Subgroups — C₁₃×#32937 #15719276

Order 3328.

1502 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#470	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₃×#467	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2848	C₂	1	2	yes	maximal
5	C₁₃×#1894	C₂	1	4	yes	maximal, complemented
6	C₁₃×#1892	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1809	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1807	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
10	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
11	C₂²×C₁₃×M₁₆	—	2	8	no	—
12	C₂²×C₁₃×M₁₆	—	2	4	no	—
13	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	—
14	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	—
15	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
16	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
18	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
19	C₁₃×#470	—	2	8	no	—
20	C₁₃×#467	—	2	4	no	—
21	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₁₃×#106	C₂²	1	2	yes	complemented
23	C₂×C₁₃×#103	C₂²	1	2	yes	complemented
24	C₂×C₁₃×#103	C₂²	1	4	yes	complemented
25	C₁₃×#385	—	2	4	no	—
26	C₁₃×#385	—	2	2	no	—
27	C₁₃×#380	C₂²	1	2	yes	—
28	C₁₃×#380	C₂²	1	4	yes	—
29	C₁₃×#379	—	2	2	no	—
30	C₁₃×#340	C₂²	1	2	yes	complemented
31	C₁₃×#340	C₂²	1	4	yes	complemented
32	C₂⁵×C₁₃	D₄	1	1	yes	characteristic
33	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
34	C₂³×C₄×C₁₃	—	2	4	no	—
35	C₂³×C₄×C₁₃	—	2	2	no	—
36	C₂³×C₄×C₁₃	—	2	4	no	—
37	C₂³×C₄×C₁₃	—	2	2	no	—
38	C₂³×C₄×C₁₃	D₄	1	2	yes	—
39	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
40	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
41	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
42	C₂×C₁₃×Q₁₆	—	2	2	no	—
43	C₂×C₁₃×Q₁₆	—	2	4	no	—
44	C₂×C₁₃×M₁₆	—	2	32	no	—
45	C₂×C₁₃×M₁₆	—	2	4	no	—
46	C₂×C₁₃×M₁₆	—	2	4	no	—
47	C₂×C₁₃×M₁₆	—	2	4	no	—
48	C₂×C₁₃×M₁₆	—	2	4	no	—
49	C₂×C₁₃×M₁₆	—	2	4	no	—
50	C₂×C₁₃×M₁₆	D₄	1	8	yes	—
51	C₂²×C₈×C₁₃	—	2	2	no	—
52	C₂²×C₈×C₁₃	—	2	4	no	—
53	C₂²×C₈×C₁₃	—	2	4	no	—
54	C₂²×C₈×C₁₃	D₄	1	4	yes	—
55	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
56	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
58	C₁₃×C₂²⋊Q₈	—	2	4	no	—
59	C₁₃×C₂²⋊Q₈	—	2	8	no	—
60	C₁₃×C₂²⋊Q₈	—	2	4	no	—
61	C₁₃×C₂²⋊Q₈	—	2	8	no	—
62	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
63	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
64	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
65	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
66	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
67	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
68	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
69	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
70	C₁₃×#107	—	2	2	no	—
71	C₁₃×#106	—	2	4	no	—
72	C₁₃×#103	—	2	4	no	—
