Subgroups — C₁₃×#18676 #15705015

Order 3328.

912 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3502	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3246	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3167	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#3037	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#1653	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1645	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1626	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1623	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1550	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1493	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#137	—	2	1	no	—
13	Q₈²×C₁₃	—	2	1	no	—
14	Q₈²×C₁₃	C₂²	1	2	yes	—
15	C₁₃×#557	—	2	1	no	—
16	C₁₃×#557	—	2	2	no	—
17	C₁₃×#557	—	2	2	no	—
18	C₁₃×#557	C₂²	1	2	yes	—
19	C₁₃×#544	—	2	2	no	—
20	C₁₃×#544	—	2	1	no	—
21	C₁₃×#533	—	2	2	no	—
22	C₁₃×#533	C₂²	1	1	yes	characteristic
23	C₁₃×#533	C₂²	1	1	yes	characteristic
24	C₁₃×#532	C₂²	1	1	yes	characteristic
25	C₁₃×#519	—	2	1	no	—
26	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
27	C₁₃×#498	C₂²	1	1	yes	characteristic
28	C₁₃×#492	C₂²	1	1	yes	characteristic
29	C₁₃×#487	C₂²	1	1	yes	characteristic
30	C₁₃×#486	C₂²	1	1	yes	characteristic
31	C₁₃×#476	—	2	1	no	—
32	C₁₃×#475	C₂²	1	2	yes	—
33	C₁₃×#465	—	2	2	no	—
34	C₁₃×#465	—	2	2	no	—
35	C₁₃×#464	—	2	2	no	—
36	C₁₃×#462	C₂²	1	2	yes	—
37	C₁₃×#461	—	2	1	no	—
38	C₁₃×#460	C₂²	1	2	yes	—
39	C₁₃×#460	C₂²	1	2	yes	—
40	C₄×C₁₃×SD₁₆	—	2	2	no	—
41	C₁₃×#423	C₂²	1	1	yes	characteristic
42	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
43	C₁₃×#417	—	2	1	no	—
44	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
45	C₁₃×#333	C₂²	1	2	yes	—
46	C₁₃×#332	C₂²	1	2	yes	—
47	C₁₃×Q₈⋊C₈	C₂²	1	2	yes	—
48	C₁₃×Q₈⋊C₈	C₂²	1	2	yes	—
49	C₁₃×Q₈⋊C₈	C₂²	1	2	yes	—
50	C₁₃×Q₈⋊C₈	C₂²	1	2	yes	—
51	C₂×C₁₃×#41	—	2	1	no	—
52	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
53	C₁₃×#137	—	4	4	no	—
54	C₂×C₁₃×Q₁₆	—	2	2	no	—
55	C₂×C₁₃×SD₁₆	—	2	2	no	—
56	C₂×C₁₃×SD₁₆	—	2	2	no	—
57	C₂×C₁₃×SD₁₆	—	2	2	no	—
58	C₂×C₁₃×M₁₆	—	2	1	no	—
59	C₂²×C₈×C₁₃	—	2	1	no	—
60	C₂²×C₈×C₁₃	—	2	1	no	—
61	C₁₃×C₄⋊Q₈	—	2	4	no	—
62	C₁₃×C₄⋊Q₈	—	2	2	no	—
63	C₁₃×C₄⋊Q₈	—	2	2	no	—
64	C₁₃×C₄⋊Q₈	—	2	4	no	—
65	C₁₃×C₄⋊Q₈	—	2	2	no	—
66	C₁₃×C₄⋊Q₈	—	2	2	no	—
67	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
68	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
69	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
