Subgroups — #16743552

Order 3328.

1818 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13128639	C₂	1	2	yes	maximal, complemented
2	#13127792	C₂	1	4	yes	maximal, complemented
3	#13127733	C₂	1	4	yes	maximal, complemented
4	#13127703	C₂	1	4	yes	maximal, complemented
5	#13127701	C₂	1	2	yes	maximal, complemented
6	D₈×Dic₂₆	C₂	1	2	yes	maximal, complemented
7	#13125372	C₂	1	2	yes	maximal, complemented
8	#13125350	C₂	1	1	yes	maximal, characteristic, complemented
9	#13124663	C₂	1	4	yes	maximal, complemented
10	#13124633	C₂	1	2	yes	maximal, complemented
11	#13123770	C₂	1	1	yes	maximal, characteristic, complemented
12	#13123688	C₂	1	2	yes	maximal
13	C₂×C₄×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic
14	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
16	#11719503	C₂²	1	4	yes	—
17	C₂×#88178	—	2	4	no	—
18	#11719248	—	2	2	no	—
19	#11719248	C₂²	1	4	yes	complemented
20	#11719244	—	2	4	no	—
21	#11719244	C₂²	1	8	yes	complemented
22	D₄×Dic₂₆	—	2	2	no	—
23	D₄×Dic₂₆	C₂²	1	4	yes	complemented
24	#11719205	C₂²	1	4	yes	—
25	#11719188	—	2	4	no	—
26	#11719175	C₂²	1	2	yes	—
27	#11719175	C₂²	1	1	yes	characteristic
28	C₄×C₁₃×D₈	C₂²	1	2	yes	—
29	C₄×C₁₃×D₈	C₂²	1	2	yes	—
30	C₄×C₁₃×D₈	C₂²	1	2	yes	—
31	C₄×C₁₃×D₈	C₂²	1	2	yes	—
32	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×#102	C₂²	1	2	yes	—
34	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
35	#11718876	C₂²	1	4	yes	—
36	#11718813	C₂²	1	8	yes	—
37	D₈×Dic₁₃	C₂²	1	4	yes	—
38	D₈×Dic₁₃	C₂²	1	4	yes	—
39	#11718767	C₂²	1	2	yes	—
40	#11718767	C₂²	1	2	yes	—
41	#11718763	C₂²	1	2	yes	—
42	#11718762	C₂²	1	2	yes	—
43	#11718670	C₂²	1	8	yes	complemented
44	#11718669	C₂²	1	4	yes	complemented
45	#11718668	C₂²	1	4	yes	complemented
46	#11718625	C₂²	1	4	yes	—
47	#11718585	C₂²	1	1	yes	characteristic
48	#11718539	C₂²	1	4	yes	complemented
49	#11718537	C₂²	1	8	yes	complemented
50	#11718535	C₂²	1	4	yes	complemented
51	#11718427	C₂²	1	8	yes	complemented
52	#11718424	C₂²	1	8	yes	complemented
53	#11718422	C₂²	1	8	yes	complemented
54	#11718420	C₂²	1	8	yes	complemented
55	#11718344	C₂²	1	2	yes	complemented
56	#11718344	C₂²	1	2	yes	complemented
57	#11718343	C₂²	1	1	yes	characteristic, complemented
58	#11718343	C₂²	1	1	yes	characteristic, complemented
59	#11718341	C₂²	1	2	yes	complemented
60	#11718340	C₂²	1	2	yes	complemented
61	#11718340	C₂²	1	2	yes	complemented
62	C₈×Dic₂₆	C₂²	1	2	yes	complemented
63	C₈×Dic₂₆	C₂²	1	2	yes	complemented
64	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
