Subgroups — #16726337

Order 3328.

3178 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11719455	C₂	1	1	yes	maximal, characteristic
2	C₂×D₁₃×#131	C₂	1	1	yes	maximal, characteristic
3	#13128035	C₂	1	1	yes	maximal, characteristic
4	#13123265	C₂	1	3	yes	maximal, complemented
5	#13123264	C₂	1	1	yes	maximal, characteristic, complemented
6	#13123263	C₂	1	3	yes	maximal, complemented
7	#13123262	C₂	1	1	yes	maximal, characteristic, complemented
8	#13123258	C₂	1	3	yes	maximal, complemented
9	#131×Dic₁₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×#88155	C₂	1	3	yes	maximal, complemented
11	#13123253	C₂	1	3	yes	maximal, complemented
12	#13123252	C₂	1	3	yes	maximal, complemented
13	C₂×#11718350	C₂	1	3	yes	maximal, complemented
14	D₁₃×#405	C₂	1	3	yes	maximal, complemented
15	C₄×C₁₃×#131	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#41×D₁₃	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
19	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
20	#41×Dic₁₃	C₂²	1	1	yes	characteristic
21	C₂×#88202	C₂²	1	1	yes	characteristic
22	C₂×#88202	C₂²	1	1	yes	characteristic
23	#11719455	C₄	1	16	yes	complemented
24	D₁₃×#131	C₄	1	16	yes	complemented
25	C₂×#88161	C₂²	1	3	yes	—
26	C₂×#88161	C₂²	1	3	yes	—
27	C₂×M₁₆×D₁₃	C₂²	1	3	yes	—
28	C₂×M₁₆×D₁₃	C₂²	1	3	yes	—
29	C₂×#88155	C₂²	1	3	yes	—
30	C₂×#88155	C₂²	1	3	yes	—
31	C₂²×#6094	C₂²	1	3	yes	—
32	C₂²×C₈×D₁₃	C₂²	1	3	yes	—
33	#11719279	C₄	1	2	yes	—
34	#11719277	C₄	1	2	yes	—
35	#11719251	C₄	1	6	yes	—
36	#11719250	C₄	1	6	yes	—
37	#11719227	C₂²	1	3	yes	—
38	D₁₃×#117	C₂²	1	3	yes	—
39	C₄×#6127	C₂²	1	3	yes	—
40	C₂×#88126	C₂²	1	3	yes	—
41	C₁₃×#405	C₂²	1	3	yes	complemented
42	C₁₃×#405	C₂²	1	3	yes	complemented
43	C₄×C₁₃×M₁₆	C₂²	1	3	yes	complemented
44	C₂×C₄×C₈×C₁₃	C₂²	1	3	yes	complemented
45	#11718783	C₂²	1	3	yes	complemented
46	#11718783	C₂²	1	3	yes	complemented
47	M₁₆×Dic₁₃	C₂²	1	3	yes	complemented
48	M₁₆×Dic₁₃	C₂²	1	3	yes	complemented
49	#11718762	C₂²	1	3	yes	complemented
50	#11718762	C₂²	1	3	yes	complemented
51	C₂×#88055	C₂²	1	3	yes	complemented
52	C₂×C₈×Dic₁₃	C₂²	1	3	yes	complemented
53	#11718658	C₂²	1	3	yes	complemented
54	#11718658	C₂²	1	3	yes	complemented
55	C₄×#6099	C₂²	1	3	yes	complemented
56	C₂×#88043	C₂²	1	3	yes	complemented
57	#11718369	C₂²	1	6	yes	—
58	#11718369	C₂²	1	6	yes	complemented
59	#11718368	C₂²	1	6	yes	complemented
60	D₁₃×#97	C₂²	1	6	yes	complemented
61	#11718350	C₂²	1	3	yes	—
