Subgroups — C₁₃×#32943 #15719282

Order 3328.

1316 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×#131	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#473	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₃×#467	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3007	C₂	1	2	yes	maximal
5	C₁₃×#1908	C₂	1	4	yes	maximal, complemented
6	C₁₃×#1901	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1816	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1810	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
10	C₂×C₁₃×#137	C₂²	1	4	yes	—
11	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
12	C₂×C₁₃×#131	—	2	8	no	—
13	C₂×C₁₃×#131	—	2	1	no	—
14	C₂×C₁₃×#131	—	2	1	no	—
15	C₂×C₁₃×#131	C₂²	1	2	yes	—
16	C₂×C₁₃×#131	C₂²	1	2	yes	—
17	C₂²×C₁₃×M₁₆	—	2	1	no	—
18	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
19	C₂³×C₈×C₁₃	—	2	1	no	—
20	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
22	C₁₃×#473	—	2	8	no	—
23	C₁₃×#467	—	2	1	no	—
24	C₁₃×#467	—	2	1	no	—
25	C₁₃×#467	—	2	1	no	—
26	C₁₃×#467	—	2	1	no	—
27	C₁₃×#452	—	2	4	no	—
28	C₁₃×#451	—	2	2	no	—
29	C₁₃×#450	—	2	2	no	—
30	C₂×C₁₃×#108	C₂²	1	2	yes	complemented
31	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic, complemented
32	C₁₃×#417	C₂²	1	4	yes	—
33	C₂×C₁₃×#103	C₂²	1	2	yes	complemented
34	C₂×C₁₃×#101	C₂²	1	4	yes	complemented
35	C₁₃×#407	C₂²	1	2	yes	—
36	C₁₃×#343	C₂²	1	4	yes	complemented
37	C₁₃×#341	C₂²	1	2	yes	complemented
38	C₂×C₁₃×#41	—	2	4	no	—
39	C₂×C₁₃×#41	—	2	4	no	—
40	C₂×C₁₃×#41	—	2	1	no	—
41	C₂×C₁₃×#41	—	2	1	no	—
42	C₂×C₁₃×#41	D₄	1	2	yes	—
43	C₂×C₁₃×#41	C₂³	1	2	yes	—
44	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
45	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
46	C₂²×D₄×C₁₃	—	2	1	no	—
47	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
48	C₂³×C₄×C₁₃	—	2	1	no	—
49	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
50	C₁₃×#137	—	2	8	no	—
51	C₁₃×#137	—	2	8	no	—
52	C₂×C₁₃×Q₁₆	—	2	4	no	—
53	C₂×C₁₃×Q₁₆	—	2	1	no	—
54	C₂×C₁₃×Q₁₆	—	2	1	no	—
55	C₂×C₁₃×Q₁₆	—	2	4	no	—
56	C₂×C₁₃×SD₁₆	—	2	4	no	—
57	C₁₃×#131	—	2	8	no	—
58	C₁₃×#131	—	2	8	no	—
59	C₁₃×#131	—	2	4	no	—
60	C₁₃×#131	—	2	4	no	—
61	C₁₃×#131	—	2	4	no	—
62	C₁₃×#131	D₄	1	8	yes	—
63	C₂×C₁₃×M₁₆	—	2	8	no	—
64	C₂×C₁₃×M₁₆	—	2	1	no	—
65	C₂×C₁₃×M₁₆	—	2	4	no	—
66	C₂×C₁₃×M₁₆	—	2	2	no	—
67	C₂×C₁₃×M₁₆	—	2	2	no	—
68	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
69	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
70	C₂²×C₈×C₁₃	—	2	8	no	—
71	C₂²×C₈×C₁₃	—	2	1	no	—
72	C₂²×C₈×C₁₃	—	2	2	no	—
73	C₂²×C₈×C₁₃	—	2	2	no	—
74	C₂²×C₈×C₁₃	—	2	4	no	—