65	C₂³×C₄×C₁₃	—	2	2	no	—
66	C₂²×Dic₂₆	—	2	4	no	—
67	C₂×C₁₃×D₈	Q₈	1	8	yes	complemented
68	C₂×C₁₃×D₈	C₂³	1	2	yes	—
69	C₂×C₁₃×D₈	C₂³	1	2	yes	—
70	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
72	C₄×D₄×C₁₃	—	2	2	no	—
73	C₄×D₄×C₁₃	—	2	2	no	—
74	C₄×D₄×C₁₃	C₂³	1	4	yes	—
75	C₄×D₄×C₁₃	C₂³	1	4	yes	—
76	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
77	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
78	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
79	C₂×C₂²⋊Dic₁₃	—	2	8	no	—
80	D₄×Dic₁₃	—	2	4	no	—
81	D₄×Dic₁₃	—	2	4	no	—
82	D₄×Dic₁₃	C₂³	1	8	yes	—
83	D₄×Dic₁₃	C₂³	1	8	yes	—
84	#88180	C₂³	1	4	yes	—
85	#88180	C₂³	1	2	yes	—
86	C₂×C₄⋊Dic₁₃	—	2	4	no	—
87	#88178	—	2	2	no	—
88	#88178	—	2	2	no	—
89	#88178	—	2	4	no	—
90	#88178	—	2	8	no	—
91	#88178	—	2	4	no	—
92	#88178	—	2	8	no	—
93	#88178	D₄	1	2	yes	—
94	#88178	D₄	1	2	yes	—
95	C₂×#6101	—	2	8	no	—
96	C₂×#6099	C₂³	1	2	yes	—
97	#88144	—	2	4	no	—
98	#88144	C₂³	1	8	yes	—
99	#88142	—	2	4	no	—
100	#88142	C₂³	1	8	yes	—
101	#88132	—	2	8	no	—
102	#88132	—	2	8	no	—
103	#88132	—	2	8	no	—
104	#88132	—	2	8	no	—
105	#88124	D₄	1	2	yes	—
106	#88124	C₂³	1	4	yes	—
107	#88123	D₄	1	1	yes	characteristic
108	#88123	D₄	1	1	yes	characteristic
109	#88123	C₂³	1	2	yes	—
110	#88123	C₂³	1	2	yes	—
111	C₄×Dic₂₆	—	2	2	no	—
112	C₄×Dic₂₆	—	2	2	no	—
113	C₄×Dic₂₆	C₂³	1	2	yes	—
114	C₄×Dic₂₆	C₂³	1	2	yes	—
115	C₁₃×#107	C₂³	1	2	yes	—
116	C₁₃×#107	C₂³	1	2	yes	—
117	C₁₃×#102	C₂³	1	4	yes	—
118	C₁₃×#102	C₂³	1	4	yes	—
119	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
120	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
121	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
122	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
123	#88072	C₂³	1	8	yes	—
124	#88072	C₂³	1	8	yes	—
125	#88058	C₂³	1	2	yes	—
126	#88058	C₂³	1	2	yes	—
127	#88058	C₂³	1	2	yes	—
128	#88058	C₂³	1	2	yes	—
129	#88057	C₂³	1	4	yes	—
130	#88057	C₂³	1	4	yes	—
131	#88055	C₂³	1	4	yes	—
132	#88054	C₂³	1	4	yes	—
133	#88054	C₂³	1	4	yes	—
134	C₈×Dic₁₃	C₂³	1	4	yes	—
135	#88048	C₂³	1	8	yes	—
136	#88047	C₂³	1	8	yes	—
137	C₄⋊#1055	C₂³	1	2	yes	—
138	C₄⋊#1055	C₂³	1	2	yes	—
139	#61370	—	13	1	no	maximal, Sylow
140	C₂⁴×C₁₃	—	2	2	no	—
141	C₂×D₄×C₁₃	—	2	2	no	—
142	C₂×D₄×C₁₃	—	2	4	no	—
143	C₂×D₄×C₁₃	C₂×Q₈	1	8	yes	complemented
144	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
145	C₂²×C₄×C₁₃	—	2	2	no	—
146	C₂²×C₄×C₁₃	—	2	4	no	—
147	C₂²×C₄×C₁₃	—	2	4	no	—
148	C₂²×C₄×C₁₃	—	8	4	no	—
149	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