62	#11718350	C₂²	1	1	yes	characteristic
63	#11718350	C₂²	1	3	yes	—
64	#11718350	C₂²	1	3	yes	—
65	#11718350	C₂²	1	3	yes	complemented
66	#11718350	C₂²	1	3	yes	complemented
67	#11718350	C₂²	1	3	yes	complemented
68	#11718350	C₂²	1	3	yes	complemented
69	#11718350	C₂²	1	6	yes	complemented
70	C₄×#6094	C₂²	1	6	yes	complemented
71	C₄×C₈×D₁₃	C₂²	1	6	yes	complemented
72	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
73	#41×D₁₃	C₂×C₄	1	8	yes	—
74	#41×D₁₃	C₂×C₄	1	8	yes	—
75	C₂×#6131	C₂×C₄	1	1	yes	characteristic
76	C₂×Q₈×D₁₃	C₂×C₄	1	1	yes	characteristic
77	C₂×#6129	C₂×C₄	1	3	yes	—
78	C₂×D₄×D₁₃	C₂×C₄	1	3	yes	—
79	C₂×#6127	C₂³	1	3	yes	—
80	C₂²×C₄×D₁₃	C₂³	1	3	yes	—
81	C₁₃×#131	C₂×C₄	1	8	yes	complemented
82	C₁₃×#131	C₂×C₄	1	8	yes	complemented
83	C₂×C₁₃×M₁₆	C₂³	1	3	yes	—
84	C₂×C₁₃×M₁₆	C₂³	1	3	yes	—
85	C₂²×C₈×C₁₃	C₂³	1	3	yes	—
86	C₂²×C₈×C₁₃	C₂³	1	3	yes	—
87	C₄×Q₈×C₁₃	C₂×C₄	1	2	yes	—
88	C₄×D₄×C₁₃	C₂×C₄	1	6	yes	—
89	C₁₃×#117	C₂³	1	3	yes	—
90	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
91	#88202	C₂×C₄	1	8	yes	complemented
92	#88202	C₂×C₄	1	8	yes	complemented
93	Q₈×Dic₁₃	C₂×C₄	1	2	yes	—
94	D₄×Dic₁₃	C₂×C₄	1	6	yes	—
95	C₄×C₂²⋊D₁₃	C₂×C₄	1	12	yes	—
96	C₂×#6103	C₂×C₄	1	6	yes	—
97	#88180	C₂³	1	3	yes	—
98	C₂×#6101	C₂×C₄	1	6	yes	—
99	C₂×C₄×Dic₁₃	C₂³	1	3	yes	—
100	C₂×#6099	C₂³	1	3	yes	—
101	C₂×#6099	C₂³	1	3	yes	—
102	C₂²×#1055	C₂³	1	3	yes	—
103	C₂²×#1055	C₂³	1	3	yes	—
104	#88161	C₂×C₄	1	24	yes	complemented
105	#88161	C₂×C₄	1	24	yes	complemented
106	M₁₆×D₁₃	C₂×C₄	1	24	yes	complemented
107	M₁₆×D₁₃	C₂×C₄	1	24	yes	complemented
108	#88155	C₂×C₄	1	24	yes	complemented
109	#88155	C₂×C₄	1	24	yes	complemented
110	C₂×#6094	C₂×C₄	1	24	yes	complemented
111	C₂×#6094	C₂³	1	1	yes	characteristic
112	C₂×#6094	C₂³	1	3	yes	—
113	C₂×#6094	C₂³	1	3	yes	—
114	C₂×#6094	C₂³	1	3	yes	—
115	C₂×#6094	C₂³	1	6	yes	—
116	C₂×C₈×D₁₃	C₂×C₄	1	24	yes	complemented
117	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
118	C₂×C₈×D₁₃	C₂³	1	3	yes	—
119	C₂×C₈×D₁₃	C₂³	1	3	yes	—
120	C₂×C₈×D₁₃	C₂³	1	3	yes	—
121	C₂×C₈×D₁₃	C₂³	1	6	yes	—
122	#88147	C₂×C₄	1	6	yes	—
123	#88146	C₂×C₄	1	6	yes	—
124	C₄⋊C₄×D₁₃	C₂×C₄	1	6	yes	—
125	#88141	C₂×C₄	1	6	yes	—
126	#88135	C₂×C₄	1	12	yes	—
127	C₂²⋊C₄×D₁₃	C₂×C₄	1	6	yes	—
128	#88131	C₂×C₄	1	6	yes	—
129	C₄×D₅₂	C₂×C₄	1	6	yes	—
130	#88126	C₂×C₄	1	6	yes	—
131	#88126	C₂×C₄	1	6	yes	—
132	#88126	C₂³	1	1	yes	characteristic
133	#88126	C₂³	1	3	yes	—
134	#88126	C₂³	1	3	yes	—
