Subgroups — C₁₀₁×#20314 #38802465

Order 25856.

716 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₀₁×#3354	C₂	1	2	yes	maximal, complemented
2	C₁₀₁×#3272	C₂	1	2	yes	maximal, complemented
3	C₁₀₁×#1705	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₀₁×#1691	C₂	1	2	yes	maximal, complemented
5	C₁₀₁×#1685	C₂	1	2	yes	maximal, complemented
6	C₁₀₁×#1654	C₂	1	2	yes	maximal, complemented
7	C₁₀₁×#1629	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₀₁×#1624	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₀₁×#1589	C₂	1	2	yes	maximal, complemented
10	C₂×AGL(1,ℤ/8)×C₁₀₁	—	2	2	no	—
11	#555×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
12	#547×C₁₀₁	C₂²	1	2	yes	—
13	D₄²×C₁₀₁	C₂²	1	1	yes	characteristic
14	#498×C₁₀₁	C₂²	1	2	yes	complemented
15	#498×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
16	#492×C₁₀₁	C₂²	1	2	yes	—
17	#492×C₁₀₁	C₂²	1	1	yes	characteristic
18	#482×C₁₀₁	—	2	2	no	—
19	#481×C₁₀₁	—	2	2	no	—
20	#476×C₁₀₁	C₂²	1	2	yes	—
21	#474×C₁₀₁	C₂²	1	2	yes	complemented
22	#469×C₁₀₁	—	2	2	no	—
23	#468×C₁₀₁	—	2	2	no	—
24	#461×C₁₀₁	C₂²	1	2	yes	—
25	#459×C₁₀₁	C₂²	1	2	yes	—
26	#450×C₁₀₁	—	2	2	no	—
27	#449×C₁₀₁	—	2	2	no	—
28	C₄×D₈×C₁₀₁	C₂²	1	2	yes	—
29	#436×C₁₀₁	C₂²	1	2	yes	—
30	#436×C₁₀₁	C₂²	1	2	yes	complemented
31	#428×C₁₀₁	—	2	2	no	—
32	#335×C₁₀₁	C₂²	1	2	yes	complemented
33	#333×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
34	#332×C₁₀₁	C₂²	1	2	yes	complemented
35	#331×C₁₀₁	C₂²	1	1	yes	characteristic
36	D₄⋊C₈×C₁₀₁	C₂²	1	2	yes	—
37	D₄⋊C₈×C₁₀₁	C₂²	1	2	yes	complemented
38	C₈²×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
39	C₂×#41×C₁₀₁	—	2	2	no	—
40	C₂²×D₄×C₁₀₁	—	2	2	no	—
41	AGL(1,ℤ/8)×C₁₀₁	—	4	8	no	—
42	C₂×SD₁₆×C₁₀₁	—	2	2	no	—
43	C₂×SD₁₆×C₁₀₁	—	2	2	no	—
44	C₂×SD₁₆×C₁₀₁	—	2	2	no	—
45	C₂×SD₁₆×C₁₀₁	—	4	1	no	—
46	C₂×D₈×C₁₀₁	—	2	2	no	—
47	C₂×D₈×C₁₀₁	D₄	1	2	yes	—
48	C₂×M₁₆×C₁₀₁	—	2	2	no	—
49	C₂×M₁₆×C₁₀₁	—	2	2	no	—
50	C₄⋊Q₈×C₁₀₁	C₂³	1	2	yes	—
51	C₄⋊Q₈×C₁₀₁	C₂³	1	1	yes	characteristic
52	#127×C₁₀₁	C₂³	1	1	yes	characteristic
