Subgroups — #410×D₁₀₁ #27179586

Order 12928.

788 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	C₂×#41×D₁₀₁	C₂	1	1	yes	maximal, characteristic
2	#117×D₁₀₁	C₂	1	2	yes	maximal, complemented
3	#20265151	C₂	1	1	yes	maximal, characteristic, complemented
4	#20265150	C₂	1	2	yes	maximal, complemented
5	#20265149	C₂	1	4	yes	maximal, complemented
6	#99×D₁₀₁	C₂	1	4	yes	maximal, complemented
7	#410×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#13108075	C₄	1	1	yes	characteristic, complemented
9	C₂×#13108074	C₄	1	2	yes	complemented
10	C₂×#13108074	C₂²	1	1	yes	characteristic
11	C₂×#13108073	C₄	1	1	yes	characteristic, complemented
12	C₂×#13108073	C₂²	1	2	yes	—
13	#41×D₁₀₁	—	2	2	no	—
14	#41×D₁₀₁	—	2	2	no	—
15	#41×D₁₀₁	—	2	2	no	—
16	#41×D₁₀₁	—	2	2	no	—
17	C₂×Q₈×D₁₀₁	C₄	1	1	yes	characteristic, complemented
18	C₂×D₄×D₁₀₁	C₄	1	1	yes	characteristic, complemented
19	C₂×D₄×D₁₀₁	C₂²	1	2	yes	—
20	C₂²×C₄×D₁₀₁	C₄	1	2	yes	complemented
21	C₂²×C₄×D₁₀₁	C₂²	1	1	yes	characteristic
22	#15692214	C₂²	1	2	yes	complemented
23	#15692213	—	2	2	no	—
24	#15692212	—	2	2	no	—
25	#15692211	C₂²	1	4	yes	complemented
26	C₄⋊C₄×D₁₀₁	—	2	2	no	—
27	C₂²⋊C₄×D₁₀₁	C₂²	1	4	yes	—
28	C₄²×D₁₀₁	—	2	2	no	—
29	#15692170	C₂²	1	4	yes	complemented
30	#15692169	C₂²	1	8	yes	complemented
31	C₂×#41×C₁₀₁	C₂²	1	1	yes	characteristic
32	#117×C₁₀₁	C₂²	1	2	yes	complemented
33	#99×C₁₀₁	C₂²	1	4	yes	complemented
34	C₂³×D₁₀₁	C₂×C₄	1	2	yes	—
35	C₂³×D₁₀₁	C₂³	1	1	yes	characteristic
36	#13108075	—	2	2	no	—
37	#13108075	—	2	2	no	—
38	#13108074	—	2	2	no	—
39	#13108074	—	2	2	no	—
40	#13108074	—	2	4	no	—
41	#13108074	—	2	4	no	—
42	#13108073	—	2	4	no	—
43	#13108073	—	2	4	no	—
44	#13108073	—	2	2	no	—
45	#13108073	—	2	2	no	—
46	C₂×Dic₂₀₂	C₂×C₄	1	1	yes	characteristic, complemented
47	C₂×Dic₂₀₂	C₂×C₄	1	2	yes	complemented
48	Q₈×D₁₀₁	—	2	2	no	—
49	Q₈×D₁₀₁	—	2	2	no	—
50	C₂×D₄₀₄	C₂×C₄	1	2	yes	—
51	C₂×D₄₀₄	C₂×C₄	1	1	yes	characteristic, complemented
52	C₂×C₂²⋊D₁₀₁	C₂×C₄	1	2	yes	—
53	C₂×C₂²⋊D₁₀₁	C₂×C₄	1	2	yes	complemented
54	C₂×C₂²⋊D₁₀₁	C₂³	1	2	yes	—
55	D₄×D₁₀₁	—	2	4	no	—
56	D₄×D₁₀₁	—	2	4	no	—