135	#88126	C₂³	1	3	yes	—
136	C₄²×D₁₃	C₂³	1	6	yes	—
137	C₄×Dic₂₆	C₂×C₄	1	6	yes	—
138	C₁₃×#97	C₂³	1	6	yes	—
139	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
140	C₄×C₈×C₁₃	C₂³	1	3	yes	—
141	C₄×C₈×C₁₃	C₂³	1	3	yes	—
142	C₄×C₈×C₁₃	C₂³	1	3	yes	—
143	#88055	C₂³	1	1	yes	characteristic
144	#88055	C₂³	1	3	yes	—
145	#88055	C₂³	1	3	yes	—
146	#88055	C₂³	1	3	yes	—
147	#88055	C₂³	1	6	yes	—
148	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
149	C₈×Dic₁₃	C₂³	1	3	yes	—
150	C₈×Dic₁₃	C₂³	1	3	yes	—
151	C₈×Dic₁₃	C₂³	1	3	yes	—
152	C₈×Dic₁₃	C₂³	1	6	yes	—
153	#88043	C₂³	1	3	yes	—
154	#88043	C₂³	1	3	yes	—
155	#88043	C₂³	1	1	yes	characteristic
156	#88043	C₂³	1	3	yes	—
157	C₄×#1055	C₂³	1	6	yes	—
158	#60058	—	13	1	no	maximal, Sylow
159	C₂³×D₁₃	C₂²×C₄	1	3	yes	—
160	C₁₃×#41	C₂²×C₄	1	4	yes	—
161	C₁₃×#41	C₂²×C₄	1	4	yes	—
162	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
163	C₂×D₄×C₁₃	C₂²×C₄	1	3	yes	—
164	C₂²×C₄×C₁₃	C₂²×C₄	1	6	yes	—
165	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
166	C₂×C₂²⋊D₁₃	C₂²×C₄	1	6	yes	—
167	C₂²×Dic₁₃	C₂²×C₄	1	6	yes	—
168	C₂²×Dic₁₃	C₂²×C₄	1	3	yes	—
169	#6131	C₄²	1	8	yes	—
170	Q₈×D₁₃	C₄²	1	8	yes	—
171	#6129	C₄²	1	24	yes	—
172	D₄×D₁₃	C₄²	1	24	yes	—
173	#6127	C₂²×C₄	1	12	yes	—
174	#6127	C₂²×C₄	1	12	yes	—
175	C₂×D₅₂	C₂²×C₄	1	3	yes	—
176	C₂×C₄×D₁₃	C₂²×C₄	1	12	yes	—
177	C₂×C₄×D₁₃	C₂²×C₄	1	3	yes	—
178	C₂×C₄×D₁₃	C₂²×C₄	1	3	yes	—
179	C₂×C₄×D₁₃	C₂²×C₄	1	12	yes	—
180	C₂×C₄×D₁₃	C₂²×C₄	1	12	yes	—
181	C₂×C₄×D₁₃	C₂⁴	1	3	yes	—
182	C₂×C₄×D₁₃	C₂⁴	1	1	yes	characteristic
183	C₂×Dic₂₆	C₂²×C₄	1	3	yes	—
184	C₁₃×M₁₆	C₂²×C₄	1	12	yes	—
185	C₁₃×M₁₆	C₂²×C₄	1	12	yes	—
186	C₂×C₈×C₁₃	C₂²×C₄	1	12	yes	—
187	C₂×C₈×C₁₃	C₂²×C₄	1	12	yes	—
188	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
189	C₂×C₈×C₁₃	C₂⁴	1	3	yes	—
190	C₂×C₈×C₁₃	C₂⁴	1	3	yes	—
191	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
192	C₁₃×C₄⋊C₄	C₂²×C₄	1	6	yes	—
193	C₁₃×C₂²⋊C₄	C₂²×C₄	1	6	yes	—
194	C₄²×C₁₃	C₂²×C₄	1	6	yes	—
195	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
196	C₄²×C₁₃	C₂⁴	1	3	yes	—
197	C₂²⋊Dic₁₃	C₂²×C₄	1	6	yes	—
198	#6103	C₂²×C₄	1	2	yes	—
199	#6103	C₂²×C₄	1	6	yes	—
200	#6103	C₂²×C₄	1	6	yes	—
201	#6103	C₂²×C₄	1	6	yes	—
202	C₄⋊Dic₁₃	C₂²×C₄	1	6	yes	—
203	#6101	C₂²×C₄	1	6	yes	—
204	#6101	C₂²×C₄	1	2	yes	—
205	#6101	C₂²×C₄	1	6	yes	—
206	#6101	C₂²×C₄	1	6	yes	—
207	C₄×Dic₁₃	C₂²×C₄	1	12	yes	—
208	C₄×Dic₁₃	C₂²×C₄	1	6	yes	—
209	C₄×Dic₁₃	C₂⁴	1	3	yes	—
