Subgroups — #556×D₂₆₉ #46824427

Order 34432.

1112 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31771329	C₂	1	1	yes	maximal, characteristic, complemented
2	#31771328	C₂	1	1	yes	maximal, characteristic, complemented
3	#31771327	C₂	1	2	yes	maximal, complemented
4	#31771326	C₂	1	2	yes	maximal, complemented
5	#31771325	C₂	1	1	yes	maximal, characteristic, complemented
6	#31771324	C₂	1	2	yes	maximal, complemented
7	#31771323	C₂	1	2	yes	maximal, complemented
8	#31771322	C₂	1	4	yes	maximal, complemented
9	C₄⋊Q₈×D₂₆₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#126×D₂₆₉	C₂	1	4	yes	maximal, complemented
11	#124×D₂₆₉	C₂	1	2	yes	maximal
12	C₂²⋊Q₈×D₂₆₉	C₂	1	2	yes	maximal, complemented
13	C₄×Q₈×D₂₆₉	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×Q₈×D₂₆₉	C₂	1	2	yes	maximal, complemented
15	C₄×D₄×D₂₆₉	C₂	1	1	yes	maximal, characteristic
16	#117×D₂₆₉	C₂	1	2	yes	maximal, complemented
17	#556×C₂₆₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×Q₈×D₂₆₉	C₂²	1	2	yes	—
19	C₂×Q₈×D₂₆₉	C₂²	1	1	yes	characteristic
20	C₂×D₄×D₂₆₉	C₂²	1	1	yes	characteristic
21	C₂²×C₄×D₂₆₉	C₂²	1	2	yes	—
22	#22575453	C₂²	1	1	yes	characteristic, complemented
23	#22575452	C₂²	1	2	yes	complemented
24	#22575452	C₂²	1	2	yes	complemented
25	#22575451	C₂²	1	2	yes	complemented
26	#22575448	C₂²	1	4	yes	complemented
27	#22575448	C₂²	1	4	yes	complemented
28	#22575448	C₂²	1	4	yes	complemented
29	#22575447	C₂²	1	4	yes	complemented
30	#22575446	C₂²	1	4	yes	complemented
31	#22575446	C₂²	1	4	yes	complemented
32	#22575446	C₂²	1	4	yes	complemented
33	#22575442	C₂²	1	2	yes	—
34	#22575441	C₂²	1	2	yes	—
35	#22575440	C₂²	1	2	yes	—
36	#22575439	C₂²	1	4	yes	—
37	#22575439	C₂²	1	4	yes	—
38	#22575433	C₂²	1	2	yes	complemented
39	#22575432	C₂²	1	2	yes	complemented
40	#22575431	C₂²	1	4	yes	complemented
41	#22575430	C₂²	1	4	yes	complemented
42	#22575429	C₂²	1	2	yes	complemented
43	Q₈×Dic₂₆₉	C₂²	1	2	yes	complemented
44	Q₈×Dic₂₆₉	C₂²	1	1	yes	characteristic, complemented
45	C₄×Dic₅₃₈	C₂²	1	4	yes	complemented
