Subgroups — C₁₃×#33722 #15720061

Order 3328.

826 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#510	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#509	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#508	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₁₃×SD₃₂	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#3156	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#3155	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2251	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2250	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2249	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2248	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2108	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#137	—	2	1	no	—
13	C₂×C₁₃×AGL(1,ℤ/8)	—	2	1	no	—
14	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
16	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
18	C₁₃×#536	—	2	1	no	—
19	C₁₃×#535	—	2	1	no	—
20	C₁₃×#510	—	2	4	no	—
21	C₁₃×#509	—	2	4	no	—
22	C₁₃×#508	—	2	4	no	—
23	C₂×C₁₃×Q₃₂	C₂²	1	2	yes	complemented
24	C₂×C₁₃×Q₃₂	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₁₃×SD₃₂	—	2	4	no	—
26	C₂×C₁₃×SD₃₂	C₂²	1	2	yes	—
27	C₂×C₁₃×SD₃₂	C₂²	1	2	yes	—
28	C₂×C₁₃×SD₃₂	C₂²	1	2	yes	—
29	C₂×C₁₃×SD₃₂	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₁₃×SD₃₂	C₂²	1	2	yes	complemented
31	C₂×C₁₃×SD₃₂	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₁₃×D₁₆	C₂²	1	2	yes	—
33	C₂×C₁₃×D₁₆	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₁₃×M₃₂	C₂²	1	1	yes	characteristic
35	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
36	C₁₃×#497	—	2	2	no	—
37	C₁₃×#496	—	2	2	no	—
38	C₁₃×#495	C₂²	1	2	yes	—
39	C₁₃×#495	C₂²	1	2	yes	complemented
40	C₁₃×#494	C₂²	1	2	yes	complemented
41	C₁₃×#493	C₂²	1	2	yes	—
42	C₁₃×#405	C₂²	1	1	yes	characteristic
43	C₁₃×#346	C₂²	1	2	yes	complemented
44	C₄×C₁₃×C₁₆	C₂²	1	2	yes	complemented
45	C₂×C₁₃×#41	—	2	1	no	—
46	C₂×C₁₃×#41	—	2	1	no	—
47	C₂²×Q₈×C₁₃	—	2	1	no	—
48	C₂²×D₄×C₁₃	—	2	1	no	—
49	C₁₃×#137	—	4	4	no	—
50	C₁₃×AGL(1,ℤ/8)	—	4	4	no	—
51	C₁₃×#135	—	2	2	no	—
52	C₁₃×#135	—	2	2	no	—
53	C₁₃×#135	—	2	2	no	—
54	C₁₃×#135	—	2	2	no	—
55	C₂×C₁₃×Q₁₆	—	2	2	no	—
56	C₂×C₁₃×Q₁₆	—	2	2	no	—
57	C₂×C₁₃×Q₁₆	—	2	2	no	—
58	C₂×C₁₃×Q₁₆	—	2	1	no	—
59	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
60	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
61	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
62	C₂×C₁₃×SD₁₆	—	2	2	no	—
63	C₂×C₁₃×SD₁₆	—	2	2	no	—
64	C₂×C₁₃×SD₁₆	—	2	1	no	—
65	C₂×C₁₃×SD₁₆	—	2	1	no	—
66	C₂×C₁₃×D₈	—	2	2	no	—
67	C₂×C₁₃×D₈	—	2	2	no	—
