Subgroups — C₂×#31771322 #46824428

Order 34432.

1112 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31771322	C₂	1	16	yes	maximal, direct product factor
2	C₂×#22575452	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#22575448	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#22575448	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#22575446	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#22575439	C₂	1	1	yes	maximal, characteristic
7	C₂×#22575439	C₂	1	1	yes	maximal, characteristic
8	C₂×#22575431	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#22575430	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₄×Dic₅₃₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#22575418	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#22575418	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#22575413	C₂	1	1	yes	maximal, characteristic
14	C₂×#22575410	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#22575409	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#126×C₂₆₉	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×Dic₅₃₈	C₂²	1	1	yes	characteristic
18	C₂²×Dic₅₃₈	C₂²	1	1	yes	characteristic
19	C₂²×Dic₅₃₈	C₂²	1	1	yes	characteristic
20	C₂²×C₂²⋊D₂₆₉	C₂²	1	1	yes	characteristic
21	C₂³×Dic₂₆₉	C₂²	1	1	yes	characteristic
22	C₂²×C₄×D₂₆₉	C₂²	1	1	yes	characteristic
23	#22575452	C₂²	1	8	yes	complemented
24	#22575448	C₂²	1	8	yes	complemented
25	#22575448	C₂²	1	8	yes	complemented
26	#22575446	C₂²	1	8	yes	complemented
27	#22575439	C₂²	1	8	yes	—
28	#22575439	C₂²	1	8	yes	—
29	#22575431	C₂²	1	8	yes	complemented
30	#22575430	C₂²	1	8	yes	complemented
31	C₄×Dic₅₃₈	C₂²	1	8	yes	complemented
32	#22575418	C₂²	1	8	yes	complemented
33	#22575418	C₂²	1	8	yes	complemented
34	#22575413	C₂²	1	8	yes	—
35	#22575410	C₂²	1	8	yes	complemented
36	#22575409	C₂²	1	8	yes	complemented
37	C₂×C₄⋊Dic₂₆₉	C₂²	1	1	yes	characteristic
38	C₂×C₄⋊Dic₂₆₉	C₂²	1	1	yes	characteristic
39	C₂×#16864381	C₂²	1	1	yes	characteristic
40	C₂×#16864381	C₂²	1	1	yes	characteristic
41	C₂×#16864381	C₂²	1	1	yes	characteristic
42	C₂×#16864381	C₂²	1	1	yes	characteristic
43	C₂×#16864381	C₂²	1	1	yes	characteristic
44	C₂×#16864381	C₂²	1	1	yes	characteristic
45	C₂×#16864381	C₂²	1	1	yes	characteristic
46	C₂×C₂²⋊Dic₂₆₉	C₂²	1	1	yes	characteristic
