Subgroups — C₁₀₁×#23900 #38806051

Order 25856.

3520 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₀₁×#3484	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#120×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×B(4,𝔽₂)×C₁₀₁	C₂	1	2	yes	maximal, complemented
4	C₁₀₁×#2846	C₂	1	2	yes	maximal, complemented
5	C₁₀₁×#2021	C₂	1	4	yes	maximal, complemented
6	C₁₀₁×#1898	C₂	1	2	yes	maximal, complemented
7	C₁₀₁×#1889	C₂	1	2	yes	maximal, complemented
8	C₁₀₁×#1781	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂⁶×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
10	C₂×H(5,𝔽₂)×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
11	C₂³×D₄×C₁₀₁	—	2	1	no	—
12	C₂³×D₄×C₁₀₁	C₂²	1	1	yes	characteristic
13	#546×C₁₀₁	—	2	4	no	—
14	D₄²×C₁₀₁	—	2	4	no	—
15	#535×C₁₀₁	—	2	1	no	—
16	#534×C₁₀₁	—	2	1	no	—
17	#534×C₁₀₁	C₂²	1	2	yes	complemented
18	#525×C₁₀₁	—	2	1	no	—
19	C₂×#120×C₁₀₁	—	2	1	no	—
20	C₂×#120×C₁₀₁	—	2	1	no	—
21	C₂×#120×C₁₀₁	—	2	1	no	—
22	C₂×#120×C₁₀₁	—	2	8	no	—
23	C₂×#120×C₁₀₁	—	2	4	no	—
24	C₂×#120×C₁₀₁	C₂²	1	2	yes	—
25	C₂×#120×C₁₀₁	C₂²	1	2	yes	—
26	C₂×#120×C₁₀₁	C₂²	1	2	yes	complemented
27	C₂×#120×C₁₀₁	C₂²	1	4	yes	complemented
28	#518×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
29	C₂²×C₂²⋊C₄×C₁₀₁	—	2	1	no	—
30	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
31	B(4,𝔽₂)×C₁₀₁	—	2	8	no	—
32	C₂×#99×C₁₀₁	C₂²	1	2	yes	complemented
33	C₂×#99×C₁₀₁	C₂²	1	4	yes	complemented
34	C₂×#99×C₁₀₁	C₂²	1	2	yes	complemented
35	#379×C₁₀₁	—	2	4	no	—
36	#379×C₁₀₁	C₂²	1	4	yes	complemented
37	#379×C₁₀₁	C₂²	1	2	yes	complemented
38	#342×C₁₀₁	C₂²	1	4	yes	complemented
39	C₂⁵×C₁₀₁	—	2	1	no	—
40	C₂⁵×C₁₀₁	—	2	1	no	—
41	C₂⁵×C₁₀₁	—	2	4	no	—
42	C₂⁵×C₁₀₁	—	2	4	no	—
43	C₂⁵×C₁₀₁	—	4	8	no	—
44	C₂⁵×C₁₀₁	—	4	2	no	—
45	C₂⁵×C₁₀₁	D₄	1	1	yes	characteristic, complemented
46	C₂⁵×C₁₀₁	C₂³	1	2	yes	—
47	C₂⁵×C₁₀₁	C₂³	1	1	yes	characteristic
48	H(5,𝔽₂)×C₁₀₁	—	2	4	no	—
49	H(5,𝔽₂)×C₁₀₁	—	4	2	no	—
50	C₂×#41×C₁₀₁	—	2	1	no	—
51	C₂×#41×C₁₀₁	—	2	2	no	—
52	C₂²×D₄×C₁₀₁	—	2	8	no	—
53	C₂²×D₄×C₁₀₁	—	2	2	no	—
54	C₂²×D₄×C₁₀₁	—	2	2	no	—
55	C₂²×D₄×C₁₀₁	—	2	1	no	—
56	C₂²×D₄×C₁₀₁	—	2	4	no	—
57	C₂²×D₄×C₁₀₁	—	2	2	no	—
58	C₂²×D₄×C₁₀₁	—	2	2	no	—
59	C₂²×D₄×C₁₀₁	—	2	4	no	—
60	C₂²×D₄×C₁₀₁	—	2	4	no	—
61	C₂²×D₄×C₁₀₁	—	4	2	no	—
62	C₂²×D₄×C₁₀₁	—	4	8	no	—
63	C₂²×D₄×C₁₀₁	D₄	1	1	yes	characteristic, complemented
64	C₂²×D₄×C₁₀₁	D₄	1	1	yes	characteristic, complemented
65	C₂²×D₄×C₁₀₁	D₄	1	4	yes	complemented
66	C₂²×D₄×C₁₀₁	C₂³	1	1	yes	characteristic
67	C₂²×D₄×C₁₀₁	C₂³	1	1	yes	characteristic
68	C₂²×D₄×C₁₀₁	C₂³	1	2	yes	—
69	C₂³×C₄×C₁₀₁	—	2	1	no	—
70	C₂³×C₄×C₁₀₁	D₄	1	1	yes	characteristic, complemented
71	#127×C₁₀₁	—	2	2	no	—
72	#124×C₁₀₁	—	2	2	no	—
73	#123×C₁₀₁	—	2	2	no	—
74	#123×C₁₀₁	—	2	2	no	—
75	#123×C₁₀₁	—	2	2	no	—
76	C₂²⋊Q₈×C₁₀₁	—	2	2	no	—
77	#121×C₁₀₁	—	2	2	no	—
78	#121×C₁₀₁	—	2	4	no	—
79	#121×C₁₀₁	—	2	4	no	—
80	#121×C₁₀₁	—	2	4	no	—
81	#120×C₁₀₁	—	2	8	no	—
82	#120×C₁₀₁	—	2	8	no	—
83	#120×C₁₀₁	—	2	4	no	—