152	C₂²×Dic₁₃	—	2	8	no	—
153	C₂²×Dic₁₃	—	2	8	no	—
154	C₂×Dic₂₆	—	2	2	no	—
155	C₂×Dic₂₆	—	2	2	no	—
156	C₂×Dic₂₆	—	2	8	no	—
157	C₂×Dic₂₆	—	8	8	no	—
158	C₂×Dic₂₆	C₂×D₄	1	2	yes	—
159	C₂×Dic₂₆	C₂×D₄	1	2	yes	—
160	C₁₃×D₈	C₂×Q₈	1	8	yes	complemented
161	C₁₃×D₈	C₂×Q₈	1	8	yes	complemented
162	C₂×C₈×C₁₃	—	2	2	no	—
163	C₂×C₈×C₁₃	C₂×Q₈	1	4	yes	complemented
164	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
165	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
166	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
167	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
168	C₁₃×C₄⋊C₄	—	2	2	no	—
169	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
170	C₁₃×C₂²⋊C₄	—	2	4	no	—
171	C₁₃×C₂²⋊C₄	—	2	4	no	—
172	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
173	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
174	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
175	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
176	C₂²⋊Dic₁₃	—	2	4	no	—
177	C₂²⋊Dic₁₃	—	2	8	no	—
178	C₂²⋊Dic₁₃	—	2	8	no	—
179	C₂²⋊Dic₁₃	C₂×D₄	1	4	yes	—
180	C₄⋊Dic₁₃	—	2	2	no	—
181	C₄⋊Dic₁₃	—	2	2	no	—
182	C₄⋊Dic₁₃	—	2	8	no	—
183	C₄⋊Dic₁₃	C₂×D₄	1	2	yes	—
184	C₄⋊Dic₁₃	C₂×D₄	1	2	yes	—
185	C₄⋊Dic₁₃	C₂×D₄	1	2	yes	—
186	C₄⋊Dic₁₃	C₂×D₄	1	2	yes	—
187	C₄⋊Dic₁₃	C₂⁴	1	4	yes	—
188	C₄⋊Dic₁₃	C₂⁴	1	4	yes	—
189	#6101	—	2	4	no	—
190	#6101	—	2	4	no	—
191	#6101	—	2	8	no	—
192	#6101	—	2	8	no	—
193	#6101	C₂×D₄	1	4	yes	—
194	#6101	C₂×D₄	1	4	yes	—
195	C₄×Dic₁₃	—	2	4	no	—
196	C₄×Dic₁₃	C₂⁴	1	4	yes	—
197	#6099	—	2	4	no	—
198	C₂×#1055	C₂⁴	1	4	yes	—
199	#3501	—	13	2	no	—
200	#3389	—	13	4	no	—
201	#3384	—	13	4	no	—
202	#3380	—	13	2	no	—
203	#3380	—	13	4	no	—
204	Q₈×D₈	—	13	2	no	—
205	#3164	—	13	2	no	—
206	#3160	—	13	1	no	—
207	#3081	—	13	4	no	—
208	#3077	—	13	2	no	—
209	#2960	—	13	1	no	—
210	#2948	—	13	2	no	—
211	C₂×C₄×D₈	D₁₃	1	1	yes	characteristic
212	C₂³×C₁₃	—	2	4	no	—
213	C₂³×C₁₃	—	2	8	no	—
214	C₂³×C₁₃	—	8	2	no	—
215	C₂³×C₁₃	—	8	2	no	—
216	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
217	D₄×C₁₃	—	2	8	no	—
218	D₄×C₁₃	—	2	4	no	—
219	D₄×C₁₃	C₂²×Q₈	1	8	yes	—
220	C₂×C₄×C₁₃	—	2	2	no	—
221	C₂×C₄×C₁₃	—	2	4	no	—
222	C₂×C₄×C₁₃	—	4	1	no	—
223	C₂×C₄×C₁₃	—	4	8	no	—
224	C₂×C₄×C₁₃	—	8	4	no	—
225	C₂×C₄×C₁₃	—	8	2	no	—
226	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
227	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
228	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
229	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
