Subgroups — C₁₃×#23734 #15710073

Order 3328.

1218 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#428	C₂	1	2	yes	maximal, complemented
2	C₂×C₁₃×#417	C₂	1	2	yes	maximal
3	C₁₃×#2297	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₃×#384	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2096	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2095	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2094	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2093	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1728	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
11	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	—
12	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
13	C₂²×C₁₃×C₄⋊C₄	—	2	2	no	—
14	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
15	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
16	C₁₃×#428	—	2	8	no	—
17	C₂×C₁₃×#107	C₂²	1	4	yes	—
18	C₂×C₁₃×#106	C₂²	1	4	yes	—
19	C₁₃×#417	—	2	8	no	—
20	C₂×C₁₃×#103	C₂²	1	4	yes	—
21	C₂×C₁₃×#102	C₂²	1	4	yes	—
22	C₁₃×#391	C₂²	1	1	yes	characteristic
23	C₁₃×#391	C₂²	1	1	yes	characteristic
24	C₁₃×#390	C₂²	1	1	yes	characteristic
25	C₁₃×#390	C₂²	1	1	yes	characteristic
26	C₁₃×#386	—	2	2	no	—
27	C₁₃×#384	—	2	2	no	—
28	C₁₃×#384	C₂²	1	2	yes	—
29	C₁₃×#384	C₂²	1	2	yes	—
30	C₄×C₁₃×C₂²⋊C₄	—	2	2	no	—
31	C₁₃×#336	C₂²	1	2	yes	—
32	C₁₃×#336	C₂²	1	2	yes	—
33	C₂×C₁₃×#41	—	2	2	no	—
34	C₂×C₁₃×#41	—	2	4	no	—
35	C₂×C₁₃×#41	—	2	4	no	—
36	C₂×C₁₃×#41	Q₈	1	4	yes	—
37	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
38	C₂²×D₄×C₁₃	—	2	1	no	—
39	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
40	C₂³×C₄×C₁₃	—	2	1	no	—
41	C₂³×C₄×C₁₃	—	2	2	no	—
42	C₂³×C₄×C₁₃	D₄	1	2	yes	—
43	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
44	C₂×C₁₃×M₁₆	—	2	4	no	—
45	C₂×C₁₃×M₁₆	—	2	4	no	—
46	C₂×C₁₃×M₁₆	D₄	1	8	yes	—
47	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
48	C₁₃×#117	—	2	4	no	—
49	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
50	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
51	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
52	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
53	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
54	C₂×C₁₃×C₄⋊C₄	—	4	8	no	—
55	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
56	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
57	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
58	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
59	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
60	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
61	C₂×C₄²×C₁₃	—	2	4	no	—
62	C₂×C₄²×C₁₃	—	2	1	no	—
63	C₂×C₄²×C₁₃	D₄	1	2	yes	—
64	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
