Subgroups — #16743557

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	#13128637	C₂	1	2	yes	maximal, complemented
2	#13127797	C₂	1	4	yes	maximal, complemented
3	#13127740	C₂	1	4	yes	maximal, complemented
4	#13127705	C₂	1	2	yes	maximal, complemented
5	#13127700	C₂	1	4	yes	maximal, complemented
6	#13127688	C₂	1	2	yes	maximal, complemented
7	#13125376	C₂	1	2	yes	maximal, complemented
8	#13124670	C₂	1	4	yes	maximal, complemented
9	#13124629	C₂	1	2	yes	maximal, complemented
10	#13123770	C₂	1	1	yes	maximal, characteristic, complemented
11	#13123687	C₂	1	2	yes	maximal
12	C₂×C₄×D₁₀₄	C₂	1	1	yes	maximal, characteristic
13	C₁₃×#3160	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#533	C₂²	1	2	yes	—
15	C₂²×D₁₀₄	C₂²	1	1	yes	characteristic
16	#11719435	C₂²	1	4	yes	complemented
17	#11719432	C₂²	1	4	yes	complemented
18	#11719395	C₂²	1	8	yes	complemented
19	#11719339	—	2	4	no	—
20	D₁₃×C₂²⋊Q₈	—	2	4	no	—
21	#11719284	—	2	4	no	—
22	#11719284	—	2	2	no	—
23	Q₈×D₅₂	—	2	2	no	—
24	#11719226	C₂²	1	4	yes	—
25	#11719224	C₂²	1	4	yes	—
26	C₂×C₄×D₅₂	C₂²	1	2	yes	—
27	#11719175	C₂²	1	1	yes	characteristic
28	C₁₃×#500	C₂²	1	1	yes	characteristic, complemented
29	C₁₃×#500	C₂²	1	1	yes	characteristic, complemented
30	C₁₃×#499	C₂²	1	2	yes	complemented
31	C₁₃×#499	C₂²	1	2	yes	complemented
32	C₁₃×#498	C₂²	1	2	yes	complemented
33	C₁₃×#427	C₂²	1	2	yes	—
34	C₁₃×#427	C₂²	1	2	yes	—
35	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
36	C₂×#88061	C₂²	1	2	yes	—
37	C₂×#88058	C₂²	1	1	yes	characteristic
38	#11718763	C₂²	1	2	yes	—
39	#11718762	C₂²	1	2	yes	—
40	#11718748	C₂²	1	4	yes	complemented
41	#11718745	C₂²	1	4	yes	complemented
42	#11718727	C₂²	1	8	yes	complemented
43	#11718662	C₂²	1	4	yes	—
44	#11718656	C₂²	1	4	yes	—
45	#11718585	C₂²	1	1	yes	characteristic
46	#11718552	C₂²	1	8	yes	complemented
47	#11718551	C₂²	1	8	yes	complemented
48	#11718539	C₂²	1	4	yes	complemented
49	#11718535	C₂²	1	4	yes	complemented
50	#11718533	C₂²	1	4	yes	—
51	#11718533	C₂²	1	4	yes	—
52	#11718532	C₂²	1	8	yes	complemented
53	#11718531	C₂²	1	8	yes	complemented
54	#11718530	C₂²	1	8	yes	—
55	#11718517	C₂²	1	8	yes	complemented
56	C₄×D₁₀₄	C₂²	1	2	yes	—
57	C₄×D₁₀₄	C₂²	1	2	yes	—
58	C₄×D₁₀₄	C₂²	1	2	yes	—
59	C₄×D₁₀₄	C₂²	1	2	yes	—
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	C₂×Q₈×D₁₃	—	2	4	no	—
65	C₂²×D₅₂	C₂³	1	2	yes	—
66	C₂²×C₄×D₁₃	—	2	2	no	—
67	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
68	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
