Subgroups — C₁₃×#33846 #15720185

Order 3328.

718 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#508	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₃×D₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3280	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2249	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2216	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2215	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2210	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2187	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2186	C₂	1	2	yes	maximal, complemented
10	C₄×C₁₃×D₁₆	C₂	1	1	yes	maximal, characteristic, complemented
11	D₄×C₁₃×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#135	C₂²	1	2	yes	complemented
13	C₂²×C₁₃×D₈	C₂²	1	2	yes	—
14	C₁₃×#546	—	2	2	no	—
15	C₁₃×#508	—	2	4	no	—
16	C₂×C₁₃×Q₃₂	C₂²	1	1	yes	characteristic, complemented
17	C₂×C₁₃×SD₃₂	C₂²	1	2	yes	complemented
18	C₂×C₁₃×SD₃₂	C₂²	1	2	yes	complemented
19	C₂×C₁₃×D₁₆	—	2	4	no	—
20	C₂×C₁₃×D₁₆	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×D₁₆	C₂²	1	2	yes	—
22	C₂×C₁₃×D₁₆	C₂²	1	1	yes	characteristic
23	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
24	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic, complemented
25	C₁₃×#495	C₂²	1	2	yes	complemented
26	C₁₃×#467	C₂²	1	2	yes	—
27	C₁₃×#466	C₂²	1	2	yes	complemented
28	C₁₃×#463	—	2	2	no	—
29	C₁₃×#450	—	2	2	no	—
30	C₁₃×#449	—	2	2	no	—
31	C₄×C₁₃×D₈	C₂²	1	2	yes	complemented
32	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
33	C₁₃×#366	C₂²	1	1	yes	characteristic, complemented
34	C₁₃×C₄⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
35	C₁₃×#358	C₂²	1	2	yes	complemented
36	C₁₃×#357	C₂²	1	2	yes	complemented
37	C₁₃×#357	C₂²	1	2	yes	complemented
38	C₁₃×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
39	C₁₃×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
40	C₄×C₁₃×C₁₆	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₁₃×#41	—	2	2	no	—
42	C₂²×D₄×C₁₃	—	2	2	no	—
43	C₁₃×#135	—	2	4	no	—
44	C₁₃×#135	—	4	2	no	—
45	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
46	C₂×C₁₃×SD₁₆	—	2	2	no	—
47	C₂×C₁₃×SD₁₆	—	2	2	no	—
48	C₂×C₁₃×D₈	—	2	4	no	—
49	C₂×C₁₃×D₈	—	2	2	no	—
50	C₂×C₁₃×D₈	—	4	2	no	—
51	C₂×C₁₃×D₈	C₂³	1	2	yes	—
52	C₂×C₁₃×D₈	C₂³	1	2	yes	—
53	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
55	C₁₃×#124	—	2	2	no	—
56	C₁₃×#123	—	4	2	no	—
57	C₁₃×C₂²⋊Q₈	—	2	2	no	—
58	C₁₃×#121	—	2	2	no	—
59	C₁₃×#121	—	4	2	no	—
60	C₁₃×#120	—	4	2	no	—
61	C₄×D₄×C₁₃	—	2	2	no	—
62	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
63	C₂×C₁₃×C₂²⋊C₄	—	4	2	no	—
64	C₁₃×Q₃₂	—	2	2	no	—
65	C₁₃×SD₃₂	—	2	4	no	—
66	C₁₃×SD₃₂	—	4	2	no	—
67	C₁₃×D₁₆	—	2	4	no	—
68	C₁₃×D₁₆	—	2	2	no	—
69	C₁₃×D₁₆	D₄	1	4	yes	complemented
70	C₂×C₁₃×C₁₆	—	2	2	no	—
71	C₂×C₁₃×C₁₆	—	2	2	no	—
72	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
73	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
74	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
75	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
