Subgroups — C₁₃×#33968 #15720307

Order 3328.

516 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3396	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3393	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2251	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2250	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2249	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2211	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2211	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2210	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2210	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2208	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2207	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#2183	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#2177	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#2176	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₁₃×SD₃₂	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#559	—	2	1	no	—
17	C₁₃×#556	—	2	1	no	—
18	C₂×C₁₃×Q₃₂	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×Q₃₂	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×SD₃₂	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×SD₃₂	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×SD₃₂	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×SD₃₂	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×SD₃₂	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×D₁₆	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×D₁₆	C₂²	1	1	yes	characteristic
27	C₁₃×#495	C₂²	1	1	yes	characteristic
28	C₁₃×#495	C₂²	1	1	yes	characteristic
29	C₁₃×#495	C₂²	1	1	yes	characteristic
30	C₁₃×#495	C₂²	1	1	yes	characteristic
31	C₁₃×#494	C₂²	1	1	yes	characteristic
32	C₁₃×#493	C₂²	1	1	yes	characteristic
33	C₁₃×#464	—	2	1	no	—
34	C₁₃×#464	—	2	1	no	—
35	C₁₃×#463	—	2	1	no	—
36	C₁₃×#463	—	2	1	no	—
37	C₁₃×#461	—	2	1	no	—
38	C₁₃×#460	—	2	1	no	—
39	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
40	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
41	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
42	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
43	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
44	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
45	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
46	C₁₃×#367	C₂²	1	1	yes	characteristic
47	C₁₃×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
48	C₁₃×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
49	C₁₃×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
50	C₁₃×#358	C₂²	1	1	yes	characteristic
51	C₁₃×#358	C₂²	1	1	yes	characteristic
52	C₁₃×#358	C₂²	1	1	yes	characteristic
53	C₁₃×#357	C₂²	1	1	yes	characteristic
54	C₁₃×#357	C₂²	1	1	yes	characteristic
55	C₁₃×#357	C₂²	1	1	yes	characteristic
56	C₁₃×#346	C₂²	1	1	yes	characteristic
57	C₁₃×#346	C₂²	1	1	yes	characteristic
58	C₄×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
59	C₂×C₁₃×Q₁₆	—	2	1	no	—
60	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
61	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
