Subgroups — #46824305

Order 34432.

1140 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31771232	C₂	1	1	yes	maximal, characteristic, complemented
2	#31771227	C₂	1	1	yes	maximal, characteristic, complemented
3	#31771225	C₂	1	2	yes	maximal, complemented
4	#31771210	C₂	1	1	yes	maximal, characteristic, complemented
5	#31771207	C₂	1	2	yes	maximal, complemented
6	#31771206	C₂	1	1	yes	maximal, characteristic, complemented
7	#31771194	C₂	1	2	yes	maximal, complemented
8	#31771189	C₂	1	2	yes	maximal, complemented
9	#31771185	C₂	1	1	yes	maximal, characteristic, complemented
10	#31771173	C₂	1	1	yes	maximal, characteristic, complemented
11	#31771171	C₂	1	1	yes	maximal, characteristic, complemented
12	#31771156	C₂	1	1	yes	maximal, characteristic, complemented
13	#31771154	C₂	1	2	yes	maximal, complemented
14	#31771150	C₂	1	1	yes	maximal, characteristic, complemented
15	#31771141	C₂	1	1	yes	maximal, characteristic, complemented
16	#31771138	C₂	1	2	yes	maximal, complemented
17	#31771134	C₂	1	1	yes	maximal, characteristic, complemented
18	#31771118	C₂	1	2	yes	maximal, complemented
19	#31771113	C₂	1	2	yes	maximal, complemented
20	C₄×#16864403	C₂	1	1	yes	maximal, characteristic, complemented
21	#31771073	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×D₄×D₂₆₉	C₂	1	1	yes	maximal, characteristic, complemented
23	#542×C₂₆₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#16864403	C₂²	1	1	yes	characteristic
25	C₂×#16864403	C₂²	1	2	yes	complemented
26	C₂×#16864402	C₂²	1	1	yes	characteristic
27	C₂×#16864401	C₂²	1	2	yes	complemented
28	C₂×D₄×D₂₆₉	C₂²	1	1	yes	characteristic
29	C₂²×C₄×D₂₆₉	C₂²	1	2	yes	—
30	#22575452	C₂²	1	1	yes	characteristic, complemented
31	#22575451	C₂²	1	2	yes	complemented
32	#22575450	C₂²	1	1	yes	characteristic
33	#22575449	C₂²	1	1	yes	characteristic
34	#22575449	C₂²	1	2	yes	—
35	#22575448	C₂²	1	2	yes	complemented
36	#22575447	C₂²	1	2	yes	complemented
37	#22575446	C₂²	1	2	yes	complemented
38	#22575445	C₂²	1	1	yes	characteristic, complemented
39	#22575444	C₂²	1	1	yes	characteristic, complemented
40	#22575443	C₂²	1	2	yes	complemented
41	#22575442	C₂²	1	1	yes	characteristic
42	#22575442	C₂²	1	2	yes	complemented
43	#22575441	C₂²	1	2	yes	complemented
44	#22575439	C₂²	1	2	yes	—
45	#22575439	C₂²	1	2	yes	complemented
46	#22575438	C₂²	1	2	yes	complemented
47	#22575438	C₂²	1	2	yes	complemented
48	#22575438	C₂²	1	2	yes	complemented
49	#22575437	C₂²	1	2	yes	complemented
50	#22575436	C₂²	1	2	yes	complemented
51	#22575435	C₂²	1	2	yes	complemented
52	#22575435	C₂²	1	2	yes	complemented
53	#22575431	C₂²	1	2	yes	—
54	#22575431	C₂²	1	2	yes	complemented
55	#22575431	C₂²	1	2	yes	complemented
56	#22575429	C₂²	1	2	yes	—
57	#22575429	C₂²	1	1	yes	characteristic, complemented
58	#22575428	C₂²	1	1	yes	characteristic
59	#22575428	C₂²	1	2	yes	—
60	#22575428	C₂²	1	1	yes	characteristic, complemented
61	#22575428	C₂²	1	2	yes	complemented
62	#22575427	C₂²	1	1	yes	characteristic
63	#22575427	C₂²	1	1	yes	characteristic, complemented
