Subgroups — #16727265

Order 3328.

2604 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13129605	C₂	1	1	yes	maximal, characteristic
2	#13129549	C₂	1	2	yes	maximal, complemented
3	#13123754	C₂	1	1	yes	maximal, characteristic, complemented
4	#13123750	C₂	1	4	yes	maximal, complemented
5	#13123743	C₂	1	2	yes	maximal, complemented
6	#13123741	C₂	1	4	yes	maximal, complemented
7	#13123735	C₂	1	2	yes	maximal, complemented
8	#13123734	C₂	1	4	yes	maximal, complemented
9	C₂×#11718858	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#11718555	C₂	1	1	yes	maximal, characteristic, complemented
11	D₁₃×#444	C₂	1	4	yes	maximal, complemented
12	#13123444	C₂	1	1	yes	maximal, characteristic, complemented
13	#13123382	C₂	1	2	yes	maximal, complemented
14	#13123263	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#2957	C₂	1	1	yes	maximal, characteristic, complemented
16	#11719648	C₂²	1	2	yes	—
17	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
18	C₁₃×#568	C₂²	1	2	yes	complemented
19	#11719527	C₂²	1	2	yes	—
20	C₂×#88202	C₂²	1	2	yes	complemented
21	#11719476	C₄	1	2	yes	complemented
22	#11719475	C₄	1	4	yes	complemented
23	#11719474	C₄	1	2	yes	complemented
24	#11719473	C₂²	1	4	yes	—
25	D₁₃×#135	C₂²	1	4	yes	—
26	#11719471	C₄	1	2	yes	complemented
27	#11719467	C₄	1	4	yes	complemented
28	#11719462	C₄	1	2	yes	complemented
29	#11719455	—	2	4	no	—
30	#11719455	C₂²	1	8	yes	complemented
31	D₁₃×#131	—	2	4	no	—
32	D₁₃×#131	C₂²	1	8	yes	complemented
33	#11719450	—	2	4	no	—
34	#11719450	C₂²	1	2	yes	—
35	#11719450	C₂²	1	2	yes	complemented
36	C₂×#88161	—	2	4	no	—
37	C₂×#88161	C₂²	1	1	yes	characteristic
38	C₂×#88161	C₂²	1	2	yes	complemented
39	C₂×#88158	C₂²	1	1	yes	characteristic
40	C₂×#88155	C₂²	1	1	yes	characteristic
41	#11719227	C₂²	1	1	yes	characteristic
42	C₁₃×#444	C₂²	1	4	yes	complemented
43	C₁₃×#443	C₂²	1	4	yes	complemented
44	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic, complemented
45	C₁₃×#421	C₂²	1	2	yes	complemented
46	C₁₃×#405	C₂²	1	1	yes	characteristic, complemented
47	C₂×#88077	C₂²	1	2	yes	complemented
48	#11718858	C₂²	1	2	yes	complemented
49	#11718858	C₂²	1	2	yes	complemented
50	#11718858	C₂²	1	2	yes	complemented
51	#11718858	C₂²	1	2	yes	complemented
52	#11718806	C₂²	1	8	yes	complemented
53	#11718805	C₂²	1	8	yes	complemented
54	C₂×#88065	C₂²	1	2	yes	complemented
55	#11718785	C₂²	1	2	yes	complemented
56	M₁₆×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
57	C₂×#88059	C₂²	1	1	yes	characteristic, complemented
58	C₂×#88055	C₂²	1	1	yes	characteristic, complemented
59	#11718666	C₂²	1	2	yes	complemented
60	#11718658	C₂²	1	1	yes	characteristic, complemented
61	#11718555	C₂²	1	2	yes	complemented
62	#11718555	C₂²	1	2	yes	complemented
63	#11718555	C₂²	1	2	yes	complemented
64	#11718555	C₂²	1	2	yes	complemented
65	#11718554	C₂²	1	4	yes	complemented
66	D₁₃×#108	C₂²	1	4	yes	complemented
67	#11718485	C₂²	1	8	yes	complemented
68	#11718484	C₂²	1	8	yes	complemented
69	#11718482	C₂²	1	8	yes	complemented
70	D₁₃×#104	C₂²	1	8	yes	complemented
71	#11718378	C₂²	1	4	yes	complemented
72	#11718369	C₂²	1	2	yes	complemented
73	D₁₃×#97	C₂²	1	2	yes	complemented
74	#11718361	C₂²	1	4	yes	complemented
75	#11718350	C₂²	1	2	yes	complemented
76	C₄×#6094	C₂²	1	2	yes	complemented
77	C₂×C₁₃×#41	C₂³	1	2	yes	—