46	C₄×Dic₅₃₈	C₂²	1	2	yes	complemented
47	C₄×Dic₅₃₈	C₂²	1	2	yes	complemented
48	C₄×Dic₅₃₈	C₂²	1	1	yes	characteristic, complemented
49	#22575418	C₂²	1	2	yes	complemented
50	#22575418	C₂²	1	4	yes	complemented
51	#22575418	C₂²	1	1	yes	characteristic, complemented
52	#22575418	C₂²	1	2	yes	complemented
53	C₄×D₁₀₇₆	C₂²	1	1	yes	characteristic
54	D₄×Dic₂₆₉	C₂²	1	1	yes	characteristic
55	#22575415	C₂²	1	1	yes	characteristic
56	C₄×C₂²⋊D₂₆₉	C₂²	1	2	yes	—
57	#22575413	C₂²	1	2	yes	—
58	#22575412	C₂²	1	2	yes	complemented
59	#22575411	C₂²	1	2	yes	complemented
60	#22575411	C₂²	1	2	yes	complemented
61	#22575410	C₂²	1	4	yes	complemented
62	#22575409	C₂²	1	4	yes	complemented
63	C₄⋊C₄×D₂₆₉	C₂²	1	2	yes	—
64	C₄⋊C₄×D₂₆₉	C₂²	1	2	yes	—
65	C₄⋊C₄×D₂₆₉	C₂²	1	1	yes	characteristic
66	C₄⋊C₄×D₂₆₉	C₂²	1	1	yes	characteristic
67	C₄⋊C₄×D₂₆₉	C₂²	1	4	yes	—
68	C₄⋊C₄×D₂₆₉	C₂²	1	2	yes	—
69	C₂²⋊C₄×D₂₆₉	C₂²	1	4	yes	—
70	C₂²⋊C₄×D₂₆₉	C₂²	1	2	yes	—
71	C₂²⋊C₄×D₂₆₉	C₂²	1	4	yes	—
72	C₄²×D₂₆₉	C₂²	1	1	yes	characteristic
73	C₄²×D₂₆₉	C₂²	1	4	yes	—
74	C₄²×D₂₆₉	C₂²	1	2	yes	—
75	C₄⋊Q₈×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
76	#126×C₂₆₉	C₂²	1	4	yes	complemented
77	#124×C₂₆₉	C₂²	1	2	yes	—
78	C₂²⋊Q₈×C₂₆₉	C₂²	1	2	yes	complemented
79	C₄×Q₈×C₂₆₉	C₂²	1	2	yes	complemented
80	C₄×Q₈×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
81	C₄×D₄×C₂₆₉	C₂²	1	1	yes	characteristic
82	#117×C₂₆₉	C₂²	1	2	yes	complemented
83	C₂³×D₂₆₉	C₂³	1	2	yes	—
84	C₂×Dic₅₃₈	C₂³	1	2	yes	—
85	C₂×Dic₅₃₈	C₂³	1	1	yes	characteristic
86	C₂×Dic₅₃₈	C₂³	1	4	yes	—
87	C₂×Dic₅₃₈	C₂³	1	2	yes	—
88	Q₈×D₂₆₉	—	2	4	no	—
89	Q₈×D₂₆₉	—	2	8	no	—
90	C₂×D₁₀₇₆	C₂³	1	1	yes	characteristic
91	C₂×C₂²⋊D₂₆₉	C₂³	1	2	yes	—
92	D₄×D₂₆₉	—	2	4	no	—
93	C₂²×Dic₂₆₉	C₂³	1	2	yes	—
94	C₂×C₄×D₂₆₉	—	2	8	no	—
95	C₂×C₄×D₂₆₉	C₂³	1	2	yes	—
96	C₂×C₄×D₂₆₉	C₂³	1	2	yes	—
97	C₂×C₄×D₂₆₉	C₂³	1	1	yes	characteristic
98	C₂×C₄×D₂₆₉	C₂³	1	4	yes	—
99	C₂×C₄×D₂₆₉	C₂³	1	2	yes	—
100	C₂×C₄×D₂₆₉	C₂³	1	2	yes	—
101	C₂×C₄×D₂₆₉	C₂³	1	2	yes	—
102	C₂×C₄×D₂₆₉	C₂³	1	1	yes	characteristic
