Subgroups — #46825160

Order 34432.

1058 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31771348	C₂	1	2	yes	maximal, complemented
2	#31771344	C₂	1	2	yes	maximal, complemented
3	#31771339	C₂	1	2	yes	maximal, complemented
4	#31771325	C₂	1	2	yes	maximal, complemented
5	#31771320	C₂	1	2	yes	maximal, complemented
6	#31771283	C₂	1	2	yes	maximal, complemented
7	#31771264	C₂	1	2	yes	maximal, complemented
8	#31771251	C₂	1	2	yes	maximal, complemented
9	#31771226	C₂	1	2	yes	maximal, complemented
10	#31771225	C₂	1	4	yes	maximal, complemented
11	#31771187	C₂	1	4	yes	maximal, complemented
12	#31771176	C₂	1	1	yes	maximal, characteristic, complemented
13	#31771169	C₂	1	1	yes	maximal, characteristic, complemented
14	#31771116	C₂	1	2	yes	maximal, complemented
15	#525×C₂₆₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#16864402	C₂²	1	2	yes	—
17	C₂²×Dic₅₃₈	C₂²	1	1	yes	characteristic, complemented
18	C₂²×D₁₀₇₆	C₂²	1	1	yes	characteristic, complemented
19	#22575453	C₂²	1	2	yes	complemented
20	#22575451	C₂²	1	2	yes	complemented
21	#22575449	C₂²	1	2	yes	—
22	#22575448	C₂²	1	4	yes	complemented
23	#22575446	C₂²	1	4	yes	complemented
24	#22575446	C₂²	1	4	yes	complemented
25	#22575442	C₂²	1	2	yes	complemented
26	#22575441	C₂²	1	2	yes	complemented
27	#22575440	C₂²	1	2	yes	—
28	#22575440	C₂²	1	4	yes	—
29	#22575439	C₂²	1	4	yes	complemented
30	#22575439	C₂²	1	4	yes	complemented
31	#22575439	C₂²	1	4	yes	complemented
32	#22575439	C₂²	1	4	yes	complemented
33	#22575438	C₂²	1	4	yes	complemented
34	#22575436	C₂²	1	4	yes	complemented
35	#22575435	C₂²	1	4	yes	complemented
36	#22575434	C₂²	1	2	yes	complemented
37	#22575434	C₂²	1	2	yes	complemented
38	#22575432	C₂²	1	2	yes	complemented
39	#22575432	C₂²	1	2	yes	complemented
40	#22575432	C₂²	1	2	yes	complemented
41	#22575431	C₂²	1	4	yes	complemented
42	#22575431	C₂²	1	4	yes	complemented
43	#22575427	C₂²	1	2	yes	—
44	#22575427	C₂²	1	2	yes	—
45	#22575427	C₂²	1	2	yes	complemented
46	#22575426	C₂²	1	4	yes	—
47	#22575425	C₂²	1	4	yes	complemented
48	#22575424	C₂²	1	4	yes	complemented
49	#22575422	C₂²	1	4	yes	complemented
50	#22575421	C₂²	1	2	yes	—
51	#22575421	C₂²	1	4	yes	—
52	#22575421	C₂²	1	2	yes	complemented
