Subgroups — #15860909

Order 3328.

1242 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718498	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718368	C₂	1	1	yes	maximal, characteristic
3	C₂×#11718368	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×#6094	C₂	1	1	yes	maximal, characteristic
5	C₄×C₄⋊C₄×D₁₃	C₂	1	1	yes	maximal, characteristic
6	#13114713	C₂	1	1	yes	maximal, characteristic, complemented
7	#13114711	C₂	1	1	yes	maximal, characteristic, complemented
8	#13114708	C₂	1	1	yes	maximal, characteristic, complemented
9	#13114704	C₂	1	1	yes	maximal, characteristic, complemented
10	#13114702	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×#6101	C₂	1	1	yes	maximal, characteristic, complemented
12	#13114697	C₂	1	1	yes	maximal, characteristic, complemented
13	#13114528	C₂	1	1	yes	maximal, characteristic
14	#13114528	C₂	1	1	yes	maximal, characteristic
15	C₁₃×#1771	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#6094	C₂²	1	1	yes	characteristic
17	C₂²×#6094	C₂²	1	1	yes	characteristic
18	C₂²×#6094	C₂²	1	1	yes	characteristic
19	C₂²×#6094	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊C₄×D₁₃	C₄	1	2	yes	—
21	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
22	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
23	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
28	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₂×#88055	C₂²	1	1	yes	characteristic
30	C₂×#88055	C₂²	1	1	yes	characteristic
31	C₂×#88054	C₂²	1	1	yes	characteristic
32	C₂×#88054	C₂²	1	1	yes	characteristic
33	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
34	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
35	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
36	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
37	C₄⋊C₄×Dic₁₃	C₄	1	2	yes	—
38	C₄×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic
39	C₄×#6101	C₂²	1	1	yes	characteristic
40	C₄×#6101	C₂²	1	1	yes	characteristic
41	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
42	C₂×#88043	C₂²	1	1	yes	characteristic
43	C₂×#88043	C₂²	1	1	yes	characteristic
44	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
45	#11718498	C₄	1	8	yes	complemented
46	#11718368	—	2	4	no	—
47	#11718368	C₄	1	8	yes	complemented
48	C₄×#6094	—	2	4	no	—
49	D₁₃×#95	C₄	1	2	yes	—
50	#11718310	C₄	1	2	yes	—
51	C₁₃×#336	C₂²	1	1	yes	characteristic
52	C₁₃×#336	C₂²	1	1	yes	characteristic
53	#11718142	C₂²	1	1	yes	characteristic
54	#11718142	C₂²	1	1	yes	characteristic
55	#11718142	C₂²	1	1	yes	characteristic
56	#11718142	C₂²	1	1	yes	characteristic
57	#11718116	C₂²	1	1	yes	characteristic
58	#11718116	C₂²	1	1	yes	characteristic
59	C₂²×C₄×D₁₃	C₂×C₄	1	2	yes	—
60	C₂²×C₄×D₁₃	C₂×C₄	1	2	yes	—
