Subgroups — #46824452

Order 34432.

1132 conjugacy classes of subgroups.

The subgroup lattice has 460 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	#31771321	C₂	1	1	yes	maximal, characteristic, complemented
3	#31771316	C₂	1	1	yes	maximal, characteristic, complemented
4	#31771308	C₂	1	2	yes	maximal, complemented
5	#31771297	C₂	1	2	yes	maximal, complemented
6	#31771293	C₂	1	2	yes	maximal, complemented
7	#31771282	C₂	1	4	yes	maximal, complemented
8	#31771258	C₂	1	1	yes	maximal, characteristic, complemented
9	#31771246	C₂	1	2	yes	maximal, complemented
10	#31771142	C₂	1	4	yes	maximal, complemented
11	#31771142	C₂	1	2	yes	maximal, complemented
12	#31771117	C₂	1	2	yes	maximal, complemented
13	C₄×#16864403	C₂	1	2	yes	maximal, complemented
14	C₄×#16864402	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₄×D₁₀₇₆	C₂	1	1	yes	maximal, characteristic, complemented
16	#117×D₂₆₉	C₂	1	2	yes	maximal, complemented
17	#533×C₂₆₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#16864403	C₂²	1	2	yes	—
19	C₂×#16864402	C₂²	1	1	yes	characteristic
20	C₂²×D₁₀₇₆	C₂²	1	1	yes	characteristic
21	C₂²×C₄×D₂₆₉	C₂²	1	2	yes	—
22	#22575448	C₂²	1	4	yes	complemented
23	#22575448	C₂²	1	4	yes	complemented
24	#22575448	C₂²	1	4	yes	complemented
25	#22575444	C₂²	1	4	yes	complemented
26	#22575444	C₂²	1	2	yes	complemented
27	#22575442	C₂²	1	2	yes	—
28	#22575442	C₂²	1	4	yes	complemented
29	#22575438	C₂²	1	4	yes	—
30	#22575438	C₂²	1	4	yes	complemented
31	#22575438	C₂²	1	4	yes	complemented
32	#22575437	C₂²	1	4	yes	—
33	#22575433	C₂²	1	2	yes	complemented
34	#22575433	C₂²	1	2	yes	complemented
35	#22575429	C₂²	1	2	yes	complemented
36	#22575429	C₂²	1	4	yes	complemented
37	#22575428	C₂²	1	4	yes	—
38	#22575428	C₂²	1	2	yes	—
39	#22575428	C₂²	1	2	yes	complemented
40	#22575428	C₂²	1	2	yes	complemented
41	#22575423	C₂²	1	4	yes	—
42	Q₈×Dic₂₆₉	C₂²	1	2	yes	complemented
43	C₄×Dic₅₃₈	C₂²	1	1	yes	characteristic, complemented
44	C₄×Dic₅₃₈	C₂²	1	1	yes	characteristic, complemented
45	C₄×D₁₀₇₆	C₂²	1	1	yes	characteristic
46	C₄×D₁₀₇₆	C₂²	1	2	yes	—
47	C₄×D₁₀₇₆	C₂²	1	1	yes	characteristic
48	C₄×D₁₀₇₆	C₂²	1	2	yes	—
49	C₄×D₁₀₇₆	C₂²	1	1	yes	characteristic
50	C₄×D₁₀₇₆	C₂²	1	1	yes	characteristic
51	C₄×D₁₀₇₆	C₂²	1	4	yes	complemented
52	C₄×D₁₀₇₆	C₂²	1	4	yes	complemented
53	C₄×D₁₀₇₆	C₂²	1	1	yes	characteristic, complemented