64	#22575427	C₂²	1	2	yes	complemented
65	#22575426	C₂²	1	2	yes	—
66	#22575426	C₂²	1	2	yes	—
67	#22575426	C₂²	1	2	yes	—
68	#22575426	C₂²	1	2	yes	complemented
69	#22575426	C₂²	1	2	yes	complemented
70	#22575426	C₂²	1	2	yes	complemented
71	#22575426	C₂²	1	2	yes	complemented
72	#22575425	C₂²	1	2	yes	complemented
73	#22575424	C₂²	1	1	yes	characteristic
74	#22575423	C₂²	1	2	yes	—
75	#22575423	C₂²	1	2	yes	—
76	#22575423	C₂²	1	2	yes	—
77	#22575421	C₂²	1	2	yes	—
78	Q₈×Dic₂₆₉	C₂²	1	1	yes	characteristic, complemented
79	#22575418	C₂²	1	1	yes	characteristic, complemented
80	#22575418	C₂²	1	1	yes	characteristic, complemented
81	C₄×D₁₀₇₆	C₂²	1	2	yes	—
82	C₄×D₁₀₇₆	C₂²	1	1	yes	characteristic
83	C₄×D₁₀₇₆	C₂²	1	1	yes	characteristic, complemented
84	D₄×Dic₂₆₉	C₂²	1	1	yes	characteristic
85	#22575415	C₂²	1	1	yes	characteristic
86	#22575415	C₂²	1	1	yes	characteristic
87	#22575415	C₂²	1	1	yes	characteristic
88	#22575415	C₂²	1	2	yes	—
89	#22575415	C₂²	1	2	yes	complemented
90	#22575415	C₂²	1	1	yes	characteristic, complemented
91	C₄×C₂²⋊D₂₆₉	C₂²	1	2	yes	—
92	#22575413	C₂²	1	2	yes	—
93	#22575413	C₂²	1	1	yes	characteristic
94	#22575413	C₂²	1	1	yes	characteristic
95	#22575413	C₂²	1	2	yes	complemented
96	#22575413	C₂²	1	2	yes	complemented
97	#22575413	C₂²	1	1	yes	characteristic, complemented
98	#22575413	C₂²	1	2	yes	complemented
99	#22575413	C₂²	1	1	yes	characteristic, complemented
100	#22575411	C₂²	1	1	yes	characteristic
101	#22575411	C₂²	1	2	yes	complemented
102	#22575411	C₂²	1	2	yes	complemented
103	#22575410	C₂²	1	1	yes	characteristic
104	#22575410	C₂²	1	1	yes	characteristic, complemented
105	#22575409	C₂²	1	2	yes	complemented
106	C₄⋊C₄×D₂₆₉	C₂²	1	1	yes	characteristic
107	C₂²⋊C₄×D₂₆₉	C₂²	1	2	yes	—
108	C₂×C₄×Dic₂₆₉	C₂²	1	1	yes	characteristic, complemented
109	C₄²×D₂₆₉	C₂²	1	1	yes	characteristic
110	C₄²×D₂₆₉	C₂²	1	2	yes	complemented
111	C₄²×D₂₆₉	C₂²	1	1	yes	characteristic, complemented
112	C₄⋊Q₈×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
113	#126×C₂₆₉	C₂²	1	2	yes	complemented
114	#124×C₂₆₉	C₂²	1	1	yes	characteristic
115	#124×C₂₆₉	C₂²	1	2	yes	complemented
116	#123×C₂₆₉	C₂²	1	2	yes	complemented
117	C₂²⋊Q₈×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
118	C₂²⋊Q₈×C₂₆₉	C₂²	1	2	yes	complemented
119	#121×C₂₆₉	C₂²	1	1	yes	characteristic
120	C₄×Q₈×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
121	C₄×D₄×C₂₆₉	C₂²	1	1	yes	characteristic
122	#117×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₂₆₉	C₂³	1	2	yes	—
124	#16864403	—	2	4	no	—
125	#16864403	—	4	4	no	—
126	#16864402	—	2	4	no	—
127	#16864401	—	4	4	no	—
128	C₂×Dic₅₃₈	C₂³	1	1	yes	characteristic
129	C₂×Dic₅₃₈	C₂³	1	2	yes	—
130	C₂×D₁₀₇₆	C₂³	1	1	yes	characteristic
131	C₂×D₁₀₇₆	C₂³	1	2	yes	—
132	C₂×D₁₀₇₆	C₂³	1	1	yes	characteristic
133	C₂×D₁₀₇₆	C₂³	1	1	yes	characteristic
134	C₂×D₁₀₇₆	C₂³	1	2	yes	—
135	C₂×D₁₀₇₆	C₂³	1	2	yes	—
136	C₂×D₁₀₇₆	C₂³	1	2	yes	—
137	C₂×D₁₀₇₆	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₂₆₉	C₂³	1	1	yes	characteristic