68	C₂×C₁₃×D₈	—	2	2	no	—
69	C₂×C₁₃×D₈	—	2	1	no	—
70	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
71	C₂×C₁₃×D₈	C₂³	1	2	yes	—
72	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
73	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
74	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
75	C₁₃×C₄⋊Q₈	—	2	2	no	—
76	C₁₃×#127	—	2	2	no	—
77	C₁₃×#124	—	2	2	no	—
78	C₁₃×#124	—	2	2	no	—
79	C₁₃×#123	—	4	2	no	—
80	C₁₃×C₂²⋊Q₈	—	4	2	no	—
81	C₁₃×#121	—	4	2	no	—
82	C₁₃×#120	—	4	2	no	—
83	C₁₃×#117	D₄	1	1	yes	characteristic
84	C₁₃×Q₃₂	—	2	2	no	—
85	C₁₃×Q₃₂	—	2	4	no	—
86	C₁₃×SD₃₂	—	2	4	no	—
87	C₁₃×SD₃₂	—	2	4	no	—
88	C₁₃×SD₃₂	—	2	4	no	—
89	C₁₃×SD₃₂	—	2	2	no	—
90	C₁₃×SD₃₂	—	2	2	no	—
91	C₁₃×SD₃₂	—	2	4	no	—
92	C₁₃×D₁₆	—	2	4	no	—
93	C₁₃×D₁₆	—	2	2	no	—
94	C₁₃×M₃₂	D₄	1	4	yes	complemented
95	C₂×C₁₃×C₁₆	D₄	1	4	yes	complemented
96	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
97	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
98	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
99	C₁₃×#97	D₄	1	2	yes	—
100	C₄×C₈×C₁₃	C₂³	1	2	yes	—
101	#33722	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
102	C₂⁴×C₁₃	—	4	1	no	—
103	C₁₃×#41	—	4	2	no	—
104	C₁₃×#41	—	4	2	no	—
105	C₁₃×#41	—	4	2	no	—
106	C₁₃×#41	—	4	2	no	—
107	C₂×Q₈×C₁₃	—	2	1	no	—
108	C₂×Q₈×C₁₃	—	2	2	no	—
109	C₂×Q₈×C₁₃	—	2	1	no	—
110	C₂×Q₈×C₁₃	—	4	1	no	—
111	C₂×Q₈×C₁₃	—	4	2	no	—
112	C₂×Q₈×C₁₃	—	4	2	no	—
113	C₂×D₄×C₁₃	—	2	1	no	—
114	C₂×D₄×C₁₃	—	2	2	no	—
115	C₂×D₄×C₁₃	—	2	1	no	—
116	C₂×D₄×C₁₃	—	4	1	no	—
117	C₂×D₄×C₁₃	—	4	1	no	—
118	C₂×D₄×C₁₃	—	4	2	no	—
119	C₂×D₄×C₁₃	—	4	2	no	—
120	C₂×D₄×C₁₃	—	4	1	no	—
121	C₂×D₄×C₁₃	—	4	4	no	—
122	C₂²×C₄×C₁₃	—	4	1	no	—
123	C₂²×C₄×C₁₃	—	4	1	no	—
124	C₂²×C₄×C₁₃	—	4	1	no	—
125	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
126	C₁₃×Q₁₆	—	2	2	no	—
127	C₁₃×Q₁₆	—	2	1	no	—
128	C₁₃×Q₁₆	—	2	2	no	—
129	C₁₃×Q₁₆	—	2	1	no	—
130	C₁₃×Q₁₆	—	2	1	no	—
131	C₁₃×Q₁₆	—	2	1	no	—
132	C₁₃×Q₁₆	—	4	2	no	—
133	C₁₃×Q₁₆	—	4	4	no	—
134	C₁₃×SD₁₆	—	4	2	no	—
135	C₁₃×SD₁₆	—	4	2	no	—
136	C₁₃×SD₁₆	—	4	4	no	—
137	C₁₃×SD₁₆	—	4	4	no	—
138	C₁₃×D₈	—	2	1	no	—
139	C₁₃×D₈	—	2	2	no	—
140	C₁₃×D₈	—	2	1	no	—
141	C₁₃×D₈	—	2	1	no	—
142	C₁₃×D₈	—	2	2	no	—
143	C₁₃×D₈	—	2	1	no	—
144	C₁₃×D₈	—	4	2	no	—
145	C₁₃×D₈	—	4	4	no	—
146	C₁₃×M₁₆	D₈	1	4	yes	—
147	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
148	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
149	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
150	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
151	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
152	C₁₃×C₄⋊C₄	—	4	4	no	—