54	C₄×D₁₀₇₆	C₂²	1	1	yes	characteristic, complemented
55	#22575415	C₂²	1	2	yes	—
56	#22575415	C₂²	1	4	yes	complemented
57	C₄×C₂²⋊D₂₆₉	C₂²	1	2	yes	—
58	C₄×C₂²⋊D₂₆₉	C₂²	1	2	yes	—
59	#22575412	C₂²	1	1	yes	characteristic
60	#22575411	C₂²	1	4	yes	complemented
61	#22575411	C₂²	1	2	yes	complemented
62	#22575411	C₂²	1	2	yes	complemented
63	#22575411	C₂²	1	2	yes	complemented
64	#22575410	C₂²	1	4	yes	complemented
65	#22575410	C₂²	1	2	yes	complemented
66	#22575409	C₂²	1	4	yes	—
67	C₂×C₄⋊Dic₂₆₉	C₂²	1	1	yes	characteristic
68	C₄⋊C₄×D₂₆₉	C₂²	1	2	yes	complemented
69	C₄⋊C₄×D₂₆₉	C₂²	1	2	yes	complemented
70	C₂×#16864379	C₂²	1	2	yes	—
71	C₂²⋊C₄×D₂₆₉	C₂²	1	4	yes	—
72	C₄²×D₂₆₉	C₂²	1	4	yes	complemented
73	C₄²×D₂₆₉	C₂²	1	2	yes	complemented
74	C₄⋊Q₈×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
75	C₄⋊Q₈×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
76	#125×C₂₆₉	C₂²	1	2	yes	complemented
77	C₂²⋊Q₈×C₂₆₉	C₂²	1	2	yes	—
78	C₂²⋊Q₈×C₂₆₉	C₂²	1	2	yes	—
79	C₄×Q₈×C₂₆₉	C₂²	1	2	yes	complemented
80	C₄×Q₈×C₂₆₉	C₂²	1	2	yes	complemented
81	#117×C₂₆₉	C₂²	1	2	yes	—
82	C₂×C₄²×C₂₆₉	C₂²	1	1	yes	characteristic
83	C₂³×D₂₆₉	C₂³	1	2	yes	—
84	#16864403	—	2	8	no	—
85	#16864402	—	2	4	no	—
86	C₂×Dic₅₃₈	C₂³	1	1	yes	characteristic
87	C₂×D₁₀₇₆	—	2	4	no	—
88	C₂×D₁₀₇₆	C₂³	1	4	yes	—
89	C₂×D₁₀₇₆	C₂³	1	2	yes	—
90	C₂×D₁₀₇₆	C₂³	1	1	yes	characteristic
91	C₂×D₁₀₇₆	C₂³	1	1	yes	characteristic
92	C₂×D₁₀₇₆	C₂³	1	4	yes	—
93	C₂×D₁₀₇₆	C₂³	1	1	yes	characteristic
94	C₂×C₂²⋊D₂₆₉	C₂³	1	2	yes	—
95	C₂²×Dic₂₆₉	C₂³	1	2	yes	—
96	C₂×C₄×D₂₆₉	—	2	8	no	—
97	C₂×C₄×D₂₆₉	C₂³	1	2	yes	—
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	2	yes	—
103	C₂×C₄×D₂₆₉	C₂³	1	2	yes	—
104	C₂×C₄×D₂₆₉	C₂³	1	4	yes	—
105	C₂×C₄×D₂₆₉	C₂³	1	2	yes	—
106	C₄⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
107	C₄⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
108	C₄⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
109	C₄⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
110	C₄⋊Dic₂₆₉	C₂³	1	2	yes	—
111	C₄⋊Dic₂₆₉	C₂³	1	4	yes	—
112	C₄⋊Dic₂₆₉	C₂³	1	4	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	C₂²⋊Dic₂₆₉	C₂³	1	2	yes	—
118	#16864379	C₂³	1	4	yes	—
119	#16864379	C₂³	1	4	yes	—
120	#16864379	C₂³	1	2	yes	—
121	#16864379	C₂³	1	2	yes	—
122	#16864379	C₂³	1	2	yes	—
123	#16864379	C₂³	1	2	yes	—
124	#16864379	C₂³	1	2	yes	—