69	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
70	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
71	C₁₃×#125	C₂³	1	4	yes	—
72	C₁₃×C₂²⋊Q₈	—	2	2	no	—
73	C₁₃×C₂²⋊Q₈	—	2	2	no	—
74	C₄×Q₈×C₁₃	—	2	2	no	—
75	C₄×Q₈×C₁₃	—	2	2	no	—
76	C₁₃×#117	C₂³	1	4	yes	—
77	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
78	#88200	—	2	4	no	—
79	#88200	—	2	8	no	—
80	C₂×#6103	—	2	2	no	—
81	#88180	C₂³	1	2	yes	—
82	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
83	#88178	D₄	1	2	yes	—
84	#88178	D₄	1	2	yes	—
85	C₂×#6099	C₂³	1	2	yes	—
86	C₂×D₁₀₄	Q₈	1	8	yes	complemented
87	C₂×D₁₀₄	C₂³	1	2	yes	—
88	C₂×D₁₀₄	C₂³	1	2	yes	—
89	#88151	—	2	4	no	—
90	#88151	—	2	8	no	—
91	#88150	—	2	8	no	—
92	#88150	—	2	8	no	—
93	#88150	—	2	8	no	—
94	#88147	C₂³	1	8	yes	—
95	#88147	C₂³	1	8	yes	—
96	C₄⋊C₄×D₁₃	—	2	4	no	—
97	C₄⋊C₄×D₁₃	—	2	8	no	—
98	#88144	C₂³	1	8	yes	—
99	#88142	C₂³	1	8	yes	—
100	C₂²⋊C₄×D₁₃	—	2	8	no	—
101	#88132	—	2	8	no	—
102	C₄×D₅₂	—	2	2	no	—
103	C₄×D₅₂	—	2	2	no	—
104	C₄×D₅₂	—	2	4	no	—
105	C₄×D₅₂	—	2	4	no	—
106	C₄×D₅₂	C₂³	1	4	yes	—
107	C₄×D₅₂	C₂³	1	4	yes	—
108	#88124	—	2	4	no	—
109	#88124	D₄	1	2	yes	—
110	#88123	—	2	4	no	—
111	#88123	D₄	1	1	yes	characteristic
112	#88123	D₄	1	1	yes	characteristic
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×#107	C₂³	1	2	yes	—
118	C₁₃×#107	C₂³	1	2	yes	—
119	C₁₃×#106	C₂³	1	4	yes	—
120	C₁₃×#106	C₂³	1	4	yes	—
121	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
122	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
123	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
124	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
125	#88061	C₂³	1	4	yes	—
126	#88061	C₂³	1	4	yes	—
127	#88058	C₂³	1	2	yes	—
128	#88058	C₂³	1	2	yes	—
129	#88055	C₂³	1	4	yes	—
130	#88054	C₂³	1	4	yes	—
131	#88054	C₂³	1	4	yes	—
132	C₈×Dic₁₃	C₂³	1	4	yes	—
133	#88049	C₂³	1	8	yes	—
134	#88049	C₂³	1	8	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	C₂³×D₁₃	—	2	2	no	—
141	C₂×Q₈×C₁₃	—	2	2	no	—
142	C₂×Q₈×C₁₃	—	2	2	no	—
143	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
146	C₂²×Dic₁₃	—	2	2	no	—
147	Q₈×D₁₃	—	8	8	no	—
148	C₂×D₅₂	—	2	2	no	—
149	C₂×D₅₂	—	2	4	no	—
150	C₂×D₅₂	C₂×Q₈	1	8	yes	complemented
151	C₂×D₅₂	C₂⁴	1	4	yes	—
152	C₂×C₄×D₁₃	—	2	4	no	—
153	C₂×C₄×D₁₃	—	2	4	no	—
154	C₂×C₄×D₁₃	—	2	8	no	—
155	C₂×C₄×D₁₃	—	2	8	no	—
156	C₂×C₄×D₁₃	—	8	4	no	—
157	C₂×Dic₂₆	—	2	8	no	—
158	C₂×Dic₂₆	C₂×D₄	1	2	yes	—
159	C₂×Dic₂₆	C₂×D₄	1	2	yes	—
160	C₂×C₈×C₁₃	—	2	2	no	—