84	#120×C₁₀₁	—	2	2	no	—
85	#120×C₁₀₁	—	2	2	no	—
86	#120×C₁₀₁	—	2	2	no	—
87	#120×C₁₀₁	—	2	2	no	—
88	#120×C₁₀₁	—	2	4	no	—
89	#120×C₁₀₁	—	2	4	no	—
90	#120×C₁₀₁	—	2	2	no	—
91	#120×C₁₀₁	—	2	4	no	—
92	#120×C₁₀₁	—	2	4	no	—
93	#120×C₁₀₁	—	2	8	no	—
94	#120×C₁₀₁	—	4	4	no	—
95	#120×C₁₀₁	—	4	16	no	—
96	#120×C₁₀₁	D₄	1	8	yes	complemented
97	C₄×D₄×C₁₀₁	—	2	4	no	—
98	C₄×D₄×C₁₀₁	—	2	4	no	—
99	#117×C₁₀₁	—	2	1	no	—
100	C₂×C₂²⋊C₄×C₁₀₁	—	2	8	no	—
101	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
102	C₂×C₂²⋊C₄×C₁₀₁	—	2	1	no	—
103	C₂×C₂²⋊C₄×C₁₀₁	—	2	1	no	—
104	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
105	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
106	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
107	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
108	C₂×C₂²⋊C₄×C₁₀₁	—	2	8	no	—
109	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
110	C₂×C₂²⋊C₄×C₁₀₁	D₄	1	4	yes	complemented
111	C₂×C₂²⋊C₄×C₁₀₁	C₂³	1	4	yes	—
112	C₂×C₂²⋊C₄×C₁₀₁	C₂³	1	2	yes	—
113	C₂×C₂²⋊C₄×C₁₀₁	C₂³	1	2	yes	—
114	#99×C₁₀₁	—	2	4	no	—
115	#99×C₁₀₁	—	2	8	no	—
116	#99×C₁₀₁	—	4	2	no	—
117	C₂⁴×C₁₀₁	—	2	4	no	—
118	C₂⁴×C₁₀₁	—	2	8	no	—
119	C₂⁴×C₁₀₁	—	2	4	no	—
120	C₂⁴×C₁₀₁	—	2	2	no	—
121	C₂⁴×C₁₀₁	—	2	2	no	—
122	C₂⁴×C₁₀₁	—	2	2	no	—
123	C₂⁴×C₁₀₁	—	2	4	no	—
124	C₂⁴×C₁₀₁	—	2	16	no	—
125	C₂⁴×C₁₀₁	—	2	1	no	—
126	C₂⁴×C₁₀₁	—	2	2	no	—
127	C₂⁴×C₁₀₁	—	2	2	no	—
128	C₂⁴×C₁₀₁	—	2	4	no	—
129	C₂⁴×C₁₀₁	—	2	2	no	—
130	C₂⁴×C₁₀₁	—	4	8	no	—
131	C₂⁴×C₁₀₁	—	4	4	no	—
132	C₂⁴×C₁₀₁	—	4	1	no	—
133	C₂⁴×C₁₀₁	—	4	16	no	—
134	C₂⁴×C₁₀₁	—	4	2	no	—
135	C₂⁴×C₁₀₁	—	4	4	no	—
136	C₂⁴×C₁₀₁	—	4	16	no	—
137	C₂⁴×C₁₀₁	—	4	8	no	—
138	C₂⁴×C₁₀₁	—	4	32	no	—
139	C₂⁴×C₁₀₁	—	4	2	no	—
140	C₂⁴×C₁₀₁	—	4	8	no	—
141	C₂⁴×C₁₀₁	—	4	4	no	—
142	C₂⁴×C₁₀₁	—	4	32	no	—
143	C₂⁴×C₁₀₁	—	4	2	no	—
144	C₂⁴×C₁₀₁	—	4	2	no	—
145	C₂⁴×C₁₀₁	C₂×D₄	1	1	yes	characteristic
146	C₂⁴×C₁₀₁	C₂×D₄	1	4	yes	—
147	C₂⁴×C₁₀₁	C₂×D₄	1	1	yes	characteristic
148	C₂⁴×C₁₀₁	C₂×D₄	1	1	yes	characteristic
149	C₂⁴×C₁₀₁	C₂×D₄	1	1	yes	characteristic
150	C₂⁴×C₁₀₁	C₂×D₄	1	4	yes	complemented
151	C₂⁴×C₁₀₁	C₂×D₄	1	2	yes	complemented
152	C₂⁴×C₁₀₁	C₂⁴	1	1	yes	characteristic
153	#41×C₁₀₁	—	4	8	no	—
154	#41×C₁₀₁	—	4	2	no	—
155	#41×C₁₀₁	—	4	2	no	—
156	C₂×Q₈×C₁₀₁	—	2	1	no	—
157	C₂×D₄×C₁₀₁	—	2	2	no	—
158	C₂×D₄×C₁₀₁	—	2	2	no	—
159	C₂×D₄×C₁₀₁	—	2	8	no	—
160	C₂×D₄×C₁₀₁	—	2	2	no	—
161	C₂×D₄×C₁₀₁	—	2	1	no	—
162	C₂×D₄×C₁₀₁	—	2	4	no	—
163	C₂×D₄×C₁₀₁	—	2	2	no	—
164	C₂×D₄×C₁₀₁	—	2	2	no	—
165	C₂×D₄×C₁₀₁	—	2	2	no	—
166	C₂×D₄×C₁₀₁	—	2	8	no	—
167	C₂×D₄×C₁₀₁	—	2	4	no	—
168	C₂×D₄×C₁₀₁	—	2	2	no	—
169	C₂×D₄×C₁₀₁	—	2	2	no	—
170	C₂×D₄×C₁₀₁	—	2	2	no	—
171	C₂×D₄×C₁₀₁	—	2	2	no	—
172	C₂×D₄×C₁₀₁	—	2	2	no	—
173	C₂×D₄×C₁₀₁	—	2	4	no	—
174	C₂×D₄×C₁₀₁	—	2	4	no	—
175	C₂×D₄×C₁₀₁	—	2	4	no	—
176	C₂×D₄×C₁₀₁	—	2	2	no	—
177	C₂×D₄×C₁₀₁	—	4	1	no	—
178	C₂×D₄×C₁₀₁	—	4	1	no	—
179	C₂×D₄×C₁₀₁	—	4	16	no	—
180	C₂×D₄×C₁₀₁	—	4	8	no	—
181	C₂×D₄×C₁₀₁	—	4	8	no	—
182	C₂×D₄×C₁₀₁	—	4	8	no	—
183	C₂×D₄×C₁₀₁	—	4	32	no	—
184	C₂×D₄×C₁₀₁	—	4	2	no	—