57	D₄×D₁₀₁	—	2	2	no	—
58	D₄×D₁₀₁	—	2	2	no	—
59	C₂²×Dic₁₀₁	C₂×C₄	1	2	yes	complemented
60	C₂²×Dic₁₀₁	C₂³	1	1	yes	characteristic
61	C₂×C₄×D₁₀₁	—	2	2	no	—
62	C₂×C₄×D₁₀₁	—	2	2	no	—
63	C₂×C₄×D₁₀₁	—	2	2	no	—
64	C₂×C₄×D₁₀₁	—	2	2	no	—
65	C₂×C₄×D₁₀₁	—	2	4	no	—
66	C₂×C₄×D₁₀₁	C₂×C₄	1	2	yes	—
67	C₂×C₄×D₁₀₁	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄×D₁₀₁	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄×D₁₀₁	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄×D₁₀₁	C₂×C₄	1	1	yes	characteristic
71	C₂×C₄×D₁₀₁	C₂×C₄	1	2	yes	complemented
72	C₂×C₄×D₁₀₁	C₂×C₄	1	2	yes	complemented
73	C₂×C₄×D₁₀₁	D₄	1	2	yes	—
74	C₂×C₄×D₁₀₁	D₄	1	2	yes	—
75	C₂×C₄×D₁₀₁	D₄	1	2	yes	—
76	C₂×C₄×D₁₀₁	D₄	1	2	yes	—
77	C₄⋊Dic₁₀₁	—	2	2	no	—
78	#13108053	—	2	4	no	—
79	C₂²⋊Dic₁₀₁	C₂³	1	4	yes	—
80	#13108051	—	2	4	no	—
81	C₄×Dic₁₀₁	—	2	2	no	—
82	C₄×Dic₁₀₁	—	2	4	no	—
83	#41×C₁₀₁	—	2	2	no	—
84	#41×C₁₀₁	—	2	2	no	—
85	C₂×Q₈×C₁₀₁	C₂×C₄	1	1	yes	characteristic, complemented
86	C₂×D₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic, complemented
87	C₂×D₄×C₁₀₁	C₂³	1	2	yes	—
88	C₂²×C₄×C₁₀₁	C₂×C₄	1	2	yes	complemented
89	C₂²×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
90	C₄⋊C₄×C₁₀₁	—	2	2	no	—
91	C₂²⋊C₄×C₁₀₁	C₂³	1	4	yes	—
92	C₄²×C₁₀₁	—	2	2	no	—
93	C₂³×C₁₀₁	C₂²×C₄	1	2	yes	—
94	C₂³×C₁₀₁	C₂⁴	1	1	yes	characteristic
95	C₂²×D₁₀₁	—	2	2	no	—
96	C₂²×D₁₀₁	—	2	2	no	—
97	C₂²×D₁₀₁	—	4	2	no	—
98	C₂²×D₁₀₁	—	4	4	no	—
99	C₂²×D₁₀₁	C₂²×C₄	1	1	yes	characteristic
100	C₂²×D₁₀₁	C₂²×C₄	1	2	yes	—
101	C₂²×D₁₀₁	C₂²×C₄	1	1	yes	characteristic
102	C₂²×D₁₀₁	C₂×D₄	1	2	yes	—
103	C₂²×D₁₀₁	C₂×D₄	1	2	yes	—
104	Q₈×C₁₀₁	—	2	2	no	—
105	D₄×C₁₀₁	—	2	4	no	—
106	D₄×C₁₀₁	—	2	2	no	—
107	C₂×C₄×C₁₀₁	—	2	2	no	—
108	C₂×C₄×C₁₀₁	—	2	2	no	—
109	C₂×C₄×C₁₀₁	—	2	4	no	—
110	C₂×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
111	C₂×C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
114	C₂×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
115	C₂²⋊D₁₀₁	—	2	4	no	—
116	C₂²⋊D₁₀₁	—	2	4	no	—
117	C₂²⋊D₁₀₁	—	2	4	no	—
118	C₂×Dic₁₀₁	—	2	2	no	—
119	C₂×Dic₁₀₁	—	2	2	no	—
120	C₂×Dic₁₀₁	—	2	4	no	—