210	C₄×Dic₁₃	C₂⁴	1	1	yes	characteristic
211	#6099	C₂²×C₄	1	12	yes	—
212	#6099	C₂²×C₄	1	12	yes	—
213	C₂×#1055	C₂²×C₄	1	12	yes	—
214	C₂×#1055	C₂²×C₄	1	12	yes	—
215	C₂×#1055	C₂⁴	1	1	yes	characteristic
216	C₂×#1055	C₂⁴	1	3	yes	—
217	C₂×#1055	C₂⁴	1	3	yes	—
218	C₂×#1055	C₂⁴	1	1	yes	characteristic
219	#6094	C₂²×C₄	1	4	yes	—
220	#6094	C₂²×C₄	1	12	yes	—
221	#6094	C₂²×C₄	1	12	yes	—
222	#6094	C₂²×C₄	1	12	yes	—
223	#6094	C₂²×C₄	1	24	yes	—
224	C₈×D₁₃	C₂²×C₄	1	4	yes	—
225	C₈×D₁₃	C₂²×C₄	1	12	yes	—
226	C₈×D₁₃	C₂²×C₄	1	12	yes	—
227	C₈×D₁₃	C₂²×C₄	1	12	yes	—
228	C₈×D₁₃	C₂²×C₄	1	24	yes	—
229	C₂×#568	—	13	1	no	—
230	C₂²×#131	—	13	1	no	—
231	#3428	—	13	1	no	—
232	#2875	—	13	3	no	—
233	#2875	—	13	3	no	—
234	#2875	—	13	1	no	—
235	#2875	—	13	1	no	—
236	C₄×#131	—	13	3	no	—
237	C₄×#131	—	13	3	no	—
238	C₄×#131	—	13	1	no	—
239	C₄×#131	D₁₃	1	1	yes	characteristic, complemented
240	#2873	—	13	3	no	—
241	#2873	—	13	3	no	—
242	C₂×#405	—	13	3	no	—
243	C₂×#405	—	13	3	no	—
244	C₂³×C₁₃	C₂³×C₄	1	3	yes	—
245	C₂²×D₁₃	—	4	6	no	—
246	C₂²×D₁₃	C₂×C₄²	1	12	yes	—
247	C₂²×D₁₃	C₂³×C₄	1	1	yes	characteristic
248	C₂²×D₁₃	C₂³×C₄	1	3	yes	—
249	Q₈×C₁₃	C₂×C₄²	1	4	yes	—
250	D₄×C₁₃	C₂×C₄²	1	12	yes	—
251	C₂×C₄×C₁₃	—	4	6	no	—
252	C₂×C₄×C₁₃	C₂³×C₄	1	6	yes	—
253	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
254	C₂×C₄×C₁₃	C₂³×C₄	1	6	yes	—
255	C₂×C₄×C₁₃	C₂³×C₄	1	6	yes	—
256	C₂×C₄×C₁₃	C₂³×C₄	1	3	yes	—
257	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
258	C₂²⋊D₁₃	C₂×C₄²	1	24	yes	—
259	C₂×Dic₁₃	—	4	6	no	—
260	C₂×Dic₁₃	C₂×C₄²	1	12	yes	—
261	C₂×Dic₁₃	C₂³×C₄	1	2	yes	—
262	C₂×Dic₁₃	C₂³×C₄	1	6	yes	—
263	C₂×Dic₁₃	C₂³×C₄	1	3	yes	—
264	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
265	D₅₂	C₂×C₄²	1	12	yes	—
266	C₄×D₁₃	—	4	12	no	—
267	C₄×D₁₃	C₂×C₄²	1	12	yes	—
268	C₄×D₁₃	C₂×C₄²	1	12	yes	—
269	C₄×D₁₃	C₂³×C₄	1	2	yes	—
270	C₄×D₁₃	C₂³×C₄	1	6	yes	—
271	C₄×D₁₃	C₂³×C₄	1	6	yes	—
272	C₄×D₁₃	C₂³×C₄	1	2	yes	—
273	Dic₂₆	C₂×C₄²	1	12	yes	—
274	C₈×C₁₃	C₂³×C₄	1	2	yes	—
275	C₈×C₁₃	C₂³×C₄	1	6	yes	—
276	C₈×C₁₃	C₂³×C₄	1	6	yes	—
277	C₈×C₁₃	C₂³×C₄	1	2	yes	—
278	#1055	C₂³×C₄	1	2	yes	—
279	#1055	C₂³×C₄	1	6	yes	—
280	#1055	C₂³×C₄	1	6	yes	—
281	#1055	C₂³×C₄	1	2	yes	—
282	C₂²×#41	—	13	1	no	—
283	#568	—	13	16	no	—
284	C₂×#131	—	13	1	no	—
285	C₂×#131	—	13	1	no	—
286	C₂×#131	—	13	16	no	—
287	C₂×#131	—	13	3	no	—
288	C₂×#131	—	13	3	no	—
289	C₂×#131	—	13	3	no	—
290	C₂×#131	—	13	3	no	—
291	C₂×#131	C₂×D₁₃	1	1	yes	characteristic
