Subgroups — C₁₃×#18003 #15704342

Order 3328.

594 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3104	C₂	1	1	yes	maximal, characteristic
2	Q₈×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2962	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1593	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1587	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1587	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1579	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1570	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#1493	C₂	1	1	yes	maximal, characteristic
10	C₂×C₁₃×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic
11	C₁₃×#1451	C₂	1	1	yes	maximal, characteristic
12	C₁₃×#533	C₂²	1	1	yes	characteristic
13	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
14	C₁₃×#484	C₄	1	2	yes	—
15	C₁₃×#477	C₄	1	1	yes	characteristic
16	C₁₃×#477	C₄	1	1	yes	characteristic
17	C₁₃×#462	C₄	1	1	yes	characteristic
18	C₁₃×#462	C₄	1	1	yes	characteristic
19	C₁₃×#451	C₄	1	2	yes	—
20	C₁₃×#446	—	2	2	no	—
21	C₁₃×#446	—	2	2	no	—
22	C₁₃×#446	C₂²	1	2	yes	—
23	C₁₃×#446	C₂²	1	2	yes	—
24	C₈×Q₈×C₁₃	C₂²	1	2	yes	—
25	C₈×Q₈×C₁₃	C₂²	1	2	yes	—
26	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
27	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
28	C₁₃×#431	C₂²	1	1	yes	characteristic
29	C₁₃×#424	—	2	1	no	—
30	C₁₃×#423	—	2	1	no	—
31	C₁₃×#423	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
33	C₁₃×#405	—	2	1	no	—
34	C₄×C₁₃×M₁₆	—	2	1	no	—
35	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
37	C₁₃×#334	C₂²	1	2	yes	—
38	C₁₃×#334	C₂²	1	2	yes	—
39	C₁₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
40	C₁₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
41	C₁₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
42	C₁₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
43	C₁₃×Q₈⋊C₈	C₂²	1	2	yes	—
44	C₁₃×Q₈⋊C₈	C₂²	1	2	yes	—
45	C₁₃×#322	C₂²	1	2	yes	—
46	C₁₃×#322	C₂²	1	2	yes	—
47	C₂²×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
48	C₂×C₁₃×Q₁₆	C₂×C₄	1	2	yes	—
49	C₂×C₁₃×Q₁₆	C₂×C₄	1	2	yes	—
50	C₂×C₁₃×M₁₆	—	2	1	no	—
51	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
52	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
53	C₂²×C₈×C₁₃	—	2	1	no	—
54	C₂²×C₈×C₁₃	—	2	1	no	—
55	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
56	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
57	C₁₃×#125	—	2	1	no	—
58	C₁₃×C₂²⋊Q₈	—	2	1	no	—
59	C₁₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
60	C₄×Q₈×C₁₃	—	2	1	no	—
61	C₄×Q₈×C₁₃	—	2	1	no	—
62	C₄×Q₈×C₁₃	—	2	1	no	—
63	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
64	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
65	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
66	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
67	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
68	C₁₃×#117	—	2	1	no	—
69	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
70	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
71	C₂×C₄²×C₁₃	—	2	1	no	—
72	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