139	C₂×C₂²⋊D₂₆₉	C₂³	1	2	yes	—
140	C₂×C₂²⋊D₂₆₉	C₂³	1	1	yes	characteristic
141	C₂×C₂²⋊D₂₆₉	C₂³	1	2	yes	—
142	C₂×C₂²⋊D₂₆₉	C₂³	1	2	yes	—
143	C₂×C₂²⋊D₂₆₉	C₂³	1	2	yes	—
144	C₂×C₂²⋊D₂₆₉	C₂³	1	2	yes	—
145	C₂×C₂²⋊D₂₆₉	C₂³	1	2	yes	—
146	D₄×D₂₆₉	—	2	4	no	—
147	C₂²×Dic₂₆₉	C₂³	1	1	yes	characteristic
148	C₂²×Dic₂₆₉	C₂³	1	2	yes	—
149	C₂²×Dic₂₆₉	C₂³	1	1	yes	characteristic
150	C₂×C₄×D₂₆₉	—	4	4	no	—
151	C₂×C₄×D₂₆₉	C₂³	1	1	yes	characteristic
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	C₂×C₄×D₂₆₉	C₂³	1	2	yes	—
156	C₂×C₄×D₂₆₉	C₂³	1	2	yes	—
157	C₂×C₄×D₂₆₉	C₂³	1	1	yes	characteristic
158	C₂×C₄×D₂₆₉	C₂³	1	1	yes	characteristic
159	C₂×C₄×D₂₆₉	C₂³	1	2	yes	—
160	C₂×C₄×D₂₆₉	C₂³	1	2	yes	—
161	C₂×C₄×D₂₆₉	C₂³	1	2	yes	—
162	C₂×C₄×D₂₆₉	C₂³	1	1	yes	characteristic
163	C₄⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
164	C₄⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
165	C₄⋊Dic₂₆₉	C₂³	1	2	yes	—
166	C₄⋊Dic₂₆₉	C₂³	1	2	yes	—
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	1	yes	characteristic
173	#16864381	C₂³	1	1	yes	characteristic
174	#16864381	C₂³	1	2	yes	—
175	#16864381	C₂³	1	2	yes	—
176	#16864381	C₂³	1	2	yes	—
177	C₂²⋊Dic₂₆₉	C₂³	1	2	yes	—
178	C₂²⋊Dic₂₆₉	C₂³	1	2	yes	—
179	#16864379	C₂³	1	2	yes	—
180	#16864379	C₂³	1	2	yes	—
181	#16864379	C₂³	1	1	yes	characteristic
182	#16864379	C₂³	1	1	yes	characteristic
183	#16864379	C₂³	1	1	yes	characteristic
184	#16864379	C₂³	1	1	yes	characteristic
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	2	yes	—
192	#16864379	C₂³	1	2	yes	—
193	#16864379	C₂³	1	2	yes	—
194	#16864379	C₂³	1	2	yes	—
195	C₄×Dic₂₆₉	C₂³	1	1	yes	characteristic
196	C₄×Dic₂₆₉	C₂³	1	1	yes	characteristic
197	C₄×Dic₂₆₉	C₂³	1	1	yes	characteristic
198	C₄×Dic₂₆₉	C₂³	1	1	yes	characteristic
199	C₄×Dic₂₆₉	C₂³	1	2	yes	—
200	C₄×Dic₂₆₉	C₂³	1	2	yes	—
201	C₄×Dic₂₆₉	C₂³	1	1	yes	characteristic
202	C₄×Dic₂₆₉	C₂³	1	1	yes	characteristic
203	C₄×Dic₂₆₉	C₂³	1	1	yes	characteristic
204	C₄×Dic₂₆₉	C₂³	1	1	yes	characteristic
205	C₂×Q₈×C₂₆₉	C₂³	1	1	yes	characteristic
206	C₂×Q₈×C₂₆₉	C₂³	1	2	yes	—
207	C₂×D₄×C₂₆₉	C₂³	1	1	yes	characteristic
208	C₂×D₄×C₂₆₉	C₂³	1	2	yes	—
209	C₂²×C₄×C₂₆₉	C₂³	1	1	yes	characteristic
210	C₂²×C₄×C₂₆₉	C₂³	1	2	yes	—
211	C₄⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
212	C₄⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
213	C₄⋊C₄×C₂₆₉	C₂³	1	2	yes	—
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	C₂²⋊C₄×C₂₆₉	C₂³	1	2	yes	—
219	C₂²⋊C₄×C₂₆₉	C₂³	1	2	yes	—
220	C₂²⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
221	C₂²⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
222	C₂²⋊C₄×C₂₆₉	C₂³	1	2	yes	—
223	C₂²⋊C₄×C₂₆₉	C₂³	1	2	yes	—
224	C₂²⋊C₄×C₂₆₉	C₂³	1	2	yes	—
225	C₄²×C₂₆₉	C₂³	1	1	yes	characteristic
226	C₄²×C₂₆₉	C₂³	1	1	yes	characteristic
227	C₄²×C₂₆₉	C₂³	1	2	yes	—
228	C₂²×D₂₆₉	—	2	4	no	—
229	C₂²×D₂₆₉	—	4	2	no	—
230	C₂²×D₂₆₉	—	4	2	no	—
231	C₂²×D₂₆₉	C₂⁴	1	2	yes	—
232	C₂²×D₂₆₉	C₂⁴	1	1	yes	characteristic
233	C₂²×D₂₆₉	C₂⁴	1	2	yes	—
234	C₂²×D₂₆₉	C₂⁴	1	1	yes	characteristic