61	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
62	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
63	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
65	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
66	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
67	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
68	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
69	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
71	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
72	C₂×C₄⋊Dic₁₃	C₂×C₄	1	2	yes	—
73	C₂×#6101	C₂×C₄	1	2	yes	—
74	C₂×#6101	C₂×C₄	1	2	yes	—
75	C₂×C₄×Dic₁₃	C₂×C₄	1	2	yes	—
76	C₂×C₄×Dic₁₃	C₂×C₄	1	2	yes	—
77	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
79	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
80	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
81	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
82	C₂²×#1055	C₂³	1	1	yes	characteristic
83	C₂²×#1055	C₂³	1	1	yes	characteristic
84	C₂²×#1055	C₂³	1	1	yes	characteristic
85	C₂²×#1055	C₂³	1	1	yes	characteristic
86	C₂×#6094	—	2	2	no	—
87	C₂×#6094	—	2	2	no	—
88	C₂×#6094	—	2	2	no	—
89	C₂×#6094	—	2	2	no	—
90	C₂×#6094	—	2	2	no	—
91	C₂×#6094	—	2	2	no	—
92	C₂×#6094	C₂×C₄	1	4	yes	—
93	C₂×#6094	C₂×C₄	1	4	yes	—
94	C₂×#6094	C₂×C₄	1	4	yes	—
95	C₂×#6094	C₂×C₄	1	4	yes	—
96	C₂×#6094	D₄	1	4	yes	—
97	C₂×#6094	Q₈	1	4	yes	—
98	C₄⋊C₄×D₁₃	—	2	8	no	—
99	C₄²×D₁₃	—	2	2	no	—
100	C₄²×D₁₃	—	2	2	no	—
101	C₄²×D₁₃	—	2	2	no	—
102	C₄²×D₁₃	—	2	2	no	—
103	C₄²×D₁₃	C₂×C₄	1	4	yes	—
104	C₄²×D₁₃	C₂×C₄	1	4	yes	—
105	C₁₃×C₄⋊C₈	C₂×C₄	1	4	yes	complemented
106	C₁₃×#97	—	2	2	no	—
107	C₁₃×#97	C₂×C₄	1	4	yes	complemented
108	C₄×C₈×C₁₃	—	2	2	no	—
109	C₁₃×#95	C₂×C₄	1	2	yes	—
110	#88071	C₂×C₄	1	2	yes	—
111	#88071	C₂×C₄	1	2	yes	—
112	#88071	C₂×C₄	1	2	yes	—
113	#88055	—	2	2	no	—
114	#88055	—	2	2	no	—
115	#88054	C₂×C₄	1	4	yes	complemented
116	#88054	C₂×C₄	1	4	yes	complemented
117	C₈×Dic₁₃	—	2	2	no	—
118	C₈×Dic₁₃	—	2	2	no	—
119	C₈×Dic₁₃	C₂×C₄	1	4	yes	complemented
120	C₈×Dic₁₃	C₂×C₄	1	4	yes	complemented
121	C₄⋊#1055	C₂×C₄	1	4	yes	complemented
122	#88043	—	2	2	no	—
123	#88043	C₂×C₄	1	4	yes	complemented
124	C₄×#1055	—	2	2	no	—
125	C₄⋊C₄×M₁₆	—	13	1	no	maximal, Sylow
126	C₂³×D₁₃	C₂²×C₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
128	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
131	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
132	C₂²×Dic₁₃	C₂²×C₄	1	2	yes	—
133	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
134	C₂²×Dic₁₃	C₂²×C₄	1	2	yes	—
135	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
136	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
137	C₂×C₄×D₁₃	—	2	4	no	—
138	C₂×C₄×D₁₃	—	2	4	no	—
139	C₂×C₄×D₁₃	—	2	4	no	—