103	C₂×C₄×D₂₆₉	C₂³	1	1	yes	characteristic
104	C₄⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
105	C₄⋊Dic₂₆₉	C₂³	1	2	yes	—
106	C₄⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
107	C₄⋊Dic₂₆₉	C₂³	1	4	yes	—
108	C₄⋊Dic₂₆₉	C₂³	1	2	yes	—
109	C₄⋊Dic₂₆₉	C₂³	1	2	yes	—
110	#16864381	C₂³	1	2	yes	—
111	#16864381	C₂³	1	4	yes	—
112	#16864381	C₂³	1	2	yes	—
113	#16864381	C₂³	1	4	yes	—
114	#16864381	C₂³	1	4	yes	—
115	#16864381	C₂³	1	2	yes	—
116	#16864381	C₂³	1	2	yes	—
117	#16864381	C₂³	1	4	yes	—
118	C₂²⋊Dic₂₆₉	C₂³	1	4	yes	—
119	C₂²⋊Dic₂₆₉	C₂³	1	2	yes	—
120	C₂²⋊Dic₂₆₉	C₂³	1	4	yes	—
121	#16864379	C₂³	1	4	yes	—
122	#16864379	C₂³	1	4	yes	—
123	#16864379	C₂³	1	2	yes	—
124	#16864379	C₂³	1	2	yes	—
125	#16864379	C₂³	1	4	yes	—
126	#16864379	C₂³	1	4	yes	—
127	C₄×Dic₂₆₉	C₂³	1	4	yes	—
128	C₄×Dic₂₆₉	C₂³	1	4	yes	—
129	C₄×Dic₂₆₉	C₂³	1	4	yes	—
130	C₄×Dic₂₆₉	C₂³	1	1	yes	characteristic
131	C₄×Dic₂₆₉	C₂³	1	1	yes	characteristic
132	C₄×Dic₂₆₉	C₂³	1	1	yes	characteristic
133	C₄×Dic₂₆₉	C₂³	1	2	yes	—
134	C₄×Dic₂₆₉	C₂³	1	2	yes	—
135	C₄×Dic₂₆₉	C₂³	1	2	yes	—
136	C₂×Q₈×C₂₆₉	C₂³	1	1	yes	characteristic
137	C₂×Q₈×C₂₆₉	C₂³	1	2	yes	—
138	C₂×D₄×C₂₆₉	C₂³	1	1	yes	characteristic
139	C₂²×C₄×C₂₆₉	C₂³	1	2	yes	—
140	C₄⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
141	C₄⋊C₄×C₂₆₉	C₂³	1	2	yes	—
142	C₄⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
143	C₄⋊C₄×C₂₆₉	C₂³	1	4	yes	—
144	C₄⋊C₄×C₂₆₉	C₂³	1	2	yes	—
145	C₄⋊C₄×C₂₆₉	C₂³	1	2	yes	—
146	C₂²⋊C₄×C₂₆₉	C₂³	1	4	yes	—
147	C₂²⋊C₄×C₂₆₉	C₂³	1	2	yes	—
148	C₂²⋊C₄×C₂₆₉	C₂³	1	4	yes	—
149	C₄²×C₂₆₉	C₂³	1	4	yes	—
150	C₄²×C₂₆₉	C₂³	1	1	yes	characteristic
151	C₄²×C₂₆₉	C₂³	1	2	yes	—
152	C₂²×D₂₆₉	—	2	4	no	—
153	C₂²×D₂₆₉	—	2	4	no	—
154	C₂²×D₂₆₉	—	2	4	no	—
155	C₂²×D₂₆₉	C₂⁴	1	2	yes	—
156	C₂²×D₂₆₉	C₂⁴	1	1	yes	characteristic
157	Dic₅₃₈	—	2	2	no	—
158	Dic₅₃₈	—	2	4	no	—
159	Dic₅₃₈	—	2	4	no	—
160	Dic₅₃₈	—	2	8	no	—
161	D₁₀₇₆	—	2	2	no	—
162	C₂²⋊D₂₆₉	—	2	4	no	—
163	C₂×Dic₂₆₉	—	2	4	no	—
164	C₂×Dic₂₆₉	C₂⁴	1	2	yes	—
165	C₂×Dic₂₆₉	C₂⁴	1	2	yes	—