70	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
71	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
72	C₁₃×#127	C₂³	1	1	yes	characteristic
73	C₁₃×#125	—	2	4	no	—
74	C₁₃×#125	—	2	4	no	—
75	C₁₃×#125	—	2	2	no	—
76	C₁₃×#125	—	2	4	no	—
77	C₁₃×#125	—	2	2	no	—
78	C₁₃×#125	—	2	1	no	—
79	C₁₃×#125	—	2	1	no	—
80	C₁₃×#124	—	2	1	no	—
81	C₁₃×C₂²⋊Q₈	—	2	4	no	—
82	C₁₃×C₂²⋊Q₈	—	2	1	no	—
83	C₁₃×C₂²⋊Q₈	—	2	1	no	—
84	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
85	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
86	C₁₃×#121	—	2	1	no	—
87	C₁₃×#121	—	2	1	no	—
88	C₄×Q₈×C₁₃	—	2	2	no	—
89	C₄×Q₈×C₁₃	—	2	2	no	—
90	C₄×Q₈×C₁₃	—	2	4	no	—
91	C₄×Q₈×C₁₃	—	2	2	no	—
92	C₄×Q₈×C₁₃	—	2	2	no	—
93	C₄×Q₈×C₁₃	—	2	2	no	—
94	C₄×Q₈×C₁₃	—	2	2	no	—
95	C₄×Q₈×C₁₃	—	2	1	no	—
96	C₄×Q₈×C₁₃	—	2	1	no	—
97	C₄×Q₈×C₁₃	—	2	1	no	—
98	C₄×Q₈×C₁₃	—	2	1	no	—
99	C₄×Q₈×C₁₃	D₄	1	2	yes	—
100	C₄×Q₈×C₁₃	D₄	1	2	yes	—
101	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
102	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
103	C₄×D₄×C₁₃	—	2	1	no	—
104	C₄×D₄×C₁₃	—	2	1	no	—
105	C₁₃×#117	—	2	4	no	—
106	C₁₃×#117	—	2	1	no	—
107	C₁₃×#117	—	2	1	no	—
108	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
109	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
110	C₂×C₄²×C₁₃	—	2	1	no	—
111	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
112	C₁₃×#106	—	2	2	no	—
113	C₁₃×#106	—	2	2	no	—
114	C₁₃×C₄⋊C₈	—	2	1	no	—
115	C₁₃×C₄⋊C₈	—	2	1	no	—
116	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
117	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
118	C₁₃×#103	—	2	2	no	—
119	C₁₃×#103	—	2	2	no	—
120	C₁₃×#103	—	2	2	no	—
121	C₁₃×#102	—	2	2	no	—
122	C₁₃×#102	—	2	2	no	—
123	C₁₃×#102	—	2	2	no	—
124	C₄×C₈×C₁₃	—	2	1	no	—
125	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
126	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
127	#18676	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
128	C₁₃×#41	—	4	2	no	—
129	C₁₃×#41	—	4	2	no	—
130	C₂×Q₈×C₁₃	—	2	4	no	—
131	C₂×Q₈×C₁₃	—	2	1	no	—
132	C₂×Q₈×C₁₃	—	2	1	no	—
133	C₂×Q₈×C₁₃	—	2	2	no	—
134	C₂×Q₈×C₁₃	—	2	1	no	—
135	C₂×Q₈×C₁₃	—	2	1	no	—
136	C₂×Q₈×C₁₃	SD₁₆	1	4	yes	complemented
137	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
138	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
139	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
140	C₂×D₄×C₁₃	—	2	1	no	—
141	C₂×D₄×C₁₃	—	2	1	no	—
142	C₂×D₄×C₁₃	—	2	1	no	—
143	C₂×D₄×C₁₃	—	4	1	no	—
144	C₂²×C₄×C₁₃	—	2	1	no	—
145	C₂²×C₄×C₁₃	—	2	1	no	—