75	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
76	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
77	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
78	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
79	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
81	C₁₃×C₂²⋊Q₈	—	2	2	no	—
82	C₁₃×C₂²⋊Q₈	—	2	2	no	—
83	C₁₃×C₂²⋊Q₈	—	2	2	no	—
84	C₁₃×C₂²⋊Q₈	—	2	2	no	—
85	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
86	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
87	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
88	C₁₃×#108	—	2	4	no	—
89	C₁₃×#107	—	2	1	no	—
90	C₁₃×#107	—	2	1	no	—
91	C₁₃×#103	—	2	4	no	—
92	C₁₃×#103	—	2	2	no	—
93	C₁₃×#103	—	2	2	no	—
94	C₁₃×#102	—	2	4	no	—
95	C₁₃×#101	—	2	8	no	—
96	C₁₃×C₂²⋊C₈	—	2	2	no	—
97	C₁₃×C₂²⋊C₈	—	2	2	no	—
98	#32943	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
99	C₂⁴×C₁₃	—	2	1	no	—
100	C₂⁴×C₁₃	#41	1	1	yes	characteristic
101	C₁₃×#41	—	2	4	no	—
102	C₁₃×#41	—	2	8	no	—
103	C₁₃×#41	—	2	4	no	—
104	C₁₃×#41	—	2	4	no	—
105	C₁₃×#41	—	2	4	no	—
106	C₁₃×#41	—	2	2	no	—
107	C₁₃×#41	—	2	2	no	—
108	C₁₃×#41	C₂×D₄	1	4	yes	—
109	C₁₃×#41	#41	1	4	yes	—
110	C₂×Q₈×C₁₃	—	2	4	no	—
111	C₂×Q₈×C₁₃	—	2	1	no	—
112	C₂×Q₈×C₁₃	—	2	4	no	—
113	C₂×Q₈×C₁₃	—	2	2	no	—
114	C₂×Q₈×C₁₃	—	2	2	no	—
115	C₂×Q₈×C₁₃	—	2	4	no	—
116	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
117	C₂×D₄×C₁₃	—	2	8	no	—
118	C₂×D₄×C₁₃	—	2	2	no	—
119	C₂×D₄×C₁₃	—	2	2	no	—
120	C₂×D₄×C₁₃	—	2	4	no	—
121	C₂×D₄×C₁₃	—	2	1	no	—
122	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
123	C₂²×C₄×C₁₃	—	2	4	no	—
124	C₂²×C₄×C₁₃	—	2	4	no	—
125	C₂²×C₄×C₁₃	—	2	1	no	—
126	C₂²×C₄×C₁₃	—	2	2	no	—
127	C₂²×C₄×C₁₃	—	2	2	no	—
128	C₂²×C₄×C₁₃	—	2	2	no	—
129	C₂²×C₄×C₁₃	—	2	2	no	—
130	C₂²×C₄×C₁₃	—	2	2	no	—
131	C₂²×C₄×C₁₃	—	2	2	no	—
132	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
137	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
138	C₁₃×Q₁₆	—	4	8	no	—
139	C₁₃×Q₁₆	—	4	2	no	—
140	C₁₃×Q₁₆	—	4	2	no	—
141	C₁₃×SD₁₆	—	4	8	no	—
142	C₁₃×M₁₆	—	2	4	no	—
143	C₁₃×M₁₆	—	2	8	no	—
144	C₁₃×M₁₆	—	2	2	no	—
145	C₁₃×M₁₆	—	2	8	no	—
146	C₁₃×M₁₆	—	2	4	no	—
147	C₁₃×M₁₆	—	2	4	no	—
148	C₁₃×M₁₆	C₂×D₄	1	4	yes	—
149	C₂×C₈×C₁₃	—	2	4	no	—
150	C₂×C₈×C₁₃	—	2	8	no	—
151	C₂×C₈×C₁₃	—	2	2	no	—
152	C₂×C₈×C₁₃	—	2	2	no	—
153	C₂×C₈×C₁₃	—	2	2	no	—
154	C₂×C₈×C₁₃	—	2	8	no	—
155	C₂×C₈×C₁₃	—	2	2	no	—
156	C₂×C₈×C₁₃	—	2	2	no	—
157	C₂×C₈×C₁₃	—	2	2	no	—
158	C₂×C₈×C₁₃	—	2	4	no	—
159	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
160	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
161	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