76	C₁₃×#107	C₂³	1	2	yes	—
77	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
78	C₁₃×#103	—	2	2	no	—
79	C₁₃×#102	—	2	2	no	—
80	C₁₃×#102	—	2	2	no	—
81	C₁₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
82	C₁₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
83	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
84	#33846	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
85	C₂⁴×C₁₃	—	4	2	no	—
86	C₁₃×#41	—	4	4	no	—
87	C₁₃×#41	—	8	2	no	—
88	C₂×Q₈×C₁₃	—	2	2	no	—
89	C₂×D₄×C₁₃	—	2	2	no	—
90	C₂×D₄×C₁₃	—	2	2	no	—
91	C₂×D₄×C₁₃	—	4	4	no	—
92	C₂×D₄×C₁₃	—	4	2	no	—
93	C₂×D₄×C₁₃	—	4	2	no	—
94	C₂×D₄×C₁₃	—	4	2	no	—
95	C₂×D₄×C₁₃	—	8	2	no	—
96	C₂×D₄×C₁₃	D₈	1	1	yes	characteristic
97	C₂²×C₄×C₁₃	—	4	2	no	—
98	C₂²×C₄×C₁₃	—	4	2	no	—
99	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
101	C₁₃×Q₁₆	—	2	2	no	—
102	C₁₃×Q₁₆	—	2	2	no	—
103	C₁₃×SD₁₆	—	4	4	no	—
104	C₁₃×SD₁₆	—	8	2	no	—
105	C₁₃×D₈	—	2	2	no	—
106	C₁₃×D₈	—	2	2	no	—
107	C₁₃×D₈	—	2	2	no	—
108	C₁₃×D₈	—	4	4	no	—
109	C₁₃×D₈	C₂×D₄	1	4	yes	—
110	C₂×C₈×C₁₃	—	2	1	no	—
111	C₂×C₈×C₁₃	—	2	1	no	—
112	C₂×C₈×C₁₃	—	2	1	no	—
113	C₂×C₈×C₁₃	—	2	1	no	—
114	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
115	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
116	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
117	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
118	C₁₃×C₄⋊C₄	—	2	2	no	—
119	C₁₃×C₄⋊C₄	—	4	2	no	—
120	C₁₃×C₄⋊C₄	D₈	1	1	yes	characteristic
121	C₁₃×C₂²⋊C₄	—	4	2	no	—
122	C₁₃×C₂²⋊C₄	—	4	2	no	—
123	C₁₃×C₂²⋊C₄	—	4	2	no	—
124	C₁₃×C₂²⋊C₄	—	4	2	no	—
125	C₁₃×C₂²⋊C₄	—	4	2	no	—
126	C₁₃×C₂²⋊C₄	D₈	1	1	yes	characteristic
127	C₁₃×C₂²⋊C₄	D₈	1	1	yes	characteristic
128	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
129	C₁₃×C₁₆	—	2	1	no	—
130	C₁₃×C₁₆	—	2	1	no	—
131	C₁₃×C₁₆	—	2	1	no	—
132	C₁₃×C₁₆	C₂×D₄	1	2	yes	—
133	C₂×#508	C₂×C₁₃	1	1	yes	characteristic, complemented
134	C₂²×D₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
135	#3280	C₂×C₁₃	1	2	yes	complemented
136	#2249	C₂×C₁₃	1	1	yes	characteristic, complemented
137	#2216	C₂×C₁₃	1	1	yes	characteristic, complemented
138	#2215	C₂×C₁₃	1	1	yes	characteristic, complemented
139	#2210	C₂×C₁₃	1	2	yes	complemented
140	#2187	C₂×C₁₃	1	2	yes	complemented
141	#2186	C₂×C₁₃	1	2	yes	complemented
142	C₄×D₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
143	D₄×C₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
144	C₂³×C₁₃	—	4	2	no	—
145	C₂³×C₁₃	—	4	2	no	—
146	C₂³×C₁₃	—	8	4	no	—
147	C₂³×C₁₃	—	8	4	no	—
148	C₂³×C₁₃	—	16	2	no	—
149	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
150	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
151	Q₈×C₁₃	—	4	2	no	—
152	Q₈×C₁₃	—	4	2	no	—
153	D₄×C₁₃	—	2	2	no	—
154	D₄×C₁₃	—	2	4	no	—
155	D₄×C₁₃	—	4	2	no	—
156	D₄×C₁₃	—	4	2	no	—
157	D₄×C₁₃	—	4	2	no	—
158	D₄×C₁₃	—	8	4	no	—
159	D₄×C₁₃	—	8	4	no	—
160	D₄×C₁₃	—	16	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	—	4	2	no	—
166	C₂×C₄×C₁₃	—	4	2	no	—
167	C₂×C₄×C₁₃	—	8	4	no	—
168	C₂×C₄×C₁₃	—	16	2	no	—