166	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
167	C₂×Dic₂₆₉	C₂⁴	1	4	yes	—
168	C₂×Dic₂₆₉	C₂⁴	1	2	yes	—
169	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
170	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
171	C₄×D₂₆₉	—	2	4	no	—
172	C₄×D₂₆₉	—	2	4	no	—
173	C₄×D₂₆₉	—	2	8	no	—
174	C₄×D₂₆₉	—	2	4	no	—
175	C₄×D₂₆₉	—	2	2	no	—
176	C₄×D₂₆₉	—	2	4	no	—
177	C₄×D₂₆₉	—	2	4	no	—
178	C₄×D₂₆₉	#41	1	4	yes	—
179	C₄×D₂₆₉	#41	1	4	yes	—
180	C₂³×C₂₆₉	C₂⁴	1	2	yes	—
181	Q₈×C₂₆₉	—	2	2	no	—
182	Q₈×C₂₆₉	—	2	4	no	—
183	D₄×C₂₆₉	—	2	2	no	—
184	C₂×C₄×C₂₆₉	—	2	4	no	—
185	C₂×C₄×C₂₆₉	C₂⁴	1	2	yes	—
186	C₂×C₄×C₂₆₉	C₂⁴	1	2	yes	—
187	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
188	C₂×C₄×C₂₆₉	C₂⁴	1	4	yes	—
189	C₂×C₄×C₂₆₉	C₂⁴	1	2	yes	—
190	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
191	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
192	C₂²×C₂₆₉	—	2	2	no	—
193	C₂²×C₂₆₉	—	2	2	no	—
194	C₂²×C₂₆₉	—	2	2	no	—
195	C₂²×C₂₆₉	C₂⁵	1	1	yes	characteristic
196	C₂×D₂₆₉	—	2	2	no	—
197	C₂×D₂₆₉	—	2	2	no	—
198	C₂×D₂₆₉	—	2	2	no	—
199	C₂×D₂₆₉	—	4	8	no	—
200	C₂×D₂₆₉	C₂×#41	1	2	yes	—
201	C₂×D₂₆₉	C₂×#41	1	2	yes	—
202	C₂×D₂₆₉	2₋¹⁺⁴	1	2	yes	—
203	C₄×C₂₆₉	—	2	2	no	—
204	C₄×C₂₆₉	—	2	2	no	—
205	C₄×C₂₆₉	—	2	4	no	—
206	C₄×C₂₆₉	—	2	2	no	—
207	C₄×C₂₆₉	—	2	1	no	—
208	C₄×C₂₆₉	C₂×#41	1	2	yes	—
209	C₄×C₂₆₉	C₂×#41	1	2	yes	—
210	Dic₂₆₉	—	2	2	no	—
211	Dic₂₆₉	—	2	2	no	—
212	Dic₂₆₉	—	2	4	no	—
213	Dic₂₆₉	—	2	2	no	—
214	Dic₂₆₉	—	2	1	no	—
215	Dic₂₆₉	C₂×#41	1	2	yes	—
216	Dic₂₆₉	C₂×#41	1	2	yes	—
217	C₂×C₂₆₉	—	4	2	no	—
218	C₂×C₂₆₉	C₂²×#41	1	1	yes	characteristic
219	C₂×C₂₆₉	C₂²×#41	1	1	yes	characteristic
220	C₂×C₂₆₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
221	D₂₆₉	—	4	2	no	—
222	D₂₆₉	#556	1	4	yes	direct product factor
223	C₂₆₉	C₂×#556	1	1	yes	characteristic, complemented, Sylow
224	C₂×#556	—	269	1	no	maximal, Sylow
225	#556	—	269	1	no	—
226	#556	—	269	4	no	—
227	#556	—	269	2	no	—
228	#556	—	269	2	no	—
229	#556	—	269	2	no	—
230	#556	—	269	1	no	—
231	#556	—	269	1	no	—
232	#556	—	269	2	no	—