65	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
66	C₁₃×#107	—	2	8	no	—
67	C₁₃×#106	—	2	8	no	—
68	C₁₃×#103	—	2	8	no	—
69	C₁₃×#102	—	2	8	no	—
70	C₁₃×#95	—	2	2	no	—
71	C₁₃×#95	—	2	2	no	—
72	#23734	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
73	C₂⁴×C₁₃	—	2	1	no	—
74	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
75	C₁₃×#41	—	2	16	no	—
76	C₁₃×#41	—	4	8	no	—
77	C₂×Q₈×C₁₃	—	2	1	no	—
78	C₂×Q₈×C₁₃	—	2	2	no	—
79	C₂×Q₈×C₁₃	—	2	2	no	—
80	C₂×Q₈×C₁₃	C₂×Q₈	1	2	yes	—
81	C₂×D₄×C₁₃	—	2	4	no	—
82	C₂×D₄×C₁₃	—	2	2	no	—
83	C₂×D₄×C₁₃	—	2	2	no	—
84	C₂×D₄×C₁₃	—	2	1	no	—
85	C₂×D₄×C₁₃	—	4	2	no	—
86	C₂×D₄×C₁₃	—	4	2	no	—
87	C₂×D₄×C₁₃	C₂×Q₈	1	2	yes	—
88	C₂²×C₄×C₁₃	—	2	4	no	—
89	C₂²×C₄×C₁₃	—	2	4	no	—
90	C₂²×C₄×C₁₃	—	2	4	no	—
91	C₂²×C₄×C₁₃	—	2	1	no	—
92	C₂²×C₄×C₁₃	—	2	4	no	—
93	C₂²×C₄×C₁₃	—	2	1	no	—
94	C₂²×C₄×C₁₃	—	2	1	no	—
95	C₂²×C₄×C₁₃	—	2	4	no	—
96	C₂²×C₄×C₁₃	—	4	2	no	—
97	C₂²×C₄×C₁₃	—	4	2	no	—
98	C₂²×C₄×C₁₃	—	4	8	no	—
99	C₂²×C₄×C₁₃	—	4	4	no	—
100	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
101	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
104	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
105	C₂²×C₄×C₁₃	#41	1	4	yes	—
106	C₂²×C₄×C₁₃	#41	1	2	yes	—
107	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
108	C₁₃×M₁₆	—	2	16	no	—
109	C₂×C₈×C₁₃	—	2	4	no	—
110	C₂×C₈×C₁₃	—	2	4	no	—
111	C₂×C₈×C₁₃	C₂×D₄	1	8	yes	—
112	C₁₃×C₄⋊C₄	—	2	4	no	—
113	C₁₃×C₄⋊C₄	—	2	2	no	—
114	C₁₃×C₄⋊C₄	—	2	4	no	—
115	C₁₃×C₄⋊C₄	—	2	2	no	—
116	C₁₃×C₄⋊C₄	—	4	8	no	—
117	C₁₃×C₄⋊C₄	—	4	4	no	—
118	C₁₃×C₄⋊C₄	—	4	8	no	—
119	C₁₃×C₂²⋊C₄	—	4	2	no	—
120	C₁₃×C₂²⋊C₄	—	4	4	no	—
121	C₁₃×C₂²⋊C₄	—	4	4	no	—
122	C₄²×C₁₃	—	2	4	no	—
123	C₄²×C₁₃	—	2	2	no	—
124	C₄²×C₁₃	—	2	2	no	—
125	C₄²×C₁₃	—	4	2	no	—
126	C₂×#428	C₂×C₁₃	1	2	yes	complemented
127	C₂×#417	C₂×C₁₃	1	2	yes	—
128	#2297	C₂×C₁₃	1	1	yes	characteristic
129	C₂×#384	C₂×C₁₃	1	1	yes	characteristic, complemented
130	#2096	C₂×C₁₃	1	2	yes	complemented
131	#2095	C₂×C₁₃	1	2	yes	complemented
132	#2094	C₂×C₁₃	1	2	yes	complemented
133	#2093	C₂×C₁₃	1	2	yes	complemented
134	#1728	C₂×C₁₃	1	1	yes	characteristic, complemented
135	C₂³×C₁₃	—	2	2	no	—
136	C₂³×C₁₃	—	2	2	no	—
137	C₂³×C₁₃	—	2	2	no	—
138	C₂³×C₁₃	—	4	1	no	—
139	C₂³×C₁₃	—	4	1	no	—
140	C₂³×C₁₃	—	4	2	no	—
141	C₂³×C₁₃	—	4	2	no	—
142	C₂³×C₁₃	C₂²⋊Q₈	1	2	yes	—
143	C₂³×C₁₃	#123	1	2	yes	—
144	C₂³×C₁₃	#127	1	2	yes	—
145	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
146	Q₈×C₁₃	—	2	4	no	—
147	Q₈×C₁₃	—	4	2	no	—
148	D₄×C₁₃	—	2	4	no	—
149	D₄×C₁₃	—	4	8	no	—
150	D₄×C₁₃	—	4	2	no	—
151	C₂×C₄×C₁₃	—	2	16	no	—
152	C₂×C₄×C₁₃	—	2	2	no	—
153	C₂×C₄×C₁₃	—	2	2	no	—
154	C₂×C₄×C₁₃	—	2	2	no	—
155	C₂×C₄×C₁₃	—	2	2	no	—
156	C₂×C₄×C₁₃	—	2	2	no	—
157	C₂×C₄×C₁₃	—	4	1	no	—
