Subgroups — C₁₃×#23704 #15710043

Order 3328.

820 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	C₂×C₄×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#433	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2323	C₂	1	2	yes	maximal
4	C₁₃×#2087	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2076	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#2066	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2056	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2035	C₂	1	2	yes	maximal
9	C₁₃×#2001	C₂	1	1	yes	maximal, characteristic
10	C₄×C₁₃×#106	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1763	C₂	1	2	yes	maximal, complemented
12	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
14	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
15	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
16	C₄×C₁₃×Q₁₆	—	2	4	no	—
17	C₁₃×#433	—	2	4	no	—
18	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#106	C₂²	1	2	yes	—
20	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#103	C₂²	1	2	yes	—
23	C₂×C₁₃×#103	C₂²	1	2	yes	—
24	C₂×C₁₃×#103	C₂²	1	2	yes	—
25	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
29	C₁₃×#391	C₂²	1	2	yes	—
30	C₁₃×#389	—	2	2	no	—
31	C₁₃×#389	C₂²	1	2	yes	—
32	C₁₃×#388	—	2	2	no	—
33	C₁₃×#388	—	2	2	no	—
34	C₁₃×#387	—	2	2	no	—
35	C₁₃×#380	C₂²	1	2	yes	—
36	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
37	C₁₃×#340	C₂²	1	1	yes	characteristic
38	C₁₃×#340	C₂²	1	2	yes	—
39	C₁₃×#340	C₂²	1	2	yes	—
40	C₁₃×#340	C₂²	1	1	yes	characteristic
41	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
42	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
43	C₂×C₁₃×Q₁₆	—	2	4	no	—
44	C₂×C₁₃×Q₁₆	—	2	2	no	—
45	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
49	C₁₃×C₂²⋊Q₈	—	2	4	no	—
50	C₁₃×C₂²⋊Q₈	—	2	4	no	—
51	C₄×Q₈×C₁₃	—	2	4	no	—
52	C₄×Q₈×C₁₃	—	2	4	no	—
53	C₁₃×#117	—	2	2	no	—
54	C₁₃×#117	—	2	2	no	—
55	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
56	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
57	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
58	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
59	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
60	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
61	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
62	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
63	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
64	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
65	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
66	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
67	C₂×C₄²×C₁₃	—	2	2	no	—
68	C₂×C₄²×C₁₃	—	2	2	no	—
69	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
71	C₁₃×#107	—	2	2	no	—
72	C₁₃×#106	—	2	4	no	—
73	C₁₃×C₄⋊C₈	—	2	2	no	—
74	C₁₃×C₄⋊C₈	—	2	2	no	—
75	C₁₃×#103	—	2	4	no	—
76	C₁₃×#103	—	2	4	no	—
77	C₁₃×#103	—	2	4	no	—
78	C₁₃×C₂²⋊C₈	—	2	2	no	—
79	C₁₃×C₂²⋊C₈	—	2	2	no	—
80	C₁₃×#97	—	2	2	no	—
81	C₄×C₈×C₁₃	D₄	1	4	yes	—
82	C₁₃×#95	—	2	2	no	—
83	C₁₃×#95	—	2	2	no	—
84	C₁₃×#95	—	2	2	no	—
85	C₁₃×#95	—	2	2	no	—
86	C₁₃×#95	—	2	2	no	—
87	#23704	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
88	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
89	C₂×Q₈×C₁₃	—	2	2	no	—
90	C₂×Q₈×C₁₃	—	2	2	no	—
91	C₂×Q₈×C₁₃	—	2	2	no	—
92	C₂×Q₈×C₁₃	—	2	2	no	—
93	C₂×Q₈×C₁₃	—	2	2	no	—
94	C₂×Q₈×C₁₃	#41	1	4	yes	—