230	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
231	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
232	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
233	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
234	C₂×Dic₁₃	—	2	4	no	—
235	C₂×Dic₁₃	—	2	4	no	—
236	C₂×Dic₁₃	—	8	8	no	—
237	C₂×Dic₁₃	—	8	8	no	—
238	C₂×Dic₁₃	C₂²×D₄	1	4	yes	—
239	C₂×Dic₁₃	C₂²×D₄	1	4	yes	—
240	Dic₂₆	—	2	4	no	—
241	Dic₂₆	—	4	2	no	—
242	Dic₂₆	—	4	4	no	—
243	Dic₂₆	—	8	8	no	—
244	Dic₂₆	—	8	2	no	—
245	C₈×C₁₃	—	2	1	no	—
246	C₈×C₁₃	—	2	1	no	—
247	C₈×C₁₃	C₂²×Q₈	1	2	yes	—
248	C₈×C₁₃	C₂²×Q₈	1	2	yes	—
249	#1055	—	2	4	no	—
250	C₂²×D₈	C₂×D₁₃	1	1	yes	characteristic
251	#554	—	13	4	no	—
252	#554	—	13	8	no	—
253	#554	—	26	4	no	—
254	#554	—	26	2	no	—
255	D₄×Q₈	—	13	4	no	—
256	D₄×Q₈	—	26	2	no	—
257	#544	—	13	4	no	—
258	#543	—	26	4	no	—
259	#533	—	13	1	no	—
260	#533	—	13	2	no	—
261	C₂×C₂²⋊Q₈	—	26	4	no	—
262	#518	—	13	4	no	—
263	C₂×C₄×D₄	C₂×D₁₃	1	2	yes	—
264	#501	—	13	8	no	—
265	#500	—	13	4	no	—
266	#500	—	13	1	no	—
267	#500	—	13	1	no	—
268	#499	—	13	4	no	—
269	#499	—	13	2	no	—
270	#499	—	13	2	no	—
271	#498	—	13	2	no	—
272	#478	—	13	8	no	—
273	#478	—	13	8	no	—
274	#478	—	13	8	no	—
275	#476	—	13	4	no	—
276	#476	—	13	8	no	—
277	#474	—	13	4	no	—
278	#474	—	13	8	no	—
279	#446	—	13	2	no	—
280	#446	—	13	2	no	—
281	C₈×Q₈	—	13	2	no	—
282	C₈×Q₈	—	13	2	no	—
283	#442	—	13	8	no	—
284	C₄×D₈	—	13	4	no	—
285	C₄×D₈	—	13	4	no	—
286	C₄×D₈	C₂×D₁₃	1	2	yes	—
287	C₄×D₈	C₂×D₁₃	1	2	yes	—
288	C₄×D₈	C₂×D₁₃	1	2	yes	—
289	C₄×D₈	C₂×D₁₃	1	2	yes	—
290	#428	—	13	4	no	—
291	#427	—	13	2	no	—
292	#427	—	13	2	no	—
293	C₂×#107	C₂×D₁₃	1	1	yes	characteristic
294	#424	—	13	2	no	—
295	#423	—	13	1	no	—
296	#418	—	13	4	no	—
297	C₂×#102	C₂×D₁₃	1	2	yes	—
298	#405	—	13	2	no	—
299	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
300	C₂²×C₁₃	—	2	1	no	—
301	C₂²×C₁₃	—	2	1	no	—
302	C₂²×C₁₃	—	2	8	no	—
303	C₂²×C₁₃	—	4	4	no	—
304	C₂²×C₁₃	—	4	4	no	—
305	C₂²×C₁₃	—	8	8	no	—
306	C₂²×C₁₃	D₄×Q₈	1	2	yes	—
307	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
308	C₄×C₁₃	—	2	1	no	—
309	C₄×C₁₃	—	2	1	no	—
310	C₄×C₁₃	—	2	1	no	—
311	C₄×C₁₃	—	4	4	no	—
312	C₄×C₁₃	D₄×Q₈	1	2	yes	—
313	C₄×C₁₃	#576	1	2	yes	—
314	C₄×C₁₃	C₂³×Q₈	1	1	yes	characteristic
315	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
316	Dic₁₃	—	2	4	no	—
317	Dic₁₃	—	2	4	no	—
318	Dic₁₃	—	4	4	no	—
319	Dic₁₃	—	4	4	no	—
320	C₂²×Q₈	—	26	4	no	—
321	C₂²×D₄	C₂²×D₁₃	1	2	yes	—
322	C₂³×C₄	—	2	2	no	—
323	C₂×D₈	Dic₂₆	1	8	yes	complemented
324	C₂×D₈	C₂²×D₁₃	1	2	yes	—