158	C₂×C₄×C₁₃	—	4	1	no	—
159	C₂×C₄×C₁₃	—	4	8	no	—
160	C₂×C₄×C₁₃	—	4	1	no	—
161	C₂×C₄×C₁₃	—	4	1	no	—
162	C₂×C₄×C₁₃	—	4	4	no	—
163	C₂×C₄×C₁₃	—	4	2	no	—
164	C₂×C₄×C₁₃	—	4	8	no	—
165	C₂×C₄×C₁₃	—	4	2	no	—
166	C₂×C₄×C₁₃	—	8	8	no	—
167	C₂×C₄×C₁₃	C₂²⋊Q₈	1	8	yes	—
168	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
169	C₂×C₄×C₁₃	#123	1	8	yes	—
170	C₂×C₄×C₁₃	#123	1	2	yes	—
171	C₂×C₄×C₁₃	#127	1	2	yes	—
172	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
173	C₂×C₄×C₁₃	#137	1	4	yes	—
174	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
175	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
176	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
177	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
178	C₈×C₁₃	—	2	8	no	—
179	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
180	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	—
181	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
182	C₂²×C₄⋊C₄	—	2	2	no	—
183	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
184	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
185	#428	—	2	8	no	—
186	C₂×#107	C₂²×C₁₃	1	4	yes	—
187	C₂×#106	C₂²×C₁₃	1	4	yes	—
188	#417	—	2	8	no	—
189	C₂×#103	C₂²×C₁₃	1	4	yes	—
190	C₂×#102	C₂²×C₁₃	1	4	yes	—
191	#391	C₂²×C₁₃	1	1	yes	characteristic
192	#391	C₂²×C₁₃	1	1	yes	characteristic
193	#390	C₂²×C₁₃	1	1	yes	characteristic
194	#390	C₂²×C₁₃	1	1	yes	characteristic
195	#386	—	2	2	no	—
196	#384	—	2	2	no	—
197	#384	C₂²×C₁₃	1	2	yes	—
198	#384	C₂²×C₁₃	1	2	yes	—
199	C₄×C₂²⋊C₄	—	2	2	no	—
200	#336	C₂²×C₁₃	1	2	yes	—
201	#336	C₂²×C₁₃	1	2	yes	—
202	C₂²×C₁₃	—	2	4	no	—
203	C₂²×C₁₃	—	2	4	no	—
204	C₂²×C₁₃	—	2	2	no	—
205	C₂²×C₁₃	—	2	2	no	—
206	C₂²×C₁₃	—	4	4	no	—
207	C₂²×C₁₃	—	4	2	no	—
208	C₂²×C₁₃	—	8	2	no	—
209	C₂²×C₁₃	—	8	1	no	—
210	C₂²×C₁₃	—	8	1	no	—
211	C₂²×C₁₃	#399	1	4	yes	—
212	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
213	C₂²×C₁₃	C₂×#123	1	1	yes	characteristic
214	C₂²×C₁₃	C₂×#127	1	1	yes	characteristic
215	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
216	C₂²×C₁₃	C₂×#137	1	2	yes	—
217	C₄×C₁₃	—	2	4	no	—
218	C₄×C₁₃	—	2	4	no	—
219	C₄×C₁₃	—	4	2	no	—
220	C₄×C₁₃	—	8	1	no	—
221	C₄×C₁₃	—	8	4	no	—
222	C₄×C₁₃	—	8	1	no	—
223	C₄×C₁₃	#399	1	4	yes	—
224	C₄×C₁₃	C₂×C₂²⋊Q₈	1	2	yes	—
225	C₄×C₁₃	C₂×#123	1	2	yes	—
226	C₂×#41	—	2	2	no	—
227	C₂×#41	—	2	4	no	—
228	C₂×#41	—	2	4	no	—
229	C₂×#41	Q₈×C₁₃	1	4	yes	—
230	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
231	C₂²×D₄	—	2	1	no	—
232	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
233	C₂³×C₄	—	2	1	no	—
234	C₂³×C₄	—	2	2	no	—
235	C₂³×C₄	D₄×C₁₃	1	2	yes	—
236	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
237	C₂×M₁₆	—	2	4	no	—
238	C₂×M₁₆	—	2	4	no	—
239	C₂×M₁₆	D₄×C₁₃	1	8	yes	—
