Subgroups — #46825131

Order 34432.

1014 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31771359	C₂	1	2	yes	maximal, complemented
2	#31771357	C₂	1	2	yes	maximal, complemented
3	#31771294	C₂	1	1	yes	maximal, characteristic, complemented
4	#31771293	C₂	1	1	yes	maximal, characteristic, complemented
5	#31771290	C₂	1	1	yes	maximal, characteristic, complemented
6	#31771279	C₂	1	2	yes	maximal, complemented
7	#31771278	C₂	1	2	yes	maximal, complemented
8	Q₈×D₁₀₇₆	C₂	1	1	yes	maximal, characteristic, complemented
9	D₄×Dic₅₃₈	C₂	1	1	yes	maximal, characteristic, complemented
10	#31771268	C₂	1	1	yes	maximal, characteristic, complemented
11	#31771268	C₂	1	1	yes	maximal, characteristic, complemented
12	#31771235	C₂	1	2	yes	maximal, complemented
13	#31771233	C₂	1	2	yes	maximal, complemented
14	#31771218	C₂	1	1	yes	maximal, characteristic, complemented
15	#31771213	C₂	1	1	yes	maximal, characteristic, complemented
16	#31771199	C₂	1	2	yes	maximal, complemented
17	#31771196	C₂	1	2	yes	maximal, complemented
18	#31771181	C₂	1	1	yes	maximal, characteristic, complemented
19	#31771178	C₂	1	1	yes	maximal, characteristic, complemented
20	#31771114	C₂	1	1	yes	maximal, characteristic
21	C₂×#22575433	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂²⋊Q₈×D₂₆₉	C₂	1	1	yes	maximal, characteristic, complemented
23	#552×C₂₆₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#16864402	C₂²	1	1	yes	characteristic
25	C₂²×Dic₅₃₈	C₂²	1	1	yes	characteristic
26	C₂²×Dic₅₃₈	C₂²	1	1	yes	characteristic, complemented
27	C₂×Q₈×D₂₆₉	C₂²	1	1	yes	characteristic
28	C₂×Q₈×D₂₆₉	C₂²	1	1	yes	characteristic, complemented
29	C₂²×C₄×D₂₆₉	C₂²	1	1	yes	characteristic
30	#22575453	C₂²	1	2	yes	complemented
31	#22575453	C₂²	1	1	yes	characteristic, complemented
32	#22575453	C₂²	1	2	yes	complemented
33	#22575452	C₂²	1	2	yes	complemented
34	#22575452	C₂²	1	2	yes	complemented
35	#22575452	C₂²	1	2	yes	complemented
36	#22575452	C₂²	1	2	yes	complemented
37	#22575451	C₂²	1	1	yes	characteristic, complemented
38	#22575448	C₂²	1	2	yes	—
39	#22575448	C₂²	1	2	yes	—
40	#22575448	C₂²	1	2	yes	—
41	#22575448	C₂²	1	2	yes	complemented
42	#22575448	C₂²	1	2	yes	complemented
43	#22575447	C₂²	1	2	yes	—
44	#22575446	C₂²	1	2	yes	complemented
45	#22575445	C₂²	1	2	yes	complemented
46	#22575445	C₂²	1	2	yes	complemented
47	#22575444	C₂²	1	2	yes	complemented
48	#22575444	C₂²	1	2	yes	complemented
49	#22575444	C₂²	1	1	yes	characteristic, complemented
50	#22575444	C₂²	1	2	yes	complemented
51	#22575443	C₂²	1	2	yes	complemented
52	#22575443	C₂²	1	2	yes	complemented
53	#22575441	C₂²	1	2	yes	—
54	#22575439	C₂²	1	2	yes	—
55	#22575438	C₂²	1	2	yes	—
56	#22575438	C₂²	1	2	yes	—
57	#22575438	C₂²	1	1	yes	characteristic
58	#22575437	C₂²	1	2	yes	—
59	#22575437	C₂²	1	2	yes	complemented
60	#22575436	C₂²	1	2	yes	—
61	#22575435	C₂²	1	2	yes	—
62	#22575435	C₂²	1	1	yes	characteristic
63	#22575435	C₂²	1	2	yes	complemented