47	C₂×C₂²⋊Dic₂₆₉	C₂²	1	1	yes	characteristic
48	C₂×#16864379	C₂²	1	1	yes	characteristic
49	C₂×#16864379	C₂²	1	1	yes	characteristic
50	C₂×#16864379	C₂²	1	1	yes	characteristic
51	C₂×#16864379	C₂²	1	1	yes	characteristic
52	C₂×#16864379	C₂²	1	1	yes	characteristic
53	C₂×C₄×Dic₂₆₉	C₂²	1	1	yes	characteristic
54	C₂×C₄×Dic₂₆₉	C₂²	1	1	yes	characteristic
55	C₂×C₄×Dic₂₆₉	C₂²	1	1	yes	characteristic
56	C₂×C₄×Dic₂₆₉	C₂²	1	1	yes	characteristic
57	C₂×C₄×Dic₂₆₉	C₂²	1	1	yes	characteristic
58	C₂×C₄×Dic₂₆₉	C₂²	1	1	yes	characteristic
59	#126×C₂₆₉	C₂²	1	8	yes	complemented
60	C₂×C₄⋊C₄×C₂₆₉	C₂²	1	1	yes	characteristic
61	C₂×C₄⋊C₄×C₂₆₉	C₂²	1	1	yes	characteristic
62	C₂×C₄⋊C₄×C₂₆₉	C₂²	1	1	yes	characteristic
63	C₂×C₂²⋊C₄×C₂₆₉	C₂²	1	1	yes	characteristic
64	C₂×C₂²⋊C₄×C₂₆₉	C₂²	1	1	yes	characteristic
65	C₂×C₂²⋊C₄×C₂₆₉	C₂²	1	1	yes	characteristic
66	C₂×C₄²×C₂₆₉	C₂²	1	1	yes	characteristic
67	C₂³×D₂₆₉	C₂³	1	1	yes	characteristic
68	C₂×Dic₅₃₈	—	2	4	no	—
69	C₂×Dic₅₃₈	—	2	4	no	—
70	C₂×Dic₅₃₈	—	2	4	no	—
71	C₂×Dic₅₃₈	C₂³	1	4	yes	—
72	C₂×Dic₅₃₈	C₂³	1	4	yes	—
73	C₂×Dic₅₃₈	C₂³	1	4	yes	—
74	C₂×C₂²⋊D₂₆₉	—	2	4	no	—
75	C₂×C₂²⋊D₂₆₉	C₂³	1	4	yes	—
76	C₂²×Dic₂₆₉	—	2	4	no	—
77	C₂²×Dic₂₆₉	C₂³	1	1	yes	characteristic
78	C₂²×Dic₂₆₉	C₂³	1	1	yes	characteristic
79	C₂²×Dic₂₆₉	C₂³	1	1	yes	characteristic
80	C₂²×Dic₂₆₉	C₂³	1	1	yes	characteristic
81	C₂²×Dic₂₆₉	C₂³	1	1	yes	characteristic
82	C₂²×Dic₂₆₉	C₂³	1	4	yes	—
83	C₂²×Dic₂₆₉	C₂³	1	1	yes	characteristic
84	C₂²×Dic₂₆₉	C₂³	1	1	yes	characteristic
85	C₂×C₄×D₂₆₉	—	2	4	no	—
86	C₂×C₄×D₂₆₉	C₂³	1	4	yes	—
87	C₄⋊Dic₂₆₉	C₂³	1	4	yes	—
88	C₄⋊Dic₂₆₉	C₂³	1	4	yes	—
89	#16864381	C₂³	1	4	yes	—
90	#16864381	C₂³	1	4	yes	—
91	#16864381	C₂³	1	4	yes	—
92	#16864381	C₂³	1	4	yes	—
93	#16864381	C₂³	1	4	yes	—
94	#16864381	C₂³	1	4	yes	—
95	#16864381	C₂³	1	4	yes	—
96	C₂²⋊Dic₂₆₉	C₂³	1	4	yes	—
97	C₂²⋊Dic₂₆₉	C₂³	1	4	yes	—
98	#16864379	C₂³	1	4	yes	—
99	#16864379	C₂³	1	4	yes	—
100	#16864379	C₂³	1	4	yes	—
101	#16864379	C₂³	1	4	yes	—
102	#16864379	C₂³	1	4	yes	—
103	C₄×Dic₂₆₉	C₂³	1	4	yes	—
104	C₄×Dic₂₆₉	C₂³	1	4	yes	—
105	C₄×Dic₂₆₉	C₂³	1	4	yes	—
106	C₄×Dic₂₆₉	C₂³	1	4	yes	—
107	C₄×Dic₂₆₉	C₂³	1	4	yes	—
108	C₄×Dic₂₆₉	C₂³	1	4	yes	—
109	C₂⁴×C₂₆₉	C₂³	1	1	yes	characteristic
110	C₂²×C₄×C₂₆₉	C₂³	1	1	yes	characteristic
111	C₂²×C₄×C₂₆₉	C₂³	1	1	yes	characteristic
112	C₂²×C₄×C₂₆₉	C₂³	1	1	yes	characteristic