146	C₂²×C₄×C₁₃	—	4	1	no	—
147	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
150	C₁₃×Q₁₆	—	4	4	no	—
151	C₁₃×SD₁₆	—	4	4	no	—
152	C₁₃×SD₁₆	—	4	4	no	—
153	C₁₃×SD₁₆	—	8	2	no	—
154	C₁₃×M₁₆	—	4	2	no	—
155	C₂×C₈×C₁₃	—	2	1	no	—
156	C₂×C₈×C₁₃	—	2	1	no	—
157	C₂×C₈×C₁₃	—	2	2	no	—
158	C₂×C₈×C₁₃	—	2	2	no	—
159	C₂×C₈×C₁₃	—	4	2	no	—
160	C₂×C₈×C₁₃	—	8	1	no	—
161	C₁₃×C₄⋊C₄	—	2	4	no	—
162	C₁₃×C₄⋊C₄	—	2	4	no	—
163	C₁₃×C₄⋊C₄	—	2	4	no	—
164	C₁₃×C₄⋊C₄	—	2	4	no	—
165	C₁₃×C₄⋊C₄	—	2	4	no	—
166	C₁₃×C₄⋊C₄	—	2	2	no	—
167	C₁₃×C₄⋊C₄	—	2	1	no	—
168	C₁₃×C₄⋊C₄	—	2	1	no	—
169	C₁₃×C₄⋊C₄	—	2	1	no	—
170	C₁₃×C₄⋊C₄	—	2	2	no	—
171	C₁₃×C₄⋊C₄	—	2	2	no	—
172	C₁₃×C₄⋊C₄	—	2	1	no	—
173	C₁₃×C₄⋊C₄	—	2	2	no	—
174	C₁₃×C₄⋊C₄	—	2	2	no	—
175	C₁₃×C₄⋊C₄	—	2	1	no	—
176	C₁₃×C₄⋊C₄	—	2	1	no	—
177	C₁₃×C₄⋊C₄	—	2	1	no	—
178	C₁₃×C₄⋊C₄	—	2	2	no	—
179	C₁₃×C₄⋊C₄	—	2	1	no	—
180	C₁₃×C₄⋊C₄	—	2	1	no	—
181	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
182	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
183	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
184	C₁₃×C₂²⋊C₄	—	2	2	no	—
185	C₁₃×C₂²⋊C₄	—	2	2	no	—
186	C₁₃×C₂²⋊C₄	—	4	1	no	—
187	C₁₃×C₂²⋊C₄	—	4	1	no	—
188	C₄²×C₁₃	—	2	4	no	—
189	C₄²×C₁₃	—	2	4	no	—
190	C₄²×C₁₃	—	2	2	no	—
191	C₄²×C₁₃	—	2	2	no	—
192	C₄²×C₁₃	—	2	2	no	—
193	C₄²×C₁₃	—	2	2	no	—
194	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
195	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
196	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
197	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
198	#3502	C₂×C₁₃	1	1	yes	characteristic, complemented
199	#3246	C₂×C₁₃	1	1	yes	characteristic
200	#3167	C₂×C₁₃	1	1	yes	characteristic
201	#3037	C₂×C₁₃	1	1	yes	characteristic
202	#1653	C₂×C₁₃	1	2	yes	complemented
203	#1645	C₂×C₁₃	1	2	yes	complemented
204	#1626	C₂×C₁₃	1	2	yes	complemented
205	#1623	C₂×C₁₃	1	2	yes	complemented
206	#1550	C₂×C₁₃	1	1	yes	characteristic, complemented
207	#1493	C₂×C₁₃	1	1	yes	characteristic, complemented
208	C₂×Q₈⋊C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
209	C₂³×C₁₃	—	4	1	no	—
210	C₂³×C₁₃	#120	1	1	yes	characteristic
211	Q₈×C₁₃	—	2	2	no	—
212	Q₈×C₁₃	—	2	4	no	—
213	Q₈×C₁₃	—	2	2	no	—
214	Q₈×C₁₃	—	2	2	no	—
215	Q₈×C₁₃	—	4	2	no	—
216	Q₈×C₁₃	—	4	1	no	—
217	Q₈×C₁₃	—	4	1	no	—
218	Q₈×C₁₃	—	4	1	no	—
219	Q₈×C₁₃	—	4	1	no	—
220	Q₈×C₁₃	—	8	1	no	—
221	Q₈×C₁₃	—	8	4	no	—
222	Q₈×C₁₃	C₂×SD₁₆	1	4	yes	—
223	D₄×C₁₃	—	4	2	no	—
224	D₄×C₁₃	—	4	1	no	—
225	D₄×C₁₃	—	4	1	no	—
226	D₄×C₁₃	—	4	1	no	—
227	D₄×C₁₃	—	4	1	no	—
228	D₄×C₁₃	—	8	2	no	—