153	C₁₃×C₄⋊C₄	D₈	1	2	yes	—
154	C₁₃×C₂²⋊C₄	—	4	4	no	—
155	C₁₃×C₂²⋊C₄	—	4	4	no	—
156	C₁₃×C₂²⋊C₄	D₈	1	2	yes	—
157	C₄²×C₁₃	C₂×D₄	1	2	yes	—
158	C₁₃×C₁₆	C₂×D₄	1	2	yes	—
159	C₁₃×C₁₆	C₂×D₄	1	2	yes	—
160	C₁₃×C₁₆	C₂×D₄	1	4	yes	—
161	C₂×#510	C₂×C₁₃	1	1	yes	characteristic, complemented
162	C₂×#509	C₂×C₁₃	1	1	yes	characteristic, complemented
163	C₂×#508	C₂×C₁₃	1	1	yes	characteristic, complemented
164	C₂²×SD₃₂	C₂×C₁₃	1	1	yes	characteristic, complemented
165	#3156	C₂×C₁₃	1	1	yes	characteristic, complemented
166	#3155	C₂×C₁₃	1	1	yes	characteristic, complemented
167	#2251	C₂×C₁₃	1	2	yes	complemented
168	#2250	C₂×C₁₃	1	2	yes	complemented
169	#2249	C₂×C₁₃	1	2	yes	complemented
170	#2248	C₂×C₁₃	1	2	yes	complemented
171	#2108	C₂×C₁₃	1	1	yes	characteristic, complemented
172	C₂³×C₁₃	—	4	1	no	—
173	C₂³×C₁₃	—	4	2	no	—
174	C₂³×C₁₃	—	4	1	no	—
175	C₂³×C₁₃	—	8	2	no	—
176	C₂³×C₁₃	—	16	2	no	—
177	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
178	Q₈×C₁₃	—	4	1	no	—
179	Q₈×C₁₃	—	4	1	no	—
180	Q₈×C₁₃	—	4	2	no	—
181	Q₈×C₁₃	—	4	1	no	—
182	Q₈×C₁₃	—	4	2	no	—
183	Q₈×C₁₃	—	4	1	no	—
184	Q₈×C₁₃	—	8	2	no	—
185	D₄×C₁₃	—	4	2	no	—
186	D₄×C₁₃	—	4	1	no	—
187	D₄×C₁₃	—	4	1	no	—
188	D₄×C₁₃	—	4	1	no	—
189	D₄×C₁₃	—	4	2	no	—
190	D₄×C₁₃	—	4	1	no	—
191	D₄×C₁₃	—	8	2	no	—
192	D₄×C₁₃	—	8	2	no	—
193	D₄×C₁₃	—	8	2	no	—
194	D₄×C₁₃	—	16	4	no	—
195	C₂×C₄×C₁₃	—	4	1	no	—
196	C₂×C₄×C₁₃	—	4	2	no	—
197	C₂×C₄×C₁₃	—	4	1	no	—
198	C₂×C₄×C₁₃	—	8	2	no	—
199	C₂×C₄×C₁₃	—	8	2	no	—
200	C₂×C₄×C₁₃	—	8	2	no	—
201	C₂×C₄×C₁₃	#127	1	2	yes	—
202	C₂×C₄×C₁₃	C₂×D₈	1	4	yes	—
203	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
204	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
205	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
206	C₈×C₁₃	#127	1	2	yes	—
207	C₈×C₁₃	C₂×D₈	1	4	yes	—
208	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
209	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
210	C₂×#137	—	2	1	no	—
211	C₂×AGL(1,ℤ/8)	—	2	1	no	—
212	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
213	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
214	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
215	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
216	#536	—	2	1	no	—
217	#535	—	2	1	no	—
218	#510	—	2	4	no	—
219	#509	—	2	4	no	—
220	#508	—	2	4	no	—
221	C₂×Q₃₂	C₂²×C₁₃	1	1	yes	characteristic, complemented
222	C₂×Q₃₂	C₂²×C₁₃	1	2	yes	complemented
223	C₂×SD₃₂	—	2	4	no	—
224	C₂×SD₃₂	C₂²×C₁₃	1	2	yes	—
225	C₂×SD₃₂	C₂²×C₁₃	1	2	yes	—
226	C₂×SD₃₂	C₂²×C₁₃	1	2	yes	—
227	C₂×SD₃₂	C₂²×C₁₃	1	1	yes	characteristic, complemented
228	C₂×SD₃₂	C₂²×C₁₃	1	1	yes	characteristic, complemented