113	C₂²×C₄×C₂₆₉	C₂³	1	1	yes	characteristic
114	C₂²×C₄×C₂₆₉	C₂³	1	1	yes	characteristic
115	C₂²×C₄×C₂₆₉	C₂³	1	1	yes	characteristic
116	C₄⋊C₄×C₂₆₉	C₂³	1	4	yes	—
117	C₄⋊C₄×C₂₆₉	C₂³	1	4	yes	—
118	C₄⋊C₄×C₂₆₉	C₂³	1	4	yes	—
119	C₂²⋊C₄×C₂₆₉	C₂³	1	4	yes	—
120	C₂²⋊C₄×C₂₆₉	C₂³	1	4	yes	—
121	C₂²⋊C₄×C₂₆₉	C₂³	1	4	yes	—
122	C₄²×C₂₆₉	C₂³	1	4	yes	—
123	C₂²×D₂₆₉	—	2	2	no	—
124	C₂²×D₂₆₉	—	2	2	no	—
125	C₂²×D₂₆₉	—	2	2	no	—
126	C₂²×D₂₆₉	C₂⁴	1	2	yes	—
127	Dic₅₃₈	—	2	8	no	—
128	Dic₅₃₈	—	2	8	no	—
129	Dic₅₃₈	—	2	8	no	—
130	C₂²⋊D₂₆₉	—	2	8	no	—
131	C₂×Dic₂₆₉	—	2	2	no	—
132	C₂×Dic₂₆₉	—	2	2	no	—
133	C₂×Dic₂₆₉	—	2	2	no	—
134	C₂×Dic₂₆₉	—	2	2	no	—
135	C₂×Dic₂₆₉	—	2	2	no	—
136	C₂×Dic₂₆₉	—	2	8	no	—
137	C₂×Dic₂₆₉	#41	1	4	yes	—
138	C₂×Dic₂₆₉	#41	1	4	yes	—
139	C₂×Dic₂₆₉	C₂⁴	1	2	yes	—
140	C₂×Dic₂₆₉	C₂⁴	1	2	yes	—
141	C₂×Dic₂₆₉	C₂⁴	1	2	yes	—
142	C₂×Dic₂₆₉	C₂⁴	1	2	yes	—
143	C₂×Dic₂₆₉	C₂⁴	1	2	yes	—
144	C₂×Dic₂₆₉	C₂⁴	1	2	yes	—
145	C₂×Dic₂₆₉	C₂⁴	1	2	yes	—
146	C₄×D₂₆₉	—	2	8	no	—
147	C₂³×C₂₆₉	—	2	2	no	—
148	C₂³×C₂₆₉	—	2	2	no	—
149	C₂³×C₂₆₉	—	2	2	no	—
150	C₂³×C₂₆₉	C₂⁴	1	2	yes	—
151	C₂³×C₂₆₉	C₂⁴	1	1	yes	characteristic
152	C₂×C₄×C₂₆₉	—	2	2	no	—
153	C₂×C₄×C₂₆₉	—	2	2	no	—
154	C₂×C₄×C₂₆₉	—	2	2	no	—
155	C₂×C₄×C₂₆₉	—	2	2	no	—
156	C₂×C₄×C₂₆₉	—	2	2	no	—
157	C₂×C₄×C₂₆₉	—	2	2	no	—
158	C₂×C₄×C₂₆₉	C₂⁴	1	2	yes	—
159	C₂×C₄×C₂₆₉	C₂⁴	1	2	yes	—
160	C₂×C₄×C₂₆₉	C₂⁴	1	2	yes	—
161	C₂×C₄×C₂₆₉	C₂⁴	1	2	yes	—
162	C₂×C₄×C₂₆₉	C₂⁴	1	2	yes	—
163	C₂×C₄×C₂₆₉	C₂⁴	1	2	yes	—
164	C₂²×C₂₆₉	—	2	2	no	—
165	C₂²×C₂₆₉	—	2	2	no	—
166	C₂²×C₂₆₉	—	2	2	no	—
167	C₂²×C₂₆₉	—	4	4	no	—
168	C₂²×C₂₆₉	C₂×#41	1	2	yes	—
169	C₂²×C₂₆₉	C₂×#41	1	2	yes	—
170	C₂²×C₂₆₉	2₋¹⁺⁴	1	2	yes	—
171	C₂²×C₂₆₉	C₂⁵	1	1	yes	characteristic
172	C₂×D₂₆₉	—	2	2	no	—
173	C₂×D₂₆₉	—	2	2	no	—
174	C₂×D₂₆₉	—	2	2	no	—
175	C₂×D₂₆₉	—	4	4	no	—
176	C₄×C₂₆₉	—	2	2	no	—
177	C₄×C₂₆₉	—	2	2	no	—
178	C₄×C₂₆₉	—	2	2	no	—
179	C₄×C₂₆₉	—	2	2	no	—
180	C₄×C₂₆₉	—	2	2	no	—
181	C₄×C₂₆₉	—	2	2	no	—
182	Dic₂₆₉	—	2	2	no	—
183	Dic₂₆₉	—	2	2	no	—
184	Dic₂₆₉	—	2	2	no	—
185	Dic₂₆₉	—	2	2	no	—
186	Dic₂₆₉	—	2	2	no	—
187	Dic₂₆₉	C₂×#41	1	4	yes	—
188	Dic₂₆₉	C₂×#41	1	4	yes	—
189	C₂×C₂₆₉	—	4	2	no	—
190	C₂×C₂₆₉	#556	1	4	yes	complemented
191	C₂×C₂₆₉	C₂²×#41	1	1	yes	characteristic
192	C₂×C₂₆₉	C₂²×#41	1	1	yes	characteristic
193	C₂×C₂₆₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