240	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
241	#117	—	2	4	no	—
242	C₂×C₄⋊C₄	—	2	4	no	—
243	C₂×C₄⋊C₄	—	2	4	no	—
244	C₂×C₄⋊C₄	—	2	4	no	—
245	C₂×C₄⋊C₄	—	2	4	no	—
246	C₂×C₄⋊C₄	—	2	2	no	—
247	C₂×C₄⋊C₄	—	4	8	no	—
248	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
249	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
250	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
251	C₂×C₂²⋊C₄	—	2	1	no	—
252	C₂×C₂²⋊C₄	—	2	2	no	—
253	C₂×C₂²⋊C₄	—	2	2	no	—
254	C₂×C₄²	—	2	4	no	—
255	C₂×C₄²	—	2	1	no	—
256	C₂×C₄²	D₄×C₁₃	1	2	yes	—
257	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
258	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
259	#107	—	2	8	no	—
260	#106	—	2	8	no	—
261	#103	—	2	8	no	—
262	#102	—	2	8	no	—
263	#95	—	2	2	no	—
264	#95	—	2	2	no	—
265	C₂×C₁₃	—	2	4	no	—
266	C₂×C₁₃	—	8	2	no	—
267	C₂×C₁₃	C₂×#399	1	1	yes	characteristic
268	C₂×C₁₃	#3079	1	2	yes	—
269	C₂×C₁₃	#3092	1	2	yes	—
270	C₂×C₁₃	#3151	1	1	yes	characteristic
271	C₂×C₁₃	#3152	1	1	yes	characteristic
272	C₂⁴	—	2	1	no	—
273	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
274	#41	—	2	16	no	—
275	#41	—	4	8	no	—
276	C₂×Q₈	—	2	1	no	—
277	C₂×Q₈	—	2	2	no	—
278	C₂×Q₈	—	2	2	no	—
279	C₂×Q₈	C₂×Q₈×C₁₃	1	2	yes	—
280	C₂×D₄	—	2	4	no	—
281	C₂×D₄	—	2	2	no	—
282	C₂×D₄	—	2	2	no	—
283	C₂×D₄	—	2	1	no	—
284	C₂×D₄	—	4	2	no	—
285	C₂×D₄	—	4	2	no	—
286	C₂×D₄	C₂×Q₈×C₁₃	1	2	yes	—
287	C₂²×C₄	—	2	4	no	—
288	C₂²×C₄	—	2	4	no	—
289	C₂²×C₄	—	2	4	no	—
290	C₂²×C₄	—	2	1	no	—
291	C₂²×C₄	—	2	4	no	—
292	C₂²×C₄	—	2	1	no	—
293	C₂²×C₄	—	2	1	no	—
294	C₂²×C₄	—	2	4	no	—
295	C₂²×C₄	—	4	2	no	—
296	C₂²×C₄	—	4	2	no	—
297	C₂²×C₄	—	4	8	no	—
298	C₂²×C₄	—	4	4	no	—
299	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
300	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
301	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
302	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
303	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
304	C₂²×C₄	C₁₃×#41	1	4	yes	—
305	C₂²×C₄	C₁₃×#41	1	2	yes	—
306	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
307	M₁₆	—	2	16	no	—
308	C₂×C₈	—	2	4	no	—
309	C₂×C₈	—	2	4	no	—
310	C₂×C₈	C₂×D₄×C₁₃	1	8	yes	—
311	C₄⋊C₄	—	2	4	no	—
312	C₄⋊C₄	—	2	2	no	—
313	C₄⋊C₄	—	2	4	no	—
314	C₄⋊C₄	—	2	2	no	—
315	C₄⋊C₄	—	4	8	no	—
316	C₄⋊C₄	—	4	4	no	—
317	C₄⋊C₄	—	4	8	no	—
318	C₂²⋊C₄	—	4	2	no	—
319	C₂²⋊C₄	—	4	4	no	—
320	C₂²⋊C₄	—	4	4	no	—
321	C₄²	—	2	4	no	—
322	C₄²	—	2	2	no	—
323	C₄²	—	2	2	no	—
324	C₄²	—	4	2	no	—
325	C₁₃	#23734	1	1	yes	characteristic, direct product factor, Sylow
326	C₂³	—	2	2	no	—
327	C₂³	—	2	2	no	—
328	C₂³	—	2	2	no	—
329	C₂³	—	4	1	no	—
330	C₂³	—	4	1	no	—
331	C₂³	—	4	2	no	—
332	C₂³	—	4	2	no	—
333	C₂³	C₁₃×C₂²⋊Q₈	1	2	yes	—
