Subgroups — C₁₀₁×#18549 #38800700

Order 25856.

1040 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₀₁×#3483	C₂	1	1	yes	maximal, characteristic
2	C₁₀₁×#3152	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₀₁×#3079	C₂	1	2	yes	maximal, complemented
4	C₁₀₁×#1634	C₂	1	2	yes	maximal, complemented
5	C₁₀₁×#1633	C₂	1	2	yes	maximal, complemented
6	C₁₀₁×#1631	C₂	1	4	yes	maximal, complemented
7	C₁₀₁×#1560	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₀₁×#1489	C₂	1	2	yes	maximal, complemented
9	C₂×#137×C₁₀₁	—	2	2	no	—
10	Q₈²×C₁₀₁	C₂²	1	1	yes	characteristic
11	#555×C₁₀₁	—	2	2	no	—
12	#555×C₁₀₁	—	2	2	no	—
13	#555×C₁₀₁	C₂²	1	1	yes	characteristic
14	#550×C₁₀₁	—	2	2	no	—
15	#550×C₁₀₁	C₂²	1	2	yes	—
16	#532×C₁₀₁	—	2	2	no	—
17	#532×C₁₀₁	—	2	2	no	—
18	#532×C₁₀₁	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊Q₈×C₁₀₁	C₂²	1	1	yes	characteristic
20	C₄×#41×C₁₀₁	—	2	2	no	—
21	C₄×#41×C₁₀₁	C₂²	1	2	yes	—
22	#497×C₁₀₁	—	2	2	no	—
23	#494×C₁₀₁	C₂²	1	2	yes	—
24	#492×C₁₀₁	C₂²	1	2	yes	—
25	#477×C₁₀₁	C₂²	1	4	yes	—
26	#476×C₁₀₁	C₂²	1	4	yes	—
27	#475×C₁₀₁	—	2	2	no	—
28	#474×C₁₀₁	—	2	2	no	—
29	#428×C₁₀₁	—	2	2	no	—
30	#423×C₁₀₁	C₂²	1	2	yes	—
31	#417×C₁₀₁	—	2	2	no	—
32	C₄×M₁₆×C₁₀₁	C₂²	1	1	yes	characteristic
33	#333×C₁₀₁	C₂²	1	2	yes	—
34	#331×C₁₀₁	C₂²	1	2	yes	—
35	Q₈⋊C₈×C₁₀₁	C₂²	1	4	yes	—
36	D₄⋊C₈×C₁₀₁	C₂²	1	4	yes	—
37	C₂×#41×C₁₀₁	—	2	2	no	—
38	C₂×#41×C₁₀₁	—	2	2	no	—
39	C₂×#41×C₁₀₁	D₄	1	2	yes	—
40	C₂×#41×C₁₀₁	D₄	1	2	yes	—
41	C₂²×Q₈×C₁₀₁	—	2	1	no	—
42	#137×C₁₀₁	—	4	8	no	—
43	C₂×Q₁₆×C₁₀₁	—	2	4	no	—
44	C₂×SD₁₆×C₁₀₁	—	2	4	no	—
45	C₂×M₁₆×C₁₀₁	—	2	1	no	—
46	C₂×M₁₆×C₁₀₁	—	2	2	no	—
47	C₄⋊Q₈×C₁₀₁	—	2	2	no	—
48	C₄⋊Q₈×C₁₀₁	—	2	2	no	—
49	C₄⋊Q₈×C₁₀₁	—	2	2	no	—
50	C₄⋊Q₈×C₁₀₁	—	2	1	no	—
51	C₄⋊Q₈×C₁₀₁	C₂³	1	2	yes	—
52	C₄⋊Q₈×C₁₀₁	C₂³	1	1	yes	characteristic
53	#127×C₁₀₁	—	2	2	no	—
54	#127×C₁₀₁	—	2	2	no	—
55	#127×C₁₀₁	C₂³	1	1	yes	characteristic
56	#124×C₁₀₁	—	2	2	no	—
57	#124×C₁₀₁	—	2	4	no	—
58	#124×C₁₀₁	—	2	2	no	—
59	#124×C₁₀₁	D₄	1	2	yes	—
60	#121×C₁₀₁	—	2	4	no	—
61	#121×C₁₀₁	—	2	4	no	—
62	#121×C₁₀₁	—	2	2	no	—
63	#121×C₁₀₁	—	2	4	no	—
64	#121×C₁₀₁	—	2	2	no	—