140	C₂×C₄×D₁₃	—	2	4	no	—
141	C₂×C₄×D₁₃	—	2	4	no	—
142	C₂×C₄×D₁₃	—	4	2	no	—
143	C₂×C₄×D₁₃	—	4	2	no	—
144	C₂×C₄×D₁₃	—	4	2	no	—
145	C₂×C₄×D₁₃	C₄²	1	4	yes	—
146	C₂×C₄×D₁₃	C₄²	1	4	yes	—
147	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
148	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
149	C₂×C₄×D₁₃	C₂×D₄	1	2	yes	—
150	C₂×C₄×D₁₃	C₂×Q₈	1	2	yes	—
151	C₂×C₄×D₁₃	#41	1	2	yes	—
152	C₂×C₄×D₁₃	#41	1	2	yes	—
153	C₂×C₈×C₁₃	—	2	1	no	—
154	C₂×C₈×C₁₃	—	2	1	no	—
155	C₂×C₈×C₁₃	—	2	1	no	—
156	C₂×C₈×C₁₃	—	2	1	no	—
157	C₂×C₈×C₁₃	—	2	1	no	—
158	C₂×C₈×C₁₃	—	2	1	no	—
159	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
160	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
161	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
162	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
163	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
164	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
165	C₁₃×C₄⋊C₄	—	2	4	no	—
166	C₄²×C₁₃	—	2	1	no	—
167	C₄²×C₁₃	—	2	1	no	—
168	C₄²×C₁₃	—	2	1	no	—
169	C₄²×C₁₃	—	2	1	no	—
170	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
171	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
172	C₄⋊Dic₁₃	—	2	4	no	—
173	#6101	—	2	4	no	—
174	#6101	M₁₆	1	8	yes	complemented
175	C₄×Dic₁₃	—	2	1	no	—
176	C₄×Dic₁₃	—	2	1	no	—
177	C₄×Dic₁₃	—	2	1	no	—
178	C₄×Dic₁₃	—	2	1	no	—
179	C₄×Dic₁₃	—	2	4	no	—
180	C₄×Dic₁₃	—	2	4	no	—
181	C₄×Dic₁₃	C₄²	1	4	yes	—
182	C₄×Dic₁₃	C₄²	1	4	yes	—
183	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
184	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
185	C₂×#1055	—	2	1	no	—
186	C₂×#1055	—	2	1	no	—
187	C₂×#1055	—	2	1	no	—
188	C₂×#1055	—	2	1	no	—
189	C₂×#1055	—	2	1	no	—
190	C₂×#1055	—	2	1	no	—
191	C₂×#1055	C₂²×C₄	1	2	yes	—
192	C₂×#1055	C₂²×C₄	1	2	yes	—
193	C₂×#1055	C₂²×C₄	1	2	yes	—
194	C₂×#1055	C₂²×C₄	1	2	yes	—
195	C₂×#1055	C₂×D₄	1	2	yes	—
196	C₂×#1055	C₂×Q₈	1	2	yes	—
197	#6094	—	2	8	no	—
198	#6094	—	2	8	no	—
199	#6094	—	2	8	no	—
200	#6094	C₄⋊C₄	1	16	yes	complemented
201	C₂×#423	—	13	1	no	—
202	C₂×C₄×M₁₆	—	13	1	no	—
203	C₂×C₄×M₁₆	—	13	1	no	—
204	C₂×C₄×M₁₆	—	13	1	no	—
205	C₂×C₄×C₄⋊C₄	—	13	1	no	—
206	#1771	—	13	1	no	—
207	#1771	—	13	1	no	—
208	#1771	—	13	1	no	—
209	#1771	D₁₃	1	1	yes	characteristic, complemented
210	#1770	—	13	1	no	—
211	#1770	—	13	1	no	—
212	C₈×C₄⋊C₄	—	13	1	no	—
213	C₈×C₄⋊C₄	—	13	1	no	—
214	#1728	—	13	1	no	—
215	#1728	—	13	1	no	—
216	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
217	C₂²×D₁₃	—	2	2	no	—
218	C₂²×D₁₃	—	2	2	no	—
219	C₂²×D₁₃	C₂×C₄²	1	2	yes	—
220	C₂²×D₁₃	C₄×D₄	1	2	yes	—
221	C₂²×D₁₃	C₄×Q₈	1	2	yes	—
222	C₂×C₄×C₁₃	—	2	2	no	—
223	C₂×C₄×C₁₃	—	2	2	no	—
224	C₂×C₄×C₁₃	—	2	2	no	—
225	C₂×C₄×C₁₃	—	2	2	no	—
226	C₂×C₄×C₁₃	—	2	2	no	—