64	#22575433	C₂²	1	1	yes	characteristic
65	#22575433	C₂²	1	1	yes	characteristic
66	#22575433	C₂²	1	1	yes	characteristic
67	#22575433	C₂²	1	2	yes	—
68	#22575433	C₂²	1	2	yes	—
69	#22575433	C₂²	1	1	yes	characteristic
70	#22575433	C₂²	1	1	yes	characteristic
71	#22575433	C₂²	1	2	yes	—
72	#22575433	C₂²	1	1	yes	characteristic, complemented
73	#22575433	C₂²	1	1	yes	characteristic, complemented
74	#22575433	C₂²	1	2	yes	complemented
75	#22575432	C₂²	1	1	yes	characteristic
76	#22575432	C₂²	1	1	yes	characteristic, complemented
77	#22575431	C₂²	1	1	yes	characteristic
78	#22575431	C₂²	1	2	yes	—
79	#22575431	C₂²	1	2	yes	—
80	#22575431	C₂²	1	2	yes	complemented
81	#22575430	C₂²	1	2	yes	—
82	#22575430	C₂²	1	1	yes	characteristic
83	#22575430	C₂²	1	2	yes	—
84	#22575430	C₂²	1	2	yes	—
85	#22575430	C₂²	1	2	yes	complemented
86	#22575430	C₂²	1	2	yes	complemented
87	#22575429	C₂²	1	1	yes	characteristic
88	#22575426	C₂²	1	1	yes	characteristic
89	#22575425	C₂²	1	1	yes	characteristic
90	#22575423	C₂²	1	1	yes	characteristic
91	#22575421	C₂²	1	1	yes	characteristic
92	C₄×Dic₅₃₈	C₂²	1	1	yes	characteristic, complemented
93	#22575418	C₂²	1	1	yes	characteristic, complemented
94	#22575418	C₂²	1	1	yes	characteristic, complemented
95	C₄×D₁₀₇₆	C₂²	1	2	yes	—
96	C₄×D₁₀₇₆	C₂²	1	1	yes	characteristic
97	D₄×Dic₂₆₉	C₂²	1	2	yes	—
98	C₄×C₂²⋊D₂₆₉	C₂²	1	1	yes	characteristic
99	C₄×C₂²⋊D₂₆₉	C₂²	1	1	yes	characteristic
100	#22575413	C₂²	1	2	yes	—
101	#22575413	C₂²	1	2	yes	—
102	#22575412	C₂²	1	2	yes	—
103	#22575411	C₂²	1	2	yes	—
104	#22575411	C₂²	1	1	yes	characteristic, complemented
105	#22575410	C₂²	1	1	yes	characteristic
106	#22575410	C₂²	1	2	yes	—
107	C₂×C₄⋊Dic₂₆₉	C₂²	1	2	yes	—
108	C₄⋊C₄×D₂₆₉	C₂²	1	2	yes	—
109	C₄⋊C₄×D₂₆₉	C₂²	1	1	yes	characteristic
110	C₂×#16864379	C₂²	1	2	yes	—
111	C₂²⋊C₄×D₂₆₉	C₂²	1	2	yes	—
112	#126×C₂₆₉	C₂²	1	2	yes	complemented
113	#125×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
114	#125×C₂₆₉	C₂²	1	2	yes	complemented
115	#123×C₂₆₉	C₂²	1	2	yes	—
116	C₂²⋊Q₈×C₂₆₉	C₂²	1	1	yes	characteristic
117	C₂²⋊Q₈×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
118	C₄×Q₈×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₄×C₂₆₉	C₂²	1	1	yes	characteristic
120	#117×C₂₆₉	C₂²	1	2	yes	—
121	#117×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
122	C₂×C₄⋊C₄×C₂₆₉	C₂²	1	1	yes	characteristic
123	C₂³×D₂₆₉	C₂³	1	1	yes	characteristic
124	#16864402	—	4	2	no	—
125	C₂×Dic₅₃₈	—	4	2	no	—
126	C₂×Dic₅₃₈	—	4	2	no	—
127	C₂×Dic₅₃₈	C₂³	1	1	yes	characteristic
128	C₂×Dic₅₃₈	C₂³	1	1	yes	characteristic
129	C₂×Dic₅₃₈	C₂³	1	1	yes	characteristic
130	C₂×Dic₅₃₈	C₂³	1	2	yes	—
131	C₂×Dic₅₃₈	C₂³	1	2	yes	—
132	C₂×Dic₅₃₈	C₂³	1	1	yes	characteristic
133	C₂×Dic₅₃₈	C₂³	1	2	yes	—
134	C₂×Dic₅₃₈	C₂³	1	2	yes	—
135	Q₈×D₂₆₉	—	4	2	no	—
136	Q₈×D₂₆₉	—	4	2	no	—
137	C₂×D₁₀₇₆	C₂³	1	1	yes	characteristic
138	C₂×D₁₀₇₆	C₂³	1	1	yes	characteristic
139	C₂×C₂²⋊D₂₆₉	C₂³	1	1	yes	characteristic