65	#121×C₁₀₁	—	2	2	no	—
66	C₄×Q₈×C₁₀₁	—	2	2	no	—
67	C₄×Q₈×C₁₀₁	D₄	1	2	yes	—
68	C₄×Q₈×C₁₀₁	C₂³	1	2	yes	—
69	C₄×D₄×C₁₀₁	—	2	4	no	—
70	C₄×D₄×C₁₀₁	—	2	4	no	—
71	C₄×D₄×C₁₀₁	—	2	2	no	—
72	C₄×D₄×C₁₀₁	—	2	2	no	—
73	C₄×D₄×C₁₀₁	—	2	2	no	—
74	C₄×D₄×C₁₀₁	—	2	2	no	—
75	C₄×D₄×C₁₀₁	D₄	1	2	yes	—
76	C₄×D₄×C₁₀₁	C₂³	1	2	yes	—
77	#117×C₁₀₁	—	2	4	no	—
78	#117×C₁₀₁	—	2	2	no	—
79	#117×C₁₀₁	—	2	2	no	—
80	#117×C₁₀₁	D₄	1	2	yes	—
81	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
82	C₂×C₄²×C₁₀₁	—	2	2	no	—
83	C₂×C₄²×C₁₀₁	—	2	2	no	—
84	C₂×C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
85	#107×C₁₀₁	—	2	4	no	—
86	#106×C₁₀₁	—	2	4	no	—
87	C₄⋊C₈×C₁₀₁	—	2	2	no	—
88	C₄⋊C₈×C₁₀₁	C₂³	1	4	yes	—
89	#103×C₁₀₁	—	2	4	no	—
90	#102×C₁₀₁	—	2	4	no	—
91	#97×C₁₀₁	—	2	1	no	—
92	C₄×C₈×C₁₀₁	C₂³	1	2	yes	—
93	#41×C₁₀₁	—	2	4	no	—
94	#41×C₁₀₁	—	4	2	no	—
95	#41×C₁₀₁	—	4	4	no	—
96	#41×C₁₀₁	—	4	4	no	—
97	#41×C₁₀₁	—	4	4	no	—
98	#41×C₁₀₁	—	8	4	no	—
99	C₂×Q₈×C₁₀₁	—	2	2	no	—
100	C₂×Q₈×C₁₀₁	—	2	2	no	—
101	C₂×Q₈×C₁₀₁	—	4	4	no	—
102	C₂×Q₈×C₁₀₁	—	4	1	no	—
103	C₂×Q₈×C₁₀₁	C₂×D₄	1	2	yes	—
104	C₂×Q₈×C₁₀₁	C₂×D₄	1	2	yes	—
105	C₂×D₄×C₁₀₁	—	2	4	no	—
106	C₂×D₄×C₁₀₁	—	2	2	no	—
107	C₂×D₄×C₁₀₁	—	2	2	no	—
108	C₂×D₄×C₁₀₁	—	2	4	no	—
109	C₂×D₄×C₁₀₁	—	2	2	no	—
110	C₂×D₄×C₁₀₁	—	2	2	no	—
111	C₂×D₄×C₁₀₁	C₂×D₄	1	2	yes	—
112	C₂×D₄×C₁₀₁	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₁₀₁	—	2	4	no	—
114	C₂²×C₄×C₁₀₁	—	2	2	no	—
115	C₂²×C₄×C₁₀₁	—	2	2	no	—
116	C₂²×C₄×C₁₀₁	—	2	2	no	—
117	C₂²×C₄×C₁₀₁	—	2	2	no	—
118	C₂²×C₄×C₁₀₁	—	4	1	no	—
119	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
120	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
121	Q₁₆×C₁₀₁	—	4	8	no	—
122	SD₁₆×C₁₀₁	—	4	8	no	—
123	M₁₆×C₁₀₁	—	2	4	no	—
124	M₁₆×C₁₀₁	—	4	4	no	—
125	C₂×C₈×C₁₀₁	—	2	2	no	—
126	C₂×C₈×C₁₀₁	—	2	4	no	—
127	C₄⋊C₄×C₁₀₁	—	2	4	no	—
128	C₄⋊C₄×C₁₀₁	—	2	2	no	—
129	C₄⋊C₄×C₁₀₁	—	2	2	no	—
130	C₄⋊C₄×C₁₀₁	—	2	2	no	—
131	C₄⋊C₄×C₁₀₁	—	2	4	no	—
132	C₄⋊C₄×C₁₀₁	—	4	2	no	—
133	C₄⋊C₄×C₁₀₁	C₂×D₄	1	2	yes	—
134	C₄⋊C₄×C₁₀₁	C₂×D₄	1	2	yes	—
135	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
136	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
