Subgroups — C₁₀₁×#26492 #38808643

Order 25856.

834 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#499×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#442×C₁₀₁	C₂	1	1	yes	maximal, characteristic
3	C₁₀₁×#2454	C₂	1	2	yes	maximal, complemented
4	C₁₀₁×#2067	C₂	1	2	yes	maximal, complemented
5	C₁₀₁×#2025	C₂	1	2	yes	maximal, complemented
6	C₁₀₁×#1972	C₂	1	1	yes	maximal, characteristic
7	C₁₀₁×#1970	C₂	1	1	yes	maximal, characteristic
8	C₁₀₁×#1944	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₀₁×#1943	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₀₁×#1862	C₂	1	2	yes	maximal, complemented
11	C₁₀₁×#1771	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×D₈×C₁₀₁	C₂²	1	1	yes	characteristic
13	C₂×#125×C₁₀₁	C₂²	1	2	yes	—
14	C₂×C₄×D₄×C₁₀₁	C₂²	1	2	yes	—
15	#499×C₁₀₁	—	2	4	no	—
16	#442×C₁₀₁	—	2	4	no	—
17	C₂×#107×C₁₀₁	C₂²	1	2	yes	—
18	C₂×#107×C₁₀₁	C₂²	1	1	yes	characteristic
19	C₂×#106×C₁₀₁	C₂²	1	1	yes	characteristic
20	C₂×#106×C₁₀₁	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊C₈×C₁₀₁	C₂²	1	1	yes	characteristic
22	C₂×#102×C₁₀₁	C₂²	1	2	yes	—
23	C₂×#102×C₁₀₁	C₂²	1	2	yes	—
24	C₂×#102×C₁₀₁	C₂²	1	2	yes	—
25	C₂×#97×C₁₀₁	C₂²	1	1	yes	characteristic
26	C₂×#97×C₁₀₁	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₁₀₁	C₂²	1	1	yes	characteristic
28	#399×C₁₀₁	—	2	2	no	—
29	#396×C₁₀₁	—	2	2	no	—
30	#390×C₁₀₁	C₂²	1	2	yes	—
31	#390×C₁₀₁	C₂²	1	2	yes	—
32	#389×C₁₀₁	C₂²	1	2	yes	—
33	#389×C₁₀₁	C₂²	1	2	yes	—
34	#385×C₁₀₁	—	2	2	no	—
35	#380×C₁₀₁	—	2	2	no	—
36	C₄×C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
37	#340×C₁₀₁	C₂²	1	2	yes	—
38	#340×C₁₀₁	C₂²	1	2	yes	—
39	#336×C₁₀₁	C₂²	1	1	yes	characteristic
40	#336×C₁₀₁	C₂²	1	1	yes	characteristic
41	C₂²×D₄×C₁₀₁	C₂³	1	2	yes	—
42	C₂³×C₄×C₁₀₁	—	2	2	no	—
43	C₂×D₈×C₁₀₁	—	2	2	no	—
44	C₂×D₈×C₁₀₁	—	2	2	no	—
45	C₂×D₈×C₁₀₁	Q₈	1	4	yes	—
46	C₂²×C₈×C₁₀₁	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₁₀₁	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₁₀₁	C₂³	1	1	yes	characteristic
49	C₂²×C₈×C₁₀₁	C₂³	1	1	yes	characteristic
50	#125×C₁₀₁	—	2	4	no	—
51	#125×C₁₀₁	—	4	2	no	—
52	C₄×D₄×C₁₀₁	—	2	4	no	—
53	C₄×D₄×C₁₀₁	—	4	2	no	—
54	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
55	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