140	C₂×C₂²⋊D₂₆₉	C₂³	1	1	yes	characteristic
141	C₂×C₂²⋊D₂₆₉	C₂³	1	1	yes	characteristic
142	C₂×C₂²⋊D₂₆₉	C₂³	1	1	yes	characteristic
143	C₂²×Dic₂₆₉	C₂³	1	2	yes	—
144	C₂²×Dic₂₆₉	C₂³	1	1	yes	characteristic
145	C₂²×Dic₂₆₉	C₂³	1	2	yes	—
146	C₂×C₄×D₂₆₉	—	4	2	no	—
147	C₂×C₄×D₂₆₉	C₂³	1	2	yes	—
148	C₂×C₄×D₂₆₉	C₂³	1	1	yes	characteristic
149	C₂×C₄×D₂₆₉	C₂³	1	1	yes	characteristic
150	C₂×C₄×D₂₆₉	C₂³	1	1	yes	characteristic
151	C₂×C₄×D₂₆₉	C₂³	1	2	yes	—
152	C₂×C₄×D₂₆₉	C₂³	1	1	yes	characteristic
153	C₂×C₄×D₂₆₉	C₂³	1	2	yes	—
154	C₂×C₄×D₂₆₉	C₂³	1	1	yes	characteristic
155	C₄⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
156	C₄⋊Dic₂₆₉	C₂³	1	2	yes	—
157	C₄⋊Dic₂₆₉	C₂³	1	2	yes	—
158	C₄⋊Dic₂₆₉	C₂³	1	2	yes	—
159	C₄⋊Dic₂₆₉	C₂³	1	2	yes	—
160	C₄⋊Dic₂₆₉	C₂³	1	2	yes	—
161	C₄⋊Dic₂₆₉	C₂³	1	2	yes	—
162	C₄⋊Dic₂₆₉	C₂³	1	2	yes	—
163	C₄⋊Dic₂₆₉	C₂³	1	2	yes	—
164	C₄⋊Dic₂₆₉	C₂³	1	2	yes	—
165	C₄⋊Dic₂₆₉	C₂³	1	2	yes	—
166	C₄⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
167	#16864381	C₂³	1	2	yes	—
168	#16864381	C₂³	1	2	yes	—
169	#16864381	C₂³	1	2	yes	—
170	#16864381	C₂³	1	1	yes	characteristic
171	#16864381	C₂³	1	1	yes	characteristic
172	#16864381	C₂³	1	2	yes	—
173	#16864381	C₂³	1	2	yes	—
174	#16864381	C₂³	1	2	yes	—
175	#16864381	C₂³	1	2	yes	—
176	#16864381	C₂³	1	1	yes	characteristic
177	#16864381	C₂³	1	1	yes	characteristic
178	#16864381	C₂³	1	2	yes	—
179	#16864381	C₂³	1	2	yes	—
180	#16864381	C₂³	1	2	yes	—
181	C₂²⋊Dic₂₆₉	C₂³	1	2	yes	—
182	C₂²⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
183	C₂²⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
184	C₂²⋊Dic₂₆₉	C₂³	1	2	yes	—
185	#16864379	C₂³	1	2	yes	—
186	#16864379	C₂³	1	2	yes	—
187	#16864379	C₂³	1	2	yes	—
188	#16864379	C₂³	1	2	yes	—
189	#16864379	C₂³	1	2	yes	—
190	#16864379	C₂³	1	2	yes	—
191	#16864379	C₂³	1	1	yes	characteristic
192	#16864379	C₂³	1	1	yes	characteristic
193	#16864379	C₂³	1	1	yes	characteristic
194	#16864379	C₂³	1	1	yes	characteristic
195	#16864379	C₂³	1	2	yes	—
196	#16864379	C₂³	1	2	yes	—
197	#16864379	C₂³	1	1	yes	characteristic
198	#16864379	C₂³	1	1	yes	characteristic
199	#16864379	C₂³	1	2	yes	—
200	C₄×Dic₂₆₉	C₂³	1	2	yes	—
201	C₄×Dic₂₆₉	C₂³	1	1	yes	characteristic
202	C₄×Dic₂₆₉	C₂³	1	2	yes	—
203	C₄×Dic₂₆₉	C₂³	1	2	yes	—
204	C₄×Dic₂₆₉	C₂³	1	2	yes	—
205	C₂×Q₈×C₂₆₉	C₂³	1	1	yes	characteristic
206	C₂×D₄×C₂₆₉	C₂³	1	1	yes	characteristic
207	C₂²×C₄×C₂₆₉	C₂³	1	2	yes	—
208	C₂²×C₄×C₂₆₉	C₂³	1	1	yes	characteristic
209	C₂²×C₄×C₂₆₉	C₂³	1	1	yes	characteristic
210	C₄⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
211	C₄⋊C₄×C₂₆₉	C₂³	1	2	yes	—
212	C₄⋊C₄×C₂₆₉	C₂³	1	2	yes	—
213	C₄⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
214	C₄⋊C₄×C₂₆₉	C₂³	1	2	yes	—
215	C₄⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
216	C₄⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
217	C₄⋊C₄×C₂₆₉	C₂³	1	2	yes	—
218	C₄⋊C₄×C₂₆₉	C₂³	1	2	yes	—
219	C₄⋊C₄×C₂₆₉	C₂³	1	2	yes	—