78	#88257	—	2	2	no	—
79	#88257	C₂×C₄	1	4	yes	—
80	#88256	—	2	2	no	—
81	#88256	C₂×C₄	1	4	yes	—
82	#41×D₁₃	—	2	4	no	—
83	#41×D₁₃	C₂³	1	8	yes	—
84	#88254	C₂×C₄	1	4	yes	—
85	#88251	—	2	4	no	—
86	#88251	C₂×C₄	1	4	yes	—
87	C₂×#6127	—	2	4	no	—
88	C₂×#6127	C₂³	1	2	yes	—
89	C₂×#6127	C₂³	1	1	yes	characteristic
90	C₁₃×#135	C₂×C₄	1	2	yes	complemented
91	C₁₃×#135	C₂×C₄	1	2	yes	complemented
92	C₁₃×#135	C₂³	1	2	yes	—
93	C₁₃×#135	C₂³	1	2	yes	—
94	C₂×C₁₃×Q₁₆	C₂×C₄	1	1	yes	characteristic, complemented
95	C₂×C₁₃×SD₁₆	C₂×C₄	1	2	yes	complemented
96	C₂×C₁₃×D₈	C₂×C₄	1	1	yes	characteristic, complemented
97	C₁₃×#131	—	2	4	no	—
98	C₁₃×#131	C₂³	1	8	yes	—
99	C₂×C₁₃×M₁₆	—	2	4	no	—
100	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
101	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
102	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
103	C₁₃×#117	C₂³	1	1	yes	characteristic
104	#88205	C₂×C₄	1	4	yes	complemented
105	#88204	C₂³	1	8	yes	—
106	#88203	C₂×C₄	1	4	yes	complemented
107	#88202	—	2	2	no	—
108	#88202	—	2	2	no	—
109	#88202	C₂³	1	4	yes	—
110	#88202	C₂³	1	4	yes	—
111	#88196	C₂×C₄	1	4	yes	complemented
112	#88186	C₂×C₄	1	4	yes	complemented
113	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
114	C₂×#6099	—	2	2	no	—
115	C₂×#6099	C₂³	1	2	yes	—
116	C₂×#6099	C₂³	1	1	yes	characteristic
117	C₂²×#1055	—	2	2	no	—
118	C₂²×#1055	C₂³	1	1	yes	characteristic
119	#88173	C₂×C₄	1	4	yes	complemented
120	#88172	C₂×C₄	1	8	yes	complemented
121	Q₁₆×D₁₃	C₂×C₄	1	4	yes	complemented
122	#88170	C₂×C₄	1	8	yes	complemented
123	#88169	C₂×C₄	1	8	yes	complemented
124	#88168	C₂×C₄	1	8	yes	complemented
125	SD₁₆×D₁₃	C₂×C₄	1	8	yes	complemented
126	#88166	C₂×C₄	1	4	yes	complemented
127	#88165	C₂×C₄	1	8	yes	complemented
128	D₈×D₁₃	C₂×C₄	1	4	yes	complemented
129	#88161	—	2	4	no	—
130	#88161	—	2	4	no	—
131	#88161	—	2	2	no	—
132	#88161	—	2	2	no	—
133	#88161	—	2	8	no	—
134	#88161	—	2	8	no	—
135	#88161	D₄	1	4	yes	—
136	#88161	D₄	1	4	yes	—
137	#88161	C₂³	1	4	yes	—
138	#88161	C₂³	1	4	yes	—
139	M₁₆×D₁₃	—	2	4	no	—
140	M₁₆×D₁₃	—	2	8	no	—
141	M₁₆×D₁₃	—	2	8	no	—
142	M₁₆×D₁₃	C₂³	1	8	yes	—
143	C₂×Dic₅₂	C₂×C₄	1	1	yes	characteristic, complemented
144	#88158	C₂×C₄	1	2	yes	complemented
145	#88158	C₂×C₄	1	2	yes	complemented
146	#88158	C₂³	1	2	yes	—
147	#88158	C₂³	1	2	yes	—
148	C₂×D₁₀₄	C₂×C₄	1	1	yes	characteristic, complemented
149	C₂×#6095	C₂×C₄	1	2	yes	complemented
150	#88155	—	2	4	no	—
151	#88155	—	2	8	no	—
152	#88155	—	2	8	no	—
153	#88155	C₂×C₄	1	2	yes	—
154	#88155	C₂×C₄	1	2	yes	—
155	#88155	C₂×C₄	1	2	yes	—
156	#88155	C₂×C₄	1	2	yes	—
157	#88155	C₂³	1	8	yes	—
158	C₂×#6094	—	2	2	no	—
159	C₂×#6094	—	2	8	no	—
160	C₂×#6094	C₂³	1	2	yes	—
161	C₂×#6094	C₂³	1	2	yes	—
162	C₂×C₈×D₁₃	—	2	2	no	—
163	C₂×C₈×D₁₃	—	2	8	no	—
164	C₂×C₈×D₁₃	C₂³	1	2	yes	—
165	C₂×C₈×D₁₃	C₂³	1	2	yes	—
166	#88147	—	2	1	no	—
167	#88141	—	2	1	no	—
168	#88135	—	2	2	no	—
169	#88126	C₂³	1	2	yes	—
170	C₄²×D₁₃	C₂³	1	2	yes	—
171	C₁₃×#108	C₂³	1	2	yes	—
172	C₁₃×#108	C₂³	1	2	yes	—
173	C₁₃×#104	C₂³	1	8	yes	—
174	C₁₃×#97	C₂³	1	2	yes	—
175	C₄×C₈×C₁₃	C₂³	1	2	yes	—
176	#88077	C₂³	1	4	yes	—
177	#88077	C₂³	1	4	yes	—
178	#88065	C₂³	1	4	yes	—
179	#88065	C₂³	1	4	yes	—
180	#88062	C₂³	1	8	yes	—
181	#88059	C₂³	1	2	yes	—
182	#88059	C₂³	1	2	yes	—
183	#88055	C₂³	1	1	yes	characteristic
