Subgroups — C₂×#20265973 #27185875

Order 12928.

1484 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13108073	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#41×D₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
3	#20265973	C₂	1	16	yes	maximal, direct product factor
4	C₂×#15692288	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#15692285	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#15692284	C₂	1	2	yes	maximal, complemented
7	C₂×#15692281	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#15692279	C₂	1	2	yes	maximal, complemented
9	C₂×#15692276	C₂	1	2	yes	maximal, complemented
10	C₂×#15692274	C₂	1	2	yes	maximal, complemented
11	C₂×M₁₆×D₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×AGL(1,ℤ/8)×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#13108075	C₂²	1	1	yes	characteristic, complemented
14	C₂×#13108074	—	2	1	no	—
15	C₂×#13108074	C₂²	1	1	yes	characteristic
16	C₂×#13108073	—	2	1	no	—
17	C₂×#13108073	—	2	1	no	—
18	C₂×#13108073	—	2	4	no	—
19	C₂×#13108073	—	2	1	no	—
20	C₂×#13108073	C₂²	1	2	yes	—
21	C₂×#13108073	C₂²	1	1	yes	characteristic, complemented
22	C₂×#13108073	C₂²	1	2	yes	complemented
23	C₂×#13108073	C₂²	1	8	yes	complemented
24	#41×D₁₀₁	—	2	4	no	—
25	#41×D₁₀₁	C₂²	1	8	yes	complemented
26	C₂²×Dic₂₀₂	C₂²	1	1	yes	characteristic, complemented
27	C₂×Q₈×D₁₀₁	C₂²	1	1	yes	characteristic, complemented
28	C₂²×C₂²⋊D₁₀₁	—	2	1	no	—
29	C₂×D₄×D₁₀₁	—	2	1	no	—
30	C₂×D₄×D₁₀₁	C₂²	1	1	yes	characteristic, complemented
31	C₂³×Dic₁₀₁	—	2	1	no	—
32	C₂²×C₄×D₁₀₁	—	2	1	no	—
33	C₂²×C₄×D₁₀₁	C₂²	1	1	yes	characteristic
34	#15692288	C₂²	1	8	yes	complemented
35	#15692285	C₂²	1	8	yes	complemented
36	#15692284	C₂²	1	16	yes	complemented
37	#15692281	C₂²	1	8	yes	complemented
38	#15692279	C₂²	1	16	yes	complemented
39	#15692276	C₂²	1	16	yes	complemented
40	#15692274	C₂²	1	16	yes	complemented
41	C₂×Dic₄₀₄	C₂²	1	2	yes	complemented
42	C₂×#13108064	C₂²	1	2	yes	complemented
43	C₂×#13108063	C₂²	1	2	yes	complemented
44	C₂×#13108062	C₂²	1	2	yes	complemented
45	C₂×#13108062	C₂²	1	2	yes	complemented