220	C₂²⋊C₄×C₂₆₉	C₂³	1	2	yes	—
221	C₂²⋊C₄×C₂₆₉	C₂³	1	2	yes	—
222	C₂²⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
223	C₂²⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
224	C₂²⋊C₄×C₂₆₉	C₂³	1	2	yes	—
225	C₄²×C₂₆₉	C₂³	1	1	yes	characteristic
226	C₄²×C₂₆₉	C₂³	1	2	yes	—
227	C₄²×C₂₆₉	C₂³	1	2	yes	—
228	C₂²×D₂₆₉	—	2	2	no	—
229	C₂²×D₂₆₉	—	2	2	no	—
230	C₂²×D₂₆₉	—	4	1	no	—
231	C₂²×D₂₆₉	C₂⁴	1	1	yes	characteristic
232	C₂²×D₂₆₉	C₂⁴	1	1	yes	characteristic
233	C₂²×D₂₆₉	C₂⁴	1	1	yes	characteristic
234	Dic₅₃₈	—	2	2	no	—
235	Dic₅₃₈	—	2	2	no	—
236	Dic₅₃₈	—	2	2	no	—
237	Dic₅₃₈	—	4	2	no	—
238	Dic₅₃₈	—	4	2	no	—
239	Dic₅₃₈	—	4	2	no	—
240	Dic₅₃₈	—	4	2	no	—
241	Dic₅₃₈	—	4	1	no	—
242	D₁₀₇₆	—	2	2	no	—
243	D₁₀₇₆	—	4	1	no	—
244	C₂²⋊D₂₆₉	—	2	2	no	—
245	C₂²⋊D₂₆₉	—	2	2	no	—
246	C₂²⋊D₂₆₉	—	4	1	no	—
247	C₂²⋊D₂₆₉	—	4	1	no	—
248	C₂×Dic₂₆₉	—	4	1	no	—
249	C₂×Dic₂₆₉	—	4	2	no	—
250	C₂×Dic₂₆₉	—	4	2	no	—
251	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
252	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
253	C₂×Dic₂₆₉	C₂⁴	1	2	yes	—
254	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
255	C₂×Dic₂₆₉	C₂⁴	1	2	yes	—
256	C₂×Dic₂₆₉	C₂⁴	1	2	yes	—
257	C₂×Dic₂₆₉	C₂⁴	1	2	yes	—
258	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
259	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
260	C₄×D₂₆₉	—	2	4	no	—
261	C₄×D₂₆₉	—	2	2	no	—
262	C₄×D₂₆₉	—	2	2	no	—
263	C₄×D₂₆₉	—	2	2	no	—
264	C₄×D₂₆₉	—	4	1	no	—
265	C₄×D₂₆₉	—	4	1	no	—
266	C₄×D₂₆₉	—	4	2	no	—
267	C₄×D₂₆₉	—	4	2	no	—
268	C₂³×C₂₆₉	C₂⁴	1	1	yes	characteristic
269	C₂³×C₂₆₉	C₂⁴	1	1	yes	characteristic
270	Q₈×C₂₆₉	—	2	2	no	—
271	D₄×C₂₆₉	—	2	2	no	—
272	C₂×C₄×C₂₆₉	—	2	4	no	—
273	C₂×C₄×C₂₆₉	—	2	2	no	—
274	C₂×C₄×C₂₆₉	—	2	2	no	—
275	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
276	C₂×C₄×C₂₆₉	C₂⁴	1	2	yes	—
277	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
278	C₂×C₄×C₂₆₉	C₂⁴	1	2	yes	—
279	C₂×C₄×C₂₆₉	C₂⁴	1	2	yes	—
280	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
281	C₂×C₄×C₂₆₉	C₂⁴	1	2	yes	—
282	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
283	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
284	C₂²×C₂₆₉	—	2	1	no	—
285	C₂²×C₂₆₉	—	2	1	no	—
286	C₂²×C₂₆₉	—	2	1	no	—
287	C₂²×C₂₆₉	—	2	1	no	—
288	C₂²×C₂₆₉	—	2	1	no	—
289	C₂²×C₂₆₉	2₋¹⁺⁴	1	2	yes	—
290	C₂²×C₂₆₉	C₂⁵	1	1	yes	characteristic
291	C₂×D₂₆₉	—	2	1	no	—
292	C₂×D₂₆₉	—	2	1	no	—
293	C₂×D₂₆₉	—	2	1	no	—
294	C₂×D₂₆₉	—	2	1	no	—
295	C₂×D₂₆₉	—	2	1	no	—
296	C₂×D₂₆₉	—	2	1	no	—
297	C₂×D₂₆₉	—	2	1	no	—
298	C₂×D₂₆₉	—	2	1	no	—
299	C₂×D₂₆₉	—	4	4	no	—
300	C₂×D₂₆₉	2₋¹⁺⁴	1	2	yes	—
301	C₄×C₂₆₉	—	2	1	no	—
302	C₄×C₂₆₉	—	2	1	no	—
303	C₄×C₂₆₉	—	2	2	no	—
304	C₄×C₂₆₉	—	2	2	no	—
305	C₄×C₂₆₉	—	2	2	no	—
306	C₄×C₂₆₉	—	2	1	no	—
307	C₄×C₂₆₉	—	2	2	no	—
308	C₄×C₂₆₉	—	2	1	no	—
309	C₄×C₂₆₉	H(5,𝔽₂)	1	2	yes	—
310	Dic₂₆₉	—	2	1	no	—
311	Dic₂₆₉	—	2	1	no	—
312	Dic₂₆₉	—	2	1	no	—
313	Dic₂₆₉	—	2	2	no	—
314	Dic₂₆₉	—	2	2	no	—
315	Dic₂₆₉	—	2	2	no	—
