
239	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
240	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
241	C₂²×C₄²	C₂²×C₁₀₁	1	1	yes	characteristic
242	C₂×#104	—	2	8	no	—
243	C₂×#104	C₂²×C₁₀₁	1	8	yes	complemented
244	#417	—	2	4	no	—
245	#417	C₂²×C₁₀₁	1	8	yes	complemented
246	C₂×#103	—	2	2	no	—
247	C₂×#102	—	2	2	no	—
248	#384	—	2	2	no	—
249	#384	C₂²×C₁₀₁	1	4	yes	complemented
250	#343	C₂²×C₁₀₁	1	4	yes	complemented
251	C₂×#41	—	2	2	no	—
252	C₂×#41	—	2	2	no	—
253	C₂×#41	—	2	4	no	—
254	C₂×#41	—	2	4	no	—
255	C₂×#41	—	2	4	no	—
256	C₂×#41	—	2	4	no	—
257	C₂×#41	D₄×C₁₀₁	1	4	yes	—
258	C₂×#41	C₂³×C₁₀₁	1	4	yes	—
259	C₂²×Q₈	D₄×C₁₀₁	1	2	yes	—
260	C₂²×D₄	—	2	2	no	—
261	C₂²×D₄	—	2	2	no	—
262	C₂²×D₄	D₄×C₁₀₁	1	2	yes	—
263	C₂³×C₄	—	2	1	no	—
264	C₂³×C₄	—	2	2	no	—
265	C₂³×C₄	—	2	1	no	—
266	C₂³×C₄	D₄×C₁₀₁	1	2	yes	—
267	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
268	C₂×M₁₆	—	2	2	no	—
269	C₂×M₁₆	—	2	4	no	—
270	C₂×M₁₆	—	2	4	no	—
271	C₂×M₁₆	C₂³×C₁₀₁	1	4	yes	—
272	C₂²×C₈	—	2	2	no	—
273	C₂²⋊Q₈	—	2	8	no	—
274	C₂²⋊Q₈	—	2	8	no	—
275	#121	—	2	8	no	—
276	#121	—	2	8	no	—
277	#121	—	2	8	no	—
278	#121	—	2	8	no	—
279	C₂×C₄⋊C₄	—	2	2	no	—
280	C₂×C₄⋊C₄	—	2	2	no	—
281	C₂×C₄⋊C₄	—	2	2	no	—
282	C₂×C₄⋊C₄	—	2	2	no	—
283	C₂×C₄⋊C₄	—	2	2	no	—
284	C₂×C₄⋊C₄	—	2	8	no	—
285	C₂×C₄⋊C₄	—	2	1	no	—
286	C₂×C₄⋊C₄	—	4	8	no	—
287	C₂×C₄⋊C₄	D₄×C₁₀₁	1	2	yes	—
288	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	2	yes	—
289	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	2	yes	—
290	C₂×C₂²⋊C₄	—	2	4	no	—
291	C₂×C₄²	—	2	1	no	—
292	C₂×C₄²	—	2	2	no	—
293	C₂×C₄²	D₄×C₁₀₁	1	4	yes	complemented
294	C₂×C₄²	C₂³×C₁₀₁	1	2	yes	—
295	#104	—	2	16	no	—
296	#103	—	2	8	no	—
297	#102	—	2	8	no	—
298	C₂⁴	—	2	2	no	—
299	C₂⁴	C₂×D₄×C₁₀₁	1	1	yes	characteristic
300	#41	—	2	8	no	—
301	#41	—	2	8	no	—
302	#41	—	2	4	no	—
303	#41	—	2	4	no	—
304	#41	—	2	4	no	—
305	#41	—	2	4	no	—
306	#41	—	4	4	no	—
307	#41	—	4	4	no	—
308	#41	—	4	4	no	—
309	#41	—	4	4	no	—
310	C₂×Q₈	—	2	2	no	—
311	C₂×Q₈	—	2	4	no	—
312	C₂×Q₈	—	2	4	no	—
313	C₂×Q₈	C₂×D₄×C₁₀₁	1	4	yes	—
314	C₂×D₄	—	2	4	no	—
315	C₂×D₄	—	2	4	no	—
316	C₂×D₄	—	2	8	no	—
317	C₂×D₄	—	2	2	no	—
318	C₂×D₄	—	2	4	no	—
319	C₂×D₄	—	2	4	no	—
320	C₂×D₄	—	4	4	no	—
321	C₂×D₄	—	4	4	no	—
322	C₂×D₄	—	8	4	no	—
