Subgroups — C₁₃×#18652 #15704991

Order 3328.

938 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3503	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3229	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#498	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3039	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#1653	C₂	1	4	yes	maximal, complemented
6	C₁₃×#1651	C₂	1	4	yes	maximal, complemented
7	C₁₃×#1549	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1493	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1476	C₂	1	1	yes	maximal, characteristic
10	C₂×C₁₃×#137	—	2	1	no	—
11	Q₈²×C₁₃	—	2	1	no	—
12	C₁₃×#557	C₂²	1	2	yes	—
13	C₁₃×#554	—	2	1	no	—
14	C₁₃×#554	—	2	2	no	—
15	D₄×Q₈×C₁₃	—	2	2	no	—
16	D₄×Q₈×C₁₃	C₂²	1	2	yes	—
17	C₁₃×#544	—	2	2	no	—
18	C₁₃×#544	—	2	1	no	—
19	C₁₃×#533	—	2	1	no	—
20	C₁₃×#533	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
22	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
24	C₁₃×#520	—	2	1	no	—
25	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
26	C₁₃×#498	—	2	2	no	—
27	C₁₃×#498	—	2	1	no	—
28	C₁₃×#498	C₂²	1	4	yes	—
29	C₁₃×#487	—	2	1	no	—
30	C₁₃×#483	—	2	2	no	—
31	C₁₃×#475	C₂²	1	4	yes	—
32	C₁₃×#462	—	2	1	no	—
33	C₁₃×#462	C₂²	1	2	yes	—
34	C₁₃×#461	—	2	1	no	—
35	C₁₃×#461	C₂²	1	2	yes	—
36	C₁₃×#431	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×#106	—	2	2	no	—
38	C₁₃×#423	C₂²	1	1	yes	characteristic
39	C₁₃×#419	—	2	1	no	—
40	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
41	C₁₃×#332	C₂²	1	4	yes	—
42	C₁₃×Q₈⋊C₈	C₂²	1	2	yes	—
43	C₁₃×Q₈⋊C₈	C₂²	1	4	yes	—
44	C₁₃×D₄⋊C₈	C₂²	1	2	yes	—
45	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
46	C₂²×Q₈×C₁₃	—	2	2	no	—
47	C₂²×Q₈×C₁₃	—	2	1	no	—
48	C₂²×Q₈×C₁₃	—	2	1	no	—
49	C₁₃×#137	—	4	4	no	—
50	C₂×C₁₃×Q₁₆	—	2	2	no	—
51	C₂×C₁₃×SD₁₆	—	2	2	no	—
52	C₂×C₁₃×M₁₆	—	2	1	no	—
53	C₂²×C₈×C₁₃	—	2	1	no	—
54	C₁₃×C₄⋊Q₈	—	2	2	no	—
55	C₁₃×C₄⋊Q₈	—	2	2	no	—
56	C₁₃×C₄⋊Q₈	—	2	4	no	—
57	C₁₃×C₄⋊Q₈	—	2	2	no	—
58	C₁₃×C₄⋊Q₈	—	2	2	no	—
59	C₁₃×C₄⋊Q₈	—	2	1	no	—
60	C₁₃×C₄⋊Q₈	—	2	1	no	—
61	C₁₃×C₄⋊Q₈	—	2	1	no	—
62	C₁₃×C₄⋊Q₈	—	2	1	no	—
63	C₁₃×C₄⋊Q₈	—	2	1	no	—
64	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
65	C₁₃×C₄⋊Q₈	D₄	1	2	yes	—
66	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
67	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
68	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
69	C₁₃×#125	—	2	2	no	—
70	C₁₃×#125	—	2	4	no	—
71	C₁₃×#125	—	2	2	no	—
72	C₁₃×#125	—	2	1	no	—
73	C₁₃×C₂²⋊Q₈	—	2	2	no	—
74	C₁₃×C₂²⋊Q₈	—	2	4	no	—
75	C₁₃×C₂²⋊Q₈	—	2	4	no	—
76	C₁₃×C₂²⋊Q₈	—	2	1	no	—
77	C₁₃×C₂²⋊Q₈	—	2	2	no	—
78	C₁₃×C₂²⋊Q₈	—	2	4	no	—
79	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
80	C₄×Q₈×C₁₃	—	2	2	no	—
81	C₄×Q₈×C₁₃	—	2	2	no	—
82	C₄×Q₈×C₁₃	—	2	2	no	—