62	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
63	C₂×C₁₃×SD₁₆	—	2	1	no	—
64	C₂×C₁₃×SD₁₆	—	2	1	no	—
65	C₂×C₁₃×SD₁₆	—	2	1	no	—
66	C₂×C₁₃×SD₁₆	—	2	1	no	—
67	C₂×C₁₃×D₈	—	2	1	no	—
68	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
69	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
70	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
71	C₁₃×C₄⋊Q₈	—	2	1	no	—
72	C₁₃×#127	—	2	1	no	—
73	C₁₃×#126	—	4	1	no	—
74	C₁₃×#126	—	4	1	no	—
75	C₁₃×#124	—	2	1	no	—
76	C₁₃×#124	—	2	1	no	—
77	C₁₃×#124	—	2	1	no	—
78	C₁₃×#124	—	2	1	no	—
79	C₁₃×#124	—	4	1	no	—
80	C₁₃×#123	—	4	1	no	—
81	C₁₃×#123	—	4	1	no	—
82	C₁₃×C₂²⋊Q₈	—	4	1	no	—
83	C₄×Q₈×C₁₃	—	2	1	no	—
84	C₄×Q₈×C₁₃	—	2	1	no	—
85	C₄×Q₈×C₁₃	—	2	1	no	—
86	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
87	C₄×D₄×C₁₃	—	2	1	no	—
88	C₄×D₄×C₁₃	—	2	1	no	—
89	C₄×D₄×C₁₃	—	2	1	no	—
90	C₄×D₄×C₁₃	—	4	1	no	—
91	C₁₃×#117	—	4	1	no	—
92	C₁₃×Q₃₂	—	2	2	no	—
93	C₁₃×Q₃₂	—	4	1	no	—
94	C₁₃×SD₃₂	—	2	2	no	—
95	C₁₃×SD₃₂	—	4	1	no	—
96	C₁₃×SD₃₂	—	4	1	no	—
97	C₁₃×SD₃₂	—	4	1	no	—
98	C₁₃×SD₃₂	—	4	1	no	—
99	C₁₃×D₁₆	—	2	2	no	—
100	C₁₃×D₁₆	—	4	1	no	—
101	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
102	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
103	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
104	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
105	C₁₃×#107	C₂³	1	1	yes	characteristic
106	C₁₃×#107	C₂³	1	1	yes	characteristic
107	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
108	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
109	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
110	C₁₃×#103	—	2	1	no	—
111	C₁₃×#103	—	2	1	no	—
112	C₁₃×#103	—	2	1	no	—
113	C₁₃×#102	—	2	1	no	—
114	C₁₃×#102	—	2	1	no	—
115	C₁₃×#102	—	2	1	no	—
116	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
117	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
118	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
119	#33968	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
120	C₂×Q₈×C₁₃	—	2	1	no	—
121	C₂×Q₈×C₁₃	—	2	1	no	—
122	C₂×Q₈×C₁₃	—	2	1	no	—
123	C₂×Q₈×C₁₃	D₈	1	1	yes	characteristic
124	C₂×D₄×C₁₃	—	2	1	no	—
125	C₂×D₄×C₁₃	—	2	1	no	—
126	C₂×D₄×C₁₃	—	2	1	no	—
127	C₂×D₄×C₁₃	—	4	1	no	—
128	C₂×D₄×C₁₃	—	4	1	no	—
129	C₂²×C₄×C₁₃	—	4	1	no	—
130	C₂²×C₄×C₁₃	—	4	1	no	—
131	C₂²×C₄×C₁₃	—	4	1	no	—
132	C₁₃×Q₁₆	—	2	1	no	—
133	C₁₃×Q₁₆	—	2	1	no	—
134	C₁₃×Q₁₆	—	2	1	no	—
135	C₁₃×Q₁₆	—	2	1	no	—
136	C₁₃×Q₁₆	—	2	1	no	—
137	C₁₃×Q₁₆	—	2	1	no	—
138	C₁₃×Q₁₆	—	8	1	no	—
139	C₁₃×SD₁₆	—	8	1	no	—
140	C₁₃×SD₁₆	—	8	1	no	—
141	C₁₃×SD₁₆	—	8	1	no	—
142	C₁₃×SD₁₆	—	8	1	no	—
143	C₁₃×D₈	—	2	1	no	—
144	C₁₃×D₈	—	2	1	no	—
145	C₁₃×D₈	—	2	1	no	—
146	C₁₃×D₈	—	2	1	no	—
147	C₁₃×D₈	—	2	1	no	—
148	C₁₃×D₈	—	2	1	no	—
149	C₁₃×D₈	—	8	1	no	—
150	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
151	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
152	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
153	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
154	C₁₃×C₄⋊C₄	—	2	1	no	—
155	C₁₃×C₄⋊C₄	—	2	1	no	—
156	C₁₃×C₄⋊C₄	—	4	1	no	—
