Subgroups — C₁₀₁×#18292 #38800443

Order 25856.

1282 conjugacy classes of subgroups.

The subgroup lattice has 474 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, complemented
2	C₁₀₁×#3186	C₂	1	2	yes	maximal, complemented
3	C₁₀₁×#2618	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₀₁×#1610	C₂	1	4	yes	maximal, complemented
5	C₁₀₁×#1598	C₂	1	4	yes	maximal, complemented
6	C₁₀₁×#1519	C₂	1	2	yes	maximal, complemented
7	C₂×#324×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#41×C₁₀₁	—	2	1	no	—
9	#537×C₁₀₁	—	2	4	no	—
10	#537×C₁₀₁	—	2	2	no	—
11	#537×C₁₀₁	C₂²	1	4	yes	—
12	C₂×#123×C₁₀₁	—	2	1	no	—
13	C₂×C₂²⋊Q₈×C₁₀₁	—	2	2	no	—
14	C₂×#121×C₁₀₁	—	2	2	no	—
15	C₂×#121×C₁₀₁	—	2	1	no	—
16	C₂×#121×C₁₀₁	C₂²	1	2	yes	—
17	C₂×#121×C₁₀₁	C₂²	1	1	yes	characteristic
18	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
19	#480×C₁₀₁	—	2	2	no	—
20	#480×C₁₀₁	C₂²	1	4	yes	complemented
21	#466×C₁₀₁	—	2	4	no	—
22	#447×C₁₀₁	—	2	2	no	—
23	#447×C₁₀₁	C₂²	1	4	yes	complemented
24	C₂×C₂²⋊C₈×C₁₀₁	C₂²	1	2	yes	—
25	#398×C₁₀₁	C₂²	1	2	yes	complemented
26	#396×C₁₀₁	—	2	2	no	—
27	#394×C₁₀₁	C₂²	1	2	yes	complemented
28	#386×C₁₀₁	—	2	1	no	—
29	#380×C₁₀₁	C₂²	1	1	yes	characteristic
30	#327×C₁₀₁	C₂²	1	8	yes	complemented
31	#324×C₁₀₁	C₂²	1	4	yes	complemented
32	C₂×#41×C₁₀₁	—	2	4	no	—
33	C₂×#41×C₁₀₁	—	2	4	no	—
34	C₂×#41×C₁₀₁	—	4	4	no	—
35	C₂×#41×C₁₀₁	—	4	4	no	—
36	C₂²×Q₈×C₁₀₁	—	2	1	no	—
37	C₂²×D₄×C₁₀₁	—	2	1	no	—
38	C₂²×D₄×C₁₀₁	—	2	2	no	—
39	C₂²×D₄×C₁₀₁	—	2	1	no	—
40	C₂²×D₄×C₁₀₁	—	2	1	no	—
41	C₂²×D₄×C₁₀₁	D₄	1	2	yes	—
42	C₂²×D₄×C₁₀₁	C₂³	1	1	yes	characteristic
43	C₂³×C₄×C₁₀₁	—	2	2	no	—
44	C₂³×C₄×C₁₀₁	D₄	1	1	yes	characteristic
45	C₂³×C₄×C₁₀₁	D₄	1	1	yes	characteristic
46	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
47	C₂×D₈×C₁₀₁	—	2	4	no	—
48	C₂²×C₈×C₁₀₁	—	2	2	no	—
49	#123×C₁₀₁	—	4	4	no	—
50	C₂²⋊Q₈×C₁₀₁	—	2	8	no	—
51	C₂²⋊Q₈×C₁₀₁	—	2	8	no	—
52	#121×C₁₀₁	—	2	4	no	—
53	#121×C₁₀₁	—	2	8	no	—
54	#121×C₁₀₁	—	2	8	no	—
55	#121×C₁₀₁	—	2	4	no	—
56	#121×C₁₀₁	—	2	2	no	—
57	#121×C₁₀₁	—	2	2	no	—
58	#121×C₁₀₁	—	2	2	no	—
59	#121×C₁₀₁	—	2	2	no	—