53	C₄×Dic₅₃₈	C₂²	1	2	yes	complemented
54	#22575418	C₂²	1	4	yes	complemented
55	C₄×D₁₀₇₆	C₂²	1	2	yes	complemented
56	C₄×C₂²⋊D₂₆₉	C₂²	1	4	yes	complemented
57	C₄×C₂²⋊D₂₆₉	C₂²	1	4	yes	complemented
58	#22575413	C₂²	1	4	yes	complemented
59	#22575412	C₂²	1	1	yes	characteristic, complemented
60	#22575412	C₂²	1	1	yes	characteristic, complemented
61	#22575412	C₂²	1	2	yes	complemented
62	#22575411	C₂²	1	4	yes	complemented
63	C₂²⋊C₄×D₂₆₉	C₂²	1	4	yes	complemented
64	C₂×#41×C₂₆₉	C₂²	1	1	yes	characteristic
65	C₂³×C₄×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
66	#123×C₂₆₉	C₂²	1	1	yes	characteristic
67	#123×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
68	C₂²⋊Q₈×C₂₆₉	C₂²	1	2	yes	complemented
69	#121×C₂₆₉	C₂²	1	2	yes	—
70	#120×C₂₆₉	C₂²	1	1	yes	characteristic
71	#120×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
72	C₄×D₄×C₂₆₉	C₂²	1	2	yes	—
73	C₄×D₄×C₂₆₉	C₂²	1	2	yes	complemented
74	#117×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
75	C₂³×D₂₆₉	C₂³	1	2	yes	—
76	#16864402	—	4	4	no	—
77	C₂×Dic₅₃₈	—	4	2	no	—
78	C₂×Dic₅₃₈	C₂³	1	2	yes	—
79	C₂×Dic₅₃₈	C₂³	1	4	yes	—
80	C₂×Dic₅₃₈	C₂³	1	2	yes	—
81	C₂×D₁₀₇₆	—	4	2	no	—
82	C₂×D₁₀₇₆	C₂³	1	2	yes	—
83	C₂×D₁₀₇₆	C₂³	1	2	yes	—
84	C₂×C₂²⋊D₂₆₉	C₂³	1	4	yes	—
85	C₂×C₂²⋊D₂₆₉	C₂³	1	4	yes	—
86	C₂×C₂²⋊D₂₆₉	C₂³	1	4	yes	—
87	C₂×C₂²⋊D₂₆₉	C₂³	1	4	yes	—
88	C₂²×Dic₂₆₉	C₂³	1	2	yes	—
89	C₂×C₄×D₂₆₉	C₂³	1	4	yes	—
90	C₂×C₄×D₂₆₉	C₂³	1	4	yes	—
91	C₄⋊Dic₂₆₉	C₂³	1	4	yes	—
92	C₄⋊Dic₂₆₉	C₂³	1	2	yes	—
93	C₄⋊Dic₂₆₉	C₂³	1	2	yes	—
94	#16864381	C₂³	1	4	yes	—
95	#16864381	C₂³	1	4	yes	—
96	#16864381	C₂³	1	4	yes	—
97	#16864381	C₂³	1	4	yes	—
98	C₂²⋊Dic₂₆₉	C₂³	1	4	yes	—
99	C₂²⋊Dic₂₆₉	C₂³	1	2	yes	—
100	C₂²⋊Dic₂₆₉	C₂³	1	4	yes	—
101	C₂²⋊Dic₂₆₉	C₂³	1	2	yes	—
102	C₂²⋊Dic₂₆₉	C₂³	1	4	yes	—
103	C₂²⋊Dic₂₆₉	C₂³	1	4	yes	—
104	#16864379	C₂³	1	4	yes	—
105	#16864379	C₂³	1	4	yes	—
106	#16864379	C₂³	1	4	yes	—
107	#16864379	C₂³	1	4	yes	—
108	#16864379	C₂³	1	4	yes	—
109	#16864379	C₂³	1	4	yes	—
110	C₄×Dic₂₆₉	C₂³	1	2	yes	—
111	C₄×Dic₂₆₉	C₂³	1	4	yes	—
112	C₄×Dic₂₆₉	C₂³	1	2	yes	—
113	C₄×Dic₂₆₉	C₂³	1	4	yes	—
114	C₂⁴×C₂₆₉	C₂³	1	1	yes	characteristic
115	#41×C₂₆₉	—	4	2	no	—
116	C₂×Q₈×C₂₆₉	C₂³	1	1	yes	characteristic
117	C₂×D₄×C₂₆₉	C₂³	1	2	yes	—
118	C₂×D₄×C₂₆₉	C₂³	1	1	yes	characteristic
