Subgroups — #46824301

Order 34432.

1140 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31771233	C₂	1	1	yes	maximal, characteristic, complemented
2	#31771227	C₂	1	2	yes	maximal, complemented
3	#31771226	C₂	1	2	yes	maximal, complemented
4	#31771210	C₂	1	2	yes	maximal, complemented
5	#31771206	C₂	1	2	yes	maximal, complemented
6	#31771188	C₂	1	4	yes	maximal, complemented
7	#31771183	C₂	1	1	yes	maximal, characteristic, complemented
8	#31771174	C₂	1	1	yes	maximal, characteristic, complemented
9	#31771169	C₂	1	1	yes	maximal, characteristic, complemented
10	#31771155	C₂	1	2	yes	maximal, complemented
11	#31771152	C₂	1	2	yes	maximal, complemented
12	#31771142	C₂	1	2	yes	maximal, complemented
13	#31771139	C₂	1	2	yes	maximal, complemented
14	#31771114	C₂	1	4	yes	maximal, complemented
15	C₄×#16864402	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₄×D₁₀₇₆	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×#41×C₂₆₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#16864402	C₂²	1	1	yes	characteristic
19	C₂×#16864402	C₂²	1	4	yes	complemented
20	C₂²×D₁₀₇₆	C₂²	1	1	yes	characteristic
21	C₂²×C₄×D₂₆₉	C₂²	1	2	yes	—
22	#22575453	C₂²	1	2	yes	complemented
23	#22575452	C₂²	1	2	yes	complemented
24	#22575450	C₂²	1	2	yes	—
25	#22575449	C₂²	1	2	yes	—
26	#22575448	C₂²	1	4	yes	complemented
27	#22575447	C₂²	1	4	yes	complemented
28	#22575445	C₂²	1	2	yes	complemented
29	#22575444	C₂²	1	2	yes	complemented
30	#22575442	C₂²	1	2	yes	—
31	#22575441	C₂²	1	2	yes	—
32	#22575441	C₂²	1	4	yes	complemented
33	#22575439	C₂²	1	4	yes	complemented
34	#22575438	C₂²	1	4	yes	complemented
35	#22575438	C₂²	1	4	yes	complemented
36	#22575436	C₂²	1	4	yes	complemented
37	#22575435	C₂²	1	4	yes	complemented
38	#22575432	C₂²	1	2	yes	complemented
39	#22575431	C₂²	1	4	yes	complemented
40	#22575430	C₂²	1	4	yes	—
41	#22575429	C₂²	1	2	yes	complemented
42	#22575428	C₂²	1	2	yes	—
43	#22575428	C₂²	1	2	yes	—
44	#22575427	C₂²	1	2	yes	—
45	#22575427	C₂²	1	2	yes	—
46	#22575427	C₂²	1	2	yes	complemented
47	#22575427	C₂²	1	4	yes	complemented
48	#22575426	C₂²	1	4	yes	complemented
49	#22575426	C₂²	1	4	yes	complemented
50	#22575425	C₂²	1	4	yes	—
51	#22575424	C₂²	1	2	yes	complemented
52	#22575423	C₂²	1	4	yes	—
53	#22575421	C₂²	1	4	yes	—
54	C₄×Dic₅₃₈	C₂²	1	1	yes	characteristic, complemented
55	C₄×Dic₅₃₈	C₂²	1	1	yes	characteristic, complemented
56	C₄×D₁₀₇₆	C₂²	1	2	yes	—