292	C₂×#131	C₂×D₁₃	1	1	yes	characteristic
293	C₂²×M₁₆	—	13	3	no	—
294	C₂²×M₁₆	—	13	3	no	—
295	C₂²×M₁₆	—	13	3	no	—
296	C₂³×C₈	—	13	3	no	—
297	#520	—	13	2	no	—
298	#520	—	13	6	no	—
299	#519	—	13	2	no	—
300	#518	—	13	6	no	—
301	C₄×#41	—	13	1	no	—
302	C₄×#41	—	13	3	no	—
303	C₄×#41	—	13	3	no	—
304	C₄×#41	C₂×D₁₃	1	1	yes	characteristic
305	C₂×#117	—	13	3	no	—
306	C₂×#117	—	13	3	no	—
307	#405	—	13	3	no	—
308	#405	—	13	3	no	—
309	#405	—	13	3	no	—
310	#405	—	13	3	no	—
311	#405	—	13	3	no	—
312	#405	—	13	3	no	—
313	#405	—	13	6	no	—
314	#405	—	13	6	no	—
315	#405	—	13	3	no	—
316	#405	—	13	1	no	—
317	#405	—	13	3	no	—
318	#405	—	13	3	no	—
319	#405	—	13	3	no	—
320	#405	—	13	3	no	—
321	#405	—	13	3	no	—
322	#405	—	13	3	no	—
323	#405	—	13	6	no	—
324	#405	C₂×D₁₃	1	3	yes	complemented
325	#405	C₂×D₁₃	1	3	yes	complemented
326	C₄×M₁₆	—	13	3	no	—
327	C₄×M₁₆	—	13	3	no	—
328	C₄×M₁₆	—	13	3	no	—
329	C₄×M₁₆	—	13	6	no	—
330	C₄×M₁₆	—	13	6	no	—
331	C₄×M₁₆	C₂×D₁₃	1	3	yes	complemented
332	C₂×#97	—	13	3	no	—
333	C₂×#97	—	13	3	no	—
334	C₂×#97	—	13	6	no	—
335	C₂×C₄×C₈	—	13	3	no	—
336	C₂×C₄×C₈	—	13	6	no	—
337	C₂×C₄×C₈	C₂×D₁₃	1	3	yes	complemented
338	C₂²×C₁₃	—	2	6	no	—
339	C₂²×C₁₃	C₂²×C₄²	1	6	yes	—
340	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
341	C₂×D₁₃	—	2	6	no	—
342	C₂×D₁₃	—	2	2	no	—
343	C₂×D₁₃	—	4	12	no	—
344	C₂×D₁₃	C₂²×C₄²	1	2	yes	—
345	C₂×D₁₃	C₂²×C₄²	1	6	yes	—
346	C₄×C₁₃	—	2	6	no	—
347	C₄×C₁₃	—	2	2	no	—
348	C₄×C₁₃	C₂²×C₄²	1	6	yes	—
349	C₄×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
350	C₄×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
351	Dic₁₃	—	2	6	no	—
352	Dic₁₃	—	2	2	no	—
353	Dic₁₃	C₂²×C₄²	1	6	yes	—
354	Dic₁₃	C₂²×C₄²	1	2	yes	—
355	C₂×#41	—	13	8	no	—
356	C₂×#41	—	13	8	no	—
357	C₂×#41	—	13	1	no	—
358	C₂×#41	—	13	3	no	—
359	C₂×#41	—	13	3	no	—
360	C₂×#41	C₂²×D₁₃	1	1	yes	characteristic
361	C₂²×Q₈	—	13	1	no	—
362	C₂²×D₄	—	13	3	no	—
363	C₂³×C₄	—	13	3	no	—
364	#131	—	13	8	no	—
365	#131	—	13	8	no	—
366	#131	—	13	24	no	—
367	#131	—	13	24	no	—
368	#131	—	13	24	no	—
369	#131	—	13	24	no	—
370	#131	C₄×D₁₃	1	8	yes	complemented
371	#131	C₄×D₁₃	1	8	yes	complemented
372	C₂×M₁₆	—	13	3	no	—
373	C₂×M₁₆	—	13	3	no	—
374	C₂×M₁₆	—	13	24	no	—
375	C₂×M₁₆	—	13	24	no	—
376	C₂×M₁₆	—	13	24	no	—
377	C₂×M₁₆	—	13	3	no	—
378	C₂×M₁₆	—	13	1	no	—
379	C₂×M₁₆	—	13	6	no	—
380	C₂×M₁₆	—	13	3	no	—
381	C₂×M₁₆	—	13	3	no	—
382	C₂×M₁₆	C₂²×D₁₃	1	3	yes	—