121	C₂×Dic₁₀₁	C₂²×C₄	1	2	yes	—
122	C₂×Dic₁₀₁	C₂²×C₄	1	1	yes	characteristic
123	C₂×Dic₁₀₁	C₂²×C₄	1	1	yes	characteristic
124	C₂×Dic₁₀₁	C₂×D₄	1	2	yes	—
125	C₂×Dic₁₀₁	C₂×D₄	1	2	yes	—
126	D₄₀₄	—	2	4	no	—
127	D₄₀₄	—	2	2	no	—
128	C₄×D₁₀₁	—	2	2	no	—
129	C₄×D₁₀₁	—	2	2	no	—
130	C₄×D₁₀₁	—	2	2	no	—
131	C₄×D₁₀₁	—	2	2	no	—
132	C₄×D₁₀₁	—	2	2	no	—
133	C₄×D₁₀₁	—	2	2	no	—
134	C₄×D₁₀₁	—	4	8	no	—
135	C₄×D₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
136	C₄×D₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
137	C₄×D₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
138	C₄×D₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
139	C₄×D₁₀₁	C₂²⋊C₄	1	2	yes	—
140	C₄×D₁₀₁	C₂²⋊C₄	1	2	yes	—
141	C₄×D₁₀₁	C₂²⋊C₄	1	2	yes	—
142	C₄×D₁₀₁	C₂²⋊C₄	1	2	yes	—
143	C₄×D₁₀₁	C₂²⋊C₄	1	2	yes	—
144	C₄×D₁₀₁	C₂²⋊C₄	1	2	yes	—
145	Dic₂₀₂	—	2	2	no	—
146	Dic₂₀₂	—	2	4	no	—
147	C₂²×C₁₀₁	—	2	2	no	—
148	C₂²×C₁₀₁	—	4	1	no	—
149	C₂²×C₁₀₁	—	4	2	no	—
150	C₂²×C₁₀₁	C₂³×C₄	1	1	yes	characteristic
151	C₂²×C₁₀₁	C₂²×D₄	1	2	yes	—
152	C₂×D₁₀₁	—	2	4	no	—
153	C₂×D₁₀₁	—	2	2	no	—
154	C₂×D₁₀₁	—	2	2	no	—
155	C₂×D₁₀₁	—	4	1	no	—
156	C₂×D₁₀₁	—	4	2	no	—
157	C₂×D₁₀₁	—	4	4	no	—
158	C₂×D₁₀₁	—	4	4	no	—
159	C₂×D₁₀₁	—	4	2	no	—
160	C₂×D₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
161	C₂×D₁₀₁	C₂×C₂²⋊C₄	1	2	yes	—
162	C₂×D₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
163	C₄×C₁₀₁	—	2	2	no	—
164	C₄×C₁₀₁	—	4	4	no	—
165	C₄×C₁₀₁	C₂×C₂²⋊C₄	1	2	yes	—
166	C₄×C₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
167	C₄×C₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
168	Dic₁₀₁	—	2	2	no	—
169	Dic₁₀₁	—	4	4	no	—
170	Dic₁₀₁	C₂×C₂²⋊C₄	1	2	yes	—
171	Dic₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
172	Dic₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
173	C₂×C₁₀₁	—	2	2	no	—
174	C₂×C₁₀₁	—	2	1	no	—
175	C₂×C₁₀₁	—	4	2	no	—
176	C₂×C₁₀₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
177	D₁₀₁	—	2	1	no	—
178	D₁₀₁	—	2	2	no	—
179	D₁₀₁	—	4	2	no	—
180	D₁₀₁	#410	1	2	yes	direct product factor
181	C₂×#410	—	101	1	no	maximal, Sylow