83	C₄×Q₈×C₁₃	—	2	1	no	—
84	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
85	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
86	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
87	C₄×D₄×C₁₃	—	2	4	no	—
88	C₄×D₄×C₁₃	—	2	2	no	—
89	C₄×D₄×C₁₃	—	2	1	no	—
90	C₄×D₄×C₁₃	—	2	1	no	—
91	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
92	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
93	C₁₃×#117	—	2	2	no	—
94	C₁₃×#117	—	2	1	no	—
95	C₁₃×#117	—	2	1	no	—
96	C₁₃×#117	D₄	1	1	yes	characteristic
97	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
98	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
99	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
100	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
101	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
102	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
103	C₂×C₄²×C₁₃	—	2	1	no	—
104	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
105	C₁₃×#106	—	2	8	no	—
106	C₁₃×#106	—	2	4	no	—
107	C₁₃×C₄⋊C₈	—	2	1	no	—
108	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
109	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
110	C₁₃×#103	—	2	4	no	—
111	C₁₃×#103	—	2	2	no	—
112	C₁₃×#103	—	2	2	no	—
113	C₁₃×C₂²⋊C₈	—	2	1	no	—
114	C₄×C₈×C₁₃	—	2	1	no	—
115	C₄×C₈×C₁₃	—	2	1	no	—
116	C₄×C₈×C₁₃	C₂³	1	2	yes	—
117	#18652	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
118	C₁₃×#41	—	2	2	no	—
119	C₁₃×#41	SD₁₆	1	4	yes	—
120	C₂×Q₈×C₁₃	—	2	4	no	—
121	C₂×Q₈×C₁₃	—	2	1	no	—
122	C₂×Q₈×C₁₃	—	2	2	no	—
123	C₂×Q₈×C₁₃	—	2	2	no	—
124	C₂×Q₈×C₁₃	—	2	2	no	—
125	C₂×Q₈×C₁₃	—	4	1	no	—
126	C₂×Q₈×C₁₃	—	4	2	no	—
127	C₂×Q₈×C₁₃	—	4	2	no	—
128	C₂×Q₈×C₁₃	—	8	2	no	—
129	C₂×Q₈×C₁₃	—	8	4	no	—
130	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
131	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
132	C₂×D₄×C₁₃	—	2	1	no	—
133	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₃	—	2	1	no	—
135	C₂²×C₄×C₁₃	—	2	4	no	—
136	C₂²×C₄×C₁₃	—	2	2	no	—
137	C₂²×C₄×C₁₃	—	2	1	no	—
138	C₂²×C₄×C₁₃	—	2	1	no	—
139	C₂²×C₄×C₁₃	—	4	1	no	—
140	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
143	C₁₃×Q₁₆	—	4	4	no	—
144	C₁₃×SD₁₆	—	4	4	no	—
145	C₁₃×M₁₆	—	4	2	no	—
146	C₂×C₈×C₁₃	—	2	4	no	—
147	C₂×C₈×C₁₃	—	2	2	no	—
148	C₂×C₈×C₁₃	—	2	2	no	—
149	C₂×C₈×C₁₃	—	2	2	no	—
150	C₁₃×C₄⋊C₄	—	2	4	no	—
151	C₁₃×C₄⋊C₄	—	2	4	no	—
152	C₁₃×C₄⋊C₄	—	2	4	no	—
153	C₁₃×C₄⋊C₄	—	2	4	no	—
154	C₁₃×C₄⋊C₄	—	2	1	no	—
155	C₁₃×C₄⋊C₄	—	2	2	no	—
156	C₁₃×C₄⋊C₄	—	2	1	no	—
157	C₁₃×C₄⋊C₄	—	2	2	no	—
158	C₁₃×C₄⋊C₄	—	2	1	no	—
159	C₁₃×C₄⋊C₄	—	2	1	no	—
160	C₁₃×C₄⋊C₄	—	2	2	no	—
161	C₁₃×C₄⋊C₄	—	2	2	no	—
162	C₁₃×C₄⋊C₄	—	2	1	no	—
163	C₁₃×C₄⋊C₄	—	2	2	no	—
164	C₁₃×C₄⋊C₄	—	2	2	no	—
165	C₁₃×C₄⋊C₄	—	2	2	no	—
166	C₁₃×C₄⋊C₄	—	4	1	no	—
167	C₁₃×C₄⋊C₄	—	4	1	no	—