46	C₂×#13108059	C₂²	1	2	yes	complemented
47	C₂×#13108058	C₂²	1	1	yes	characteristic, complemented
48	C₂×#13108057	C₂²	1	2	yes	complemented
49	M₁₆×D₁₀₁	C₂²	1	8	yes	complemented
50	C₂×C₈×D₁₀₁	C₂²	1	2	yes	complemented
51	C₂×#41×C₁₀₁	C₂²	1	1	yes	characteristic
52	C₂²×D₄×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
53	AGL(1,ℤ/8)×C₁₀₁	C₂²	1	8	yes	complemented
54	C₂×SD₁₆×C₁₀₁	C₂²	1	2	yes	complemented
55	C₂×D₈×C₁₀₁	C₂²	1	2	yes	complemented
56	C₂×M₁₆×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
57	C₂³×D₁₀₁	—	2	1	no	—
58	C₂³×D₁₀₁	D₄	1	1	yes	characteristic
59	#13108075	—	2	2	no	—
60	#13108075	C₂³	1	4	yes	complemented
61	#13108074	—	2	2	no	—
62	#13108074	—	2	8	no	—
63	#13108074	C₂³	1	4	yes	—
64	#13108073	—	2	8	no	—
65	#13108073	—	2	2	no	—
66	#13108073	—	2	4	no	—
67	#13108073	—	2	4	no	—
68	#13108073	—	2	8	no	—
69	#13108073	—	2	8	no	—
70	#13108073	C₂³	1	8	yes	—
71	#13108073	C₂³	1	4	yes	complemented
72	#13108073	C₂³	1	8	yes	complemented
73	C₂×Dic₂₀₂	—	2	2	no	—
74	C₂×Dic₂₀₂	—	2	1	no	—
75	C₂×Dic₂₀₂	—	2	1	no	—
76	C₂×Dic₂₀₂	C₂³	1	1	yes	characteristic
77	C₂×Dic₂₀₂	C₂³	1	2	yes	—
78	C₂×Dic₂₀₂	C₂³	1	4	yes	complemented
79	Q₈×D₁₀₁	—	2	2	no	—
80	Q₈×D₁₀₁	C₂³	1	4	yes	complemented
81	C₂×D₄₀₄	—	2	1	no	—
82	C₂×D₄₀₄	C₂³	1	1	yes	characteristic
83	C₂×C₂²⋊D₁₀₁	—	2	1	no	—
84	C₂×C₂²⋊D₁₀₁	—	2	1	no	—
85	C₂×C₂²⋊D₁₀₁	—	2	2	no	—
86	C₂×C₂²⋊D₁₀₁	—	2	2	no	—
87	C₂×C₂²⋊D₁₀₁	—	2	8	no	—
88	C₂×C₂²⋊D₁₀₁	—	2	1	no	—
89	D₄×D₁₀₁	—	2	8	no	—
90	D₄×D₁₀₁	—	2	2	no	—
91	D₄×D₁₀₁	C₂³	1	4	yes	complemented
92	C₂²×Dic₁₀₁	—	2	1	no	—
93	C₂²×Dic₁₀₁	—	2	1	no	—
94	C₂²×Dic₁₀₁	—	2	2	no	—
95	C₂²×Dic₁₀₁	—	2	2	no	—
96	C₂²×Dic₁₀₁	—	2	8	no	—
97	C₂²×Dic₁₀₁	D₄	1	1	yes	characteristic
98	C₂×C₄×D₁₀₁	—	2	1	no	—
99	C₂×C₄×D₁₀₁	—	2	1	no	—
100	C₂×C₄×D₁₀₁	—	2	1	no	—
101	C₂×C₄×D₁₀₁	—	2	8	no	—
102	C₂×C₄×D₁₀₁	D₄	1	1	yes	characteristic
103	C₂×C₄×D₁₀₁	D₄	1	4	yes	—
104	C₂×C₄×D₁₀₁	D₄	1	1	yes	characteristic
105	C₂×C₄×D₁₀₁	C₂³	1	1	yes	characteristic
106	C₂×C₄×D₁₀₁	C₂³	1	4	yes	—
107	C₂×C₄×D₁₀₁	C₂³	1	1	yes	characteristic
108	Dic₄₀₄	C₂³	1	8	yes	complemented