316	Dic₂₆₉	—	2	2	no	—
317	Dic₂₆₉	—	2	1	no	—
318	Dic₂₆₉	—	2	1	no	—
319	C₂×C₂₆₉	—	2	2	no	—
320	C₂×C₂₆₉	—	4	1	no	—
321	C₂×C₂₆₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
322	C₂×C₂₆₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
323	C₂×C₂₆₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
324	D₂₆₉	—	2	2	no	—
325	D₂₆₉	—	4	1	no	—
326	D₂₆₉	—	4	1	no	—
327	C₂₆₉	#3538	1	1	yes	characteristic, complemented, Sylow
328	#3538	—	269	1	no	maximal, Sylow
329	#563	—	269	2	no	—
330	#563	—	269	2	no	—
331	#552	—	269	1	no	—
332	#552	—	269	1	no	—
333	#552	—	269	1	no	—
334	#552	D₂₆₉	1	1	yes	characteristic, complemented
335	#551	—	269	2	no	—
336	#551	—	269	2	no	—
337	D₄×Q₈	—	269	1	no	—
338	D₄×Q₈	—	269	1	no	—
339	D₄×Q₈	—	269	1	no	—
340	D₄×Q₈	—	269	1	no	—
341	#544	—	269	2	no	—
342	#544	—	269	2	no	—
343	#541	—	269	1	no	—
344	#541	—	269	1	no	—
345	#539	—	269	2	no	—
346	#539	—	269	2	no	—
347	#536	—	269	1	no	—
348	#536	—	269	1	no	—
349	#525	—	269	1	no	—
350	C₂×C₂²⋊Q₈	—	269	1	no	—
351	C₂×C₂²⋊Q₈	—	269	1	no	—
352	C₂×#41	—	269	1	no	—
353	C₂²×Q₈	—	269	1	no	—
354	C₂²×Q₈	—	269	1	no	—
355	C₂²×Q₈	—	269	1	no	—
356	C₂²×Q₈	—	269	1	no	—
357	C₂³×C₄	—	269	1	no	—
358	C₄⋊Q₈	—	269	1	no	—
359	C₄⋊Q₈	—	269	2	no	—
360	C₄⋊Q₈	—	269	2	no	—
361	C₄⋊Q₈	—	269	2	no	—
362	C₄⋊Q₈	—	269	2	no	—
363	C₄⋊Q₈	—	269	2	no	—
364	C₄⋊Q₈	—	269	1	no	—
365	C₄⋊Q₈	—	269	2	no	—
366	#126	—	269	2	no	—
367	#126	—	269	2	no	—
368	#126	—	269	2	no	—
369	#126	—	269	2	no	—
370	#126	—	269	2	no	—
371	#126	—	269	2	no	—
372	#126	—	269	2	no	—
373	#126	C₂×D₂₆₉	1	2	yes	complemented
374	#125	—	269	2	no	—
375	#125	—	269	2	no	—
376	#125	—	269	2	no	—
377	#125	—	269	1	no	—
378	#125	—	269	2	no	—
379	#125	—	269	2	no	—
380	#125	—	269	2	no	—
381	#125	—	269	2	no	—
382	#125	C₂×D₂₆₉	1	1	yes	characteristic, complemented
383	#125	C₂×D₂₆₉	1	2	yes	complemented
384	#124	—	269	2	no	—
385	#124	—	269	2	no	—
386	#123	—	269	2	no	—
387	#123	—	269	1	no	—
388	#123	—	269	2	no	—
389	#123	—	269	2	no	—
390	#123	—	269	1	no	—
391	#123	—	269	2	no	—
392	#123	—	269	2	no	—
393	#123	—	269	2	no	—
394	#123	—	269	2	no	—
395	#123	C₂×D₂₆₉	1	2	yes	—
396	C₂²⋊Q₈	—	269	1	no	—
397	C₂²⋊Q₈	—	269	1	no	—
398	C₂²⋊Q₈	—	269	1	no	—
399	C₂²⋊Q₈	—	269	1	no	—
400	C₂²⋊Q₈	—	269	1	no	—
401	C₂²⋊Q₈	—	269	1	no	—
402	C₂²⋊Q₈	—	269	2	no	—
403	C₂²⋊Q₈	—	269	1	no	—
404	C₂²⋊Q₈	—	269	1	no	—
405	C₂²⋊Q₈	—	269	2	no	—
406	C₂²⋊Q₈	—	269	2	no	—
407	C₂²⋊Q₈	—	269	1	no	—
408	C₂²⋊Q₈	—	269	1	no	—
409	C₂²⋊Q₈	—	269	1	no	—
410	C₂²⋊Q₈	—	269	2	no	—
411	C₂²⋊Q₈	—	269	2	no	—
412	C₂²⋊Q₈	—	269	2	no	—
413	C₂²⋊Q₈	—	269	2	no	—
414	C₂²⋊Q₈	—	269	2	no	—
415	C₂²⋊Q₈	—	269	1	no	—
416	C₂²⋊Q₈	—	269	2	no	—
417	C₂²⋊Q₈	—	269	2	no	—
418	C₂²⋊Q₈	—	269	2	no	—
419	C₂²⋊Q₈	—	269	2	no	—
420	C₂²⋊Q₈	C₂×D₂₆₉	1	1	yes	characteristic
421	C₂²⋊Q₈	C₂×D₂₆₉	1	1	yes	characteristic, complemented
422	#121	—	269	1	no	—
423	#121	—	269	1	no	—
424	#120	—	269	1	no	—
425	#120	—	269	1	no	—
426	C₄×Q₈	—	269	1	no	—