168	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
169	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
170	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
171	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
172	C₁₃×C₂²⋊C₄	—	2	4	no	—
173	C₁₃×C₂²⋊C₄	—	2	2	no	—
174	C₁₃×C₂²⋊C₄	—	2	1	no	—
175	C₁₃×C₂²⋊C₄	—	2	1	no	—
176	C₁₃×C₂²⋊C₄	—	2	1	no	—
177	C₄²×C₁₃	—	2	4	no	—
178	C₄²×C₁₃	—	2	1	no	—
179	C₄²×C₁₃	—	2	1	no	—
180	C₄²×C₁₃	—	2	1	no	—
181	C₄²×C₁₃	—	2	2	no	—
182	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
183	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
184	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
185	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
186	#3503	C₂×C₁₃	1	1	yes	characteristic
187	#3229	C₂×C₁₃	1	1	yes	characteristic, complemented
188	C₂×#498	C₂×C₁₃	1	1	yes	characteristic, complemented
189	#3039	C₂×C₁₃	1	1	yes	characteristic
190	#1653	C₂×C₁₃	1	4	yes	complemented
191	#1651	C₂×C₁₃	1	4	yes	complemented
192	#1549	C₂×C₁₃	1	1	yes	characteristic, complemented
193	#1493	C₂×C₁₃	1	1	yes	characteristic, complemented
194	#1476	C₂×C₁₃	1	1	yes	characteristic
195	C₂³×C₁₃	—	2	1	no	—
196	C₂³×C₁₃	#120	1	1	yes	characteristic
197	Q₈×C₁₃	—	2	1	no	—
198	Q₈×C₁₃	—	2	4	no	—
199	Q₈×C₁₃	—	4	4	no	—
200	Q₈×C₁₃	—	4	2	no	—
201	Q₈×C₁₃	—	4	2	no	—
202	Q₈×C₁₃	—	4	2	no	—
203	Q₈×C₁₃	—	8	2	no	—
204	Q₈×C₁₃	—	8	4	no	—
205	Q₈×C₁₃	—	8	2	no	—
206	Q₈×C₁₃	C₂×SD₁₆	1	2	yes	—
207	D₄×C₁₃	—	2	4	no	—
208	D₄×C₁₃	—	2	1	no	—
209	D₄×C₁₃	C₂×SD₁₆	1	2	yes	—
210	C₂×C₄×C₁₃	—	2	1	no	—
211	C₂×C₄×C₁₃	—	2	2	no	—
212	C₂×C₄×C₁₃	—	2	4	no	—
213	C₂×C₄×C₁₃	—	2	2	no	—
214	C₂×C₄×C₁₃	—	2	2	no	—
215	C₂×C₄×C₁₃	—	2	1	no	—
216	C₂×C₄×C₁₃	—	2	1	no	—
217	C₂×C₄×C₁₃	—	2	2	no	—
218	C₂×C₄×C₁₃	—	2	4	no	—
219	C₂×C₄×C₁₃	—	4	2	no	—
220	C₂×C₄×C₁₃	—	4	2	no	—
221	C₂×C₄×C₁₃	—	4	2	no	—
222	C₂×C₄×C₁₃	—	8	2	no	—
223	C₂×C₄×C₁₃	—	8	4	no	—
224	C₂×C₄×C₁₃	—	8	2	no	—
225	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
226	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
227	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
228	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
229	C₂×C₄×C₁₃	#137	1	2	yes	—
230	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
231	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
232	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
233	C₈×C₁₃	—	2	4	no	—
234	C₈×C₁₃	—	4	2	no	—
235	C₈×C₁₃	—	4	2	no	—
236	C₂×#137	—	2	1	no	—
237	Q₈²	—	2	1	no	—
238	#557	C₂²×C₁₃	1	2	yes	—
239	#554	—	2	1	no	—
240	#554	—	2	2	no	—
241	D₄×Q₈	—	2	2	no	—
242	D₄×Q₈	C₂²×C₁₃	1	2	yes	—
243	#544	—	2	2	no	—
244	#544	—	2	1	no	—
245	#533	—	2	1	no	—
246	#533	C₂²×C₁₃	1	1	yes	characteristic
247	C₂×C₄⋊Q₈	—	2	1	no	—
248	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