57	C₄×D₁₀₇₆	C₂²	1	2	yes	—
58	C₄×D₁₀₇₆	C₂²	1	2	yes	—
59	C₄×D₁₀₇₆	C₂²	1	2	yes	—
60	C₄×D₁₀₇₆	C₂²	1	4	yes	complemented
61	C₄×D₁₀₇₆	C₂²	1	1	yes	characteristic, complemented
62	C₄×D₁₀₇₆	C₂²	1	1	yes	characteristic, complemented
63	C₄×C₂²⋊D₂₆₉	C₂²	1	2	yes	—
64	C₄×C₂²⋊D₂₆₉	C₂²	1	2	yes	—
65	C₄×C₂²⋊D₂₆₉	C₂²	1	4	yes	complemented
66	#22575412	C₂²	1	1	yes	characteristic
67	#22575410	C₂²	1	4	yes	complemented
68	#22575410	C₂²	1	2	yes	complemented
69	C₂×C₄⋊Dic₂₆₉	C₂²	1	1	yes	characteristic
70	C₂×#16864379	C₂²	1	2	yes	—
71	C₄²×D₂₆₉	C₂²	1	2	yes	complemented
72	C₂×#41×C₂₆₉	C₂²	1	1	yes	characteristic
73	C₄×Q₈×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
74	C₄×Q₈×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
75	C₄×D₄×C₂₆₉	C₂²	1	2	yes	—
76	C₄×D₄×C₂₆₉	C₂²	1	2	yes	—
77	C₄×D₄×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
78	C₄×D₄×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
79	#117×C₂₆₉	C₂²	1	1	yes	characteristic
80	#117×C₂₆₉	C₂²	1	2	yes	complemented
81	C₂×C₄²×C₂₆₉	C₂²	1	1	yes	characteristic
82	C₂×C₄²×C₂₆₉	C₂²	1	2	yes	complemented
83	C₂³×D₂₆₉	C₂³	1	2	yes	—
84	#16864402	—	2	4	no	—
85	#16864402	—	4	8	no	—
86	C₂×Dic₅₃₈	C₂³	1	1	yes	characteristic
87	C₂×Dic₅₃₈	C₂³	1	4	yes	—
88	C₂×D₁₀₇₆	—	2	4	no	—
89	C₂×D₁₀₇₆	C₂³	1	2	yes	—
90	C₂×D₁₀₇₆	C₂³	1	2	yes	—
91	C₂×D₁₀₇₆	C₂³	1	1	yes	characteristic
92	C₂×D₁₀₇₆	C₂³	1	4	yes	—
93	C₂×D₁₀₇₆	C₂³	1	4	yes	—
94	C₂×C₂²⋊D₂₆₉	C₂³	1	2	yes	—
95	C₂×C₂²⋊D₂₆₉	C₂³	1	4	yes	—
96	C₂×C₂²⋊D₂₆₉	C₂³	1	4	yes	—
97	C₂×C₂²⋊D₂₆₉	C₂³	1	4	yes	—
98	C₂²×Dic₂₆₉	C₂³	1	2	yes	—
99	C₂×C₄×D₂₆₉	—	4	4	no	—
100	C₂×C₄×D₂₆₉	C₂³	1	2	yes	—
101	C₂×C₄×D₂₆₉	C₂³	1	2	yes	—
102	C₂×C₄×D₂₆₉	C₂³	1	4	yes	—
103	C₂×C₄×D₂₆₉	C₂³	1	2	yes	—
104	C₂×C₄×D₂₆₉	C₂³	1	4	yes	—
105	C₄⋊Dic₂₆₉	C₂³	1	2	yes	—
106	C₄⋊Dic₂₆₉	C₂³	1	2	yes	—
107	C₄⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
108	C₄⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
109	C₄⋊Dic₂₆₉	C₂³	1	4	yes	—
110	#16864381	C₂³	1	2	yes	—
111	#16864381	C₂³	1	2	yes	—
112	#16864381	C₂³	1	4	yes	—
113	#16864381	C₂³	1	4	yes	—
114	#16864381	C₂³	1	4	yes	—
115	C₂²⋊Dic₂₆₉	C₂³	1	2	yes	—
116	C₂²⋊Dic₂₆₉	C₂³	1	4	yes	—
117	#16864379	C₂³	1	4	yes	—
118	#16864379	C₂³	1	4	yes	—
119	#16864379	C₂³	1	2	yes	—
120	#16864379	C₂³	1	2	yes	—
121	#16864379	C₂³	1	4	yes	—
122	#16864379	C₂³	1	4	yes	—
123	#16864379	C₂³	1	4	yes	—
124	#16864379	C₂³	1	4	yes	—
125	#16864379	C₂³	1	4	yes	—
126	C₄×Dic₂₆₉	C₂³	1	2	yes	—