157	C₁₃×C₄⋊C₄	—	4	1	no	—
158	C₁₃×C₄⋊C₄	—	4	1	no	—
159	C₁₃×C₄⋊C₄	—	4	1	no	—
160	C₁₃×C₄⋊C₄	—	4	1	no	—
161	C₁₃×C₄⋊C₄	D₈	1	1	yes	characteristic
162	C₁₃×C₄⋊C₄	D₈	1	1	yes	characteristic
163	C₁₃×C₄⋊C₄	D₈	1	1	yes	characteristic
164	C₁₃×C₂²⋊C₄	—	4	1	no	—
165	C₁₃×C₂²⋊C₄	—	4	1	no	—
166	C₁₃×C₂²⋊C₄	—	4	1	no	—
167	C₁₃×C₂²⋊C₄	—	4	1	no	—
168	C₁₃×C₂²⋊C₄	—	4	1	no	—
169	C₁₃×C₂²⋊C₄	—	4	1	no	—
170	C₁₃×C₂²⋊C₄	—	4	1	no	—
171	C₁₃×C₂²⋊C₄	—	4	1	no	—
172	C₁₃×C₂²⋊C₄	—	4	1	no	—
173	C₁₃×C₂²⋊C₄	—	4	1	no	—
174	C₁₃×C₂²⋊C₄	—	4	1	no	—
175	C₄²×C₁₃	—	4	1	no	—
176	C₄²×C₁₃	—	4	1	no	—
177	C₄²×C₁₃	—	4	1	no	—
178	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
179	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
180	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
181	C₁₃×C₁₆	—	2	1	no	—
182	C₁₃×C₁₆	—	2	1	no	—
183	C₁₃×C₁₆	—	2	1	no	—
184	C₁₃×C₁₆	#41	1	2	yes	—
185	#3396	C₂×C₁₃	1	1	yes	characteristic, complemented
186	#3393	C₂×C₁₃	1	1	yes	characteristic, complemented
187	#2251	C₂×C₁₃	1	1	yes	characteristic, complemented
188	#2250	C₂×C₁₃	1	1	yes	characteristic
189	#2249	C₂×C₁₃	1	1	yes	characteristic, complemented
190	#2211	C₂×C₁₃	1	1	yes	characteristic, complemented
191	#2211	C₂×C₁₃	1	1	yes	characteristic, complemented
192	#2210	C₂×C₁₃	1	1	yes	characteristic, complemented
193	#2210	C₂×C₁₃	1	1	yes	characteristic, complemented
194	#2208	C₂×C₁₃	1	1	yes	characteristic, complemented
195	#2207	C₂×C₁₃	1	1	yes	characteristic, complemented
196	#2183	C₂×C₁₃	1	1	yes	characteristic, complemented
197	#2177	C₂×C₁₃	1	1	yes	characteristic, complemented
198	#2176	C₂×C₁₃	1	1	yes	characteristic, complemented
199	C₄×SD₃₂	C₂×C₁₃	1	1	yes	characteristic, complemented
200	C₂³×C₁₃	—	4	1	no	—
201	C₂³×C₁₃	—	4	1	no	—
202	C₂³×C₁₃	—	4	1	no	—
203	Q₈×C₁₃	—	4	1	no	—
204	Q₈×C₁₃	—	4	1	no	—
205	Q₈×C₁₃	—	4	1	no	—
206	Q₈×C₁₃	—	4	1	no	—
207	Q₈×C₁₃	—	4	1	no	—
208	Q₈×C₁₃	—	4	1	no	—
209	Q₈×C₁₃	—	4	1	no	—
210	D₄×C₁₃	—	4	1	no	—
211	D₄×C₁₃	—	4	1	no	—
212	D₄×C₁₃	—	4	1	no	—
213	D₄×C₁₃	—	4	1	no	—
214	D₄×C₁₃	—	4	1	no	—
215	D₄×C₁₃	—	4	1	no	—
216	D₄×C₁₃	—	8	2	no	—
217	D₄×C₁₃	—	16	1	no	—
218	C₂×C₄×C₁₃	—	4	1	no	—
219	C₂×C₄×C₁₃	—	4	1	no	—
220	C₂×C₄×C₁₃	—	4	1	no	—
221	C₂×C₄×C₁₃	—	4	1	no	—
222	C₂×C₄×C₁₃	—	4	1	no	—
223	C₂×C₄×C₁₃	—	8	2	no	—
224	C₂×C₄×C₁₃	—	16	1	no	—
225	C₂×C₄×C₁₃	—	16	1	no	—
226	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
227	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
228	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
229	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
230	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
231	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
232	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
233	C₈×C₁₃	—	2	1	no	—
234	C₈×C₁₃	—	2	1	no	—
235	C₈×C₁₃	—	2	1	no	—
236	C₈×C₁₃	C₂×#41	1	1	yes	characteristic
237	C₈×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
238	#559	—	2	1	no	—
239	#556	—	2	1	no	—
240	C₂×Q₃₂	C₂²×C₁₃	1	1	yes	characteristic
241	C₂×Q₃₂	C₂²×C₁₃	1	1	yes	characteristic
242	C₂×SD₃₂	C₂²×C₁₃	1	1	yes	characteristic
243	C₂×SD₃₂	C₂²×C₁₃	1	1	yes	characteristic