194	D₂₆₉	—	4	2	no	—
195	C₂₆₉	C₂×#556	1	1	yes	characteristic, complemented, Sylow
196	C₂×#556	—	269	1	no	maximal, Sylow
197	#556	—	269	16	no	—
198	C₂×C₄⋊Q₈	—	269	1	no	—
199	C₂×#126	—	269	1	no	—
200	C₂×#126	—	269	1	no	—
201	C₂×#126	—	269	1	no	—
202	C₂×#126	D₂₆₉	1	1	yes	characteristic, complemented
203	C₂×#124	—	269	1	no	—
204	C₂×#124	—	269	1	no	—
205	C₂×C₂²⋊Q₈	—	269	1	no	—
206	C₂×C₂²⋊Q₈	—	269	1	no	—
207	C₂×C₄×Q₈	—	269	1	no	—
208	C₂×C₄×Q₈	—	269	1	no	—
209	C₂×C₄×Q₈	—	269	1	no	—
210	C₂×C₄×D₄	—	269	1	no	—
211	C₂×#117	—	269	1	no	—
212	C₂×#117	—	269	1	no	—
213	C₂²×Q₈	—	269	1	no	—
214	C₂²×Q₈	—	269	1	no	—
215	C₂²×Q₈	—	269	1	no	—
216	C₂²×D₄	—	269	1	no	—
217	C₂³×C₄	—	269	1	no	—
218	C₂³×C₄	—	269	1	no	—
219	C₄⋊Q₈	—	269	8	no	—
220	#126	—	269	8	no	—
221	#126	—	269	8	no	—
222	#126	—	269	8	no	—
223	#126	C₂×D₂₆₉	1	8	yes	complemented
224	#124	—	269	8	no	—
225	#124	—	269	8	no	—
226	C₂²⋊Q₈	—	269	8	no	—
227	C₂²⋊Q₈	—	269	8	no	—
228	C₄×Q₈	—	269	8	no	—
229	C₄×Q₈	—	269	8	no	—
230	C₄×Q₈	—	269	8	no	—
231	C₄×D₄	—	269	8	no	—
232	#117	—	269	8	no	—
233	#117	—	269	8	no	—
234	C₂×C₄⋊C₄	—	269	1	no	—
235	C₂×C₄⋊C₄	—	269	1	no	—
236	C₂×C₄⋊C₄	—	269	1	no	—
237	C₂×C₄⋊C₄	—	269	1	no	—
238	C₂×C₄⋊C₄	—	269	1	no	—
239	C₂×C₄⋊C₄	—	269	1	no	—
240	C₂×C₄⋊C₄	—	269	1	no	—
241	C₂×C₄⋊C₄	—	269	1	no	—
242	C₂×C₄⋊C₄	—	269	1	no	—
243	C₂×C₄⋊C₄	C₂×D₂₆₉	1	1	yes	characteristic
244	C₂×C₄⋊C₄	C₂×D₂₆₉	1	1	yes	characteristic
245	C₂×C₄⋊C₄	C₂×D₂₆₉	1	1	yes	characteristic
246	C₂×C₂²⋊C₄	—	269	1	no	—
247	C₂×C₂²⋊C₄	—	269	1	no	—
248	C₂×C₂²⋊C₄	—	269	1	no	—
249	C₂×C₂²⋊C₄	—	269	1	no	—
250	C₂×C₂²⋊C₄	—	269	1	no	—
251	C₂×C₂²⋊C₄	—	269	1	no	—
252	C₂×C₂²⋊C₄	—	269	1	no	—
253	C₂×C₂²⋊C₄	C₂×D₂₆₉	1	1	yes	characteristic
254	C₂×C₂²⋊C₄	C₂×D₂₆₉	1	1	yes	characteristic
255	C₂×C₂²⋊C₄	C₂×D₂₆₉	1	1	yes	characteristic
256	C₂×C₄²	—	269	1	no	—
257	C₂×C₄²	—	269	1	no	—
258	C₂×C₄²	—	269	1	no	—
259	C₂×C₄²	—	269	1	no	—
260	C₂×C₄²	—	269	1	no	—
261	C₂×C₄²	—	269	1	no	—
262	C₂×C₄²	C₂×D₂₆₉	1	1	yes	characteristic
263	C₂⁴	—	269	1	no	—
264	C₂⁴	C₂²×D₂₆₉	1	1	yes	characteristic
265	C₂×Q₈	—	269	4	no	—
266	C₂×Q₈	—	269	4	no	—
267	C₂×Q₈	—	269	4	no	—
268	C₂×Q₈	—	538	4	no	—
269	C₂×Q₈	—	538	4	no	—
270	C₂×Q₈	—	538	4	no	—
271	C₂×D₄	—	269	4	no	—
272	C₂×D₄	—	538	4	no	—
273	C₂²×C₄	—	269	1	no	—
274	C₂²×C₄	—	269	1	no	—
275	C₂²×C₄	—	269	4	no	—