233	#556	D₂₆₉	1	1	yes	characteristic, direct product factor
234	C₂×C₄⋊Q₈	—	269	1	no	—
235	C₂×#126	—	269	4	no	—
236	C₂×#124	—	269	2	no	—
237	C₂×C₂²⋊Q₈	—	269	2	no	—
238	C₂×C₄×Q₈	—	269	2	no	—
239	C₂×C₄×Q₈	—	269	1	no	—
240	C₂×C₄×D₄	—	269	1	no	—
241	C₂×#117	—	269	2	no	—
242	C₂²×Q₈	—	269	1	no	—
243	C₂²×Q₈	—	269	2	no	—
244	C₂²×D₄	—	269	1	no	—
245	C₂³×C₄	—	269	2	no	—
246	C₄⋊Q₈	—	269	2	no	—
247	C₄⋊Q₈	—	269	2	no	—
248	C₄⋊Q₈	—	269	2	no	—
249	C₄⋊Q₈	—	269	1	no	—
250	C₄⋊Q₈	C₂×D₂₆₉	1	1	yes	characteristic, complemented
251	#126	—	269	4	no	—
252	#126	—	269	4	no	—
253	#126	—	269	4	no	—
254	#126	—	269	4	no	—
255	#126	—	269	4	no	—
256	#126	—	269	4	no	—
257	#126	—	269	4	no	—
258	#126	C₂×D₂₆₉	1	4	yes	complemented
259	#124	—	269	2	no	—
260	#124	—	269	2	no	—
261	#124	—	269	4	no	—
262	#124	—	269	4	no	—
263	#124	—	269	2	no	—
264	#124	C₂×D₂₆₉	1	2	yes	—
265	C₂²⋊Q₈	—	269	2	no	—
266	C₂²⋊Q₈	—	269	2	no	—
267	C₂²⋊Q₈	—	269	4	no	—
268	C₂²⋊Q₈	—	269	2	no	—
269	C₂²⋊Q₈	—	269	4	no	—
270	C₂²⋊Q₈	C₂×D₂₆₉	1	2	yes	complemented
271	C₄×Q₈	—	269	2	no	—
272	C₄×Q₈	—	269	1	no	—
273	C₄×Q₈	—	269	4	no	—
274	C₄×Q₈	—	269	2	no	—
275	C₄×Q₈	—	269	2	no	—
276	C₄×Q₈	—	269	1	no	—
277	C₄×Q₈	—	269	2	no	—
278	C₄×Q₈	—	269	4	no	—
279	C₄×Q₈	—	269	2	no	—
280	C₄×Q₈	—	269	1	no	—
281	C₄×Q₈	C₂×D₂₆₉	1	2	yes	complemented
282	C₄×Q₈	C₂×D₂₆₉	1	1	yes	characteristic, complemented
283	C₄×D₄	—	269	1	no	—
284	C₄×D₄	—	269	2	no	—
285	C₄×D₄	—	269	1	no	—
286	C₄×D₄	—	269	2	no	—
287	C₄×D₄	—	269	1	no	—
288	C₄×D₄	C₂×D₂₆₉	1	1	yes	characteristic
289	#117	—	269	2	no	—
290	#117	—	269	2	no	—
291	#117	—	269	2	no	—
292	#117	—	269	4	no	—
293	#117	—	269	4	no	—
294	#117	C₂×D₂₆₉	1	2	yes	complemented
295	C₂×C₄⋊C₄	—	269	1	no	—
296	C₂×C₄⋊C₄	—	269	2	no	—
297	C₂×C₄⋊C₄	—	269	1	no	—
298	C₂×C₄⋊C₄	—	269	4	no	—
299	C₂×C₄⋊C₄	—	269	2	no	—
300	C₂×C₄⋊C₄	—	269	2	no	—
301	C₂×C₂²⋊C₄	—	269	4	no	—
302	C₂×C₂²⋊C₄	—	269	2	no	—
303	C₂×C₂²⋊C₄	—	269	4	no	—
304	C₂×C₄²	—	269	4	no	—
305	C₂×C₄²	—	269	1	no	—
306	C₂×C₄²	—	269	2	no	—
307	C₂⁴	—	269	2	no	—
308	C₂×Q₈	—	269	2	no	—