244	C₂×SD₃₂	C₂²×C₁₃	1	1	yes	characteristic
245	C₂×SD₃₂	C₂²×C₁₃	1	1	yes	characteristic
246	C₂×SD₃₂	C₂²×C₁₃	1	1	yes	characteristic
247	C₂×D₁₆	C₂²×C₁₃	1	1	yes	characteristic
248	C₂×D₁₆	C₂²×C₁₃	1	1	yes	characteristic
249	#495	C₂²×C₁₃	1	1	yes	characteristic
250	#495	C₂²×C₁₃	1	1	yes	characteristic
251	#495	C₂²×C₁₃	1	1	yes	characteristic
252	#495	C₂²×C₁₃	1	1	yes	characteristic
253	#494	C₂²×C₁₃	1	1	yes	characteristic
254	#493	C₂²×C₁₃	1	1	yes	characteristic
255	#464	—	2	1	no	—
256	#464	—	2	1	no	—
257	#463	—	2	1	no	—
258	#463	—	2	1	no	—
259	#461	—	2	1	no	—
260	#460	—	2	1	no	—
261	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
262	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
263	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
264	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
265	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
266	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
267	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
268	#367	C₂²×C₁₃	1	1	yes	characteristic
269	C₄⋊C₁₆	C₂²×C₁₃	1	1	yes	characteristic
270	C₄⋊C₁₆	C₂²×C₁₃	1	1	yes	characteristic
271	C₄⋊C₁₆	C₂²×C₁₃	1	1	yes	characteristic
272	#358	C₂²×C₁₃	1	1	yes	characteristic
273	#358	C₂²×C₁₃	1	1	yes	characteristic
274	#358	C₂²×C₁₃	1	1	yes	characteristic
275	#357	C₂²×C₁₃	1	1	yes	characteristic
276	#357	C₂²×C₁₃	1	1	yes	characteristic
277	#357	C₂²×C₁₃	1	1	yes	characteristic
278	#346	C₂²×C₁₃	1	1	yes	characteristic
279	#346	C₂²×C₁₃	1	1	yes	characteristic
280	C₄×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
281	C₂²×C₁₃	—	8	1	no	—
282	C₂²×C₁₃	—	8	1	no	—
283	C₂²×C₁₃	—	8	1	no	—
284	C₂²×C₁₃	—	8	1	no	—
285	C₂²×C₁₃	—	8	1	no	—
286	C₂²×C₁₃	—	8	1	no	—
287	C₂²×C₁₃	—	8	1	no	—
288	C₂²×C₁₃	—	8	1	no	—
289	C₂²×C₁₃	—	8	1	no	—
290	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
291	C₄×C₁₃	—	2	1	no	—
292	C₄×C₁₃	—	2	1	no	—
293	C₄×C₁₃	—	2	1	no	—
294	C₄×C₁₃	—	2	1	no	—
295	C₄×C₁₃	—	2	1	no	—
296	C₄×C₁₃	—	2	1	no	—
297	C₄×C₁₃	—	8	1	no	—
298	C₄×C₁₃	—	8	1	no	—
299	C₄×C₁₃	—	8	1	no	—
300	C₄×C₁₃	—	8	1	no	—
301	C₄×C₁₃	—	8	1	no	—
302	C₄×C₁₃	#550	1	1	yes	characteristic
303	C₄×C₁₃	#576	1	1	yes	characteristic
304	C₂×Q₁₆	—	2	1	no	—
305	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
306	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
307	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
308	C₂×SD₁₆	—	2	1	no	—
309	C₂×SD₁₆	—	2	1	no	—
310	C₂×SD₁₆	—	2	1	no	—
311	C₂×SD₁₆	—	2	1	no	—
312	C₂×D₈	—	2	1	no	—
313	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
314	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
315	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
316	C₄⋊Q₈	—	2	1	no	—
317	#127	—	2	1	no	—
318	#126	—	4	1	no	—
319	#126	—	4	1	no	—
320	#124	—	2	1	no	—
321	#124	—	2	1	no	—
322	#124	—	2	1	no	—
323	#124	—	2	1	no	—
324	#124	—	4	1	no	—
325	#123	—	4	1	no	—
326	#123	—	4	1	no	—
327	C₂²⋊Q₈	—	4	1	no	—
328	C₄×Q₈	—	2	1	no	—
329	C₄×Q₈	—	2	1	no	—
330	C₄×Q₈	—	2	1	no	—
331	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
332	C₄×D₄	—	2	1	no	—
333	C₄×D₄	—	2	1	no	—