162	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
163	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
164	C₁₃×C₄⋊C₄	—	2	2	no	—
165	C₁₃×C₄⋊C₄	—	2	2	no	—
166	C₁₃×C₄⋊C₄	—	4	2	no	—
167	C₁₃×C₄⋊C₄	—	4	2	no	—
168	C₁₃×C₂²⋊C₄	—	4	2	no	—
169	C₁₃×C₂²⋊C₄	—	4	2	no	—
170	C₂²×#131	C₂×C₁₃	1	1	yes	characteristic
171	C₂×#473	C₂×C₁₃	1	2	yes	complemented
172	C₂×#467	C₂×C₁₃	1	1	yes	characteristic, complemented
173	#3007	C₂×C₁₃	1	2	yes	—
174	#1908	C₂×C₁₃	1	4	yes	complemented
175	#1901	C₂×C₁₃	1	2	yes	complemented
176	#1816	C₂×C₁₃	1	2	yes	complemented
177	#1810	C₂×C₁₃	1	1	yes	characteristic, complemented
178	C₂³×C₁₃	—	2	4	no	—
179	C₂³×C₁₃	—	2	2	no	—
180	C₂³×C₁₃	—	2	2	no	—
181	C₂³×C₁₃	—	2	2	no	—
182	C₂³×C₁₃	—	4	1	no	—
183	C₂³×C₁₃	—	4	2	no	—
184	C₂³×C₁₃	—	4	2	no	—
185	C₂³×C₁₃	#121	1	1	yes	characteristic
186	C₂³×C₁₃	#121	1	1	yes	characteristic
187	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
188	Q₈×C₁₃	—	2	4	no	—
189	Q₈×C₁₃	—	2	2	no	—
190	Q₈×C₁₃	—	4	2	no	—
191	Q₈×C₁₃	—	4	4	no	—
192	Q₈×C₁₃	—	4	2	no	—
193	Q₈×C₁₃	#121	1	4	yes	—
194	D₄×C₁₃	—	2	8	no	—
195	D₄×C₁₃	—	2	4	no	—
196	D₄×C₁₃	—	2	4	no	—
197	D₄×C₁₃	—	2	4	no	—
198	D₄×C₁₃	—	2	2	no	—
199	D₄×C₁₃	#121	1	4	yes	—
200	C₂×C₄×C₁₃	—	2	4	no	—
201	C₂×C₄×C₁₃	—	2	8	no	—
202	C₂×C₄×C₁₃	—	2	2	no	—
203	C₂×C₄×C₁₃	—	2	2	no	—
204	C₂×C₄×C₁₃	—	2	1	no	—
205	C₂×C₄×C₁₃	—	2	4	no	—
206	C₂×C₄×C₁₃	—	2	1	no	—
207	C₂×C₄×C₁₃	—	2	2	no	—
208	C₂×C₄×C₁₃	—	2	2	no	—
209	C₂×C₄×C₁₃	—	2	1	no	—
210	C₂×C₄×C₁₃	—	2	4	no	—
211	C₂×C₄×C₁₃	—	2	1	no	—
212	C₂×C₄×C₁₃	—	4	2	no	—
213	C₂×C₄×C₁₃	—	4	2	no	—
214	C₂×C₄×C₁₃	—	4	4	no	—
215	C₂×C₄×C₁₃	—	8	2	no	—
216	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
217	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
218	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
219	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
220	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
221	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
222	C₈×C₁₃	—	2	1	no	—
223	C₈×C₁₃	—	2	4	no	—
224	C₈×C₁₃	—	2	1	no	—
225	C₈×C₁₃	—	4	4	no	—
226	C₈×C₁₃	#120	1	2	yes	—
227	C₈×C₁₃	#120	1	2	yes	—
228	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
229	C₂×#137	C₂²×C₁₃	1	4	yes	—
230	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
231	C₂×#131	—	2	8	no	—
232	C₂×#131	—	2	1	no	—
233	C₂×#131	—	2	1	no	—
234	C₂×#131	C₂²×C₁₃	1	2	yes	—
235	C₂×#131	C₂²×C₁₃	1	2	yes	—
236	C₂²×M₁₆	—	2	1	no	—
237	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
238	C₂³×C₈	—	2	1	no	—
239	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
240	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
241	#473	—	2	8	no	—