229	C₂×C₄×C₁₃	—	2	2	no	—
230	C₂×C₄×C₁₃	—	2	4	no	—
231	C₂×C₄×C₁₃	—	2	1	no	—
232	C₂×C₄×C₁₃	—	2	1	no	—
233	C₂×C₄×C₁₃	—	2	2	no	—
234	C₂×C₄×C₁₃	—	2	2	no	—
235	C₂×C₄×C₁₃	—	2	2	no	—
236	C₂×C₄×C₁₃	—	2	2	no	—
237	C₂×C₄×C₁₃	—	2	2	no	—
238	C₂×C₄×C₁₃	—	4	1	no	—
239	C₂×C₄×C₁₃	—	4	1	no	—
240	C₂×C₄×C₁₃	—	8	1	no	—
241	C₂×C₄×C₁₃	—	8	2	no	—
242	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
243	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
244	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
245	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
246	C₂×C₄×C₁₃	#137	1	2	yes	—
247	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
248	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
249	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
250	C₈×C₁₃	—	2	2	no	—
251	C₈×C₁₃	—	4	1	no	—
252	C₈×C₁₃	—	4	2	no	—
253	C₈×C₁₃	—	4	2	no	—
254	C₂×#137	—	2	1	no	—
255	Q₈²	—	2	1	no	—
256	Q₈²	C₂²×C₁₃	1	2	yes	—
257	#557	—	2	1	no	—
258	#557	—	2	2	no	—
259	#557	—	2	2	no	—
260	#557	C₂²×C₁₃	1	2	yes	—
261	#544	—	2	2	no	—
262	#544	—	2	1	no	—
263	#533	—	2	2	no	—
264	#533	C₂²×C₁₃	1	1	yes	characteristic
265	#533	C₂²×C₁₃	1	1	yes	characteristic
266	#532	C₂²×C₁₃	1	1	yes	characteristic
267	#519	—	2	1	no	—
268	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
269	#498	C₂²×C₁₃	1	1	yes	characteristic
270	#492	C₂²×C₁₃	1	1	yes	characteristic
271	#487	C₂²×C₁₃	1	1	yes	characteristic
272	#486	C₂²×C₁₃	1	1	yes	characteristic
273	#476	—	2	1	no	—
274	#475	C₂²×C₁₃	1	2	yes	—
275	#465	—	2	2	no	—
276	#465	—	2	2	no	—
277	#464	—	2	2	no	—
278	#462	C₂²×C₁₃	1	2	yes	—
279	#461	—	2	1	no	—
280	#460	C₂²×C₁₃	1	2	yes	—
281	#460	C₂²×C₁₃	1	2	yes	—
282	C₄×SD₁₆	—	2	2	no	—
283	#423	C₂²×C₁₃	1	1	yes	characteristic
284	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
285	#417	—	2	1	no	—
286	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
287	#333	C₂²×C₁₃	1	2	yes	—
288	#332	C₂²×C₁₃	1	2	yes	—
289	Q₈⋊C₈	C₂²×C₁₃	1	2	yes	—
290	Q₈⋊C₈	C₂²×C₁₃	1	2	yes	—
291	Q₈⋊C₈	C₂²×C₁₃	1	2	yes	—
292	Q₈⋊C₈	C₂²×C₁₃	1	2	yes	—
293	C₂²×C₁₃	—	2	1	no	—
294	C₂²×C₁₃	—	2	1	no	—
295	C₂²×C₁₃	—	8	1	no	—
296	C₂²×C₁₃	—	8	1	no	—
297	C₂²×C₁₃	—	8	1	no	—
298	C₂²×C₁₃	#448	1	2	yes	—
299	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
300	C₄×C₁₃	—	2	4	no	—
301	C₄×C₁₃	—	2	1	no	—
302	C₄×C₁₃	—	2	1	no	—
303	C₄×C₁₃	—	2	1	no	—
304	C₄×C₁₃	—	4	2	no	—
305	C₄×C₁₃	—	4	2	no	—
306	C₄×C₁₃	—	4	2	no	—
307	C₄×C₁₃	—	4	2	no	—
308	C₄×C₁₃	—	4	2	no	—
309	C₄×C₁₃	—	8	1	no	—
310	C₄×C₁₃	#448	1	2	yes	—