185	C₂×D₄×C₁₀₁	—	4	2	no	—
186	C₂×D₄×C₁₀₁	—	4	8	no	—
187	C₂×D₄×C₁₀₁	—	4	8	no	—
188	C₂×D₄×C₁₀₁	—	4	16	no	—
189	C₂×D₄×C₁₀₁	—	8	4	no	—
190	C₂×D₄×C₁₀₁	C₂×D₄	1	4	yes	—
191	C₂²×C₄×C₁₀₁	—	2	4	no	—
192	C₂²×C₄×C₁₀₁	—	2	1	no	—
193	C₂²×C₄×C₁₀₁	—	2	2	no	—
194	C₂²×C₄×C₁₀₁	—	2	2	no	—
195	C₂²×C₄×C₁₀₁	—	2	2	no	—
196	C₂²×C₄×C₁₀₁	—	2	2	no	—
197	C₂²×C₄×C₁₀₁	—	2	2	no	—
198	C₂²×C₄×C₁₀₁	—	2	4	no	—
199	C₂²×C₄×C₁₀₁	—	4	1	no	—
200	C₂²×C₄×C₁₀₁	—	4	4	no	—
201	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
202	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
203	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	complemented
204	C₂²×C₄×C₁₀₁	C₂×D₄	1	4	yes	complemented
205	C₄⋊C₄×C₁₀₁	—	2	2	no	—
206	C₄⋊C₄×C₁₀₁	—	2	4	no	—
207	C₂²⋊C₄×C₁₀₁	—	2	8	no	—
208	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
209	C₂²⋊C₄×C₁₀₁	—	2	2	no	—
210	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
211	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
212	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
213	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
214	C₂²⋊C₄×C₁₀₁	—	2	2	no	—
215	C₂²⋊C₄×C₁₀₁	—	2	2	no	—
216	C₂²⋊C₄×C₁₀₁	—	2	2	no	—
217	C₂²⋊C₄×C₁₀₁	—	2	8	no	—
218	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
219	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
220	C₂²⋊C₄×C₁₀₁	—	4	8	no	—
221	C₂²⋊C₄×C₁₀₁	—	4	16	no	—
222	C₂²⋊C₄×C₁₀₁	—	4	8	no	—
223	C₂²⋊C₄×C₁₀₁	C₂×D₄	1	4	yes	complemented
224	C₄²×C₁₀₁	—	2	2	no	—
225	C₂³×C₁₀₁	—	2	1	no	—
226	C₂³×C₁₀₁	—	2	1	no	—
227	C₂³×C₁₀₁	—	2	4	no	—
228	C₂³×C₁₀₁	—	2	16	no	—
229	C₂³×C₁₀₁	—	2	16	no	—
230	C₂³×C₁₀₁	—	2	8	no	—
231	C₂³×C₁₀₁	—	2	1	no	—
232	C₂³×C₁₀₁	—	2	4	no	—
233	C₂³×C₁₀₁	—	2	1	no	—
234	C₂³×C₁₀₁	—	2	1	no	—
235	C₂³×C₁₀₁	—	2	8	no	—
236	C₂³×C₁₀₁	—	2	8	no	—
237	C₂³×C₁₀₁	—	2	8	no	—
238	C₂³×C₁₀₁	—	2	1	no	—
239	C₂³×C₁₀₁	—	2	1	no	—
240	C₂³×C₁₀₁	—	2	1	no	—
241	C₂³×C₁₀₁	—	2	2	no	—
242	C₂³×C₁₀₁	—	2	1	no	—
243	C₂³×C₁₀₁	—	2	4	no	—
244	C₂³×C₁₀₁	—	4	4	no	—
245	C₂³×C₁₀₁	—	4	2	no	—
246	C₂³×C₁₀₁	—	4	8	no	—
247	C₂³×C₁₀₁	—	4	2	no	—
248	C₂³×C₁₀₁	—	4	4	no	—
249	C₂³×C₁₀₁	—	4	8	no	—
250	C₂³×C₁₀₁	—	4	8	no	—
251	C₂³×C₁₀₁	—	4	8	no	—
252	C₂³×C₁₀₁	—	4	16	no	—
253	C₂³×C₁₀₁	—	4	8	no	—
254	C₂³×C₁₀₁	—	4	8	no	—
255	C₂³×C₁₀₁	—	4	4	no	—
256	C₂³×C₁₀₁	—	4	8	no	—
257	C₂³×C₁₀₁	—	4	8	no	—
258	C₂³×C₁₀₁	—	4	16	no	—
259	C₂³×C₁₀₁	—	4	16	no	—
260	C₂³×C₁₀₁	—	4	64	no	—
261	C₂³×C₁₀₁	—	4	8	no	—
262	C₂³×C₁₀₁	—	4	16	no	—
263	C₂³×C₁₀₁	—	4	2	no	—
264	C₂³×C₁₀₁	—	4	2	no	—
265	C₂³×C₁₀₁	—	4	8	no	—
266	C₂³×C₁₀₁	—	4	2	no	—
267	C₂³×C₁₀₁	—	4	4	no	—
268	C₂³×C₁₀₁	—	4	64	no	—
269	C₂³×C₁₀₁	—	4	16	no	—
270	C₂³×C₁₀₁	—	4	2	no	—
271	C₂³×C₁₀₁	—	4	2	no	—
272	C₂³×C₁₀₁	—	4	4	no	—
273	C₂³×C₁₀₁	—	4	8	no	—
274	C₂³×C₁₀₁	—	4	4	no	—
275	C₂³×C₁₀₁	—	8	2	no	—
276	C₂³×C₁₀₁	—	8	4	no	—
277	C₂³×C₁₀₁	—	8	2	no	—
278	C₂³×C₁₀₁	#120	1	2	yes	—
279	C₂³×C₁₀₁	#120	1	2	yes	—
280	C₂³×C₁₀₁	#120	1	2	yes	complemented
281	C₂³×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
282	C₂³×C₁₀₁	C₂²×D₄	1	2	yes	—