95	C₂²×C₄×C₁₃	—	2	2	no	—
96	C₂²×C₄×C₁₃	—	2	2	no	—
97	C₂²×C₄×C₁₃	—	2	1	no	—
98	C₂²×C₄×C₁₃	—	2	1	no	—
99	C₂²×C₄×C₁₃	—	2	2	no	—
100	C₂²×C₄×C₁₃	—	2	2	no	—
101	C₂²×C₄×C₁₃	—	2	2	no	—
102	C₂²×C₄×C₁₃	—	2	2	no	—
103	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
109	C₁₃×Q₁₆	—	2	8	no	—
110	C₂×C₈×C₁₃	—	2	2	no	—
111	C₂×C₈×C₁₃	—	2	2	no	—
112	C₂×C₈×C₁₃	—	2	1	no	—
113	C₂×C₈×C₁₃	—	2	1	no	—
114	C₂×C₈×C₁₃	—	2	2	no	—
115	C₂×C₈×C₁₃	—	2	2	no	—
116	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
117	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
118	C₁₃×C₄⋊C₄	—	2	8	no	—
119	C₁₃×C₄⋊C₄	—	2	2	no	—
120	C₁₃×C₄⋊C₄	—	2	2	no	—
121	C₁₃×C₄⋊C₄	—	2	2	no	—
122	C₁₃×C₄⋊C₄	—	2	2	no	—
123	C₁₃×C₄⋊C₄	—	2	2	no	—
124	C₁₃×C₄⋊C₄	—	2	2	no	—
125	C₁₃×C₄⋊C₄	—	2	2	no	—
126	C₁₃×C₄⋊C₄	—	4	4	no	—
127	C₁₃×C₄⋊C₄	—	8	2	no	—
128	C₁₃×C₄⋊C₄	#41	1	4	yes	—
129	C₁₃×C₂²⋊C₄	—	2	8	no	—
130	C₁₃×C₂²⋊C₄	—	2	2	no	—
131	C₁₃×C₂²⋊C₄	—	2	2	no	—
132	C₁₃×C₂²⋊C₄	—	8	2	no	—
133	C₄²×C₁₃	—	2	1	no	—
134	C₄²×C₁₃	—	2	1	no	—
135	C₄²×C₁₃	—	4	4	no	—
136	C₄²×C₁₃	—	8	2	no	—
137	C₄²×C₁₃	C₂×D₄	1	2	yes	—
138	C₄²×C₁₃	#41	1	2	yes	—
139	C₂×C₄×Q₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
140	C₂×#433	C₂×C₁₃	1	1	yes	characteristic
141	#2323	C₂×C₁₃	1	2	yes	—
142	#2087	C₂×C₁₃	1	1	yes	characteristic, complemented
143	#2076	C₂×C₁₃	1	1	yes	characteristic
144	#2066	C₂×C₁₃	1	2	yes	complemented
145	#2056	C₂×C₁₃	1	1	yes	characteristic, complemented
146	#2035	C₂×C₁₃	1	2	yes	—
147	#2001	C₂×C₁₃	1	1	yes	characteristic
148	C₄×#106	C₂×C₁₃	1	1	yes	characteristic, complemented
149	#1763	C₂×C₁₃	1	2	yes	complemented
150	C₂³×C₁₃	—	2	1	no	—
151	C₂³×C₁₃	—	2	2	no	—
152	C₂³×C₁₃	—	2	2	no	—
153	C₂³×C₁₃	—	2	1	no	—
154	C₂³×C₁₃	—	2	1	no	—
155	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
156	Q₈×C₁₃	—	2	4	no	—
157	Q₈×C₁₃	—	2	4	no	—
158	Q₈×C₁₃	—	4	2	no	—
159	Q₈×C₁₃	—	4	2	no	—
160	C₂×C₄×C₁₃	—	2	2	no	—
161	C₂×C₄×C₁₃	—	2	1	no	—
162	C₂×C₄×C₁₃	—	2	1	no	—
163	C₂×C₄×C₁₃	—	2	1	no	—
164	C₂×C₄×C₁₃	—	2	1	no	—
165	C₂×C₄×C₁₃	—	2	1	no	—
166	C₂×C₄×C₁₃	—	2	4	no	—
167	C₂×C₄×C₁₃	—	2	4	no	—
168	C₂×C₄×C₁₃	—	2	2	no	—
169	C₂×C₄×C₁₃	—	2	2	no	—
170	C₂×C₄×C₁₃	—	2	1	no	—
171	C₂×C₄×C₁₃	—	2	1	no	—
172	C₂×C₄×C₁₃	—	4	2	no	—
173	C₂×C₄×C₁₃	—	4	2	no	—
174	C₂×C₄×C₁₃	—	4	2	no	—
175	C₂×C₄×C₁₃	—	4	2	no	—
176	C₂×C₄×C₁₃	—	4	1	no	—
177	C₂×C₄×C₁₃	—	4	2	no	—
178	C₂×C₄×C₁₃	—	4	1	no	—
179	C₂×C₄×C₁₃	—	4	2	no	—
180	C₂×C₄×C₁₃	—	4	2	no	—
181	C₂×C₄×C₁₃	—	4	2	no	—
182	C₂×C₄×C₁₃	—	4	2	no	—
183	C₂×C₄×C₁₃	—	4	2	no	—
184	C₂×C₄×C₁₃	—	4	2	no	—
185	C₂×C₄×C₁₃	#121	1	2	yes	—
186	C₂×C₄×C₁₃	#121	1	2	yes	—
187	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
188	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
189	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
190	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
191	C₈×C₁₃	—	2	2	no	—
192	C₈×C₁₃	—	2	2	no	—
193	C₈×C₁₃	—	4	1	no	—
194	C₈×C₁₃	—	4	1	no	—
195	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
196	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
197	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
198	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
199	C₄×Q₁₆	—	2	4	no	—
200	#433	—	2	4	no	—
201	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
202	C₂×#106	C₂²×C₁₃	1	2	yes	—
203	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
204	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