119	C₂×D₄×C₂₆₉	C₂³	1	1	yes	characteristic
120	C₂×D₄×C₂₆₉	C₂³	1	2	yes	—
121	C₂×D₄×C₂₆₉	C₂³	1	1	yes	characteristic
122	C₂²×C₄×C₂₆₉	—	4	2	no	—
123	C₂²×C₄×C₂₆₉	C₂³	1	2	yes	—
124	C₂²×C₄×C₂₆₉	C₂³	1	1	yes	characteristic
125	C₂²×C₄×C₂₆₉	C₂³	1	1	yes	characteristic
126	C₂²×C₄×C₂₆₉	C₂³	1	1	yes	characteristic
127	C₂²×C₄×C₂₆₉	C₂³	1	1	yes	characteristic
128	C₂²×C₄×C₂₆₉	C₂³	1	2	yes	—
129	C₄⋊C₄×C₂₆₉	C₂³	1	2	yes	—
130	C₄⋊C₄×C₂₆₉	C₂³	1	2	yes	—
131	C₄⋊C₄×C₂₆₉	C₂³	1	2	yes	—
132	C₂²⋊C₄×C₂₆₉	C₂³	1	2	yes	—
133	C₂²⋊C₄×C₂₆₉	C₂³	1	2	yes	—
134	C₂²⋊C₄×C₂₆₉	C₂³	1	2	yes	—
135	C₂²⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
136	C₂²⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
137	C₂²⋊C₄×C₂₆₉	C₂³	1	2	yes	—
138	C₄²×C₂₆₉	C₂³	1	2	yes	—
139	C₂²×D₂₆₉	—	4	2	no	—
140	C₂²×D₂₆₉	—	4	4	no	—
141	C₂²×D₂₆₉	C₂⁴	1	4	yes	—
142	Dic₅₃₈	—	2	4	no	—
143	Dic₅₃₈	—	4	2	no	—
144	Dic₅₃₈	—	4	4	no	—
145	D₁₀₇₆	—	2	4	no	—
146	D₁₀₇₆	—	4	2	no	—
147	C₂²⋊D₂₆₉	—	4	4	no	—
148	C₂²⋊D₂₆₉	—	4	4	no	—
149	C₂²⋊D₂₆₉	—	4	4	no	—
150	C₂²⋊D₂₆₉	—	4	4	no	—
151	C₂×Dic₂₆₉	—	4	2	no	—
152	C₂×Dic₂₆₉	C₂⁴	1	4	yes	—
153	C₂×Dic₂₆₉	C₂⁴	1	4	yes	—
154	C₂×Dic₂₆₉	C₂⁴	1	4	yes	—
155	C₄×D₂₆₉	—	4	4	no	—
156	C₄×D₂₆₉	—	4	4	no	—
157	C₂³×C₂₆₉	—	4	1	no	—
158	C₂³×C₂₆₉	—	4	2	no	—
159	C₂³×C₂₆₉	C₂⁴	1	1	yes	characteristic
160	C₂³×C₂₆₉	C₂⁴	1	2	yes	—
161	C₂³×C₂₆₉	C₂⁴	1	1	yes	characteristic
162	C₂³×C₂₆₉	C₂⁴	1	1	yes	characteristic
163	Q₈×C₂₆₉	—	4	1	no	—
164	D₄×C₂₆₉	—	4	2	no	—
165	D₄×C₂₆₉	—	4	2	no	—
166	D₄×C₂₆₉	—	4	1	no	—
167	D₄×C₂₆₉	—	4	1	no	—
168	D₄×C₂₆₉	—	4	1	no	—
169	C₂×C₄×C₂₆₉	—	2	2	no	—
170	C₂×C₄×C₂₆₉	—	2	4	no	—
171	C₂×C₄×C₂₆₉	—	2	2	no	—
172	C₂×C₄×C₂₆₉	—	2	2	no	—
173	C₂×C₄×C₂₆₉	—	4	2	no	—
174	C₂×C₄×C₂₆₉	—	4	1	no	—
175	C₂×C₄×C₂₆₉	C₂⁴	1	2	yes	—
176	C₂×C₄×C₂₆₉	C₂⁴	1	2	yes	—
177	C₂×C₄×C₂₆₉	C₂⁴	1	2	yes	—
178	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
179	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
180	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
181	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
182	C₂²×C₂₆₉	—	2	1	no	—
183	C₂²×C₂₆₉	—	2	2	no	—
184	C₂²×C₂₆₉	—	2	1	no	—
185	C₂²×C₂₆₉	—	2	1	no	—
186	C₂²×C₂₆₉	—	2	2	no	—
187	C₂²×C₂₆₉	—	2	2	no	—
188	C₂²×C₂₆₉	—	2	2	no	—
189	C₂²×C₂₆₉	—	2	2	no	—