283	C₂³×C₁₀₁	C₂²×D₄	1	2	yes	—
284	C₂³×C₁₀₁	H(5,𝔽₂)	1	2	yes	—
285	Q₈×C₁₀₁	—	4	2	no	—
286	D₄×C₁₀₁	—	2	8	no	—
287	D₄×C₁₀₁	—	4	4	no	—
288	D₄×C₁₀₁	—	4	2	no	—
289	D₄×C₁₀₁	—	4	4	no	—
290	D₄×C₁₀₁	—	4	16	no	—
291	D₄×C₁₀₁	—	4	16	no	—
292	D₄×C₁₀₁	—	4	4	no	—
293	D₄×C₁₀₁	—	4	2	no	—
294	D₄×C₁₀₁	—	4	2	no	—
295	D₄×C₁₀₁	—	4	4	no	—
296	D₄×C₁₀₁	—	4	4	no	—
297	D₄×C₁₀₁	—	4	8	no	—
298	D₄×C₁₀₁	—	8	4	no	—
299	D₄×C₁₀₁	—	8	4	no	—
300	D₄×C₁₀₁	—	8	16	no	—
301	C₂×C₄×C₁₀₁	—	2	1	no	—
302	C₂×C₄×C₁₀₁	—	2	1	no	—
303	C₂×C₄×C₁₀₁	—	2	1	no	—
304	C₂×C₄×C₁₀₁	—	2	4	no	—
305	C₂×C₄×C₁₀₁	—	2	4	no	—
306	C₂×C₄×C₁₀₁	—	2	2	no	—
307	C₂×C₄×C₁₀₁	—	2	1	no	—
308	C₂×C₄×C₁₀₁	—	2	1	no	—
309	C₂×C₄×C₁₀₁	—	2	4	no	—
310	C₂×C₄×C₁₀₁	—	4	4	no	—
311	C₂×C₄×C₁₀₁	—	4	4	no	—
312	C₂×C₄×C₁₀₁	—	4	8	no	—
313	C₂×C₄×C₁₀₁	—	4	4	no	—
314	C₂×C₄×C₁₀₁	—	4	2	no	—
315	C₂×C₄×C₁₀₁	—	4	4	no	—
316	C₂×C₄×C₁₀₁	—	4	8	no	—
317	C₂×C₄×C₁₀₁	—	4	4	no	—
318	C₂×C₄×C₁₀₁	—	8	2	no	—
319	C₂×C₄×C₁₀₁	#120	1	2	yes	complemented
320	C₂²×C₁₀₁	—	2	4	no	—
321	C₂²×C₁₀₁	—	2	4	no	—
322	C₂²×C₁₀₁	—	2	2	no	—
323	C₂²×C₁₀₁	—	2	4	no	—
324	C₂²×C₁₀₁	—	2	2	no	—
325	C₂²×C₁₀₁	—	2	2	no	—
326	C₂²×C₁₀₁	—	2	8	no	—
327	C₂²×C₁₀₁	—	2	16	no	—
328	C₂²×C₁₀₁	—	2	2	no	—
329	C₂²×C₁₀₁	—	2	2	no	—
330	C₂²×C₁₀₁	—	2	4	no	—
331	C₂²×C₁₀₁	—	4	2	no	—
332	C₂²×C₁₀₁	—	4	2	no	—
333	C₂²×C₁₀₁	—	4	16	no	—
334	C₂²×C₁₀₁	—	4	2	no	—
335	C₂²×C₁₀₁	—	4	2	no	—
336	C₂²×C₁₀₁	—	4	4	no	—
337	C₂²×C₁₀₁	—	4	16	no	—
338	C₂²×C₁₀₁	—	4	8	no	—
339	C₂²×C₁₀₁	—	4	8	no	—
340	C₂²×C₁₀₁	—	4	2	no	—
341	C₂²×C₁₀₁	—	4	32	no	—
342	C₂²×C₁₀₁	—	4	2	no	—
343	C₂²×C₁₀₁	—	4	32	no	—
344	C₂²×C₁₀₁	—	4	4	no	—
345	C₂²×C₁₀₁	—	4	2	no	—
346	C₂²×C₁₀₁	—	4	8	no	—
347	C₂²×C₁₀₁	—	4	2	no	—
348	C₂²×C₁₀₁	—	4	1	no	—
349	C₂²×C₁₀₁	—	4	4	no	—
350	C₂²×C₁₀₁	—	4	2	no	—
351	C₂²×C₁₀₁	—	8	1	no	—
352	C₂²×C₁₀₁	—	8	8	no	—
353	C₂²×C₁₀₁	—	8	4	no	—
354	C₂²×C₁₀₁	—	8	1	no	—
355	C₂²×C₁₀₁	—	16	2	no	—
356	C₂²×C₁₀₁	B(4,𝔽₂)	1	4	yes	complemented
357	C₂²×C₁₀₁	C₂×#120	1	1	yes	characteristic
358	C₂²×C₁₀₁	C₂×#120	1	1	yes	characteristic
359	C₂²×C₁₀₁	#534	1	1	yes	characteristic
360	C₂²×C₁₀₁	D₄²	1	4	yes	—
361	C₄×C₁₀₁	—	2	2	no	—
362	C₄×C₁₀₁	—	4	4	no	—
363	C₄×C₁₀₁	—	4	1	no	—
364	C₄×C₁₀₁	—	4	2	no	—
365	C₄×C₁₀₁	—	4	4	no	—
366	C₄×C₁₀₁	—	8	4	no	—
367	#23900	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
368	C₂×C₁₀₁	—	2	1	no	—
369	C₂×C₁₀₁	—	2	4	no	—
370	C₂×C₁₀₁	—	2	1	no	—
371	C₂×C₁₀₁	—	2	4	no	—
372	C₂×C₁₀₁	—	4	8	no	—
373	C₂×C₁₀₁	—	4	2	no	—
374	C₂×C₁₀₁	—	4	2	no	—
375	C₂×C₁₀₁	—	8	1	no	—
376	C₂×C₁₀₁	—	8	2	no	—
377	C₂×C₁₀₁	#2403	1	1	yes	characteristic
378	C₂×C₁₀₁	C₂×B(4,𝔽₂)	1	2	yes	—
379	#3484	C₂×C₁₀₁	1	1	yes	characteristic, complemented
380	C₂²×#120	C₂×C₁₀₁	1	1	yes	characteristic, complemented
381	C₂×B(4,𝔽₂)	C₂×C₁₀₁	1	2	yes	complemented
382	#2846	C₂×C₁₀₁	1	2	yes	complemented
383	#2021	C₂×C₁₀₁	1	4	yes	complemented
384	#1898	C₂×C₁₀₁	1	2	yes	complemented
385	#1889	C₂×C₁₀₁	1	2	yes	complemented
386	#1781	C₂×C₁₀₁	1	1	yes	characteristic, complemented
387	C₁₀₁	#23900	1	1	yes	characteristic, direct product factor, Sylow