60	#121×C₁₀₁	D₄	1	4	yes	—
61	#121×C₁₀₁	C₂³	1	4	yes	—
62	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
63	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
64	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
65	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
66	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
67	C₂×C₄⋊C₄×C₁₀₁	D₄	1	2	yes	—
68	C₂×C₄⋊C₄×C₁₀₁	D₄	1	2	yes	—
69	C₂×C₄⋊C₄×C₁₀₁	C₂³	1	1	yes	characteristic
70	C₂×C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
71	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
72	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
73	C₂×C₂²⋊C₄×C₁₀₁	—	2	1	no	—
74	C₂×C₂²⋊C₄×C₁₀₁	—	2	1	no	—
75	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
76	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
77	#107×C₁₀₁	—	2	4	no	—
78	#102×C₁₀₁	—	2	4	no	—
79	#102×C₁₀₁	—	2	4	no	—
80	C₂²⋊C₈×C₁₀₁	—	2	2	no	—
81	C₂²⋊C₈×C₁₀₁	C₂³	1	4	yes	—
82	#95×C₁₀₁	—	2	2	no	—
83	#95×C₁₀₁	C₂³	1	2	yes	—
84	C₂⁴×C₁₀₁	—	2	2	no	—
85	C₂⁴×C₁₀₁	—	2	1	no	—
86	C₂⁴×C₁₀₁	C₂×D₄	1	1	yes	characteristic
87	#41×C₁₀₁	—	4	8	no	—
88	#41×C₁₀₁	—	4	16	no	—
89	#41×C₁₀₁	—	4	8	no	—
90	C₂×Q₈×C₁₀₁	—	2	4	no	—
91	C₂×Q₈×C₁₀₁	—	4	4	no	—
92	C₂×D₄×C₁₀₁	—	2	4	no	—
93	C₂×D₄×C₁₀₁	—	2	4	no	—
94	C₂×D₄×C₁₀₁	—	2	4	no	—
95	C₂×D₄×C₁₀₁	—	2	4	no	—
96	C₂×D₄×C₁₀₁	—	2	2	no	—
97	C₂×D₄×C₁₀₁	—	2	2	no	—
98	C₂×D₄×C₁₀₁	—	4	4	no	—
99	C₂×D₄×C₁₀₁	—	4	4	no	—
100	C₂×D₄×C₁₀₁	—	4	4	no	—
101	C₂×D₄×C₁₀₁	—	4	1	no	—
102	C₂×D₄×C₁₀₁	—	4	1	no	—
103	C₂×D₄×C₁₀₁	—	4	2	no	—
104	C₂×D₄×C₁₀₁	—	4	2	no	—
105	C₂×D₄×C₁₀₁	—	8	1	no	—
106	C₂×D₄×C₁₀₁	—	8	2	no	—
107	C₂×D₄×C₁₀₁	—	8	2	no	—
108	C₂×D₄×C₁₀₁	C₂×D₄	1	4	yes	—
109	C₂²×C₄×C₁₀₁	—	2	1	no	—
110	C₂²×C₄×C₁₀₁	—	2	1	no	—
111	C₂²×C₄×C₁₀₁	—	2	2	no	—
112	C₂²×C₄×C₁₀₁	—	2	8	no	—
113	C₂²×C₄×C₁₀₁	—	2	1	no	—
114	C₂²×C₄×C₁₀₁	—	2	2	no	—
115	C₂²×C₄×C₁₀₁	—	2	1	no	—
116	C₂²×C₄×C₁₀₁	—	2	1	no	—
117	C₂²×C₄×C₁₀₁	—	2	2	no	—
118	C₂²×C₄×C₁₀₁	—	4	8	no	—
119	C₂²×C₄×C₁₀₁	—	8	1	no	—
120	C₂²×C₄×C₁₀₁	—	8	1	no	—
121	C₂²×C₄×C₁₀₁	D₈	1	4	yes	complemented
122	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