169	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
170	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
171	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
172	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
173	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
174	C₈×C₁₃	—	2	1	no	—
175	C₈×C₁₃	—	2	1	no	—
176	C₈×C₁₃	—	2	1	no	—
177	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
178	C₈×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
179	C₂×#135	C₂²×C₁₃	1	2	yes	complemented
180	C₂²×D₈	C₂²×C₁₃	1	2	yes	—
181	#546	—	2	2	no	—
182	#508	—	2	4	no	—
183	C₂×Q₃₂	C₂²×C₁₃	1	1	yes	characteristic, complemented
184	C₂×SD₃₂	C₂²×C₁₃	1	2	yes	complemented
185	C₂×SD₃₂	C₂²×C₁₃	1	2	yes	complemented
186	C₂×D₁₆	—	2	4	no	—
187	C₂×D₁₆	C₂²×C₁₃	1	2	yes	—
188	C₂×D₁₆	C₂²×C₁₃	1	1	yes	characteristic
189	C₂×D₁₆	C₂²×C₁₃	1	1	yes	characteristic
190	C₂²×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
191	C₂²×C₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
192	#495	C₂²×C₁₃	1	2	yes	complemented
193	#467	C₂²×C₁₃	1	2	yes	—
194	#466	C₂²×C₁₃	1	2	yes	complemented
195	#463	—	2	2	no	—
196	#450	—	2	2	no	—
197	#449	—	2	2	no	—
198	C₄×D₈	C₂²×C₁₃	1	2	yes	complemented
199	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
200	#366	C₂²×C₁₃	1	1	yes	characteristic, complemented
201	C₄⋊C₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
202	#358	C₂²×C₁₃	1	2	yes	complemented
203	#357	C₂²×C₁₃	1	2	yes	complemented
204	#357	C₂²×C₁₃	1	2	yes	complemented
205	C₂²⋊C₁₆	C₂²×C₁₃	1	1	yes	characteristic
206	C₂²⋊C₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
207	C₄×C₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
208	C₂²×C₁₃	—	2	1	no	—
209	C₂²×C₁₃	—	2	1	no	—
210	C₂²×C₁₃	—	2	1	no	—
211	C₂²×C₁₃	—	2	1	no	—
212	C₂²×C₁₃	—	2	1	no	—
213	C₂²×C₁₃	—	4	4	no	—
214	C₂²×C₁₃	—	8	2	no	—
215	C₂²×C₁₃	—	8	2	no	—
216	C₂²×C₁₃	—	8	2	no	—
217	C₂²×C₁₃	—	8	2	no	—
218	C₂²×C₁₃	—	8	2	no	—
219	C₂²×C₁₃	—	16	8	no	—
220	C₂²×C₁₃	#508	1	2	yes	complemented
221	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
222	C₄×C₁₃	—	2	1	no	—
223	C₄×C₁₃	—	2	1	no	—
224	C₄×C₁₃	—	2	1	no	—
225	C₄×C₁₃	—	2	1	no	—
226	C₄×C₁₃	—	8	2	no	—
227	C₄×C₁₃	—	8	2	no	—
228	C₄×C₁₃	D₄²	1	1	yes	characteristic
229	C₄×C₁₃	#576	1	1	yes	characteristic
230	C₂×#41	—	2	2	no	—
231	C₂²×D₄	—	2	2	no	—
232	#135	—	2	4	no	—
233	#135	—	4	2	no	—
234	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
235	C₂×SD₁₆	—	2	2	no	—
236	C₂×SD₁₆	—	2	2	no	—
237	C₂×D₈	—	2	4	no	—
238	C₂×D₈	—	2	2	no	—
239	C₂×D₈	—	4	2	no	—
240	C₂×D₈	C₂³×C₁₃	1	2	yes	—
241	C₂×D₈	C₂³×C₁₃	1	2	yes	—
242	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
243	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
244	#124	—	2	2	no	—
245	#123	—	4	2	no	—
246	C₂²⋊Q₈	—	2	2	no	—
247	#121	—	2	2	no	—
248	#121	—	4	2	no	—
249	#120	—	4	2	no	—
250	C₄×D₄	—	2	2	no	—
251	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
252	C₂×C₂²⋊C₄	—	4	2	no	—
253	Q₃₂	—	2	2	no	—
254	SD₃₂	—	2	4	no	—
255	SD₃₂	—	4	2	no	—
256	D₁₆	—	2	4	no	—