388	C₂⁶	C₂²×C₁₀₁	1	1	yes	characteristic, complemented
389	C₂×H(5,𝔽₂)	C₂²×C₁₀₁	1	1	yes	characteristic, complemented
390	C₂³×D₄	—	2	1	no	—
391	C₂³×D₄	C₂²×C₁₀₁	1	1	yes	characteristic
392	#546	—	2	4	no	—
393	D₄²	—	2	4	no	—
394	#535	—	2	1	no	—
395	#534	—	2	1	no	—
396	#534	C₂²×C₁₀₁	1	2	yes	complemented
397	#525	—	2	1	no	—
398	C₂×#120	—	2	1	no	—
399	C₂×#120	—	2	1	no	—
400	C₂×#120	—	2	1	no	—
401	C₂×#120	—	2	8	no	—
402	C₂×#120	—	2	4	no	—
403	C₂×#120	C₂²×C₁₀₁	1	2	yes	—
404	C₂×#120	C₂²×C₁₀₁	1	2	yes	—
405	C₂×#120	C₂²×C₁₀₁	1	2	yes	complemented
406	C₂×#120	C₂²×C₁₀₁	1	4	yes	complemented
407	#518	C₂²×C₁₀₁	1	1	yes	characteristic, complemented
408	C₂²×C₂²⋊C₄	—	2	1	no	—
409	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic, complemented
410	B(4,𝔽₂)	—	2	8	no	—
411	C₂×#99	C₂²×C₁₀₁	1	2	yes	complemented
412	C₂×#99	C₂²×C₁₀₁	1	4	yes	complemented
413	C₂×#99	C₂²×C₁₀₁	1	2	yes	complemented
414	#379	—	2	4	no	—
415	#379	C₂²×C₁₀₁	1	4	yes	complemented
416	#379	C₂²×C₁₀₁	1	2	yes	complemented
417	#342	C₂²×C₁₀₁	1	4	yes	complemented
418	C₂⁵	—	2	1	no	—
419	C₂⁵	—	2	1	no	—
420	C₂⁵	—	2	4	no	—
421	C₂⁵	—	2	4	no	—
422	C₂⁵	—	4	8	no	—
423	C₂⁵	—	4	2	no	—
424	C₂⁵	D₄×C₁₀₁	1	1	yes	characteristic, complemented
425	C₂⁵	C₂³×C₁₀₁	1	2	yes	—
426	C₂⁵	C₂³×C₁₀₁	1	1	yes	characteristic
427	H(5,𝔽₂)	—	2	4	no	—
428	H(5,𝔽₂)	—	4	2	no	—
429	C₂×#41	—	2	1	no	—
430	C₂×#41	—	2	2	no	—
431	C₂²×D₄	—	2	8	no	—
432	C₂²×D₄	—	2	2	no	—
433	C₂²×D₄	—	2	2	no	—
434	C₂²×D₄	—	2	1	no	—
435	C₂²×D₄	—	2	4	no	—
436	C₂²×D₄	—	2	2	no	—
437	C₂²×D₄	—	2	2	no	—
438	C₂²×D₄	—	2	4	no	—
439	C₂²×D₄	—	2	4	no	—
440	C₂²×D₄	—	4	2	no	—
441	C₂²×D₄	—	4	8	no	—
442	C₂²×D₄	D₄×C₁₀₁	1	1	yes	characteristic, complemented
443	C₂²×D₄	D₄×C₁₀₁	1	1	yes	characteristic, complemented
444	C₂²×D₄	D₄×C₁₀₁	1	4	yes	complemented
445	C₂²×D₄	C₂³×C₁₀₁	1	1	yes	characteristic
446	C₂²×D₄	C₂³×C₁₀₁	1	1	yes	characteristic
447	C₂²×D₄	C₂³×C₁₀₁	1	2	yes	—
448	C₂³×C₄	—	2	1	no	—
449	C₂³×C₄	D₄×C₁₀₁	1	1	yes	characteristic, complemented
450	#127	—	2	2	no	—
451	#124	—	2	2	no	—
452	#123	—	2	2	no	—
453	#123	—	2	2	no	—
454	#123	—	2	2	no	—
455	C₂²⋊Q₈	—	2	2	no	—
456	#121	—	2	2	no	—
457	#121	—	2	4	no	—
458	#121	—	2	4	no	—
459	#121	—	2	4	no	—
460	#120	—	2	8	no	—
461	#120	—	2	8	no	—
462	#120	—	2	4	no	—
463	#120	—	2	2	no	—
464	#120	—	2	2	no	—
465	#120	—	2	2	no	—
466	#120	—	2	2	no	—
467	#120	—	2	4	no	—
468	#120	—	2	4	no	—
469	#120	—	2	2	no	—
470	#120	—	2	4	no	—
471	#120	—	2	4	no	—
472	#120	—	2	8	no	—
473	#120	—	4	4	no	—
474	#120	—	4	16	no	—
475	#120	D₄×C₁₀₁	1	8	yes	complemented
476	C₄×D₄	—	2	4	no	—
477	C₄×D₄	—	2	4	no	—
478	#117	—	2	1	no	—
479	C₂×C₂²⋊C₄	—	2	8	no	—
480	C₂×C₂²⋊C₄	—	2	2	no	—
481	C₂×C₂²⋊C₄	—	2	1	no	—
482	C₂×C₂²⋊C₄	—	2	1	no	—
483	C₂×C₂²⋊C₄	—	2	2	no	—
484	C₂×C₂²⋊C₄	—	2	2	no	—
485	C₂×C₂²⋊C₄	—	2	4	no	—
486	C₂×C₂²⋊C₄	—	2	4	no	—
487	C₂×C₂²⋊C₄	—	2	8	no	—
488	C₂×C₂²⋊C₄	—	2	4	no	—
489	C₂×C₂²⋊C₄	D₄×C₁₀₁	1	4	yes	complemented
490	C₂×C₂²⋊C₄	C₂³×C₁₀₁	1	4	yes	—
491	C₂×C₂²⋊C₄	C₂³×C₁₀₁	1	2	yes	—