235	Dic₅₃₈	—	2	2	no	—
236	Dic₅₃₈	—	4	2	no	—
237	D₁₀₇₆	—	2	2	no	—
238	D₁₀₇₆	—	2	4	no	—
239	D₁₀₇₆	—	2	2	no	—
240	D₁₀₇₆	—	2	2	no	—
241	D₁₀₇₆	—	4	2	no	—
242	D₁₀₇₆	—	4	2	no	—
243	D₁₀₇₆	—	4	2	no	—
244	D₁₀₇₆	—	4	2	no	—
245	C₂²⋊D₂₆₉	—	2	2	no	—
246	C₂²⋊D₂₆₉	—	2	4	no	—
247	C₂²⋊D₂₆₉	—	2	2	no	—
248	C₂²⋊D₂₆₉	—	4	2	no	—
249	C₂²⋊D₂₆₉	—	4	2	no	—
250	C₂²⋊D₂₆₉	—	4	2	no	—
251	C₂²⋊D₂₆₉	—	4	2	no	—
252	C₂²⋊D₂₆₉	—	4	2	no	—
253	C₂×Dic₂₆₉	—	2	4	no	—
254	C₂×Dic₂₆₉	—	2	2	no	—
255	C₂×Dic₂₆₉	—	4	1	no	—
256	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
257	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
258	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
259	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
260	C₂×Dic₂₆₉	C₂⁴	1	2	yes	—
261	C₂×Dic₂₆₉	C₂⁴	1	2	yes	—
262	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
263	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
264	C₄×D₂₆₉	—	2	2	no	—
265	C₄×D₂₆₉	—	2	4	no	—
266	C₄×D₂₆₉	—	2	2	no	—
267	C₄×D₂₆₉	—	2	4	no	—
268	C₄×D₂₆₉	—	2	4	no	—
269	C₄×D₂₆₉	—	2	2	no	—
270	C₄×D₂₆₉	—	4	2	no	—
271	C₄×D₂₆₉	—	4	2	no	—
272	C₄×D₂₆₉	—	4	1	no	—
273	C₄×D₂₆₉	—	4	1	no	—
274	C₄×D₂₆₉	—	4	2	no	—
275	C₄×D₂₆₉	#41	1	4	yes	complemented
276	C₂³×C₂₆₉	C₂⁴	1	2	yes	—
277	C₂³×C₂₆₉	C₂⁴	1	1	yes	characteristic
278	Q₈×C₂₆₉	—	2	2	no	—
279	Q₈×C₂₆₉	—	4	2	no	—
280	D₄×C₂₆₉	—	2	2	no	—
281	D₄×C₂₆₉	—	4	2	no	—
282	C₂×C₄×C₂₆₉	—	2	2	no	—
283	C₂×C₄×C₂₆₉	—	4	2	no	—
284	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
285	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
286	C₂×C₄×C₂₆₉	C₂⁴	1	2	yes	—
287	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
288	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
289	C₂×C₄×C₂₆₉	C₂⁴	1	2	yes	—
290	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
291	C₂×C₄×C₂₆₉	C₂⁴	1	2	yes	—
292	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
293	C₂²×C₂₆₉	—	2	1	no	—
294	C₂²×C₂₆₉	—	2	2	no	—
295	C₂²×C₂₆₉	—	2	2	no	—
296	C₂²×C₂₆₉	—	2	1	no	—
297	C₂²×C₂₆₉	—	2	1	no	—
298	C₂²×C₂₆₉	—	2	2	no	—
299	C₂²×C₂₆₉	C₂⁵	1	1	yes	characteristic
300	C₂×D₂₆₉	—	2	1	no	—
301	C₂×D₂₆₉	—	2	1	no	—
302	C₂×D₂₆₉	—	2	1	no	—
303	C₂×D₂₆₉	—	2	2	no	—
304	C₂×D₂₆₉	—	2	2	no	—
305	C₂×D₂₆₉	—	2	2	no	—
306	C₂×D₂₆₉	—	2	2	no	—
307	C₂×D₂₆₉	—	2	1	no	—
308	C₂×D₂₆₉	—	2	1	no	—
309	C₂×D₂₆₉	—	2	2	no	—
310	C₂×D₂₆₉	—	2	2	no	—
311	C₂×D₂₆₉	—	4	8	no	—
312	C₂×D₂₆₉	C₂×#41	1	2	yes	—
313	C₄×C₂₆₉	—	2	1	no	—
314	C₄×C₂₆₉	—	2	2	no	—
315	C₄×C₂₆₉	—	2	1	no	—
316	C₄×C₂₆₉	—	2	2	no	—
317	C₄×C₂₆₉	—	2	2	no	—
318	C₄×C₂₆₉	—	2	1	no	—
319	C₄×C₂₆₉	—	2	1	no	—
320	C₄×C₂₆₉	—	2	1	no	—
321	C₄×C₂₆₉	C₂×#41	1	2	yes	—
322	Dic₂₆₉	—	2	1	no	—
323	Dic₂₆₉	—	2	2	no	—
324	Dic₂₆₉	—	2	1	no	—
325	Dic₂₆₉	—	2	1	no	—
326	Dic₂₆₉	—	2	2	no	—
327	Dic₂₆₉	—	2	1	no	—
328	Dic₂₆₉	C₂×#41	1	2	yes	—
329	Dic₂₆₉	H(5,𝔽₂)	1	2	yes	—
330	C₂×C₂₆₉	—	4	2	no	—
331	C₂×C₂₆₉	—	4	1	no	—
332	C₂×C₂₆₉	C₂²×#41	1	1	yes	characteristic
333	C₂×C₂₆₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
334	C₂×C₂₆₉	#585	1	1	yes	characteristic
335	D₂₆₉	—	2	2	no	—
336	D₂₆₉	—	4	1	no	—