229	C₂×SD₃₂	C₂²×C₁₃	1	2	yes	complemented
230	C₂×D₁₆	C₂²×C₁₃	1	2	yes	—
231	C₂×D₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
232	C₂×M₃₂	C₂²×C₁₃	1	1	yes	characteristic
233	C₂²×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
234	#497	—	2	2	no	—
235	#496	—	2	2	no	—
236	#495	C₂²×C₁₃	1	2	yes	—
237	#495	C₂²×C₁₃	1	2	yes	complemented
238	#494	C₂²×C₁₃	1	2	yes	complemented
239	#493	C₂²×C₁₃	1	2	yes	—
240	#405	C₂²×C₁₃	1	1	yes	characteristic
241	#346	C₂²×C₁₃	1	2	yes	complemented
242	C₄×C₁₆	C₂²×C₁₃	1	2	yes	complemented
243	C₂²×C₁₃	—	2	2	no	—
244	C₂²×C₁₃	—	8	1	no	—
245	C₂²×C₁₃	—	8	1	no	—
246	C₂²×C₁₃	—	8	2	no	—
247	C₂²×C₁₃	—	8	2	no	—
248	C₂²×C₁₃	—	8	4	no	—
249	C₂²×C₁₃	—	8	2	no	—
250	C₂²×C₁₃	—	16	4	no	—
251	C₂²×C₁₃	#493	1	2	yes	—
252	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
253	C₄×C₁₃	—	2	4	no	—
254	C₄×C₁₃	—	8	1	no	—
255	C₄×C₁₃	—	8	1	no	—
256	C₄×C₁₃	—	8	2	no	—
257	C₄×C₁₃	#493	1	2	yes	—
258	C₄×C₁₃	C₂×#127	1	1	yes	characteristic
259	C₄×C₁₃	C₂²×D₈	1	1	yes	characteristic
260	C₂×#41	—	2	1	no	—
261	C₂×#41	—	2	1	no	—
262	C₂²×Q₈	—	2	1	no	—
263	C₂²×D₄	—	2	1	no	—
264	#137	—	4	4	no	—
265	AGL(1,ℤ/8)	—	4	4	no	—
266	#135	—	2	2	no	—
267	#135	—	2	2	no	—
268	#135	—	2	2	no	—
269	#135	—	2	2	no	—
270	C₂×Q₁₆	—	2	2	no	—
271	C₂×Q₁₆	—	2	2	no	—
272	C₂×Q₁₆	—	2	1	no	—
273	C₂×Q₁₆	—	2	2	no	—
274	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
275	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
276	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
277	C₂×SD₁₆	—	2	1	no	—
278	C₂×SD₁₆	—	2	1	no	—
279	C₂×SD₁₆	—	2	2	no	—
280	C₂×SD₁₆	—	2	2	no	—
281	C₂×D₈	—	2	2	no	—
282	C₂×D₈	—	2	2	no	—
283	C₂×D₈	—	2	1	no	—
284	C₂×D₈	—	2	2	no	—
285	C₂×D₈	C₂³×C₁₃	1	2	yes	—
286	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
287	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
288	C₂×M₁₆	D₄×C₁₃	1	1	yes	characteristic
289	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
290	C₄⋊Q₈	—	2	2	no	—
291	#127	—	2	2	no	—
292	#124	—	2	2	no	—
293	#124	—	2	2	no	—
294	#123	—	4	2	no	—
295	C₂²⋊Q₈	—	4	2	no	—
296	#121	—	4	2	no	—
297	#120	—	4	2	no	—
298	#117	D₄×C₁₃	1	1	yes	characteristic
299	Q₃₂	—	2	2	no	—
300	Q₃₂	—	2	4	no	—
301	SD₃₂	—	2	4	no	—
302	SD₃₂	—	2	4	no	—
303	SD₃₂	—	2	4	no	—
304	SD₃₂	—	2	2	no	—
305	SD₃₂	—	2	2	no	—
306	SD₃₂	—	2	4	no	—
307	D₁₆	—	2	4	no	—
308	D₁₆	—	2	2	no	—
309	M₃₂	D₄×C₁₃	1	4	yes	complemented
310	C₂×C₁₆	D₄×C₁₃	1	4	yes	complemented
311	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
312	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
313	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