182	C₁₀₁	C₂×#410	1	1	yes	characteristic, complemented, Sylow
183	C₂²×#41	—	101	1	no	—
184	C₂×#117	—	101	2	no	—
185	#410	—	101	1	no	—
186	#410	—	101	2	no	—
187	#410	—	101	4	no	—
188	#410	D₁₀₁	1	1	yes	characteristic, direct product factor
189	C₂×#99	—	101	4	no	—
190	C₂×#41	—	101	1	no	—
191	C₂×#41	—	101	1	no	—
192	C₂×#41	—	101	2	no	—
193	C₂×#41	—	101	2	no	—
194	C₂×#41	—	101	1	no	—
195	C₂×#41	—	202	2	no	—
196	C₂×#41	—	202	2	no	—
197	C₂×#41	—	202	2	no	—
198	C₂×#41	—	202	2	no	—
199	C₂×#41	C₂×D₁₀₁	1	1	yes	characteristic
200	C₂²×Q₈	—	101	1	no	—
201	C₂²×D₄	—	101	1	no	—
202	C₂²×D₄	—	101	2	no	—
203	C₂³×C₄	—	101	1	no	—
204	C₂³×C₄	—	101	2	no	—
205	#117	—	101	2	no	—
206	#117	—	101	4	no	—
207	#117	—	202	2	no	—
208	#117	—	202	2	no	—
209	#117	C₂×D₁₀₁	1	2	yes	complemented
210	C₂×C₄⋊C₄	—	202	2	no	—
211	C₂×C₂²⋊C₄	—	101	4	no	—
212	C₂×C₄²	—	202	2	no	—
213	#99	—	101	4	no	—
214	#99	—	101	8	no	—
215	#99	C₂×D₁₀₁	1	4	yes	complemented
216	C₂⁴	—	101	1	no	—
217	C₂⁴	—	101	2	no	—
218	#41	—	2	2	no	—
219	#41	—	2	2	no	—
220	#41	—	202	4	no	—
221	#41	—	202	4	no	—
222	#41	—	202	4	no	—
223	#41	—	202	4	no	—
224	#41	—	202	2	no	—
225	#41	—	202	2	no	—
226	#41	—	202	2	no	—
227	#41	—	202	2	no	—
228	#41	—	202	2	no	—
229	#41	—	202	2	no	—
230	C₂×Q₈	—	101	2	no	—
231	C₂×Q₈	—	101	1	no	—
232	C₂×Q₈	—	202	2	no	—
233	C₂×Q₈	—	202	2	no	—
234	C₂×Q₈	C₄×D₁₀₁	1	1	yes	characteristic, complemented
235	C₂×D₄	—	101	2	no	—
236	C₂×D₄	—	101	2	no	—
237	C₂×D₄	—	101	2	no	—
238	C₂×D₄	—	101	2	no	—
239	C₂×D₄	—	101	1	no	—
240	C₂×D₄	—	202	2	no	—
241	C₂×D₄	—	202	2	no	—
242	C₂×D₄	—	202	4	no	—
243	C₂×D₄	—	202	4	no	—
244	C₂×D₄	C₄×D₁₀₁	1	1	yes	characteristic, complemented
245	C₂×D₄	C₂²×D₁₀₁	1	2	yes	—
246	C₂²×C₄	—	101	1	no	—
247	C₂²×C₄	—	101	1	no	—
248	C₂²×C₄	—	101	1	no	—
249	C₂²×C₄	—	101	1	no	—
250	C₂²×C₄	—	101	1	no	—
251	C₂²×C₄	—	101	2	no	—
252	C₂²×C₄	—	101	2	no	—
253	C₂²×C₄	—	101	2	no	—
254	C₂²×C₄	—	101	2	no	—
255	C₂²×C₄	—	101	2	no	—
256	C₂²×C₄	—	101	2	no	—
257	C₂²×C₄	—	101	2	no	—
258	C₂²×C₄	—	101	2	no	—
259	C₂²×C₄	—	202	2	no	—
260	C₂²×C₄	—	202	2	no	—
261	C₂²×C₄	—	202	2	no	—
262	C₂²×C₄	—	202	2	no	—
