Subgroups — C₁₃×#25934 #15712273

Order 3328.

1078 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#554	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#487	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#461	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2568	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2026	C₂	1	4	yes	maximal, complemented
6	C₁₃×#1987	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1984	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1877	C₂	1	4	yes	maximal
9	C₄×C₁₃×#102	C₂	1	1	yes	maximal, characteristic
10	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
11	C₁₃×#554	—	2	4	no	—
12	C₁₃×#554	—	2	4	no	—
13	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#125	C₂²	1	2	yes	—
16	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
17	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
18	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
20	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
21	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
22	C₁₃×#487	—	2	4	no	—
23	C₁₃×#461	—	2	4	no	—
24	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#103	C₂²	1	2	yes	—
26	C₂×C₁₃×#103	C₂²	1	4	yes	—
27	C₂×C₁₃×#102	C₂²	1	2	yes	—
28	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
29	C₁₃×#400	—	2	2	no	—
30	C₁₃×#391	—	2	1	no	—
31	C₁₃×#391	C₂²	1	4	yes	—
32	C₁₃×#382	—	2	1	no	—
33	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₁₃×#340	C₂²	1	4	yes	—
35	C₁₃×#340	C₂²	1	2	yes	—
36	C₁₃×#336	C₂²	1	4	yes	—
37	C₂²×Q₈×C₁₃	—	2	1	no	—
38	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
39	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
40	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
41	C₂³×C₄×C₁₃	—	2	1	no	—
42	C₂³×C₄×C₁₃	—	2	2	no	—
43	C₂×C₁₃×SD₁₆	—	2	4	no	—
44	C₂×C₁₃×SD₁₆	—	2	8	no	—
45	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
46	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
47	C₁₃×C₄⋊Q₈	—	2	2	no	—
48	C₁₃×C₄⋊Q₈	—	2	2	no	—
49	C₁₃×C₄⋊Q₈	—	2	2	no	—
50	C₁₃×C₄⋊Q₈	D₄	1	4	yes	—
51	C₁₃×#125	—	2	4	no	—
52	C₁₃×#125	—	2	4	no	—
53	C₁₃×C₂²⋊Q₈	—	2	8	no	—
54	C₁₃×C₂²⋊Q₈	—	2	16	no	—
55	C₄×Q₈×C₁₃	—	2	2	no	—
56	C₄×Q₈×C₁₃	—	2	2	no	—
57	C₄×D₄×C₁₃	—	2	4	no	—
58	C₄×D₄×C₁₃	—	2	4	no	—
59	C₄×D₄×C₁₃	—	2	2	no	—
60	C₄×D₄×C₁₃	D₄	1	4	yes	—
61	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
62	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
63	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
64	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
65	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
66	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
67	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
68	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
69	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
70	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
71	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
72	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
73	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
74	C₂×C₄²×C₁₃	—	2	1	no	—
75	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
76	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
77	C₁₃×C₄⋊C₈	—	2	2	no	—
78	C₁₃×#103	—	2	4	no	—
79	C₁₃×#103	—	2	8	no	—
80	C₁₃×#102	—	2	4	no	—
81	C₄×C₈×C₁₃	—	2	2	no	—
82	C₁₃×#95	—	2	1	no	—
83	C₁₃×#95	—	2	4	no	—
84	C₁₃×#95	—	2	4	no	—
85	#25934	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