161	C₂×C₈×C₁₃	C₂×Q₈	1	4	yes	complemented
162	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
163	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
164	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
165	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
166	C₁₃×C₄⋊C₄	—	2	4	no	—
167	C₁₃×C₄⋊C₄	—	2	2	no	—
168	C₁₃×C₄⋊C₄	—	2	2	no	—
169	C₁₃×C₄⋊C₄	—	2	4	no	—
170	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
171	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
172	C₁₃×C₂²⋊C₄	—	2	4	no	—
173	C₄²×C₁₃	—	2	4	no	—
174	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
175	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
176	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
177	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
178	C₂²⋊Dic₁₃	C₂×D₄	1	4	yes	—
179	#6103	—	2	4	no	—
180	#6103	—	2	4	no	—
181	#6103	—	2	8	no	—
182	#6103	—	2	8	no	—
183	C₄⋊Dic₁₃	—	2	2	no	—
184	C₄⋊Dic₁₃	—	2	8	no	—
185	C₄⋊Dic₁₃	C₂×D₄	1	2	yes	—
186	C₄⋊Dic₁₃	C₂×D₄	1	2	yes	—
187	C₄⋊Dic₁₃	C₂×D₄	1	2	yes	—
188	C₄⋊Dic₁₃	C₂×D₄	1	2	yes	—
189	C₄⋊Dic₁₃	C₂⁴	1	4	yes	—
190	#6101	—	2	8	no	—
191	#6101	—	2	8	no	—
192	#6101	C₂×D₄	1	4	yes	—
193	#6101	C₂×D₄	1	4	yes	—
194	C₄×Dic₁₃	C₂⁴	1	4	yes	—
195	#6099	—	2	4	no	—
196	C₂×#1055	C₂⁴	1	4	yes	—
197	D₁₀₄	C₂×Q₈	1	8	yes	complemented
198	D₁₀₄	C₂×Q₈	1	8	yes	complemented
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	D₁₃	1	1	yes	characteristic, complemented
207	#3081	—	13	4	no	—
208	#3077	—	13	2	no	—
209	#2960	—	13	1	no	—
210	#2948	—	13	2	no	—
211	C₂×C₄×D₈	—	13	1	no	—
212	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
213	C₂²×D₁₃	—	2	4	no	—
214	C₂²×D₁₃	—	2	8	no	—
215	C₂²×D₁₃	—	8	2	no	—
216	C₂²×D₁₃	—	8	2	no	—
217	Q₈×C₁₃	—	4	4	no	—
218	Q₈×C₁₃	—	8	2	no	—
219	C₂×C₄×C₁₃	—	2	2	no	—
220	C₂×C₄×C₁₃	—	2	4	no	—
221	C₂×C₄×C₁₃	—	2	4	no	—
222	C₂×C₄×C₁₃	—	4	1	no	—
223	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
224	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
225	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
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×Q₈	1	2	yes	—
229	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
230	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
231	C₂×Dic₁₃	—	2	4	no	—
232	C₂×Dic₁₃	—	8	2	no	—
233	C₂×Dic₁₃	C₂²×D₄	1	4	yes	—
234	C₂×Dic₁₃	C₂²×D₄	1	4	yes	—
235	D₅₂	—	2	8	no	—
236	D₅₂	—	2	4	no	—
237	D₅₂	C₂²×Q₈	1	8	yes	—
238	C₄×D₁₃	—	4	8	no	—
239	C₄×D₁₃	—	8	8	no	—
240	C₄×D₁₃	—	8	8	no	—
241	C₄×D₁₃	—	8	4	no	—