137	C₂²⋊C₄×C₁₀₁	—	2	2	no	—
138	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
139	C₂²⋊C₄×C₁₀₁	—	2	2	no	—
140	C₂²⋊C₄×C₁₀₁	—	2	2	no	—
141	C₄²×C₁₀₁	—	2	2	no	—
142	C₄²×C₁₀₁	—	2	2	no	—
143	C₄²×C₁₀₁	—	2	2	no	—
144	C₄²×C₁₀₁	—	2	2	no	—
145	C₄²×C₁₀₁	—	2	2	no	—
146	C₄²×C₁₀₁	C₂×D₄	1	1	yes	characteristic
147	C₄²×C₁₀₁	C₂×D₄	1	2	yes	—
148	C₄²×C₁₀₁	C₂⁴	1	1	yes	characteristic
149	C₂³×C₁₀₁	—	2	2	no	—
150	C₂³×C₁₀₁	—	2	2	no	—
151	C₂³×C₁₀₁	#120	1	1	yes	characteristic
152	Q₈×C₁₀₁	—	2	2	no	—
153	Q₈×C₁₀₁	—	4	2	no	—
154	Q₈×C₁₀₁	—	4	4	no	—
155	Q₈×C₁₀₁	—	8	2	no	—
156	Q₈×C₁₀₁	—	8	2	no	—
157	Q₈×C₁₀₁	#137	1	4	yes	complemented
158	D₄×C₁₀₁	—	2	2	no	—
159	D₄×C₁₀₁	—	2	2	no	—
160	D₄×C₁₀₁	—	4	4	no	—
161	D₄×C₁₀₁	—	4	2	no	—
162	D₄×C₁₀₁	—	4	8	no	—
163	D₄×C₁₀₁	—	4	2	no	—
164	D₄×C₁₀₁	—	4	2	no	—
165	D₄×C₁₀₁	—	8	2	no	—
166	D₄×C₁₀₁	—	8	2	no	—
167	D₄×C₁₀₁	—	8	4	no	—
168	C₂×C₄×C₁₀₁	—	2	2	no	—
169	C₂×C₄×C₁₀₁	—	2	2	no	—
170	C₂×C₄×C₁₀₁	—	2	2	no	—
171	C₂×C₄×C₁₀₁	—	2	2	no	—
172	C₂×C₄×C₁₀₁	—	2	2	no	—
173	C₂×C₄×C₁₀₁	—	2	2	no	—
174	C₂×C₄×C₁₀₁	—	2	2	no	—
175	C₂×C₄×C₁₀₁	—	4	4	no	—
176	C₂×C₄×C₁₀₁	—	4	8	no	—
177	C₂×C₄×C₁₀₁	—	4	2	no	—
178	C₂×C₄×C₁₀₁	—	4	2	no	—
179	C₂×C₄×C₁₀₁	—	4	4	no	—
180	C₂×C₄×C₁₀₁	—	4	4	no	—
181	C₂×C₄×C₁₀₁	—	4	2	no	—
182	C₂×C₄×C₁₀₁	—	8	2	no	—
183	C₂×C₄×C₁₀₁	#120	1	2	yes	—
184	C₂×C₄×C₁₀₁	#120	1	1	yes	characteristic
185	C₂×C₄×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₄×C₁₀₁	C₂²×D₄	1	2	yes	—
187	C₈×C₁₀₁	—	2	4	no	—
188	C₈×C₁₀₁	—	4	4	no	—
189	C₂²×C₁₀₁	—	2	2	no	—
190	C₂²×C₁₀₁	—	2	1	no	—
191	C₂²×C₁₀₁	—	4	2	no	—
192	C₂²×C₁₀₁	—	4	4	no	—
193	C₂²×C₁₀₁	—	4	2	no	—
194	C₂²×C₁₀₁	—	4	2	no	—
195	C₂²×C₁₀₁	—	4	2	no	—
196	C₂²×C₁₀₁	C₂×#120	1	1	yes	characteristic
197	C₄×C₁₀₁	—	2	2	no	—
198	C₄×C₁₀₁	—	2	4	no	—
199	C₄×C₁₀₁	—	2	1	no	—
200	C₄×C₁₀₁	—	4	2	no	—
201	C₄×C₁₀₁	—	4	2	no	—
202	C₄×C₁₀₁	—	4	2	no	—
203	C₄×C₁₀₁	—	8	2	no	—
204	C₄×C₁₀₁	#453	1	2	yes	—
205	C₄×C₁₀₁	C₂×#137	1	2	yes	—
206	C₄×C₁₀₁	#575	1	2	yes	—
207	#18549	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
208	C₂×C₁₀₁	—	4	1	no	—
209	C₂×C₁₀₁	—	8	2	no	—
210	C₂×C₁₀₁	—	8	2	no	—