73	C₁₃×#107	C₂×C₄	1	2	yes	—
74	C₁₃×#107	C₂×C₄	1	2	yes	—
75	C₁₃×C₄⋊C₈	—	2	2	no	—
76	C₁₃×C₄⋊C₈	—	2	2	no	—
77	C₁₃×C₄⋊C₈	—	2	2	no	—
78	C₁₃×C₄⋊C₈	—	2	2	no	—
79	C₁₃×C₄⋊C₈	—	2	1	no	—
80	C₁₃×C₄⋊C₈	—	2	1	no	—
81	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
82	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
83	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
84	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
85	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
86	C₁₃×#103	C₂×C₄	1	2	yes	—
87	C₁₃×#103	C₂×C₄	1	2	yes	—
88	C₁₃×#103	C₂×C₄	1	2	yes	—
89	C₁₃×#103	C₂×C₄	1	2	yes	—
90	C₁₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
91	C₁₃×#97	—	2	2	no	—
92	C₁₃×#97	—	2	2	no	—
93	C₁₃×#97	D₄	1	2	yes	—
94	C₄×C₈×C₁₃	—	2	2	no	—
95	C₄×C₈×C₁₃	—	2	2	no	—
96	C₄×C₈×C₁₃	—	2	1	no	—
97	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
98	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
99	C₄×C₈×C₁₃	C₂³	1	2	yes	—
100	C₄×C₈×C₁₃	C₂³	1	2	yes	—
101	#18003	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
102	C₂×Q₈×C₁₃	—	2	1	no	—
103	C₂×Q₈×C₁₃	—	2	1	no	—
104	C₂×Q₈×C₁₃	—	2	2	no	—
105	C₂×Q₈×C₁₃	—	4	1	no	—
106	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
107	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
108	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₃	—	2	1	no	—
110	C₂²×C₄×C₁₃	—	2	1	no	—
111	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
114	C₁₃×Q₁₆	—	2	4	no	—
115	C₁₃×Q₁₆	—	4	2	no	—
116	C₁₃×M₁₆	—	2	2	no	—
117	C₁₃×M₁₆	—	2	2	no	—
118	C₁₃×M₁₆	—	4	2	no	—
119	C₂×C₈×C₁₃	—	2	1	no	—
120	C₂×C₈×C₁₃	—	2	1	no	—
121	C₂×C₈×C₁₃	—	2	2	no	—
122	C₂×C₈×C₁₃	—	2	1	no	—
123	C₂×C₈×C₁₃	—	2	1	no	—
124	C₂×C₈×C₁₃	—	4	2	no	—
125	C₂×C₈×C₁₃	—	4	2	no	—
126	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
127	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
128	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
129	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
130	C₁₃×C₄⋊C₄	—	2	1	no	—
131	C₁₃×C₄⋊C₄	—	2	1	no	—
132	C₁₃×C₄⋊C₄	—	2	1	no	—
133	C₁₃×C₄⋊C₄	—	2	1	no	—
134	C₁₃×C₄⋊C₄	—	2	1	no	—
135	C₁₃×C₄⋊C₄	—	2	1	no	—
136	C₁₃×C₄⋊C₄	—	2	2	no	—
137	C₁₃×C₄⋊C₄	—	2	1	no	—
138	C₁₃×C₄⋊C₄	—	2	1	no	—
139	C₁₃×C₄⋊C₄	—	2	2	no	—
140	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
141	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
142	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
143	C₁₃×C₂²⋊C₄	—	2	2	no	—
144	C₄²×C₁₃	—	2	1	no	—
145	C₄²×C₁₃	—	2	1	no	—
146	C₄²×C₁₃	—	2	1	no	—
147	C₄²×C₁₃	—	2	2	no	—
148	C₄²×C₁₃	—	2	1	no	—
149	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
150	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
151	C₄²×C₁₃	#41	1	1	yes	characteristic
152	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
153	#3104	C₂×C₁₃	1	1	yes	characteristic
154	Q₈×M₁₆	C₂×C₁₃	1	1	yes	characteristic
155	#2962	C₂×C₁₃	1	1	yes	characteristic
156	#1593	C₂×C₁₃	1	2	yes	complemented
157	#1587	C₂×C₁₃	1	2	yes	complemented
158	#1587	C₂×C₁₃	1	2	yes	complemented
159	#1579	C₂×C₁₃	1	2	yes	complemented
160	#1570	C₂×C₁₃	1	1	yes	characteristic