86	C₂⁴×C₁₃	—	2	1	no	—
87	C₂×Q₈×C₁₃	—	2	2	no	—
88	C₂×Q₈×C₁₃	—	2	4	no	—
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	4	no	—
94	C₂×Q₈×C₁₃	—	2	4	no	—
95	C₂×Q₈×C₁₃	—	8	2	no	—
96	C₂×D₄×C₁₃	—	2	1	no	—
97	C₂×D₄×C₁₃	—	2	2	no	—
98	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
99	C₂×D₄×C₁₃	#41	1	4	yes	—
100	C₂²×C₄×C₁₃	—	2	1	no	—
101	C₂²×C₄×C₁₃	—	2	2	no	—
102	C₂²×C₄×C₁₃	—	2	8	no	—
103	C₂²×C₄×C₁₃	—	2	4	no	—
104	C₂²×C₄×C₁₃	—	2	2	no	—
105	C₂²×C₄×C₁₃	—	2	2	no	—
106	C₂²×C₄×C₁₃	—	4	2	no	—
107	C₂²×C₄×C₁₃	—	4	2	no	—
108	C₂²×C₄×C₁₃	—	8	4	no	—
109	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
114	C₁₃×SD₁₆	—	4	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	4	no	—
119	C₂×C₈×C₁₃	—	2	2	no	—
120	C₁₃×C₄⋊C₄	—	2	8	no	—
121	C₁₃×C₄⋊C₄	—	2	8	no	—
122	C₁₃×C₄⋊C₄	—	2	2	no	—
123	C₁₃×C₄⋊C₄	—	2	4	no	—
124	C₁₃×C₄⋊C₄	—	2	4	no	—
125	C₁₃×C₄⋊C₄	—	2	1	no	—
126	C₁₃×C₄⋊C₄	—	2	2	no	—
127	C₁₃×C₄⋊C₄	—	2	2	no	—
128	C₁₃×C₄⋊C₄	—	2	2	no	—
129	C₁₃×C₄⋊C₄	—	4	2	no	—
130	C₁₃×C₄⋊C₄	—	4	2	no	—
131	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
132	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
133	C₁₃×C₂²⋊C₄	—	2	8	no	—
134	C₁₃×C₂²⋊C₄	—	2	4	no	—
135	C₄²×C₁₃	—	2	2	no	—
136	C₄²×C₁₃	—	2	2	no	—
137	C₄²×C₁₃	—	4	2	no	—
138	C₄²×C₁₃	C₂×D₄	1	2	yes	—
139	C₄²×C₁₃	C₂×D₄	1	2	yes	—
140	C₂×#554	C₂×C₁₃	1	1	yes	characteristic
141	C₂×#487	C₂×C₁₃	1	1	yes	characteristic, complemented
142	C₂×#461	C₂×C₁₃	1	1	yes	characteristic
143	#2568	C₂×C₁₃	1	1	yes	characteristic, complemented
144	#2026	C₂×C₁₃	1	4	yes	complemented
145	#1987	C₂×C₁₃	1	1	yes	characteristic, complemented
146	#1984	C₂×C₁₃	1	1	yes	characteristic, complemented
147	#1877	C₂×C₁₃	1	4	yes	—
148	C₄×#102	C₂×C₁₃	1	1	yes	characteristic
149	C₂³×C₁₃	—	2	2	no	—
150	C₂³×C₁₃	—	2	4	no	—
151	C₂³×C₁₃	—	4	1	no	—
152	C₂³×C₁₃	—	4	1	no	—
153	C₂³×C₁₃	—	4	2	no	—
154	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
155	Q₈×C₁₃	—	4	4	no	—
156	Q₈×C₁₃	—	4	2	no	—
157	Q₈×C₁₃	—	4	2	no	—
158	Q₈×C₁₃	—	4	4	no	—
159	Q₈×C₁₃	—	8	4	no	—
160	D₄×C₁₃	—	2	2	no	—
161	D₄×C₁₃	—	2	4	no	—
162	D₄×C₁₃	#124	1	4	yes	—
163	C₂×C₄×C₁₃	—	2	2	no	—
164	C₂×C₄×C₁₃	—	2	2	no	—
165	C₂×C₄×C₁₃	—	2	2	no	—
166	C₂×C₄×C₁₃	—	2	2	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	4	no	—
171	C₂×C₄×C₁₃	—	4	1	no	—
172	C₂×C₄×C₁₃	—	4	1	no	—
173	C₂×C₄×C₁₃	—	4	4	no	—
174	C₂×C₄×C₁₃	—	4	8	no	—
175	C₂×C₄×C₁₃	—	4	2	no	—
176	C₂×C₄×C₁₃	—	4	2	no	—
177	C₂×C₄×C₁₃	—	4	4	no	—
178	C₂×C₄×C₁₃	—	4	2	no	—
179	C₂×C₄×C₁₃	—	4	2	no	—
180	C₂×C₄×C₁₃	—	8	8	no	—
181	C₂×C₄×C₁₃	#120	1	2	yes	—
182	C₂×C₄×C₁₃	#120	1	2	yes	—
183	C₂×C₄×C₁₃	#135	1	2	yes	—
184	C₂×C₄×C₁₃	#137	1	2	yes	—
185	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
187	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
188	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
189	C₈×C₁₃	—	4	2	no	—
190	C₈×C₁₃	—	4	2	no	—
191	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
192	#554	—	2	4	no	—
193	#554	—	2	4	no	—
194	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
195	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
196	C₂×#125	C₂²×C₁₃	1	2	yes	—
197	C₂×C₂²⋊Q₈	—	2	1	no	—
198	C₂×C₂²⋊Q₈	—	2	2	no	—
199	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
200	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
201	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
202	C₂²×C₄⋊C₄	—	2	1	no	—
203	#487	—	2	4	no	—
204	#461	—	2	4	no	—