309	C₂×Q₈	—	269	1	no	—
310	C₂×Q₈	—	269	4	no	—
311	C₂×Q₈	—	269	2	no	—
312	C₂×Q₈	—	538	4	no	—
313	C₂×Q₈	—	538	8	no	—
314	C₂×Q₈	C₂²×D₂₆₉	1	1	yes	characteristic
315	C₂×Q₈	C₂²×D₂₆₉	1	2	yes	—
316	C₂×D₄	—	269	2	no	—
317	C₂×D₄	—	269	1	no	—
318	C₂×D₄	—	538	4	no	—
319	C₂×D₄	C₂²×D₂₆₉	1	1	yes	characteristic
320	C₂²×C₄	—	269	1	no	—
321	C₂²×C₄	—	269	1	no	—
322	C₂²×C₄	—	269	2	no	—
323	C₂²×C₄	—	269	2	no	—
324	C₂²×C₄	—	269	2	no	—
325	C₂²×C₄	—	269	1	no	—
326	C₂²×C₄	—	269	4	no	—
327	C₂²×C₄	—	269	2	no	—
328	C₂²×C₄	—	269	2	no	—
329	C₂²×C₄	—	269	2	no	—
330	C₂²×C₄	—	538	8	no	—
331	C₂²×C₄	C₂²×D₂₆₉	1	2	yes	—
332	C₄⋊C₄	—	269	2	no	—
333	C₄⋊C₄	—	269	1	no	—
334	C₄⋊C₄	—	269	4	no	—
335	C₄⋊C₄	—	269	2	no	—
336	C₄⋊C₄	—	269	2	no	—
337	C₄⋊C₄	—	269	1	no	—
338	C₄⋊C₄	—	269	4	no	—
339	C₄⋊C₄	—	269	4	no	—
340	C₄⋊C₄	—	269	4	no	—
341	C₄⋊C₄	—	269	2	no	—
342	C₄⋊C₄	—	269	2	no	—
343	C₄⋊C₄	—	269	2	no	—
344	C₄⋊C₄	—	269	4	no	—
345	C₄⋊C₄	—	269	2	no	—
346	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
347	C₄⋊C₄	C₂²×D₂₆₉	1	2	yes	—
348	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
349	C₄⋊C₄	C₂²×D₂₆₉	1	4	yes	—
350	C₄⋊C₄	C₂²×D₂₆₉	1	2	yes	—
351	C₄⋊C₄	C₂²×D₂₆₉	1	2	yes	—
352	C₂²⋊C₄	—	269	4	no	—
353	C₂²⋊C₄	—	269	2	no	—
354	C₂²⋊C₄	—	269	4	no	—
355	C₂²⋊C₄	—	269	4	no	—
356	C₂²⋊C₄	—	269	4	no	—
357	C₂²⋊C₄	—	269	2	no	—
358	C₂²⋊C₄	—	269	2	no	—
359	C₂²⋊C₄	—	269	4	no	—
360	C₂²⋊C₄	—	269	4	no	—
361	C₂²⋊C₄	C₂²×D₂₆₉	1	4	yes	—
362	C₂²⋊C₄	C₂²×D₂₆₉	1	2	yes	—
363	C₂²⋊C₄	C₂²×D₂₆₉	1	4	yes	—
364	C₄²	—	269	4	no	—
365	C₄²	—	269	4	no	—
366	C₄²	—	269	4	no	—
367	C₄²	—	269	1	no	—
368	C₄²	—	269	1	no	—
369	C₄²	—	269	1	no	—
370	C₄²	—	269	2	no	—
371	C₄²	—	269	2	no	—
372	C₄²	—	269	2	no	—
373	C₄²	C₂²×D₂₆₉	1	4	yes	—
374	C₄²	C₂²×D₂₆₉	1	1	yes	characteristic
375	C₄²	C₂²×D₂₆₉	1	2	yes	—
376	C₂³	—	269	1	no	—
377	C₂³	—	269	2	no	—
378	C₂³	—	538	4	no	—
379	C₂³	—	538	4	no	—
380	C₂³	—	538	4	no	—
381	C₂³	C₂³×D₂₆₉	1	2	yes	—
382	Q₈	—	2	2	no	—
383	Q₈	—	2	4	no	—
384	Q₈	—	538	4	no	—
385	Q₈	—	538	8	no	—
386	Q₈	—	538	2	no	—
387	Q₈	—	538	4	no	—