427	C₄×Q₈	—	269	1	no	—
428	C₄×Q₈	—	269	1	no	—
429	C₄×Q₈	C₂×D₂₆₉	1	1	yes	characteristic, complemented
430	C₄×D₄	—	269	2	no	—
431	C₄×D₄	—	269	1	no	—
432	C₄×D₄	—	269	1	no	—
433	C₄×D₄	—	269	2	no	—
434	C₄×D₄	—	269	2	no	—
435	C₄×D₄	—	269	1	no	—
436	C₄×D₄	—	269	2	no	—
437	C₄×D₄	C₂×D₂₆₉	1	1	yes	characteristic
438	#117	—	269	2	no	—
439	#117	—	269	1	no	—
440	#117	—	269	2	no	—
441	#117	—	269	1	no	—
442	#117	—	269	2	no	—
443	#117	C₂×D₂₆₉	1	2	yes	—
444	#117	C₂×D₂₆₉	1	1	yes	characteristic, complemented
445	C₂×C₄⋊C₄	—	269	2	no	—
446	C₂×C₄⋊C₄	—	269	2	no	—
447	C₂×C₄⋊C₄	—	269	1	no	—
448	C₂×C₄⋊C₄	C₂×D₂₆₉	1	1	yes	characteristic
449	C₂×C₂²⋊C₄	—	269	2	no	—
450	C₂×C₂²⋊C₄	—	269	2	no	—
451	C₂⁴	—	269	1	no	—
452	#41	—	1076	2	no	—
453	C₂×Q₈	—	269	1	no	—
454	C₂×Q₈	—	269	1	no	—
455	C₂×Q₈	—	269	1	no	—
456	C₂×Q₈	—	269	2	no	—
457	C₂×Q₈	—	269	2	no	—
458	C₂×Q₈	—	269	2	no	—
459	C₂×Q₈	—	269	2	no	—
460	C₂×Q₈	—	269	1	no	—
461	C₂×Q₈	—	1076	2	no	—
462	C₂×Q₈	—	1076	2	no	—
463	C₂×Q₈	—	1076	2	no	—
464	C₂×Q₈	—	1076	2	no	—
465	C₂×Q₈	C₂²×D₂₆₉	1	1	yes	characteristic
466	C₂×D₄	—	269	1	no	—
467	C₂×D₄	—	269	1	no	—
468	C₂×D₄	—	269	1	no	—
469	C₂×D₄	—	269	1	no	—
470	C₂×D₄	—	269	1	no	—
471	C₂×D₄	—	269	1	no	—
472	C₂×D₄	C₂²×D₂₆₉	1	1	yes	characteristic
473	C₂²×C₄	—	269	2	no	—
474	C₂²×C₄	—	269	1	no	—
475	C₂²×C₄	—	269	2	no	—
476	C₂²×C₄	—	269	2	no	—
477	C₂²×C₄	—	269	1	no	—
478	C₂²×C₄	—	269	1	no	—
479	C₂²×C₄	—	269	1	no	—
480	C₂²×C₄	—	269	2	no	—
481	C₂²×C₄	—	269	1	no	—
482	C₂²×C₄	—	269	2	no	—
483	C₂²×C₄	—	269	1	no	—
484	C₂²×C₄	—	1076	2	no	—
485	C₂²×C₄	C₂²×D₂₆₉	1	2	yes	—
486	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
487	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
488	C₄⋊C₄	—	269	1	no	—
489	C₄⋊C₄	—	269	2	no	—
490	C₄⋊C₄	—	269	2	no	—
491	C₄⋊C₄	—	269	2	no	—
492	C₄⋊C₄	—	269	2	no	—
493	C₄⋊C₄	—	269	2	no	—
494	C₄⋊C₄	—	269	2	no	—
495	C₄⋊C₄	—	269	2	no	—
496	C₄⋊C₄	—	269	2	no	—
497	C₄⋊C₄	—	269	1	no	—
498	C₄⋊C₄	—	269	1	no	—
499	C₄⋊C₄	—	269	2	no	—
500	C₄⋊C₄	—	269	2	no	—
501	C₄⋊C₄	—	269	2	no	—
502	C₄⋊C₄	—	269	2	no	—
503	C₄⋊C₄	—	269	2	no	—
504	C₄⋊C₄	—	269	2	no	—
505	C₄⋊C₄	—	269	2	no	—
506	C₄⋊C₄	—	269	2	no	—
507	C₄⋊C₄	—	269	2	no	—
508	C₄⋊C₄	—	269	1	no	—
509	C₄⋊C₄	—	269	1	no	—
510	C₄⋊C₄	—	269	1	no	—
511	C₄⋊C₄	—	269	2	no	—
512	C₄⋊C₄	—	269	2	no	—
513	C₄⋊C₄	—	269	2	no	—
514	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
515	C₄⋊C₄	C₂²×D₂₆₉	1	2	yes	—
516	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
517	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
518	C₄⋊C₄	C₂²×D₂₆₉	1	2	yes	—
519	C₄⋊C₄	C₂²×D₂₆₉	1	2	yes	—
520	C₄⋊C₄	C₂²×D₂₆₉	1	2	yes	—
521	C₄⋊C₄	C₂²×D₂₆₉	1	2	yes	—
522	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
523	C₄⋊C₄	C₂²×D₂₆₉	1	2	yes	—
524	C₂²⋊C₄	—	269	2	no	—
525	C₂²⋊C₄	—	269	1	no	—
526	C₂²⋊C₄	—	269	1	no	—
527	C₂²⋊C₄	—	269	2	no	—
528	C₂²⋊C₄	—	269	2	no	—
529	C₂²⋊C₄	—	269	2	no	—
530	C₂²⋊C₄	—	269	2	no	—
531	C₂²⋊C₄	—	269	2	no	—