127	C₄×Dic₂₆₉	C₂³	1	2	yes	—
128	C₄×Dic₂₆₉	C₂³	1	2	yes	—
129	#41×C₂₆₉	—	2	4	no	—
130	C₂×Q₈×C₂₆₉	C₂³	1	1	yes	characteristic
131	C₂×D₄×C₂₆₉	C₂³	1	2	yes	—
132	C₂×D₄×C₂₆₉	C₂³	1	1	yes	characteristic
133	C₂²×C₄×C₂₆₉	C₂³	1	1	yes	characteristic
134	C₂²×C₄×C₂₆₉	C₂³	1	2	yes	—
135	C₂²×C₄×C₂₆₉	C₂³	1	2	yes	—
136	C₂²×C₄×C₂₆₉	C₂³	1	1	yes	characteristic
137	C₂²×C₄×C₂₆₉	C₂³	1	2	yes	—
138	C₂²×C₄×C₂₆₉	C₂³	1	1	yes	characteristic
139	C₄⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
140	C₄⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
141	C₄⋊C₄×C₂₆₉	C₂³	1	2	yes	—
142	C₄⋊C₄×C₂₆₉	C₂³	1	2	yes	—
143	C₂²⋊C₄×C₂₆₉	C₂³	1	2	yes	—
144	C₂²⋊C₄×C₂₆₉	C₂³	1	2	yes	—
145	C₂²⋊C₄×C₂₆₉	C₂³	1	2	yes	—
146	C₄²×C₂₆₉	C₂³	1	1	yes	characteristic
147	C₄²×C₂₆₉	C₂³	1	1	yes	characteristic
148	C₄²×C₂₆₉	C₂³	1	2	yes	—
149	C₄²×C₂₆₉	C₂³	1	1	yes	characteristic
150	C₄²×C₂₆₉	C₂³	1	1	yes	characteristic
151	C₄²×C₂₆₉	C₂³	1	2	yes	—
152	C₄²×C₂₆₉	C₂³	1	2	yes	—
153	C₂²×D₂₆₉	—	2	4	no	—
154	C₂²×D₂₆₉	—	4	2	no	—
155	C₂²×D₂₆₉	—	4	2	no	—
156	C₂²×D₂₆₉	C₂⁴	1	4	yes	—
157	C₂²×D₂₆₉	C₂⁴	1	2	yes	—
158	Dic₅₃₈	—	2	2	no	—
159	Dic₅₃₈	—	4	4	no	—
160	D₁₀₇₆	—	2	4	no	—
161	D₁₀₇₆	—	2	4	no	—
162	D₁₀₇₆	—	2	2	no	—
163	D₁₀₇₆	—	4	4	no	—
164	D₁₀₇₆	—	4	4	no	—
165	C₂²⋊D₂₆₉	—	2	4	no	—
166	C₂²⋊D₂₆₉	—	4	4	no	—
167	C₂²⋊D₂₆₉	—	4	4	no	—
168	C₂²⋊D₂₆₉	—	4	4	no	—
169	C₂×Dic₂₆₉	—	4	2	no	—
170	C₂×Dic₂₆₉	C₂⁴	1	2	yes	—
171	C₂×Dic₂₆₉	C₂⁴	1	2	yes	—
172	C₂×Dic₂₆₉	C₂⁴	1	2	yes	—
173	C₂×Dic₂₆₉	C₂⁴	1	4	yes	—
174	C₄×D₂₆₉	—	2	4	no	—
175	C₄×D₂₆₉	—	2	8	no	—
176	C₄×D₂₆₉	—	2	4	no	—
177	C₄×D₂₆₉	—	4	4	no	—
178	C₄×D₂₆₉	—	4	2	no	—
179	C₂³×C₂₆₉	C₂⁴	1	2	yes	—
180	C₂³×C₂₆₉	C₂⁴	1	1	yes	characteristic
181	Q₈×C₂₆₉	—	2	2	no	—
182	D₄×C₂₆₉	—	2	4	no	—
183	D₄×C₂₆₉	—	2	2	no	—
184	C₂×C₄×C₂₆₉	—	2	4	no	—
185	C₂×C₄×C₂₆₉	—	2	2	no	—
186	C₂×C₄×C₂₆₉	—	2	4	no	—
187	C₂×C₄×C₂₆₉	—	4	1	no	—
188	C₂×C₄×C₂₆₉	—	4	2	no	—
189	C₂×C₄×C₂₆₉	#41	1	4	yes	complemented
190	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
191	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
192	C₂×C₄×C₂₆₉	C₂⁴	1	2	yes	—
193	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
194	C₂×C₄×C₂₆₉	C₂⁴	1	2	yes	—
195	C₂×C₄×C₂₆₉	C₂⁴	1	2	yes	—
196	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
197	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
198	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
199	C₂²×C₂₆₉	—	2	1	no	—
200	C₂²×C₂₆₉	—	2	1	no	—