388	D₄	—	2	2	no	—
389	D₄	—	538	4	no	—
390	D₄	—	538	2	no	—
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	269	1	no	—
393	C₂×C₄	—	269	1	no	—
394	C₂×C₄	—	269	4	no	—
395	C₂×C₄	—	269	4	no	—
396	C₂×C₄	—	269	2	no	—
397	C₂×C₄	—	269	2	no	—
398	C₂×C₄	—	269	1	no	—
399	C₂×C₄	—	269	4	no	—
400	C₂×C₄	—	269	2	no	—
401	C₂×C₄	—	538	4	no	—
402	C₂×C₄	—	538	4	no	—
403	C₂×C₄	—	538	4	no	—
404	C₂×C₄	—	538	8	no	—
405	C₂×C₄	—	538	4	no	—
406	C₂×C₄	—	538	2	no	—
407	C₂×C₄	—	538	4	no	—
408	C₂×C₄	—	538	4	no	—
409	C₂×C₄	C₂³×D₂₆₉	1	2	yes	—
410	C₂×C₄	C₂³×D₂₆₉	1	2	yes	—
411	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
412	C₂×C₄	C₂³×D₂₆₉	1	4	yes	—
413	C₂×C₄	C₂³×D₂₆₉	1	2	yes	—
414	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
415	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
416	C₂²	—	2	2	no	—
417	C₂²	—	2	2	no	—
418	C₂²	—	2	2	no	—
419	C₂²	—	269	2	no	—
420	C₂²	—	269	2	no	—
421	C₂²	—	269	2	no	—
422	C₂²	—	538	2	no	—
423	C₂²	—	538	2	no	—
424	C₂²	—	538	2	no	—
425	C₂²	—	1076	8	no	—
426	C₂²	C₂⁴×D₂₆₉	1	1	yes	characteristic
427	C₄	—	2	2	no	—
428	C₄	—	2	2	no	—
429	C₄	—	2	4	no	—
430	C₄	—	2	2	no	—
431	C₄	—	2	1	no	—
432	C₄	—	269	2	no	—
433	C₄	—	269	2	no	—
434	C₄	—	538	2	no	—
435	C₄	—	538	2	no	—
436	C₄	—	538	4	no	—
437	C₄	—	538	2	no	—
438	C₄	—	538	1	no	—
439	C₄	#41×D₂₆₉	1	2	yes	—
440	C₄	#41×D₂₆₉	1	2	yes	—
441	C₂	—	4	2	no	—
442	C₂	—	269	4	no	—
443	C₂	—	1076	2	no	—
444	C₂	C₂×#41×D₂₆₉	1	1	yes	characteristic
445	C₂	C₂×#41×D₂₆₉	1	1	yes	characteristic
446	C₂	2₋¹⁺⁴×D₂₆₉	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₂₆₉
commutator, socle, cosocle	C₂²×C₂₆₉	C₂⁵
Fitting	#556×C₂₆₉	C₂
prime radical	C₂×D₄×D₂₆₉	C₂²
hypercenter	#556	D₂₆₉
hypocenter	C₂₆₉	C₂×#556
LCS	G ▷ C₂²×C₂₆₉ ▷ C₂₆₉
UCS	C₁ ◁ C₂² ◁ #556

Complements

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

N	H ≅ G/N	type
1. #31771329	C₂	semidirect
2. #31771328	C₂	semidirect
3. #31771327	C₂	semidirect
4. #31771326	C₂	semidirect
5. #31771325	C₂	semidirect
6. #31771324	C₂	semidirect
7. #31771323	C₂	semidirect