211	C₂×C₁₀₁	#3007	1	2	yes	—
212	C₂×C₁₀₁	C₂×#453	1	1	yes	characteristic
213	#3483	C₂×C₁₀₁	1	1	yes	characteristic
214	#3152	C₂×C₁₀₁	1	1	yes	characteristic, complemented
215	#3079	C₂×C₁₀₁	1	2	yes	complemented
216	#1634	C₂×C₁₀₁	1	2	yes	complemented
217	#1633	C₂×C₁₀₁	1	2	yes	complemented
218	#1631	C₂×C₁₀₁	1	4	yes	complemented
219	#1560	C₂×C₁₀₁	1	1	yes	characteristic, complemented
220	#1489	C₂×C₁₀₁	1	2	yes	complemented
221	C₁₀₁	#18549	1	1	yes	characteristic, direct product factor, Sylow
222	C₂×#137	—	2	2	no	—
223	Q₈²	C₂²×C₁₀₁	1	1	yes	characteristic
224	#555	—	2	2	no	—
225	#555	—	2	2	no	—
226	#555	C₂²×C₁₀₁	1	1	yes	characteristic
227	#550	—	2	2	no	—
228	#550	C₂²×C₁₀₁	1	2	yes	—
229	#532	—	2	2	no	—
230	#532	—	2	2	no	—
231	#532	C₂²×C₁₀₁	1	1	yes	characteristic
232	C₂×C₄⋊Q₈	C₂²×C₁₀₁	1	1	yes	characteristic
233	C₄×#41	—	2	2	no	—
234	C₄×#41	C₂²×C₁₀₁	1	2	yes	—
235	#497	—	2	2	no	—
236	#494	C₂²×C₁₀₁	1	2	yes	—
237	#492	C₂²×C₁₀₁	1	2	yes	—
238	#477	C₂²×C₁₀₁	1	4	yes	—
239	#476	C₂²×C₁₀₁	1	4	yes	—
240	#475	—	2	2	no	—
241	#474	—	2	2	no	—
242	#428	—	2	2	no	—
243	#423	C₂²×C₁₀₁	1	2	yes	—
244	#417	—	2	2	no	—
245	C₄×M₁₆	C₂²×C₁₀₁	1	1	yes	characteristic
246	#333	C₂²×C₁₀₁	1	2	yes	—
247	#331	C₂²×C₁₀₁	1	2	yes	—
248	Q₈⋊C₈	C₂²×C₁₀₁	1	4	yes	—
249	D₄⋊C₈	C₂²×C₁₀₁	1	4	yes	—
250	C₂×#41	—	2	2	no	—
251	C₂×#41	—	2	2	no	—
252	C₂×#41	D₄×C₁₀₁	1	2	yes	—
253	C₂×#41	D₄×C₁₀₁	1	2	yes	—
254	C₂²×Q₈	—	2	1	no	—
255	#137	—	4	8	no	—
256	C₂×Q₁₆	—	2	4	no	—
257	C₂×SD₁₆	—	2	4	no	—
258	C₂×M₁₆	—	2	1	no	—
259	C₂×M₁₆	—	2	2	no	—
260	C₄⋊Q₈	—	2	2	no	—
261	C₄⋊Q₈	—	2	2	no	—
262	C₄⋊Q₈	—	2	2	no	—
263	C₄⋊Q₈	—	2	1	no	—
264	C₄⋊Q₈	C₂³×C₁₀₁	1	2	yes	—
265	C₄⋊Q₈	C₂³×C₁₀₁	1	1	yes	characteristic
266	#127	—	2	2	no	—
267	#127	—	2	2	no	—
268	#127	C₂³×C₁₀₁	1	1	yes	characteristic
269	#124	—	2	2	no	—
270	#124	—	2	4	no	—
271	#124	—	2	2	no	—
272	#124	D₄×C₁₀₁	1	2	yes	—
273	#121	—	2	4	no	—
274	#121	—	2	4	no	—
275	#121	—	2	2	no	—
276	#121	—	2	4	no	—
277	#121	—	2	2	no	—
278	#121	—	2	2	no	—
279	C₄×Q₈	—	2	2	no	—
280	C₄×Q₈	D₄×C₁₀₁	1	2	yes	—
281	C₄×Q₈	C₂³×C₁₀₁	1	2	yes	—
282	C₄×D₄	—	2	4	no	—
283	C₄×D₄	—	2	4	no	—
284	C₄×D₄	—	2	2	no	—