53	#124×C₁₀₁	—	4	1	no	—
54	#123×C₁₀₁	—	4	2	no	—
55	C₂²⋊Q₈×C₁₀₁	—	2	2	no	—
56	#121×C₁₀₁	—	2	2	no	—
57	#121×C₁₀₁	—	2	2	no	—
58	#121×C₁₀₁	—	2	2	no	—
59	#120×C₁₀₁	—	4	1	no	—
60	C₄×D₄×C₁₀₁	C₂³	1	2	yes	—
61	C₄×D₄×C₁₀₁	C₂³	1	2	yes	—
62	#117×C₁₀₁	—	2	2	no	—
63	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
64	#107×C₁₀₁	—	2	2	no	—
65	#107×C₁₀₁	D₄	1	2	yes	—
66	#106×C₁₀₁	—	2	2	no	—
67	#106×C₁₀₁	—	2	2	no	—
68	#106×C₁₀₁	—	2	2	no	—
69	#106×C₁₀₁	—	4	1	no	—
70	C₄⋊C₈×C₁₀₁	C₂³	1	2	yes	—
71	C₄⋊C₈×C₁₀₁	C₂³	1	2	yes	—
72	#103×C₁₀₁	—	2	2	no	—
73	#102×C₁₀₁	—	2	2	no	—
74	#102×C₁₀₁	—	2	2	no	—
75	#102×C₁₀₁	—	2	2	no	—
76	#102×C₁₀₁	D₄	1	2	yes	—
77	#102×C₁₀₁	D₄	1	2	yes	—
78	C₂²⋊C₈×C₁₀₁	—	2	2	no	—
79	C₂²⋊C₈×C₁₀₁	—	2	2	no	—
80	C₄×C₈×C₁₀₁	C₂³	1	1	yes	characteristic
81	C₄×C₈×C₁₀₁	C₂³	1	2	yes	—
82	C₂⁴×C₁₀₁	—	4	1	no	—
83	#41×C₁₀₁	—	4	4	no	—
84	#41×C₁₀₁	—	8	2	no	—
85	C₂×Q₈×C₁₀₁	—	2	2	no	—
86	C₂×Q₈×C₁₀₁	—	2	1	no	—
87	C₂×D₄×C₁₀₁	—	2	2	no	—
88	C₂×D₄×C₁₀₁	—	2	1	no	—
89	C₂×D₄×C₁₀₁	—	4	2	no	—
90	C₂×D₄×C₁₀₁	—	4	4	no	—
91	C₂×D₄×C₁₀₁	—	4	2	no	—
92	C₂×D₄×C₁₀₁	—	4	1	no	—
93	C₂×D₄×C₁₀₁	—	8	2	no	—
94	C₂×D₄×C₁₀₁	C₂×D₄	1	2	yes	—
95	C₂×D₄×C₁₀₁	C₂×D₄	1	2	yes	—
96	C₂²×C₄×C₁₀₁	—	2	2	no	—
97	C₂²×C₄×C₁₀₁	—	2	2	no	—
98	C₂²×C₄×C₁₀₁	—	4	2	no	—
99	SD₁₆×C₁₀₁	—	4	4	no	—
100	SD₁₆×C₁₀₁	—	4	4	no	—
101	SD₁₆×C₁₀₁	—	8	2	no	—
102	SD₁₆×C₁₀₁	—	8	2	no	—
103	D₈×C₁₀₁	—	2	4	no	—
104	D₈×C₁₀₁	—	4	4	no	—
105	M₁₆×C₁₀₁	—	4	4	no	—
106	M₁₆×C₁₀₁	—	4	4	no	—
107	C₂×C₈×C₁₀₁	—	2	1	no	—
108	C₂×C₈×C₁₀₁	—	2	2	no	—
109	C₂×C₈×C₁₀₁	—	2	2	no	—
110	C₂×C₈×C₁₀₁	C₂×D₄	1	2	yes	—
111	C₂×C₈×C₁₀₁	C₂×D₄	1	2	yes	—
112	C₄⋊C₄×C₁₀₁	—	2	2	no	—
113	C₄⋊C₄×C₁₀₁	—	2	2	no	—
114	C₄⋊C₄×C₁₀₁	—	2	2	no	—
115	C₄⋊C₄×C₁₀₁	—	4	2	no	—
116	C₄⋊C₄×C₁₀₁	C₂×D₄	1	2	yes	—
117	C₄⋊C₄×C₁₀₁	C₂×D₄	1	2	yes	—
118	C₂²⋊C₄×C₁₀₁	—	2	2	no	—
119	C₂²⋊C₄×C₁₀₁	—	2	2	no	—
120	C₂²⋊C₄×C₁₀₁	—	4	1	no	—
121	C₂²⋊C₄×C₁₀₁	—	4	2	no	—
122	C₂²⋊C₄×C₁₀₁	—	4	2	no	—
123	C₄²×C₁₀₁	—	4	1	no	—
124	C₄²×C₁₀₁	C₂⁴	1	1	yes	characteristic
125	C₂³×C₁₀₁	—	2	2	no	—
126	C₂³×C₁₀₁	—	2	2	no	—