242	#467	—	2	1	no	—
243	#467	—	2	1	no	—
244	#467	—	2	1	no	—
245	#467	—	2	1	no	—
246	#452	—	2	4	no	—
247	#451	—	2	2	no	—
248	#450	—	2	2	no	—
249	C₂×#108	C₂²×C₁₃	1	2	yes	complemented
250	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic, complemented
251	#417	C₂²×C₁₃	1	4	yes	—
252	C₂×#103	C₂²×C₁₃	1	2	yes	complemented
253	C₂×#101	C₂²×C₁₃	1	4	yes	complemented
254	#407	C₂²×C₁₃	1	2	yes	—
255	#343	C₂²×C₁₃	1	4	yes	complemented
256	#341	C₂²×C₁₃	1	2	yes	complemented
257	C₂²×C₁₃	—	2	1	no	—
258	C₂²×C₁₃	—	2	1	no	—
259	C₂²×C₁₃	—	2	1	no	—
260	C₂²×C₁₃	—	2	1	no	—
261	C₂²×C₁₃	—	2	1	no	—
262	C₂²×C₁₃	—	2	4	no	—
263	C₂²×C₁₃	—	2	1	no	—
264	C₂²×C₁₃	—	2	1	no	—
265	C₂²×C₁₃	—	4	4	no	—
266	C₂²×C₁₃	—	4	8	no	—
267	C₂²×C₁₃	—	4	2	no	—
268	C₂²×C₁₃	—	4	2	no	—
269	C₂²×C₁₃	#473	1	2	yes	complemented
270	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
271	C₂²×C₁₃	#525	1	2	yes	—
272	C₄×C₁₃	—	2	1	no	—
273	C₄×C₁₃	—	2	4	no	—
274	C₄×C₁₃	—	2	1	no	—
275	C₄×C₁₃	—	8	2	no	—
276	C₄×C₁₃	—	8	2	no	—
277	C₄×C₁₃	C₂×#120	1	1	yes	characteristic
278	C₄×C₁₃	C₂×#121	1	2	yes	—
279	C₄×C₁₃	#525	1	1	yes	characteristic
280	C₂×#41	—	2	4	no	—
281	C₂×#41	—	2	4	no	—
282	C₂×#41	—	2	1	no	—
283	C₂×#41	—	2	1	no	—
284	C₂×#41	D₄×C₁₃	1	2	yes	—
285	C₂×#41	C₂³×C₁₃	1	2	yes	—
286	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
287	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
288	C₂²×D₄	—	2	1	no	—
289	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
290	C₂³×C₄	—	2	1	no	—
291	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
292	#137	—	2	8	no	—
293	#137	—	2	8	no	—
294	C₂×Q₁₆	—	2	4	no	—
295	C₂×Q₁₆	—	2	1	no	—
296	C₂×Q₁₆	—	2	1	no	—
297	C₂×Q₁₆	—	2	4	no	—
298	C₂×SD₁₆	—	2	4	no	—
299	#131	—	2	8	no	—
300	#131	—	2	8	no	—
301	#131	—	2	4	no	—
302	#131	—	2	4	no	—
303	#131	—	2	4	no	—
304	#131	D₄×C₁₃	1	8	yes	—
305	C₂×M₁₆	—	2	8	no	—
306	C₂×M₁₆	—	2	1	no	—
307	C₂×M₁₆	—	2	4	no	—
308	C₂×M₁₆	—	2	2	no	—
309	C₂×M₁₆	—	2	2	no	—
310	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
311	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
312	C₂²×C₈	—	2	8	no	—
313	C₂²×C₈	—	2	1	no	—
314	C₂²×C₈	—	2	2	no	—
315	C₂²×C₈	—	2	2	no	—
316	C₂²×C₈	—	2	4	no	—
317	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
318	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
319	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
320	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
321	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
322	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
323	C₂²⋊Q₈	—	2	2	no	—
324	C₂²⋊Q₈	—	2	2	no	—
325	C₂²⋊Q₈	—	2	2	no	—
326	C₂²⋊Q₈	—	2	2	no	—