383	C₂×M₁₆	C₂²×D₁₃	1	3	yes	—
384	C₂²×C₈	—	13	3	no	—
385	C₂²×C₈	—	13	3	no	—
386	C₂²×C₈	—	13	24	no	—
387	C₂²×C₈	—	13	3	no	—
388	C₂²×C₈	—	13	3	no	—
389	C₂²×C₈	—	13	6	no	—
390	C₂²×C₈	—	13	1	no	—
391	C₂²×C₈	—	13	3	no	—
392	C₂²×C₈	C₂²×D₁₃	1	3	yes	—
393	C₂²×C₈	C₂²×D₁₃	1	3	yes	—
394	C₄×Q₈	—	13	2	no	—
395	C₄×Q₈	—	13	6	no	—
396	C₄×Q₈	—	13	6	no	—
397	C₄×Q₈	C₄×D₁₃	1	2	yes	—
398	C₄×D₄	—	13	6	no	—
399	C₄×D₄	—	13	12	no	—
400	C₄×D₄	—	13	6	no	—
401	C₄×D₄	—	13	12	no	—
402	C₄×D₄	—	13	6	no	—
403	C₄×D₄	C₄×D₁₃	1	6	yes	—
404	#117	—	13	3	no	—
405	#117	—	13	6	no	—
406	#117	—	13	6	no	—
407	#117	—	13	6	no	—
408	#117	—	13	6	no	—
409	#117	—	13	3	no	—
410	#117	—	13	1	no	—
411	#117	—	13	3	no	—
412	#117	—	13	3	no	—
413	#117	C₂²×D₁₃	1	3	yes	—
414	C₂×C₄⋊C₄	—	13	6	no	—
415	C₂×C₄⋊C₄	—	13	6	no	—
416	C₂×C₂²⋊C₄	—	13	6	no	—
417	C₂×C₂²⋊C₄	—	13	6	no	—
418	C₂×C₄²	—	13	3	no	—
419	C₂×C₄²	—	13	6	no	—
420	C₂×C₄²	C₂²×D₁₃	1	3	yes	—
421	#97	—	13	3	no	—
422	#97	—	13	1	no	—
423	#97	—	13	3	no	—
424	#97	—	13	6	no	—
425	#97	—	13	3	no	—
426	#97	—	13	3	no	—
427	#97	—	13	1	no	—
428	#97	—	13	3	no	—
429	#97	—	13	3	no	—
430	#97	C₂²×D₁₃	1	6	yes	—
431	C₄×C₈	—	13	3	no	—
432	C₄×C₈	—	13	3	no	—
433	C₄×C₈	—	13	6	no	—
434	C₄×C₈	—	13	1	no	—
435	C₄×C₈	—	13	3	no	—
436	C₄×C₈	—	13	6	no	—
437	C₄×C₈	C₂²×D₁₃	1	3	yes	—
438	C₄×C₈	C₂²×D₁₃	1	3	yes	—
439	C₄×C₈	C₂²×D₁₃	1	3	yes	—
440	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
441	C₂×C₁₃	—	2	6	no	—
442	C₂×C₁₃	C₂³×C₄²	1	1	yes	characteristic
443	C₂×C₁₃	#3573	1	2	yes	—
444	D₁₃	—	2	2	no	—
445	D₁₃	—	2	6	no	—
446	C₂⁴	—	13	3	no	—
447	#41	—	13	8	no	—
448	#41	—	13	24	no	—
449	#41	—	13	12	no	—
450	#41	—	13	12	no	—
451	#41	C₂×C₄×D₁₃	1	4	yes	—
452	#41	C₂×C₄×D₁₃	1	4	yes	—
453	C₂×Q₈	—	13	8	no	—
454	C₂×Q₈	—	13	3	no	—
455	C₂×Q₈	C₂×C₄×D₁₃	1	1	yes	characteristic
456	C₂×D₄	—	13	6	no	—
457	C₂×D₄	—	13	24	no	—
458	C₂×D₄	—	13	3	no	—
459	C₂×D₄	C₂×C₄×D₁₃	1	3	yes	—
460	C₂²×C₄	—	13	3	no	—
461	C₂²×C₄	—	13	3	no	—
462	C₂²×C₄	—	13	3	no	—
463	C₂²×C₄	—	13	12	no	—
464	C₂²×C₄	—	13	12	no	—
465	C₂²×C₄	—	13	3	no	—
466	C₂²×C₄	—	13	1	no	—
467	C₂²×C₄	—	13	6	no	—
468	C₂²×C₄	—	13	12	no	—
469	C₂²×C₄	C₂×C₄×D₁₃	1	6	yes	—
470	C₂²×C₄	C₂³×D₁₃	1	3	yes	—
471	M₁₆	—	13	12	no	—
472	M₁₆	—	13	12	no	—
473	M₁₆	—	13	12	no	—
474	M₁₆	—	13	4	no	—
475	M₁₆	—	13	24	no	—
476	M₁₆	—	13	12	no	—
477	M₁₆	—	13	12	no	—
478	M₁₆	C₂×C₄×D₁₃	1	12	yes	—
479	M₁₆	C₂×C₄×D₁₃	1	12	yes	—
480	C₂×C₈	—	13	12	no	—
481	C₂×C₈	—	13	12	no	—