325	C₂×D₈	C₂²×D₁₃	1	2	yes	—
326	C₂×M₁₆	—	13	2	no	—
327	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
328	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
329	C₄⋊Q₈	—	13	8	no	—
330	C₄⋊Q₈	—	13	1	no	—
331	C₄⋊Q₈	—	13	1	no	—
332	C₄⋊Q₈	—	13	2	no	—
333	C₄⋊Q₈	—	13	2	no	—
334	C₄⋊Q₈	—	26	4	no	—
335	#125	—	13	8	no	—
336	#125	—	13	2	no	—
337	#125	—	13	4	no	—
338	#125	—	26	4	no	—
339	C₂²⋊Q₈	—	13	2	no	—
340	C₂²⋊Q₈	—	13	2	no	—
341	C₂²⋊Q₈	—	26	8	no	—
342	C₂²⋊Q₈	—	26	8	no	—
343	C₂²⋊Q₈	—	26	8	no	—
344	C₂²⋊Q₈	—	26	8	no	—
345	C₂²⋊Q₈	—	26	8	no	—
346	C₂²⋊Q₈	—	26	4	no	—
347	C₂²⋊Q₈	—	26	8	no	—
348	C₂²⋊Q₈	—	26	4	no	—
349	C₂²⋊Q₈	—	26	2	no	—
350	C₂²⋊Q₈	—	26	2	no	—
351	C₄×Q₈	—	13	2	no	—
352	C₄×Q₈	—	13	2	no	—
353	C₄×Q₈	—	26	2	no	—
354	C₄×Q₈	—	26	2	no	—
355	C₄×D₄	—	2	2	no	—
356	C₄×D₄	—	2	2	no	—
357	C₄×D₄	—	13	8	no	—
358	C₄×D₄	—	13	8	no	—
359	C₄×D₄	—	26	4	no	—
360	C₄×D₄	—	26	4	no	—
361	C₄×D₄	C₂²×D₁₃	1	4	yes	—
362	C₄×D₄	C₂²×D₁₃	1	4	yes	—
363	#117	—	13	2	no	—
364	#117	—	13	4	no	—
365	C₂×C₄⋊C₄	—	26	8	no	—
366	C₂×C₄⋊C₄	—	26	4	no	—
367	C₂×C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
368	C₂×C₂²⋊C₄	—	2	2	no	—
369	C₂×C₂²⋊C₄	—	26	8	no	—
370	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
371	#107	—	13	2	no	—
372	#107	—	13	2	no	—
373	#107	—	13	2	no	—
374	#107	—	13	2	no	—
375	#107	—	13	8	no	—
376	#107	C₂²×D₁₃	1	2	yes	—
377	#107	C₂²×D₁₃	1	2	yes	—
378	#106	—	13	4	no	—
379	#106	—	13	4	no	—
380	#106	—	13	8	no	—
381	C₄⋊C₈	—	13	4	no	—
382	C₄⋊C₈	—	13	4	no	—
383	C₄⋊C₈	—	13	2	no	—
384	C₄⋊C₈	—	13	2	no	—
385	#102	—	13	8	no	—
386	#102	—	13	8	no	—
387	#102	C₂²×D₁₃	1	4	yes	—
388	#102	C₂²×D₁₃	1	4	yes	—
389	#97	—	13	4	no	—
390	C₄×C₈	—	13	4	no	—
391	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
392	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
393	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
394	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
395	C₂×C₁₃	—	2	2	no	—
396	C₂×C₁₃	—	4	8	no	—
397	C₂×C₁₃	C₂×D₄×Q₈	1	1	yes	characteristic
398	C₂×C₁₃	C₂×#576	1	1	yes	characteristic
399	C₂×C₁₃	#3584	1	1	yes	characteristic
400	C₂⁴	—	2	2	no	—
401	C₂×Q₈	—	13	2	no	—
402	C₂×Q₈	—	13	2	no	—
403	C₂×Q₈	—	26	8	no	—
404	C₂×Q₈	—	26	2	no	—
405	C₂×Q₈	—	26	2	no	—
406	C₂×Q₈	—	104	8	no	—
407	C₂×D₄	—	2	2	no	—
408	C₂×D₄	—	2	4	no	—
409	C₂×D₄	C₂×Dic₂₆	1	8	yes	complemented
410	C₂×D₄	C₂³×D₁₃	1	4	yes	—
411	C₂²×C₄	—	2	2	no	—
412	C₂²×C₄	—	2	4	no	—
413	C₂²×C₄	—	2	4	no	—
414	C₂²×C₄	—	8	4	no	—
415	C₂²×C₄	—	26	8	no	—
416	C₂²×C₄	—	26	8	no	—