109	#13108064	C₂³	1	8	yes	complemented
110	#13108063	C₂³	1	8	yes	complemented
111	#13108062	C₂³	1	8	yes	complemented
112	#13108062	C₂³	1	8	yes	complemented
113	#13108059	C₂³	1	8	yes	complemented
114	#13108058	C₂³	1	4	yes	complemented
115	#13108057	C₂³	1	8	yes	complemented
116	C₂×#11717579	C₂³	1	2	yes	—
117	C₈×D₁₀₁	C₂³	1	8	yes	complemented
118	C₂⁴×C₁₀₁	—	2	1	no	—
119	#41×C₁₀₁	—	2	2	no	—
120	#41×C₁₀₁	C₂³	1	4	yes	—
121	C₂×Q₈×C₁₀₁	C₂³	1	1	yes	characteristic
122	C₂×D₄×C₁₀₁	—	2	1	no	—
123	C₂×D₄×C₁₀₁	—	2	1	no	—
124	C₂×D₄×C₁₀₁	—	2	2	no	—
125	C₂×D₄×C₁₀₁	C₂³	1	1	yes	characteristic
126	C₂×D₄×C₁₀₁	C₂³	1	2	yes	—
127	C₂×D₄×C₁₀₁	C₂³	1	4	yes	complemented
128	C₂²×C₄×C₁₀₁	—	2	1	no	—
129	C₂²×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
130	SD₁₆×C₁₀₁	C₂³	1	8	yes	complemented
131	D₈×C₁₀₁	C₂³	1	8	yes	complemented
132	M₁₆×C₁₀₁	C₂³	1	4	yes	complemented
133	C₂×C₈×C₁₀₁	C₂³	1	2	yes	—
134	C₂³×C₁₀₁	—	2	1	no	—
135	C₂³×C₁₀₁	—	2	2	no	—
136	C₂³×C₁₀₁	—	2	4	no	—
137	C₂³×C₁₀₁	—	4	4	no	—
138	C₂³×C₁₀₁	C₂×D₄	1	1	yes	characteristic
139	C₂²×D₁₀₁	—	2	1	no	—
140	C₂²×D₁₀₁	—	2	4	no	—
141	C₂²×D₁₀₁	—	4	2	no	—
142	C₂²×D₁₀₁	—	4	4	no	—
143	C₂²×D₁₀₁	C₂×D₄	1	1	yes	characteristic
144	C₂²×D₁₀₁	C₂×D₄	1	1	yes	characteristic
145	C₂²×D₁₀₁	C₂×D₄	1	4	yes	—
146	Q₈×C₁₀₁	—	2	1	no	—
147	Q₈×C₁₀₁	C₂⁴	1	2	yes	—
148	D₄×C₁₀₁	—	2	4	no	—
149	D₄×C₁₀₁	—	2	2	no	—
150	D₄×C₁₀₁	—	2	4	no	—
151	D₄×C₁₀₁	—	2	1	no	—
152	D₄×C₁₀₁	C₂⁴	1	2	yes	—
153	D₄×C₁₀₁	C₂⁴	1	4	yes	—
154	C₂×C₄×C₁₀₁	—	2	1	no	—
155	C₂×C₄×C₁₀₁	—	2	4	no	—
156	C₂×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
157	C₂×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
158	C₂×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
159	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
160	C₂²⋊D₁₀₁	—	2	4	no	—
161	C₂²⋊D₁₀₁	—	2	4	no	—
162	C₂²⋊D₁₀₁	—	2	8	no	—
163	C₂²⋊D₁₀₁	—	2	8	no	—
164	C₂²⋊D₁₀₁	—	2	4	no	—
165	C₂×Dic₁₀₁	—	2	1	no	—
166	C₂×Dic₁₀₁	—	2	2	no	—
167	C₂×Dic₁₀₁	—	2	4	no	—
168	C₂×Dic₁₀₁	—	2	4	no	—
169	C₂×Dic₁₀₁	—	2	8	no	—
170	C₂×Dic₁₀₁	—	2	8	no	—
171	C₂×Dic₁₀₁	C₂×D₄	1	1	yes	characteristic