201	C₂²×C₂₆₉	—	2	2	no	—
202	C₂²×C₂₆₉	—	2	2	no	—
203	C₂²×C₂₆₉	—	2	2	no	—
204	C₂²×C₂₆₉	C₂×#41	1	2	yes	—
205	C₂²×C₂₆₉	C₂⁵	1	1	yes	characteristic
206	C₂×D₂₆₉	—	2	2	no	—
207	C₂×D₂₆₉	—	2	4	no	—
208	C₂×D₂₆₉	—	2	4	no	—
209	C₂×D₂₆₉	—	2	2	no	—
210	C₂×D₂₆₉	—	2	2	no	—
211	C₂×D₂₆₉	—	2	4	no	—
212	C₂×D₂₆₉	—	4	8	no	—
213	C₄×C₂₆₉	—	2	2	no	—
214	C₄×C₂₆₉	—	2	1	no	—
215	C₄×C₂₆₉	—	2	2	no	—
216	C₄×C₂₆₉	—	2	1	no	—
217	C₄×C₂₆₉	—	2	1	no	—
218	C₄×C₂₆₉	—	2	2	no	—
219	C₄×C₂₆₉	C₂×#41	1	2	yes	—
220	C₄×C₂₆₉	C₂×#41	1	2	yes	—
221	C₄×C₂₆₉	H(5,𝔽₂)	1	2	yes	—
222	Dic₂₆₉	—	2	2	no	—
223	Dic₂₆₉	—	2	4	no	—
224	Dic₂₆₉	—	2	2	no	—
225	Dic₂₆₉	—	2	2	no	—
226	C₂×C₂₆₉	—	2	2	no	—
227	C₂×C₂₆₉	—	4	2	no	—
228	C₂×C₂₆₉	C₂²×#41	1	1	yes	characteristic
229	C₂×C₂₆₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
230	C₂×C₂₆₉	#585	1	1	yes	characteristic
231	D₂₆₉	—	4	2	no	—
232	D₂₆₉	—	4	4	no	—
233	C₂₆₉	#3460	1	1	yes	characteristic, complemented, Sylow
234	#3460	—	269	1	no	maximal, Sylow
235	#544	—	269	1	no	—
236	#542	—	269	2	no	—
237	#542	—	269	2	no	—
238	#540	—	269	2	no	—
239	#540	—	269	2	no	—
240	#538	—	269	4	no	—
241	#537	—	269	1	no	—
242	#535	—	269	1	no	—
243	#535	—	269	1	no	—
244	#532	—	269	2	no	—
245	#532	—	269	2	no	—
246	#529	—	269	2	no	—
247	#529	—	269	2	no	—
248	#525	—	269	4	no	—
249	C₄×#41	—	269	1	no	—
250	C₄×#41	D₂₆₉	1	1	yes	characteristic, complemented
251	C₂×C₄×D₄	—	269	1	no	—
252	C₂×#41	—	269	1	no	—
253	C₂×#41	—	269	4	no	—
254	C₂×#41	C₂×D₂₆₉	1	1	yes	characteristic
255	C₂²×D₄	—	269	1	no	—
256	C₂³×C₄	—	269	2	no	—
257	C₄⋊Q₈	—	269	2	no	—
258	C₄⋊Q₈	—	269	2	no	—
259	#127	—	269	2	no	—
260	#127	—	269	2	no	—
261	#126	—	269	4	no	—
262	#126	—	269	4	no	—
263	#125	—	269	2	no	—
264	#125	—	269	2	no	—
265	#124	—	269	2	no	—
266	#124	—	269	4	no	—
267	#124	—	269	2	no	—
268	#124	—	269	4	no	—
269	#123	—	269	4	no	—
270	#123	—	269	4	no	—
271	#123	—	269	4	no	—
272	#123	—	269	4	no	—
273	C₂²⋊Q₈	—	269	2	no	—
274	C₂²⋊Q₈	—	269	2	no	—
275	C₂²⋊Q₈	—	269	4	no	—
276	C₂²⋊Q₈	—	269	4	no	—
277	#121	—	269	4	no	—
278	#121	—	269	2	no	—
279	#121	—	269	2	no	—
280	#121	—	269	2	no	—
281	#121	—	269	2	no	—
282	#121	—	269	4	no	—
283	#121	—	269	2	no	—
284	#121	—	269	2	no	—
285	#121	—	269	4	no	—
286	#121	—	269	4	no	—
287	#120	—	269	4	no	—
288	#120	—	269	4	no	—
289	C₄×Q₈	—	269	1	no	—
290	C₄×Q₈	—	269	1	no	—
291	C₄×Q₈	C₂×D₂₆₉	1	1	yes	characteristic, complemented
292	C₄×Q₈	C₂×D₂₆₉	1	1	yes	characteristic, complemented