184	#88055	C₂³	1	1	yes	characteristic
185	#88055	C₂³	1	1	yes	characteristic
186	#88055	C₂³	1	1	yes	characteristic
187	#88055	C₂³	1	2	yes	—
188	C₈×Dic₁₃	C₂³	1	2	yes	—
189	#88045	C₂³	1	8	yes	—
190	#88043	C₂³	1	2	yes	—
191	C₄×#1055	C₂³	1	2	yes	—
192	#60184	—	13	1	no	maximal, Sylow
193	C₁₃×#41	—	2	2	no	—
194	C₁₃×#41	—	2	2	no	—
195	C₁₃×#41	C₂²×C₄	1	4	yes	—
196	C₁₃×#41	C₂⁴	1	4	yes	—
197	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
198	C₂×D₄×C₁₃	—	2	2	no	—
199	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
200	C₂²×C₄×C₁₃	—	2	2	no	—
201	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
202	C₂×C₂²⋊D₁₃	—	2	2	no	—
203	C₂×C₂²⋊D₁₃	—	2	8	no	—
204	C₂×C₂²⋊D₁₃	#41	1	2	yes	—
205	C₂²×Dic₁₃	—	2	1	no	—
206	#6131	—	2	4	no	—
207	#6131	C₂²×C₄	1	8	yes	—
208	Q₈×D₁₃	—	2	4	no	—
209	Q₈×D₁₃	C₂²×C₄	1	8	yes	—
210	#6129	—	2	8	no	—
211	#6129	—	2	8	no	—
212	#6129	—	2	4	no	—
213	#6129	C₂²×C₄	1	8	yes	—
214	D₄×D₁₃	—	2	8	no	—
215	D₄×D₁₃	—	2	8	no	—
216	D₄×D₁₃	—	2	4	no	—
217	D₄×D₁₃	C₂²×C₄	1	8	yes	—
218	#6127	—	2	2	no	—
219	#6127	—	2	2	no	—
220	#6127	—	2	8	no	—
221	#6127	—	2	4	no	—
222	#6127	—	2	8	no	—
223	#6127	—	2	4	no	—
224	#6127	C₂²×C₄	1	2	yes	—
225	#6127	C₂²×C₄	1	2	yes	—
226	#6127	C₂²×C₄	1	4	yes	—
227	#6127	C₂×D₄	1	2	yes	—
228	#6127	C₂×D₄	1	2	yes	—
229	#6127	C₂⁴	1	4	yes	—
230	C₂×D₅₂	—	2	4	no	—
231	C₂×D₅₂	C₂²×C₄	1	2	yes	—
232	C₂×D₅₂	#41	1	1	yes	characteristic
233	C₂×C₄×D₁₃	—	2	2	no	—
234	C₂×C₄×D₁₃	—	2	8	no	—
235	C₂×C₄×D₁₃	—	2	2	no	—
236	C₂×C₄×D₁₃	C₂⁴	1	2	yes	—
237	C₂×Dic₂₆	—	2	4	no	—
238	C₂×Dic₂₆	C₂²×C₄	1	2	yes	—
239	C₂×Dic₂₆	#41	1	1	yes	characteristic
240	C₁₃×Q₁₆	C₂²×C₄	1	2	yes	—
241	C₁₃×Q₁₆	C₂²×C₄	1	2	yes	—
242	C₁₃×SD₁₆	C₂²×C₄	1	4	yes	—
243	C₁₃×SD₁₆	C₂²×C₄	1	4	yes	—
244	C₁₃×D₈	C₂²×C₄	1	2	yes	—
245	C₁₃×D₈	C₂²×C₄	1	2	yes	—
246	C₁₃×M₁₆	—	2	2	no	—
247	C₁₃×M₁₆	—	2	8	no	—
248	C₁₃×M₁₆	C₂×D₄	1	2	yes	—
249	C₁₃×M₁₆	C₂×D₄	1	2	yes	—
250	C₁₃×M₁₆	C₂⁴	1	4	yes	—
251	C₂×C₈×C₁₃	—	2	2	no	—
252	C₂×C₈×C₁₃	—	2	8	no	—
253	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
254	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
255	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
256	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
257	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
258	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
259	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
260	C₁₃×C₄⋊C₄	—	2	1	no	—
261	C₁₃×C₂²⋊C₄	—	2	1	no	—
262	C₄²×C₁₃	C₂⁴	1	2	yes	—
263	#6107	C₂²×C₄	1	8	yes	—
264	#6106	C₂²×C₄	1	8	yes	—
265	#6105	C₂²×C₄	1	8	yes	—
266	#6104	C₂²×C₄	1	8	yes	—
267	#6103	—	2	2	no	—
268	#6101	—	2	2	no	—
269	C₄×Dic₁₃	—	2	1	no	—
270	C₄×Dic₁₃	—	2	2	no	—
271	C₄×Dic₁₃	C₂⁴	1	1	yes	characteristic
272	C₄×Dic₁₃	C₂⁴	1	1	yes	characteristic
273	#6099	—	2	2	no	—
274	#6099	—	2	4	no	—
275	#6099	—	2	4	no	—
276	#6099	C₂²×C₄	1	2	yes	—
277	#6099	C₂²×C₄	1	2	yes	—
278	#6099	C₂⁴	1	4	yes	—
279	C₂×#1055	—	2	2	no	—
280	C₂×#1055	—	2	4	no	—
281	C₂×#1055	—	2	4	no	—
282	C₂×#1055	C₂×D₄	1	2	yes	—
283	C₂×#1055	C₂×D₄	1	2	yes	—
284	C₂×#1055	C₂⁴	1	2	yes	—
285	C₂×#1055	C₂⁴	1	1	yes	characteristic
286	C₂×#1055	C₂⁴	1	1	yes	characteristic
287	Dic₅₂	C₂²×C₄	1	2	yes	—
288	Dic₅₂	C₂²×C₄	1	2	yes	—
289	D₁₀₄	C₂²×C₄	1	2	yes	—
290	D₁₀₄	C₂²×C₄	1	2	yes	—
291	#6095	C₂²×C₄	1	4	yes	—
292	#6095	C₂²×C₄	1	4	yes	—
293	#6094	—	2	8	no	—
294	#6094	—	2	8	no	—