257	D₁₆	—	2	2	no	—
258	D₁₆	D₄×C₁₃	1	4	yes	complemented
259	C₂×C₁₆	—	2	2	no	—
260	C₂×C₁₆	—	2	2	no	—
261	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
262	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
263	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
264	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
265	#107	C₂³×C₁₃	1	2	yes	—
266	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
267	#103	—	2	2	no	—
268	#102	—	2	2	no	—
269	#102	—	2	2	no	—
270	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
271	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
272	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
273	C₂×C₁₃	—	2	2	no	—
274	C₂×C₁₃	—	4	1	no	—
275	C₂×C₁₃	—	8	4	no	—
276	C₂×C₁₃	—	16	2	no	—
277	C₂×C₁₃	D₄×D₈	1	1	yes	characteristic
278	C₂×C₁₃	C₂×#508	1	1	yes	characteristic
279	C₂×C₁₃	#3415	1	1	yes	characteristic
280	C₂⁴	—	4	2	no	—
281	#41	—	4	4	no	—
282	#41	—	8	2	no	—
283	C₂×Q₈	—	2	2	no	—
284	C₂×D₄	—	2	2	no	—
285	C₂×D₄	—	2	2	no	—
286	C₂×D₄	—	4	4	no	—
287	C₂×D₄	—	4	2	no	—
288	C₂×D₄	—	4	2	no	—
289	C₂×D₄	—	4	2	no	—
290	C₂×D₄	—	8	2	no	—
291	C₂×D₄	C₁₃×D₈	1	1	yes	characteristic
292	C₂²×C₄	—	4	2	no	—
293	C₂²×C₄	—	4	2	no	—
294	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
295	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
296	Q₁₆	—	2	2	no	—
297	Q₁₆	—	2	2	no	—
298	SD₁₆	—	4	4	no	—
299	SD₁₆	—	8	2	no	—
300	D₈	—	2	2	no	—
301	D₈	—	2	2	no	—
302	D₈	—	2	2	no	—
303	D₈	—	4	4	no	—
304	D₈	C₂×D₄×C₁₃	1	4	yes	—
305	C₂×C₈	—	2	1	no	—
306	C₂×C₈	—	2	1	no	—
307	C₂×C₈	—	2	1	no	—
308	C₂×C₈	—	2	1	no	—
309	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
310	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
311	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
312	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	—	4	2	no	—
315	C₄⋊C₄	C₁₃×D₈	1	1	yes	characteristic
316	C₂²⋊C₄	—	4	2	no	—
317	C₂²⋊C₄	—	4	2	no	—
318	C₂²⋊C₄	—	4	2	no	—
319	C₂²⋊C₄	—	4	2	no	—
320	C₂²⋊C₄	—	4	2	no	—
321	C₂²⋊C₄	C₁₃×D₈	1	1	yes	characteristic
322	C₂²⋊C₄	C₁₃×D₈	1	1	yes	characteristic
323	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
324	C₁₆	—	2	1	no	—
325	C₁₆	—	2	1	no	—
326	C₁₆	—	2	1	no	—
327	C₁₆	C₂×D₄×C₁₃	1	2	yes	—
328	C₁₃	#33846	1	1	yes	characteristic, direct product factor, Sylow
329	C₂³	—	4	2	no	—
330	C₂³	—	4	2	no	—
331	C₂³	—	8	4	no	—
332	C₂³	—	8	4	no	—
333	C₂³	—	16	2	no	—
334	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
335	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
336	Q₈	—	4	2	no	—
337	Q₈	—	4	2	no	—
338	D₄	—	2	2	no	—
339	D₄	—	2	4	no	—
340	D₄	—	4	2	no	—
341	D₄	—	4	2	no	—
342	D₄	—	4	2	no	—
343	D₄	—	8	4	no	—
344	D₄	—	8	4	no	—
345	D₄	—	16	2	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	8	4	no	—
353	C₂×C₄	—	16	2	no	—
354	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
355	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
356	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
357	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
358	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