293	C₄×D₄	—	269	2	no	—
294	C₄×D₄	—	269	2	no	—
295	C₄×D₄	—	269	4	no	—
296	C₄×D₄	—	269	2	no	—
297	C₄×D₄	—	269	2	no	—
298	C₄×D₄	—	269	2	no	—
299	C₄×D₄	—	269	2	no	—
300	C₄×D₄	—	269	1	no	—
301	C₄×D₄	—	269	1	no	—
302	C₄×D₄	—	269	4	no	—
303	C₄×D₄	C₂×D₂₆₉	1	2	yes	—
304	C₄×D₄	C₂×D₂₆₉	1	2	yes	—
305	C₄×D₄	C₂×D₂₆₉	1	1	yes	characteristic, complemented
306	C₄×D₄	C₂×D₂₆₉	1	1	yes	characteristic, complemented
307	#117	—	269	1	no	—
308	#117	—	269	2	no	—
309	#117	—	269	4	no	—
310	#117	C₂×D₂₆₉	1	1	yes	characteristic
311	#117	C₂×D₂₆₉	1	2	yes	complemented
312	C₂×C₄⋊C₄	—	269	1	no	—
313	C₂×C₂²⋊C₄	—	269	2	no	—
314	C₂×C₄²	—	269	2	no	—
315	C₂×C₄²	C₂×D₂₆₉	1	1	yes	characteristic
316	C₂×C₄²	C₂×D₂₆₉	1	2	yes	complemented
317	C₂⁴	—	269	2	no	—
318	#41	—	2	4	no	—
319	#41	—	538	4	no	—
320	#41	—	1076	8	no	—
321	C₂×Q₈	—	269	1	no	—
322	C₂×Q₈	—	269	4	no	—
323	C₂×Q₈	C₂²×D₂₆₉	1	1	yes	characteristic
324	C₂×D₄	—	269	2	no	—
325	C₂×D₄	—	269	4	no	—
326	C₂×D₄	—	269	4	no	—
327	C₂×D₄	—	269	4	no	—
328	C₂×D₄	—	269	2	no	—
329	C₂×D₄	—	269	2	no	—
330	C₂×D₄	—	269	1	no	—
331	C₂×D₄	—	269	4	no	—
332	C₂×D₄	—	269	4	no	—
333	C₂×D₄	—	538	4	no	—
334	C₂×D₄	C₂²×D₂₆₉	1	2	yes	—
335	C₂×D₄	C₂²×D₂₆₉	1	1	yes	characteristic
336	C₂²×C₄	—	269	2	no	—
337	C₂²×C₄	—	269	2	no	—
338	C₂²×C₄	—	269	2	no	—
339	C₂²×C₄	—	269	4	no	—
340	C₂²×C₄	—	269	2	no	—
341	C₂²×C₄	—	269	4	no	—
342	C₂²×C₄	—	1076	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	2	yes	—
346	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
347	C₂²×C₄	C₂²×D₂₆₉	1	2	yes	—
348	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
349	C₄⋊C₄	—	269	2	no	—
350	C₄⋊C₄	—	269	2	no	—
351	C₄⋊C₄	—	269	1	no	—
352	C₄⋊C₄	—	269	1	no	—
353	C₄⋊C₄	—	269	2	no	—
354	C₄⋊C₄	—	269	2	no	—
355	C₄⋊C₄	—	269	4	no	—
356	C₄⋊C₄	—	269	4	no	—
357	C₄⋊C₄	—	269	4	no	—
358	C₄⋊C₄	—	269	4	no	—
359	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
360	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
361	C₄⋊C₄	C₂²×D₂₆₉	1	2	yes	—
362	C₄⋊C₄	C₂²×D₂₆₉	1	2	yes	—
363	C₂²⋊C₄	—	269	2	no	—
364	C₂²⋊C₄	—	269	4	no	—
365	C₂²⋊C₄	—	269	4	no	—
366	C₂²⋊C₄	—	269	4	no	—
367	C₂²⋊C₄	—	269	2	no	—
368	C₂²⋊C₄	—	269	2	no	—
369	C₂²⋊C₄	—	269	4	no	—
370	C₂²⋊C₄	—	269	4	no	—
371	C₂²⋊C₄	—	269	4	no	—
372	C₂²⋊C₄	—	269	4	no	—
373	C₂²⋊C₄	—	269	4	no	—
374	C₂²⋊C₄	C₂²×D₂₆₉	1	2	yes	—
375	C₂²⋊C₄	C₂²×D₂₆₉	1	2	yes	—
376	C₂²⋊C₄	C₂²×D₂₆₉	1	2	yes	—
377	C₄²	—	269	2	no	—
378	C₄²	—	269	2	no	—