172	C₂×Dic₁₀₁	C₂×D₄	1	1	yes	characteristic
173	C₂×Dic₁₀₁	C₂×D₄	1	4	yes	—
174	D₄₀₄	—	2	4	no	—
175	D₄₀₄	—	2	1	no	—
176	D₄₀₄	C₂⁴	1	2	yes	—
177	C₄×D₁₀₁	—	2	4	no	—
178	C₄×D₁₀₁	—	2	4	no	—
179	C₄×D₁₀₁	—	2	4	no	—
180	C₄×D₁₀₁	C₂×D₄	1	4	yes	—
181	C₄×D₁₀₁	C₂×D₄	1	2	yes	—
182	C₄×D₁₀₁	C₂×D₄	1	2	yes	—
183	C₄×D₁₀₁	C₂×D₄	1	4	yes	—
184	C₄×D₁₀₁	C₂⁴	1	2	yes	—
185	C₄×D₁₀₁	C₂⁴	1	2	yes	—
186	Dic₂₀₂	—	2	1	no	—
187	Dic₂₀₂	—	2	2	no	—
188	Dic₂₀₂	—	2	4	no	—
189	Dic₂₀₂	—	2	4	no	—
190	Dic₂₀₂	C₂⁴	1	2	yes	—
191	Dic₂₀₂	C₂⁴	1	4	yes	—
192	C₈×C₁₀₁	C₂⁴	1	4	yes	—
193	#11717579	C₂⁴	1	4	yes	—
194	C₂²×C₁₀₁	—	2	2	no	—
195	C₂²×C₁₀₁	—	2	4	no	—
196	C₂²×C₁₀₁	—	2	2	no	—
197	C₂²×C₁₀₁	—	4	8	no	—
198	C₂²×C₁₀₁	—	4	2	no	—
199	C₂²×C₁₀₁	—	4	4	no	—
200	C₂²×C₁₀₁	C₂²×D₄	1	2	yes	—
201	C₂²×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
202	C₂×D₁₀₁	—	2	2	no	—
203	C₂×D₁₀₁	—	2	2	no	—
204	C₂×D₁₀₁	—	2	2	no	—
205	C₂×D₁₀₁	—	4	4	no	—
206	C₂×D₁₀₁	—	4	8	no	—
207	C₂×D₁₀₁	—	4	2	no	—
208	C₂×D₁₀₁	C₂²×D₄	1	2	yes	—
209	C₂×D₁₀₁	C₂²×D₄	1	2	yes	—
210	C₄×C₁₀₁	—	2	2	no	—
211	C₄×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
212	C₄×C₁₀₁	C₂²×D₄	1	2	yes	—
213	C₄×C₁₀₁	C₂⁵	1	1	yes	characteristic
214	Dic₁₀₁	—	2	2	no	—
215	Dic₁₀₁	—	2	4	no	—
216	Dic₁₀₁	C₂²×D₄	1	2	yes	—
217	Dic₁₀₁	C₂²×D₄	1	2	yes	—
218	C₂×C₁₀₁	—	2	2	no	—
219	C₂×C₁₀₁	—	4	2	no	—
220	C₂×C₁₀₁	—	4	4	no	—
221	C₂×C₁₀₁	#575	1	2	yes	complemented
222	C₂×C₁₀₁	C₂³×D₄	1	1	yes	characteristic
223	D₁₀₁	—	2	2	no	—
224	D₁₀₁	—	2	2	no	—
225	D₁₀₁	—	4	2	no	—
226	C₂×#575	—	101	1	no	maximal, Sylow
227	C₁₀₁	C₂×#575	1	1	yes	characteristic, complemented, Sylow
228	C₂²×#41	—	101	1	no	—
229	C₂²×#41	—	101	1	no	—
230	#575	—	101	16	no	—
231	C₂×#137	—	101	1	no	—
232	C₂×#137	—	101	2	no	—
233	C₂×#137	—	101	1	no	—
234	C₂×AGL(1,ℤ/8)	—	101	1	no	—
235	C₂×AGL(1,ℤ/8)	—	101	2	no	—
236	C₂×AGL(1,ℤ/8)	D₁₀₁	1	1	yes	characteristic, complemented
237	C₂×#135	—	101	2	no	—
238	C₂×#135	—	101	2	no	—
239	C₂²×M₁₆	—	101	1	no	—
240	C₂×#41	—	101	8	no	—
241	C₂×#41	—	101	1	no	—
242	C₂×#41	—	101	2	no	—
243	C₂×#41	—	101	2	no	—
244	C₂×#41	—	101	1	no	—