227	C₂×C₄×C₁₃	—	2	2	no	—
228	C₂×C₄×C₁₃	—	2	2	no	—
229	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
230	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
231	C₂×C₄×C₁₃	C₂×M₁₆	1	4	yes	—
232	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
233	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
234	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
235	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
236	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
237	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
238	C₂×Dic₁₃	—	2	2	no	—
239	C₂×Dic₁₃	—	2	2	no	—
240	C₂×Dic₁₃	—	2	2	no	—
241	C₂×Dic₁₃	—	2	2	no	—
242	C₂×Dic₁₃	—	2	2	no	—
243	C₂×Dic₁₃	—	2	2	no	—
244	C₂×Dic₁₃	C₂×C₄²	1	2	yes	—
245	C₂×Dic₁₃	C₂×C₄²	1	2	yes	—
246	C₂×Dic₁₃	C₂×C₄²	1	2	yes	—
247	C₂×Dic₁₃	C₄×D₄	1	2	yes	—
248	C₂×Dic₁₃	C₄×Q₈	1	2	yes	—
249	C₂×Dic₁₃	C₂×M₁₆	1	4	yes	—
250	C₂×Dic₁₃	C₂×M₁₆	1	4	yes	—
251	C₄×D₁₃	—	2	8	no	—
252	C₄×D₁₃	—	4	4	no	—
253	C₄×D₁₃	—	4	8	no	—
254	C₄×D₁₃	—	4	8	no	—
255	C₄×D₁₃	C₂×C₄⋊C₄	1	4	yes	—
256	C₄×D₁₃	#117	1	4	yes	—
257	C₄×D₁₃	C₄×D₄	1	4	yes	—
258	C₄×D₁₃	C₄×Q₈	1	4	yes	—
259	C₈×C₁₃	—	2	2	no	—
260	C₈×C₁₃	—	2	2	no	—
261	C₈×C₁₃	—	2	2	no	—
262	C₈×C₁₃	C₂×C₄⋊C₄	1	4	yes	complemented
263	#1055	—	2	2	no	—
264	#1055	—	2	2	no	—
265	#1055	—	2	2	no	—
266	#1055	C₂×C₄⋊C₄	1	4	yes	complemented
267	C₂²×M₁₆	—	13	1	no	—
268	C₂²×M₁₆	—	13	1	no	—
269	C₂²×M₁₆	—	13	1	no	—
270	C₂²×M₁₆	—	13	1	no	—
271	C₂²×C₄⋊C₄	—	13	2	no	—
272	C₂²×C₄²	—	13	1	no	—
273	C₂²×C₄²	—	13	1	no	—
274	C₂²×C₄²	—	13	1	no	—
275	#423	—	13	8	no	—
276	C₂×C₄⋊C₈	—	13	1	no	—
277	C₂×C₄⋊C₈	—	13	1	no	—
278	C₂×C₄⋊C₈	—	13	1	no	—
279	C₂×C₄⋊C₈	C₂×D₁₃	1	1	yes	characteristic
280	C₄×M₁₆	—	13	8	no	—
281	C₄×M₁₆	—	26	4	no	—
282	C₄×M₁₆	—	26	4	no	—
283	C₂×#97	—	13	1	no	—
284	C₂×#97	—	13	1	no	—
285	C₂×#97	—	13	1	no	—
286	C₂×#97	—	13	1	no	—
287	C₂×#97	C₂×D₁₃	1	1	yes	characteristic
288	C₂×#97	C₂×D₁₃	1	1	yes	characteristic
289	C₂×C₄×C₈	—	13	1	no	—
290	C₂×C₄×C₈	—	13	1	no	—
291	C₂×C₄×C₈	—	13	1	no	—
292	C₂×C₄×C₈	—	13	1	no	—
293	C₂×C₄×C₈	—	13	1	no	—
294	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
295	C₄×C₄⋊C₄	—	13	2	no	—
296	C₄×C₄⋊C₄	—	13	1	no	—
297	C₄×C₄⋊C₄	—	13	1	no	—
298	C₄×C₄⋊C₄	—	13	1	no	—
299	C₄×C₄⋊C₄	—	13	2	no	—
300	C₄×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
301	C₂×#95	—	13	2	no	—
302	#336	—	13	1	no	—
303	#336	—	13	1	no	—
304	#336	—	13	1	no	—
305	#336	—	13	1	no	—
306	#336	—	13	1	no	—
307	#336	—	13	1	no	—
308	#336	C₂×D₁₃	1	1	yes	characteristic
309	#336	C₂×D₁₃	1	1	yes	characteristic
310	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
311	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
312	C₂²×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
313	C₂²×C₁₃	C₂²×M₁₆	1	2	yes	—