379	C₄²	—	269	2	no	—
380	C₄²	C₂²×D₂₆₉	1	1	yes	characteristic
381	C₄²	C₂²×D₂₆₉	1	1	yes	characteristic
382	C₄²	C₂²×D₂₆₉	1	2	yes	—
383	C₄²	C₂²×D₂₆₉	1	2	yes	—
384	C₄²	C₂²×D₂₆₉	1	1	yes	characteristic
385	C₄²	C₂²×D₂₆₉	1	1	yes	characteristic
386	C₄²	C₂²×D₂₆₉	1	2	yes	—
387	C₂³	—	269	4	no	—
388	C₂³	—	269	2	no	—
389	C₂³	—	538	4	no	—
390	C₂³	—	1076	2	no	—
391	C₂³	—	1076	2	no	—
392	C₂³	C₂³×D₂₆₉	1	2	yes	—
393	C₂³	C₂³×D₂₆₉	1	1	yes	characteristic
394	Q₈	—	2	2	no	—
395	Q₈	—	538	2	no	—
396	Q₈	—	1076	4	no	—
397	D₄	—	2	4	no	—
398	D₄	—	2	2	no	—
399	D₄	—	538	4	no	—
400	D₄	—	538	4	no	—
401	D₄	—	538	4	no	—
402	D₄	—	538	2	no	—
403	D₄	—	1076	4	no	—
404	D₄	—	1076	4	no	—
405	D₄	—	1076	4	no	—
406	D₄	—	1076	4	no	—
407	D₄	—	1076	4	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	4	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	269	2	no	—
414	C₂×C₄	—	269	2	no	—
415	C₂×C₄	—	269	2	no	—
416	C₂×C₄	—	269	4	no	—
417	C₂×C₄	—	538	4	no	—
418	C₂×C₄	—	538	8	no	—
419	C₂×C₄	—	538	4	no	—
420	C₂×C₄	—	1076	4	no	—
421	C₂×C₄	—	1076	2	no	—
422	C₂×C₄	—	1076	2	no	—
423	C₂×C₄	#16864402	1	4	yes	complemented
424	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
425	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
426	C₂×C₄	C₂³×D₂₆₉	1	2	yes	—
427	C₂×C₄	C₂³×D₂₆₉	1	2	yes	—
428	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
429	C₂×C₄	C₂³×D₂₆₉	1	2	yes	—
430	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
431	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
432	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
433	C₂²	—	2	1	no	—
434	C₂²	—	2	1	no	—
435	C₂²	—	2	2	no	—
436	C₂²	—	2	2	no	—
437	C₂²	—	2	2	no	—
438	C₂²	—	538	2	no	—
439	C₂²	—	538	4	no	—
440	C₂²	—	538	4	no	—
441	C₂²	—	538	2	no	—
442	C₂²	—	538	2	no	—
443	C₂²	—	538	4	no	—
444	C₂²	—	1076	8	no	—
445	C₂²	C₂×#16864402	1	2	yes	—
446	C₂²	C₂⁴×D₂₆₉	1	1	yes	characteristic
447	C₄	—	2	2	no	—
448	C₄	—	2	1	no	—
449	C₄	—	2	2	no	—
450	C₄	—	2	1	no	—
451	C₄	—	2	1	no	—
452	C₄	—	2	2	no	—
453	C₄	—	538	2	no	—
454	C₄	—	538	4	no	—
455	C₄	—	538	2	no	—
456	C₄	—	538	2	no	—
457	C₄	C₂×#16864402	1	2	yes	—
458	C₄	C₂×#16864402	1	2	yes	—
459	C₄	#22575499	1	2	yes	—
460	C₂	—	2	2	no	—
461	C₂	—	4	2	no	—
462	C₂	—	1076	4	no	—
463	C₂	—	1076	2	no	—
464	C₂	C₂²×#16864402	1	1	yes	characteristic
465	C₂	C₂×#22575499	1	1	yes	characteristic
466	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	C₄×#41×C₂₆₉	C₂