245	C₂×#41	—	101	8	no	—
246	C₂×#41	—	101	1	no	—
247	C₂×#41	—	202	1	no	—
248	C₂×#41	—	202	1	no	—
249	C₂×#41	—	202	1	no	—
250	C₂×#41	—	202	4	no	—
251	C₂×#41	—	202	1	no	—
252	C₂×#41	—	202	4	no	—
253	C₂×#41	C₂×D₁₀₁	1	1	yes	characteristic
254	C₂²×Q₈	—	101	1	no	—
255	C₂²×Q₈	—	101	1	no	—
256	C₂²×D₄	—	101	1	no	—
257	C₂²×D₄	—	202	1	no	—
258	C₂²×D₄	—	202	1	no	—
259	C₂²×D₄	C₂×D₁₀₁	1	1	yes	characteristic, complemented
260	C₂³×C₄	—	101	1	no	—
261	C₂³×C₄	—	202	1	no	—
262	C₂³×C₄	—	202	1	no	—
263	#137	—	101	8	no	—
264	#137	—	101	16	no	—
265	#137	—	101	8	no	—
266	AGL(1,ℤ/8)	—	101	8	no	—
267	AGL(1,ℤ/8)	—	101	16	no	—
268	AGL(1,ℤ/8)	C₂×D₁₀₁	1	8	yes	complemented
269	#135	—	101	16	no	—
270	#135	—	101	16	no	—
271	C₂×Q₁₆	—	101	2	no	—
272	C₂×Q₁₆	—	101	2	no	—
273	C₂×SD₁₆	—	101	2	no	—
274	C₂×SD₁₆	—	101	2	no	—
275	C₂×SD₁₆	—	101	2	no	—
276	C₂×SD₁₆	C₂×D₁₀₁	1	2	yes	complemented
277	C₂×D₈	—	101	2	no	—
278	C₂×D₈	C₂×D₁₀₁	1	2	yes	complemented
279	C₂×M₁₆	—	101	1	no	—
280	C₂×M₁₆	—	101	8	no	—
281	C₂×M₁₆	—	101	2	no	—
282	C₂×M₁₆	C₂×D₁₀₁	1	1	yes	characteristic, complemented
283	C₂²×C₈	—	101	2	no	—
284	C₂⁴	—	2	1	no	—
285	C₂⁴	—	101	1	no	—
286	C₂⁴	—	202	1	no	—
287	#41	—	2	2	no	—
288	#41	—	101	4	no	—
289	#41	—	101	8	no	—
290	#41	—	101	8	no	—
291	#41	—	101	4	no	—
292	#41	—	101	4	no	—
293	#41	—	202	8	no	—
294	#41	—	202	8	no	—
295	#41	—	202	8	no	—
296	#41	—	202	4	no	—
297	#41	—	202	4	no	—
298	#41	—	202	8	no	—
299	#41	—	202	2	no	—
300	#41	—	202	2	no	—
301	#41	—	202	2	no	—
302	#41	C₂²×D₁₀₁	1	4	yes	—
303	C₂×Q₈	—	101	4	no	—
304	C₂×Q₈	—	101	1	no	—
305	C₂×Q₈	—	101	2	no	—
306	C₂×Q₈	—	101	4	no	—
307	C₂×Q₈	—	202	1	no	—
308	C₂×Q₈	—	202	2	no	—
309	C₂×Q₈	—	202	2	no	—
310	C₂×Q₈	—	202	1	no	—
311	C₂×Q₈	C₂²×D₁₀₁	1	1	yes	characteristic
312	C₂×D₄	—	2	1	no	—
313	C₂×D₄	—	2	2	no	—
314	C₂×D₄	—	2	1	no	—
315	C₂×D₄	—	101	4	no	—
316	C₂×D₄	—	101	1	no	—
317	C₂×D₄	—	202	1	no	—
318	C₂×D₄	—	202	2	no	—
319	C₂×D₄	—	202	1	no	—
320	C₂×D₄	—	202	8	no	—
321	C₂×D₄	—	202	8	no	—
322	C₂×D₄	—	202	1	no	—
323	C₂×D₄	—	202	2	no	—
324	C₂×D₄	—	202	2	no	—
325	C₂×D₄	—	202	1	no	—