276	C₂²×C₄	—	269	1	no	—
277	C₂²×C₄	—	269	1	no	—
278	C₂²×C₄	—	269	1	no	—
279	C₂²×C₄	—	269	1	no	—
280	C₂²×C₄	—	269	1	no	—
281	C₂²×C₄	—	269	4	no	—
282	C₂²×C₄	—	538	4	no	—
283	C₂²×C₄	—	538	4	no	—
284	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
285	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
286	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
287	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
288	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
289	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
290	C₄⋊C₄	—	269	4	no	—
291	C₄⋊C₄	—	269	4	no	—
292	C₄⋊C₄	—	269	4	no	—
293	C₄⋊C₄	—	269	4	no	—
294	C₄⋊C₄	—	269	4	no	—
295	C₄⋊C₄	—	269	4	no	—
296	C₄⋊C₄	—	269	4	no	—
297	C₄⋊C₄	—	269	4	no	—
298	C₄⋊C₄	—	269	4	no	—
299	C₄⋊C₄	C₂²×D₂₆₉	1	4	yes	—
300	C₄⋊C₄	C₂²×D₂₆₉	1	4	yes	—
301	C₄⋊C₄	C₂²×D₂₆₉	1	4	yes	—
302	C₂²⋊C₄	—	269	4	no	—
303	C₂²⋊C₄	—	269	4	no	—
304	C₂²⋊C₄	—	269	4	no	—
305	C₂²⋊C₄	—	269	4	no	—
306	C₂²⋊C₄	—	269	4	no	—
307	C₂²⋊C₄	—	269	4	no	—
308	C₂²⋊C₄	—	269	4	no	—
309	C₂²⋊C₄	C₂²×D₂₆₉	1	4	yes	—
310	C₂²⋊C₄	C₂²×D₂₆₉	1	4	yes	—
311	C₂²⋊C₄	C₂²×D₂₆₉	1	4	yes	—
312	C₄²	—	269	4	no	—
313	C₄²	—	269	4	no	—
314	C₄²	—	269	4	no	—
315	C₄²	—	269	4	no	—
316	C₄²	—	269	4	no	—
317	C₄²	—	269	4	no	—
318	C₄²	C₂²×D₂₆₉	1	4	yes	—
319	C₂³	—	2	2	no	—
320	C₂³	—	2	2	no	—
321	C₂³	—	2	2	no	—
322	C₂³	—	269	2	no	—
323	C₂³	—	538	2	no	—
324	C₂³	—	538	2	no	—
325	C₂³	—	538	2	no	—
326	C₂³	C₂³×D₂₆₉	1	2	yes	—
327	C₂³	C₂³×D₂₆₉	1	1	yes	characteristic
328	Q₈	—	538	8	no	—
329	Q₈	—	538	8	no	—
330	Q₈	—	538	8	no	—
331	D₄	—	538	8	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	269	4	no	—
339	C₂×C₄	—	269	4	no	—
340	C₂×C₄	—	269	2	no	—
341	C₂×C₄	—	269	2	no	—
342	C₂×C₄	—	269	2	no	—
343	C₂×C₄	—	269	2	no	—
344	C₂×C₄	—	269	2	no	—
345	C₂×C₄	—	269	2	no	—
346	C₂×C₄	—	269	2	no	—
347	C₂×C₄	—	538	8	no	—
348	C₂×C₄	—	538	8	no	—
349	C₂×C₄	—	538	2	no	—
350	C₂×C₄	—	538	2	no	—
351	C₂×C₄	—	538	2	no	—
352	C₂×C₄	—	538	2	no	—
353	C₂×C₄	—	538	2	no	—
354	C₂×C₄	C₂³×D₂₆₉	1	2	yes	—
355	C₂×C₄	C₂³×D₂₆₉	1	2	yes	—
356	C₂×C₄	C₂³×D₂₆₉	1	2	yes	—
357	C₂×C₄	C₂³×D₂₆₉	1	2	yes	—
358	C₂×C₄	C₂³×D₂₆₉	1	2	yes	—
359	C₂×C₄	C₂³×D₂₆₉	1	2	yes	—
360	C₂²	—	2	2	no	—
361	C₂²	—	2	2	no	—
362	C₂²	—	2	2	no	—
363	C₂²	—	4	4	no	—
364	C₂²	—	538	2	no	—
365	C₂²	—	538	2	no	—
366	C₂²	—	538	2	no	—