127	C₂³×C₁₀₁	—	4	1	no	—
128	C₂³×C₁₀₁	—	8	4	no	—
129	C₂³×C₁₀₁	—	16	1	no	—
130	Q₈×C₁₀₁	—	4	2	no	—
131	Q₈×C₁₀₁	—	4	2	no	—
132	Q₈×C₁₀₁	—	8	1	no	—
133	D₄×C₁₀₁	—	2	2	no	—
134	D₄×C₁₀₁	—	2	2	no	—
135	D₄×C₁₀₁	—	2	2	no	—
136	D₄×C₁₀₁	—	2	2	no	—
137	D₄×C₁₀₁	—	4	2	no	—
138	D₄×C₁₀₁	—	4	2	no	—
139	D₄×C₁₀₁	—	8	1	no	—
140	D₄×C₁₀₁	—	8	4	no	—
141	D₄×C₁₀₁	—	8	4	no	—
142	D₄×C₁₀₁	—	16	1	no	—
143	C₂×C₄×C₁₀₁	—	2	2	no	—
144	C₂×C₄×C₁₀₁	—	2	2	no	—
145	C₂×C₄×C₁₀₁	—	4	2	no	—
146	C₂×C₄×C₁₀₁	—	4	2	no	—
147	C₂×C₄×C₁₀₁	—	4	2	no	—
148	C₂×C₄×C₁₀₁	—	4	2	no	—
149	C₂×C₄×C₁₀₁	—	4	1	no	—
150	C₂×C₄×C₁₀₁	—	4	2	no	—
151	C₂×C₄×C₁₀₁	—	8	4	no	—
152	C₂×C₄×C₁₀₁	C₂²×D₄	1	2	yes	—
153	C₂×C₄×C₁₀₁	H(5,𝔽₂)	1	1	yes	characteristic
154	C₈×C₁₀₁	—	2	2	no	—
155	C₈×C₁₀₁	—	2	2	no	—
156	C₈×C₁₀₁	—	4	2	no	—
157	C₈×C₁₀₁	—	4	2	no	—
158	C₈×C₁₀₁	AGL(1,ℤ/8)	1	4	yes	complemented
159	C₂²×C₁₀₁	—	4	2	no	—
160	C₂²×C₁₀₁	—	4	2	no	—
161	C₂²×C₁₀₁	—	4	2	no	—
162	C₂²×C₁₀₁	—	4	2	no	—
163	C₂²×C₁₀₁	—	4	2	no	—
164	C₂²×C₁₀₁	—	4	2	no	—
165	C₂²×C₁₀₁	—	8	2	no	—
166	C₂²×C₁₀₁	—	8	1	no	—
167	C₂²×C₁₀₁	—	16	4	no	—
168	C₂²×C₁₀₁	D₄²	1	1	yes	characteristic
169	C₄×C₁₀₁	—	2	1	no	—
170	C₄×C₁₀₁	—	4	2	no	—
171	C₄×C₁₀₁	—	4	2	no	—
172	C₄×C₁₀₁	—	8	2	no	—
173	C₄×C₁₀₁	—	8	1	no	—
174	C₄×C₁₀₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
175	C₄×C₁₀₁	#577	1	2	yes	—
176	#20314	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
177	C₂×C₁₀₁	—	8	2	no	—
178	C₂×C₁₀₁	—	8	2	no	—
179	C₂×C₁₀₁	—	16	1	no	—
180	C₂×C₁₀₁	#3272	1	2	yes	—
181	C₂×C₁₀₁	#3291	1	1	yes	characteristic
182	#3354	C₂×C₁₀₁	1	2	yes	complemented
183	#3272	C₂×C₁₀₁	1	2	yes	complemented
184	#1705	C₂×C₁₀₁	1	1	yes	characteristic, complemented
185	#1691	C₂×C₁₀₁	1	2	yes	complemented
186	#1685	C₂×C₁₀₁	1	2	yes	complemented
187	#1654	C₂×C₁₀₁	1	2	yes	complemented
188	#1629	C₂×C₁₀₁	1	1	yes	characteristic, complemented
189	#1624	C₂×C₁₀₁	1	1	yes	characteristic, complemented
190	#1589	C₂×C₁₀₁	1	2	yes	complemented
191	C₁₀₁	#20314	1	1	yes	characteristic, direct product factor, Sylow