73	C₁₃×#103	—	2	8	no	—
74	C₁₃×#95	—	2	2	no	—
75	C₁₃×#95	—	2	4	no	—
76	#32937	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
77	C₂⁴×C₁₃	—	2	4	no	—
78	C₂⁴×C₁₃	—	2	2	no	—
79	C₂⁴×C₁₃	—	2	4	no	—
80	C₂⁴×C₁₃	—	4	2	no	—
81	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
82	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
83	C₂×Q₈×C₁₃	—	2	2	no	—
84	C₂×Q₈×C₁₃	—	2	4	no	—
85	C₂×Q₈×C₁₃	—	2	2	no	—
86	C₂×Q₈×C₁₃	—	2	4	no	—
87	C₂²×C₄×C₁₃	—	2	8	no	—
88	C₂²×C₄×C₁₃	—	2	8	no	—
89	C₂²×C₄×C₁₃	—	2	16	no	—
90	C₂²×C₄×C₁₃	—	2	4	no	—
91	C₂²×C₄×C₁₃	—	2	2	no	—
92	C₂²×C₄×C₁₃	—	2	4	no	—
93	C₂²×C₄×C₁₃	—	2	4	no	—
94	C₂²×C₄×C₁₃	—	2	4	no	—
95	C₂²×C₄×C₁₃	—	2	2	no	—
96	C₂²×C₄×C₁₃	—	2	2	no	—
97	C₂²×C₄×C₁₃	—	2	2	no	—
98	C₂²×C₄×C₁₃	—	2	2	no	—
99	C₂²×C₄×C₁₃	—	2	2	no	—
100	C₂²×C₄×C₁₃	—	2	2	no	—
101	C₂²×C₄×C₁₃	—	2	4	no	—
102	C₂²×C₄×C₁₃	—	2	2	no	—
103	C₂²×C₄×C₁₃	—	2	2	no	—
104	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
108	C₂²×C₄×C₁₃	#41	1	4	yes	—
109	C₂²×C₄×C₁₃	#41	1	2	yes	—
110	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
111	C₁₃×Q₁₆	—	4	4	no	—
112	C₁₃×M₁₆	—	2	16	no	—
113	C₁₃×M₁₆	—	2	16	no	—
114	C₂×C₈×C₁₃	—	2	8	no	—
115	C₂×C₈×C₁₃	—	2	2	no	—
116	C₂×C₈×C₁₃	—	2	2	no	—
117	C₂×C₈×C₁₃	—	2	2	no	—
118	C₂×C₈×C₁₃	—	2	8	no	—
119	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
120	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
121	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
122	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
123	C₁₃×C₄⋊C₄	—	2	4	no	—
124	C₁₃×C₄⋊C₄	—	2	2	no	—
125	C₁₃×C₄⋊C₄	—	2	4	no	—
126	C₁₃×C₄⋊C₄	—	2	2	no	—
127	C₁₃×C₄⋊C₄	—	4	4	no	—
128	C₁₃×C₄⋊C₄	—	4	8	no	—
129	C₁₃×C₂²⋊C₄	—	4	8	no	—
130	C₁₃×C₂²⋊C₄	—	4	8	no	—
131	C₁₃×C₂²⋊C₄	—	4	4	no	—
132	C₁₃×C₂²⋊C₄	—	4	4	no	—
133	C₂³×M₁₆	C₂×C₁₃	1	1	yes	characteristic
134	C₂×#470	C₂×C₁₃	1	2	yes	complemented
135	C₂×#467	C₂×C₁₃	1	1	yes	characteristic, complemented
136	#2848	C₂×C₁₃	1	2	yes	—
137	#1894	C₂×C₁₃	1	4	yes	complemented
138	#1892	C₂×C₁₃	1	2	yes	complemented
139	#1809	C₂×C₁₃	1	2	yes	complemented
140	#1807	C₂×C₁₃	1	1	yes	characteristic, complemented
141	C₂³×C₁₃	—	2	2	no	—
142	C₂³×C₁₃	—	2	2	no	—
143	C₂³×C₁₃	—	2	8	no	—
144	C₂³×C₁₃	—	2	2	no	—
145	C₂³×C₁₃	—	2	2	no	—
146	C₂³×C₁₃	—	2	4	no	—
147	C₂³×C₁₃	—	2	4	no	—
148	C₂³×C₁₃	—	4	16	no	—
149	C₂³×C₁₃	—	4	4	no	—
150	C₂³×C₁₃	—	4	4	no	—
151	C₂³×C₁₃	#121	1	4	yes	—
152	C₂³×C₁₃	#121	1	2	yes	—
153	C₂³×C₁₃	#137	1	4	yes	—
154	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
155	Q₈×C₁₃	—	4	2	no	—
156	Q₈×C₁₃	—	4	2	no	—
157	Q₈×C₁₃	—	4	4	no	—
158	C₂×C₄×C₁₃	—	2	8	no	—
159	C₂×C₄×C₁₃	—	2	16	no	—
160	C₂×C₄×C₁₃	—	2	2	no	—
161	C₂×C₄×C₁₃	—	2	2	no	—
162	C₂×C₄×C₁₃	—	2	2	no	—
163	C₂×C₄×C₁₃	—	2	2	no	—
164	C₂×C₄×C₁₃	—	2	4	no	—
165	C₂×C₄×C₁₃	—	2	2	no	—
166	C₂×C₄×C₁₃	—	2	4	no	—
167	C₂×C₄×C₁₃	—	2	4	no	—
168	C₂×C₄×C₁₃	—	2	4	no	—