hypercenter	C₄×#41	D₂₆₉
hypocenter	C₂₆₉	#3460
LCS	G ▷ C₂²×C₂₆₉ ▷ C₂₆₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×#41

Complements

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

N	H ≅ G/N	type
1. #31771233	C₂	semidirect
2. #31771227	C₂	semidirect
3. #31771226	C₂	semidirect
4. #31771210	C₂	semidirect
5. #31771206	C₂	semidirect
6. #31771188	C₂	semidirect
7. #31771183	C₂	semidirect
8. #31771174	C₂	semidirect
9. #31771169	C₂	semidirect
10. #31771155	C₂	semidirect
11. #31771152	C₂	semidirect
12. #31771142	C₂	semidirect
13. #31771139	C₂	semidirect
14. #31771114	C₂	semidirect
15. C₄×#16864402	C₂	semidirect
16. C₂×C₄×D₁₀₇₆	C₂	semidirect
17. C₄×#41×C₂₆₉	C₂	semidirect
19. C₂×#16864402	C₂²	semidirect
22. #22575453	C₂²	semidirect
23. #22575452	C₂²	semidirect
26. #22575448	C₂²	semidirect
27. #22575447	C₂²	semidirect
28. #22575445	C₂²	semidirect
29. #22575444	C₂²	semidirect
32. #22575441	C₂²	semidirect
33. #22575439	C₂²	semidirect
34. #22575438	C₂²	semidirect
35. #22575438	C₂²	semidirect
36. #22575436	C₂²	semidirect
37. #22575435	C₂²	semidirect
38. #22575432	C₂²	semidirect
39. #22575431	C₂²	semidirect
41. #22575429	C₂²	semidirect
46. #22575427	C₂²	semidirect
47. #22575427	C₂²	semidirect
48. #22575426	C₂²	semidirect
49. #22575426	C₂²	semidirect
51. #22575424	C₂²	semidirect
54. C₄×Dic₅₃₈	C₂²	semidirect
55. C₄×Dic₅₃₈	C₂²	semidirect
60. C₄×D₁₀₇₆	C₂²	semidirect
61. C₄×D₁₀₇₆	C₂²	semidirect
62. C₄×D₁₀₇₆	C₂²	semidirect
65. C₄×C₂²⋊D₂₆₉	C₂²	semidirect
67. #22575410	C₂²	semidirect
68. #22575410	C₂²	semidirect
71. C₄²×D₂₆₉	C₂²	semidirect
73. C₄×Q₈×C₂₆₉	C₂²	semidirect
74. C₄×Q₈×C₂₆₉	C₂²	semidirect
77. C₄×D₄×C₂₆₉	C₂²	semidirect
78. C₄×D₄×C₂₆₉	C₂²	semidirect
80. #117×C₂₆₉	C₂²	semidirect
82. C₂×C₄²×C₂₆₉	C₂²	semidirect
189. C₂×C₄×C₂₆₉	#41	semidirect
233. C₂₆₉	#3460	semidirect
250. C₄×#41	D₂₆₉	semidirect
291. C₄×Q₈	C₂×D₂₆₉	semidirect
292. C₄×Q₈	C₂×D₂₆₉	semidirect
305. C₄×D₄	C₂×D₂₆₉	semidirect
306. C₄×D₄	C₂×D₂₆₉	semidirect
311. #117	C₂×D₂₆₉	semidirect
316. C₂×C₄²	C₂×D₂₆₉	semidirect
423. C₂×C₄	#16864402	semidirect

Maximal subgroups

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

subgroup	index
#31771233	2
#31771227	2
#31771226	2
#31771210	2
#31771206	2
#31771188	2
#31771183	2
#31771174	2
#31771169	2
#31771155	2
#31771152	2
#31771142	2
#31771139	2
#31771114	2
C₄×#16864402	2
C₂×C₄×D₁₀₇₆	2
C₄×#41×C₂₆₉	2
#3460	269