334	C₄×D₄	—	2	1	no	—
335	C₄×D₄	—	4	1	no	—
336	#117	—	4	1	no	—
337	Q₃₂	—	2	2	no	—
338	Q₃₂	—	4	1	no	—
339	SD₃₂	—	2	2	no	—
340	SD₃₂	—	4	1	no	—
341	SD₃₂	—	4	1	no	—
342	SD₃₂	—	4	1	no	—
343	SD₃₂	—	4	1	no	—
344	D₁₆	—	2	2	no	—
345	D₁₆	—	4	1	no	—
346	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
347	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
348	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
349	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
350	#107	C₂³×C₁₃	1	1	yes	characteristic
351	#107	C₂³×C₁₃	1	1	yes	characteristic
352	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
353	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
354	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
355	#103	—	2	1	no	—
356	#103	—	2	1	no	—
357	#103	—	2	1	no	—
358	#102	—	2	1	no	—
359	#102	—	2	1	no	—
360	#102	—	2	1	no	—
361	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
362	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
363	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
364	C₂×C₁₃	—	16	1	no	—
365	C₂×C₁₃	—	16	1	no	—
366	C₂×C₁₃	—	16	1	no	—
367	C₂×C₁₃	#3391	1	1	yes	characteristic
368	C₂×C₁₃	#3414	1	1	yes	characteristic
369	C₂×C₁₃	#3416	1	1	yes	characteristic
370	C₂×Q₈	—	2	1	no	—
371	C₂×Q₈	—	2	1	no	—
372	C₂×Q₈	—	2	1	no	—
373	C₂×Q₈	C₁₃×D₈	1	1	yes	characteristic
374	C₂×D₄	—	2	1	no	—
375	C₂×D₄	—	2	1	no	—
376	C₂×D₄	—	2	1	no	—
377	C₂×D₄	—	4	1	no	—
378	C₂×D₄	—	4	1	no	—
379	C₂²×C₄	—	4	1	no	—
380	C₂²×C₄	—	4	1	no	—
381	C₂²×C₄	—	4	1	no	—
382	Q₁₆	—	2	1	no	—
383	Q₁₆	—	2	1	no	—
384	Q₁₆	—	2	1	no	—
385	Q₁₆	—	2	1	no	—
386	Q₁₆	—	2	1	no	—
387	Q₁₆	—	2	1	no	—
388	Q₁₆	—	8	1	no	—
389	SD₁₆	—	8	1	no	—
390	SD₁₆	—	8	1	no	—
391	SD₁₆	—	8	1	no	—
392	SD₁₆	—	8	1	no	—
393	D₈	—	2	1	no	—
394	D₈	—	2	1	no	—
395	D₈	—	2	1	no	—
396	D₈	—	2	1	no	—
397	D₈	—	2	1	no	—
398	D₈	—	2	1	no	—
399	D₈	—	8	1	no	—
400	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
401	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
402	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
403	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
404	C₄⋊C₄	—	2	1	no	—
405	C₄⋊C₄	—	2	1	no	—
406	C₄⋊C₄	—	4	1	no	—
407	C₄⋊C₄	—	4	1	no	—
408	C₄⋊C₄	—	4	1	no	—
409	C₄⋊C₄	—	4	1	no	—
410	C₄⋊C₄	—	4	1	no	—
411	C₄⋊C₄	C₁₃×D₈	1	1	yes	characteristic
412	C₄⋊C₄	C₁₃×D₈	1	1	yes	characteristic
413	C₄⋊C₄	C₁₃×D₈	1	1	yes	characteristic
414	C₂²⋊C₄	—	4	1	no	—
415	C₂²⋊C₄	—	4	1	no	—
416	C₂²⋊C₄	—	4	1	no	—
417	C₂²⋊C₄	—	4	1	no	—
418	C₂²⋊C₄	—	4	1	no	—
419	C₂²⋊C₄	—	4	1	no	—
420	C₂²⋊C₄	—	4	1	no	—
421	C₂²⋊C₄	—	4	1	no	—
422	C₂²⋊C₄	—	4	1	no	—
423	C₂²⋊C₄	—	4	1	no	—
424	C₂²⋊C₄	—	4	1	no	—
425	C₄²	—	4	1	no	—
426	C₄²	—	4	1	no	—
427	C₄²	—	4	1	no	—
428	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
429	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
430	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
431	C₁₆	—	2	1	no	—
432	C₁₆	—	2	1	no	—
433	C₁₆	—	2	1	no	—
434	C₁₆	C₁₃×#41	1	2	yes	—
435	C₁₃	#33968	1	1	yes	characteristic, direct product factor, Sylow
436	C₂³	—	4	1	no	—
437	C₂³	—	4	1	no	—
438	C₂³	—	4	1	no	—
439	Q₈	—	4	1	no	—