192	C₂×AGL(1,ℤ/8)	—	2	2	no	—
193	#555	C₂²×C₁₀₁	1	1	yes	characteristic, complemented
194	#547	C₂²×C₁₀₁	1	2	yes	—
195	D₄²	C₂²×C₁₀₁	1	1	yes	characteristic
196	#498	C₂²×C₁₀₁	1	2	yes	complemented
197	#498	C₂²×C₁₀₁	1	1	yes	characteristic, complemented
198	#492	C₂²×C₁₀₁	1	2	yes	—
199	#492	C₂²×C₁₀₁	1	1	yes	characteristic
200	#482	—	2	2	no	—
201	#481	—	2	2	no	—
202	#476	C₂²×C₁₀₁	1	2	yes	—
203	#474	C₂²×C₁₀₁	1	2	yes	complemented
204	#469	—	2	2	no	—
205	#468	—	2	2	no	—
206	#461	C₂²×C₁₀₁	1	2	yes	—
207	#459	C₂²×C₁₀₁	1	2	yes	—
208	#450	—	2	2	no	—
209	#449	—	2	2	no	—
210	C₄×D₈	C₂²×C₁₀₁	1	2	yes	—
211	#436	C₂²×C₁₀₁	1	2	yes	—
212	#436	C₂²×C₁₀₁	1	2	yes	complemented
213	#428	—	2	2	no	—
214	#335	C₂²×C₁₀₁	1	2	yes	complemented
215	#333	C₂²×C₁₀₁	1	1	yes	characteristic, complemented
216	#332	C₂²×C₁₀₁	1	2	yes	complemented
217	#331	C₂²×C₁₀₁	1	1	yes	characteristic
218	D₄⋊C₈	C₂²×C₁₀₁	1	2	yes	—
219	D₄⋊C₈	C₂²×C₁₀₁	1	2	yes	complemented
220	C₈²	C₂²×C₁₀₁	1	1	yes	characteristic, complemented
221	C₂×#41	—	2	2	no	—
222	C₂²×D₄	—	2	2	no	—
223	AGL(1,ℤ/8)	—	4	8	no	—
224	C₂×SD₁₆	—	2	2	no	—
225	C₂×SD₁₆	—	2	2	no	—
226	C₂×SD₁₆	—	2	2	no	—
227	C₂×SD₁₆	—	4	1	no	—
228	C₂×D₈	—	2	2	no	—
229	C₂×D₈	D₄×C₁₀₁	1	2	yes	—
230	C₂×M₁₆	—	2	2	no	—
231	C₂×M₁₆	—	2	2	no	—
232	C₄⋊Q₈	C₂³×C₁₀₁	1	2	yes	—
233	C₄⋊Q₈	C₂³×C₁₀₁	1	1	yes	characteristic
234	#127	C₂³×C₁₀₁	1	1	yes	characteristic
235	#124	—	4	1	no	—
236	#123	—	4	2	no	—
237	C₂²⋊Q₈	—	2	2	no	—
238	#121	—	2	2	no	—
239	#121	—	2	2	no	—
240	#121	—	2	2	no	—
241	#120	—	4	1	no	—
242	C₄×D₄	C₂³×C₁₀₁	1	2	yes	—
243	C₄×D₄	C₂³×C₁₀₁	1	2	yes	—
244	#117	—	2	2	no	—
245	C₂×C₄⋊C₄	—	2	2	no	—
246	#107	—	2	2	no	—
247	#107	D₄×C₁₀₁	1	2	yes	—
248	#106	—	2	2	no	—
249	#106	—	2	2	no	—
250	#106	—	2	2	no	—
251	#106	—	4	1	no	—
252	C₄⋊C₈	C₂³×C₁₀₁	1	2	yes	—
253	C₄⋊C₈	C₂³×C₁₀₁	1	2	yes	—
254	#103	—	2	2	no	—
255	#102	—	2	2	no	—
256	#102	—	2	2	no	—
257	#102	—	2	2	no	—
258	#102	D₄×C₁₀₁	1	2	yes	—
259	#102	D₄×C₁₀₁	1	2	yes	—
260	C₂²⋊C₈	—	2	2	no	—
261	C₂²⋊C₈	—	2	2	no	—
262	C₄×C₈	C₂³×C₁₀₁	1	1	yes	characteristic