125	#16864379	C₂³	1	2	yes	—
126	#16864379	C₂³	1	4	yes	—
127	#16864379	C₂³	1	4	yes	—
128	#16864379	C₂³	1	4	yes	—
129	#16864379	C₂³	1	4	yes	—
130	C₄×Dic₂₆₉	C₂³	1	2	yes	—
131	C₄×Dic₂₆₉	C₂³	1	4	yes	—
132	C₄×Dic₂₆₉	C₂³	1	4	yes	—
133	C₄×Dic₂₆₉	C₂³	1	2	yes	—
134	C₄×Dic₂₆₉	C₂³	1	2	yes	—
135	C₂×Q₈×C₂₆₉	C₂³	1	2	yes	—
136	C₂×Q₈×C₂₆₉	C₂³	1	2	yes	—
137	C₂²×C₄×C₂₆₉	C₂³	1	1	yes	characteristic
138	C₂²×C₄×C₂₆₉	C₂³	1	1	yes	characteristic
139	C₂²×C₄×C₂₆₉	C₂³	1	1	yes	characteristic
140	C₄⋊C₄×C₂₆₉	C₂³	1	2	yes	—
141	C₄⋊C₄×C₂₆₉	C₂³	1	2	yes	—
142	C₄⋊C₄×C₂₆₉	C₂³	1	2	yes	—
143	C₄⋊C₄×C₂₆₉	C₂³	1	4	yes	—
144	C₄⋊C₄×C₂₆₉	C₂³	1	4	yes	—
145	C₄⋊C₄×C₂₆₉	C₂³	1	2	yes	—
146	C₂²⋊C₄×C₂₆₉	C₂³	1	4	yes	—
147	C₄²×C₂₆₉	C₂³	1	1	yes	characteristic
148	C₄²×C₂₆₉	C₂³	1	4	yes	—
149	C₄²×C₂₆₉	C₂³	1	1	yes	characteristic
150	C₄²×C₂₆₉	C₂³	1	1	yes	characteristic
151	C₄²×C₂₆₉	C₂³	1	1	yes	characteristic
152	C₂²×D₂₆₉	—	2	4	no	—
153	C₂²×D₂₆₉	—	2	4	no	—
154	C₂²×D₂₆₉	—	4	2	no	—
155	C₂²×D₂₆₉	C₂⁴	1	2	yes	—
156	C₂²×D₂₆₉	C₂⁴	1	2	yes	—
157	C₂²×D₂₆₉	C₂⁴	1	2	yes	—
158	Dic₅₃₈	—	2	2	no	—
159	D₁₀₇₆	—	2	4	no	—
160	D₁₀₇₆	—	2	8	no	—
161	D₁₀₇₆	—	2	2	no	—
162	D₁₀₇₆	—	2	2	no	—
163	D₁₀₇₆	—	4	4	no	—
164	D₁₀₇₆	#41	1	4	yes	complemented
165	C₂²⋊D₂₆₉	—	2	4	no	—
166	C₂×Dic₂₆₉	—	2	4	no	—
167	C₂×Dic₂₆₉	C₂⁴	1	2	yes	—
168	C₂×Dic₂₆₉	C₂⁴	1	2	yes	—
169	C₂×Dic₂₆₉	C₂⁴	1	2	yes	—
170	C₂×Dic₂₆₉	C₂⁴	1	2	yes	—
171	C₂×Dic₂₆₉	C₂⁴	1	2	yes	—
172	C₄×D₂₆₉	—	2	8	no	—
173	C₄×D₂₆₉	—	2	4	no	—
174	C₄×D₂₆₉	—	2	4	no	—
175	C₄×D₂₆₉	—	2	4	no	—
176	C₄×D₂₆₉	—	2	4	no	—
177	C₄×D₂₆₉	—	2	4	no	—
178	C₄×D₂₆₉	—	2	4	no	—
179	C₄×D₂₆₉	—	4	2	no	—
180	C₄×D₂₆₉	—	4	4	no	—
181	C₂³×C₂₆₉	C₂⁴	1	1	yes	characteristic
182	Q₈×C₂₆₉	—	2	4	no	—
183	Q₈×C₂₆₉	—	4	2	no	—
184	C₂×C₄×C₂₆₉	—	2	2	no	—
185	C₂×C₄×C₂₆₉	—	4	1	no	—
186	C₂×C₄×C₂₆₉	#41	1	4	yes	complemented
187	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
188	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
189	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
190	C₂×C₄×C₂₆₉	C₂⁴	1	4	yes	—
191	C₂×C₄×C₂₆₉	C₂⁴	1	4	yes	—
192	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
193	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
194	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
195	C₂²×C₂₆₉	—	2	1	no	—
196	C₂²×C₂₆₉	—	2	1	no	—
197	C₂²×C₂₆₉	C₂×#41	1	2	yes	—
198	C₂²×C₂₆₉	C₂⁵	1	1	yes	characteristic
199	C₂×D₂₆₉	—	2	2	no	—