190	C₂²×C₂₆₉	—	2	2	no	—
191	C₂²×C₂₆₉	—	4	4	no	—
192	C₂²×C₂₆₉	C₂⁵	1	1	yes	characteristic
193	C₂×D₂₆₉	—	2	4	no	—
194	C₂×D₂₆₉	—	2	4	no	—
195	C₂×D₂₆₉	—	2	4	no	—
196	C₂×D₂₆₉	—	8	4	no	—
197	C₄×C₂₆₉	—	2	1	no	—
198	C₄×C₂₆₉	—	2	2	no	—
199	C₄×C₂₆₉	—	2	1	no	—
200	C₄×C₂₆₉	—	2	1	no	—
201	C₄×C₂₆₉	—	2	2	no	—
202	C₄×C₂₆₉	—	2	2	no	—
203	C₄×C₂₆₉	H(5,𝔽₂)	1	2	yes	—
204	Dic₂₆₉	—	2	4	no	—
205	Dic₂₆₉	—	2	4	no	—
206	Dic₂₆₉	—	2	4	no	—
207	C₂×C₂₆₉	—	4	1	no	—
208	C₂×C₂₆₉	—	4	1	no	—
209	C₂×C₂₆₉	—	4	1	no	—
210	C₂×C₂₆₉	—	4	2	no	—
211	C₂×C₂₆₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
212	C₂×C₂₆₉	#585	1	2	yes	—
213	D₂₆₉	—	4	4	no	—
214	C₂₆₉	#3540	1	1	yes	characteristic, complemented, Sylow
215	#3540	—	269	1	no	maximal, Sylow
216	H(3,𝔽₄)	—	269	2	no	—
217	#560	—	269	2	no	—
218	#559	—	269	2	no	—
219	#556	—	269	2	no	—
220	#555	—	269	2	no	—
221	#551	—	269	2	no	—
222	#548	—	269	2	no	—
223	#546	—	269	2	no	—
224	#542	—	269	4	no	—
225	#542	—	269	2	no	—
226	#538	—	269	4	no	—
227	#536	—	269	1	no	—
228	#535	—	269	1	no	—
229	#525	—	269	2	no	—
230	#525	D₂₆₉	1	1	yes	characteristic, complemented
231	C₂×#41	—	269	2	no	—
232	C₂×#41	C₂×D₂₆₉	1	1	yes	characteristic
233	C₂²×Q₈	—	269	1	no	—
234	C₂²×D₄	—	269	1	no	—
235	C₂³×C₄	C₂×D₂₆₉	1	1	yes	characteristic, complemented
236	C₄⋊Q₈	—	269	2	no	—
237	C₄⋊Q₈	—	269	2	no	—
238	#127	—	269	2	no	—
239	#126	—	269	4	no	—
240	#126	—	269	4	no	—
241	#126	—	269	4	no	—
242	#124	—	269	2	no	—
243	#124	—	269	2	no	—
244	#124	—	269	4	no	—
245	#124	—	269	4	no	—
246	#124	—	269	4	no	—
247	#124	—	269	4	no	—
248	#124	—	269	4	no	—
249	#124	—	269	2	no	—
250	#123	—	269	2	no	—
251	#123	—	269	2	no	—
252	#123	—	269	4	no	—
253	#123	—	269	4	no	—
254	#123	—	269	4	no	—
255	#123	C₂×D₂₆₉	1	1	yes	characteristic
256	#123	C₂×D₂₆₉	1	1	yes	characteristic, complemented
257	C₂²⋊Q₈	—	269	2	no	—
258	C₂²⋊Q₈	—	269	2	no	—
259	C₂²⋊Q₈	—	269	2	no	—
260	C₂²⋊Q₈	—	269	4	no	—
261	C₂²⋊Q₈	—	269	4	no	—
262	C₂²⋊Q₈	C₂×D₂₆₉	1	2	yes	complemented
263	#121	—	269	4	no	—
264	#121	—	269	4	no	—
265	#121	—	269	2	no	—
266	#121	—	269	2	no	—
267	#121	—	269	2	no	—
268	#121	—	269	4	no	—
269	#121	C₂×D₂₆₉	1	2	yes	—
270	#120	—	269	4	no	—
271	#120	—	269	2	no	—
272	#120	—	269	2	no	—
273	#120	—	269	4	no	—