323	C₂×D₄	C₂×D₄×C₁₀₁	1	4	yes	—
324	C₂²×C₄	—	2	4	no	—
325	C₂²×C₄	—	2	4	no	—
326	C₂²×C₄	—	2	4	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	—	2	4	no	—
332	C₂²×C₄	—	2	4	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	4	4	no	—
335	C₂²×C₄	—	4	4	no	—
336	C₂²×C₄	—	4	4	no	—
337	C₂²×C₄	—	4	4	no	—
338	C₂²×C₄	—	4	1	no	—
339	C₂²×C₄	—	4	1	no	—
340	C₂²×C₄	C₂×D₄×C₁₀₁	1	4	yes	—
341	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
342	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
343	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
344	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
345	C₂²×C₄	#41×C₁₀₁	1	4	yes	—
346	C₂²×C₄	#41×C₁₀₁	1	2	yes	—
347	C₂²×C₄	C₂⁴×C₁₀₁	1	1	yes	characteristic
348	M₁₆	—	2	4	no	—
349	M₁₆	—	2	4	no	—
350	M₁₆	—	4	4	no	—
351	C₂×C₈	—	2	4	no	—
352	C₂×C₈	—	4	4	no	—
353	C₄⋊C₄	—	2	8	no	—
354	C₄⋊C₄	—	2	4	no	—
355	C₄⋊C₄	—	2	4	no	—
356	C₄⋊C₄	—	2	4	no	—
357	C₄⋊C₄	—	4	16	no	—
358	C₄⋊C₄	—	4	2	no	—
359	C₂²⋊C₄	—	2	16	no	—
360	C₄²	—	2	4	no	—
361	C₄²	—	2	2	no	—
362	C₄²	C₂×D₄×C₁₀₁	1	4	yes	complemented
363	C₂³	—	2	2	no	—
364	C₂³	—	2	2	no	—
365	C₂³	—	2	4	no	—
366	C₂³	—	4	4	no	—
367	C₂³	—	4	4	no	—
368	C₂³	—	4	4	no	—
369	C₂³	#120×C₁₀₁	1	1	yes	characteristic
370	C₂³	#120×C₁₀₁	1	1	yes	characteristic
371	C₂³	#121×C₁₀₁	1	2	yes	—
372	C₂³	#124×C₁₀₁	1	2	yes	—
373	C₂³	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
374	Q₈	—	2	4	no	—
375	Q₈	—	2	4	no	—
376	Q₈	—	4	4	no	—
377	D₄	—	2	4	no	—
378	D₄	—	2	4	no	—
379	D₄	—	4	4	no	—
380	D₄	—	4	4	no	—
381	D₄	—	4	8	no	—
382	D₄	—	4	4	no	—
383	D₄	—	8	8	no	—
384	C₂×C₄	—	2	4	no	—
385	C₂×C₄	—	2	4	no	—
386	C₂×C₄	—	2	16	no	—
387	C₂×C₄	—	2	4	no	—
388	C₂×C₄	—	2	4	no	—
389	C₂×C₄	—	2	4	no	—
390	C₂×C₄	—	4	4	no	—
391	C₂×C₄	—	4	4	no	—
392	C₂×C₄	—	4	4	no	—
393	C₂×C₄	—	4	4	no	—
394	C₂×C₄	—	4	8	no	—
395	C₂×C₄	—	4	4	no	—
396	C₂×C₄	—	4	4	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	8	2	no	—
399	C₂×C₄	—	8	2	no	—
400	C₂×C₄	—	8	2	no	—
401	C₂×C₄	#120×C₁₀₁	1	2	yes	—
402	C₂×C₄	#121×C₁₀₁	1	4	yes	—
403	C₂×C₄	#121×C₁₀₁	1	4	yes	—
404	C₂×C₄	#121×C₁₀₁	1	2	yes	—
405	C₂×C₄	#123×C₁₀₁	1	4	yes	—
406	C₂×C₄	#123×C₁₀₁	1	4	yes	—
407	C₂×C₄	#124×C₁₀₁	1	2	yes	—
408	C₂×C₄	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
409	C₂×C₄	C₂²×D₄×C₁₀₁	1	2	yes	—