123	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
128	D₈×C₁₀₁	—	8	4	no	—
129	C₂×C₈×C₁₀₁	—	2	4	no	—
130	C₂×C₈×C₁₀₁	—	8	2	no	—
131	C₄⋊C₄×C₁₀₁	—	2	4	no	—
132	C₄⋊C₄×C₁₀₁	—	2	4	no	—
133	C₄⋊C₄×C₁₀₁	—	2	2	no	—
134	C₄⋊C₄×C₁₀₁	—	2	4	no	—
135	C₄⋊C₄×C₁₀₁	—	2	2	no	—
136	C₄⋊C₄×C₁₀₁	—	4	4	no	—
137	C₄⋊C₄×C₁₀₁	—	8	1	no	—
138	C₄⋊C₄×C₁₀₁	C₂×D₄	1	4	yes	—
139	C₂²⋊C₄×C₁₀₁	—	2	8	no	—
140	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
141	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
142	C₂²⋊C₄×C₁₀₁	—	4	2	no	—
143	C₂²⋊C₄×C₁₀₁	—	4	2	no	—
144	C₂²⋊C₄×C₁₀₁	—	4	4	no	—
145	C₂²⋊C₄×C₁₀₁	—	8	2	no	—
146	C₂³×C₁₀₁	—	2	4	no	—
147	C₂³×C₁₀₁	—	4	1	no	—
148	C₂³×C₁₀₁	—	4	1	no	—
149	C₂³×C₁₀₁	—	4	4	no	—
150	C₂³×C₁₀₁	—	4	4	no	—
151	C₂³×C₁₀₁	—	4	2	no	—
152	C₂³×C₁₀₁	—	4	2	no	—
153	C₂³×C₁₀₁	—	4	4	no	—
154	C₂³×C₁₀₁	—	4	1	no	—
155	C₂³×C₁₀₁	—	4	1	no	—
156	C₂³×C₁₀₁	—	4	1	no	—
157	C₂³×C₁₀₁	#120	1	1	yes	characteristic
158	C₂³×C₁₀₁	#120	1	1	yes	characteristic
159	C₂³×C₁₀₁	C₂×D₈	1	2	yes	—
160	C₂³×C₁₀₁	AGL(1,ℤ/8)	1	2	yes	—
161	C₂³×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
162	Q₈×C₁₀₁	—	4	8	no	—
163	D₄×C₁₀₁	—	4	4	no	—
164	D₄×C₁₀₁	—	4	8	no	—
165	D₄×C₁₀₁	—	4	4	no	—
166	D₄×C₁₀₁	—	4	4	no	—
167	D₄×C₁₀₁	—	4	4	no	—
168	D₄×C₁₀₁	—	4	8	no	—
169	D₄×C₁₀₁	—	8	2	no	—
170	D₄×C₁₀₁	—	8	4	no	—
171	D₄×C₁₀₁	—	8	2	no	—
172	D₄×C₁₀₁	—	8	2	no	—
173	C₂×C₄×C₁₀₁	—	2	2	no	—
174	C₂×C₄×C₁₀₁	—	2	2	no	—
175	C₂×C₄×C₁₀₁	—	2	4	no	—
176	C₂×C₄×C₁₀₁	—	2	4	no	—
177	C₂×C₄×C₁₀₁	—	2	2	no	—
178	C₂×C₄×C₁₀₁	—	2	4	no	—
179	C₂×C₄×C₁₀₁	—	4	1	no	—
180	C₂×C₄×C₁₀₁	—	4	2	no	—
181	C₂×C₄×C₁₀₁	—	4	2	no	—
182	C₂×C₄×C₁₀₁	—	4	1	no	—
183	C₂×C₄×C₁₀₁	—	4	16	no	—
184	C₂×C₄×C₁₀₁	—	4	2	no	—
185	C₂×C₄×C₁₀₁	—	4	4	no	—
186	C₂×C₄×C₁₀₁	—	4	2	no	—
187	C₂×C₄×C₁₀₁	—	4	2	no	—
188	C₂×C₄×C₁₀₁	—	4	2	no	—
189	C₂×C₄×C₁₀₁	—	4	1	no	—
190	C₂×C₄×C₁₀₁	—	4	2	no	—
191	C₂×C₄×C₁₀₁	—	4	1	no	—
192	C₂×C₄×C₁₀₁	—	4	1	no	—
193	C₂×C₄×C₁₀₁	—	8	1	no	—
194	C₂×C₄×C₁₀₁	#120	1	2	yes	—
195	C₂×C₄×C₁₀₁	C₂×D₈	1	4	yes	—
196	C₂×C₄×C₁₀₁	C₂²×D₄	1	2	yes	—
197	C₈×C₁₀₁	—	4	4	no	—
198	C₂²×C₁₀₁	—	2	1	no	—
199	C₂²×C₁₀₁	—	2	1	no	—
200	C₂²×C₁₀₁	—	2	1	no	—
201	C₂²×C₁₀₁	—	2	1	no	—