311	C₄×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
312	C₄×C₁₃	C₂×#137	1	1	yes	characteristic
313	C₄×C₁₃	#577	1	1	yes	characteristic
314	C₄×C₁₃	#578	1	1	yes	characteristic
315	C₂×#41	—	2	1	no	—
316	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
317	#137	—	4	4	no	—
318	C₂×Q₁₆	—	2	2	no	—
319	C₂×SD₁₆	—	2	2	no	—
320	C₂×SD₁₆	—	2	2	no	—
321	C₂×SD₁₆	—	2	2	no	—
322	C₂×M₁₆	—	2	1	no	—
323	C₂²×C₈	—	2	1	no	—
324	C₂²×C₈	—	2	1	no	—
325	C₄⋊Q₈	—	2	4	no	—
326	C₄⋊Q₈	—	2	2	no	—
327	C₄⋊Q₈	—	2	2	no	—
328	C₄⋊Q₈	—	2	4	no	—
329	C₄⋊Q₈	—	2	2	no	—
330	C₄⋊Q₈	—	2	2	no	—
331	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
332	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
333	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
334	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
335	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
336	#127	C₂³×C₁₃	1	1	yes	characteristic
337	#125	—	2	4	no	—
338	#125	—	2	4	no	—
339	#125	—	2	2	no	—
340	#125	—	2	4	no	—
341	#125	—	2	2	no	—
342	#125	—	2	1	no	—
343	#125	—	2	1	no	—
344	#124	—	2	1	no	—
345	C₂²⋊Q₈	—	2	4	no	—
346	C₂²⋊Q₈	—	2	1	no	—
347	C₂²⋊Q₈	—	2	1	no	—
348	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
349	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
350	#121	—	2	1	no	—
351	#121	—	2	1	no	—
352	C₄×Q₈	—	2	2	no	—
353	C₄×Q₈	—	2	2	no	—
354	C₄×Q₈	—	2	4	no	—
355	C₄×Q₈	—	2	2	no	—
356	C₄×Q₈	—	2	2	no	—
357	C₄×Q₈	—	2	2	no	—
358	C₄×Q₈	—	2	2	no	—
359	C₄×Q₈	—	2	1	no	—
360	C₄×Q₈	—	2	1	no	—
361	C₄×Q₈	—	2	1	no	—
362	C₄×Q₈	—	2	1	no	—
363	C₄×Q₈	D₄×C₁₃	1	2	yes	—
364	C₄×Q₈	D₄×C₁₃	1	2	yes	—
365	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
366	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
367	C₄×D₄	—	2	1	no	—
368	C₄×D₄	—	2	1	no	—
369	#117	—	2	4	no	—
370	#117	—	2	1	no	—
371	#117	—	2	1	no	—
372	C₂×C₄⋊C₄	—	2	1	no	—
373	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
374	C₂×C₄²	—	2	1	no	—
375	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
376	#106	—	2	2	no	—
377	#106	—	2	2	no	—
378	C₄⋊C₈	—	2	1	no	—
379	C₄⋊C₈	—	2	1	no	—
380	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
381	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
382	#103	—	2	2	no	—
383	#103	—	2	2	no	—
384	#103	—	2	2	no	—
385	#102	—	2	2	no	—
386	#102	—	2	2	no	—
387	#102	—	2	2	no	—
388	C₄×C₈	—	2	1	no	—
389	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
390	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
391	C₂×C₁₃	—	2	2	no	—
392	C₂×C₁₃	—	16	1	no	—
393	C₂×C₁₃	C₂×#448	1	1	yes	characteristic