274	#120	C₂×D₂₆₉	1	1	yes	characteristic
275	#120	C₂×D₂₆₉	1	1	yes	characteristic, complemented
276	C₄×Q₈	—	269	4	no	—
277	C₄×Q₈	—	269	2	no	—
278	C₄×D₄	—	269	4	no	—
279	C₄×D₄	—	269	4	no	—
280	C₄×D₄	—	269	4	no	—
281	C₄×D₄	—	269	2	no	—
282	C₄×D₄	C₂×D₂₆₉	1	2	yes	—
283	C₄×D₄	C₂×D₂₆₉	1	2	yes	complemented
284	#117	—	269	2	no	—
285	#117	—	269	1	no	—
286	#117	—	269	1	no	—
287	#117	—	269	4	no	—
288	#117	C₂×D₂₆₉	1	1	yes	characteristic, complemented
289	C₂×C₂²⋊C₄	—	269	4	no	—
290	C₂⁴	—	269	2	no	—
291	C₂⁴	C₂²×D₂₆₉	1	1	yes	characteristic
292	#41	—	4	2	no	—
293	#41	—	1076	4	no	—
294	C₂×Q₈	—	269	2	no	—
295	C₂×Q₈	—	269	4	no	—
296	C₂×Q₈	—	269	2	no	—
297	C₂×Q₈	—	1076	2	no	—
298	C₂×Q₈	C₂²×D₂₆₉	1	1	yes	characteristic
299	C₂×D₄	—	269	4	no	—
300	C₂×D₄	—	269	4	no	—
301	C₂×D₄	—	269	4	no	—
302	C₂×D₄	—	269	4	no	—
303	C₂×D₄	—	269	2	no	—
304	C₂×D₄	—	269	2	no	—
305	C₂×D₄	—	1076	2	no	—
306	C₂×D₄	C₂²×D₂₆₉	1	2	yes	—
307	C₂×D₄	C₂²×D₂₆₉	1	2	yes	—
308	C₂×D₄	C₂²×D₂₆₉	1	1	yes	characteristic
309	C₂×D₄	C₂²×D₂₆₉	1	1	yes	characteristic
310	C₂×D₄	C₂²×D₂₆₉	1	1	yes	characteristic
311	C₂²×C₄	—	4	2	no	—
312	C₂²×C₄	—	269	2	no	—
313	C₂²×C₄	—	269	4	no	—
314	C₂²×C₄	—	269	4	no	—
315	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
316	C₂²×C₄	C₂²×D₂₆₉	1	2	yes	—
317	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
318	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
319	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
320	C₂²×C₄	C₂²×D₂₆₉	1	2	yes	—
321	C₄⋊C₄	—	269	2	no	—
322	C₄⋊C₄	—	269	2	no	—
323	C₄⋊C₄	—	269	4	no	—
324	C₄⋊C₄	—	269	4	no	—
325	C₄⋊C₄	—	269	4	no	—
326	C₄⋊C₄	—	269	4	no	—
327	C₄⋊C₄	—	269	4	no	—
328	C₄⋊C₄	C₂²×D₂₆₉	1	2	yes	—
329	C₄⋊C₄	C₂²×D₂₆₉	1	2	yes	—
330	C₄⋊C₄	C₂²×D₂₆₉	1	2	yes	—
331	C₂²⋊C₄	—	269	4	no	—
332	C₂²⋊C₄	—	269	2	no	—
333	C₂²⋊C₄	—	269	4	no	—
334	C₂²⋊C₄	—	269	2	no	—
335	C₂²⋊C₄	—	269	4	no	—
336	C₂²⋊C₄	—	269	4	no	—
337	C₂²⋊C₄	—	269	4	no	—
338	C₂²⋊C₄	—	269	4	no	—
339	C₂²⋊C₄	—	269	4	no	—
340	C₂²⋊C₄	—	269	4	no	—
341	C₂²⋊C₄	—	269	4	no	—
342	C₂²⋊C₄	—	269	4	no	—
343	C₂²⋊C₄	C₂²×D₂₆₉	1	2	yes	—
344	C₂²⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
345	C₂²⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
346	C₂²⋊C₄	C₂²×D₂₆₉	1	2	yes	—
347	C₂²⋊C₄	C₂²×D₂₆₉	1	2	yes	—