417	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
418	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
419	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
420	D₈	C₂×Dic₂₆	1	8	yes	complemented
421	D₈	C₂×Dic₂₆	1	8	yes	complemented
422	M₁₆	—	26	4	no	—
423	C₂×C₈	—	2	2	no	—
424	C₂×C₈	—	13	4	no	—
425	C₂×C₈	C₂×Dic₂₆	1	4	yes	complemented
426	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
427	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
428	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
429	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
430	C₄⋊C₄	—	2	2	no	—
431	C₄⋊C₄	—	13	4	no	—
432	C₄⋊C₄	—	13	2	no	—
433	C₄⋊C₄	—	13	2	no	—
434	C₄⋊C₄	—	13	2	no	—
435	C₄⋊C₄	—	13	4	no	—
436	C₄⋊C₄	—	13	2	no	—
437	C₄⋊C₄	—	13	4	no	—
438	C₄⋊C₄	—	13	4	no	—
439	C₄⋊C₄	—	26	8	no	—
440	C₄⋊C₄	—	26	8	no	—
441	C₄⋊C₄	—	26	8	no	—
442	C₄⋊C₄	—	26	4	no	—
443	C₄⋊C₄	—	26	2	no	—
444	C₄⋊C₄	—	26	4	no	—
445	C₄⋊C₄	—	26	2	no	—
446	C₄⋊C₄	C₂³×D₁₃	1	4	yes	—
447	C₂²⋊C₄	—	2	4	no	—
448	C₂²⋊C₄	—	2	4	no	—
449	C₂²⋊C₄	—	13	4	no	—
450	C₂²⋊C₄	—	26	8	no	—
451	C₂²⋊C₄	—	26	8	no	—
452	C₂²⋊C₄	—	26	4	no	—
453	C₄²	—	13	4	no	—
454	C₄²	—	26	4	no	—
455	C₄²	D₄×D₁₃	1	1	yes	characteristic
456	C₄²	D₄×D₁₃	1	1	yes	characteristic
457	C₄²	C₂³×D₁₃	1	1	yes	characteristic
458	C₄²	C₂³×D₁₃	1	1	yes	characteristic
459	C₁₃	#61370	1	1	yes	characteristic, complemented, Sylow
460	C₂³	—	2	4	no	—
461	C₂³	—	2	8	no	—
462	C₂³	—	8	2	no	—
463	C₂³	—	8	2	no	—
464	C₂³	C₂×D₄×D₁₃	1	1	yes	characteristic
465	Q₈	—	26	4	no	—
466	Q₈	—	52	2	no	—
467	Q₈	—	52	4	no	—
468	Q₈	—	104	2	no	—
469	Q₈	—	104	8	no	—
470	D₄	—	2	8	no	—
471	D₄	—	2	4	no	—
472	D₄	C₂²×Dic₂₆	1	8	yes	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	4	no	—
475	C₂×C₄	—	4	1	no	—
476	C₂×C₄	—	4	8	no	—
477	C₂×C₄	—	8	4	no	—
478	C₂×C₄	—	8	2	no	—
479	C₂×C₄	—	13	4	no	—
480	C₂×C₄	—	13	4	no	—
481	C₂×C₄	—	26	4	no	—
482	C₂×C₄	—	26	4	no	—
483	C₂×C₄	—	104	8	no	—
484	C₂×C₄	—	104	8	no	—
485	C₂×C₄	C₂²×Dic₂₆	1	2	yes	—
486	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
487	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
488	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
489	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
490	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
491	C₂×C₄	#88257	1	2	yes	—
492	C₂×C₄	C₂⁴×D₁₃	1	1	yes	characteristic
493	C₈	—	2	1	no	—
494	C₈	—	2	1	no	—
495	C₈	—	26	4	no	—
496	C₈	C₂²×Dic₂₆	1	2	yes	—
497	C₈	C₂²×Dic₂₆	1	2	yes	—
498	C₂²	—	2	1	no	—
499	C₂²	—	2	1	no	—
500	C₂²	—	2	8	no	—