492	C₂×C₂²⋊C₄	C₂³×C₁₀₁	1	2	yes	—
493	#99	—	2	4	no	—
494	#99	—	2	8	no	—
495	#99	—	4	2	no	—
496	C₂⁴	—	2	4	no	—
497	C₂⁴	—	2	8	no	—
498	C₂⁴	—	2	4	no	—
499	C₂⁴	—	2	2	no	—
500	C₂⁴	—	2	2	no	—
501	C₂⁴	—	2	2	no	—
502	C₂⁴	—	2	4	no	—
503	C₂⁴	—	2	16	no	—
504	C₂⁴	—	2	1	no	—
505	C₂⁴	—	2	2	no	—
506	C₂⁴	—	2	2	no	—
507	C₂⁴	—	2	4	no	—
508	C₂⁴	—	2	2	no	—
509	C₂⁴	—	4	4	no	—
510	C₂⁴	—	4	8	no	—
511	C₂⁴	—	4	1	no	—
512	C₂⁴	—	4	16	no	—
513	C₂⁴	—	4	4	no	—
514	C₂⁴	—	4	2	no	—
515	C₂⁴	—	4	16	no	—
516	C₂⁴	—	4	8	no	—
517	C₂⁴	—	4	32	no	—
518	C₂⁴	—	4	8	no	—
519	C₂⁴	—	4	2	no	—
520	C₂⁴	—	4	4	no	—
521	C₂⁴	—	4	32	no	—
522	C₂⁴	—	4	2	no	—
523	C₂⁴	—	4	2	no	—
524	C₂⁴	C₂×D₄×C₁₀₁	1	1	yes	characteristic
525	C₂⁴	C₂×D₄×C₁₀₁	1	4	yes	—
526	C₂⁴	C₂×D₄×C₁₀₁	1	1	yes	characteristic
527	C₂⁴	C₂×D₄×C₁₀₁	1	1	yes	characteristic
528	C₂⁴	C₂×D₄×C₁₀₁	1	1	yes	characteristic
529	C₂⁴	C₂×D₄×C₁₀₁	1	4	yes	complemented
530	C₂⁴	C₂×D₄×C₁₀₁	1	2	yes	complemented
531	C₂⁴	C₂⁴×C₁₀₁	1	1	yes	characteristic
532	#41	—	4	8	no	—
533	#41	—	4	2	no	—
534	#41	—	4	2	no	—
535	C₂×Q₈	—	2	1	no	—
536	C₂×D₄	—	2	2	no	—
537	C₂×D₄	—	2	2	no	—
538	C₂×D₄	—	2	8	no	—
539	C₂×D₄	—	2	2	no	—
540	C₂×D₄	—	2	1	no	—
541	C₂×D₄	—	2	4	no	—
542	C₂×D₄	—	2	2	no	—
543	C₂×D₄	—	2	2	no	—
544	C₂×D₄	—	2	2	no	—
545	C₂×D₄	—	2	8	no	—
546	C₂×D₄	—	2	4	no	—
547	C₂×D₄	—	2	2	no	—
548	C₂×D₄	—	2	2	no	—
549	C₂×D₄	—	2	2	no	—
550	C₂×D₄	—	2	2	no	—
551	C₂×D₄	—	2	2	no	—
552	C₂×D₄	—	2	4	no	—
553	C₂×D₄	—	2	4	no	—
554	C₂×D₄	—	2	4	no	—
555	C₂×D₄	—	2	2	no	—
556	C₂×D₄	—	4	1	no	—
557	C₂×D₄	—	4	1	no	—
558	C₂×D₄	—	4	16	no	—
559	C₂×D₄	—	4	8	no	—
560	C₂×D₄	—	4	8	no	—
561	C₂×D₄	—	4	8	no	—
562	C₂×D₄	—	4	32	no	—
563	C₂×D₄	—	4	2	no	—
564	C₂×D₄	—	4	2	no	—
565	C₂×D₄	—	4	8	no	—
566	C₂×D₄	—	4	8	no	—
567	C₂×D₄	—	4	16	no	—
568	C₂×D₄	—	8	4	no	—
569	C₂×D₄	C₂×D₄×C₁₀₁	1	4	yes	—
570	C₂²×C₄	—	2	4	no	—
571	C₂²×C₄	—	2	1	no	—
572	C₂²×C₄	—	2	2	no	—
573	C₂²×C₄	—	2	2	no	—
574	C₂²×C₄	—	2	2	no	—
575	C₂²×C₄	—	2	2	no	—
576	C₂²×C₄	—	2	2	no	—
577	C₂²×C₄	—	2	4	no	—
578	C₂²×C₄	—	4	1	no	—
579	C₂²×C₄	—	4	4	no	—
580	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
581	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
582	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	complemented
583	C₂²×C₄	C₂×D₄×C₁₀₁	1	4	yes	complemented
584	C₄⋊C₄	—	2	2	no	—
585	C₄⋊C₄	—	2	4	no	—
586	C₂²⋊C₄	—	2	8	no	—
587	C₂²⋊C₄	—	2	4	no	—
588	C₂²⋊C₄	—	2	2	no	—
589	C₂²⋊C₄	—	2	4	no	—
590	C₂²⋊C₄	—	2	4	no	—
591	C₂²⋊C₄	—	2	4	no	—
592	C₂²⋊C₄	—	2	4	no	—
593	C₂²⋊C₄	—	2	2	no	—
594	C₂²⋊C₄	—	2	2	no	—
595	C₂²⋊C₄	—	2	2	no	—
596	C₂²⋊C₄	—	2	8	no	—
597	C₂²⋊C₄	—	2	4	no	—
598	C₂²⋊C₄	—	2	4	no	—
599	C₂²⋊C₄	—	4	8	no	—
600	C₂²⋊C₄	—	4	16	no	—
601	C₂²⋊C₄	—	4	8	no	—
602	C₂²⋊C₄	C₂×D₄×C₁₀₁	1	4	yes	complemented
603	C₄²	—	2	2	no	—
604	C₂³	—	2	4	no	—
605	C₂³	—	2	1	no	—
606	C₂³	—	2	1	no	—
607	C₂³	—	2	16	no	—
608	C₂³	—	2	16	no	—
609	C₂³	—	2	8	no	—
610	C₂³	—	2	8	no	—
611	C₂³	—	2	1	no	—
612	C₂³	—	2	4	no	—
613	C₂³	—	2	1	no	—
614	C₂³	—	2	1	no	—
615	C₂³	—	2	8	no	—