8. #31771322	C₂	semidirect
9. C₄⋊Q₈×D₂₆₉	C₂	semidirect
10. #126×D₂₆₉	C₂	semidirect
12. C₂²⋊Q₈×D₂₆₉	C₂	semidirect
13. C₄×Q₈×D₂₆₉	C₂	semidirect
14. C₄×Q₈×D₂₆₉	C₂	semidirect
16. #117×D₂₆₉	C₂	semidirect
17. #556×C₂₆₉	C₂	semidirect
22. #22575453	C₂²	semidirect
23. #22575452	C₂²	semidirect
24. #22575452	C₂²	semidirect
25. #22575451	C₂²	semidirect
26. #22575448	C₂²	semidirect
27. #22575448	C₂²	semidirect
28. #22575448	C₂²	semidirect
29. #22575447	C₂²	semidirect
30. #22575446	C₂²	semidirect
31. #22575446	C₂²	semidirect
32. #22575446	C₂²	semidirect
38. #22575433	C₂²	semidirect
39. #22575432	C₂²	semidirect
40. #22575431	C₂²	semidirect
41. #22575430	C₂²	semidirect
42. #22575429	C₂²	semidirect
43. Q₈×Dic₂₆₉	C₂²	semidirect
44. Q₈×Dic₂₆₉	C₂²	semidirect
45. C₄×Dic₅₃₈	C₂²	semidirect
46. C₄×Dic₅₃₈	C₂²	semidirect
47. C₄×Dic₅₃₈	C₂²	semidirect
48. C₄×Dic₅₃₈	C₂²	semidirect
49. #22575418	C₂²	semidirect
50. #22575418	C₂²	semidirect
51. #22575418	C₂²	semidirect
52. #22575418	C₂²	semidirect
58. #22575412	C₂²	semidirect
59. #22575411	C₂²	semidirect
60. #22575411	C₂²	semidirect
61. #22575410	C₂²	semidirect
62. #22575409	C₂²	semidirect
75. C₄⋊Q₈×C₂₆₉	C₂²	semidirect
76. #126×C₂₆₉	C₂²	semidirect
78. C₂²⋊Q₈×C₂₆₉	C₂²	semidirect
79. C₄×Q₈×C₂₆₉	C₂²	semidirect
80. C₄×Q₈×C₂₆₉	C₂²	semidirect
82. #117×C₂₆₉	C₂²	semidirect
222. D₂₆₉	#556	direct (N × H)
223. C₂₆₉	C₂×#556	semidirect
233. #556	D₂₆₉	direct (N × H)
250. C₄⋊Q₈	C₂×D₂₆₉	semidirect
258. #126	C₂×D₂₆₉	semidirect
270. C₂²⋊Q₈	C₂×D₂₆₉	semidirect
281. C₄×Q₈	C₂×D₂₆₉	semidirect
282. C₄×Q₈	C₂×D₂₆₉	semidirect
294. #117	C₂×D₂₆₉	semidirect

Maximal subgroups

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

subgroup	index
#31771329	2
#31771328	2
#31771327	2
#31771326	2
#31771325	2
#31771324	2
#31771323	2
#31771322	2
C₄⋊Q₈×D₂₆₉	2
#126×D₂₆₉	2
#124×D₂₆₉	2
C₂²⋊Q₈×D₂₆₉	2
C₄×Q₈×D₂₆₉	2
C₄×D₄×D₂₆₉	2
#117×D₂₆₉	2
#556×C₂₆₉	2
C₂×#556	269

Subgroups — #556×D269 #46824427

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #556×D₂₆₉ #46824427