327	C₂×C₄⋊C₄	—	2	2	no	—
328	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
329	C₂×C₂²⋊C₄	—	2	2	no	—
330	#108	—	2	4	no	—
331	#107	—	2	1	no	—
332	#107	—	2	1	no	—
333	#103	—	2	4	no	—
334	#103	—	2	2	no	—
335	#103	—	2	2	no	—
336	#102	—	2	4	no	—
337	#101	—	2	8	no	—
338	C₂²⋊C₈	—	2	2	no	—
339	C₂²⋊C₈	—	2	2	no	—
340	C₂×C₁₃	—	2	2	no	—
341	C₂×C₁₃	—	2	2	no	—
342	C₂×C₁₃	—	4	1	no	—
343	C₂×C₁₃	—	4	4	no	—
344	C₂×C₁₃	#2847	1	1	yes	characteristic
345	C₂×C₁₃	C₂×#473	1	1	yes	characteristic
346	C₂×C₁₃	#3067	1	1	yes	characteristic
347	C₂⁴	—	2	1	no	—
348	C₂⁴	C₁₃×#41	1	1	yes	characteristic
349	#41	—	2	4	no	—
350	#41	—	2	8	no	—
351	#41	—	2	4	no	—
352	#41	—	2	4	no	—
353	#41	—	2	4	no	—
354	#41	—	2	2	no	—
355	#41	—	2	2	no	—
356	#41	C₂×D₄×C₁₃	1	4	yes	—
357	#41	C₁₃×#41	1	4	yes	—
358	C₂×Q₈	—	2	4	no	—
359	C₂×Q₈	—	2	1	no	—
360	C₂×Q₈	—	2	4	no	—
361	C₂×Q₈	—	2	2	no	—
362	C₂×Q₈	—	2	2	no	—
363	C₂×Q₈	—	2	4	no	—
364	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
365	C₂×D₄	—	2	8	no	—
366	C₂×D₄	—	2	2	no	—
367	C₂×D₄	—	2	2	no	—
368	C₂×D₄	—	2	4	no	—
369	C₂×D₄	—	2	1	no	—
370	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
371	C₂²×C₄	—	2	4	no	—
372	C₂²×C₄	—	2	4	no	—
373	C₂²×C₄	—	2	1	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
381	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
382	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
383	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
384	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
385	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
386	Q₁₆	—	4	8	no	—
387	Q₁₆	—	4	2	no	—
388	Q₁₆	—	4	2	no	—
389	SD₁₆	—	4	8	no	—
390	M₁₆	—	2	4	no	—
391	M₁₆	—	2	8	no	—
392	M₁₆	—	2	2	no	—
393	M₁₆	—	2	8	no	—
394	M₁₆	—	2	4	no	—
395	M₁₆	—	2	4	no	—
396	M₁₆	C₂×D₄×C₁₃	1	4	yes	—
397	C₂×C₈	—	2	4	no	—
398	C₂×C₈	—	2	8	no	—
399	C₂×C₈	—	2	2	no	—
400	C₂×C₈	—	2	2	no	—
401	C₂×C₈	—	2	2	no	—
402	C₂×C₈	—	2	8	no	—
403	C₂×C₈	—	2	2	no	—
404	C₂×C₈	—	2	2	no	—
405	C₂×C₈	—	2	2	no	—
406	C₂×C₈	—	2	4	no	—
407	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
408	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
409	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
410	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
411	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
412	C₄⋊C₄	—	2	2	no	—
413	C₄⋊C₄	—	2	2	no	—
414	C₄⋊C₄	—	4	2	no	—
415	C₄⋊C₄	—	4	2	no	—
416	C₂²⋊C₄	—	4	2	no	—
417	C₂²⋊C₄	—	4	2	no	—
418	C₁₃	#32943	1	1	yes	characteristic, direct product factor, Sylow
419	C₂³	—	2	4	no	—
420	C₂³	—	2	2	no	—
421	C₂³	—	2	2	no	—
422	C₂³	—	2	2	no	—
423	C₂³	—	4	1	no	—
424	C₂³	—	4	2	no	—
425	C₂³	—	4	2	no	—