337	D₂₆₉	—	4	2	no	—
338	D₂₆₉	—	4	2	no	—
339	C₂₆₉	#3460	1	1	yes	characteristic, complemented, Sylow
340	#3460	—	269	1	no	maximal, Sylow
341	#544	—	269	1	no	—
342	#542	—	269	2	no	—
343	#542	—	269	1	no	—
344	#542	D₂₆₉	1	1	yes	characteristic, complemented
345	#540	—	269	2	no	—
346	#540	—	269	1	no	—
347	#540	—	269	1	no	—
348	#538	—	269	2	no	—
349	#538	—	269	2	no	—
350	#537	—	269	1	no	—
351	#535	—	269	1	no	—
352	#535	—	269	1	no	—
353	#532	—	269	1	no	—
354	#532	—	269	2	no	—
355	#532	—	269	1	no	—
356	#529	—	269	2	no	—
357	#529	—	269	1	no	—
358	#529	—	269	1	no	—
359	#525	—	269	2	no	—
360	#525	—	269	2	no	—
361	C₄×#41	—	269	1	no	—
362	C₄×#41	—	269	1	no	—
363	C₂×C₄×D₄	—	269	1	no	—
364	C₂×#41	—	269	1	no	—
365	C₂×#41	—	269	2	no	—
366	C₂×#41	—	269	2	no	—
367	C₂×#41	—	269	1	no	—
368	C₂²×D₄	—	269	1	no	—
369	C₂³×C₄	—	269	2	no	—
370	C₄⋊Q₈	—	269	2	no	—
371	C₄⋊Q₈	—	269	1	no	—
372	C₄⋊Q₈	C₂×D₂₆₉	1	1	yes	characteristic, complemented
373	#127	—	269	2	no	—
374	#127	—	269	1	no	—
375	#127	—	269	1	no	—
376	#126	—	269	2	no	—
377	#126	—	269	2	no	—
378	#126	—	269	2	no	—
379	#126	C₂×D₂₆₉	1	2	yes	complemented
380	#125	—	269	2	no	—
381	#125	—	269	1	no	—
382	#125	—	269	1	no	—
383	#124	—	269	1	no	—
384	#124	—	269	2	no	—
385	#124	—	269	2	no	—
386	#124	—	269	2	no	—
387	#124	—	269	2	no	—
388	#124	C₂×D₂₆₉	1	1	yes	characteristic
389	#124	C₂×D₂₆₉	1	2	yes	complemented
390	#123	—	269	2	no	—
391	#123	—	269	2	no	—
392	#123	—	269	2	no	—
393	#123	—	269	2	no	—
394	#123	—	269	2	no	—
395	#123	—	269	2	no	—
396	#123	—	269	2	no	—
397	#123	C₂×D₂₆₉	1	2	yes	complemented
398	C₂²⋊Q₈	—	269	2	no	—
399	C₂²⋊Q₈	—	269	1	no	—
400	C₂²⋊Q₈	—	269	2	no	—
401	C₂²⋊Q₈	—	269	2	no	—
402	C₂²⋊Q₈	—	269	2	no	—
403	C₂²⋊Q₈	C₂×D₂₆₉	1	2	yes	complemented
404	C₂²⋊Q₈	C₂×D₂₆₉	1	1	yes	characteristic, complemented
405	#121	—	269	1	no	—
406	#121	—	269	2	no	—
407	#121	—	269	2	no	—
408	#121	—	269	1	no	—
409	#121	—	269	1	no	—
410	#121	—	269	2	no	—
411	#121	—	269	1	no	—
412	#121	—	269	1	no	—
413	#121	—	269	2	no	—
414	#121	—	269	2	no	—
415	#121	—	269	2	no	—
416	#121	—	269	2	no	—
417	#121	—	269	2	no	—
418	#121	—	269	2	no	—
419	#121	—	269	2	no	—
420	#121	—	269	2	no	—
421	#121	C₂×D₂₆₉	1	1	yes	characteristic
422	#120	—	269	2	no	—
423	#120	—	269	2	no	—
424	#120	—	269	2	no	—
425	#120	—	269	2	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	1	no	—
431	C₄×D₄	—	269	2	no	—
432	C₄×D₄	—	269	1	no	—
433	C₄×D₄	—	269	2	no	—
434	C₄×D₄	—	269	1	no	—
435	C₄×D₄	—	269	1	no	—
436	C₄×D₄	—	269	1	no	—
437	C₄×D₄	—	269	2	no	—
438	C₄×D₄	—	269	2	no	—
439	C₄×D₄	—	269	1	no	—
440	C₄×D₄	—	269	1	no	—
441	C₄×D₄	—	269	1	no	—
442	C₄×D₄	—	269	1	no	—
443	C₄×D₄	—	269	2	no	—
444	C₄×D₄	—	269	2	no	—
445	C₄×D₄	—	269	2	no	—
446	C₄×D₄	—	269	1	no	—
447	C₄×D₄	—	269	2	no	—
448	C₄×D₄	—	269	1	no	—
449	C₄×D₄	C₂×D₂₆₉	1	1	yes	characteristic
450	#117	—	269	1	no	—
451	#117	—	269	2	no	—
452	#117	—	269	2	no	—
453	#117	—	269	2	no	—
454	#117	—	269	1	no	—
455	#117	—	269	1	no	—
456	#117	C₂×D₂₆₉	1	1	yes	characteristic, complemented
457	C₂×C₄⋊C₄	—	269	1	no	—