348	C₂²⋊C₄	C₂²×D₂₆₉	1	2	yes	—
349	C₄²	—	269	2	no	—
350	C₄²	—	269	4	no	—
351	C₄²	—	269	2	no	—
352	C₄²	—	269	4	no	—
353	C₄²	C₂²×D₂₆₉	1	2	yes	—
354	C₂³	—	4	1	no	—
355	C₂³	—	4	2	no	—
356	C₂³	—	269	4	no	—
357	C₂³	—	1076	2	no	—
358	C₂³	—	1076	4	no	—
359	C₂³	C₂³×D₂₆₉	1	1	yes	characteristic
360	C₂³	C₂³×D₂₆₉	1	1	yes	characteristic
361	C₂³	C₂³×D₂₆₉	1	2	yes	—
362	C₂³	C₂³×D₂₆₉	1	1	yes	characteristic
363	Q₈	—	4	1	no	—
364	Q₈	—	538	4	no	—
365	Q₈	—	1076	2	no	—
366	Q₈	—	1076	4	no	—
367	D₄	—	4	1	no	—
368	D₄	—	4	1	no	—
369	D₄	—	4	1	no	—
370	D₄	—	4	2	no	—
371	D₄	—	4	2	no	—
372	D₄	—	538	4	no	—
373	D₄	—	1076	2	no	—
374	D₄	—	1076	4	no	—
375	D₄	—	1076	4	no	—
376	D₄	—	1076	4	no	—
377	D₄	—	1076	4	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	4	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	269	4	no	—
385	C₂×C₄	—	269	4	no	—
386	C₂×C₄	—	269	4	no	—
387	C₂×C₄	—	1076	4	no	—
388	C₂×C₄	—	1076	4	no	—
389	C₂×C₄	—	1076	2	no	—
390	C₂×C₄	C₂³×D₂₆₉	1	2	yes	—
391	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
392	C₂×C₄	C₂³×D₂₆₉	1	2	yes	—
393	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
394	C₂×C₄	C₂³×D₂₆₉	1	2	yes	—
395	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
396	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
397	C₂²	—	2	1	no	—
398	C₂²	—	2	2	no	—
399	C₂²	—	2	1	no	—
400	C₂²	—	2	1	no	—
401	C₂²	—	2	2	no	—
402	C₂²	—	2	2	no	—
403	C₂²	—	2	2	no	—
404	C₂²	—	2	2	no	—
405	C₂²	—	2	2	no	—
406	C₂²	—	4	4	no	—
407	C₂²	—	538	4	no	—
408	C₂²	—	538	4	no	—
409	C₂²	—	538	4	no	—
410	C₂²	—	2152	4	no	—
411	C₂²	C₂⁴×D₂₆₉	1	1	yes	characteristic
412	C₄	—	2	2	no	—
413	C₄	—	2	1	no	—
414	C₄	—	2	1	no	—
415	C₄	—	2	1	no	—
416	C₄	—	2	2	no	—
417	C₄	—	2	2	no	—
418	C₄	—	538	4	no	—
419	C₄	—	538	4	no	—
420	C₄	—	538	4	no	—
421	C₄	#22575498	1	2	yes	—
422	C₂	—	4	1	no	—
423	C₂	—	4	2	no	—
424	C₂	—	4	1	no	—
425	C₂	—	4	1	no	—
426	C₂	—	1076	4	no	—
427	C₂	C₂×#22575498	1	1	yes	characteristic
428	C₂	#31771441	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₂₆₉
commutator, socle, cosocle	C₂²×C₂₆₉	C₂⁵
Fitting	#525×C₂₆₉	C₂
hypercenter	#525	D₂₆₉
hypocenter	C₂₆₉	#3540
LCS	G ▷ C₂²×C₂₆₉ ▷ C₂₆₉
UCS	C₁ ◁ C₂² ◁ #525

Complements

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

N	H ≅ G/N	type