205	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
206	C₂×#103	C₂²×C₁₃	1	4	yes	—
207	C₂×#103	C₂²×C₁₃	1	2	yes	—
208	C₂×#102	C₂²×C₁₃	1	2	yes	—
209	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
210	#400	—	2	2	no	—
211	#391	—	2	1	no	—
212	#391	C₂²×C₁₃	1	4	yes	—
213	#382	—	2	1	no	—
214	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
215	#340	C₂²×C₁₃	1	4	yes	—
216	#340	C₂²×C₁₃	1	2	yes	—
217	#336	C₂²×C₁₃	1	4	yes	—
218	C₂²×C₁₃	—	2	4	no	—
219	C₂²×C₁₃	—	4	4	no	—
220	C₂²×C₁₃	—	4	4	no	—
221	C₂²×C₁₃	—	4	2	no	—
222	C₂²×C₁₃	—	4	2	no	—
223	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
224	C₂²×C₁₃	#548	1	2	yes	—
225	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
226	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
227	C₂²×C₁₃	#577	1	2	yes	—
228	C₄×C₁₃	—	2	2	no	—
229	C₄×C₁₃	—	4	2	no	—
230	C₄×C₁₃	—	4	2	no	—
231	C₄×C₁₃	—	4	2	no	—
232	C₄×C₁₃	—	4	4	no	—
233	C₄×C₁₃	—	8	2	no	—
234	C₄×C₁₃	—	8	2	no	—
235	C₄×C₁₃	#452	1	4	yes	—
236	C₄×C₁₃	C₂×#124	1	1	yes	characteristic
237	C₄×C₁₃	#536	1	1	yes	characteristic
238	C₄×C₁₃	#548	1	2	yes	—
239	C₂²×Q₈	—	2	1	no	—
240	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
241	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
242	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
243	C₂³×C₄	—	2	1	no	—
244	C₂³×C₄	—	2	2	no	—
245	C₂×SD₁₆	—	2	4	no	—
246	C₂×SD₁₆	—	2	8	no	—
247	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
248	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
249	C₄⋊Q₈	—	2	2	no	—
250	C₄⋊Q₈	—	2	2	no	—
251	C₄⋊Q₈	—	2	2	no	—
252	C₄⋊Q₈	D₄×C₁₃	1	4	yes	—
253	#125	—	2	4	no	—
254	#125	—	2	4	no	—
255	C₂²⋊Q₈	—	2	8	no	—
256	C₂²⋊Q₈	—	2	16	no	—
257	C₄×Q₈	—	2	2	no	—
258	C₄×Q₈	—	2	2	no	—
259	C₄×D₄	—	2	4	no	—
260	C₄×D₄	—	2	4	no	—
261	C₄×D₄	—	2	2	no	—
262	C₄×D₄	D₄×C₁₃	1	4	yes	—
263	C₂×C₄⋊C₄	—	2	8	no	—
264	C₂×C₄⋊C₄	—	2	2	no	—
265	C₂×C₄⋊C₄	—	2	1	no	—
266	C₂×C₄⋊C₄	—	2	2	no	—
267	C₂×C₄⋊C₄	—	2	1	no	—
268	C₂×C₄⋊C₄	—	2	1	no	—
269	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
270	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
271	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
272	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
273	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
274	C₂×C₂²⋊C₄	—	2	2	no	—
275	C₂×C₂²⋊C₄	—	2	1	no	—
276	C₂×C₄²	—	2	1	no	—
277	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
278	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
279	C₄⋊C₈	—	2	2	no	—
280	#103	—	2	4	no	—
281	#103	—	2	8	no	—
282	#102	—	2	4	no	—
283	C₄×C₈	—	2	2	no	—
284	#95	—	2	1	no	—
285	#95	—	2	4	no	—
286	#95	—	2	4	no	—
287	C₂×C₁₃	—	4	4	no	—
288	C₂×C₁₃	#2436	1	1	yes	characteristic
289	C₂×C₁₃	C₂×#452	1	1	yes	characteristic
290	C₂×C₁₃	#3009	1	1	yes	characteristic
291	C₂×C₁₃	#3360	1	2	yes	—
292	C₂×C₁₃	#3372	1	2	yes	—
293	C₂⁴	—	2	1	no	—
294	C₂×Q₈	—	2	2	no	—
295	C₂×Q₈	—	2	4	no	—
296	C₂×Q₈	—	2	2	no	—
297	C₂×Q₈	—	2	2	no	—
298	C₂×Q₈	—	2	2	no	—
299	C₂×Q₈	—	2	2	no	—
300	C₂×Q₈	—	2	4	no	—
301	C₂×Q₈	—	2	4	no	—
302	C₂×Q₈	—	8	2	no	—
303	C₂×D₄	—	2	1	no	—
304	C₂×D₄	—	2	2	no	—
305	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
306	C₂×D₄	C₁₃×#41	1	4	yes	—
307	C₂²×C₄	—	2	1	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	8	no	—
310	C₂²×C₄	—	2	4	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	4	2	no	—
314	C₂²×C₄	—	4	2	no	—
315	C₂²×C₄	—	8	4	no	—
316	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
317	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