202	C₂²×C₁₀₁	—	2	1	no	—
203	C₂²×C₁₀₁	—	2	1	no	—
204	C₂²×C₁₀₁	—	4	2	no	—
205	C₂²×C₁₀₁	—	4	2	no	—
206	C₂²×C₁₀₁	—	4	4	no	—
207	C₂²×C₁₀₁	—	4	4	no	—
208	C₂²×C₁₀₁	—	4	4	no	—
209	C₂²×C₁₀₁	—	8	8	no	—
210	C₂²×C₁₀₁	—	8	2	no	—
211	C₂²×C₁₀₁	—	8	2	no	—
212	C₂²×C₁₀₁	—	8	1	no	—
213	C₂²×C₁₀₁	—	8	1	no	—
214	C₂²×C₁₀₁	—	8	1	no	—
215	C₂²×C₁₀₁	#447	1	2	yes	—
216	C₂²×C₁₀₁	#447	1	2	yes	—
217	C₂²×C₁₀₁	C₂×#120	1	1	yes	characteristic
218	C₂²×C₁₀₁	C₂²×D₈	1	1	yes	characteristic
219	C₂²×C₁₀₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
220	C₄×C₁₀₁	—	2	4	no	—
221	C₄×C₁₀₁	—	2	2	no	—
222	C₄×C₁₀₁	—	2	2	no	—
223	C₄×C₁₀₁	—	4	4	no	—
224	C₄×C₁₀₁	—	4	2	no	—
225	C₄×C₁₀₁	—	8	2	no	—
226	C₄×C₁₀₁	—	8	1	no	—
227	#18292	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
228	C₂×C₁₀₁	—	2	1	no	—
229	C₂×C₁₀₁	—	2	2	no	—
230	C₂×C₁₀₁	—	2	1	no	—
231	C₂×C₁₀₁	—	2	2	no	—
232	C₂×C₁₀₁	—	8	4	no	—
233	C₂×C₁₀₁	—	16	1	no	—
234	C₂×C₁₀₁	C₂×#447	1	1	yes	characteristic
235	C₂×C₁₀₁	#3020	1	1	yes	characteristic
236	C₂×C₁₀₁	#3026	1	1	yes	characteristic
237	C₂×#537	C₂×C₁₀₁	1	1	yes	characteristic, complemented
238	#3186	C₂×C₁₀₁	1	2	yes	complemented
239	#2618	C₂×C₁₀₁	1	1	yes	characteristic, complemented
240	#1610	C₂×C₁₀₁	1	4	yes	complemented
241	#1598	C₂×C₁₀₁	1	4	yes	complemented
242	#1519	C₂×C₁₀₁	1	2	yes	complemented
243	C₂×#324	C₂×C₁₀₁	1	1	yes	characteristic, complemented
244	C₁₀₁	#18292	1	1	yes	characteristic, direct product factor, Sylow
245	C₂²×#41	—	2	1	no	—
246	#537	—	2	4	no	—
247	#537	—	2	2	no	—
248	#537	C₂²×C₁₀₁	1	4	yes	—
249	C₂×#123	—	2	1	no	—
250	C₂×C₂²⋊Q₈	—	2	2	no	—
251	C₂×#121	—	2	2	no	—
252	C₂×#121	—	2	1	no	—
253	C₂×#121	C₂²×C₁₀₁	1	2	yes	—
254	C₂×#121	C₂²×C₁₀₁	1	1	yes	characteristic
255	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
256	#480	—	2	2	no	—
257	#480	C₂²×C₁₀₁	1	4	yes	complemented
258	#466	—	2	4	no	—
259	#447	—	2	2	no	—
260	#447	C₂²×C₁₀₁	1	4	yes	complemented
261	C₂×C₂²⋊C₈	C₂²×C₁₀₁	1	2	yes	—
262	#398	C₂²×C₁₀₁	1	2	yes	complemented
263	#396	—	2	2	no	—
264	#394	C₂²×C₁₀₁	1	2	yes	complemented
265	#386	—	2	1	no	—
266	#380	C₂²×C₁₀₁	1	1	yes	characteristic