394	C₂×C₁₃	#3013	1	1	yes	characteristic
395	C₂×C₁₃	#3018	1	1	yes	characteristic
396	#41	—	4	2	no	—
397	#41	—	4	2	no	—
398	C₂×Q₈	—	2	4	no	—
399	C₂×Q₈	—	2	1	no	—
400	C₂×Q₈	—	2	1	no	—
401	C₂×Q₈	—	2	2	no	—
402	C₂×Q₈	—	2	1	no	—
403	C₂×Q₈	—	2	1	no	—
404	C₂×Q₈	C₁₃×SD₁₆	1	4	yes	complemented
405	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
406	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
407	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
408	C₂×D₄	—	2	1	no	—
409	C₂×D₄	—	2	1	no	—
410	C₂×D₄	—	2	1	no	—
411	C₂×D₄	—	4	1	no	—
412	C₂²×C₄	—	2	1	no	—
413	C₂²×C₄	—	2	1	no	—
414	C₂²×C₄	—	4	1	no	—
415	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
416	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
417	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
418	Q₁₆	—	4	4	no	—
419	SD₁₆	—	4	4	no	—
420	SD₁₆	—	4	4	no	—
421	SD₁₆	—	8	2	no	—
422	M₁₆	—	4	2	no	—
423	C₂×C₈	—	2	1	no	—
424	C₂×C₈	—	2	1	no	—
425	C₂×C₈	—	2	2	no	—
426	C₂×C₈	—	2	2	no	—
427	C₂×C₈	—	4	2	no	—
428	C₂×C₈	—	8	1	no	—
429	C₄⋊C₄	—	2	4	no	—
430	C₄⋊C₄	—	2	4	no	—
431	C₄⋊C₄	—	2	4	no	—
432	C₄⋊C₄	—	2	4	no	—
433	C₄⋊C₄	—	2	4	no	—
434	C₄⋊C₄	—	2	2	no	—
435	C₄⋊C₄	—	2	1	no	—
436	C₄⋊C₄	—	2	1	no	—
437	C₄⋊C₄	—	2	1	no	—
438	C₄⋊C₄	—	2	2	no	—
439	C₄⋊C₄	—	2	2	no	—
440	C₄⋊C₄	—	2	1	no	—
441	C₄⋊C₄	—	2	2	no	—
442	C₄⋊C₄	—	2	2	no	—
443	C₄⋊C₄	—	2	1	no	—
444	C₄⋊C₄	—	2	1	no	—
445	C₄⋊C₄	—	2	1	no	—
446	C₄⋊C₄	—	2	2	no	—
447	C₄⋊C₄	—	2	1	no	—
448	C₄⋊C₄	—	2	1	no	—
449	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
450	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
451	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
452	C₂²⋊C₄	—	2	2	no	—
453	C₂²⋊C₄	—	2	2	no	—
454	C₂²⋊C₄	—	4	1	no	—
455	C₂²⋊C₄	—	4	1	no	—
456	C₄²	—	2	4	no	—
457	C₄²	—	2	4	no	—
458	C₄²	—	2	2	no	—
459	C₄²	—	2	2	no	—
460	C₄²	—	2	2	no	—
461	C₄²	—	2	2	no	—
462	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
463	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
464	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
465	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
466	C₁₃	#18676	1	1	yes	characteristic, direct product factor, Sylow
467	C₂³	—	4	1	no	—
468	C₂³	C₁₃×#120	1	1	yes	characteristic
469	Q₈	—	2	4	no	—
470	Q₈	—	2	2	no	—
471	Q₈	—	2	2	no	—
472	Q₈	—	2	2	no	—
473	Q₈	—	4	2	no	—
474	Q₈	—	4	1	no	—
475	Q₈	—	4	1	no	—
476	Q₈	—	4	1	no	—
477	Q₈	—	4	1	no	—
478	Q₈	—	8	1	no	—
479	Q₈	—	8	4	no	—
480	Q₈	C₂×C₁₃×SD₁₆	1	4	yes	—
481	D₄	—	4	2	no	—
482	D₄	—	4	1	no	—