169	C₂×C₄×C₁₃	—	2	4	no	—
170	C₂×C₄×C₁₃	—	4	2	no	—
171	C₂×C₄×C₁₃	—	4	4	no	—
172	C₂×C₄×C₁₃	—	4	2	no	—
173	C₂×C₄×C₁₃	—	4	4	no	—
174	C₂×C₄×C₁₃	—	4	4	no	—
175	C₂×C₄×C₁₃	—	4	4	no	—
176	C₂×C₄×C₁₃	—	4	4	no	—
177	C₂×C₄×C₁₃	#121	1	2	yes	—
178	C₂×C₄×C₁₃	#121	1	4	yes	—
179	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
180	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
181	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
182	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
183	C₈×C₁₃	—	2	4	no	—
184	C₈×C₁₃	—	2	2	no	—
185	C₈×C₁₃	#120	1	4	yes	—
186	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
187	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
188	C₂²×M₁₆	—	2	8	no	—
189	C₂²×M₁₆	—	2	4	no	—
190	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	—
191	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	—
192	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
193	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
194	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
195	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
196	#470	—	2	8	no	—
197	#467	—	2	4	no	—
198	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic, complemented
199	C₂×#106	C₂²×C₁₃	1	2	yes	complemented
200	C₂×#103	C₂²×C₁₃	1	4	yes	complemented
201	C₂×#103	C₂²×C₁₃	1	2	yes	complemented
202	#385	—	2	4	no	—
203	#385	—	2	2	no	—
204	#380	C₂²×C₁₃	1	2	yes	—
205	#380	C₂²×C₁₃	1	4	yes	—
206	#379	—	2	2	no	—
207	#340	C₂²×C₁₃	1	2	yes	complemented
208	#340	C₂²×C₁₃	1	4	yes	complemented
209	C₂²×C₁₃	—	2	2	no	—
210	C₂²×C₁₃	—	2	2	no	—
211	C₂²×C₁₃	—	2	8	no	—
212	C₂²×C₁₃	—	2	4	no	—
213	C₂²×C₁₃	—	2	8	no	—
214	C₂²×C₁₃	—	4	16	no	—
215	C₂²×C₁₃	—	4	2	no	—
216	C₂²×C₁₃	—	4	2	no	—
217	C₂²×C₁₃	—	4	4	no	—
218	C₂²×C₁₃	#470	1	4	yes	complemented
219	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
220	C₂²×C₁₃	C₂×#121	1	2	yes	—
221	C₂²×C₁₃	C₂×#137	1	2	yes	—
222	C₂²×C₁₃	#575	1	2	yes	—
223	C₄×C₁₃	—	2	2	no	—
224	C₄×C₁₃	—	2	4	no	—
225	C₄×C₁₃	—	8	2	no	—
226	C₄×C₁₃	—	8	2	no	—
227	C₄×C₁₃	—	8	4	no	—
228	C₄×C₁₃	C₂×#120	1	1	yes	characteristic
229	C₄×C₁₃	#525	1	1	yes	characteristic
230	C₄×C₁₃	#525	1	2	yes	—
231	C₂⁵	D₄×C₁₃	1	1	yes	characteristic
232	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
233	C₂³×C₄	—	2	4	no	—
234	C₂³×C₄	—	2	2	no	—
235	C₂³×C₄	—	2	4	no	—
236	C₂³×C₄	—	2	2	no	—
237	C₂³×C₄	D₄×C₁₃	1	2	yes	—
238	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
239	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
240	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
241	C₂×Q₁₆	—	2	2	no	—
242	C₂×Q₁₆	—	2	4	no	—
243	C₂×M₁₆	—	2	32	no	—
244	C₂×M₁₆	—	2	4	no	—
245	C₂×M₁₆	—	2	4	no	—
246	C₂×M₁₆	—	2	4	no	—
247	C₂×M₁₆	—	2	4	no	—
248	C₂×M₁₆	—	2	4	no	—
249	C₂×M₁₆	D₄×C₁₃	1	8	yes	—
250	C₂²×C₈	—	2	2	no	—
251	C₂²×C₈	—	2	4	no	—
252	C₂²×C₈	—	2	4	no	—