482	C₂×C₈	—	13	1	no	—
483	C₂×C₈	—	13	3	no	—
484	C₂×C₈	—	13	3	no	—
485	C₂×C₈	—	13	1	no	—
486	C₂×C₈	—	13	4	no	—
487	C₂×C₈	—	13	12	no	—
488	C₂×C₈	—	13	12	no	—
489	C₂×C₈	—	13	12	no	—
490	C₂×C₈	—	13	24	no	—
491	C₂×C₈	C₂×C₄×D₁₃	1	12	yes	—
492	C₂×C₈	C₂×C₄×D₁₃	1	12	yes	—
493	C₂×C₈	C₂³×D₁₃	1	3	yes	—
494	C₂×C₈	C₂³×D₁₃	1	3	yes	—
495	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
496	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
497	C₄⋊C₄	—	13	6	no	—
498	C₄⋊C₄	—	13	2	no	—
499	C₄⋊C₄	—	13	6	no	—
500	C₄⋊C₄	—	13	6	no	—
501	C₄⋊C₄	—	13	6	no	—
502	C₄⋊C₄	C₂×C₄×D₁₃	1	6	yes	—
503	C₂²⋊C₄	—	13	6	no	—
504	C₂²⋊C₄	—	13	6	no	—
505	C₂²⋊C₄	—	13	2	no	—
506	C₂²⋊C₄	—	13	6	no	—
507	C₂²⋊C₄	—	13	6	no	—
508	C₂²⋊C₄	C₂×C₄×D₁₃	1	6	yes	—
509	C₄²	—	13	12	no	—
510	C₄²	—	13	6	no	—
511	C₄²	—	13	1	no	—
512	C₄²	—	13	3	no	—
513	C₄²	C₂×C₄×D₁₃	1	6	yes	—
514	C₄²	C₂³×D₁₃	1	3	yes	—
515	C₄²	C₂³×D₁₃	1	1	yes	characteristic
516	C₁₃	#60058	1	1	yes	characteristic, complemented, Sylow
517	C₂³	—	13	1	no	—
518	C₂³	—	13	3	no	—
519	C₂³	—	13	12	no	—
520	C₂³	—	52	6	no	—
521	C₂³	C₂²×C₄×D₁₃	1	3	yes	—
522	Q₈	—	13	12	no	—
523	Q₈	C₄²×D₁₃	1	4	yes	—
524	D₄	—	13	24	no	—
525	D₄	—	13	12	no	—
526	D₄	C₄²×D₁₃	1	12	yes	—
527	C₂×C₄	—	4	6	no	—
528	C₂×C₄	—	13	12	no	—
529	C₂×C₄	—	13	3	no	—
530	C₂×C₄	—	13	1	no	—
531	C₂×C₄	—	13	12	no	—
532	C₂×C₄	—	13	12	no	—
533	C₂×C₄	—	13	2	no	—
534	C₂×C₄	—	13	6	no	—
535	C₂×C₄	—	13	6	no	—
536	C₂×C₄	—	13	2	no	—
537	C₂×C₄	—	13	6	no	—
538	C₂×C₄	—	13	2	no	—
539	C₂×C₄	—	52	12	no	—
540	C₂×C₄	—	52	6	no	—
541	C₂×C₄	C₂²×C₄×D₁₃	1	6	yes	—
542	C₂×C₄	C₂²×C₄×D₁₃	1	2	yes	—
543	C₂×C₄	C₂²×C₄×D₁₃	1	3	yes	—
544	C₂×C₄	C₂²×C₄×D₁₃	1	6	yes	—
545	C₂×C₄	C₂²×C₄×D₁₃	1	6	yes	—
546	C₂×C₄	C₂⁴×D₁₃	1	1	yes	characteristic
547	C₈	—	13	2	no	—
548	C₈	—	13	6	no	—
549	C₈	—	13	6	no	—
550	C₈	—	13	2	no	—
551	C₈	C₂²×C₄×D₁₃	1	2	yes	—
552	C₈	C₂²×C₄×D₁₃	1	6	yes	—
553	C₈	C₂²×C₄×D₁₃	1	6	yes	—
554	C₈	C₂²×C₄×D₁₃	1	2	yes	—
555	C₂²	—	2	6	no	—
556	C₂²	—	13	2	no	—
557	C₂²	—	13	6	no	—
558	C₂²	—	26	6	no	—
559	C₂²	—	26	2	no	—
560	C₂²	—	52	12	no	—
561	C₂²	C₂×C₄²×D₁₃	1	6	yes	—
562	C₂²	C₂³×C₄×D₁₃	1	1	yes	characteristic
563	C₄	—	2	2	no	—
564	C₄	—	2	6	no	—
565	C₄	—	13	2	no	—
566	C₄	—	13	6	no	—
567	C₄	—	26	6	no	—
568	C₄	—	26	2	no	—
569	C₄	C₂×C₄²×D₁₃	1	6	yes	—
570	C₄	C₂³×C₄×D₁₃	1	1	yes	characteristic
571	C₄	C₂³×C₄×D₁₃	1	1	yes	characteristic
572	C₂	—	2	6	no	—
573	C₂	—	26	2	no	—
574	C₂	—	26	6	no	—
575	C₂	C₂²×C₄²×D₁₃	1	1	yes	characteristic