295	#6094	—	2	4	no	—
296	#6094	—	2	4	no	—
297	#6094	C₂²×C₄	1	4	yes	—
298	#6094	C₂²×C₄	1	4	yes	—
299	#6094	C₂×D₄	1	8	yes	—
300	C₈×D₁₃	—	2	8	no	—
301	C₈×D₁₃	—	2	8	no	—
302	C₈×D₁₃	—	2	4	no	—
303	C₈×D₁₃	—	2	4	no	—
304	C₈×D₁₃	C₂²×C₄	1	4	yes	—
305	C₈×D₁₃	C₂²×C₄	1	4	yes	—
306	C₈×D₁₃	C₂×D₄	1	8	yes	—
307	#3584	—	13	1	no	—
308	#3573	—	13	2	no	—
309	#2957	—	13	4	no	—
310	#2957	—	13	1	no	—
311	#2957	D₁₃	1	1	yes	characteristic, complemented
312	#2956	—	13	4	no	—
313	#2956	—	13	2	no	—
314	#2955	—	13	4	no	—
315	#2955	—	13	2	no	—
316	C₂×#444	—	13	4	no	—
317	C₂×#444	—	13	1	no	—
318	C₂×#444	—	13	1	no	—
319	#2916	—	13	1	no	—
320	#2901	—	13	2	no	—
321	#2875	—	13	1	no	—
322	C₂³×C₁₃	—	2	2	no	—
323	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
324	C₂²×D₁₃	—	2	2	no	—
325	C₂²×D₁₃	—	2	8	no	—
326	C₂²×D₁₃	C₂×#41	1	2	yes	—
327	Q₈×C₁₃	—	2	2	no	—
328	Q₈×C₁₃	C₂³×C₄	1	4	yes	—
329	D₄×C₁₃	—	2	4	no	—
330	D₄×C₁₃	—	2	4	no	—
331	D₄×C₁₃	—	2	2	no	—
332	D₄×C₁₃	C₂³×C₄	1	4	yes	—
333	C₂×C₄×C₁₃	—	2	2	no	—
334	C₂×C₄×C₁₃	—	2	4	no	—
335	C₂×C₄×C₁₃	—	2	4	no	—
336	C₂×C₄×C₁₃	—	2	2	no	—
337	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
338	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
339	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
340	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
341	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
342	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
343	C₂²⋊D₁₃	—	2	4	no	—
344	C₂²⋊D₁₃	—	2	4	no	—
345	C₂²⋊D₁₃	—	2	8	no	—
346	C₂²⋊D₁₃	—	2	8	no	—
347	C₂²⋊D₁₃	C₄×D₄	1	4	yes	—
348	C₂²⋊D₁₃	C₄×D₄	1	4	yes	—
349	C₂×Dic₁₃	—	2	2	no	—
350	C₂×Dic₁₃	—	2	8	no	—
351	C₂×Dic₁₃	—	2	1	no	—
352	C₂×Dic₁₃	—	2	1	no	—
353	C₂×Dic₁₃	—	8	1	no	—
354	C₂×Dic₁₃	C₂×#41	1	2	yes	—
355	D₅₂	—	2	8	no	—
356	D₅₂	—	2	2	no	—
357	D₅₂	C₄×D₄	1	2	yes	—
358	D₅₂	C₄×D₄	1	2	yes	—
359	D₅₂	C₂³×C₄	1	4	yes	—
360	C₄×D₁₃	—	2	8	no	—
361	C₄×D₁₃	—	2	4	no	—
362	C₄×D₁₃	—	2	4	no	—
363	C₄×D₁₃	—	2	8	no	—
364	C₄×D₁₃	—	8	2	no	—
365	C₄×D₁₃	C₂³×C₄	1	4	yes	—
366	C₄×D₁₃	C₂²×D₄	1	4	yes	—
367	Dic₂₆	—	2	2	no	—
368	Dic₂₆	—	2	8	no	—
369	Dic₂₆	C₄×D₄	1	2	yes	—
370	Dic₂₆	C₄×D₄	1	2	yes	—
371	Dic₂₆	C₂³×C₄	1	4	yes	—
372	C₈×C₁₃	—	2	4	no	—
373	C₈×C₁₃	C₂³×C₄	1	1	yes	characteristic
374	C₈×C₁₃	C₂³×C₄	1	1	yes	characteristic
375	C₈×C₁₃	C₂³×C₄	1	1	yes	characteristic
376	C₈×C₁₃	C₂³×C₄	1	1	yes	characteristic
377	C₈×C₁₃	C₂²×D₄	1	4	yes	—
378	#1055	—	2	4	no	—
379	#1055	C₂³×C₄	1	4	yes	—
380	#1055	C₂²×D₄	1	2	yes	—
381	#1055	C₂²×D₄	1	2	yes	—
382	#585	—	13	2	no	—
383	#578	—	13	2	no	—
384	#578	—	13	2	no	—
385	#577	—	13	4	no	—
386	#577	—	13	4	no	—
387	#576	—	13	2	no	—
388	#576	—	13	2	no	—
389	#575	—	13	2	no	—
390	#575	—	13	4	no	—
391	C₂×#135	—	13	4	no	—
392	C₂×#135	—	13	1	no	—
393	C₂×#135	C₂×D₁₃	1	1	yes	characteristic
394	#568	—	13	2	no	—
395	#568	—	13	8	no	—
396	#568	—	13	2	no	—
397	#568	—	26	4	no	—
398	#568	—	26	4	no	—
399	#568	C₂×D₁₃	1	2	yes	complemented
400	C₂×#131	—	13	1	no	—
401	C₂×#131	—	13	1	no	—
402	C₂×#131	—	13	2	no	—
403	C₂×#131	—	13	8	no	—
404	C₂×#131	—	13	2	no	—
405	C₂×#131	—	26	4	no	—
406	C₂×#131	—	26	4	no	—
407	C₄×#41	—	13	1	no	—
408	#444	—	13	2	no	—
409	#444	—	13	2	no	—
410	#444	—	13	2	no	—
411	#444	—	13	2	no	—
412	#444	—	13	8	no	—
413	#444	—	13	2	no	—
414	#444	—	13	2	no	—
415	#444	—	13	2	no	—
416	#444	—	13	2	no	—