253	C₂²×C₈	D₄×C₁₃	1	4	yes	—
254	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
255	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
256	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
257	C₂²⋊Q₈	—	2	4	no	—
258	C₂²⋊Q₈	—	2	8	no	—
259	C₂²⋊Q₈	—	2	4	no	—
260	C₂²⋊Q₈	—	2	8	no	—
261	C₂×C₄⋊C₄	—	2	2	no	—
262	C₂×C₄⋊C₄	—	2	4	no	—
263	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
264	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
265	C₂×C₂²⋊C₄	—	2	4	no	—
266	C₂×C₂²⋊C₄	—	2	2	no	—
267	C₂×C₂²⋊C₄	—	2	4	no	—
268	C₂×C₂²⋊C₄	—	2	2	no	—
269	#107	—	2	2	no	—
270	#106	—	2	4	no	—
271	#103	—	2	4	no	—
272	#103	—	2	8	no	—
273	#95	—	2	2	no	—
274	#95	—	2	4	no	—
275	C₂×C₁₃	—	2	4	no	—
276	C₂×C₁₃	—	4	4	no	—
277	C₂×C₁₃	#2847	1	1	yes	characteristic
278	C₂×C₁₃	C₂×#470	1	1	yes	characteristic
279	C₂×C₁₃	#3054	1	1	yes	characteristic
280	C₂×C₁₃	#3056	1	4	yes	—
281	C₂⁴	—	2	4	no	—
282	C₂⁴	—	2	2	no	—
283	C₂⁴	—	2	4	no	—
284	C₂⁴	—	4	2	no	—
285	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
286	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
287	C₂×Q₈	—	2	2	no	—
288	C₂×Q₈	—	2	4	no	—
289	C₂×Q₈	—	2	2	no	—
290	C₂×Q₈	—	2	4	no	—
291	C₂²×C₄	—	2	8	no	—
292	C₂²×C₄	—	2	8	no	—
293	C₂²×C₄	—	2	16	no	—
294	C₂²×C₄	—	2	4	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	2	4	no	—
297	C₂²×C₄	—	2	4	no	—
298	C₂²×C₄	—	2	4	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	2	4	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
309	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
310	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
311	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
312	C₂²×C₄	C₁₃×#41	1	4	yes	—
313	C₂²×C₄	C₁₃×#41	1	2	yes	—
314	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
315	Q₁₆	—	4	4	no	—
316	M₁₆	—	2	16	no	—
317	M₁₆	—	2	16	no	—
318	C₂×C₈	—	2	8	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	8	no	—
323	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
324	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
325	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
326	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
327	C₄⋊C₄	—	2	4	no	—
328	C₄⋊C₄	—	2	2	no	—
329	C₄⋊C₄	—	2	4	no	—
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	4	4	no	—
332	C₄⋊C₄	—	4	8	no	—
333	C₂²⋊C₄	—	4	8	no	—
334	C₂²⋊C₄	—	4	8	no	—
335	C₂²⋊C₄	—	4	4	no	—
336	C₂²⋊C₄	—	4	4	no	—
337	C₁₃	#32937	1	1	yes	characteristic, direct product factor, Sylow
338	C₂³	—	2	2	no	—
339	C₂³	—	2	2	no	—
340	C₂³	—	2	8	no	—
341	C₂³	—	2	2	no	—
342	C₂³	—	2	2	no	—
343	C₂³	—	2	4	no	—
344	C₂³	—	2	4	no	—
345	C₂³	—	4	16	no	—
346	C₂³	—	4	4	no	—
347	C₂³	—	4	4	no	—
348	C₂³	C₁₃×#121	1	4	yes	—
349	C₂³	C₁₃×#121	1	2	yes	—
350	C₂³	C₁₃×#137	1	4	yes	—
351	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
352	Q₈	—	4	2	no	—