242	Dic₂₆	—	2	4	no	—
243	Dic₂₆	—	4	2	no	—
244	Dic₂₆	—	8	8	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	—	13	1	no	—
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	C₂×D₁₃	1	2	yes	—
261	C₂×C₂²⋊Q₈	—	26	4	no	—
262	#518	—	13	4	no	—
263	C₂×C₄×D₄	—	13	2	no	—
264	#501	—	13	8	no	—
265	#500	—	13	4	no	—
266	#500	C₂×D₁₃	1	1	yes	characteristic, complemented
267	#500	C₂×D₁₃	1	1	yes	characteristic, complemented
268	#499	—	13	4	no	—
269	#499	C₂×D₁₃	1	2	yes	complemented
270	#499	C₂×D₁₃	1	2	yes	complemented
271	#498	C₂×D₁₃	1	2	yes	complemented
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	—	13	2	no	—
287	C₄×D₈	—	13	2	no	—
288	C₄×D₈	—	13	2	no	—
289	C₄×D₈	—	13	2	no	—
290	#428	—	13	4	no	—
291	#427	C₂×D₁₃	1	2	yes	—
292	#427	C₂×D₁₃	1	2	yes	—
293	C₂×#107	—	13	1	no	—
294	#424	—	13	2	no	—
295	#423	—	13	1	no	—
296	#418	—	13	4	no	—
297	C₂×#102	—	13	2	no	—
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	D₄×Q₈	1	2	yes	—
303	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
304	C₂×D₁₃	—	2	8	no	—
305	C₂×D₁₃	—	4	4	no	—
306	C₂×D₁₃	—	4	4	no	—
307	C₂×D₁₃	—	8	8	no	—
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	—	4	4	no	—
313	C₄×C₁₃	D₄×Q₈	1	2	yes	—
314	C₄×C₁₃	#576	1	2	yes	—
315	C₄×C₁₃	C₂³×Q₈	1	1	yes	characteristic
316	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
317	Dic₁₃	—	2	4	no	—
318	Dic₁₃	—	2	4	no	—
319	Dic₁₃	—	4	4	no	—
320	C₂²×Q₈	—	26	4	no	—
321	C₂²×D₄	—	13	2	no	—
322	C₂³×C₄	—	26	2	no	—
323	C₂×D₈	—	13	8	no	—
324	C₂×D₈	—	13	2	no	—
325	C₂×D₈	—	13	2	no	—
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	—	26	4	no	—
333	C₄⋊Q₈	C₂²×D₁₃	1	2	yes	—
334	C₄⋊Q₈	C₂²×D₁₃	1	2	yes	—
335	#125	—	13	8	no	—
336	#125	—	13	2	no	—
337	#125	—	26	4	no	—
338	#125	C₂²×D₁₃	1	4	yes	—
339	C₂²⋊Q₈	—	2	2	no	—
340	C₂²⋊Q₈	—	2	2	no	—
341	C₂²⋊Q₈	—	13	2	no	—
342	C₂²⋊Q₈	—	13	2	no	—
343	C₂²⋊Q₈	—	26	8	no	—
344	C₂²⋊Q₈	—	26	8	no	—
345	C₂²⋊Q₈	—	26	8	no	—
346	C₂²⋊Q₈	—	26	8	no	—
347	C₂²⋊Q₈	—	26	4	no	—
348	C₂²⋊Q₈	—	26	8	no	—
349	C₂²⋊Q₈	—	26	4	no	—
350	C₂²⋊Q₈	—	26	8	no	—
351	C₄×Q₈	—	2	2	no	—
352	C₄×Q₈	—	2	2	no	—
353	C₄×Q₈	—	13	2	no	—
354	C₄×Q₈	—	13	2	no	—
355	C₄×D₄	—	13	8	no	—
356	C₄×D₄	—	13	8	no	—
357	C₄×D₄	—	13	4	no	—
358	C₄×D₄	—	13	4	no	—
359	C₄×D₄	—	26	4	no	—
360	C₄×D₄	—	26	4	no	—
361	C₄×D₄	—	26	2	no	—
362	C₄×D₄	—	26	2	no	—
363	#117	—	13	2	no	—
364	#117	C₂²×D₁₃	1	4	yes	—
365	C₂×C₄⋊C₄	—	13	2	no	—
366	C₂×C₄⋊C₄	—	26	8	no	—
367	C₂×C₄⋊C₄	—	26	4	no	—
368	C₂×C₂²⋊C₄	—	26	8	no	—
369	C₂×C₂²⋊C₄	—	26	2	no	—