314	#97	D₄×C₁₃	1	2	yes	—
315	C₄×C₈	C₂³×C₁₃	1	2	yes	—
316	C₂×C₁₃	—	2	2	no	—
317	C₂×C₁₃	—	16	1	no	—
318	C₂×C₁₃	—	16	1	no	—
319	C₂×C₁₃	—	16	2	no	—
320	C₂×C₁₃	C₂×#493	1	1	yes	characteristic
321	C₂×C₁₃	#3416	1	2	yes	—
322	C₂⁴	—	4	1	no	—
323	#41	—	4	2	no	—
324	#41	—	4	2	no	—
325	#41	—	4	2	no	—
326	#41	—	4	2	no	—
327	C₂×Q₈	—	2	1	no	—
328	C₂×Q₈	—	2	2	no	—
329	C₂×Q₈	—	2	1	no	—
330	C₂×Q₈	—	4	1	no	—
331	C₂×Q₈	—	4	2	no	—
332	C₂×Q₈	—	4	2	no	—
333	C₂×D₄	—	2	1	no	—
334	C₂×D₄	—	2	2	no	—
335	C₂×D₄	—	2	1	no	—
336	C₂×D₄	—	4	1	no	—
337	C₂×D₄	—	4	1	no	—
338	C₂×D₄	—	4	2	no	—
339	C₂×D₄	—	4	2	no	—
340	C₂×D₄	—	4	1	no	—
341	C₂×D₄	—	4	4	no	—
342	C₂²×C₄	—	4	1	no	—
343	C₂²×C₄	—	4	1	no	—
344	C₂²×C₄	—	4	1	no	—
345	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
346	Q₁₆	—	2	2	no	—
347	Q₁₆	—	2	1	no	—
348	Q₁₆	—	2	2	no	—
349	Q₁₆	—	2	1	no	—
350	Q₁₆	—	2	1	no	—
351	Q₁₆	—	2	1	no	—
352	Q₁₆	—	4	2	no	—
353	Q₁₆	—	4	4	no	—
354	SD₁₆	—	4	2	no	—
355	SD₁₆	—	4	2	no	—
356	SD₁₆	—	4	4	no	—
357	SD₁₆	—	4	4	no	—
358	D₈	—	2	1	no	—
359	D₈	—	2	2	no	—
360	D₈	—	2	1	no	—
361	D₈	—	2	1	no	—
362	D₈	—	2	2	no	—
363	D₈	—	2	1	no	—
364	D₈	—	4	2	no	—
365	D₈	—	4	4	no	—
366	M₁₆	C₁₃×D₈	1	4	yes	—
367	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
368	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
369	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
370	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
371	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
372	C₄⋊C₄	—	4	4	no	—
373	C₄⋊C₄	C₁₃×D₈	1	2	yes	—
374	C₂²⋊C₄	—	4	4	no	—
375	C₂²⋊C₄	—	4	4	no	—
376	C₂²⋊C₄	C₁₃×D₈	1	2	yes	—
377	C₄²	C₂×D₄×C₁₃	1	2	yes	—
378	C₁₆	C₂×D₄×C₁₃	1	2	yes	—
379	C₁₆	C₂×D₄×C₁₃	1	2	yes	—
380	C₁₆	C₂×D₄×C₁₃	1	4	yes	—
381	C₁₃	#33722	1	1	yes	characteristic, direct product factor, Sylow
382	C₂³	—	4	1	no	—
383	C₂³	—	4	2	no	—
384	C₂³	—	4	1	no	—
385	C₂³	—	8	2	no	—
386	C₂³	—	16	2	no	—
387	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
388	Q₈	—	4	1	no	—
389	Q₈	—	4	1	no	—
390	Q₈	—	4	2	no	—
391	Q₈	—	4	1	no	—
392	Q₈	—	4	2	no	—
393	Q₈	—	4	1	no	—
394	Q₈	—	8	2	no	—
395	D₄	—	4	2	no	—
396	D₄	—	4	1	no	—
397	D₄	—	4	1	no	—
398	D₄	—	4	1	no	—
399	D₄	—	4	2	no	—
400	D₄	—	4	1	no	—
401	D₄	—	8	2	no	—
402	D₄	—	8	2	no	—
403	D₄	—	8	2	no	—
404	D₄	—	16	4	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	8	2	no	—
409	C₂×C₄	—	8	2	no	—
410	C₂×C₄	—	8	2	no	—
411	C₂×C₄	C₁₃×#127	1	2	yes	—
412	C₂×C₄	C₂×C₁₃×D₈	1	4	yes	—
413	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
414	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
415	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