249	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
250	#520	—	2	1	no	—
251	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
252	#498	—	2	2	no	—
253	#498	—	2	1	no	—
254	#498	C₂²×C₁₃	1	4	yes	—
255	#487	—	2	1	no	—
256	#483	—	2	2	no	—
257	#475	C₂²×C₁₃	1	4	yes	—
258	#462	—	2	1	no	—
259	#462	C₂²×C₁₃	1	2	yes	—
260	#461	—	2	1	no	—
261	#461	C₂²×C₁₃	1	2	yes	—
262	#431	C₂²×C₁₃	1	1	yes	characteristic
263	C₂×#106	—	2	2	no	—
264	#423	C₂²×C₁₃	1	1	yes	characteristic
265	#419	—	2	1	no	—
266	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
267	#332	C₂²×C₁₃	1	4	yes	—
268	Q₈⋊C₈	C₂²×C₁₃	1	4	yes	—
269	Q₈⋊C₈	C₂²×C₁₃	1	2	yes	—
270	D₄⋊C₈	C₂²×C₁₃	1	2	yes	—
271	C₂²×C₁₃	—	2	1	no	—
272	C₂²×C₁₃	—	2	1	no	—
273	C₂²×C₁₃	—	2	2	no	—
274	C₂²×C₁₃	—	4	1	no	—
275	C₂²×C₁₃	—	4	1	no	—
276	C₂²×C₁₃	#448	1	2	yes	—
277	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
278	C₄×C₁₃	—	2	2	no	—
279	C₄×C₁₃	—	2	1	no	—
280	C₄×C₁₃	—	2	1	no	—
281	C₄×C₁₃	—	4	1	no	—
282	C₄×C₁₃	—	4	2	no	—
283	C₄×C₁₃	—	4	4	no	—
284	C₄×C₁₃	—	4	1	no	—
285	C₄×C₁₃	—	4	2	no	—
286	C₄×C₁₃	—	8	2	no	—
287	C₄×C₁₃	#448	1	2	yes	—
288	C₄×C₁₃	#456	1	2	yes	—
289	C₄×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
290	C₄×C₁₃	C₂×#137	1	1	yes	characteristic
291	C₄×C₁₃	#577	1	2	yes	—
292	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
293	C₂²×Q₈	—	2	2	no	—
294	C₂²×Q₈	—	2	1	no	—
295	C₂²×Q₈	—	2	1	no	—
296	#137	—	4	4	no	—
297	C₂×Q₁₆	—	2	2	no	—
298	C₂×SD₁₆	—	2	2	no	—
299	C₂×M₁₆	—	2	1	no	—
300	C₂²×C₈	—	2	1	no	—
301	C₄⋊Q₈	—	2	2	no	—
302	C₄⋊Q₈	—	2	2	no	—
303	C₄⋊Q₈	—	2	4	no	—
304	C₄⋊Q₈	—	2	2	no	—
305	C₄⋊Q₈	—	2	2	no	—
306	C₄⋊Q₈	—	2	1	no	—
307	C₄⋊Q₈	—	2	1	no	—
308	C₄⋊Q₈	—	2	1	no	—
309	C₄⋊Q₈	—	2	1	no	—
310	C₄⋊Q₈	—	2	1	no	—
311	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
312	C₄⋊Q₈	D₄×C₁₃	1	2	yes	—
313	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
314	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
315	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
316	#125	—	2	2	no	—
317	#125	—	2	4	no	—
318	#125	—	2	2	no	—
319	#125	—	2	1	no	—
320	C₂²⋊Q₈	—	2	2	no	—
321	C₂²⋊Q₈	—	2	4	no	—
322	C₂²⋊Q₈	—	2	4	no	—
323	C₂²⋊Q₈	—	2	1	no	—
324	C₂²⋊Q₈	—	2	2	no	—
325	C₂²⋊Q₈	—	2	4	no	—
326	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
327	C₄×Q₈	—	2	2	no	—
328	C₄×Q₈	—	2	2	no	—
329	C₄×Q₈	—	2	2	no	—
330	C₄×Q₈	—	2	1	no	—
331	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
332	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
333	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
334	C₄×D₄	—	2	4	no	—
335	C₄×D₄	—	2	2	no	—
336	C₄×D₄	—	2	1	no	—
337	C₄×D₄	—	2	1	no	—
338	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
339	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
340	#117	—	2	2	no	—