200	C₂×D₂₆₉	—	2	2	no	—
201	C₂×D₂₆₉	—	2	2	no	—
202	C₂×D₂₆₉	—	2	2	no	—
203	C₂×D₂₆₉	—	2	2	no	—
204	C₂×D₂₆₉	—	2	2	no	—
205	C₂×D₂₆₉	—	2	2	no	—
206	C₂×D₂₆₉	—	2	2	no	—
207	C₂×D₂₆₉	—	4	8	no	—
208	C₂×D₂₆₉	C₂×#41	1	4	yes	—
209	C₄×C₂₆₉	—	2	1	no	—
210	C₄×C₂₆₉	—	2	4	no	—
211	C₄×C₂₆₉	—	2	1	no	—
212	C₄×C₂₆₉	—	2	1	no	—
213	C₄×C₂₆₉	—	2	4	no	—
214	C₄×C₂₆₉	C₂×#41	1	2	yes	—
215	C₄×C₂₆₉	C₂×#41	1	2	yes	—
216	C₄×C₂₆₉	C₂×#41	1	2	yes	—
217	Dic₂₆₉	—	2	2	no	—
218	Dic₂₆₉	—	2	2	no	—
219	Dic₂₆₉	—	2	2	no	—
220	Dic₂₆₉	—	2	2	no	—
221	Dic₂₆₉	—	2	2	no	—
222	C₂×C₂₆₉	—	2	2	no	—
223	C₂×C₂₆₉	C₂²×#41	1	1	yes	characteristic
224	C₂×C₂₆₉	C₂²×#41	1	1	yes	characteristic
225	C₂×C₂₆₉	#585	1	1	yes	characteristic
226	D₂₆₉	—	2	4	no	—
227	D₂₆₉	—	4	2	no	—
228	D₂₆₉	—	4	2	no	—
229	C₂₆₉	#3475	1	1	yes	characteristic, complemented, Sylow
230	#3475	—	269	1	no	maximal, Sylow
231	#556	—	269	1	no	—
232	#555	—	269	1	no	—
233	#554	—	269	1	no	—
234	#553	—	269	2	no	—
235	#552	—	269	2	no	—
236	#552	—	269	2	no	—
237	#551	—	269	4	no	—
238	#547	—	269	1	no	—
239	#546	—	269	2	no	—
240	#533	D₂₆₉	1	1	yes	characteristic, complemented
241	#529	—	269	4	no	—
242	#529	—	269	2	no	—
243	#525	—	269	2	no	—
244	C₄×#41	—	269	2	no	—
245	C₄×#41	—	269	1	no	—
246	C₂×C₄×D₄	—	269	1	no	—
247	C₂×#117	—	269	2	no	—
248	C₂×#41	—	269	2	no	—
249	C₂×#41	—	269	1	no	—
250	C₂²×D₄	—	269	1	no	—
251	C₂³×C₄	—	269	2	no	—
252	C₄⋊Q₈	C₂×D₂₆₉	1	1	yes	characteristic, complemented
253	C₄⋊Q₈	C₂×D₂₆₉	1	1	yes	characteristic, complemented
254	#126	—	269	4	no	—
255	#126	—	269	4	no	—
256	#126	—	269	4	no	—
257	#125	—	269	4	no	—
258	#125	—	269	2	no	—
259	#125	C₂×D₂₆₉	1	2	yes	complemented
260	#124	—	269	2	no	—
261	#124	—	269	4	no	—
262	#123	—	269	4	no	—
263	#123	—	269	4	no	—
264	#123	—	269	4	no	—
265	#123	—	269	4	no	—
266	C₂²⋊Q₈	—	269	2	no	—
267	C₂²⋊Q₈	—	269	4	no	—
268	C₂²⋊Q₈	—	269	2	no	—
269	C₂²⋊Q₈	—	269	2	no	—
270	C₂²⋊Q₈	C₂×D₂₆₉	1	2	yes	—
271	C₂²⋊Q₈	C₂×D₂₆₉	1	2	yes	—
272	#121	—	269	2	no	—
273	#121	—	269	2	no	—
274	#121	—	269	4	no	—
275	#121	—	269	2	no	—
276	#120	—	269	4	no	—
277	C₄×Q₈	—	269	2	no	—
278	C₄×Q₈	—	269	1	no	—
279	C₄×Q₈	—	269	1	no	—
280	C₄×Q₈	C₂×D₂₆₉	1	2	yes	complemented
281	C₄×Q₈	C₂×D₂₆₉	1	2	yes	complemented
282	C₄×D₄	—	269	2	no	—
283	C₄×D₄	—	269	2	no	—
284	C₄×D₄	—	269	2	no	—
285	C₄×D₄	—	269	4	no	—
286	C₄×D₄	—	269	1	no	—
287	C₄×D₄	—	269	1	no	—