263	C₂²×C₄	—	202	4	no	—
264	C₂²×C₄	C₄×D₁₀₁	1	2	yes	complemented
265	C₂²×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
266	C₄⋊C₄	—	2	2	no	—
267	C₄⋊C₄	—	202	4	no	—
268	C₄⋊C₄	—	202	2	no	—
269	C₂²⋊C₄	—	101	4	no	—
270	C₂²⋊C₄	—	202	4	no	—
271	C₂²⋊C₄	C₂²×D₁₀₁	1	4	yes	—
272	C₄²	—	2	2	no	—
273	C₄²	—	202	4	no	—
274	C₄²	—	202	2	no	—
275	C₂³	—	101	1	no	—
276	C₂³	—	101	2	no	—
277	C₂³	—	101	1	no	—
278	C₂³	—	101	2	no	—
279	C₂³	—	101	2	no	—
280	C₂³	—	404	4	no	—
281	C₂³	—	404	2	no	—
282	C₂³	—	202	2	no	—
283	C₂³	—	202	2	no	—
284	C₂³	C₂×C₄×D₁₀₁	1	2	yes	—
285	C₂³	C₂³×D₁₀₁	1	1	yes	characteristic
286	Q₈	—	2	2	no	—
287	Q₈	—	202	4	no	—
288	Q₈	—	202	2	no	—
289	D₄	—	2	4	no	—
290	D₄	—	2	2	no	—
291	D₄	—	202	4	no	—
292	D₄	—	202	4	no	—
293	D₄	—	202	4	no	—
294	D₄	—	202	4	no	—
295	D₄	—	202	2	no	—
296	C₂×C₄	—	2	2	no	—
297	C₂×C₄	—	2	2	no	—
298	C₂×C₄	—	2	4	no	—
299	C₂×C₄	—	101	1	no	—
300	C₂×C₄	—	101	1	no	—
301	C₂×C₄	—	101	2	no	—
302	C₂×C₄	—	101	2	no	—
303	C₂×C₄	—	101	1	no	—
304	C₂×C₄	—	101	1	no	—
305	C₂×C₄	—	101	2	no	—
306	C₂×C₄	—	101	2	no	—
307	C₂×C₄	—	101	2	no	—
308	C₂×C₄	—	101	2	no	—
309	C₂×C₄	—	101	2	no	—
310	C₂×C₄	—	101	1	no	—
311	C₂×C₄	—	101	1	no	—
312	C₂×C₄	—	101	2	no	—
313	C₂×C₄	—	101	2	no	—
314	C₂×C₄	—	404	8	no	—
315	C₂×C₄	—	202	2	no	—
316	C₂×C₄	—	202	2	no	—
317	C₂×C₄	—	202	2	no	—
318	C₂×C₄	—	202	2	no	—
319	C₂×C₄	—	202	2	no	—
320	C₂×C₄	—	202	2	no	—
321	C₂×C₄	—	202	4	no	—
322	C₂×C₄	—	202	2	no	—
323	C₂×C₄	—	202	2	no	—
324	C₂×C₄	C₂×C₄×D₁₀₁	1	2	yes	—
325	C₂×C₄	C₂×C₄×D₁₀₁	1	1	yes	characteristic
326	C₂×C₄	C₂×C₄×D₁₀₁	1	1	yes	characteristic
327	C₂×C₄	D₄×D₁₀₁	1	2	yes	—
328	C₂×C₄	D₄×D₁₀₁	1	2	yes	—
329	C₂²	—	2	2	no	—
330	C₂²	—	4	1	no	—
331	C₂²	—	4	2	no	—
332	C₂²	—	101	1	no	—
333	C₂²	—	101	1	no	—
334	C₂²	—	101	2	no	—
335	C₂²	—	404	2	no	—
336	C₂²	—	404	2	no	—
337	C₂²	—	404	1	no	—
338	C₂²	—	404	4	no	—
339	C₂²	—	404	4	no	—
340	C₂²	—	202	4	no	—
341	C₂²	—	202	2	no	—
342	C₂²	—	202	2	no	—
343	C₂²	C₂²×C₄×D₁₀₁	1	1	yes	characteristic
344	C₂²	C₂×D₄×D₁₀₁	1	2	yes	—
345	C₄	—	2	2	no	—
346	C₄	—	4	4	no	—
347	C₄	—	101	1	no	—
348	C₄	—	101	1	no	—