263	C₄×C₈	C₂³×C₁₀₁	1	2	yes	—
264	C₂⁴	—	4	1	no	—
265	#41	—	4	4	no	—
266	#41	—	8	2	no	—
267	C₂×Q₈	—	2	2	no	—
268	C₂×Q₈	—	2	1	no	—
269	C₂×D₄	—	2	2	no	—
270	C₂×D₄	—	2	1	no	—
271	C₂×D₄	—	4	2	no	—
272	C₂×D₄	—	4	4	no	—
273	C₂×D₄	—	4	2	no	—
274	C₂×D₄	—	4	1	no	—
275	C₂×D₄	—	8	2	no	—
276	C₂×D₄	C₂×D₄×C₁₀₁	1	2	yes	—
277	C₂×D₄	C₂×D₄×C₁₀₁	1	2	yes	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	4	2	no	—
281	SD₁₆	—	4	4	no	—
282	SD₁₆	—	4	4	no	—
283	SD₁₆	—	8	2	no	—
284	SD₁₆	—	8	2	no	—
285	D₈	—	2	4	no	—
286	D₈	—	4	4	no	—
287	M₁₆	—	4	4	no	—
288	M₁₆	—	4	4	no	—
289	C₂×C₈	—	2	1	no	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	2	2	no	—
292	C₂×C₈	C₂×D₄×C₁₀₁	1	2	yes	—
293	C₂×C₈	C₂×D₄×C₁₀₁	1	2	yes	—
294	C₄⋊C₄	—	2	2	no	—
295	C₄⋊C₄	—	2	2	no	—
296	C₄⋊C₄	—	2	2	no	—
297	C₄⋊C₄	—	4	2	no	—
298	C₄⋊C₄	C₂×D₄×C₁₀₁	1	2	yes	—
299	C₄⋊C₄	C₂×D₄×C₁₀₁	1	2	yes	—
300	C₂²⋊C₄	—	2	2	no	—
301	C₂²⋊C₄	—	2	2	no	—
302	C₂²⋊C₄	—	4	1	no	—
303	C₂²⋊C₄	—	4	2	no	—
304	C₂²⋊C₄	—	4	2	no	—
305	C₄²	—	4	1	no	—
306	C₄²	C₂⁴×C₁₀₁	1	1	yes	characteristic
307	C₂³	—	2	2	no	—
308	C₂³	—	2	2	no	—
309	C₂³	—	4	1	no	—
310	C₂³	—	8	4	no	—
311	C₂³	—	16	1	no	—
312	Q₈	—	4	2	no	—
313	Q₈	—	4	2	no	—
314	Q₈	—	8	1	no	—
315	D₄	—	2	2	no	—
316	D₄	—	2	2	no	—
317	D₄	—	2	2	no	—
318	D₄	—	2	2	no	—
319	D₄	—	4	2	no	—
320	D₄	—	4	2	no	—
321	D₄	—	8	1	no	—
322	D₄	—	8	4	no	—
323	D₄	—	8	4	no	—
324	D₄	—	16	1	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	4	2	no	—
328	C₂×C₄	—	4	2	no	—
329	C₂×C₄	—	4	2	no	—
330	C₂×C₄	—	4	2	no	—
331	C₂×C₄	—	4	1	no	—
332	C₂×C₄	—	4	2	no	—
333	C₂×C₄	—	8	4	no	—
334	C₂×C₄	C₂²×D₄×C₁₀₁	1	2	yes	—
335	C₂×C₄	H(5,𝔽₂)×C₁₀₁	1	1	yes	characteristic
336	C₈	—	2	2	no	—
337	C₈	—	2	2	no	—
338	C₈	—	4	2	no	—
339	C₈	—	4	2	no	—
340	C₈	AGL(1,ℤ/8)×C₁₀₁	1	4	yes	complemented
341	C₂²	—	4	2	no	—
342	C₂²	—	4	2	no	—
343	C₂²	—	4	2	no	—
344	C₂²	—	4	2	no	—
345	C₂²	—	4	2	no	—
346	C₂²	—	4	2	no	—
347	C₂²	—	8	2	no	—
348	C₂²	—	8	1	no	—
349	C₂²	—	16	4	no	—
350	C₂²	D₄²×C₁₀₁	1	1	yes	characteristic
351	C₄	—	2	1	no	—
352	C₄	—	4	2	no	—