501	C₂²	—	4	4	no	—
502	C₂²	—	4	4	no	—
503	C₂²	—	8	8	no	—
504	C₂²	D₄×Dic₂₆	1	2	yes	—
505	C₂²	C₂²×D₄×D₁₃	1	1	yes	characteristic
506	C₄	—	2	1	no	—
507	C₄	—	2	1	no	—
508	C₄	—	2	1	no	—
509	C₄	—	4	4	no	—
510	C₄	—	26	4	no	—
511	C₄	—	26	4	no	—
512	C₄	—	52	4	no	—
513	C₄	—	52	4	no	—
514	C₄	D₄×Dic₂₆	1	2	yes	—
515	C₄	#11719462	1	2	yes	—
516	C₄	C₂³×Dic₂₆	1	1	yes	characteristic
517	C₄	C₂×#88257	1	1	yes	characteristic
518	C₂	—	2	2	no	—
519	C₂	—	4	8	no	—
520	C₂	C₂×D₄×Dic₂₆	1	1	yes	characteristic
521	C₂	C₂×#11719462	1	1	yes	characteristic
522	C₂	#13129605	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₄×D₁₃
commutator, cosocle	C₂×C₄×C₁₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₁₃
Fitting	C₂×C₄×C₁₃×D₈	C₂
socle	C₂²×C₁₃	C₂³×D₄
prime radical	C₂²×C₁₃×D₈	C₂²
hypercenter	C₂×C₄×D₈	D₁₃
hypocenter	C₁₃	#61370
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄×D₈

Complements

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

N	H ≅ G/N	type
1. #13128639	C₂	semidirect
2. #13127792	C₂	semidirect
3. #13127733	C₂	semidirect
4. #13127703	C₂	semidirect
5. #13127701	C₂	semidirect
6. D₈×Dic₂₆	C₂	semidirect
7. #13125372	C₂	semidirect
8. #13125350	C₂	semidirect
9. #13124663	C₂	semidirect
10. #13124633	C₂	semidirect
11. #13123770	C₂	semidirect
19. #11719248	C₂²	semidirect
21. #11719244	C₂²	semidirect
23. D₄×Dic₂₆	C₂²	semidirect
43. #11718670	C₂²	semidirect
44. #11718669	C₂²	semidirect
45. #11718668	C₂²	semidirect
48. #11718539	C₂²	semidirect
49. #11718537	C₂²	semidirect
50. #11718535	C₂²	semidirect
51. #11718427	C₂²	semidirect
52. #11718424	C₂²	semidirect
53. #11718422	C₂²	semidirect
54. #11718420	C₂²	semidirect
55. #11718344	C₂²	semidirect
56. #11718344	C₂²	semidirect
57. #11718343	C₂²	semidirect
58. #11718343	C₂²	semidirect
59. #11718341	C₂²	semidirect
60. #11718340	C₂²	semidirect
61. #11718340	C₂²	semidirect
62. C₈×Dic₂₆	C₂²	semidirect
63. C₈×Dic₂₆	C₂²	semidirect
67. C₂×C₁₃×D₈	Q₈	semidirect
143. C₂×D₄×C₁₃	C₂×Q₈	semidirect
160. C₁₃×D₈	C₂×Q₈	semidirect
161. C₁₃×D₈	C₂×Q₈	semidirect
163. C₂×C₈×C₁₃	C₂×Q₈	semidirect
323. C₂×D₈	Dic₂₆	semidirect
409. C₂×D₄	C₂×Dic₂₆	semidirect
420. D₈	C₂×Dic₂₆	semidirect
421. D₈	C₂×Dic₂₆	semidirect
425. C₂×C₈	C₂×Dic₂₆	semidirect
459. C₁₃	#61370	semidirect

Maximal subgroups

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

subgroup	index
#13128639	2
#13127792	2
#13127733	2
#13127703	2
#13127701	2
D₈×Dic₂₆	2
#13125372	2
#13125350	2
#13124663	2
#13124633	2
#13123770	2
#13123688	2
C₂×C₄×C₁₃×D₈	2
#61370	13