458	C₂×C₂²⋊C₄	—	269	2	no	—
459	C₂×C₄²	—	269	1	no	—
460	C₂×C₄²	—	269	1	no	—
461	C₂×C₄²	—	269	2	no	—
462	C₂×C₄²	—	269	1	no	—
463	C₂⁴	—	269	2	no	—
464	#41	—	538	4	no	—
465	#41	—	538	4	no	—
466	#41	—	1076	4	no	—
467	#41	—	1076	4	no	—
468	C₂×Q₈	—	269	1	no	—
469	C₂×Q₈	—	269	2	no	—
470	C₂×Q₈	C₂²×D₂₆₉	1	1	yes	characteristic
471	C₂×Q₈	C₂²×D₂₆₉	1	2	yes	—
472	C₂×D₄	—	269	1	no	—
473	C₂×D₄	—	269	2	no	—
474	C₂×D₄	—	269	1	no	—
475	C₂×D₄	—	269	2	no	—
476	C₂×D₄	—	269	2	no	—
477	C₂×D₄	—	269	2	no	—
478	C₂×D₄	—	269	2	no	—
479	C₂×D₄	—	269	2	no	—
480	C₂×D₄	—	269	1	no	—
481	C₂×D₄	—	269	2	no	—
482	C₂×D₄	—	269	1	no	—
483	C₂×D₄	—	269	1	no	—
484	C₂×D₄	—	269	2	no	—
485	C₂×D₄	—	269	2	no	—
486	C₂×D₄	—	269	2	no	—
487	C₂×D₄	—	269	2	no	—
488	C₂×D₄	—	538	4	no	—
489	C₂×D₄	C₂²×D₂₆₉	1	1	yes	characteristic
490	C₂×D₄	C₂²×D₂₆₉	1	2	yes	—
491	C₂²×C₄	—	269	1	no	—
492	C₂²×C₄	—	269	1	no	—
493	C₂²×C₄	—	269	2	no	—
494	C₂²×C₄	—	269	1	no	—
495	C₂²×C₄	—	269	2	no	—
496	C₂²×C₄	—	269	1	no	—
497	C₂²×C₄	—	269	1	no	—
498	C₂²×C₄	—	269	2	no	—
499	C₂²×C₄	—	269	1	no	—
500	C₂²×C₄	—	269	2	no	—
501	C₂²×C₄	—	269	1	no	—
502	C₂²×C₄	—	269	1	no	—
503	C₂²×C₄	—	269	2	no	—
504	C₂²×C₄	—	269	2	no	—
505	C₂²×C₄	—	269	2	no	—
506	C₂²×C₄	—	1076	4	no	—
507	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
508	C₂²×C₄	C₂²×D₂₆₉	1	2	yes	—
509	C₄⋊C₄	—	269	2	no	—
510	C₄⋊C₄	—	269	1	no	—
511	C₄⋊C₄	—	269	1	no	—
512	C₄⋊C₄	—	269	1	no	—
513	C₄⋊C₄	—	269	1	no	—
514	C₄⋊C₄	—	269	1	no	—
515	C₄⋊C₄	—	269	1	no	—
516	C₄⋊C₄	—	269	2	no	—
517	C₄⋊C₄	—	269	2	no	—
518	C₄⋊C₄	—	269	2	no	—
519	C₄⋊C₄	—	269	2	no	—
520	C₄⋊C₄	—	269	2	no	—
521	C₄⋊C₄	—	269	2	no	—
522	C₄⋊C₄	—	269	2	no	—
523	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
524	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
525	C₄⋊C₄	C₂²×D₂₆₉	1	2	yes	—
526	C₄⋊C₄	C₂²×D₂₆₉	1	2	yes	—
527	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
528	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
529	C₄⋊C₄	C₂²×D₂₆₉	1	2	yes	—
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	2	no	—
535	C₂²⋊C₄	—	269	1	no	—
536	C₂²⋊C₄	—	269	1	no	—
537	C₂²⋊C₄	—	269	2	no	—
538	C₂²⋊C₄	—	269	1	no	—
539	C₂²⋊C₄	—	269	2	no	—
540	C₂²⋊C₄	—	269	1	no	—
541	C₂²⋊C₄	—	269	2	no	—
542	C₂²⋊C₄	—	269	2	no	—
543	C₂²⋊C₄	—	269	2	no	—
544	C₂²⋊C₄	—	269	2	no	—
545	C₂²⋊C₄	—	269	2	no	—
546	C₂²⋊C₄	—	269	2	no	—
547	C₂²⋊C₄	—	269	2	no	—
548	C₂²⋊C₄	C₂²×D₂₆₉	1	2	yes	—
549	C₂²⋊C₄	C₂²×D₂₆₉	1	2	yes	—
550	C₂²⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
551	C₂²⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
552	C₂²⋊C₄	C₂²×D₂₆₉	1	2	yes	—
553	C₂²⋊C₄	C₂²×D₂₆₉	1	2	yes	—
554	C₂²⋊C₄	C₂²×D₂₆₉	1	2	yes	—
555	C₄²	—	269	1	no	—
556	C₄²	—	269	1	no	—
557	C₄²	—	269	1	no	—
558	C₄²	—	269	1	no	—
559	C₄²	—	269	2	no	—
560	C₄²	—	269	1	no	—
561	C₄²	—	269	2	no	—
562	C₄²	—	269	1	no	—
563	C₄²	—	269	1	no	—
564	C₄²	—	269	1	no	—
565	C₄²	C₂²×D₂₆₉	1	1	yes	characteristic
566	C₄²	C₂²×D₂₆₉	1	1	yes	characteristic
567	C₄²	C₂²×D₂₆₉	1	2	yes	—
568	C₂³	—	269	1	no	—
569	C₂³	—	269	2	no	—