267	#327	C₂²×C₁₀₁	1	8	yes	complemented
268	#324	C₂²×C₁₀₁	1	4	yes	complemented
269	C₂×#41	—	2	4	no	—
270	C₂×#41	—	2	4	no	—
271	C₂×#41	—	4	4	no	—
272	C₂×#41	—	4	4	no	—
273	C₂²×Q₈	—	2	1	no	—
274	C₂²×D₄	—	2	1	no	—
275	C₂²×D₄	—	2	2	no	—
276	C₂²×D₄	—	2	1	no	—
277	C₂²×D₄	—	2	1	no	—
278	C₂²×D₄	D₄×C₁₀₁	1	2	yes	—
279	C₂²×D₄	C₂³×C₁₀₁	1	1	yes	characteristic
280	C₂³×C₄	—	2	2	no	—
281	C₂³×C₄	D₄×C₁₀₁	1	1	yes	characteristic
282	C₂³×C₄	D₄×C₁₀₁	1	1	yes	characteristic
283	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
284	C₂×D₈	—	2	4	no	—
285	C₂²×C₈	—	2	2	no	—
286	#123	—	4	4	no	—
287	C₂²⋊Q₈	—	2	8	no	—
288	C₂²⋊Q₈	—	2	8	no	—
289	#121	—	2	4	no	—
290	#121	—	2	8	no	—
291	#121	—	2	8	no	—
292	#121	—	2	4	no	—
293	#121	—	2	2	no	—
294	#121	—	2	2	no	—
295	#121	—	2	2	no	—
296	#121	—	2	2	no	—
297	#121	D₄×C₁₀₁	1	4	yes	—
298	#121	C₂³×C₁₀₁	1	4	yes	—
299	C₂×C₄⋊C₄	—	2	1	no	—
300	C₂×C₄⋊C₄	—	2	2	no	—
301	C₂×C₄⋊C₄	—	2	2	no	—
302	C₂×C₄⋊C₄	—	2	2	no	—
303	C₂×C₄⋊C₄	—	2	1	no	—
304	C₂×C₄⋊C₄	D₄×C₁₀₁	1	2	yes	—
305	C₂×C₄⋊C₄	D₄×C₁₀₁	1	2	yes	—
306	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	1	yes	characteristic
307	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	2	yes	—
308	C₂×C₂²⋊C₄	—	2	2	no	—
309	C₂×C₂²⋊C₄	—	2	2	no	—
310	C₂×C₂²⋊C₄	—	2	1	no	—
311	C₂×C₂²⋊C₄	—	2	1	no	—
312	C₂×C₂²⋊C₄	—	2	2	no	—
313	C₂×C₂²⋊C₄	—	2	2	no	—
314	#107	—	2	4	no	—
315	#102	—	2	4	no	—
316	#102	—	2	4	no	—
317	C₂²⋊C₈	—	2	2	no	—
318	C₂²⋊C₈	C₂³×C₁₀₁	1	4	yes	—
319	#95	—	2	2	no	—
320	#95	C₂³×C₁₀₁	1	2	yes	—
321	C₂⁴	—	2	2	no	—
322	C₂⁴	—	2	1	no	—
323	C₂⁴	C₂×D₄×C₁₀₁	1	1	yes	characteristic
324	#41	—	4	16	no	—
325	#41	—	4	8	no	—
326	#41	—	4	8	no	—
327	C₂×Q₈	—	2	4	no	—
328	C₂×Q₈	—	4	4	no	—
329	C₂×D₄	—	2	4	no	—
330	C₂×D₄	—	2	4	no	—
331	C₂×D₄	—	2	4	no	—
332	C₂×D₄	—	2	4	no	—
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	—	2	2	no	—
335	C₂×D₄	—	4	4	no	—
336	C₂×D₄	—	4	4	no	—
337	C₂×D₄	—	4	4	no	—
338	C₂×D₄	—	4	1	no	—
339	C₂×D₄	—	4	1	no	—
340	C₂×D₄	—	4	2	no	—
341	C₂×D₄	—	4	2	no	—
342	C₂×D₄	—	8	1	no	—
343	C₂×D₄	—	8	2	no	—
344	C₂×D₄	—	8	2	no	—
345	C₂×D₄	C₂×D₄×C₁₀₁	1	4	yes	—