341	#117	—	2	1	no	—
342	#117	—	2	1	no	—
343	#117	D₄×C₁₃	1	1	yes	characteristic
344	C₂×C₄⋊C₄	—	2	2	no	—
345	C₂×C₄⋊C₄	—	2	2	no	—
346	C₂×C₄⋊C₄	—	2	1	no	—
347	C₂×C₄⋊C₄	—	2	1	no	—
348	C₂×C₄⋊C₄	—	2	1	no	—
349	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
350	C₂×C₄²	—	2	1	no	—
351	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
352	#106	—	2	8	no	—
353	#106	—	2	4	no	—
354	C₄⋊C₈	—	2	1	no	—
355	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
356	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
357	#103	—	2	4	no	—
358	#103	—	2	2	no	—
359	#103	—	2	2	no	—
360	C₂²⋊C₈	—	2	1	no	—
361	C₄×C₈	—	2	1	no	—
362	C₄×C₈	—	2	1	no	—
363	C₄×C₈	C₂³×C₁₃	1	2	yes	—
364	C₂×C₁₃	—	2	2	no	—
365	C₂×C₁₃	—	4	2	no	—
366	C₂×C₁₃	C₂×#448	1	1	yes	characteristic
367	C₂×C₁₃	#3009	1	1	yes	characteristic
368	C₂×C₁₃	C₂×#456	1	1	yes	characteristic
369	#41	—	2	2	no	—
370	#41	C₁₃×SD₁₆	1	4	yes	—
371	C₂×Q₈	—	2	4	no	—
372	C₂×Q₈	—	2	1	no	—
373	C₂×Q₈	—	2	2	no	—
374	C₂×Q₈	—	2	2	no	—
375	C₂×Q₈	—	2	2	no	—
376	C₂×Q₈	—	4	1	no	—
377	C₂×Q₈	—	4	2	no	—
378	C₂×Q₈	—	4	2	no	—
379	C₂×Q₈	—	8	2	no	—
380	C₂×Q₈	—	8	4	no	—
381	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
382	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
383	C₂×D₄	—	2	1	no	—
384	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
385	C₂²×C₄	—	2	1	no	—
386	C₂²×C₄	—	2	4	no	—
387	C₂²×C₄	—	2	2	no	—
388	C₂²×C₄	—	2	1	no	—
389	C₂²×C₄	—	2	1	no	—
390	C₂²×C₄	—	4	1	no	—
391	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
392	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
393	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
394	Q₁₆	—	4	4	no	—
395	SD₁₆	—	4	4	no	—
396	M₁₆	—	4	2	no	—
397	C₂×C₈	—	2	4	no	—
398	C₂×C₈	—	2	2	no	—
399	C₂×C₈	—	2	2	no	—
400	C₂×C₈	—	2	2	no	—
401	C₄⋊C₄	—	2	4	no	—
402	C₄⋊C₄	—	2	4	no	—
403	C₄⋊C₄	—	2	4	no	—
404	C₄⋊C₄	—	2	4	no	—
405	C₄⋊C₄	—	2	1	no	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	—	2	1	no	—
408	C₄⋊C₄	—	2	2	no	—
409	C₄⋊C₄	—	2	1	no	—
410	C₄⋊C₄	—	2	1	no	—
411	C₄⋊C₄	—	2	2	no	—
412	C₄⋊C₄	—	2	2	no	—
413	C₄⋊C₄	—	2	1	no	—
414	C₄⋊C₄	—	2	2	no	—
415	C₄⋊C₄	—	2	2	no	—
416	C₄⋊C₄	—	2	2	no	—
417	C₄⋊C₄	—	4	1	no	—
418	C₄⋊C₄	—	4	1	no	—
419	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
420	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
421	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
422	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
423	C₂²⋊C₄	—	2	4	no	—
424	C₂²⋊C₄	—	2	2	no	—
425	C₂²⋊C₄	—	2	1	no	—
426	C₂²⋊C₄	—	2	1	no	—
427	C₂²⋊C₄	—	2	1	no	—
428	C₄²	—	2	4	no	—
429	C₄²	—	2	1	no	—
430	C₄²	—	2	1	no	—
431	C₄²	—	2	1	no	—
432	C₄²	—	2	2	no	—
433	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
434	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