570	C₂³	—	269	1	no	—
571	C₂³	—	269	2	no	—
572	C₂³	—	538	4	no	—
573	C₂³	—	1076	2	no	—
574	C₂³	—	1076	2	no	—
575	C₂³	C₂³×D₂₆₉	1	2	yes	—
576	C₂³	C₂³×D₂₆₉	1	1	yes	characteristic
577	Q₈	—	2	2	no	—
578	Q₈	—	4	2	no	—
579	Q₈	—	538	2	no	—
580	Q₈	—	1076	2	no	—
581	D₄	—	2	2	no	—
582	D₄	—	4	2	no	—
583	D₄	—	538	2	no	—
584	D₄	—	538	4	no	—
585	D₄	—	538	4	no	—
586	D₄	—	538	2	no	—
587	D₄	—	538	2	no	—
588	D₄	—	538	2	no	—
589	D₄	—	538	2	no	—
590	D₄	—	1076	2	no	—
591	D₄	—	1076	2	no	—
592	D₄	—	1076	2	no	—
593	D₄	—	1076	2	no	—
594	D₄	—	1076	2	no	—
595	D₄	—	1076	2	no	—
596	D₄	—	1076	2	no	—
597	D₄	—	1076	2	no	—
598	D₄	—	1076	2	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	4	2	no	—
601	C₂×C₄	—	269	1	no	—
602	C₂×C₄	—	269	1	no	—
603	C₂×C₄	—	269	4	no	—
604	C₂×C₄	—	269	1	no	—
605	C₂×C₄	—	269	1	no	—
606	C₂×C₄	—	269	2	no	—
607	C₂×C₄	—	269	1	no	—
608	C₂×C₄	—	269	1	no	—
609	C₂×C₄	—	269	2	no	—
610	C₂×C₄	—	538	2	no	—
611	C₂×C₄	—	538	4	no	—
612	C₂×C₄	—	538	4	no	—
613	C₂×C₄	—	538	4	no	—
614	C₂×C₄	—	538	2	no	—
615	C₂×C₄	—	538	4	no	—
616	C₂×C₄	—	538	2	no	—
617	C₂×C₄	—	538	2	no	—
618	C₂×C₄	—	1076	2	no	—
619	C₂×C₄	—	1076	2	no	—
620	C₂×C₄	—	1076	1	no	—
621	C₂×C₄	—	1076	2	no	—
622	C₂×C₄	—	1076	1	no	—
623	C₂×C₄	—	1076	1	no	—
624	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
625	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
626	C₂×C₄	C₂³×D₂₆₉	1	2	yes	—
627	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
628	C₂×C₄	C₂³×D₂₆₉	1	2	yes	—
629	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
630	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
631	C₂×C₄	C₂³×D₂₆₉	1	2	yes	—
632	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
633	C₂²	—	2	1	no	—
634	C₂²	—	2	2	no	—
635	C₂²	—	2	2	no	—
636	C₂²	—	2	1	no	—
637	C₂²	—	2	1	no	—
638	C₂²	—	2	2	no	—
639	C₂²	—	269	2	no	—
640	C₂²	—	538	1	no	—
641	C₂²	—	538	1	no	—
642	C₂²	—	538	2	no	—
643	C₂²	—	538	1	no	—
644	C₂²	—	538	2	no	—
645	C₂²	—	538	2	no	—
646	C₂²	—	538	1	no	—
647	C₂²	—	538	2	no	—
648	C₂²	—	538	2	no	—
649	C₂²	—	538	1	no	—
650	C₂²	—	538	2	no	—
651	C₂²	—	1076	8	no	—
652	C₂²	C₂⁴×D₂₆₉	1	1	yes	characteristic
653	C₄	—	2	1	no	—
654	C₄	—	2	2	no	—
655	C₄	—	2	1	no	—
656	C₄	—	2	2	no	—
657	C₄	—	2	2	no	—
658	C₄	—	2	1	no	—
659	C₄	—	2	1	no	—
660	C₄	—	2	1	no	—
661	C₄	—	269	2	no	—
662	C₄	—	269	2	no	—
663	C₄	—	538	1	no	—
664	C₄	—	538	2	no	—
665	C₄	—	538	1	no	—
666	C₄	—	538	1	no	—
667	C₄	—	538	2	no	—
668	C₄	—	538	1	no	—
669	C₄	#41×D₂₆₉	1	2	yes	—
670	C₂	—	4	2	no	—
671	C₂	—	4	1	no	—
672	C₂	—	538	2	no	—
673	C₂	—	1076	2	no	—
674	C₂	—	1076	2	no	—
675	C₂	—	1076	1	no	—
676	C₂	C₂×#41×D₂₆₉	1	1	yes	characteristic
677	C₂	H(5,𝔽₂)×D₂₆₉	1	1	yes	characteristic
678	C₂	#31771442	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₂₆₉
commutator, socle, cosocle	C₂²×C₂₆₉	C₂⁵
Fitting	#542×C₂₆₉	C₂
hypercenter	#542	D₂₆₉
hypocenter	C₂₆₉	#3460
LCS	G ▷ C₂²×C₂₆₉ ▷ C₂₆₉
UCS	C₁ ◁ C₂² ◁ #542

Complements

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

N	H ≅ G/N	type
1. #31771232	C₂	semidirect
2. #31771227	C₂	semidirect