353	Q₈	—	4	2	no	—
354	Q₈	—	4	4	no	—
355	C₂×C₄	—	2	8	no	—
356	C₂×C₄	—	2	16	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	2	4	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	4	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	4	no	—
371	C₂×C₄	—	4	4	no	—
372	C₂×C₄	—	4	4	no	—
373	C₂×C₄	—	4	4	no	—
374	C₂×C₄	C₁₃×#121	1	2	yes	—
375	C₂×C₄	C₁₃×#121	1	4	yes	—
376	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
377	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
378	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
379	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
380	C₈	—	2	4	no	—
381	C₈	—	2	2	no	—
382	C₈	C₁₃×#120	1	4	yes	—
383	C₂²	—	2	2	no	—
384	C₂²	—	2	8	no	—
385	C₂²	—	2	2	no	—
386	C₂²	—	2	8	no	—
387	C₂²	—	2	4	no	—
388	C₂²	—	4	16	no	—
389	C₂²	—	4	2	no	—
390	C₂²	—	4	2	no	—
391	C₂²	—	4	4	no	—
392	C₂²	C₁₃×#470	1	4	yes	complemented
393	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
394	C₂²	C₂×C₁₃×#121	1	2	yes	—
395	C₂²	C₂×C₁₃×#137	1	2	yes	—
396	C₂²	C₁₃×#575	1	2	yes	—
397	C₄	—	2	2	no	—
398	C₄	—	2	4	no	—
399	C₄	—	8	2	no	—
400	C₄	—	8	4	no	—
401	C₄	—	8	2	no	—
402	C₄	C₂×C₁₃×#120	1	1	yes	characteristic
403	C₄	C₁₃×#525	1	1	yes	characteristic
404	C₄	C₁₃×#525	1	2	yes	—
405	C₂	—	2	4	no	—
406	C₂	—	4	4	no	—
407	C₂	C₁₃×#2847	1	1	yes	characteristic
408	C₂	C₂×C₁₃×#470	1	1	yes	characteristic
409	C₂	C₁₃×#3054	1	1	yes	characteristic
410	C₂	C₁₃×#3056	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂⁵×C₁₃	D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂⁴×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#470	C₂	semidirect
3. C₂×C₁₃×#467	C₂	semidirect
5. C₁₃×#1894	C₂	semidirect
6. C₁₃×#1892	C₂	semidirect
7. C₁₃×#1809	C₂	semidirect
8. C₁₃×#1807	C₂	semidirect
10. C₂²×C₁₃×Q₁₆	C₂²	semidirect
21. C₂×C₁₃×#107	C₂²	semidirect
22. C₂×C₁₃×#106	C₂²	semidirect
23. C₂×C₁₃×#103	C₂²	semidirect
24. C₂×C₁₃×#103	C₂²	semidirect
30. C₁₃×#340	C₂²	semidirect
31. C₁₃×#340	C₂²	semidirect
76. #32937	C₁₃	direct (N × H)
134. C₂×#470	C₂×C₁₃	semidirect
135. C₂×#467	C₂×C₁₃	semidirect
137. #1894	C₂×C₁₃	semidirect
138. #1892	C₂×C₁₃	semidirect
139. #1809	C₂×C₁₃	semidirect
140. #1807	C₂×C₁₃	semidirect
187. C₂²×Q₁₆	C₂²×C₁₃	semidirect
198. C₂×#107	C₂²×C₁₃	semidirect
199. C₂×#106	C₂²×C₁₃	semidirect
200. C₂×#103	C₂²×C₁₃	semidirect
201. C₂×#103	C₂²×C₁₃	semidirect
207. #340	C₂²×C₁₃	semidirect
208. #340	C₂²×C₁₃	semidirect
218. C₂²×C₁₃	#470	semidirect
337. C₁₃	#32937	direct (N × H)
392. C₂²	C₁₃×#470	semidirect

Maximal subgroups

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

subgroup	index
C₂³×C₁₃×M₁₆	2
C₂×C₁₃×#470	2
C₂×C₁₃×#467	2
C₁₃×#2848	2
C₁₃×#1894	2
C₁₃×#1892	2
C₁₃×#1809	2
C₁₃×#1807	2
#32937	13

Subgroups — C13×#32937 #15719276

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#32937 #15719276