359	C₈	—	2	1	no	—
360	C₈	—	2	1	no	—
361	C₈	—	2	1	no	—
362	C₈	C₂²×D₄×C₁₃	1	1	yes	characteristic
363	C₈	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
364	C₂²	—	2	1	no	—
365	C₂²	—	2	1	no	—
366	C₂²	—	2	1	no	—
367	C₂²	—	2	1	no	—
368	C₂²	—	2	1	no	—
369	C₂²	—	4	4	no	—
370	C₂²	—	8	2	no	—
371	C₂²	—	8	2	no	—
372	C₂²	—	8	2	no	—
373	C₂²	—	8	2	no	—
374	C₂²	—	8	2	no	—
375	C₂²	—	16	8	no	—
376	C₂²	C₁₃×#508	1	2	yes	complemented
377	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
378	C₄	—	2	1	no	—
379	C₄	—	2	1	no	—
380	C₄	—	2	1	no	—
381	C₄	—	2	1	no	—
382	C₄	—	8	2	no	—
383	C₄	—	8	2	no	—
384	C₄	D₄²×C₁₃	1	1	yes	characteristic
385	C₄	C₁₃×#576	1	1	yes	characteristic
386	C₂	—	2	2	no	—
387	C₂	—	4	1	no	—
388	C₂	—	8	4	no	—
389	C₂	—	16	2	no	—
390	C₂	D₄×C₁₃×D₈	1	1	yes	characteristic
391	C₂	C₂×C₁₃×#508	1	1	yes	characteristic
392	C₂	C₁₃×#3415	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₄×D₄×C₁₃ ◁ C₈×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#508	C₂	semidirect
2. C₂²×C₁₃×D₁₆	C₂	semidirect
3. C₁₃×#3280	C₂	semidirect
4. C₁₃×#2249	C₂	semidirect
5. C₁₃×#2216	C₂	semidirect
6. C₁₃×#2215	C₂	semidirect
7. C₁₃×#2210	C₂	semidirect
8. C₁₃×#2187	C₂	semidirect
9. C₁₃×#2186	C₂	semidirect
10. C₄×C₁₃×D₁₆	C₂	semidirect
11. D₄×C₁₃×C₁₆	C₂	semidirect
12. C₂×C₁₃×#135	C₂²	semidirect
16. C₂×C₁₃×Q₃₂	C₂²	semidirect
17. C₂×C₁₃×SD₃₂	C₂²	semidirect
18. C₂×C₁₃×SD₃₂	C₂²	semidirect
24. C₂²×C₁₃×C₁₆	C₂²	semidirect
25. C₁₃×#495	C₂²	semidirect
27. C₁₃×#466	C₂²	semidirect
31. C₄×C₁₃×D₈	C₂²	semidirect
33. C₁₃×#366	C₂²	semidirect
34. C₁₃×C₄⋊C₁₆	C₂²	semidirect
35. C₁₃×#358	C₂²	semidirect
36. C₁₃×#357	C₂²	semidirect
37. C₁₃×#357	C₂²	semidirect
39. C₁₃×C₂²⋊C₁₆	C₂²	semidirect
40. C₄×C₁₃×C₁₆	C₂²	semidirect
69. C₁₃×D₁₆	D₄	semidirect
84. #33846	C₁₃	direct (N × H)
133. C₂×#508	C₂×C₁₃	semidirect
134. C₂²×D₁₆	C₂×C₁₃	semidirect
135. #3280	C₂×C₁₃	semidirect
136. #2249	C₂×C₁₃	semidirect
137. #2216	C₂×C₁₃	semidirect
138. #2215	C₂×C₁₃	semidirect
139. #2210	C₂×C₁₃	semidirect
140. #2187	C₂×C₁₃	semidirect
141. #2186	C₂×C₁₃	semidirect
142. C₄×D₁₆	C₂×C₁₃	semidirect
143. D₄×C₁₆	C₂×C₁₃	semidirect
179. C₂×#135	C₂²×C₁₃	semidirect
183. C₂×Q₃₂	C₂²×C₁₃	semidirect
184. C₂×SD₃₂	C₂²×C₁₃	semidirect
185. C₂×SD₃₂	C₂²×C₁₃	semidirect
191. C₂²×C₁₆	C₂²×C₁₃	semidirect
192. #495	C₂²×C₁₃	semidirect
194. #466	C₂²×C₁₃	semidirect
198. C₄×D₈	C₂²×C₁₃	semidirect
200. #366	C₂²×C₁₃	semidirect
201. C₄⋊C₁₆	C₂²×C₁₃	semidirect
202. #358	C₂²×C₁₃	semidirect
203. #357	C₂²×C₁₃	semidirect
204. #357	C₂²×C₁₃	semidirect
206. C₂²⋊C₁₆	C₂²×C₁₃	semidirect
207. C₄×C₁₆	C₂²×C₁₃	semidirect
220. C₂²×C₁₃	#508	semidirect
258. D₁₆	D₄×C₁₃	semidirect
328. C₁₃	#33846	direct (N × H)
376. C₂²	C₁₃×#508	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#508	2
C₂²×C₁₃×D₁₆	2
C₁₃×#3280	2
C₁₃×#2249	2
C₁₃×#2216	2
C₁₃×#2215	2
C₁₃×#2210	2
C₁₃×#2187	2
C₁₃×#2186	2
C₄×C₁₃×D₁₆	2
D₄×C₁₃×C₁₆	2
#33846	13

Subgroups — C13×#33846 #15720185

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33846 #15720185