314	C₂²×C₁₃	#568	1	2	yes	—
315	C₂×D₁₃	—	2	2	no	—
316	C₂×D₁₃	—	2	2	no	—
317	C₂×D₁₃	—	2	4	no	—
318	C₂×D₁₃	—	2	4	no	—
319	C₂×D₁₃	C₄×C₄⋊C₄	1	4	yes	—
320	C₄×C₁₃	—	2	2	no	—
321	C₄×C₁₃	—	2	2	no	—
322	C₄×C₁₃	—	2	4	no	—
323	C₄×C₁₃	—	4	2	no	—
324	C₄×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
325	C₄×C₁₃	C₂×#117	1	1	yes	characteristic
326	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
327	C₄×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
328	Dic₁₃	—	2	2	no	—
329	Dic₁₃	—	2	4	no	—
330	Dic₁₃	—	4	2	no	—
331	Dic₁₃	C₄×C₄⋊C₄	1	4	yes	—
332	Dic₁₃	C₄×M₁₆	1	4	yes	complemented
333	C₂³×C₄	—	13	1	no	—
334	C₂³×C₄	—	13	1	no	—
335	C₂³×C₄	—	13	1	no	—
336	C₂³×C₄	—	13	2	no	—
337	C₂³×C₄	—	13	2	no	—
338	C₂×M₁₆	—	13	4	no	—
339	C₂×M₁₆	—	13	4	no	—
340	C₂×M₁₆	—	13	4	no	—
341	C₂×M₁₆	—	13	4	no	—
342	C₂×M₁₆	—	13	4	no	—
343	C₂×M₁₆	—	13	4	no	—
344	C₂×M₁₆	—	26	2	no	—
345	C₂×M₁₆	—	26	2	no	—
346	C₂×M₁₆	—	26	2	no	—
347	C₂×M₁₆	—	26	2	no	—
348	C₂×M₁₆	—	26	2	no	—
349	C₂×M₁₆	—	26	2	no	—
350	C₂²×C₈	—	13	1	no	—
351	C₂²×C₈	—	13	1	no	—
352	C₂²×C₈	—	13	1	no	—
353	C₂²×C₈	—	13	1	no	—
354	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
355	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
356	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
357	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
358	C₂×C₄⋊C₄	—	13	2	no	—
359	C₂×C₄⋊C₄	—	13	2	no	—
360	C₂×C₄⋊C₄	—	13	2	no	—
361	C₂×C₄⋊C₄	—	26	8	no	—
362	C₂×C₄⋊C₄	C₄×D₁₃	1	2	yes	—
363	C₂×C₄²	—	13	1	no	—
364	C₂×C₄²	—	13	1	no	—
365	C₂×C₄²	—	13	1	no	—
366	C₂×C₄²	—	13	4	no	—
367	C₂×C₄²	—	13	4	no	—
368	C₂×C₄²	—	13	2	no	—
369	C₂×C₄²	—	13	2	no	—
370	C₂×C₄²	—	13	1	no	—
371	C₂×C₄²	—	13	1	no	—
372	C₂×C₄²	—	26	2	no	—
373	C₂×C₄²	—	26	2	no	—
374	C₂×C₄²	—	26	2	no	—
375	C₂×C₄²	—	26	2	no	—
376	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
377	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
378	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
379	C₄⋊C₈	—	13	4	no	—
380	C₄⋊C₈	—	13	4	no	—
381	C₄⋊C₈	—	13	4	no	—
382	C₄⋊C₈	C₄×D₁₃	1	4	yes	complemented
383	#97	—	2	2	no	—
384	#97	—	13	4	no	—
385	#97	—	26	2	no	—
386	#97	—	26	2	no	—
387	#97	—	26	2	no	—
388	#97	C₄×D₁₃	1	4	yes	complemented
389	C₄×C₈	—	2	2	no	—
390	C₄×C₈	—	13	4	no	—
391	C₄×C₈	—	13	4	no	—
392	C₄×C₈	—	26	2	no	—
393	C₄×C₈	—	26	2	no	—
394	C₄×C₈	—	26	2	no	—
395	#95	—	13	2	no	—
396	#95	—	13	2	no	—
397	#95	—	13	2	no	—
398	#95	C₄×D₁₃	1	2	yes	—
399	C₂×C₁₃	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
400	C₂×C₁₃	C₂×C₄×M₁₆	1	1	yes	characteristic
401	C₂×C₁₃	#2873	1	1	yes	characteristic
402	C₂×C₁₃	D₄×M₁₆	1	2	yes	—
403	C₂×C₁₃	Q₈×M₁₆	1	2	yes	—
404	D₁₃	—	2	4	no	—
405	C₂⁴	—	13	1	no	—
406	C₂²×C₄	—	13	1	no	—
407	C₂²×C₄	—	13	1	no	—