417	#444	—	13	8	no	—
418	#444	—	13	4	no	—
419	#444	C₂×D₁₃	1	4	yes	complemented
420	#443	—	13	8	no	—
421	#443	—	13	8	no	—
422	#443	—	13	4	no	—
423	#443	C₂×D₁₃	1	4	yes	complemented
424	#430	—	13	2	no	—
425	#430	—	13	4	no	—
426	C₂×#108	—	13	1	no	—
427	C₂×#108	—	13	4	no	—
428	C₂×#108	C₂×D₁₃	1	1	yes	characteristic, complemented
429	#421	—	13	2	no	—
430	#421	—	13	8	no	—
431	#421	C₂×D₁₃	1	2	yes	complemented
432	C₂×#104	—	13	2	no	—
433	C₂×#104	—	13	2	no	—
434	C₂×#104	—	13	8	no	—
435	#405	—	13	1	no	—
436	#405	—	13	2	no	—
437	#405	—	13	2	no	—
438	#405	C₂×D₁₃	1	1	yes	characteristic, complemented
439	C₄×M₁₆	—	13	1	no	—
440	C₄×M₁₆	—	13	2	no	—
441	C₂×#97	—	13	1	no	—
442	C₂×#97	—	13	2	no	—
443	C₂²×C₁₃	—	2	4	no	—
444	C₂²×C₁₃	—	4	1	no	—
445	C₂²×C₁₃	—	8	2	no	—
446	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
447	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
448	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
449	C₂×D₁₃	—	2	4	no	—
450	C₂×D₁₃	—	4	2	no	—
451	C₂×D₁₃	—	8	8	no	—
452	C₂×D₁₃	—	8	2	no	—
453	C₂×D₁₃	C₂×C₄×D₄	1	4	yes	—
454	C₄×C₁₃	—	2	4	no	—
455	C₄×C₁₃	—	4	2	no	—
456	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
457	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
458	C₄×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
459	C₄×C₁₃	C₂³×D₄	1	1	yes	characteristic
460	Dic₁₃	—	2	4	no	—
461	Dic₁₃	—	4	1	no	—
462	Dic₁₃	—	4	1	no	—
463	Dic₁₃	C₂×C₄×D₄	1	4	yes	—
464	2₋¹⁺⁴	—	13	4	no	—
465	2₋¹⁺⁴	—	13	4	no	—
466	2₋¹⁺⁴	—	26	2	no	—
467	H(5,𝔽₂)	—	13	4	no	—
468	H(5,𝔽₂)	—	13	4	no	—
469	H(5,𝔽₂)	—	26	4	no	—
470	H(5,𝔽₂)	—	26	2	no	—
471	C₂×#41	—	13	1	no	—
472	C₂×#41	—	13	8	no	—
473	C₂×#41	—	13	2	no	—
474	C₂×#41	—	26	4	no	—
475	C₂×#41	—	26	4	no	—
476	C₂×#41	C₂²×D₁₃	1	2	yes	—
477	#137	—	13	4	no	—
478	#137	—	13	4	no	—
479	#137	—	13	8	no	—
480	#137	—	13	8	no	—
481	AGL(1,ℤ/8)	—	13	4	no	—
482	AGL(1,ℤ/8)	—	13	4	no	—
483	AGL(1,ℤ/8)	—	13	8	no	—
484	AGL(1,ℤ/8)	—	13	8	no	—
485	#135	—	13	8	no	—
486	#135	—	13	4	no	—
487	#135	—	13	8	no	—
488	#135	—	13	4	no	—
489	#135	—	13	2	no	—
490	#135	—	13	2	no	—
491	#135	—	13	2	no	—
492	#135	—	13	2	no	—
493	#135	C₄×D₁₃	1	2	yes	complemented
494	#135	C₄×D₁₃	1	2	yes	complemented
495	#135	C₂²×D₁₃	1	2	yes	—
496	#135	C₂²×D₁₃	1	2	yes	—
497	C₂×Q₁₆	—	13	4	no	—
498	C₂×Q₁₆	—	13	1	no	—
499	C₂×Q₁₆	C₄×D₁₃	1	1	yes	characteristic, complemented
500	C₂×SD₁₆	—	13	8	no	—
501	C₂×SD₁₆	—	13	2	no	—
502	C₂×SD₁₆	C₄×D₁₃	1	2	yes	complemented
503	C₂×D₈	—	13	4	no	—
504	C₂×D₈	—	13	1	no	—
505	C₂×D₈	C₄×D₁₃	1	1	yes	characteristic, complemented
506	#131	—	2	4	no	—
507	#131	—	13	4	no	—
508	#131	—	13	4	no	—
509	#131	—	13	2	no	—
510	#131	—	13	2	no	—
511	#131	—	13	2	no	—
512	#131	—	13	2	no	—
513	#131	—	13	4	no	—
514	#131	—	13	4	no	—
515	#131	—	13	4	no	—
516	#131	—	13	4	no	—
517	#131	—	13	8	no	—
518	#131	—	26	8	no	—
519	#131	—	26	8	no	—
520	#131	—	26	4	no	—
521	#131	—	26	2	no	—
522	#131	—	26	8	no	—
523	#131	—	26	2	no	—
524	#131	—	26	2	no	—
525	#131	—	26	2	no	—
526	#131	—	26	8	no	—
527	#131	—	26	4	no	—
528	#131	—	26	4	no	—
529	#131	C₂²×D₁₃	1	8	yes	—
530	C₂×M₁₆	—	2	4	no	—
531	C₂×M₁₆	—	13	1	no	—
532	C₂×M₁₆	—	13	2	no	—
533	C₂×M₁₆	—	13	2	no	—
534	C₂×M₁₆	—	13	2	no	—
535	C₂×M₁₆	—	13	8	no	—
536	C₂×M₁₆	—	26	2	no	—
537	C₂×M₁₆	—	26	8	no	—
538	C₂×M₁₆	—	26	8	no	—
539	C₂×M₁₆	—	26	2	no	—
540	C₂×M₁₆	—	26	8	no	—