326	C₂×D₄	C₂²×D₁₀₁	1	2	yes	—
327	C₂×D₄	C₂²×D₁₀₁	1	1	yes	characteristic
328	C₂×D₄	C₂²×D₁₀₁	1	4	yes	complemented
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	101	1	no	—
331	C₂²×C₄	—	101	1	no	—
332	C₂²×C₄	—	101	4	no	—
333	C₂²×C₄	—	101	1	no	—
334	C₂²×C₄	—	101	1	no	—
335	C₂²×C₄	—	101	1	no	—
336	C₂²×C₄	—	101	4	no	—
337	C₂²×C₄	—	202	1	no	—
338	C₂²×C₄	—	202	8	no	—
339	C₂²×C₄	—	202	1	no	—
340	C₂²×C₄	—	202	8	no	—
341	C₂²×C₄	—	202	1	no	—
342	C₂²×C₄	—	202	2	no	—
343	C₂²×C₄	—	202	2	no	—
344	C₂²×C₄	—	202	1	no	—
345	C₂²×C₄	—	202	1	no	—
346	C₂²×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
347	Q₁₆	—	101	8	no	—
348	Q₁₆	—	101	8	no	—
349	SD₁₆	—	101	8	no	—
350	SD₁₆	—	101	8	no	—
351	SD₁₆	—	101	8	no	—
352	SD₁₆	C₂²×D₁₀₁	1	8	yes	complemented
353	D₈	—	101	8	no	—
354	D₈	C₂²×D₁₀₁	1	8	yes	complemented
355	M₁₆	—	101	4	no	—
356	M₁₆	—	101	8	no	—
357	M₁₆	C₂²×D₁₀₁	1	4	yes	complemented
358	C₂×C₈	—	101	2	no	—
359	C₂×C₈	—	101	8	no	—
360	C₂×C₈	C₂²×D₁₀₁	1	2	yes	—
361	C₂³	—	2	4	no	—
362	C₂³	—	2	1	no	—
363	C₂³	—	2	2	no	—
364	C₂³	—	4	4	no	—
365	C₂³	—	101	4	no	—
366	C₂³	—	101	1	no	—
367	C₂³	—	101	1	no	—
368	C₂³	—	404	2	no	—
369	C₂³	—	404	4	no	—
370	C₂³	—	202	4	no	—
371	C₂³	—	202	1	no	—
372	C₂³	D₄×D₁₀₁	1	1	yes	characteristic
373	Q₈	—	2	1	no	—
374	Q₈	—	101	2	no	—
375	Q₈	—	101	4	no	—
376	Q₈	—	202	4	no	—
377	Q₈	—	202	4	no	—
378	Q₈	—	202	1	no	—
379	Q₈	—	202	2	no	—
380	Q₈	C₂³×D₁₀₁	1	2	yes	—
381	D₄	—	2	4	no	—
382	D₄	—	2	2	no	—
383	D₄	—	2	4	no	—
384	D₄	—	2	1	no	—
385	D₄	—	101	2	no	—
386	D₄	—	202	4	no	—
387	D₄	—	202	4	no	—
388	D₄	—	202	4	no	—
389	D₄	—	202	8	no	—
390	D₄	—	202	8	no	—
391	D₄	—	202	4	no	—
392	D₄	—	202	1	no	—
393	D₄	C₂³×D₁₀₁	1	4	yes	—
394	D₄	C₂³×D₁₀₁	1	2	yes	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	4	no	—
397	C₂×C₄	—	101	4	no	—
398	C₂×C₄	—	101	1	no	—
399	C₂×C₄	—	101	1	no	—
400	C₂×C₄	—	101	4	no	—
401	C₂×C₄	—	101	2	no	—
402	C₂×C₄	—	101	2	no	—
403	C₂×C₄	—	101	4	no	—
404	C₂×C₄	—	101	2	no	—
405	C₂×C₄	—	101	2	no	—
406	C₂×C₄	—	202	4	no	—
407	C₂×C₄	—	202	4	no	—
408	C₂×C₄	—	202	4	no	—