408	C₂²×C₄	—	13	2	no	—
409	C₂²×C₄	—	13	2	no	—
410	C₂²×C₄	—	13	2	no	—
411	C₂²×C₄	—	13	2	no	—
412	C₂²×C₄	—	13	2	no	—
413	C₂²×C₄	—	13	2	no	—
414	C₂²×C₄	—	13	1	no	—
415	C₂²×C₄	—	13	2	no	—
416	C₂²×C₄	—	13	4	no	—
417	C₂²×C₄	—	13	4	no	—
418	C₂²×C₄	—	13	2	no	—
419	C₂²×C₄	—	26	4	no	—
420	C₂²×C₄	—	26	4	no	—
421	C₂²×C₄	—	26	4	no	—
422	C₂²×C₄	—	26	4	no	—
423	C₂²×C₄	—	26	4	no	—
424	C₂²×C₄	—	52	2	no	—
425	C₂²×C₄	—	52	2	no	—
426	C₂²×C₄	—	52	2	no	—
427	C₂²×C₄	C₂×C₄×D₁₃	1	2	yes	—
428	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
429	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
430	C₂²×C₄	C₂×C₄×D₁₃	1	2	yes	—
431	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
432	M₁₆	—	13	16	no	—
433	M₁₆	—	26	8	no	—
434	M₁₆	—	26	8	no	—
435	M₁₆	—	26	8	no	—
436	C₂×C₈	—	2	1	no	—
437	C₂×C₈	—	2	1	no	—
438	C₂×C₈	—	2	1	no	—
439	C₂×C₈	—	2	1	no	—
440	C₂×C₈	—	2	1	no	—
441	C₂×C₈	—	2	1	no	—
442	C₂×C₈	—	13	2	no	—
443	C₂×C₈	—	13	2	no	—
444	C₂×C₈	—	13	2	no	—
445	C₂×C₈	—	13	2	no	—
446	C₂×C₈	—	13	2	no	—
447	C₂×C₈	—	13	2	no	—
448	C₂×C₈	—	26	1	no	—
449	C₂×C₈	—	26	1	no	—
450	C₂×C₈	—	26	1	no	—
451	C₂×C₈	—	26	1	no	—
452	C₂×C₈	—	26	1	no	—
453	C₂×C₈	—	26	1	no	—
454	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
455	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
456	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
457	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
458	C₂×C₈	D₄×D₁₃	1	2	yes	—
459	C₂×C₈	Q₈×D₁₃	1	2	yes	—
460	C₄⋊C₄	—	2	4	no	—
461	C₄⋊C₄	—	13	8	no	—
462	C₄⋊C₄	—	26	4	no	—
463	C₄⋊C₄	—	26	4	no	—
464	C₄²	—	2	1	no	—
465	C₄²	—	2	1	no	—
466	C₄²	—	2	1	no	—
467	C₄²	—	2	1	no	—
468	C₄²	—	13	4	no	—
469	C₄²	—	13	4	no	—
470	C₄²	—	13	2	no	—
471	C₄²	—	13	2	no	—
472	C₄²	—	26	4	no	—
473	C₄²	—	26	4	no	—
474	C₄²	—	26	1	no	—
475	C₄²	—	26	1	no	—
476	C₄²	—	26	1	no	—
477	C₄²	—	26	1	no	—
478	C₄²	C₂×C₄×D₁₃	1	2	yes	—
479	C₄²	C₂×C₄×D₁₃	1	2	yes	—
480	C₁₃	C₄⋊C₄×M₁₆	1	1	yes	characteristic, complemented, Sylow
481	C₂³	—	13	2	no	—
482	C₂³	—	13	2	no	—
483	C₂³	—	13	2	no	—
484	C₂³	—	26	2	no	—
485	C₂³	—	26	2	no	—
486	C₂³	C₂²×C₄×D₁₃	1	1	yes	characteristic
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	13	2	no	—
495	C₂×C₄	—	13	2	no	—
496	C₂×C₄	—	13	4	no	—
497	C₂×C₄	—	13	2	no	—
498	C₂×C₄	—	13	2	no	—
499	C₂×C₄	—	13	4	no	—
500	C₂×C₄	—	13	4	no	—
501	C₂×C₄	—	13	4	no	—
502	C₂×C₄	—	13	4	no	—
503	C₂×C₄	—	13	2	no	—
504	C₂×C₄	—	13	4	no	—
505	C₂×C₄	—	26	8	no	—
506	C₂×C₄	—	26	2	no	—
507	C₂×C₄	—	26	2	no	—
508	C₂×C₄	—	26	2	no	—
509	C₂×C₄	—	26	2	no	—
510	C₂×C₄	—	26	2	no	—
511	C₂×C₄	—	26	2	no	—
512	C₂×C₄	—	52	4	no	—
513	C₂×C₄	—	52	8	no	—
514	C₂×C₄	—	52	8	no	—
515	C₂×C₄	C₄²×D₁₃	1	2	yes	—
516	C₂×C₄	C₄²×D₁₃	1	2	yes	—
517	C₂×C₄	M₁₆×D₁₃	1	4	yes	—
518	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