370	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
371	#107	—	13	2	no	—
372	#107	—	13	2	no	—
373	#107	—	13	8	no	—
374	#107	C₂²×D₁₃	1	2	yes	—
375	#107	C₂²×D₁₃	1	2	yes	—
376	#107	C₂²×D₁₃	1	2	yes	—
377	#107	C₂²×D₁₃	1	2	yes	—
378	#106	—	13	8	no	—
379	#106	C₂²×D₁₃	1	4	yes	—
380	#106	C₂²×D₁₃	1	4	yes	—
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	4	no	—
386	#102	—	13	4	no	—
387	#102	—	13	8	no	—
388	#102	—	13	8	no	—
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	C₂×D₄×Q₈	1	1	yes	characteristic
397	C₂×C₁₃	C₂×#576	1	1	yes	characteristic
398	C₂×C₁₃	#3584	1	1	yes	characteristic
399	D₁₃	—	4	8	no	—
400	C₂⁴	—	26	2	no	—
401	C₂×Q₈	—	2	2	no	—
402	C₂×Q₈	—	2	2	no	—
403	C₂×Q₈	—	13	2	no	—
404	C₂×Q₈	—	13	2	no	—
405	C₂×Q₈	—	26	8	no	—
406	C₂×Q₈	—	104	8	no	—
407	C₂×D₄	—	13	8	no	—
408	C₂×D₄	—	13	4	no	—
409	C₂×D₄	—	26	2	no	—
410	C₂×D₄	—	26	4	no	—
411	C₂²×C₄	—	26	8	no	—
412	C₂²×C₄	—	26	8	no	—
413	C₂²×C₄	—	26	2	no	—
414	C₂²×C₄	—	26	4	no	—
415	C₂²×C₄	—	26	4	no	—
416	C₂²×C₄	—	104	4	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	—	13	8	no	—
421	D₈	—	13	8	no	—
422	M₁₆	—	26	4	no	—
423	C₂×C₈	—	2	2	no	—
424	C₂×C₈	—	13	4	no	—
425	C₂×C₈	Q₈×D₁₃	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	4	no	—
431	C₄⋊C₄	—	2	2	no	—
432	C₄⋊C₄	—	2	4	no	—
433	C₄⋊C₄	—	2	2	no	—
434	C₄⋊C₄	—	13	4	no	—
435	C₄⋊C₄	—	13	2	no	—
436	C₄⋊C₄	—	13	2	no	—
437	C₄⋊C₄	—	13	2	no	—
438	C₄⋊C₄	—	13	4	no	—
439	C₄⋊C₄	—	13	2	no	—
440	C₄⋊C₄	—	13	4	no	—
441	C₄⋊C₄	—	26	8	no	—
442	C₄⋊C₄	—	26	8	no	—
443	C₄⋊C₄	—	26	8	no	—
444	C₄⋊C₄	—	26	2	no	—
445	C₄⋊C₄	C₂³×D₁₃	1	4	yes	—
446	C₄⋊C₄	C₂³×D₁₃	1	4	yes	—
447	C₂²⋊C₄	—	2	4	no	—
448	C₂²⋊C₄	—	13	4	no	—
449	C₂²⋊C₄	—	26	8	no	—
450	C₂²⋊C₄	—	26	8	no	—
451	C₂²⋊C₄	—	26	4	no	—
452	C₂²⋊C₄	—	26	4	no	—
453	C₄²	—	2	4	no	—
454	C₄²	—	13	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	—	26	4	no	—
461	C₂³	—	26	8	no	—
462	C₂³	—	104	2	no	—
463	C₂³	—	104	2	no	—
464	C₂³	C₂×D₄×D₁₃	1	1	yes	characteristic
465	Q₈	—	4	4	no	—
466	Q₈	—	8	2	no	—
467	Q₈	—	26	4	no	—
468	Q₈	—	52	2	no	—
469	Q₈	—	104	8	no	—
470	D₄	—	13	8	no	—
471	D₄	—	26	8	no	—
472	D₄	—	26	4	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	4	no	—
475	C₂×C₄	—	2	4	no	—
476	C₂×C₄	—	4	1	no	—
477	C₂×C₄	—	13	4	no	—
478	C₂×C₄	—	13	4	no	—
479	C₂×C₄	—	26	4	no	—
480	C₂×C₄	—	52	8	no	—
481	C₂×C₄	—	104	4	no	—
482	C₂×C₄	—	104	8	no	—
483	C₂×C₄	—	104	8	no	—
484	C₂×C₄	—	104	2	no	—
485	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