3. #31771225	C₂	semidirect
4. #31771210	C₂	semidirect
5. #31771207	C₂	semidirect
6. #31771206	C₂	semidirect
7. #31771194	C₂	semidirect
8. #31771189	C₂	semidirect
9. #31771185	C₂	semidirect
10. #31771173	C₂	semidirect
11. #31771171	C₂	semidirect
12. #31771156	C₂	semidirect
13. #31771154	C₂	semidirect
14. #31771150	C₂	semidirect
15. #31771141	C₂	semidirect
16. #31771138	C₂	semidirect
17. #31771134	C₂	semidirect
18. #31771118	C₂	semidirect
19. #31771113	C₂	semidirect
20. C₄×#16864403	C₂	semidirect
21. #31771073	C₂	semidirect
22. C₄×D₄×D₂₆₉	C₂	semidirect
23. #542×C₂₆₉	C₂	semidirect
25. C₂×#16864403	C₂²	semidirect
27. C₂×#16864401	C₂²	semidirect
30. #22575452	C₂²	semidirect
31. #22575451	C₂²	semidirect
35. #22575448	C₂²	semidirect
36. #22575447	C₂²	semidirect
37. #22575446	C₂²	semidirect
38. #22575445	C₂²	semidirect
39. #22575444	C₂²	semidirect
40. #22575443	C₂²	semidirect
42. #22575442	C₂²	semidirect
43. #22575441	C₂²	semidirect
45. #22575439	C₂²	semidirect
46. #22575438	C₂²	semidirect
47. #22575438	C₂²	semidirect
48. #22575438	C₂²	semidirect
49. #22575437	C₂²	semidirect
50. #22575436	C₂²	semidirect
51. #22575435	C₂²	semidirect
52. #22575435	C₂²	semidirect
54. #22575431	C₂²	semidirect
55. #22575431	C₂²	semidirect
57. #22575429	C₂²	semidirect
60. #22575428	C₂²	semidirect
61. #22575428	C₂²	semidirect
63. #22575427	C₂²	semidirect
64. #22575427	C₂²	semidirect
68. #22575426	C₂²	semidirect
69. #22575426	C₂²	semidirect
70. #22575426	C₂²	semidirect
71. #22575426	C₂²	semidirect
72. #22575425	C₂²	semidirect
78. Q₈×Dic₂₆₉	C₂²	semidirect
79. #22575418	C₂²	semidirect
80. #22575418	C₂²	semidirect
83. C₄×D₁₀₇₆	C₂²	semidirect
89. #22575415	C₂²	semidirect
90. #22575415	C₂²	semidirect
95. #22575413	C₂²	semidirect
96. #22575413	C₂²	semidirect
97. #22575413	C₂²	semidirect
98. #22575413	C₂²	semidirect
99. #22575413	C₂²	semidirect
101. #22575411	C₂²	semidirect
102. #22575411	C₂²	semidirect
104. #22575410	C₂²	semidirect
105. #22575409	C₂²	semidirect
108. C₂×C₄×Dic₂₆₉	C₂²	semidirect
110. C₄²×D₂₆₉	C₂²	semidirect
111. C₄²×D₂₆₉	C₂²	semidirect
112. C₄⋊Q₈×C₂₆₉	C₂²	semidirect
113. #126×C₂₆₉	C₂²	semidirect
115. #124×C₂₆₉	C₂²	semidirect
116. #123×C₂₆₉	C₂²	semidirect
117. C₂²⋊Q₈×C₂₆₉	C₂²	semidirect
118. C₂²⋊Q₈×C₂₆₉	C₂²	semidirect
120. C₄×Q₈×C₂₆₉	C₂²	semidirect
122. #117×C₂₆₉	C₂²	semidirect
275. C₄×D₂₆₉	#41	semidirect
339. C₂₆₉	#3460	semidirect
344. #542	D₂₆₉	semidirect
372. C₄⋊Q₈	C₂×D₂₆₉	semidirect
379. #126	C₂×D₂₆₉	semidirect
389. #124	C₂×D₂₆₉	semidirect
397. #123	C₂×D₂₆₉	semidirect
403. C₂²⋊Q₈	C₂×D₂₆₉	semidirect
404. C₂²⋊Q₈	C₂×D₂₆₉	semidirect
429. C₄×Q₈	C₂×D₂₆₉	semidirect
456. #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
#31771232	2
#31771227	2
#31771225	2
#31771210	2
#31771207	2
#31771206	2
#31771194	2
#31771189	2
#31771185	2
#31771173	2
#31771171	2
#31771156	2
#31771154	2
#31771150	2
#31771141	2
#31771138	2
#31771134	2
#31771118	2
#31771113	2
C₄×#16864403	2
#31771073	2
C₄×D₄×D₂₆₉	2
#542×C₂₆₉	2
#3460	269