409	C₂×C₄	—	202	8	no	—
410	C₂×C₄	—	202	8	no	—
411	C₂×C₄	—	202	4	no	—
412	C₂×C₄	—	202	1	no	—
413	C₂×C₄	—	202	2	no	—
414	C₂×C₄	—	202	4	no	—
415	C₂×C₄	D₄×D₁₀₁	1	2	yes	—
416	C₂×C₄	D₄×D₁₀₁	1	1	yes	characteristic
417	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
418	C₂×C₄	C₂³×D₁₀₁	1	1	yes	characteristic
419	C₈	—	101	4	no	—
420	C₈	C₂³×D₁₀₁	1	4	yes	—
421	C₂²	—	2	2	no	—
422	C₂²	—	2	2	no	—
423	C₂²	—	2	4	no	—
424	C₂²	—	4	8	no	—
425	C₂²	—	4	4	no	—
426	C₂²	—	4	2	no	—
427	C₂²	—	101	2	no	—
428	C₂²	—	101	2	no	—
429	C₂²	—	404	4	no	—
430	C₂²	—	404	8	no	—
431	C₂²	—	404	2	no	—
432	C₂²	—	202	2	no	—
433	C₂²	—	202	2	no	—
434	C₂²	—	202	2	no	—
435	C₂²	C₂×D₄×D₁₀₁	1	2	yes	—
436	C₂²	C₂×D₄×D₁₀₁	1	1	yes	characteristic
437	C₄	—	2	2	no	—
438	C₄	—	101	2	no	—
439	C₄	—	101	2	no	—
440	C₄	—	202	2	no	—
441	C₄	—	202	4	no	—
442	C₄	C₂×D₄×D₁₀₁	1	2	yes	—
443	C₄	C₂×D₄×D₁₀₁	1	1	yes	characteristic
444	C₄	C₂⁴×D₁₀₁	1	1	yes	characteristic
445	C₂	—	2	2	no	—
446	C₂	—	4	4	no	—
447	C₂	—	4	2	no	—
448	C₂	—	404	2	no	—
449	C₂	—	202	2	no	—
450	C₂	—	202	2	no	—
451	C₂	#20265973	1	2	yes	direct product factor
452	C₂	C₂²×D₄×D₁₀₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₀₁
commutator, cosocle	C₄×C₁₀₁	C₂⁵
Frattini	C₄	C₂⁴×D₁₀₁
Fitting	C₂×AGL(1,ℤ/8)×C₁₀₁	C₂
socle	C₂²×C₁₀₁	C₂²×D₄
hypercenter	C₂×AGL(1,ℤ/8)	D₁₀₁
hypocenter	C₁₀₁	C₂×#575
LCS	G ▷ C₄×C₁₀₁ ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×AGL(1,ℤ/8)

Complements

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

N	H ≅ G/N	type
1. C₂²×#13108073	C₂	semidirect
2. C₂×#41×D₁₀₁	C₂	semidirect
3. #20265973	C₂	direct (N × H)
4. C₂×#15692288	C₂	semidirect
5. C₂×#15692285	C₂	semidirect
6. C₂×#15692284	C₂	semidirect
7. C₂×#15692281	C₂	semidirect
8. C₂×#15692279	C₂	semidirect
9. C₂×#15692276	C₂	semidirect
10. C₂×#15692274	C₂	semidirect
11. C₂×M₁₆×D₁₀₁	C₂	semidirect
12. C₂×AGL(1,ℤ/8)×C₁₀₁	C₂	semidirect
13. C₂×#13108075	C₂²	semidirect
21. C₂×#13108073	C₂²	semidirect
22. C₂×#13108073	C₂²	semidirect
23. C₂×#13108073	C₂²	semidirect
25. #41×D₁₀₁	C₂²	semidirect
26. C₂²×Dic₂₀₂	C₂²	semidirect