285	C₄×D₄	—	2	2	no	—
286	C₄×D₄	—	2	2	no	—
287	C₄×D₄	—	2	2	no	—
288	C₄×D₄	D₄×C₁₀₁	1	2	yes	—
289	C₄×D₄	C₂³×C₁₀₁	1	2	yes	—
290	#117	—	2	4	no	—
291	#117	—	2	2	no	—
292	#117	—	2	2	no	—
293	#117	D₄×C₁₀₁	1	2	yes	—
294	C₂×C₄⋊C₄	—	2	2	no	—
295	C₂×C₄²	—	2	2	no	—
296	C₂×C₄²	—	2	2	no	—
297	C₂×C₄²	C₂³×C₁₀₁	1	1	yes	characteristic
298	#107	—	2	4	no	—
299	#106	—	2	4	no	—
300	C₄⋊C₈	—	2	2	no	—
301	C₄⋊C₈	C₂³×C₁₀₁	1	4	yes	—
302	#103	—	2	4	no	—
303	#102	—	2	4	no	—
304	#97	—	2	1	no	—
305	C₄×C₈	C₂³×C₁₀₁	1	2	yes	—
306	#41	—	2	4	no	—
307	#41	—	4	2	no	—
308	#41	—	4	4	no	—
309	#41	—	4	4	no	—
310	#41	—	4	4	no	—
311	#41	—	8	4	no	—
312	C₂×Q₈	—	2	2	no	—
313	C₂×Q₈	—	2	2	no	—
314	C₂×Q₈	—	4	4	no	—
315	C₂×Q₈	—	4	1	no	—
316	C₂×Q₈	C₂×D₄×C₁₀₁	1	2	yes	—
317	C₂×Q₈	C₂×D₄×C₁₀₁	1	2	yes	—
318	C₂×D₄	—	2	4	no	—
319	C₂×D₄	—	2	2	no	—
320	C₂×D₄	—	2	2	no	—
321	C₂×D₄	—	2	4	no	—
322	C₂×D₄	—	2	2	no	—
323	C₂×D₄	—	2	2	no	—
324	C₂×D₄	C₂×D₄×C₁₀₁	1	2	yes	—
325	C₂×D₄	C₂×D₄×C₁₀₁	1	2	yes	—
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	—	4	1	no	—
332	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
333	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
334	Q₁₆	—	4	8	no	—
335	SD₁₆	—	4	8	no	—
336	M₁₆	—	2	4	no	—
337	M₁₆	—	4	4	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	2	4	no	—
340	C₄⋊C₄	—	2	4	no	—
341	C₄⋊C₄	—	2	2	no	—
342	C₄⋊C₄	—	2	2	no	—
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	—	2	4	no	—
345	C₄⋊C₄	—	4	2	no	—
346	C₄⋊C₄	C₂×D₄×C₁₀₁	1	2	yes	—
347	C₄⋊C₄	C₂×D₄×C₁₀₁	1	2	yes	—
348	C₂²⋊C₄	—	2	4	no	—
349	C₂²⋊C₄	—	2	4	no	—
350	C₂²⋊C₄	—	2	2	no	—
351	C₂²⋊C₄	—	2	4	no	—
352	C₂²⋊C₄	—	2	2	no	—
353	C₂²⋊C₄	—	2	2	no	—
354	C₄²	—	2	2	no	—
355	C₄²	—	2	2	no	—
356	C₄²	—	2	2	no	—
357	C₄²	—	2	2	no	—
358	C₄²	—	2	2	no	—
359	C₄²	C₂×D₄×C₁₀₁	1	1	yes	characteristic
360	C₄²	C₂×D₄×C₁₀₁	1	2	yes	—
361	C₄²	C₂⁴×C₁₀₁	1	1	yes	characteristic
362	C₂³	—	2	2	no	—
363	C₂³	—	2	2	no	—
364	C₂³	#120×C₁₀₁	1	1	yes	characteristic
365	Q₈	—	2	2	no	—
366	Q₈	—	4	2	no	—
367	Q₈	—	4	4	no	—
368	Q₈	—	8	2	no	—
369	Q₈	—	8	2	no	—
370	Q₈	#137×C₁₀₁	1	4	yes	complemented
371	D₄	—	2	2	no	—
372	D₄	—	2	2	no	—