161	#1493	C₂×C₁₃	1	1	yes	characteristic
162	C₂×Q₈⋊C₈	C₂×C₁₃	1	1	yes	characteristic
163	#1451	C₂×C₁₃	1	1	yes	characteristic
164	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
165	Q₈×C₁₃	—	2	1	no	—
166	Q₈×C₁₃	—	2	2	no	—
167	Q₈×C₁₃	—	2	1	no	—
168	Q₈×C₁₃	—	2	1	no	—
169	Q₈×C₁₃	—	2	2	no	—
170	Q₈×C₁₃	—	4	2	no	—
171	Q₈×C₁₃	—	8	1	no	—
172	Q₈×C₁₃	#131	1	2	yes	—
173	C₂×C₄×C₁₃	—	2	1	no	—
174	C₂×C₄×C₁₃	—	2	1	no	—
175	C₂×C₄×C₁₃	—	2	1	no	—
176	C₂×C₄×C₁₃	—	2	1	no	—
177	C₂×C₄×C₁₃	—	2	1	no	—
178	C₂×C₄×C₁₃	—	2	1	no	—
179	C₂×C₄×C₁₃	—	2	2	no	—
180	C₂×C₄×C₁₃	—	2	2	no	—
181	C₂×C₄×C₁₃	—	4	1	no	—
182	C₂×C₄×C₁₃	—	4	2	no	—
183	C₂×C₄×C₁₃	—	8	1	no	—
184	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
185	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
186	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
187	C₂×C₄×C₁₃	#137	1	2	yes	—
188	C₂×C₄×C₁₃	#137	1	2	yes	—
189	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
190	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
191	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
192	C₈×C₁₃	—	2	2	no	—
193	C₈×C₁₃	—	2	2	no	—
194	C₈×C₁₃	—	2	2	no	—
195	C₈×C₁₃	—	2	2	no	—
196	C₈×C₁₃	—	2	2	no	—
197	C₈×C₁₃	—	4	1	no	—
198	C₈×C₁₃	—	4	1	no	—
199	C₈×C₁₃	—	4	1	no	—
200	C₈×C₁₃	—	4	2	no	—
201	#533	C₂²×C₁₃	1	1	yes	characteristic
202	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
203	#484	C₄×C₁₃	1	2	yes	—
204	#477	C₄×C₁₃	1	1	yes	characteristic
205	#477	C₄×C₁₃	1	1	yes	characteristic
206	#462	C₄×C₁₃	1	1	yes	characteristic
207	#462	C₄×C₁₃	1	1	yes	characteristic
208	#451	C₄×C₁₃	1	2	yes	—
209	#446	—	2	2	no	—
210	#446	—	2	2	no	—
211	#446	C₂²×C₁₃	1	2	yes	—
212	#446	C₂²×C₁₃	1	2	yes	—
213	C₈×Q₈	C₂²×C₁₃	1	2	yes	—
214	C₈×Q₈	C₂²×C₁₃	1	2	yes	—
215	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
216	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
217	#431	C₂²×C₁₃	1	1	yes	characteristic
218	#424	—	2	1	no	—
219	#423	—	2	1	no	—
220	#423	C₂²×C₁₃	1	1	yes	characteristic
221	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
222	#405	—	2	1	no	—
223	C₄×M₁₆	—	2	1	no	—
224	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
225	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
226	#334	C₂²×C₁₃	1	2	yes	—
227	#334	C₂²×C₁₃	1	2	yes	—
228	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
229	Q₈⋊C₈	C₂²×C₁₃	1	2	yes	—
230	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
231	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
232	Q₈⋊C₈	C₂²×C₁₃	1	2	yes	—
233	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
234	#322	C₂²×C₁₃	1	2	yes	—
235	#322	C₂²×C₁₃	1	2	yes	—
236	C₂²×C₁₃	—	2	1	no	—
237	C₂²×C₁₃	—	2	1	no	—
238	C₂²×C₁₃	#441	1	2	yes	—
239	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
240	C₄×C₁₃	—	2	1	no	—
241	C₄×C₁₃	—	2	2	no	—
242	C₄×C₁₃	—	2	1	no	—
243	C₄×C₁₃	—	2	1	no	—
244	C₄×C₁₃	—	4	1	no	—
245	C₄×C₁₃	—	4	2	no	—
246	C₄×C₁₃	—	4	1	no	—
247	C₄×C₁₃	—	4	1	no	—
248	C₄×C₁₃	—	4	2	no	—
249	C₄×C₁₃	#441	1	2	yes	—
250	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
251	C₄×C₁₃	#568	1	1	yes	characteristic
252	C₄×C₁₃	C₂×#137	1	1	yes	characteristic