616	C₂³	—	2	8	no	—
617	C₂³	—	2	1	no	—
618	C₂³	—	2	1	no	—
619	C₂³	—	2	2	no	—
620	C₂³	—	2	1	no	—
621	C₂³	—	2	1	no	—
622	C₂³	—	2	4	no	—
623	C₂³	—	4	4	no	—
624	C₂³	—	4	2	no	—
625	C₂³	—	4	8	no	—
626	C₂³	—	4	2	no	—
627	C₂³	—	4	4	no	—
628	C₂³	—	4	8	no	—
629	C₂³	—	4	8	no	—
630	C₂³	—	4	8	no	—
631	C₂³	—	4	16	no	—
632	C₂³	—	4	8	no	—
633	C₂³	—	4	8	no	—
634	C₂³	—	4	4	no	—
635	C₂³	—	4	8	no	—
636	C₂³	—	4	8	no	—
637	C₂³	—	4	16	no	—
638	C₂³	—	4	16	no	—
639	C₂³	—	4	64	no	—
640	C₂³	—	4	8	no	—
641	C₂³	—	4	16	no	—
642	C₂³	—	4	2	no	—
643	C₂³	—	4	2	no	—
644	C₂³	—	4	8	no	—
645	C₂³	—	4	2	no	—
646	C₂³	—	4	4	no	—
647	C₂³	—	4	64	no	—
648	C₂³	—	4	16	no	—
649	C₂³	—	4	8	no	—
650	C₂³	—	4	2	no	—
651	C₂³	—	4	2	no	—
652	C₂³	—	4	4	no	—
653	C₂³	—	4	4	no	—
654	C₂³	—	8	2	no	—
655	C₂³	—	8	4	no	—
656	C₂³	—	8	2	no	—
657	C₂³	#120×C₁₀₁	1	2	yes	—
658	C₂³	#120×C₁₀₁	1	2	yes	—
659	C₂³	#120×C₁₀₁	1	2	yes	complemented
660	C₂³	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
661	C₂³	C₂²×D₄×C₁₀₁	1	2	yes	—
662	C₂³	C₂²×D₄×C₁₀₁	1	2	yes	—
663	C₂³	H(5,𝔽₂)×C₁₀₁	1	2	yes	—
664	Q₈	—	4	2	no	—
665	D₄	—	2	8	no	—
666	D₄	—	4	4	no	—
667	D₄	—	4	2	no	—
668	D₄	—	4	4	no	—
669	D₄	—	4	16	no	—
670	D₄	—	4	16	no	—
671	D₄	—	4	4	no	—
672	D₄	—	4	8	no	—
673	D₄	—	4	2	no	—
674	D₄	—	4	2	no	—
675	D₄	—	4	4	no	—
676	D₄	—	4	4	no	—
677	D₄	—	8	4	no	—
678	D₄	—	8	4	no	—
679	D₄	—	8	16	no	—
680	C₂×C₄	—	2	1	no	—
681	C₂×C₄	—	2	1	no	—
682	C₂×C₄	—	2	4	no	—
683	C₂×C₄	—	2	1	no	—
684	C₂×C₄	—	2	4	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	1	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	2	4	no	—
689	C₂×C₄	—	4	4	no	—
690	C₂×C₄	—	4	4	no	—
691	C₂×C₄	—	4	8	no	—
692	C₂×C₄	—	4	4	no	—
693	C₂×C₄	—	4	2	no	—
694	C₂×C₄	—	4	4	no	—
695	C₂×C₄	—	4	8	no	—
696	C₂×C₄	—	4	4	no	—
697	C₂×C₄	—	8	2	no	—
698	C₂×C₄	#120×C₁₀₁	1	2	yes	complemented
699	C₂²	—	2	4	no	—
700	C₂²	—	2	4	no	—
701	C₂²	—	2	2	no	—
702	C₂²	—	2	4	no	—
703	C₂²	—	2	2	no	—
704	C₂²	—	2	2	no	—
705	C₂²	—	2	8	no	—
706	C₂²	—	2	16	no	—
707	C₂²	—	2	2	no	—
708	C₂²	—	2	2	no	—
709	C₂²	—	2	4	no	—
710	C₂²	—	4	2	no	—
711	C₂²	—	4	2	no	—
712	C₂²	—	4	16	no	—
713	C₂²	—	4	2	no	—
714	C₂²	—	4	2	no	—
715	C₂²	—	4	4	no	—
716	C₂²	—	4	16	no	—
717	C₂²	—	4	8	no	—
718	C₂²	—	4	32	no	—
719	C₂²	—	4	8	no	—
720	C₂²	—	4	2	no	—
721	C₂²	—	4	2	no	—
722	C₂²	—	4	32	no	—
723	C₂²	—	4	4	no	—
724	C₂²	—	4	2	no	—
725	C₂²	—	4	8	no	—
726	C₂²	—	4	2	no	—
727	C₂²	—	4	1	no	—
728	C₂²	—	4	4	no	—
729	C₂²	—	4	2	no	—
730	C₂²	—	8	1	no	—
731	C₂²	—	8	8	no	—
732	C₂²	—	8	4	no	—
733	C₂²	—	8	1	no	—
734	C₂²	—	16	2	no	—
735	C₂²	B(4,𝔽₂)×C₁₀₁	1	4	yes	complemented
736	C₂²	C₂×#120×C₁₀₁	1	1	yes	characteristic
737	C₂²	C₂×#120×C₁₀₁	1	1	yes	characteristic
738	C₂²	#534×C₁₀₁	1	1	yes	characteristic
739	C₂²	D₄²×C₁₀₁	1	4	yes	—
740	C₄	—	2	2	no	—
741	C₄	—	4	4	no	—
742	C₄	—	4	1	no	—
743	C₄	—	4	2	no	—
744	C₄	—	4	4	no	—
745	C₄	—	8	4	no	—
746	C₂	—	2	1	no	—
747	C₂	—	2	4	no	—
748	C₂	—	2	4	no	—
749	C₂	—	2	1	no	—
750	C₂	—	4	8	no	—
751	C₂	—	4	2	no	—
752	C₂	—	4	2	no	—