353	C₄	—	4	2	no	—
354	C₄	—	8	2	no	—
355	C₄	—	8	1	no	—
356	C₄	C₂×AGL(1,ℤ/8)×C₁₀₁	1	2	yes	—
357	C₄	#577×C₁₀₁	1	2	yes	—
358	C₂	—	8	2	no	—
359	C₂	—	8	2	no	—
360	C₂	—	16	1	no	—
361	C₂	C₁₀₁×#3272	1	2	yes	—
362	C₂	C₁₀₁×#3291	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₀₁	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₀₁
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₁ ◁ C₄²×C₁₀₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₀₁×#3354	C₂	semidirect
2. C₁₀₁×#3272	C₂	semidirect
3. C₁₀₁×#1705	C₂	semidirect
4. C₁₀₁×#1691	C₂	semidirect
5. C₁₀₁×#1685	C₂	semidirect
6. C₁₀₁×#1654	C₂	semidirect
7. C₁₀₁×#1629	C₂	semidirect
8. C₁₀₁×#1624	C₂	semidirect
9. C₁₀₁×#1589	C₂	semidirect
11. #555×C₁₀₁	C₂²	semidirect
14. #498×C₁₀₁	C₂²	semidirect
15. #498×C₁₀₁	C₂²	semidirect
21. #474×C₁₀₁	C₂²	semidirect
30. #436×C₁₀₁	C₂²	semidirect
32. #335×C₁₀₁	C₂²	semidirect
33. #333×C₁₀₁	C₂²	semidirect
34. #332×C₁₀₁	C₂²	semidirect
37. D₄⋊C₈×C₁₀₁	C₂²	semidirect
38. C₈²×C₁₀₁	C₂²	semidirect
158. C₈×C₁₀₁	AGL(1,ℤ/8)	semidirect
176. #20314	C₁₀₁	direct (N × H)
182. #3354	C₂×C₁₀₁	semidirect
183. #3272	C₂×C₁₀₁	semidirect
184. #1705	C₂×C₁₀₁	semidirect
185. #1691	C₂×C₁₀₁	semidirect
186. #1685	C₂×C₁₀₁	semidirect
187. #1654	C₂×C₁₀₁	semidirect
188. #1629	C₂×C₁₀₁	semidirect
189. #1624	C₂×C₁₀₁	semidirect
190. #1589	C₂×C₁₀₁	semidirect
191. C₁₀₁	#20314	direct (N × H)
193. #555	C₂²×C₁₀₁	semidirect
196. #498	C₂²×C₁₀₁	semidirect
197. #498	C₂²×C₁₀₁	semidirect
203. #474	C₂²×C₁₀₁	semidirect
212. #436	C₂²×C₁₀₁	semidirect
214. #335	C₂²×C₁₀₁	semidirect
215. #333	C₂²×C₁₀₁	semidirect
216. #332	C₂²×C₁₀₁	semidirect
219. D₄⋊C₈	C₂²×C₁₀₁	semidirect
220. C₈²	C₂²×C₁₀₁	semidirect
340. C₈	AGL(1,ℤ/8)×C₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₁₀₁×#3354	2
C₁₀₁×#3272	2
C₁₀₁×#1705	2
C₁₀₁×#1691	2
C₁₀₁×#1685	2
C₁₀₁×#1654	2
C₁₀₁×#1629	2
C₁₀₁×#1624	2
C₁₀₁×#1589	2
#20314	101

Subgroups — C101×#20314 #38802465

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#20314 #38802465