541	C₂×M₁₆	—	26	4	no	—
542	C₂×M₁₆	C₂²×D₁₃	1	2	yes	—
543	C₂×M₁₆	C₂²×D₁₃	1	1	yes	characteristic
544	C₂²×C₈	—	13	1	no	—
545	C₂²×C₈	—	13	2	no	—
546	C₂²×C₈	—	13	2	no	—
547	C₂²×C₈	—	26	2	no	—
548	C₂²×C₈	—	26	8	no	—
549	C₂²×C₈	—	26	2	no	—
550	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
551	C₄×Q₈	—	26	1	no	—
552	C₄×D₄	—	26	2	no	—
553	C₄×D₄	—	26	1	no	—
554	#117	—	13	2	no	—
555	#117	C₂²×D₁₃	1	1	yes	characteristic
556	C₂×C₄²	—	13	1	no	—
557	C₂×C₄²	—	13	2	no	—
558	#108	—	13	8	no	—
559	#108	—	13	2	no	—
560	#108	—	13	2	no	—
561	#108	C₂²×D₁₃	1	2	yes	—
562	#108	C₂²×D₁₃	1	2	yes	—
563	#104	—	13	4	no	—
564	#104	—	13	4	no	—
565	#104	—	13	4	no	—
566	#104	—	13	4	no	—
567	#104	—	13	8	no	—
568	#104	C₂²×D₁₃	1	8	yes	—
569	#97	—	13	1	no	—
570	#97	—	13	2	no	—
571	#97	—	13	1	no	—
572	#97	—	13	1	no	—
573	#97	—	13	1	no	—
574	#97	—	13	2	no	—
575	#97	C₂²×D₁₃	1	2	yes	—
576	C₄×C₈	—	13	2	no	—
577	C₄×C₈	—	13	2	no	—
578	C₄×C₈	C₂²×D₁₃	1	2	yes	—
579	C₂×C₁₃	—	2	1	no	—
580	C₂×C₁₃	—	2	1	no	—
581	C₂×C₁₃	—	2	1	no	—
582	C₂×C₁₃	—	4	4	no	—
583	C₂×C₁₃	C₂²×C₄×D₄	1	1	yes	characteristic
584	D₁₃	—	2	4	no	—
585	D₁₃	—	4	4	no	—
586	#41	—	2	2	no	—
587	#41	—	2	2	no	—
588	#41	—	13	2	no	—
589	#41	—	13	2	no	—
590	#41	—	13	2	no	—
591	#41	—	13	2	no	—
592	#41	—	13	8	no	—
593	#41	—	13	8	no	—
594	#41	—	13	4	no	—
595	#41	—	13	4	no	—
596	#41	—	26	8	no	—
597	#41	—	26	8	no	—
598	#41	—	26	4	no	—
599	#41	—	26	4	no	—
600	#41	—	26	8	no	—
601	#41	—	26	8	no	—
602	#41	—	26	4	no	—
603	#41	—	26	4	no	—
604	#41	—	26	2	no	—
605	#41	—	26	2	no	—
606	#41	C₂×C₄×D₁₃	1	4	yes	—
607	#41	C₂³×D₁₃	1	4	yes	—
608	C₂×Q₈	—	13	1	no	—
609	C₂×Q₈	—	13	8	no	—
610	C₂×Q₈	—	13	2	no	—
611	C₂×Q₈	—	26	4	no	—
612	C₂×Q₈	—	26	4	no	—
613	C₂×Q₈	C₂×C₄×D₁₃	1	2	yes	—
614	C₂×D₄	—	2	2	no	—
615	C₂×D₄	—	13	2	no	—
616	C₂×D₄	—	13	8	no	—
617	C₂×D₄	—	13	2	no	—
618	C₂×D₄	—	13	1	no	—
619	C₂×D₄	—	26	4	no	—
620	C₂×D₄	—	26	8	no	—
621	C₂×D₄	—	26	4	no	—
622	C₂×D₄	—	26	8	no	—
623	C₂×D₄	—	26	8	no	—
624	C₂×D₄	—	26	2	no	—
625	C₂×D₄	C₂×C₄×D₁₃	1	2	yes	—
626	C₂²×C₄	—	2	2	no	—
627	C₂²×C₄	—	13	2	no	—
628	C₂²×C₄	—	26	8	no	—
629	C₂²×C₄	—	26	2	no	—
630	C₂²×C₄	—	26	2	no	—
631	C₂²×C₄	—	26	1	no	—
632	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
633	Q₁₆	—	13	8	no	—
634	Q₁₆	—	13	2	no	—
635	Q₁₆	—	13	2	no	—
636	Q₁₆	C₂×C₄×D₁₃	1	2	yes	—
637	Q₁₆	C₂×C₄×D₁₃	1	2	yes	—
638	SD₁₆	—	13	8	no	—
639	SD₁₆	—	13	8	no	—
640	SD₁₆	—	13	4	no	—
641	SD₁₆	—	13	4	no	—
642	SD₁₆	C₂×C₄×D₁₃	1	4	yes	—
643	SD₁₆	C₂×C₄×D₁₃	1	4	yes	—
644	D₈	—	13	8	no	—
645	D₈	—	13	2	no	—
646	D₈	—	13	2	no	—
647	D₈	C₂×C₄×D₁₃	1	2	yes	—
648	D₈	C₂×C₄×D₁₃	1	2	yes	—
649	M₁₆	—	2	2	no	—
650	M₁₆	—	2	8	no	—
651	M₁₆	—	13	2	no	—
652	M₁₆	—	13	2	no	—
653	M₁₆	—	13	4	no	—
654	M₁₆	—	13	4	no	—
655	M₁₆	—	13	8	no	—
656	M₁₆	—	13	4	no	—
657	M₁₆	—	26	4	no	—
658	M₁₆	—	26	4	no	—
659	M₁₆	—	26	8	no	—
660	M₁₆	—	26	4	no	—
661	M₁₆	—	26	4	no	—
662	M₁₆	—	26	2	no	—
663	M₁₆	—	26	8	no	—
664	M₁₆	D₄×D₁₃	1	2	yes	—
665	M₁₆	D₄×D₁₃	1	2	yes	—
666	M₁₆	C₂³×D₁₃	1	4	yes	—
667	C₂×C₈	—	2	2	no	—
668	C₂×C₈	—	2	8	no	—
669	C₂×C₈	—	13	2	no	—
670	C₂×C₈	—	13	2	no	—
671	C₂×C₈	—	13	2	no	—
672	C₂×C₈	—	13	1	no	—
673	C₂×C₈	—	13	1	no	—
674	C₂×C₈	—	13	4	no	—
675	C₂×C₈	—	13	4	no	—
676	C₂×C₈	—	13	8	no	—
677	C₂×C₈	—	26	4	no	—
678	C₂×C₈	—	26	4	no	—
679	C₂×C₈	—	26	8	no	—
680	C₂×C₈	—	26	4	no	—
681	C₂×C₈	—	26	4	no	—