367	C₂²	—	1076	4	no	—
368	C₂²	#41×D₂₆₉	1	2	yes	—
369	C₂²	#41×D₂₆₉	1	2	yes	—
370	C₂²	#22575500	1	2	yes	—
371	C₂²	C₂⁴×D₂₆₉	1	1	yes	characteristic
372	C₄	—	2	2	no	—
373	C₄	—	2	2	no	—
374	C₄	—	2	2	no	—
375	C₄	—	2	2	no	—
376	C₄	—	2	2	no	—
377	C₄	—	2	2	no	—
378	C₄	—	269	4	no	—
379	C₄	—	269	4	no	—
380	C₄	—	538	2	no	—
381	C₄	—	538	2	no	—
382	C₄	—	538	2	no	—
383	C₄	—	538	2	no	—
384	C₄	—	538	2	no	—
385	C₂	—	4	2	no	—
386	C₂	—	1076	2	no	—
387	C₂	#31771322	1	4	yes	direct product factor
388	C₂	C₂×#41×D₂₆₉	1	1	yes	characteristic
389	C₂	C₂×#41×D₂₆₉	1	1	yes	characteristic
390	C₂	C₂×#22575500	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂³×D₂₆₉
commutator, cosocle	C₂²×C₂₆₉	C₂⁵
Frattini	C₂²	C₂⁴×D₂₆₉
Fitting	C₂×#126×C₂₆₉	C₂
socle	C₂³×C₂₆₉	C₂⁴
prime radical	C₂²×C₂²⋊D₂₆₉	C₂²
hypercenter	C₂×#126	D₂₆₉
hypocenter	C₂₆₉	C₂×#556
LCS	G ▷ C₂²×C₂₆₉ ▷ C₂₆₉
UCS	C₁ ◁ C₂³ ◁ C₂×#126

Complements

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

N	H ≅ G/N	type
1. #31771322	C₂	direct (N × H)
2. C₂×#22575452	C₂	semidirect
3. C₂×#22575448	C₂	semidirect
4. C₂×#22575448	C₂	semidirect
5. C₂×#22575446	C₂	semidirect
8. C₂×#22575431	C₂	semidirect
9. C₂×#22575430	C₂	semidirect
10. C₂×C₄×Dic₅₃₈	C₂	semidirect
11. C₂×#22575418	C₂	semidirect
12. C₂×#22575418	C₂	semidirect
14. C₂×#22575410	C₂	semidirect
15. C₂×#22575409	C₂	semidirect
16. C₂×#126×C₂₆₉	C₂	semidirect
23. #22575452	C₂²	semidirect
24. #22575448	C₂²	semidirect
25. #22575448	C₂²	semidirect
26. #22575446	C₂²	semidirect
29. #22575431	C₂²	semidirect
30. #22575430	C₂²	semidirect
31. C₄×Dic₅₃₈	C₂²	semidirect
32. #22575418	C₂²	semidirect
33. #22575418	C₂²	semidirect
35. #22575410	C₂²	semidirect
36. #22575409	C₂²	semidirect
59. #126×C₂₆₉	C₂²	semidirect
190. C₂×C₂₆₉	#556	semidirect
195. C₂₆₉	C₂×#556	semidirect
202. C₂×#126	D₂₆₉	semidirect
223. #126	C₂×D₂₆₉	semidirect
387. C₂	#31771322	direct (N × H)

Maximal subgroups

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

subgroup	index
#31771322	2
C₂×#22575452	2
C₂×#22575448	2
C₂×#22575446	2
C₂×#22575439	2
C₂×#22575431	2
C₂×#22575430	2
C₂×C₄×Dic₅₃₈	2
C₂×#22575418	2
C₂×#22575413	2
C₂×#22575410	2
C₂×#22575409	2
C₂×#126×C₂₆₉	2
C₂×#556	269

Subgroups — C2×#31771322 #46824428

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#31771322 #46824428