435	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
436	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
437	C₁₃	#18652	1	1	yes	characteristic, direct product factor, Sylow
438	C₂³	—	2	1	no	—
439	C₂³	C₁₃×#120	1	1	yes	characteristic
440	Q₈	—	2	1	no	—
441	Q₈	—	2	4	no	—
442	Q₈	—	4	2	no	—
443	Q₈	—	4	4	no	—
444	Q₈	—	4	2	no	—
445	Q₈	—	4	2	no	—
446	Q₈	—	8	2	no	—
447	Q₈	—	8	4	no	—
448	Q₈	—	8	2	no	—
449	Q₈	C₂×C₁₃×SD₁₆	1	2	yes	—
450	D₄	—	2	4	no	—
451	D₄	—	2	1	no	—
452	D₄	C₂×C₁₃×SD₁₆	1	2	yes	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	4	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	1	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	4	no	—
462	C₂×C₄	—	4	2	no	—
463	C₂×C₄	—	4	2	no	—
464	C₂×C₄	—	4	2	no	—
465	C₂×C₄	—	8	2	no	—
466	C₂×C₄	—	8	4	no	—
467	C₂×C₄	—	8	2	no	—
468	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
469	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
470	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
471	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
472	C₂×C₄	C₁₃×#137	1	2	yes	—
473	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
474	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
475	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
476	C₈	—	2	4	no	—
477	C₈	—	4	2	no	—
478	C₈	—	4	2	no	—
479	C₂²	—	2	1	no	—
480	C₂²	—	2	1	no	—
481	C₂²	—	2	2	no	—
482	C₂²	—	4	1	no	—
483	C₂²	—	4	1	no	—
484	C₂²	C₁₃×#448	1	2	yes	—
485	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
486	C₄	—	2	1	no	—
487	C₄	—	2	1	no	—
488	C₄	—	2	2	no	—
489	C₄	—	4	1	no	—
490	C₄	—	4	2	no	—
491	C₄	—	4	4	no	—
492	C₄	—	4	1	no	—
493	C₄	—	4	2	no	—
494	C₄	—	8	2	no	—
495	C₄	C₁₃×#448	1	2	yes	—
496	C₄	C₁₃×#456	1	2	yes	—
497	C₄	C₂²×C₁₃×SD₁₆	1	1	yes	characteristic
498	C₄	C₂×C₁₃×#137	1	1	yes	characteristic
499	C₄	C₁₃×#577	1	2	yes	—
500	C₂	—	2	2	no	—
501	C₂	—	4	2	no	—
502	C₂	C₂×C₁₃×#448	1	1	yes	characteristic
503	C₂	C₁₃×#3009	1	1	yes	characteristic
504	C₂	C₂×C₁₃×#456	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#41	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#3229	C₂	semidirect
3. C₂×C₁₃×#498	C₂	semidirect
5. C₁₃×#1653	C₂	semidirect
6. C₁₃×#1651	C₂	semidirect
7. C₁₃×#1549	C₂	semidirect
8. C₁₃×#1493	C₂	semidirect
117. #18652	C₁₃	direct (N × H)
187. #3229	C₂×C₁₃	semidirect
188. C₂×#498	C₂×C₁₃	semidirect
190. #1653	C₂×C₁₃	semidirect
191. #1651	C₂×C₁₃	semidirect
192. #1549	C₂×C₁₃	semidirect
193. #1493	C₂×C₁₃	semidirect
437. C₁₃	#18652	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#3503	2
C₁₃×#3229	2
C₂×C₁₃×#498	2
C₁₃×#3039	2
C₁₃×#1653	2
C₁₃×#1651	2
C₁₃×#1549	2
C₁₃×#1493	2
C₁₃×#1476	2
#18652	13

Subgroups — C13×#18652 #15704991

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#18652 #15704991