410	C₂×C₄	C₂×#41×C₁₀₁	1	2	yes	—
411	C₂×C₄	C₂×#41×C₁₀₁	1	1	yes	characteristic
412	C₈	—	4	4	no	—
413	C₂²	—	2	1	no	—
414	C₂²	—	2	1	no	—
415	C₂²	—	2	1	no	—
416	C₂²	—	2	1	no	—
417	C₂²	—	2	4	no	—
418	C₂²	—	2	4	no	—
419	C₂²	—	4	4	no	—
420	C₂²	—	4	4	no	—
421	C₂²	—	4	4	no	—
422	C₂²	—	8	8	no	—
423	C₂²	#394×C₁₀₁	1	2	yes	—
424	C₂²	#394×C₁₀₁	1	2	yes	—
425	C₂²	#453×C₁₀₁	1	2	yes	—
426	C₂²	#456×C₁₀₁	1	2	yes	—
427	C₂²	C₂×#120×C₁₀₁	1	1	yes	characteristic
428	C₂²	C₂×#121×C₁₀₁	1	1	yes	characteristic
429	C₂²	C₂×#124×C₁₀₁	1	1	yes	characteristic
430	C₄	—	2	8	no	—
431	C₄	—	4	4	no	—
432	C₄	—	4	4	no	—
433	C₄	—	8	2	no	—
434	C₄	#394×C₁₀₁	1	4	yes	—
435	C₄	C₂×#121×C₁₀₁	1	2	yes	—
436	C₄	C₂×#123×C₁₀₁	1	2	yes	—
437	C₂	—	2	1	no	—
438	C₂	—	2	1	no	—
439	C₂	—	2	2	no	—
440	C₂	—	8	4	no	—
441	C₂	C₁₀₁×#2039	1	4	yes	direct product factor
442	C₂	C₂×#394×C₁₀₁	1	1	yes	characteristic
443	C₂	C₂×#453×C₁₀₁	1	1	yes	characteristic
444	C₂	C₂×#456×C₁₀₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₀₁	#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₀₁
prime radical	C₂×#537×C₁₀₁	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₀₁ ◁ C₂³×C₄×C₁₀₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×#104×C₁₀₁	C₂	semidirect
3. C₂×#417×C₁₀₁	C₂	semidirect
4. C₂×#384×C₁₀₁	C₂	semidirect
5. C₁₀₁×#2039	C₂	direct (N × H)
6. C₂×#343×C₁₀₁	C₂	semidirect
20. C₂×#104×C₁₀₁	C₂²	semidirect
22. #417×C₁₀₁	C₂²	semidirect
26. #384×C₁₀₁	C₂²	semidirect
27. #343×C₁₀₁	C₂²	semidirect
70. C₂×C₄²×C₁₀₁	D₄	semidirect
139. C₄²×C₁₀₁	C₂×D₄	semidirect
214. C₂×#2039	C₁₀₁	direct (N × H)
219. C₂×C₁₀₁	#2039	direct (N × H)
224. C₂²×#104	C₂×C₁₀₁	semidirect
225. C₂×#417	C₂×C₁₀₁	semidirect
226. C₂×#384	C₂×C₁₀₁	semidirect
227. #2039	C₂×C₁₀₁	direct (N × H)
228. C₂×#343	C₂×C₁₀₁	semidirect
229. C₁₀₁	C₂×#2039	direct (N × H)
243. C₂×#104	C₂²×C₁₀₁	semidirect
245. #417	C₂²×C₁₀₁	semidirect
249. #384	C₂²×C₁₀₁	semidirect
250. #343	C₂²×C₁₀₁	semidirect
293. C₂×C₄²	D₄×C₁₀₁	semidirect
362. C₄²	C₂×D₄×C₁₀₁	semidirect
441. C₂	C₁₀₁×#2039	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×#537×C₁₀₁	2
C₂²×#104×C₁₀₁	2
C₂×#417×C₁₀₁	2
C₂×#384×C₁₀₁	2
C₁₀₁×#2039	2
C₂×#343×C₁₀₁	2
C₂×#2039	101

Subgroups — C2×C101×#2039 #38805647

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₀₁×#2039 #38805647