288	C₄×D₄	—	269	2	no	—
289	C₄×D₄	—	269	1	no	—
290	C₄×D₄	—	269	2	no	—
291	C₄×D₄	—	269	1	no	—
292	C₄×D₄	—	269	4	no	—
293	C₄×D₄	—	269	1	no	—
294	C₄×D₄	—	269	1	no	—
295	C₄×D₄	—	269	4	no	—
296	#117	—	269	1	no	—
297	#117	—	269	2	no	—
298	#117	—	269	2	no	—
299	#117	—	269	4	no	—
300	#117	—	269	2	no	—
301	#117	—	269	4	no	—
302	#117	—	269	4	no	—
303	#117	—	269	2	no	—
304	#117	C₂×D₂₆₉	1	2	yes	—
305	C₂×C₄⋊C₄	—	269	1	no	—
306	C₂×C₄⋊C₄	—	269	2	no	—
307	C₂×C₄⋊C₄	—	269	2	no	—
308	C₂×C₂²⋊C₄	—	269	2	no	—
309	C₂×C₂²⋊C₄	—	269	4	no	—
310	C₂×C₄²	—	269	4	no	—
311	C₂×C₄²	—	269	2	no	—
312	C₂×C₄²	C₂×D₂₆₉	1	1	yes	characteristic
313	C₂⁴	—	269	2	no	—
314	#41	—	538	8	no	—
315	#41	—	538	4	no	—
316	C₂×Q₈	—	269	1	no	—
317	C₂×Q₈	C₂²×D₂₆₉	1	2	yes	—
318	C₂×Q₈	C₂²×D₂₆₉	1	2	yes	—
319	C₂×D₄	—	269	2	no	—
320	C₂×D₄	—	269	1	no	—
321	C₂×D₄	—	269	4	no	—
322	C₂×D₄	—	269	1	no	—
323	C₂×D₄	—	269	2	no	—
324	C₂×D₄	—	269	1	no	—
325	C₂×D₄	—	269	4	no	—
326	C₂×D₄	—	538	4	no	—
327	C₂²×C₄	—	269	2	no	—
328	C₂²×C₄	—	269	4	no	—
329	C₂²×C₄	—	269	2	no	—
330	C₂²×C₄	—	269	2	no	—
331	C₂²×C₄	—	269	2	no	—
332	C₂²×C₄	—	269	2	no	—
333	C₂²×C₄	—	269	2	no	—
334	C₂²×C₄	—	269	2	no	—
335	C₂²×C₄	—	269	4	no	—
336	C₂²×C₄	—	269	2	no	—
337	C₂²×C₄	—	538	8	no	—
338	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
339	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
340	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
341	C₄⋊C₄	—	269	1	no	—
342	C₄⋊C₄	—	269	1	no	—
343	C₄⋊C₄	—	269	1	no	—
344	C₄⋊C₄	—	269	4	no	—
345	C₄⋊C₄	—	269	4	no	—
346	C₄⋊C₄	—	269	1	no	—
347	C₄⋊C₄	—	269	2	no	—
348	C₄⋊C₄	—	269	2	no	—
349	C₄⋊C₄	—	269	4	no	—
350	C₄⋊C₄	—	269	2	no	—
351	C₄⋊C₄	—	269	4	no	—
352	C₄⋊C₄	C₂²×D₂₆₉	1	2	yes	—
353	C₄⋊C₄	C₂²×D₂₆₉	1	2	yes	—
354	C₄⋊C₄	C₂²×D₂₆₉	1	2	yes	—
355	C₄⋊C₄	C₂²×D₂₆₉	1	4	yes	—
356	C₄⋊C₄	C₂²×D₂₆₉	1	4	yes	—
357	C₄⋊C₄	C₂²×D₂₆₉	1	2	yes	—
358	C₂²⋊C₄	—	269	2	no	—
359	C₂²⋊C₄	—	269	2	no	—
360	C₂²⋊C₄	—	269	4	no	—
361	C₂²⋊C₄	—	269	4	no	—
362	C₂²⋊C₄	—	269	2	no	—
363	C₂²⋊C₄	—	269	2	no	—
364	C₂²⋊C₄	—	269	2	no	—
365	C₂²⋊C₄	—	269	4	no	—
366	C₂²⋊C₄	—	269	2	no	—
367	C₂²⋊C₄	—	269	4	no	—
368	C₂²⋊C₄	—	269	2	no	—
369	C₂²⋊C₄	—	269	4	no	—
370	C₂²⋊C₄	—	269	4	no	—
371	C₂²⋊C₄	C₂²×D₂₆₉	1	4	yes	—
372	C₄²	—	269	4	no	—
373	C₄²	—	269	4	no	—
374	C₄²	—	269	2	no	—
375	C₄²	—	269	2	no	—
376	C₄²	—	269	2	no	—
377	C₄²	C₂²×D₂₆₉	1	1	yes	characteristic