253	C₄×C₁₃	C₂×#137	1	1	yes	characteristic
254	C₂²×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
255	C₂×Q₁₆	C₂×C₄×C₁₃	1	2	yes	—
256	C₂×Q₁₆	C₂×C₄×C₁₃	1	2	yes	—
257	C₂×M₁₆	—	2	1	no	—
258	C₂×M₁₆	D₄×C₁₃	1	1	yes	characteristic
259	C₂×M₁₆	D₄×C₁₃	1	1	yes	characteristic
260	C₂²×C₈	—	2	1	no	—
261	C₂²×C₈	—	2	1	no	—
262	C₄⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
263	C₄⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
264	#125	—	2	1	no	—
265	C₂²⋊Q₈	—	2	1	no	—
266	C₂²⋊Q₈	C₂×C₄×C₁₃	1	2	yes	—
267	C₄×Q₈	—	2	1	no	—
268	C₄×Q₈	—	2	1	no	—
269	C₄×Q₈	—	2	1	no	—
270	C₄×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
271	C₄×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
272	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
273	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
274	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
275	#117	—	2	1	no	—
276	C₂×C₄⋊C₄	—	2	1	no	—
277	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
278	C₂×C₄²	—	2	1	no	—
279	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
280	#107	C₂×C₄×C₁₃	1	2	yes	—
281	#107	C₂×C₄×C₁₃	1	2	yes	—
282	C₄⋊C₈	—	2	2	no	—
283	C₄⋊C₈	—	2	2	no	—
284	C₄⋊C₈	—	2	2	no	—
285	C₄⋊C₈	—	2	2	no	—
286	C₄⋊C₈	—	2	1	no	—
287	C₄⋊C₈	—	2	1	no	—
288	C₄⋊C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
289	C₄⋊C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
290	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
291	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
292	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
293	#103	C₂×C₄×C₁₃	1	2	yes	—
294	#103	C₂×C₄×C₁₃	1	2	yes	—
295	#103	C₂×C₄×C₁₃	1	2	yes	—
296	#103	C₂×C₄×C₁₃	1	2	yes	—
297	C₂²⋊C₈	C₂×C₄×C₁₃	1	2	yes	—
298	#97	—	2	2	no	—
299	#97	—	2	2	no	—
300	#97	D₄×C₁₃	1	2	yes	—
301	C₄×C₈	—	2	2	no	—
302	C₄×C₈	—	2	2	no	—
303	C₄×C₈	—	2	1	no	—
304	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
305	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
306	C₄×C₈	C₂³×C₁₃	1	2	yes	—
307	C₄×C₈	C₂³×C₁₃	1	2	yes	—
308	C₂×C₁₃	—	2	2	no	—
309	C₂×C₁₃	#2933	1	1	yes	characteristic
310	C₂×C₁₃	C₂×#441	1	1	yes	characteristic
311	C₂×C₁₃	#2956	1	1	yes	characteristic
312	C₂×Q₈	—	2	1	no	—
313	C₂×Q₈	—	2	1	no	—
314	C₂×Q₈	—	2	2	no	—
315	C₂×Q₈	—	4	1	no	—
316	C₂×Q₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
317	C₂×Q₈	C₂²×C₄×C₁₃	1	2	yes	—
318	C₂×Q₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
319	C₂²×C₄	—	2	1	no	—
320	C₂²×C₄	—	2	1	no	—
321	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
322	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
323	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
324	Q₁₆	—	2	4	no	—
325	Q₁₆	—	4	2	no	—
326	M₁₆	—	2	2	no	—
327	M₁₆	—	2	2	no	—
328	M₁₆	—	4	2	no	—
329	C₂×C₈	—	2	1	no	—
330	C₂×C₈	—	2	1	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	2	1	no	—
333	C₂×C₈	—	2	1	no	—
334	C₂×C₈	—	4	2	no	—
335	C₂×C₈	—	4	2	no	—
336	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
337	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
338	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
339	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