334	C₂³	C₁₃×#123	1	2	yes	—
335	C₂³	C₁₃×#127	1	2	yes	—
336	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
337	Q₈	—	2	4	no	—
338	Q₈	—	4	2	no	—
339	D₄	—	2	4	no	—
340	D₄	—	4	8	no	—
341	D₄	—	4	2	no	—
342	C₂×C₄	—	2	16	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	4	1	no	—
349	C₂×C₄	—	4	1	no	—
350	C₂×C₄	—	4	8	no	—
351	C₂×C₄	—	4	1	no	—
352	C₂×C₄	—	4	1	no	—
353	C₂×C₄	—	4	4	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	8	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	8	8	no	—
358	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
359	C₂×C₄	C₁₃×C₂²⋊Q₈	1	8	yes	—
360	C₂×C₄	C₁₃×#123	1	2	yes	—
361	C₂×C₄	C₁₃×#123	1	8	yes	—
362	C₂×C₄	C₁₃×#127	1	2	yes	—
363	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	4	yes	—
364	C₂×C₄	C₁₃×#137	1	4	yes	—
365	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
366	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
367	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
368	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
369	C₈	—	2	8	no	—
370	C₂²	—	2	4	no	—
371	C₂²	—	2	4	no	—
372	C₂²	—	2	2	no	—
373	C₂²	—	2	2	no	—
374	C₂²	—	4	4	no	—
375	C₂²	—	4	2	no	—
376	C₂²	—	8	2	no	—
377	C₂²	—	8	1	no	—
378	C₂²	—	8	1	no	—
379	C₂²	C₁₃×#399	1	4	yes	—
380	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
381	C₂²	C₂×C₁₃×#123	1	1	yes	characteristic
382	C₂²	C₂×C₁₃×#127	1	1	yes	characteristic
383	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
384	C₂²	C₂×C₁₃×#137	1	2	yes	—
385	C₄	—	2	4	no	—
386	C₄	—	2	4	no	—
387	C₄	—	4	2	no	—
388	C₄	—	8	1	no	—
389	C₄	—	8	4	no	—
390	C₄	—	8	1	no	—
391	C₄	C₁₃×#399	1	4	yes	—
392	C₄	C₂×C₁₃×C₂²⋊Q₈	1	2	yes	—
393	C₄	C₂×C₁₃×#123	1	2	yes	—
394	C₂	—	2	4	no	—
395	C₂	—	8	2	no	—
396	C₂	C₂×C₁₃×#399	1	1	yes	characteristic
397	C₂	C₁₃×#3079	1	2	yes	—
398	C₂	C₁₃×#3092	1	2	yes	—
399	C₂	C₁₃×#3151	1	1	yes	characteristic
400	C₂	C₁₃×#3152	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×C₁₃×#41	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#428	C₂	semidirect
4. C₂×C₁₃×#384	C₂	semidirect
5. C₁₃×#2096	C₂	semidirect
6. C₁₃×#2095	C₂	semidirect
7. C₁₃×#2094	C₂	semidirect
8. C₁₃×#2093	C₂	semidirect
9. C₁₃×#1728	C₂	semidirect
72. #23734	C₁₃	direct (N × H)
126. C₂×#428	C₂×C₁₃	semidirect
129. C₂×#384	C₂×C₁₃	semidirect
130. #2096	C₂×C₁₃	semidirect
131. #2095	C₂×C₁₃	semidirect
132. #2094	C₂×C₁₃	semidirect
133. #2093	C₂×C₁₃	semidirect
134. #1728	C₂×C₁₃	semidirect
325. C₁₃	#23734	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×#428	2
C₂×C₁₃×#417	2
C₁₃×#2297	2
C₂×C₁₃×#384	2
C₁₃×#2096	2
C₁₃×#2095	2
C₁₃×#2094	2
C₁₃×#2093	2
C₁₃×#1728	2
#23734	13

Subgroups — C13×#23734 #15710073

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#23734 #15710073