378	C₄²	C₂²×D₂₆₉	1	1	yes	characteristic
379	C₄²	C₂²×D₂₆₉	1	1	yes	characteristic
380	C₄²	C₂²×D₂₆₉	1	4	yes	—
381	C₄²	C₂²×D₂₆₉	1	1	yes	characteristic
382	C₂³	—	269	2	no	—
383	C₂³	—	269	2	no	—
384	C₂³	—	269	2	no	—
385	C₂³	—	538	4	no	—
386	C₂³	—	538	4	no	—
387	C₂³	—	1076	2	no	—
388	C₂³	C₂³×D₂₆₉	1	1	yes	characteristic
389	Q₈	—	2	4	no	—
390	Q₈	—	4	2	no	—
391	Q₈	—	538	2	no	—
392	D₄	—	269	4	no	—
393	D₄	—	538	4	no	—
394	D₄	—	538	8	no	—
395	D₄	—	538	4	no	—
396	D₄	—	538	2	no	—
397	D₄	—	538	2	no	—
398	D₄	—	1076	4	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	269	2	no	—
402	C₂×C₄	—	269	2	no	—
403	C₂×C₄	—	269	2	no	—
404	C₂×C₄	—	269	2	no	—
405	C₂×C₄	—	269	2	no	—
406	C₂×C₄	—	538	8	no	—
407	C₂×C₄	—	538	4	no	—
408	C₂×C₄	—	538	4	no	—
409	C₂×C₄	—	538	4	no	—
410	C₂×C₄	—	538	4	no	—
411	C₂×C₄	—	538	4	no	—
412	C₂×C₄	—	538	4	no	—
413	C₂×C₄	—	538	4	no	—
414	C₂×C₄	—	1076	2	no	—
415	C₂×C₄	—	1076	4	no	—
416	C₂×C₄	#16864403	1	4	yes	complemented
417	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
418	C₂×C₄	C₂³×D₂₆₉	1	4	yes	—
419	C₂×C₄	C₂³×D₂₆₉	1	4	yes	—
420	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
421	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
422	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
423	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
424	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
425	C₂²	—	2	1	no	—
426	C₂²	—	2	1	no	—
427	C₂²	—	269	4	no	—
428	C₂²	—	538	2	no	—
429	C₂²	—	538	2	no	—
430	C₂²	—	538	2	no	—
431	C₂²	—	538	2	no	—
432	C₂²	—	538	2	no	—
433	C₂²	—	538	2	no	—
434	C₂²	—	538	2	no	—
435	C₂²	—	538	2	no	—
436	C₂²	—	1076	8	no	—
437	C₂²	C₂×#16864403	1	2	yes	—
438	C₂²	C₂⁴×D₂₆₉	1	1	yes	characteristic
439	C₄	—	2	1	no	—
440	C₄	—	2	4	no	—
441	C₄	—	2	1	no	—
442	C₄	—	2	1	no	—
443	C₄	—	2	4	no	—
444	C₄	—	538	2	no	—
445	C₄	—	538	2	no	—
446	C₄	—	538	2	no	—
447	C₄	—	538	2	no	—
448	C₄	—	538	2	no	—
449	C₄	#41×D₂₆₉	1	2	yes	—
450	C₄	C₂×#16864403	1	2	yes	—
451	C₄	C₂×#16864403	1	2	yes	—
452	C₂	—	2	2	no	—
453	C₂	—	538	4	no	—
454	C₂	—	1076	2	no	—
455	C₂	—	1076	2	no	—
456	C₂	C₂×#41×D₂₆₉	1	1	yes	characteristic
457	C₂	C₂²×#16864403	1	1	yes	characteristic
458	C₂	#31771441	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₂₆₉
commutator, socle, cosocle	C₂²×C₂₆₉	C₂⁵
Frattini	C₂²	C₂⁴×D₂₆₉
Fitting	#533×C₂₆₉	C₂
hypercenter	#533	D₂₆₉