340	C₄⋊C₄	—	2	1	no	—
341	C₄⋊C₄	—	2	1	no	—
342	C₄⋊C₄	—	2	1	no	—
343	C₄⋊C₄	—	2	1	no	—
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	2	1	no	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	2	1	no	—
348	C₄⋊C₄	—	2	1	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
351	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
352	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
353	C₂²⋊C₄	—	2	2	no	—
354	C₄²	—	2	1	no	—
355	C₄²	—	2	1	no	—
356	C₄²	—	2	1	no	—
357	C₄²	—	2	2	no	—
358	C₄²	—	2	1	no	—
359	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
360	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
361	C₄²	C₁₃×#41	1	1	yes	characteristic
362	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
363	C₁₃	#18003	1	1	yes	characteristic, direct product factor, Sylow
364	C₂³	C₄×D₄×C₁₃	1	1	yes	characteristic
365	Q₈	—	2	1	no	—
366	Q₈	—	2	2	no	—
367	Q₈	—	2	1	no	—
368	Q₈	—	2	1	no	—
369	Q₈	—	2	2	no	—
370	Q₈	—	4	2	no	—
371	Q₈	—	8	1	no	—
372	Q₈	C₁₃×#131	1	2	yes	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	8	1	no	—
384	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
385	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
386	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
387	C₂×C₄	C₁₃×#137	1	2	yes	—
388	C₂×C₄	C₁₃×#137	1	2	yes	—
389	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
390	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
391	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
392	C₈	—	2	2	no	—
393	C₈	—	2	2	no	—
394	C₈	—	2	2	no	—
395	C₈	—	2	2	no	—
396	C₈	—	2	2	no	—
397	C₈	—	4	1	no	—
398	C₈	—	4	1	no	—
399	C₈	—	4	1	no	—
400	C₈	—	4	2	no	—
401	C₂²	—	2	1	no	—
402	C₂²	—	2	1	no	—
403	C₂²	C₁₃×#441	1	2	yes	—
404	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
405	C₄	—	2	1	no	—
406	C₄	—	2	2	no	—
407	C₄	—	2	1	no	—
408	C₄	—	2	1	no	—
409	C₄	—	4	1	no	—
410	C₄	—	4	2	no	—
411	C₄	—	4	1	no	—
412	C₄	—	4	1	no	—
413	C₄	—	4	2	no	—
414	C₄	C₁₃×#441	1	2	yes	—
415	C₄	C₂×C₁₃×#131	1	1	yes	characteristic
416	C₄	C₁₃×#568	1	1	yes	characteristic
417	C₄	C₂×C₁₃×#137	1	1	yes	characteristic
418	C₄	C₂×C₁₃×#137	1	1	yes	characteristic
419	C₂	—	2	2	no	—
420	C₂	C₁₃×#2933	1	1	yes	characteristic
421	C₂	C₂×C₁₃×#441	1	1	yes	characteristic
422	C₂	C₁₃×#2956	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₄²	C₂⁴×C₁₃
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	C₂³×C₁₃	C₄×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₄×C₁₃×M₁₆ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₁₃×#1593	C₂	semidirect
5. C₁₃×#1587	C₂	semidirect
6. C₁₃×#1587	C₂	semidirect
7. C₁₃×#1579	C₂	semidirect
101. #18003	C₁₃	direct (N × H)
156. #1593	C₂×C₁₃	semidirect
157. #1587	C₂×C₁₃	semidirect
158. #1587	C₂×C₁₃	semidirect
159. #1579	C₂×C₁₃	semidirect
363. C₁₃	#18003	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×#3104	2
Q₈×C₁₃×M₁₆	2
C₁₃×#2962	2
C₁₃×#1593	2
C₁₃×#1587	2
C₁₃×#1579	2
C₁₃×#1570	2
C₁₃×#1493	2
C₂×C₁₃×Q₈⋊C₈	2
C₁₃×#1451	2
#18003	13

Subgroups — C13×#18003 #15704342

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#18003 #15704342