753	C₂	—	8	1	no	—
754	C₂	—	8	2	no	—
755	C₂	C₁₀₁×#2403	1	1	yes	characteristic
756	C₂	C₂×B(4,𝔽₂)×C₁₀₁	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₀₁	C₂×#120
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₁₀₁
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₁ ◁ C₂⁵×C₁₀₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₀₁×#3484	C₂	semidirect
2. C₂²×#120×C₁₀₁	C₂	semidirect
3. C₂×B(4,𝔽₂)×C₁₀₁	C₂	semidirect
4. C₁₀₁×#2846	C₂	semidirect
5. C₁₀₁×#2021	C₂	semidirect
6. C₁₀₁×#1898	C₂	semidirect
7. C₁₀₁×#1889	C₂	semidirect
8. C₁₀₁×#1781	C₂	semidirect
9. C₂⁶×C₁₀₁	C₂²	semidirect
10. C₂×H(5,𝔽₂)×C₁₀₁	C₂²	semidirect
17. #534×C₁₀₁	C₂²	semidirect
26. C₂×#120×C₁₀₁	C₂²	semidirect
27. C₂×#120×C₁₀₁	C₂²	semidirect
28. #518×C₁₀₁	C₂²	semidirect
30. C₂²×C₂²⋊C₄×C₁₀₁	C₂²	semidirect
32. C₂×#99×C₁₀₁	C₂²	semidirect
33. C₂×#99×C₁₀₁	C₂²	semidirect
34. C₂×#99×C₁₀₁	C₂²	semidirect
36. #379×C₁₀₁	C₂²	semidirect
37. #379×C₁₀₁	C₂²	semidirect
38. #342×C₁₀₁	C₂²	semidirect
45. C₂⁵×C₁₀₁	D₄	semidirect
63. C₂²×D₄×C₁₀₁	D₄	semidirect
64. C₂²×D₄×C₁₀₁	D₄	semidirect
65. C₂²×D₄×C₁₀₁	D₄	semidirect
70. C₂³×C₄×C₁₀₁	D₄	semidirect
96. #120×C₁₀₁	D₄	semidirect
110. C₂×C₂²⋊C₄×C₁₀₁	D₄	semidirect
150. C₂⁴×C₁₀₁	C₂×D₄	semidirect
151. C₂⁴×C₁₀₁	C₂×D₄	semidirect
203. C₂²×C₄×C₁₀₁	C₂×D₄	semidirect
204. C₂²×C₄×C₁₀₁	C₂×D₄	semidirect
223. C₂²⋊C₄×C₁₀₁	C₂×D₄	semidirect
280. C₂³×C₁₀₁	#120	semidirect
319. C₂×C₄×C₁₀₁	#120	semidirect
356. C₂²×C₁₀₁	B(4,𝔽₂)	semidirect
367. #23900	C₁₀₁	direct (N × H)
379. #3484	C₂×C₁₀₁	semidirect
380. C₂²×#120	C₂×C₁₀₁	semidirect
381. C₂×B(4,𝔽₂)	C₂×C₁₀₁	semidirect
382. #2846	C₂×C₁₀₁	semidirect
383. #2021	C₂×C₁₀₁	semidirect
384. #1898	C₂×C₁₀₁	semidirect
385. #1889	C₂×C₁₀₁	semidirect
386. #1781	C₂×C₁₀₁	semidirect
387. C₁₀₁	#23900	direct (N × H)
388. C₂⁶	C₂²×C₁₀₁	semidirect
389. C₂×H(5,𝔽₂)	C₂²×C₁₀₁	semidirect
396. #534	C₂²×C₁₀₁	semidirect
405. C₂×#120	C₂²×C₁₀₁	semidirect
406. C₂×#120	C₂²×C₁₀₁	semidirect
407. #518	C₂²×C₁₀₁	semidirect
409. C₂²×C₂²⋊C₄	C₂²×C₁₀₁	semidirect
411. C₂×#99	C₂²×C₁₀₁	semidirect
412. C₂×#99	C₂²×C₁₀₁	semidirect
413. C₂×#99	C₂²×C₁₀₁	semidirect
415. #379	C₂²×C₁₀₁	semidirect
416. #379	C₂²×C₁₀₁	semidirect
417. #342	C₂²×C₁₀₁	semidirect
424. C₂⁵	D₄×C₁₀₁	semidirect
442. C₂²×D₄	D₄×C₁₀₁	semidirect
443. C₂²×D₄	D₄×C₁₀₁	semidirect
444. C₂²×D₄	D₄×C₁₀₁	semidirect
449. C₂³×C₄	D₄×C₁₀₁	semidirect
475. #120	D₄×C₁₀₁	semidirect
489. C₂×C₂²⋊C₄	D₄×C₁₀₁	semidirect
529. C₂⁴	C₂×D₄×C₁₀₁	semidirect
530. C₂⁴	C₂×D₄×C₁₀₁	semidirect
582. C₂²×C₄	C₂×D₄×C₁₀₁	semidirect
583. C₂²×C₄	C₂×D₄×C₁₀₁	semidirect
602. C₂²⋊C₄	C₂×D₄×C₁₀₁	semidirect
659. C₂³	#120×C₁₀₁	semidirect
698. C₂×C₄	#120×C₁₀₁	semidirect
735. C₂²	B(4,𝔽₂)×C₁₀₁	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₀₁×#3484	2
C₂²×#120×C₁₀₁	2
C₂×B(4,𝔽₂)×C₁₀₁	2
C₁₀₁×#2846	2
C₁₀₁×#2021	2
C₁₀₁×#1898	2
C₁₀₁×#1889	2
C₁₀₁×#1781	2
#23900	101

Subgroups — C101×#23900 #38806051

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#23900 #38806051