1. #31771348	C₂	semidirect
2. #31771344	C₂	semidirect
3. #31771339	C₂	semidirect
4. #31771325	C₂	semidirect
5. #31771320	C₂	semidirect
6. #31771283	C₂	semidirect
7. #31771264	C₂	semidirect
8. #31771251	C₂	semidirect
9. #31771226	C₂	semidirect
10. #31771225	C₂	semidirect
11. #31771187	C₂	semidirect
12. #31771176	C₂	semidirect
13. #31771169	C₂	semidirect
14. #31771116	C₂	semidirect
15. #525×C₂₆₉	C₂	semidirect
17. C₂²×Dic₅₃₈	C₂²	semidirect
18. C₂²×D₁₀₇₆	C₂²	semidirect
19. #22575453	C₂²	semidirect
20. #22575451	C₂²	semidirect
22. #22575448	C₂²	semidirect
23. #22575446	C₂²	semidirect
24. #22575446	C₂²	semidirect
25. #22575442	C₂²	semidirect
26. #22575441	C₂²	semidirect
29. #22575439	C₂²	semidirect
30. #22575439	C₂²	semidirect
31. #22575439	C₂²	semidirect
32. #22575439	C₂²	semidirect
33. #22575438	C₂²	semidirect
34. #22575436	C₂²	semidirect
35. #22575435	C₂²	semidirect
36. #22575434	C₂²	semidirect
37. #22575434	C₂²	semidirect
38. #22575432	C₂²	semidirect
39. #22575432	C₂²	semidirect
40. #22575432	C₂²	semidirect
41. #22575431	C₂²	semidirect
42. #22575431	C₂²	semidirect
45. #22575427	C₂²	semidirect
47. #22575425	C₂²	semidirect
48. #22575424	C₂²	semidirect
49. #22575422	C₂²	semidirect
52. #22575421	C₂²	semidirect
53. C₄×Dic₅₃₈	C₂²	semidirect
54. #22575418	C₂²	semidirect
55. C₄×D₁₀₇₆	C₂²	semidirect
56. C₄×C₂²⋊D₂₆₉	C₂²	semidirect
57. C₄×C₂²⋊D₂₆₉	C₂²	semidirect
58. #22575413	C₂²	semidirect
59. #22575412	C₂²	semidirect
60. #22575412	C₂²	semidirect
61. #22575412	C₂²	semidirect
62. #22575411	C₂²	semidirect
63. C₂²⋊C₄×D₂₆₉	C₂²	semidirect
65. C₂³×C₄×C₂₆₉	C₂²	semidirect
67. #123×C₂₆₉	C₂²	semidirect
68. C₂²⋊Q₈×C₂₆₉	C₂²	semidirect
71. #120×C₂₆₉	C₂²	semidirect
73. C₄×D₄×C₂₆₉	C₂²	semidirect
74. #117×C₂₆₉	C₂²	semidirect
214. C₂₆₉	#3540	semidirect
230. #525	D₂₆₉	semidirect
235. C₂³×C₄	C₂×D₂₆₉	semidirect
256. #123	C₂×D₂₆₉	semidirect
262. C₂²⋊Q₈	C₂×D₂₆₉	semidirect
275. #120	C₂×D₂₆₉	semidirect
283. C₄×D₄	C₂×D₂₆₉	semidirect
288. #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
#31771348	2
#31771344	2
#31771339	2
#31771325	2
#31771320	2
#31771283	2
#31771264	2
#31771251	2
#31771226	2
#31771225	2
#31771187	2
#31771176	2
#31771169	2
#31771116	2
#525×C₂₆₉	2
#3540	269