682	C₂×C₈	—	26	2	no	—
683	C₂×C₈	—	26	8	no	—
684	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
685	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
686	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
687	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
688	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
689	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
690	C₂×C₈	C₂³×D₁₃	1	2	yes	—
691	C₄⋊C₄	—	2	1	no	—
692	C₄⋊C₄	—	26	2	no	—
693	C₂²⋊C₄	—	2	1	no	—
694	C₂²⋊C₄	—	26	2	no	—
695	C₄²	—	13	1	no	—
696	C₄²	—	13	1	no	—
697	C₄²	—	26	2	no	—
698	C₄²	—	26	1	no	—
699	C₄²	C₂³×D₁₃	1	2	yes	—
700	C₁₃	#60184	1	1	yes	characteristic, complemented, Sylow
701	C₂³	—	2	2	no	—
702	C₂³	—	13	2	no	—
703	C₂³	—	26	8	no	—
704	C₂³	—	26	2	no	—
705	C₂³	#41×D₁₃	1	1	yes	characteristic
706	Q₈	—	2	2	no	—
707	Q₈	—	13	2	no	—
708	Q₈	—	13	2	no	—
709	Q₈	—	13	4	no	—
710	Q₈	—	26	8	no	—
711	Q₈	—	26	2	no	—
712	Q₈	C₂²×C₄×D₁₃	1	4	yes	—
713	D₄	—	2	4	no	—
714	D₄	—	2	4	no	—
715	D₄	—	2	2	no	—
716	D₄	—	13	4	no	—
717	D₄	—	13	4	no	—
718	D₄	—	13	2	no	—
719	D₄	—	13	2	no	—
720	D₄	—	13	4	no	—
721	D₄	—	26	8	no	—
722	D₄	—	26	8	no	—
723	D₄	—	26	8	no	—
724	D₄	—	26	4	no	—
725	D₄	—	26	4	no	—
726	D₄	—	26	2	no	—
727	D₄	C₂²×C₄×D₁₃	1	4	yes	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	4	no	—
730	C₂×C₄	—	2	4	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	13	2	no	—
733	C₂×C₄	—	13	4	no	—
734	C₂×C₄	—	13	4	no	—
735	C₂×C₄	—	26	8	no	—
736	C₂×C₄	—	26	8	no	—
737	C₂×C₄	—	26	8	no	—
738	C₂×C₄	—	26	2	no	—
739	C₂×C₄	—	26	4	no	—
740	C₂×C₄	—	26	4	no	—
741	C₂×C₄	—	26	1	no	—
742	C₂×C₄	—	26	1	no	—
743	C₂×C₄	—	104	2	no	—
744	C₂×C₄	—	104	1	no	—
745	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
746	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
747	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
748	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
749	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
750	C₂×C₄	C₂⁴×D₁₃	1	1	yes	characteristic
751	C₈	—	2	4	no	—
752	C₈	—	13	4	no	—
753	C₈	—	13	2	no	—
754	C₈	—	13	2	no	—
755	C₈	—	26	4	no	—
756	C₈	C₂²×C₄×D₁₃	1	1	yes	characteristic
757	C₈	C₂²×C₄×D₁₃	1	1	yes	characteristic
758	C₈	C₂²×C₄×D₁₃	1	1	yes	characteristic
759	C₈	C₂²×C₄×D₁₃	1	1	yes	characteristic
760	C₈	C₂×D₄×D₁₃	1	4	yes	—
761	C₂²	—	2	4	no	—
762	C₂²	—	4	1	no	—
763	C₂²	—	8	2	no	—
764	C₂²	—	13	4	no	—
765	C₂²	—	26	4	no	—
766	C₂²	—	52	2	no	—
767	C₂²	—	104	2	no	—
768	C₂²	—	104	8	no	—
769	C₂²	C₄×D₄×D₁₃	1	1	yes	characteristic
770	C₂²	C₄×D₄×D₁₃	1	1	yes	characteristic
771	C₂²	C₂×#41×D₁₃	1	1	yes	characteristic
772	C₄	—	2	4	no	—
773	C₄	—	4	2	no	—
774	C₄	—	13	4	no	—
775	C₄	—	26	4	no	—
776	C₄	—	52	1	no	—
777	C₄	—	52	1	no	—
778	C₄	C₄×D₄×D₁₃	1	1	yes	characteristic
779	C₄	C₄×D₄×D₁₃	1	1	yes	characteristic
780	C₄	C₂³×C₄×D₁₃	1	1	yes	characteristic
781	C₄	C₂²×D₄×D₁₃	1	1	yes	characteristic
782	C₂	—	2	1	no	—
783	C₂	—	2	1	no	—
784	C₂	—	2	1	no	—
785	C₂	—	4	4	no	—
786	C₂	—	26	4	no	—
787	C₂	—	52	4	no	—
788	C₂	C₂×C₄×D₄×D₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²×D₄×D₁₃
commutator	C₄×C₁₃	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₁₃
Fitting	C₁₃×#2957	C₂
socle	C₂×C₁₃	C₂²×C₄×D₄
prime radical	#13129605	C₂
cosocle	C₂×C₄×C₁₃	C₂⁵
hypercenter	#2957	D₁₃
hypocenter	C₁₃	#60184