27. C₂×Q₈×D₁₀₁	C₂²	semidirect
30. C₂×D₄×D₁₀₁	C₂²	semidirect
34. #15692288	C₂²	semidirect
35. #15692285	C₂²	semidirect
36. #15692284	C₂²	semidirect
37. #15692281	C₂²	semidirect
38. #15692279	C₂²	semidirect
39. #15692276	C₂²	semidirect
40. #15692274	C₂²	semidirect
41. C₂×Dic₄₀₄	C₂²	semidirect
42. C₂×#13108064	C₂²	semidirect
43. C₂×#13108063	C₂²	semidirect
44. C₂×#13108062	C₂²	semidirect
45. C₂×#13108062	C₂²	semidirect
46. C₂×#13108059	C₂²	semidirect
47. C₂×#13108058	C₂²	semidirect
48. C₂×#13108057	C₂²	semidirect
49. M₁₆×D₁₀₁	C₂²	semidirect
50. C₂×C₈×D₁₀₁	C₂²	semidirect
52. C₂²×D₄×C₁₀₁	C₂²	semidirect
53. AGL(1,ℤ/8)×C₁₀₁	C₂²	semidirect
54. C₂×SD₁₆×C₁₀₁	C₂²	semidirect
55. C₂×D₈×C₁₀₁	C₂²	semidirect
56. C₂×M₁₆×C₁₀₁	C₂²	semidirect
60. #13108075	C₂³	semidirect
71. #13108073	C₂³	semidirect
72. #13108073	C₂³	semidirect
78. C₂×Dic₂₀₂	C₂³	semidirect
80. Q₈×D₁₀₁	C₂³	semidirect
91. D₄×D₁₀₁	C₂³	semidirect
108. Dic₄₀₄	C₂³	semidirect
109. #13108064	C₂³	semidirect
110. #13108063	C₂³	semidirect
111. #13108062	C₂³	semidirect
112. #13108062	C₂³	semidirect
113. #13108059	C₂³	semidirect
114. #13108058	C₂³	semidirect
115. #13108057	C₂³	semidirect
117. C₈×D₁₀₁	C₂³	semidirect
127. C₂×D₄×C₁₀₁	C₂³	semidirect
130. SD₁₆×C₁₀₁	C₂³	semidirect
131. D₈×C₁₀₁	C₂³	semidirect
132. M₁₆×C₁₀₁	C₂³	semidirect
221. C₂×C₁₀₁	#575	semidirect
227. C₁₀₁	C₂×#575	semidirect
236. C₂×AGL(1,ℤ/8)	D₁₀₁	semidirect
259. C₂²×D₄	C₂×D₁₀₁	semidirect
268. AGL(1,ℤ/8)	C₂×D₁₀₁	semidirect
276. C₂×SD₁₆	C₂×D₁₀₁	semidirect
278. C₂×D₈	C₂×D₁₀₁	semidirect
282. C₂×M₁₆	C₂×D₁₀₁	semidirect
328. C₂×D₄	C₂²×D₁₀₁	semidirect
352. SD₁₆	C₂²×D₁₀₁	semidirect
354. D₈	C₂²×D₁₀₁	semidirect
357. M₁₆	C₂²×D₁₀₁	semidirect
451. C₂	#20265973	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#13108073	2
C₂×#41×D₁₀₁	2
#20265973	2
C₂×#15692288	2
C₂×#15692285	2
C₂×#15692284	2
C₂×#15692281	2
C₂×#15692279	2
C₂×#15692276	2
C₂×#15692274	2
C₂×M₁₆×D₁₀₁	2
C₂×AGL(1,ℤ/8)×C₁₀₁	2
C₂×#575	101

Subgroups — C2×#20265973 #27185875

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20265973 #27185875