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×Q₈×D₁₃	1	2	yes	—
491	C₂×C₄	#88254	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	C₂×Q₈×D₁₃	1	2	yes	—
497	C₈	C₂×Q₈×D₁₃	1	2	yes	—
498	C₂²	—	2	1	no	—
499	C₂²	—	2	1	no	—
500	C₂²	—	26	8	no	—
501	C₂²	—	52	4	no	—
502	C₂²	—	52	4	no	—
503	C₂²	—	104	8	no	—
504	C₂²	#11719432	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	—	4	4	no	—
511	C₄	—	26	4	no	—
512	C₄	—	26	4	no	—
513	C₄	—	52	4	no	—
514	C₄	#11719432	1	2	yes	—
515	C₄	#11719474	1	2	yes	—
516	C₄	C₂²×Q₈×D₁₃	1	1	yes	characteristic
517	C₄	C₂×#88254	1	1	yes	characteristic
518	C₂	—	2	2	no	—
519	C₂	—	52	8	no	—
520	C₂	C₂×#11719432	1	1	yes	characteristic
521	C₂	C₂×#11719474	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	C₁₃×#3160	C₂
socle	C₂²×C₁₃	C₂³×D₄
prime radical	C₂²×D₁₀₄	C₂²
hypercenter	#3160	D₁₃
hypocenter	C₁₃	#61370
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3160

Complements

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

N	H ≅ G/N	type
1. #13128637	C₂	semidirect
2. #13127797	C₂	semidirect
3. #13127740	C₂	semidirect
4. #13127705	C₂	semidirect
5. #13127700	C₂	semidirect
6. #13127688	C₂	semidirect
7. #13125376	C₂	semidirect
8. #13124670	C₂	semidirect
9. #13124629	C₂	semidirect
10. #13123770	C₂	semidirect
13. C₁₃×#3160	C₂	semidirect
16. #11719435	C₂²	semidirect
17. #11719432	C₂²	semidirect
18. #11719395	C₂²	semidirect
28. C₁₃×#500	C₂²	semidirect
29. C₁₃×#500	C₂²	semidirect
30. C₁₃×#499	C₂²	semidirect
31. C₁₃×#499	C₂²	semidirect
32. C₁₃×#498	C₂²	semidirect
40. #11718748	C₂²	semidirect
41. #11718745	C₂²	semidirect
42. #11718727	C₂²	semidirect
46. #11718552	C₂²	semidirect
47. #11718551	C₂²	semidirect
48. #11718539	C₂²	semidirect
49. #11718535	C₂²	semidirect
52. #11718532	C₂²	semidirect
53. #11718531	C₂²	semidirect
55. #11718517	C₂²	semidirect
60. #11718340	C₂²	semidirect
61. #11718340	C₂²	semidirect
62. C₈×Dic₂₆	C₂²	semidirect
63. C₈×Dic₂₆	C₂²	semidirect
86. C₂×D₁₀₄	Q₈	semidirect
150. C₂×D₅₂	C₂×Q₈	semidirect
161. C₂×C₈×C₁₃	C₂×Q₈	semidirect
197. D₁₀₄	C₂×Q₈	semidirect
198. D₁₀₄	C₂×Q₈	semidirect
206. #3160	D₁₃	semidirect
266. #500	C₂×D₁₃	semidirect
267. #500	C₂×D₁₃	semidirect
269. #499	C₂×D₁₃	semidirect
270. #499	C₂×D₁₃	semidirect
271. #498	C₂×D₁₃	semidirect
425. C₂×C₈	Q₈×D₁₃	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
#13128637	2
#13127797	2
#13127740	2
#13127705	2
#13127700	2
#13127688	2
#13125376	2
#13124670	2
#13124629	2
#13123770	2
#13123687	2
C₂×C₄×D₁₀₄	2
C₁₃×#3160	2
#61370	13