576	C₂	#13129547	1	2	yes	—

	subgroup	G/H
center	C₂×C₈	C₂³×D₁₃
commutator	C₂×C₁₃	C₂³×C₄²
Frattini	C₂×C₄	C₂⁴×D₁₃
Fitting	C₄×C₁₃×#131	C₂
socle	C₂²×C₁₃	C₂⁴×C₄
prime radical	C₂×#41×D₁₃	C₂²
cosocle	C₂×C₄×C₁₃	C₂⁵
hypercenter	C₄×#131	D₁₃
hypocenter	C₁₃	#60058
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₈ ◁ C₄×#131

Complements

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

N	H ≅ G/N	type
4. #13123265	C₂	semidirect
5. #13123264	C₂	semidirect
6. #13123263	C₂	semidirect
7. #13123262	C₂	semidirect
8. #13123258	C₂	semidirect
9. #131×Dic₁₃	C₂	semidirect
10. C₄×#88155	C₂	semidirect
11. #13123253	C₂	semidirect
12. #13123252	C₂	semidirect
13. C₂×#11718350	C₂	semidirect
14. D₁₃×#405	C₂	semidirect
15. C₄×C₁₃×#131	C₂	semidirect
23. #11719455	C₄	semidirect
24. D₁₃×#131	C₄	semidirect
41. C₁₃×#405	C₂²	semidirect
42. C₁₃×#405	C₂²	semidirect
43. C₄×C₁₃×M₁₆	C₂²	semidirect
44. C₂×C₄×C₈×C₁₃	C₂²	semidirect
45. #11718783	C₂²	semidirect
46. #11718783	C₂²	semidirect
47. M₁₆×Dic₁₃	C₂²	semidirect
48. M₁₆×Dic₁₃	C₂²	semidirect
49. #11718762	C₂²	semidirect
50. #11718762	C₂²	semidirect
51. C₂×#88055	C₂²	semidirect
52. C₂×C₈×Dic₁₃	C₂²	semidirect
53. #11718658	C₂²	semidirect
54. #11718658	C₂²	semidirect
55. C₄×#6099	C₂²	semidirect
56. C₂×#88043	C₂²	semidirect
58. #11718369	C₂²	semidirect
59. #11718368	C₂²	semidirect
60. D₁₃×#97	C₂²	semidirect
65. #11718350	C₂²	semidirect
66. #11718350	C₂²	semidirect
67. #11718350	C₂²	semidirect
68. #11718350	C₂²	semidirect
69. #11718350	C₂²	semidirect
70. C₄×#6094	C₂²	semidirect
71. C₄×C₈×D₁₃	C₂²	semidirect
81. C₁₃×#131	C₂×C₄	semidirect
82. C₁₃×#131	C₂×C₄	semidirect
91. #88202	C₂×C₄	semidirect
92. #88202	C₂×C₄	semidirect
104. #88161	C₂×C₄	semidirect
105. #88161	C₂×C₄	semidirect
106. M₁₆×D₁₃	C₂×C₄	semidirect
107. M₁₆×D₁₃	C₂×C₄	semidirect
108. #88155	C₂×C₄	semidirect
109. #88155	C₂×C₄	semidirect
110. C₂×#6094	C₂×C₄	semidirect
116. C₂×C₈×D₁₃	C₂×C₄	semidirect
239. C₄×#131	D₁₃	semidirect
324. #405	C₂×D₁₃	semidirect
325. #405	C₂×D₁₃	semidirect
331. C₄×M₁₆	C₂×D₁₃	semidirect
337. C₂×C₄×C₈	C₂×D₁₃	semidirect
370. #131	C₄×D₁₃	semidirect
371. #131	C₄×D₁₃	semidirect
516. C₁₃	#60058	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11719455	2
C₂×D₁₃×#131	2
#13128035	2
#13123265	2
#13123264	2
#13123263	2
#13123262	2
#13123258	2
#131×Dic₁₃	2
C₄×#88155	2
#13123253	2
#13123252	2
C₂×#11718350	2
D₁₃×#405	2
C₄×C₁₃×#131	2
#60058	13