56	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
57	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
58	C₂×C₄⋊C₄×C₁₀₁	D₄	1	2	yes	—
59	C₂×C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
60	C₂×C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
61	C₂×C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
62	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
63	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
64	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
65	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
66	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
67	C₂×C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
68	C₂×C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
69	C₂×C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
70	#107×C₁₀₁	—	2	2	no	—
71	#107×C₁₀₁	—	2	4	no	—
72	#106×C₁₀₁	—	2	2	no	—
73	#106×C₁₀₁	D₄	1	4	yes	—
74	C₄⋊C₈×C₁₀₁	—	2	2	no	—
75	#102×C₁₀₁	—	2	4	no	—
76	#102×C₁₀₁	—	2	4	no	—
77	#102×C₁₀₁	—	4	2	no	—
78	#97×C₁₀₁	—	2	2	no	—
79	#97×C₁₀₁	—	2	2	no	—
80	C₄×C₈×C₁₀₁	—	2	2	no	—
81	#95×C₁₀₁	—	2	2	no	—
82	#95×C₁₀₁	—	2	2	no	—
83	#95×C₁₀₁	D₄	1	2	yes	—
84	C₂⁴×C₁₀₁	—	2	2	no	—
85	C₂×D₄×C₁₀₁	—	2	2	no	—
86	C₂×D₄×C₁₀₁	—	2	2	no	—
87	C₂×D₄×C₁₀₁	—	2	2	no	—
88	C₂×D₄×C₁₀₁	—	2	2	no	—
89	C₂×D₄×C₁₀₁	—	2	2	no	—
90	C₂×D₄×C₁₀₁	C₂×Q₈	1	4	yes	—
91	C₂²×C₄×C₁₀₁	—	2	2	no	—
92	C₂²×C₄×C₁₀₁	—	2	2	no	—
93	C₂²×C₄×C₁₀₁	—	2	2	no	—
94	C₂²×C₄×C₁₀₁	—	4	4	no	—
95	C₂²×C₄×C₁₀₁	—	4	4	no	—
96	C₂²×C₄×C₁₀₁	—	8	2	no	—
97	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
99	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
101	C₂²×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
102	D₈×C₁₀₁	—	2	8	no	—
103	C₂×C₈×C₁₀₁	—	2	1	no	—
104	C₂×C₈×C₁₀₁	—	2	1	no	—
105	C₂×C₈×C₁₀₁	—	2	1	no	—
106	C₂×C₈×C₁₀₁	—	2	1	no	—
107	C₂×C₈×C₁₀₁	—	2	1	no	—
108	C₂×C₈×C₁₀₁	—	2	1	no	—
109	C₂×C₈×C₁₀₁	—	2	1	no	—
110	C₂×C₈×C₁₀₁	—	2	1	no	—
111	C₂×C₈×C₁₀₁	C₂×D₄	1	2	yes	—
112	C₂×C₈×C₁₀₁	C₂×Q₈	1	2	yes	—
113	C₂×C₈×C₁₀₁	#41	1	2	yes	—
114	C₂×C₈×C₁₀₁	#41	1	2	yes	—
115	C₄⋊C₄×C₁₀₁	—	2	2	no	—
116	C₄⋊C₄×C₁₀₁	—	2	2	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	—	4	2	no	—
121	C₄⋊C₄×C₁₀₁	—	4	4	no	—
122	C₄⋊C₄×C₁₀₁	—	4	4	no	—
123	C₄⋊C₄×C₁₀₁	—	8	2	no	—
124	C₄⋊C₄×C₁₀₁	—	8	2	no	—
125	C₄⋊C₄×C₁₀₁	C₂×D₄	1	4	yes	—