416	C₈	C₁₃×#127	1	2	yes	—
417	C₈	C₂×C₁₃×D₈	1	4	yes	—
418	C₈	C₂²×D₄×C₁₃	1	1	yes	characteristic
419	C₈	C₂²×D₄×C₁₃	1	1	yes	characteristic
420	C₂²	—	2	2	no	—
421	C₂²	—	8	1	no	—
422	C₂²	—	8	1	no	—
423	C₂²	—	8	2	no	—
424	C₂²	—	8	2	no	—
425	C₂²	—	8	4	no	—
426	C₂²	—	8	2	no	—
427	C₂²	—	16	4	no	—
428	C₂²	C₁₃×#493	1	2	yes	—
429	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
430	C₄	—	2	4	no	—
431	C₄	—	8	1	no	—
432	C₄	—	8	1	no	—
433	C₄	—	8	2	no	—
434	C₄	C₁₃×#493	1	2	yes	—
435	C₄	C₂×C₁₃×#127	1	1	yes	characteristic
436	C₄	C₂²×C₁₃×D₈	1	1	yes	characteristic
437	C₂	—	2	2	no	—
438	C₂	—	16	2	no	—
439	C₂	—	16	1	no	—
440	C₂	—	16	1	no	—
441	C₂	C₂×C₁₃×#493	1	1	yes	characteristic
442	C₂	C₁₃×#3416	1	2	yes	—

	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 ◁ C₁₃×#117 ◁ C₁₃×#405 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#510	C₂	semidirect
2. C₂×C₁₃×#509	C₂	semidirect
3. C₂×C₁₃×#508	C₂	semidirect
4. C₂²×C₁₃×SD₃₂	C₂	semidirect
5. C₁₃×#3156	C₂	semidirect
6. C₁₃×#3155	C₂	semidirect
7. C₁₃×#2251	C₂	semidirect
8. C₁₃×#2250	C₂	semidirect
9. C₁₃×#2249	C₂	semidirect
10. C₁₃×#2248	C₂	semidirect
11. C₁₃×#2108	C₂	semidirect
23. C₂×C₁₃×Q₃₂	C₂²	semidirect
24. C₂×C₁₃×Q₃₂	C₂²	semidirect
29. C₂×C₁₃×SD₃₂	C₂²	semidirect
30. C₂×C₁₃×SD₃₂	C₂²	semidirect
31. C₂×C₁₃×SD₃₂	C₂²	semidirect
33. C₂×C₁₃×D₁₆	C₂²	semidirect
39. C₁₃×#495	C₂²	semidirect
40. C₁₃×#494	C₂²	semidirect
43. C₁₃×#346	C₂²	semidirect
44. C₄×C₁₃×C₁₆	C₂²	semidirect
94. C₁₃×M₃₂	D₄	semidirect
95. C₂×C₁₃×C₁₆	D₄	semidirect
101. #33722	C₁₃	direct (N × H)
161. C₂×#510	C₂×C₁₃	semidirect
162. C₂×#509	C₂×C₁₃	semidirect
163. C₂×#508	C₂×C₁₃	semidirect
164. C₂²×SD₃₂	C₂×C₁₃	semidirect
165. #3156	C₂×C₁₃	semidirect
166. #3155	C₂×C₁₃	semidirect
167. #2251	C₂×C₁₃	semidirect
168. #2250	C₂×C₁₃	semidirect
169. #2249	C₂×C₁₃	semidirect
170. #2248	C₂×C₁₃	semidirect
171. #2108	C₂×C₁₃	semidirect
221. C₂×Q₃₂	C₂²×C₁₃	semidirect
222. C₂×Q₃₂	C₂²×C₁₃	semidirect
227. C₂×SD₃₂	C₂²×C₁₃	semidirect
228. C₂×SD₃₂	C₂²×C₁₃	semidirect
229. C₂×SD₃₂	C₂²×C₁₃	semidirect
231. C₂×D₁₆	C₂²×C₁₃	semidirect
237. #495	C₂²×C₁₃	semidirect
238. #494	C₂²×C₁₃	semidirect
241. #346	C₂²×C₁₃	semidirect
242. C₄×C₁₆	C₂²×C₁₃	semidirect
309. M₃₂	D₄×C₁₃	semidirect
310. C₂×C₁₆	D₄×C₁₃	semidirect
381. C₁₃	#33722	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×#510	2
C₂×C₁₃×#509	2
C₂×C₁₃×#508	2
C₂²×C₁₃×SD₃₂	2
C₁₃×#3156	2
C₁₃×#3155	2
C₁₃×#2251	2
C₁₃×#2250	2
C₁₃×#2249	2
C₁₃×#2248	2
C₁₃×#2108	2
#33722	13

Subgroups — C13×#33722 #15720061

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33722 #15720061