483	D₄	—	4	1	no	—
484	D₄	—	4	1	no	—
485	D₄	—	4	1	no	—
486	D₄	—	8	2	no	—
487	C₂×C₄	—	2	4	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	1	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	4	1	no	—
497	C₂×C₄	—	4	1	no	—
498	C₂×C₄	—	8	1	no	—
499	C₂×C₄	—	8	2	no	—
500	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
501	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
502	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
503	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
504	C₂×C₄	C₁₃×#137	1	2	yes	—
505	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
506	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
507	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
508	C₈	—	2	2	no	—
509	C₈	—	4	1	no	—
510	C₈	—	4	2	no	—
511	C₈	—	4	2	no	—
512	C₂²	—	2	1	no	—
513	C₂²	—	2	1	no	—
514	C₂²	—	8	1	no	—
515	C₂²	—	8	1	no	—
516	C₂²	—	8	1	no	—
517	C₂²	C₁₃×#448	1	2	yes	—
518	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
519	C₄	—	2	1	no	—
520	C₄	—	2	1	no	—
521	C₄	—	2	1	no	—
522	C₄	—	2	4	no	—
523	C₄	—	4	2	no	—
524	C₄	—	4	2	no	—
525	C₄	—	4	2	no	—
526	C₄	—	4	2	no	—
527	C₄	—	4	2	no	—
528	C₄	—	8	1	no	—
529	C₄	C₁₃×#448	1	2	yes	—
530	C₄	C₂²×C₁₃×SD₁₆	1	1	yes	characteristic
531	C₄	C₂×C₁₃×#137	1	1	yes	characteristic
532	C₄	C₁₃×#577	1	1	yes	characteristic
533	C₄	C₁₃×#578	1	1	yes	characteristic
534	C₂	—	2	2	no	—
535	C₂	—	16	1	no	—
536	C₂	C₂×C₁₃×#448	1	1	yes	characteristic
537	C₂	C₁₃×#3013	1	1	yes	characteristic
538	C₂	C₁₃×#3018	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃
prime radical	C₁₃×#532	C₂²
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
1. C₁₃×#3502	C₂	semidirect
5. C₁₃×#1653	C₂	semidirect
6. C₁₃×#1645	C₂	semidirect
7. C₁₃×#1626	C₂	semidirect
8. C₁₃×#1623	C₂	semidirect
9. C₁₃×#1550	C₂	semidirect
10. C₁₃×#1493	C₂	semidirect
11. C₂×C₁₃×Q₈⋊C₈	C₂	semidirect
127. #18676	C₁₃	direct (N × H)
136. C₂×Q₈×C₁₃	SD₁₆	semidirect
198. #3502	C₂×C₁₃	semidirect
202. #1653	C₂×C₁₃	semidirect
203. #1645	C₂×C₁₃	semidirect
204. #1626	C₂×C₁₃	semidirect
205. #1623	C₂×C₁₃	semidirect
206. #1550	C₂×C₁₃	semidirect
207. #1493	C₂×C₁₃	semidirect
208. C₂×Q₈⋊C₈	C₂×C₁₃	semidirect
404. C₂×Q₈	C₁₃×SD₁₆	semidirect
466. C₁₃	#18676	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×#3502	2
C₁₃×#3246	2
C₁₃×#3167	2
C₁₃×#3037	2
C₁₃×#1653	2
C₁₃×#1645	2
C₁₃×#1626	2
C₁₃×#1623	2
C₁₃×#1550	2
C₁₃×#1493	2
C₂×C₁₃×Q₈⋊C₈	2
#18676	13

Subgroups — C13×#18676 #15705015

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#18676 #15705015