126	C₂²⋊C₄×C₁₀₁	—	4	4	no	—
127	C₂²⋊C₄×C₁₀₁	—	4	4	no	—
128	C₂²⋊C₄×C₁₀₁	—	8	2	no	—
129	C₂²⋊C₄×C₁₀₁	—	8	2	no	—
130	C₂²⋊C₄×C₁₀₁	—	8	2	no	—
131	C₄²×C₁₀₁	—	2	1	no	—
132	C₄²×C₁₀₁	—	2	1	no	—
133	C₄²×C₁₀₁	—	2	1	no	—
134	C₄²×C₁₀₁	—	2	1	no	—
135	C₄²×C₁₀₁	—	2	1	no	—
136	C₄²×C₁₀₁	—	2	1	no	—
137	C₂³×C₁₀₁	—	2	4	no	—
138	C₂³×C₁₀₁	—	4	2	no	—
139	C₂³×C₁₀₁	—	4	2	no	—
140	C₂³×C₁₀₁	—	4	2	no	—
141	C₂³×C₁₀₁	—	4	2	no	—
142	C₂³×C₁₀₁	—	4	2	no	—
143	C₂³×C₁₀₁	—	4	2	no	—
144	C₂³×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
145	D₄×C₁₀₁	—	2	4	no	—
146	D₄×C₁₀₁	—	2	4	no	—
147	D₄×C₁₀₁	—	4	2	no	—
148	D₄×C₁₀₁	—	4	2	no	—
149	C₂×C₄×C₁₀₁	—	2	1	no	—
150	C₂×C₄×C₁₀₁	—	2	1	no	—
151	C₂×C₄×C₁₀₁	—	2	2	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	—	2	2	no	—
157	C₂×C₄×C₁₀₁	—	2	2	no	—
158	C₂×C₄×C₁₀₁	—	2	2	no	—
159	C₂×C₄×C₁₀₁	—	2	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	—	4	2	no	—
167	C₂×C₄×C₁₀₁	—	4	2	no	—
168	C₂×C₄×C₁₀₁	—	8	8	no	—
169	C₂×C₄×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
170	C₂×C₄×C₁₀₁	C₂²×Q₈	1	1	yes	characteristic
171	C₂×C₄×C₁₀₁	C₂×#41	1	1	yes	characteristic
172	C₂×C₄×C₁₀₁	C₂×#41	1	1	yes	characteristic
173	C₂×C₄×C₁₀₁	H(5,𝔽₂)	1	1	yes	characteristic
174	C₂×C₄×C₁₀₁	2₋¹⁺⁴	1	1	yes	characteristic
175	C₈×C₁₀₁	—	2	2	no	—
176	C₈×C₁₀₁	—	4	1	no	—
177	C₈×C₁₀₁	—	4	1	no	—
178	C₈×C₁₀₁	C₂²⋊Q₈	1	4	yes	—
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	—	8	2	no	—
184	C₂²×C₁₀₁	—	8	2	no	—
185	C₂²×C₁₀₁	—	8	2	no	—
186	C₂²×C₁₀₁	#532	1	1	yes	characteristic
187	C₂²×C₁₀₁	D₄²	1	1	yes	characteristic
188	C₂²×C₁₀₁	D₄×Q₈	1	1	yes	characteristic
189	C₂²×C₁₀₁	#575	1	2	yes	—
190	C₂²×C₁₀₁	#576	1	2	yes	—
191	C₄×C₁₀₁	—	4	1	no	—
192	C₄×C₁₀₁	—	4	1	no	—
193	C₄×C₁₀₁	—	4	2	no	—
194	C₄×C₁₀₁	—	4	2	no	—
195	C₄×C₁₀₁	—	4	4	no	—
196	C₄×C₁₀₁	—	8	2	no	—
197	C₄×C₁₀₁	—	8	2	no	—
198	C₄×C₁₀₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
199	C₄×C₁₀₁	#542	1	1	yes	characteristic
200	C₄×C₁₀₁	#548	1	1	yes	characteristic
201	C₄×C₁₀₁	#554	1	1	yes	characteristic
202	#26492	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
203	C₂×C₁₀₁	—	8	4	no	—
204	C₂×C₁₀₁	#2452	1	1	yes	characteristic
205	C₂×C₁₀₁	#3176	1	1	yes	characteristic
206	C₂×C₁₀₁	#3183	1	1	yes	characteristic
207	C₂×C₁₀₁	#3268	1	2	yes	—
208	C₂×C₁₀₁	#3389	1	2	yes	—