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	8	no	—
350	C₂²×C₄	—	2	1	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	1	no	—
353	C₂²×C₄	—	2	1	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	4	8	no	—
356	C₂²×C₄	—	8	1	no	—
357	C₂²×C₄	—	8	1	no	—
358	C₂²×C₄	D₈×C₁₀₁	1	4	yes	complemented
359	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
360	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
361	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
362	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
363	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
364	C₂²×C₄	C₂⁴×C₁₀₁	1	1	yes	characteristic
365	D₈	—	8	4	no	—
366	C₂×C₈	—	2	4	no	—
367	C₂×C₈	—	8	2	no	—
368	C₄⋊C₄	—	2	4	no	—
369	C₄⋊C₄	—	2	4	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	2	4	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	4	4	no	—
374	C₄⋊C₄	—	8	1	no	—
375	C₄⋊C₄	C₂×D₄×C₁₀₁	1	4	yes	—
376	C₂²⋊C₄	—	2	8	no	—
377	C₂²⋊C₄	—	2	4	no	—
378	C₂²⋊C₄	—	2	4	no	—
379	C₂²⋊C₄	—	4	2	no	—
380	C₂²⋊C₄	—	4	2	no	—
381	C₂²⋊C₄	—	4	4	no	—
382	C₂²⋊C₄	—	8	2	no	—
383	C₂³	—	2	4	no	—
384	C₂³	—	4	1	no	—
385	C₂³	—	4	1	no	—
386	C₂³	—	4	4	no	—
387	C₂³	—	4	4	no	—
388	C₂³	—	4	2	no	—
389	C₂³	—	4	2	no	—
390	C₂³	—	4	4	no	—
391	C₂³	—	4	1	no	—
392	C₂³	—	4	1	no	—
393	C₂³	—	4	1	no	—
394	C₂³	#120×C₁₀₁	1	1	yes	characteristic
395	C₂³	#120×C₁₀₁	1	1	yes	characteristic
396	C₂³	C₂×D₈×C₁₀₁	1	2	yes	—
397	C₂³	AGL(1,ℤ/8)×C₁₀₁	1	2	yes	—
398	C₂³	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
399	Q₈	—	4	8	no	—
400	D₄	—	4	4	no	—
401	D₄	—	4	8	no	—
402	D₄	—	4	4	no	—
403	D₄	—	4	8	no	—
404	D₄	—	4	4	no	—
405	D₄	—	4	4	no	—
406	D₄	—	8	2	no	—
407	D₄	—	8	4	no	—
408	D₄	—	8	2	no	—
409	D₄	—	8	2	no	—
410	C₂×C₄	—	2	4	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	4	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	4	16	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	4	4	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	8	1	no	—
431	C₂×C₄	#120×C₁₀₁	1	2	yes	—
432	C₂×C₄	C₂×D₈×C₁₀₁	1	4	yes	—
433	C₂×C₄	C₂²×D₄×C₁₀₁	1	2	yes	—
434	C₈	—	4	4	no	—