318	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
319	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
320	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
321	SD₁₆	—	4	8	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	2	4	no	—
326	C₂×C₈	—	2	2	no	—
327	C₄⋊C₄	—	2	8	no	—
328	C₄⋊C₄	—	2	8	no	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	2	4	no	—
331	C₄⋊C₄	—	2	4	no	—
332	C₄⋊C₄	—	2	1	no	—
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	4	2	no	—
337	C₄⋊C₄	—	4	2	no	—
338	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
339	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
340	C₂²⋊C₄	—	2	8	no	—
341	C₂²⋊C₄	—	2	4	no	—
342	C₄²	—	2	2	no	—
343	C₄²	—	2	2	no	—
344	C₄²	—	4	2	no	—
345	C₄²	C₂×D₄×C₁₃	1	2	yes	—
346	C₄²	C₂×D₄×C₁₃	1	2	yes	—
347	C₁₃	#25934	1	1	yes	characteristic, direct product factor, Sylow
348	C₂³	—	2	2	no	—
349	C₂³	—	2	4	no	—
350	C₂³	—	4	1	no	—
351	C₂³	—	4	1	no	—
352	C₂³	—	4	2	no	—
353	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
354	Q₈	—	4	4	no	—
355	Q₈	—	4	2	no	—
356	Q₈	—	4	2	no	—
357	Q₈	—	4	4	no	—
358	Q₈	—	8	4	no	—
359	D₄	—	2	2	no	—
360	D₄	—	2	4	no	—
361	D₄	C₁₃×#124	1	4	yes	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	4	no	—
370	C₂×C₄	—	4	1	no	—
371	C₂×C₄	—	4	1	no	—
372	C₂×C₄	—	4	4	no	—
373	C₂×C₄	—	4	8	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	4	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	8	8	no	—
380	C₂×C₄	C₁₃×#120	1	2	yes	—
381	C₂×C₄	C₁₃×#120	1	2	yes	—
382	C₂×C₄	C₁₃×#135	1	2	yes	—
383	C₂×C₄	C₁₃×#137	1	2	yes	—
384	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
385	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
386	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
387	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
388	C₈	—	4	2	no	—
389	C₈	—	4	2	no	—
390	C₂²	—	2	4	no	—
391	C₂²	—	4	2	no	—
392	C₂²	—	4	4	no	—
393	C₂²	—	4	4	no	—
394	C₂²	—	4	2	no	—
395	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
396	C₂²	C₁₃×#548	1	2	yes	—
397	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
398	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
399	C₂²	C₁₃×#577	1	2	yes	—
400	C₄	—	2	2	no	—
401	C₄	—	4	2	no	—
402	C₄	—	4	4	no	—
403	C₄	—	4	2	no	—
404	C₄	—	4	2	no	—
405	C₄	—	8	2	no	—
406	C₄	—	8	2	no	—
407	C₄	C₁₃×#452	1	4	yes	—
408	C₄	C₂×C₁₃×#124	1	1	yes	characteristic
409	C₄	C₁₃×#536	1	1	yes	characteristic
410	C₄	C₁₃×#548	1	2	yes	—
411	C₂	—	4	4	no	—
412	C₂	C₁₃×#2436	1	1	yes	characteristic
413	C₂	C₂×C₁₃×#452	1	1	yes	characteristic
414	C₂	C₁₃×#3009	1	1	yes	characteristic
415	C₂	C₁₃×#3360	1	2	yes	—
416	C₂	C₁₃×#3372	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×D₄×C₁₃	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄×Q₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#487	C₂	semidirect
4. C₁₃×#2568	C₂	semidirect
5. C₁₃×#2026	C₂	semidirect
6. C₁₃×#1987	C₂	semidirect
7. C₁₃×#1984	C₂	semidirect
85. #25934	C₁₃	direct (N × H)
141. C₂×#487	C₂×C₁₃	semidirect
143. #2568	C₂×C₁₃	semidirect
144. #2026	C₂×C₁₃	semidirect
145. #1987	C₂×C₁₃	semidirect
146. #1984	C₂×C₁₃	semidirect
347. C₁₃	#25934	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×C₁₃×#554	2
C₂×C₁₃×#487	2
C₂×C₁₃×#461	2
C₁₃×#2568	2
C₁₃×#2026	2
C₁₃×#1987	2
C₁₃×#1984	2
C₁₃×#1877	2
C₄×C₁₃×#102	2
#25934	13

Subgroups — C13×#25934 #15712273

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25934 #15712273