209	C₂×#499	C₂×C₁₀₁	1	1	yes	characteristic, complemented
210	C₂×#442	C₂×C₁₀₁	1	1	yes	characteristic
211	#2454	C₂×C₁₀₁	1	2	yes	complemented
212	#2067	C₂×C₁₀₁	1	2	yes	complemented
213	#2025	C₂×C₁₀₁	1	2	yes	complemented
214	#1972	C₂×C₁₀₁	1	1	yes	characteristic
215	#1970	C₂×C₁₀₁	1	1	yes	characteristic
216	#1944	C₂×C₁₀₁	1	1	yes	characteristic, complemented
217	#1943	C₂×C₁₀₁	1	1	yes	characteristic, complemented
218	#1862	C₂×C₁₀₁	1	2	yes	complemented
219	#1771	C₂×C₁₀₁	1	1	yes	characteristic, complemented
220	C₁₀₁	#26492	1	1	yes	characteristic, direct product factor, Sylow
221	C₂²×D₈	C₂²×C₁₀₁	1	1	yes	characteristic
222	C₂×#125	C₂²×C₁₀₁	1	2	yes	—
223	C₂×C₄×D₄	C₂²×C₁₀₁	1	2	yes	—
224	#499	—	2	4	no	—
225	#442	—	2	4	no	—
226	C₂×#107	C₂²×C₁₀₁	1	2	yes	—
227	C₂×#107	C₂²×C₁₀₁	1	1	yes	characteristic
228	C₂×#106	C₂²×C₁₀₁	1	1	yes	characteristic
229	C₂×#106	C₂²×C₁₀₁	1	1	yes	characteristic
230	C₂×C₄⋊C₈	C₂²×C₁₀₁	1	1	yes	characteristic
231	C₂×#102	C₂²×C₁₀₁	1	2	yes	—
232	C₂×#102	C₂²×C₁₀₁	1	2	yes	—
233	C₂×#102	C₂²×C₁₀₁	1	2	yes	—
234	C₂×#97	C₂²×C₁₀₁	1	1	yes	characteristic
235	C₂×#97	C₂²×C₁₀₁	1	1	yes	characteristic
236	C₂×C₄×C₈	C₂²×C₁₀₁	1	1	yes	characteristic
237	#399	—	2	2	no	—
238	#396	—	2	2	no	—
239	#390	C₂²×C₁₀₁	1	2	yes	—
240	#390	C₂²×C₁₀₁	1	2	yes	—
241	#389	C₂²×C₁₀₁	1	2	yes	—
242	#389	C₂²×C₁₀₁	1	2	yes	—
243	#385	—	2	2	no	—
244	#380	—	2	2	no	—
245	C₄×C₄⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
246	#340	C₂²×C₁₀₁	1	2	yes	—
247	#340	C₂²×C₁₀₁	1	2	yes	—
248	#336	C₂²×C₁₀₁	1	1	yes	characteristic
249	#336	C₂²×C₁₀₁	1	1	yes	characteristic
250	C₂²×D₄	C₂³×C₁₀₁	1	2	yes	—
251	C₂³×C₄	—	2	2	no	—
252	C₂×D₈	—	2	2	no	—
253	C₂×D₈	—	2	2	no	—
254	C₂×D₈	Q₈×C₁₀₁	1	4	yes	—
255	C₂²×C₈	C₂³×C₁₀₁	1	1	yes	characteristic
256	C₂²×C₈	C₂³×C₁₀₁	1	1	yes	characteristic
257	C₂²×C₈	C₂³×C₁₀₁	1	1	yes	characteristic
258	C₂²×C₈	C₂³×C₁₀₁	1	1	yes	characteristic
259	#125	—	2	4	no	—
260	#125	—	4	2	no	—
261	C₄×D₄	—	2	4	no	—
262	C₄×D₄	—	4	2	no	—
263	C₂×C₄⋊C₄	—	2	2	no	—
264	C₂×C₄⋊C₄	—	2	2	no	—
265	C₂×C₄⋊C₄	—	2	2	no	—
266	C₂×C₄⋊C₄	—	2	2	no	—
267	C₂×C₄⋊C₄	D₄×C₁₀₁	1	2	yes	—
268	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	2	yes	—
269	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	2	yes	—
270	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	2	yes	—