435	C₂²	—	2	1	no	—
436	C₂²	—	2	1	no	—
437	C₂²	—	2	1	no	—
438	C₂²	—	2	1	no	—
439	C₂²	—	2	1	no	—
440	C₂²	—	2	1	no	—
441	C₂²	—	4	2	no	—
442	C₂²	—	4	2	no	—
443	C₂²	—	4	4	no	—
444	C₂²	—	4	4	no	—
445	C₂²	—	4	4	no	—
446	C₂²	—	8	8	no	—
447	C₂²	—	8	2	no	—
448	C₂²	—	8	2	no	—
449	C₂²	—	8	1	no	—
450	C₂²	—	8	1	no	—
451	C₂²	—	8	1	no	—
452	C₂²	#447×C₁₀₁	1	2	yes	—
453	C₂²	#447×C₁₀₁	1	2	yes	—
454	C₂²	C₂×#120×C₁₀₁	1	1	yes	characteristic
455	C₂²	C₂²×D₈×C₁₀₁	1	1	yes	characteristic
456	C₂²	C₂×AGL(1,ℤ/8)×C₁₀₁	1	1	yes	characteristic
457	C₄	—	2	4	no	—
458	C₄	—	2	2	no	—
459	C₄	—	2	2	no	—
460	C₄	—	4	4	no	—
461	C₄	—	4	2	no	—
462	C₄	—	8	2	no	—
463	C₄	—	8	1	no	—
464	C₂	—	2	1	no	—
465	C₂	—	2	2	no	—
466	C₂	—	2	1	no	—
467	C₂	—	2	2	no	—
468	C₂	—	8	4	no	—
469	C₂	—	16	1	no	—
470	C₂	C₂×#447×C₁₀₁	1	1	yes	characteristic
471	C₂	C₁₀₁×#3020	1	1	yes	characteristic
472	C₂	C₁₀₁×#3026	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×#537×C₁₀₁	C₂	semidirect
2. C₁₀₁×#3186	C₂	semidirect
3. C₁₀₁×#2618	C₂	semidirect
4. C₁₀₁×#1610	C₂	semidirect
5. C₁₀₁×#1598	C₂	semidirect
6. C₁₀₁×#1519	C₂	semidirect
7. C₂×#324×C₁₀₁	C₂	semidirect
20. #480×C₁₀₁	C₂²	semidirect
23. #447×C₁₀₁	C₂²	semidirect
25. #398×C₁₀₁	C₂²	semidirect
27. #394×C₁₀₁	C₂²	semidirect
30. #327×C₁₀₁	C₂²	semidirect
31. #324×C₁₀₁	C₂²	semidirect
121. C₂²×C₄×C₁₀₁	D₈	semidirect
227. #18292	C₁₀₁	direct (N × H)
237. C₂×#537	C₂×C₁₀₁	semidirect
238. #3186	C₂×C₁₀₁	semidirect
239. #2618	C₂×C₁₀₁	semidirect
240. #1610	C₂×C₁₀₁	semidirect
241. #1598	C₂×C₁₀₁	semidirect
242. #1519	C₂×C₁₀₁	semidirect
243. C₂×#324	C₂×C₁₀₁	semidirect
244. C₁₀₁	#18292	direct (N × H)
257. #480	C₂²×C₁₀₁	semidirect
260. #447	C₂²×C₁₀₁	semidirect
262. #398	C₂²×C₁₀₁	semidirect
264. #394	C₂²×C₁₀₁	semidirect
267. #327	C₂²×C₁₀₁	semidirect
268. #324	C₂²×C₁₀₁	semidirect
358. C₂²×C₄	D₈×C₁₀₁	semidirect

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
C₁₀₁×#3186	2
C₁₀₁×#2618	2
C₁₀₁×#1610	2
C₁₀₁×#1598	2
C₁₀₁×#1519	2
C₂×#324×C₁₀₁	2
#18292	101

Subgroups — C101×#18292 #38800443

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#18292 #38800443