373	D₄	—	4	4	no	—
374	D₄	—	4	2	no	—
375	D₄	—	4	8	no	—
376	D₄	—	4	2	no	—
377	D₄	—	4	2	no	—
378	D₄	—	8	2	no	—
379	D₄	—	8	2	no	—
380	D₄	—	8	4	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	4	4	no	—
389	C₂×C₄	—	4	8	no	—
390	C₂×C₄	—	4	4	no	—
391	C₂×C₄	—	4	4	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	8	2	no	—
396	C₂×C₄	#120×C₁₀₁	1	2	yes	—
397	C₂×C₄	#120×C₁₀₁	1	1	yes	characteristic
398	C₂×C₄	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
399	C₂×C₄	C₂²×D₄×C₁₀₁	1	2	yes	—
400	C₈	—	2	4	no	—
401	C₈	—	4	4	no	—
402	C₂²	—	2	2	no	—
403	C₂²	—	2	1	no	—
404	C₂²	—	4	2	no	—
405	C₂²	—	4	4	no	—
406	C₂²	—	4	2	no	—
407	C₂²	—	4	2	no	—
408	C₂²	—	4	2	no	—
409	C₂²	C₂×#120×C₁₀₁	1	1	yes	characteristic
410	C₄	—	2	2	no	—
411	C₄	—	2	4	no	—
412	C₄	—	2	1	no	—
413	C₄	—	4	2	no	—
414	C₄	—	4	2	no	—
415	C₄	—	4	2	no	—
416	C₄	—	8	2	no	—
417	C₄	#453×C₁₀₁	1	2	yes	—
418	C₄	C₂×#137×C₁₀₁	1	2	yes	—
419	C₄	#575×C₁₀₁	1	2	yes	—
420	C₂	—	4	1	no	—
421	C₂	—	8	2	no	—
422	C₂	—	8	2	no	—
423	C₂	C₁₀₁×#3007	1	2	yes	—
424	C₂	C₂×#453×C₁₀₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₀₁	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₀₁
prime radical	C₁₀₁×#3483	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₁ ◁ C₂×C₄²×C₁₀₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₀₁×#3152	C₂	semidirect
3. C₁₀₁×#3079	C₂	semidirect
4. C₁₀₁×#1634	C₂	semidirect
5. C₁₀₁×#1633	C₂	semidirect
6. C₁₀₁×#1631	C₂	semidirect
7. C₁₀₁×#1560	C₂	semidirect
8. C₁₀₁×#1489	C₂	semidirect
157. Q₈×C₁₀₁	#137	semidirect
207. #18549	C₁₀₁	direct (N × H)
214. #3152	C₂×C₁₀₁	semidirect
215. #3079	C₂×C₁₀₁	semidirect
216. #1634	C₂×C₁₀₁	semidirect
217. #1633	C₂×C₁₀₁	semidirect
218. #1631	C₂×C₁₀₁	semidirect
219. #1560	C₂×C₁₀₁	semidirect
220. #1489	C₂×C₁₀₁	semidirect
221. C₁₀₁	#18549	direct (N × H)
370. Q₈	#137×C₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₁₀₁×#3483	2
C₁₀₁×#3152	2
C₁₀₁×#3079	2
C₁₀₁×#1634	2
C₁₀₁×#1633	2
C₁₀₁×#1631	2
C₁₀₁×#1560	2
C₁₀₁×#1489	2
#18549	101

Subgroups — C101×#18549 #38800700

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#18549 #38800700