532	C₂²⋊C₄	—	269	2	no	—
533	C₂²⋊C₄	—	269	2	no	—
534	C₂²⋊C₄	—	269	1	no	—
535	C₂²⋊C₄	—	269	1	no	—
536	C₂²⋊C₄	—	269	1	no	—
537	C₂²⋊C₄	—	269	1	no	—
538	C₂²⋊C₄	—	269	2	no	—
539	C₂²⋊C₄	—	269	1	no	—
540	C₂²⋊C₄	—	269	1	no	—
541	C₂²⋊C₄	—	269	2	no	—
542	C₂²⋊C₄	—	269	2	no	—
543	C₂²⋊C₄	C₂²×D₂₆₉	1	2	yes	—
544	C₂²⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
545	C₂²⋊C₄	C₂²×D₂₆₉	1	2	yes	—
546	C₂²⋊C₄	C₂²×D₂₆₉	1	2	yes	—
547	C₂²⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
548	C₄²	—	269	2	no	—
549	C₄²	—	269	1	no	—
550	C₄²	—	269	2	no	—
551	C₄²	—	269	2	no	—
552	C₄²	—	269	2	no	—
553	C₄²	C₂²×D₂₆₉	1	2	yes	—
554	C₄²	C₂²×D₂₆₉	1	1	yes	characteristic
555	C₄²	C₂²×D₂₆₉	1	2	yes	—
556	C₂³	—	269	1	no	—
557	C₂³	—	269	1	no	—
558	C₂³	—	269	1	no	—
559	C₂³	—	538	2	no	—
560	C₂³	—	538	2	no	—
561	C₂³	—	1076	1	no	—
562	C₂³	C₂³×D₂₆₉	1	1	yes	characteristic
563	C₂³	C₂³×D₂₆₉	1	1	yes	characteristic
564	Q₈	—	2	2	no	—
565	Q₈	—	538	2	no	—
566	Q₈	—	538	2	no	—
567	Q₈	—	538	2	no	—
568	Q₈	—	1076	2	no	—
569	Q₈	—	1076	2	no	—
570	Q₈	—	1076	2	no	—
571	Q₈	—	1076	2	no	—
572	Q₈	—	1076	1	no	—
573	D₄	—	2	2	no	—
574	D₄	—	538	2	no	—
575	D₄	—	538	2	no	—
576	D₄	—	538	2	no	—
577	D₄	—	1076	1	no	—
578	D₄	—	1076	1	no	—
579	D₄	—	1076	1	no	—
580	C₂×C₄	—	2	4	no	—
581	C₂×C₄	—	2	2	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	269	1	no	—
584	C₂×C₄	—	269	1	no	—
585	C₂×C₄	—	269	2	no	—
586	C₂×C₄	—	269	1	no	—
587	C₂×C₄	—	269	2	no	—
588	C₂×C₄	—	269	2	no	—
589	C₂×C₄	—	269	2	no	—
590	C₂×C₄	—	269	1	no	—
591	C₂×C₄	—	269	1	no	—
592	C₂×C₄	—	538	4	no	—
593	C₂×C₄	—	538	2	no	—
594	C₂×C₄	—	538	2	no	—
595	C₂×C₄	—	538	2	no	—
596	C₂×C₄	—	1076	1	no	—
597	C₂×C₄	—	1076	1	no	—
598	C₂×C₄	—	1076	2	no	—
599	C₂×C₄	—	1076	2	no	—
600	C₂×C₄	—	1076	1	no	—
601	C₂×C₄	—	1076	2	no	—
602	C₂×C₄	—	1076	2	no	—
603	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
604	C₂×C₄	C₂³×D₂₆₉	1	2	yes	—
605	C₂×C₄	C₂³×D₂₆₉	1	2	yes	—
606	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
607	C₂×C₄	C₂³×D₂₆₉	1	2	yes	—
608	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
609	C₂×C₄	C₂³×D₂₆₉	1	2	yes	—
610	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
611	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
612	C₂²	—	2	1	no	—
613	C₂²	—	2	1	no	—
614	C₂²	—	2	1	no	—
615	C₂²	—	2	1	no	—
616	C₂²	—	2	1	no	—
617	C₂²	—	269	2	no	—
618	C₂²	—	538	1	no	—
619	C₂²	—	538	1	no	—
620	C₂²	—	538	1	no	—
621	C₂²	—	538	1	no	—
622	C₂²	—	538	1	no	—
623	C₂²	—	538	1	no	—
624	C₂²	—	538	1	no	—
625	C₂²	—	538	1	no	—
626	C₂²	—	1076	4	no	—
627	C₂²	#22575500	1	2	yes	—
628	C₂²	C₂⁴×D₂₆₉	1	1	yes	characteristic
629	C₄	—	2	1	no	—
630	C₄	—	2	1	no	—
631	C₄	—	2	2	no	—
632	C₄	—	2	2	no	—
633	C₄	—	2	1	no	—
634	C₄	—	2	2	no	—
635	C₄	—	2	2	no	—
636	C₄	—	2	1	no	—
637	C₄	—	538	1	no	—
638	C₄	—	538	1	no	—
639	C₄	—	538	1	no	—
640	C₄	—	538	2	no	—
641	C₄	—	538	2	no	—
642	C₄	—	538	2	no	—
643	C₄	—	538	2	no	—
644	C₄	—	538	1	no	—
645	C₄	—	538	1	no	—