hypocenter	C₂₆₉	#3475
LCS	G ▷ C₂²×C₂₆₉ ▷ C₂₆₉
UCS	C₁ ◁ C₂×C₄ ◁ #533

Complements

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

N	H ≅ G/N	type
1. #31771329	C₂	semidirect
2. #31771321	C₂	semidirect
3. #31771316	C₂	semidirect
4. #31771308	C₂	semidirect
5. #31771297	C₂	semidirect
6. #31771293	C₂	semidirect
7. #31771282	C₂	semidirect
8. #31771258	C₂	semidirect
9. #31771246	C₂	semidirect
10. #31771142	C₂	semidirect
11. #31771142	C₂	semidirect
12. #31771117	C₂	semidirect
13. C₄×#16864403	C₂	semidirect
14. C₄×#16864402	C₂	semidirect
15. C₂×C₄×D₁₀₇₆	C₂	semidirect
16. #117×D₂₆₉	C₂	semidirect
17. #533×C₂₆₉	C₂	semidirect
22. #22575448	C₂²	semidirect
23. #22575448	C₂²	semidirect
24. #22575448	C₂²	semidirect
25. #22575444	C₂²	semidirect
26. #22575444	C₂²	semidirect
28. #22575442	C₂²	semidirect
30. #22575438	C₂²	semidirect
31. #22575438	C₂²	semidirect
33. #22575433	C₂²	semidirect
34. #22575433	C₂²	semidirect
35. #22575429	C₂²	semidirect
36. #22575429	C₂²	semidirect
39. #22575428	C₂²	semidirect
40. #22575428	C₂²	semidirect
42. Q₈×Dic₂₆₉	C₂²	semidirect
43. C₄×Dic₅₃₈	C₂²	semidirect
44. C₄×Dic₅₃₈	C₂²	semidirect
51. C₄×D₁₀₇₆	C₂²	semidirect
52. C₄×D₁₀₇₆	C₂²	semidirect
53. C₄×D₁₀₇₆	C₂²	semidirect
54. C₄×D₁₀₇₆	C₂²	semidirect
56. #22575415	C₂²	semidirect
60. #22575411	C₂²	semidirect
61. #22575411	C₂²	semidirect
62. #22575411	C₂²	semidirect
63. #22575411	C₂²	semidirect
64. #22575410	C₂²	semidirect
65. #22575410	C₂²	semidirect
68. C₄⋊C₄×D₂₆₉	C₂²	semidirect
69. C₄⋊C₄×D₂₆₉	C₂²	semidirect
72. C₄²×D₂₆₉	C₂²	semidirect
73. C₄²×D₂₆₉	C₂²	semidirect
74. C₄⋊Q₈×C₂₆₉	C₂²	semidirect
75. C₄⋊Q₈×C₂₆₉	C₂²	semidirect
76. #125×C₂₆₉	C₂²	semidirect
79. C₄×Q₈×C₂₆₉	C₂²	semidirect
80. C₄×Q₈×C₂₆₉	C₂²	semidirect
164. D₁₀₇₆	#41	semidirect
186. C₂×C₄×C₂₆₉	#41	semidirect
229. C₂₆₉	#3475	semidirect
240. #533	D₂₆₉	semidirect
252. C₄⋊Q₈	C₂×D₂₆₉	semidirect
253. C₄⋊Q₈	C₂×D₂₆₉	semidirect
259. #125	C₂×D₂₆₉	semidirect
280. C₄×Q₈	C₂×D₂₆₉	semidirect
281. C₄×Q₈	C₂×D₂₆₉	semidirect
416. C₂×C₄	#16864403	semidirect

Maximal subgroups

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

subgroup	index
#31771329	2
#31771321	2
#31771316	2
#31771308	2
#31771297	2
#31771293	2
#31771282	2
#31771258	2
#31771246	2
#31771142	2
#31771117	2
C₄×#16864403	2
C₄×#16864402	2
C₂×C₄×D₁₀₇₆	2
#117×D₂₆₉	2
#533×C₂₆₉	2
#3475	269