271	C₂×C₂²⋊C₄	—	2	2	no	—
272	C₂×C₂²⋊C₄	—	2	2	no	—
273	C₂×C₂²⋊C₄	—	2	2	no	—
274	C₂×C₂²⋊C₄	—	2	2	no	—
275	C₂×C₂²⋊C₄	—	2	2	no	—
276	C₂×C₄²	C₂³×C₁₀₁	1	1	yes	characteristic
277	C₂×C₄²	C₂³×C₁₀₁	1	1	yes	characteristic
278	C₂×C₄²	C₂³×C₁₀₁	1	1	yes	characteristic
279	#107	—	2	2	no	—
280	#107	—	2	4	no	—
281	#106	—	2	2	no	—
282	#106	D₄×C₁₀₁	1	4	yes	—
283	C₄⋊C₈	—	2	2	no	—
284	#102	—	2	4	no	—
285	#102	—	2	4	no	—
286	#102	—	4	2	no	—
287	#97	—	2	2	no	—
288	#97	—	2	2	no	—
289	C₄×C₈	—	2	2	no	—
290	#95	—	2	2	no	—
291	#95	—	2	2	no	—
292	#95	D₄×C₁₀₁	1	2	yes	—
293	C₂⁴	—	2	2	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	—	2	2	no	—
299	C₂×D₄	C₂×Q₈×C₁₀₁	1	4	yes	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	4	4	no	—
304	C₂²×C₄	—	4	4	no	—
305	C₂²×C₄	—	8	2	no	—
306	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
307	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
308	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
309	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
310	C₂²×C₄	C₂⁴×C₁₀₁	1	1	yes	characteristic
311	D₈	—	2	8	no	—
312	C₂×C₈	—	2	1	no	—
313	C₂×C₈	—	2	1	no	—
314	C₂×C₈	—	2	1	no	—
315	C₂×C₈	—	2	1	no	—
316	C₂×C₈	—	2	1	no	—
317	C₂×C₈	—	2	1	no	—
318	C₂×C₈	—	2	1	no	—
319	C₂×C₈	—	2	1	no	—
320	C₂×C₈	C₂×D₄×C₁₀₁	1	2	yes	—
321	C₂×C₈	C₂×Q₈×C₁₀₁	1	2	yes	—
322	C₂×C₈	#41×C₁₀₁	1	2	yes	—
323	C₂×C₈	#41×C₁₀₁	1	2	yes	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	2	2	no	—
326	C₄⋊C₄	—	2	2	no	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	2	2	no	—
329	C₄⋊C₄	—	4	2	no	—
330	C₄⋊C₄	—	4	4	no	—
331	C₄⋊C₄	—	4	4	no	—
332	C₄⋊C₄	—	8	2	no	—
333	C₄⋊C₄	—	8	2	no	—
334	C₄⋊C₄	C₂×D₄×C₁₀₁	1	4	yes	—
335	C₂²⋊C₄	—	4	4	no	—
336	C₂²⋊C₄	—	4	4	no	—
337	C₂²⋊C₄	—	8	2	no	—
338	C₂²⋊C₄	—	8	2	no	—
339	C₂²⋊C₄	—	8	2	no	—
340	C₄²	—	2	1	no	—
341	C₄²	—	2	1	no	—
342	C₄²	—	2	1	no	—
343	C₄²	—	2	1	no	—
344	C₄²	—	2	1	no	—
345	C₄²	—	2	1	no	—
346	C₂³	—	2	4	no	—
347	C₂³	—	4	2	no	—
348	C₂³	—	4	2	no	—
349	C₂³	—	4	2	no	—
350	C₂³	—	4	2	no	—
351	C₂³	—	4	2	no	—
352	C₂³	—	4	2	no	—
353	C₂³	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
354	D₄	—	2	4	no	—
355	D₄	—	2	4	no	—
356	D₄	—	4	2	no	—
357	D₄	—	4	2	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	8	8	no	—