205	C₂×#103	C₂²×C₁₃	1	2	yes	—
206	C₂×#103	C₂²×C₁₃	1	2	yes	—
207	C₂×#103	C₂²×C₁₃	1	2	yes	—
208	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
209	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
210	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
211	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
212	#391	C₂²×C₁₃	1	2	yes	—
213	#389	—	2	2	no	—
214	#389	C₂²×C₁₃	1	2	yes	—
215	#388	—	2	2	no	—
216	#388	—	2	2	no	—
217	#387	—	2	2	no	—
218	#380	C₂²×C₁₃	1	2	yes	—
219	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
220	#340	C₂²×C₁₃	1	1	yes	characteristic
221	#340	C₂²×C₁₃	1	2	yes	—
222	#340	C₂²×C₁₃	1	1	yes	characteristic
223	#340	C₂²×C₁₃	1	2	yes	—
224	C₂²×C₁₃	—	4	2	no	—
225	C₂²×C₁₃	—	4	2	no	—
226	C₂²×C₁₃	—	4	1	no	—
227	C₂²×C₁₃	—	4	1	no	—
228	C₂²×C₁₃	—	4	1	no	—
229	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
230	C₂²×C₁₃	#525	1	2	yes	—
231	C₂²×C₁₃	#577	1	2	yes	—
232	C₂²×C₁₃	#578	1	1	yes	characteristic
233	C₂²×C₁₃	#578	1	1	yes	characteristic
234	C₄×C₁₃	—	2	2	no	—
235	C₄×C₁₃	—	2	2	no	—
236	C₄×C₁₃	—	4	4	no	—
237	C₄×C₁₃	—	4	1	no	—
238	C₄×C₁₃	—	4	4	no	—
239	C₄×C₁₃	—	4	1	no	—
240	C₄×C₁₃	—	4	1	no	—
241	C₄×C₁₃	—	8	2	no	—
242	C₄×C₁₃	—	8	2	no	—
243	C₄×C₁₃	#525	1	1	yes	characteristic
244	C₄×C₁₃	#529	1	2	yes	—
245	C₄×C₁₃	#532	1	1	yes	characteristic
246	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
247	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
248	C₂×Q₁₆	—	2	4	no	—
249	C₂×Q₁₆	—	2	2	no	—
250	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
251	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
252	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
253	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
254	C₂²⋊Q₈	—	2	4	no	—
255	C₂²⋊Q₈	—	2	4	no	—
256	C₄×Q₈	—	2	4	no	—
257	C₄×Q₈	—	2	4	no	—
258	#117	—	2	2	no	—
259	#117	—	2	2	no	—
260	C₂×C₄⋊C₄	—	2	2	no	—
261	C₂×C₄⋊C₄	—	2	2	no	—
262	C₂×C₄⋊C₄	—	2	2	no	—
263	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
264	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
265	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
266	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
267	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
268	C₂×C₂²⋊C₄	—	2	2	no	—
269	C₂×C₂²⋊C₄	—	2	2	no	—
270	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
271	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
272	C₂×C₄²	—	2	2	no	—
273	C₂×C₄²	—	2	2	no	—
274	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
275	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
276	#107	—	2	2	no	—
277	#106	—	2	4	no	—
278	C₄⋊C₈	—	2	2	no	—
279	C₄⋊C₈	—	2	2	no	—
280	#103	—	2	4	no	—
281	#103	—	2	4	no	—
282	#103	—	2	4	no	—
283	C₂²⋊C₈	—	2	2	no	—
284	C₂²⋊C₈	—	2	2	no	—
285	#97	—	2	2	no	—
286	C₄×C₈	D₄×C₁₃	1	4	yes	—
287	#95	—	2	2	no	—
288	#95	—	2	2	no	—
289	#95	—	2	2	no	—
290	#95	—	2	2	no	—
291	#95	—	2	2	no	—
292	C₂×C₁₃	—	8	1	no	—
293	C₂×C₁₃	#2392	1	1	yes	characteristic
294	C₂×C₁₃	#3059	1	1	yes	characteristic
295	C₂×C₁₃	#3060	1	1	yes	characteristic
296	C₂×C₁₃	#3120	1	2	yes	—
297	C₂×C₁₃	#3121	1	2	yes	—
298	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
299	C₂×Q₈	—	2	2	no	—
300	C₂×Q₈	—	2	2	no	—
301	C₂×Q₈	—	2	2	no	—
302	C₂×Q₈	—	2	2	no	—
303	C₂×Q₈	—	2	2	no	—
304	C₂×Q₈	C₁₃×#41	1	4	yes	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	2	1	no	—