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄ ◁ C₂×M₁₆ ◁ #2957

Complements

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

N	H ≅ G/N	type
2. #13129549	C₂	semidirect
3. #13123754	C₂	semidirect
4. #13123750	C₂	semidirect
5. #13123743	C₂	semidirect
6. #13123741	C₂	semidirect
7. #13123735	C₂	semidirect
8. #13123734	C₂	semidirect
9. C₂×#11718858	C₂	semidirect
10. C₂×#11718555	C₂	semidirect
11. D₁₃×#444	C₂	semidirect
12. #13123444	C₂	semidirect
13. #13123382	C₂	semidirect
14. #13123263	C₂	semidirect
15. C₁₃×#2957	C₂	semidirect
18. C₁₃×#568	C₂²	semidirect
20. C₂×#88202	C₂²	semidirect
21. #11719476	C₄	semidirect
22. #11719475	C₄	semidirect
23. #11719474	C₄	semidirect
26. #11719471	C₄	semidirect
27. #11719467	C₄	semidirect
28. #11719462	C₄	semidirect
30. #11719455	C₂²	semidirect
32. D₁₃×#131	C₂²	semidirect
35. #11719450	C₂²	semidirect
38. C₂×#88161	C₂²	semidirect
42. C₁₃×#444	C₂²	semidirect
43. C₁₃×#443	C₂²	semidirect
44. C₂×C₁₃×#108	C₂²	semidirect
45. C₁₃×#421	C₂²	semidirect
46. C₁₃×#405	C₂²	semidirect
47. C₂×#88077	C₂²	semidirect
48. #11718858	C₂²	semidirect
49. #11718858	C₂²	semidirect
50. #11718858	C₂²	semidirect
51. #11718858	C₂²	semidirect
52. #11718806	C₂²	semidirect
53. #11718805	C₂²	semidirect
54. C₂×#88065	C₂²	semidirect
55. #11718785	C₂²	semidirect
56. M₁₆×Dic₁₃	C₂²	semidirect
57. C₂×#88059	C₂²	semidirect
58. C₂×#88055	C₂²	semidirect
59. #11718666	C₂²	semidirect
60. #11718658	C₂²	semidirect
61. #11718555	C₂²	semidirect
62. #11718555	C₂²	semidirect
63. #11718555	C₂²	semidirect
64. #11718555	C₂²	semidirect
65. #11718554	C₂²	semidirect
66. D₁₃×#108	C₂²	semidirect
67. #11718485	C₂²	semidirect
68. #11718484	C₂²	semidirect
69. #11718482	C₂²	semidirect
70. D₁₃×#104	C₂²	semidirect
71. #11718378	C₂²	semidirect
72. #11718369	C₂²	semidirect
73. D₁₃×#97	C₂²	semidirect
74. #11718361	C₂²	semidirect
75. #11718350	C₂²	semidirect
76. C₄×#6094	C₂²	semidirect
90. C₁₃×#135	C₂×C₄	semidirect
91. C₁₃×#135	C₂×C₄	semidirect
94. C₂×C₁₃×Q₁₆	C₂×C₄	semidirect
95. C₂×C₁₃×SD₁₆	C₂×C₄	semidirect
96. C₂×C₁₃×D₈	C₂×C₄	semidirect
104. #88205	C₂×C₄	semidirect
106. #88203	C₂×C₄	semidirect
111. #88196	C₂×C₄	semidirect
112. #88186	C₂×C₄	semidirect
119. #88173	C₂×C₄	semidirect
120. #88172	C₂×C₄	semidirect
121. Q₁₆×D₁₃	C₂×C₄	semidirect
122. #88170	C₂×C₄	semidirect
123. #88169	C₂×C₄	semidirect
124. #88168	C₂×C₄	semidirect
125. SD₁₆×D₁₃	C₂×C₄	semidirect
126. #88166	C₂×C₄	semidirect
127. #88165	C₂×C₄	semidirect
128. D₈×D₁₃	C₂×C₄	semidirect
143. C₂×Dic₅₂	C₂×C₄	semidirect
144. #88158	C₂×C₄	semidirect
145. #88158	C₂×C₄	semidirect
148. C₂×D₁₀₄	C₂×C₄	semidirect
149. C₂×#6095	C₂×C₄	semidirect
311. #2957	D₁₃	semidirect
399. #568	C₂×D₁₃	semidirect
419. #444	C₂×D₁₃	semidirect
423. #443	C₂×D₁₃	semidirect
428. C₂×#108	C₂×D₁₃	semidirect
431. #421	C₂×D₁₃	semidirect
438. #405	C₂×D₁₃	semidirect
493. #135	C₄×D₁₃	semidirect
494. #135	C₄×D₁₃	semidirect
499. C₂×Q₁₆	C₄×D₁₃	semidirect
502. C₂×SD₁₆	C₄×D₁₃	semidirect
505. C₂×D₈	C₄×D₁₃	semidirect
700. C₁₃	#60184	semidirect

Maximal subgroups

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

subgroup	index
#13129605	2
#13129549	2
#13123754	2
#13123750	2
#13123743	2
#13123741	2
#13123735	2
#13123734	2
C₂×#11718858	2
C₂×#11718555	2
D₁₃×#444	2
#13123444	2
#13123382	2
#13123263	2
C₁₃×#2957	2
#60184	13