646	C₄	#22575499	1	2	yes	—
647	C₂	—	2	2	no	—
648	C₂	—	4	1	no	—
649	C₂	—	538	2	no	—
650	C₂	—	1076	1	no	—
651	C₂	—	1076	1	no	—
652	C₂	C₂×#22575499	1	1	yes	characteristic
653	C₂	2₋¹⁺⁴×D₂₆₉	1	1	yes	characteristic
654	C₂	C₂×#22575500	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₂₆₉
commutator, socle, cosocle	C₂²×C₂₆₉	C₂⁵
Fitting	#552×C₂₆₉	C₂
prime radical	#31771114	C₂
hypercenter	#552	D₂₆₉
hypocenter	C₂₆₉	#3538
LCS	G ▷ C₂²×C₂₆₉ ▷ C₂₆₉
UCS	C₁ ◁ C₂² ◁ #552

Complements

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

N	H ≅ G/N	type
1. #31771359	C₂	semidirect
2. #31771357	C₂	semidirect
3. #31771294	C₂	semidirect
4. #31771293	C₂	semidirect
5. #31771290	C₂	semidirect
6. #31771279	C₂	semidirect
7. #31771278	C₂	semidirect
8. Q₈×D₁₀₇₆	C₂	semidirect
9. D₄×Dic₅₃₈	C₂	semidirect
10. #31771268	C₂	semidirect
11. #31771268	C₂	semidirect
12. #31771235	C₂	semidirect
13. #31771233	C₂	semidirect
14. #31771218	C₂	semidirect
15. #31771213	C₂	semidirect
16. #31771199	C₂	semidirect
17. #31771196	C₂	semidirect
18. #31771181	C₂	semidirect
19. #31771178	C₂	semidirect
21. C₂×#22575433	C₂	semidirect
22. C₂²⋊Q₈×D₂₆₉	C₂	semidirect
23. #552×C₂₆₉	C₂	semidirect
26. C₂²×Dic₅₃₈	C₂²	semidirect
28. C₂×Q₈×D₂₆₉	C₂²	semidirect
30. #22575453	C₂²	semidirect
31. #22575453	C₂²	semidirect
32. #22575453	C₂²	semidirect
33. #22575452	C₂²	semidirect
34. #22575452	C₂²	semidirect
35. #22575452	C₂²	semidirect
36. #22575452	C₂²	semidirect
37. #22575451	C₂²	semidirect
41. #22575448	C₂²	semidirect
42. #22575448	C₂²	semidirect
44. #22575446	C₂²	semidirect
45. #22575445	C₂²	semidirect
46. #22575445	C₂²	semidirect
47. #22575444	C₂²	semidirect
48. #22575444	C₂²	semidirect
49. #22575444	C₂²	semidirect
50. #22575444	C₂²	semidirect
51. #22575443	C₂²	semidirect
52. #22575443	C₂²	semidirect
59. #22575437	C₂²	semidirect
63. #22575435	C₂²	semidirect
72. #22575433	C₂²	semidirect
73. #22575433	C₂²	semidirect
74. #22575433	C₂²	semidirect
76. #22575432	C₂²	semidirect
80. #22575431	C₂²	semidirect
85. #22575430	C₂²	semidirect
86. #22575430	C₂²	semidirect
92. C₄×Dic₅₃₈	C₂²	semidirect
93. #22575418	C₂²	semidirect
94. #22575418	C₂²	semidirect
104. #22575411	C₂²	semidirect
112. #126×C₂₆₉	C₂²	semidirect
113. #125×C₂₆₉	C₂²	semidirect
114. #125×C₂₆₉	C₂²	semidirect
117. C₂²⋊Q₈×C₂₆₉	C₂²	semidirect
118. C₄×Q₈×C₂₆₉	C₂²	semidirect
121. #117×C₂₆₉	C₂²	semidirect
327. C₂₆₉	#3538	semidirect
334. #552	D₂₆₉	semidirect
373. #126	C₂×D₂₆₉	semidirect
382. #125	C₂×D₂₆₉	semidirect
383. #125	C₂×D₂₆₉	semidirect
421. C₂²⋊Q₈	C₂×D₂₆₉	semidirect
429. C₄×Q₈	C₂×D₂₆₉	semidirect
444. #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
#31771359	2
#31771357	2
#31771294	2
#31771293	2
#31771290	2
#31771279	2
#31771278	2
Q₈×D₁₀₇₆	2
D₄×Dic₅₃₈	2
#31771268	2
#31771235	2
#31771233	2
#31771218	2
#31771213	2
#31771199	2
#31771196	2
#31771181	2
#31771178	2
#31771114	2
C₂×#22575433	2
C₂²⋊Q₈×D₂₆₉	2
#552×C₂₆₉	2
#3538	269