349	C₄	—	101	2	no	—
350	C₄	—	404	4	no	—
351	C₄	—	202	2	no	—
352	C₄	C₂²⋊C₄×D₁₀₁	1	1	yes	characteristic
353	C₄	C₂²⋊C₄×D₁₀₁	1	2	yes	—
354	C₄	C₂²⋊C₄×D₁₀₁	1	1	yes	characteristic
355	C₂	—	2	2	no	—
356	C₂	—	2	1	no	—
357	C₂	—	4	2	no	—
358	C₂	—	101	2	no	—
359	C₂	—	404	2	no	—
360	C₂	—	202	1	no	—
361	C₂	—	202	2	no	—
362	C₂	C₂×C₂²⋊C₄×D₁₀₁	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²⋊C₄×D₁₀₁
commutator	C₂²×C₁₀₁	C₂³×C₄
Frattini	C₂³	C₂³×D₁₀₁
Fitting	#410×C₁₀₁	C₂
socle	C₂×C₁₀₁	C₂²×C₂²⋊C₄
prime radical	C₂×#41×D₁₀₁	C₂
cosocle	C₂³×C₁₀₁	C₂⁴
hypercenter	#410	D₁₀₁
hypocenter	C₁₀₁	C₂×#410
LCS	G ▷ C₂²×C₁₀₁ ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #410

Complements

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

N	H ≅ G/N	type
2. #117×D₁₀₁	C₂	semidirect
3. #20265151	C₂	semidirect
4. #20265150	C₂	semidirect
5. #20265149	C₂	semidirect
6. #99×D₁₀₁	C₂	semidirect
7. #410×C₁₀₁	C₂	semidirect
8. C₂×#13108075	C₄	semidirect
9. C₂×#13108074	C₄	semidirect
11. C₂×#13108073	C₄	semidirect
17. C₂×Q₈×D₁₀₁	C₄	semidirect
18. C₂×D₄×D₁₀₁	C₄	semidirect
20. C₂²×C₄×D₁₀₁	C₄	semidirect
22. #15692214	C₂²	semidirect
25. #15692211	C₂²	semidirect
29. #15692170	C₂²	semidirect
30. #15692169	C₂²	semidirect
32. #117×C₁₀₁	C₂²	semidirect
33. #99×C₁₀₁	C₂²	semidirect
46. C₂×Dic₂₀₂	C₂×C₄	semidirect
47. C₂×Dic₂₀₂	C₂×C₄	semidirect
51. C₂×D₄₀₄	C₂×C₄	semidirect
53. C₂×C₂²⋊D₁₀₁	C₂×C₄	semidirect
59. C₂²×Dic₁₀₁	C₂×C₄	semidirect
71. C₂×C₄×D₁₀₁	C₂×C₄	semidirect
72. C₂×C₄×D₁₀₁	C₂×C₄	semidirect
85. C₂×Q₈×C₁₀₁	C₂×C₄	semidirect
86. C₂×D₄×C₁₀₁	C₂×C₄	semidirect
88. C₂²×C₄×C₁₀₁	C₂×C₄	semidirect
180. D₁₀₁	#410	direct (N × H)
182. C₁₀₁	C₂×#410	semidirect
188. #410	D₁₀₁	direct (N × H)
209. #117	C₂×D₁₀₁	semidirect
215. #99	C₂×D₁₀₁	semidirect
234. C₂×Q₈	C₄×D₁₀₁	semidirect
244. C₂×D₄	C₄×D₁₀₁	semidirect
264. C₂²×C₄	C₄×D₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#41×D₁₀₁	2
#117×D₁₀₁	2
#20265151	2
#20265150	2
#20265149	2
#99×D₁₀₁	2
#410×C₁₀₁	2
C₂×#410	101

Subgroups — #410×D101 #27179586

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #410×D₁₀₁ #27179586