378	C₂×C₄	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
379	C₂×C₄	C₂²×Q₈×C₁₀₁	1	1	yes	characteristic
380	C₂×C₄	C₂×#41×C₁₀₁	1	1	yes	characteristic
381	C₂×C₄	C₂×#41×C₁₀₁	1	1	yes	characteristic
382	C₂×C₄	H(5,𝔽₂)×C₁₀₁	1	1	yes	characteristic
383	C₂×C₄	2₋¹⁺⁴×C₁₀₁	1	1	yes	characteristic
384	C₈	—	2	2	no	—
385	C₈	—	4	1	no	—
386	C₈	—	4	1	no	—
387	C₈	C₂²⋊Q₈×C₁₀₁	1	4	yes	—
388	C₂²	—	4	4	no	—
389	C₂²	—	4	4	no	—
390	C₂²	—	4	4	no	—
391	C₂²	—	8	2	no	—
392	C₂²	—	8	2	no	—
393	C₂²	—	8	2	no	—
394	C₂²	—	8	2	no	—
395	C₂²	#532×C₁₀₁	1	1	yes	characteristic
396	C₂²	D₄²×C₁₀₁	1	1	yes	characteristic
397	C₂²	D₄×Q₈×C₁₀₁	1	1	yes	characteristic
398	C₂²	#575×C₁₀₁	1	2	yes	—
399	C₂²	#576×C₁₀₁	1	2	yes	—
400	C₄	—	4	1	no	—
401	C₄	—	4	1	no	—
402	C₄	—	4	2	no	—
403	C₄	—	4	2	no	—
404	C₄	—	4	4	no	—
405	C₄	—	8	2	no	—
406	C₄	—	8	2	no	—
407	C₄	C₂×C₂²⋊Q₈×C₁₀₁	1	1	yes	characteristic
408	C₄	#542×C₁₀₁	1	1	yes	characteristic
409	C₄	#548×C₁₀₁	1	1	yes	characteristic
410	C₄	#554×C₁₀₁	1	1	yes	characteristic
411	C₂	—	8	4	no	—
412	C₂	C₁₀₁×#2452	1	1	yes	characteristic
413	C₂	C₁₀₁×#3176	1	1	yes	characteristic
414	C₂	C₁₀₁×#3183	1	1	yes	characteristic
415	C₂	C₁₀₁×#3268	1	2	yes	—
416	C₂	C₁₀₁×#3389	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₀₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₀₁
prime radical	C₂²×D₈×C₁₀₁	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₀₁ ◁ C₄×C₄⋊C₄×C₁₀₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#499×C₁₀₁	C₂	semidirect
3. C₁₀₁×#2454	C₂	semidirect
4. C₁₀₁×#2067	C₂	semidirect
5. C₁₀₁×#2025	C₂	semidirect
8. C₁₀₁×#1944	C₂	semidirect
9. C₁₀₁×#1943	C₂	semidirect
10. C₁₀₁×#1862	C₂	semidirect
11. C₁₀₁×#1771	C₂	semidirect
202. #26492	C₁₀₁	direct (N × H)
209. C₂×#499	C₂×C₁₀₁	semidirect
211. #2454	C₂×C₁₀₁	semidirect
212. #2067	C₂×C₁₀₁	semidirect
213. #2025	C₂×C₁₀₁	semidirect
216. #1944	C₂×C₁₀₁	semidirect
217. #1943	C₂×C₁₀₁	semidirect
218. #1862	C₂×C₁₀₁	semidirect
219. #1771	C₂×C₁₀₁	semidirect
220. C₁₀₁	#26492	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×#499×C₁₀₁	2
C₂×#442×C₁₀₁	2
C₁₀₁×#2454	2
C₁₀₁×#2067	2
C₁₀₁×#2025	2
C₁₀₁×#1972	2
C₁₀₁×#1970	2
C₁₀₁×#1944	2
C₁₀₁×#1943	2
C₁₀₁×#1862	2
C₁₀₁×#1771	2
#26492	101

Subgroups — C101×#26492 #38808643

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#26492 #38808643