308	C₂²×C₄	—	2	1	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
314	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
315	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
316	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
317	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
318	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
319	Q₁₆	—	2	8	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	1	no	—
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
327	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
328	C₄⋊C₄	—	2	8	no	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	4	4	no	—
337	C₄⋊C₄	—	8	2	no	—
338	C₄⋊C₄	C₁₃×#41	1	4	yes	—
339	C₂²⋊C₄	—	2	8	no	—
340	C₂²⋊C₄	—	2	2	no	—
341	C₂²⋊C₄	—	2	2	no	—
342	C₂²⋊C₄	—	8	2	no	—
343	C₄²	—	2	1	no	—
344	C₄²	—	2	1	no	—
345	C₄²	—	4	4	no	—
346	C₄²	—	8	2	no	—
347	C₄²	C₂×D₄×C₁₃	1	2	yes	—
348	C₄²	C₁₃×#41	1	2	yes	—
349	C₁₃	#23704	1	1	yes	characteristic, direct product factor, Sylow
350	C₂³	—	2	1	no	—
351	C₂³	—	2	2	no	—
352	C₂³	—	2	2	no	—
353	C₂³	—	2	1	no	—
354	C₂³	—	2	1	no	—
355	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
356	Q₈	—	2	4	no	—
357	Q₈	—	2	4	no	—
358	Q₈	—	4	2	no	—
359	Q₈	—	4	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	2	4	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	1	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	C₁₃×#121	1	2	yes	—
386	C₂×C₄	C₁₃×#121	1	2	yes	—
387	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
388	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
389	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
390	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
391	C₈	—	2	2	no	—
392	C₈	—	2	2	no	—
393	C₈	—	4	1	no	—
394	C₈	—	4	1	no	—
395	C₂²	—	4	1	no	—
396	C₂²	—	4	1	no	—
397	C₂²	—	4	2	no	—
398	C₂²	—	4	2	no	—
399	C₂²	—	4	1	no	—
400	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
401	C₂²	C₁₃×#525	1	2	yes	—
402	C₂²	C₁₃×#577	1	2	yes	—
403	C₂²	C₁₃×#578	1	1	yes	characteristic
404	C₂²	C₁₃×#578	1	1	yes	characteristic
405	C₄	—	2	2	no	—
406	C₄	—	2	2	no	—
407	C₄	—	4	1	no	—
408	C₄	—	4	1	no	—
409	C₄	—	4	4	no	—
410	C₄	—	4	1	no	—
411	C₄	—	4	4	no	—
412	C₄	—	8	2	no	—
413	C₄	—	8	2	no	—
414	C₄	C₁₃×#525	1	1	yes	characteristic
415	C₄	C₁₃×#529	1	2	yes	—
416	C₄	C₁₃×#532	1	1	yes	characteristic
417	C₂	—	8	1	no	—
418	C₂	C₁₃×#2392	1	1	yes	characteristic
419	C₂	C₁₃×#3059	1	1	yes	characteristic
420	C₂	C₁₃×#3060	1	1	yes	characteristic
421	C₂	C₁₃×#3120	1	2	yes	—
422	C₂	C₁₃×#3121	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂⁴×C₁₃	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₁₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄×C₁₃×Q₁₆	C₂	semidirect
4. C₁₃×#2087	C₂	semidirect
6. C₁₃×#2066	C₂	semidirect
7. C₁₃×#2056	C₂	semidirect
10. C₄×C₁₃×#106	C₂	semidirect
11. C₁₃×#1763	C₂	semidirect
87. #23704	C₁₃	direct (N × H)
139. C₂×C₄×Q₁₆	C₂×C₁₃	semidirect
142. #2087	C₂×C₁₃	semidirect
144. #2066	C₂×C₁₃	semidirect
145. #2056	C₂×C₁₃	semidirect
148. C₄×#106	C₂×C₁₃	semidirect
149. #1763	C₂×C₁₃	semidirect
349. C₁₃	#23704	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄×C₁₃×Q₁₆	2
C₂×C₁₃×#433	2
C₁₃×#2323	2
C₁₃×#2087	2
C₁₃×#2076	2
C₁₃×#2066	2
C₁₃×#2056	2
C₁₃×#2035	2
C₁₃×#2001	2
C₄×C₁₃×#106	2
C₁₃×#1763	2
#23704	13

Subgroups — C13×#23704 #15710043

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#23704 #15710043