440	Q₈	—	4	1	no	—
441	Q₈	—	4	1	no	—
442	Q₈	—	4	1	no	—
443	Q₈	—	4	1	no	—
444	Q₈	—	4	1	no	—
445	Q₈	—	4	1	no	—
446	D₄	—	4	1	no	—
447	D₄	—	4	1	no	—
448	D₄	—	4	1	no	—
449	D₄	—	4	1	no	—
450	D₄	—	4	1	no	—
451	D₄	—	4	1	no	—
452	D₄	—	8	2	no	—
453	D₄	—	16	1	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	—	4	1	no	—
456	C₂×C₄	—	4	1	no	—
457	C₂×C₄	—	4	1	no	—
458	C₂×C₄	—	4	1	no	—
459	C₂×C₄	—	8	2	no	—
460	C₂×C₄	—	16	1	no	—
461	C₂×C₄	—	16	1	no	—
462	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
463	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
464	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
465	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
466	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
467	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
468	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
469	C₈	—	2	1	no	—
470	C₈	—	2	1	no	—
471	C₈	—	2	1	no	—
472	C₈	C₂×C₁₃×#41	1	1	yes	characteristic
473	C₈	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
474	C₂²	—	8	1	no	—
475	C₂²	—	8	1	no	—
476	C₂²	—	8	1	no	—
477	C₂²	—	8	1	no	—
478	C₂²	—	8	1	no	—
479	C₂²	—	8	1	no	—
480	C₂²	—	8	1	no	—
481	C₂²	—	8	1	no	—
482	C₂²	—	8	1	no	—
483	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
484	C₄	—	2	1	no	—
485	C₄	—	2	1	no	—
486	C₄	—	2	1	no	—
487	C₄	—	2	1	no	—
488	C₄	—	2	1	no	—
489	C₄	—	2	1	no	—
490	C₄	—	8	1	no	—
491	C₄	—	8	1	no	—
492	C₄	—	8	1	no	—
493	C₄	—	8	1	no	—
494	C₄	—	8	1	no	—
495	C₄	C₁₃×#550	1	1	yes	characteristic
496	C₄	C₁₃×#576	1	1	yes	characteristic
497	C₂	—	16	1	no	—
498	C₂	—	16	1	no	—
499	C₂	—	16	1	no	—
500	C₂	C₁₃×#3391	1	1	yes	characteristic
501	C₂	C₁₃×#3414	1	1	yes	characteristic
502	C₂	C₁₃×#3416	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
prime radical	C₁₃×#2250	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₄×Q₈×C₁₃ ◁ C₈×Q₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3396	C₂	semidirect
2. C₁₃×#3393	C₂	semidirect
3. C₁₃×#2251	C₂	semidirect
5. C₁₃×#2249	C₂	semidirect
6. C₁₃×#2211	C₂	semidirect
7. C₁₃×#2211	C₂	semidirect
8. C₁₃×#2210	C₂	semidirect
9. C₁₃×#2210	C₂	semidirect
10. C₁₃×#2208	C₂	semidirect
11. C₁₃×#2207	C₂	semidirect
12. C₁₃×#2183	C₂	semidirect
13. C₁₃×#2177	C₂	semidirect
14. C₁₃×#2176	C₂	semidirect
15. C₄×C₁₃×SD₃₂	C₂	semidirect
119. #33968	C₁₃	direct (N × H)
185. #3396	C₂×C₁₃	semidirect
186. #3393	C₂×C₁₃	semidirect
187. #2251	C₂×C₁₃	semidirect
189. #2249	C₂×C₁₃	semidirect
190. #2211	C₂×C₁₃	semidirect
191. #2211	C₂×C₁₃	semidirect
192. #2210	C₂×C₁₃	semidirect
193. #2210	C₂×C₁₃	semidirect
194. #2208	C₂×C₁₃	semidirect
195. #2207	C₂×C₁₃	semidirect
196. #2183	C₂×C₁₃	semidirect
197. #2177	C₂×C₁₃	semidirect
198. #2176	C₂×C₁₃	semidirect
199. C₄×SD₃₂	C₂×C₁₃	semidirect
435. C₁₃	#33968	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#3396	2
C₁₃×#3393	2
C₁₃×#2251	2
C₁₃×#2250	2
C₁₃×#2249	2
C₁₃×#2211	2
C₁₃×#2210	2
C₁₃×#2208	2
C₁₃×#2207	2
C₁₃×#2183	2
C₁₃×#2177	2
C₁₃×#2176	2
C₄×C₁₃×SD₃₂	2
#33968	13

Subgroups — C13×#33968 #15720307

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33968 #15720307