519	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
520	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
521	C₂×C₄	C₂×Q₈×D₁₃	1	1	yes	characteristic
522	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
523	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
524	C₈	—	2	2	no	—
525	C₈	—	2	2	no	—
526	C₈	—	2	2	no	—
527	C₈	—	13	4	no	—
528	C₈	—	26	2	no	—
529	C₈	—	26	2	no	—
530	C₈	—	26	2	no	—
531	C₈	C₄⋊C₄×D₁₃	1	4	yes	complemented
532	C₂²	—	13	4	no	—
533	C₂²	—	26	2	no	—
534	C₂²	—	26	2	no	—
535	C₂²	—	26	4	no	—
536	C₂²	—	26	4	no	—
537	C₂²	C₂×C₄²×D₁₃	1	1	yes	characteristic
538	C₂²	C₄×D₄×D₁₃	1	1	yes	characteristic
539	C₂²	C₄×Q₈×D₁₃	1	1	yes	characteristic
540	C₂²	C₂×M₁₆×D₁₃	1	2	yes	—
541	C₂²	#11719455	1	2	yes	—
542	C₄	—	2	2	no	—
543	C₄	—	2	2	no	—
544	C₄	—	2	4	no	—
545	C₄	—	4	2	no	—
546	C₄	—	13	4	no	—
547	C₄	—	13	4	no	—
548	C₄	—	26	2	no	—
549	C₄	—	26	4	no	—
550	C₄	—	52	2	no	—
551	C₄	C₂×C₄⋊C₄×D₁₃	1	1	yes	characteristic
552	C₄	D₁₃×#117	1	1	yes	characteristic
553	C₄	C₄×D₄×D₁₃	1	1	yes	characteristic
554	C₄	C₄×Q₈×D₁₃	1	1	yes	characteristic
555	C₂	—	26	4	no	—
556	C₂	C₄×C₄⋊C₄×D₁₃	1	1	yes	characteristic
557	C₂	C₄×M₁₆×D₁₃	1	1	yes	characteristic
558	C₂	#13123252	1	1	yes	characteristic
559	C₂	#13123569	1	2	yes	—
560	C₂	#13123788	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₁₃
commutator	C₂²×C₁₃	C₂²×C₄²
Fitting	C₁₃×#1771	C₂
socle	C₂³×C₁₃	C₂³×C₄
prime radical	C₂³×D₁₃	C₂²×C₄
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	#1771	D₁₃
hypocenter	C₁₃	C₄⋊C₄×M₁₆
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ #1771

Complements

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

N	H ≅ G/N	type
6. #13114713	C₂	semidirect
7. #13114711	C₂	semidirect
8. #13114708	C₂	semidirect
9. #13114704	C₂	semidirect
10. #13114702	C₂	semidirect
11. C₈×#6101	C₂	semidirect
12. #13114697	C₂	semidirect
15. C₁₃×#1771	C₂	semidirect
45. #11718498	C₄	semidirect
47. #11718368	C₄	semidirect
105. C₁₃×C₄⋊C₈	C₂×C₄	semidirect
107. C₁₃×#97	C₂×C₄	semidirect
115. #88054	C₂×C₄	semidirect
116. #88054	C₂×C₄	semidirect
119. C₈×Dic₁₃	C₂×C₄	semidirect
120. C₈×Dic₁₃	C₂×C₄	semidirect
121. C₄⋊#1055	C₂×C₄	semidirect
123. #88043	C₂×C₄	semidirect
174. #6101	M₁₆	semidirect
200. #6094	C₄⋊C₄	semidirect
209. #1771	D₁₃	semidirect
262. C₈×C₁₃	C₂×C₄⋊C₄	semidirect
266. #1055	C₂×C₄⋊C₄	semidirect
332. Dic₁₃	C₄×M₁₆	semidirect
382. C₄⋊C₈	C₄×D₁₃	semidirect
388. #97	C₄×D₁₃	semidirect
480. C₁₃	C₄⋊C₄×M₁₆	semidirect
531. C₈	C₄⋊C₄×D₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718498	2
C₂×#11718368	2
C₂×C₄×#6094	2
C₄×C₄⋊C₄×D₁₃	2
#13114713	2
#13114711	2
#13114708	2
#13114704	2
#13114702	2
C₈×#6101	2
#13114697	2
#13114528	2
C₁₃×#1771	2
C₄⋊C₄×M₁₆	13