426	C₂³	C₁₃×#121	1	1	yes	characteristic
427	C₂³	C₁₃×#121	1	1	yes	characteristic
428	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
429	Q₈	—	2	4	no	—
430	Q₈	—	2	2	no	—
431	Q₈	—	4	2	no	—
432	Q₈	—	4	4	no	—
433	Q₈	—	4	2	no	—
434	Q₈	C₁₃×#121	1	4	yes	—
435	D₄	—	2	8	no	—
436	D₄	—	2	4	no	—
437	D₄	—	2	4	no	—
438	D₄	—	2	4	no	—
439	D₄	—	2	2	no	—
440	D₄	C₁₃×#121	1	4	yes	—
441	C₂×C₄	—	2	4	no	—
442	C₂×C₄	—	2	8	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	4	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	4	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	4	2	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	4	4	no	—
456	C₂×C₄	—	8	2	no	—
457	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
458	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
459	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
460	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
461	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
462	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
463	C₈	—	2	1	no	—
464	C₈	—	2	4	no	—
465	C₈	—	2	1	no	—
466	C₈	—	4	4	no	—
467	C₈	C₁₃×#120	1	2	yes	—
468	C₈	C₁₃×#120	1	2	yes	—
469	C₂²	—	2	1	no	—
470	C₂²	—	2	1	no	—
471	C₂²	—	2	1	no	—
472	C₂²	—	2	1	no	—
473	C₂²	—	2	1	no	—
474	C₂²	—	2	1	no	—
475	C₂²	—	2	1	no	—
476	C₂²	—	2	4	no	—
477	C₂²	—	4	4	no	—
478	C₂²	—	4	8	no	—
479	C₂²	—	4	2	no	—
480	C₂²	—	4	2	no	—
481	C₂²	C₁₃×#473	1	2	yes	complemented
482	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
483	C₂²	C₁₃×#525	1	2	yes	—
484	C₄	—	2	1	no	—
485	C₄	—	2	4	no	—
486	C₄	—	2	1	no	—
487	C₄	—	8	2	no	—
488	C₄	—	8	2	no	—
489	C₄	C₂×C₁₃×#120	1	1	yes	characteristic
490	C₄	C₂×C₁₃×#121	1	2	yes	—
491	C₄	C₁₃×#525	1	1	yes	characteristic
492	C₂	—	2	2	no	—
493	C₂	—	2	2	no	—
494	C₂	—	4	1	no	—
495	C₂	—	4	4	no	—
496	C₂	C₁₃×#2847	1	1	yes	characteristic
497	C₂	C₂×C₁₃×#473	1	1	yes	characteristic
498	C₂	C₁₃×#3067	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×C₁₃×#41	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂³×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#473	C₂	semidirect
3. C₂×C₁₃×#467	C₂	semidirect
5. C₁₃×#1908	C₂	semidirect
6. C₁₃×#1901	C₂	semidirect
7. C₁₃×#1816	C₂	semidirect
8. C₁₃×#1810	C₂	semidirect
11. C₂²×C₁₃×Q₁₆	C₂²	semidirect
30. C₂×C₁₃×#108	C₂²	semidirect
31. C₂×C₁₃×#107	C₂²	semidirect
33. C₂×C₁₃×#103	C₂²	semidirect
34. C₂×C₁₃×#101	C₂²	semidirect
36. C₁₃×#343	C₂²	semidirect
37. C₁₃×#341	C₂²	semidirect
98. #32943	C₁₃	direct (N × H)
171. C₂×#473	C₂×C₁₃	semidirect
172. C₂×#467	C₂×C₁₃	semidirect
174. #1908	C₂×C₁₃	semidirect
175. #1901	C₂×C₁₃	semidirect
176. #1816	C₂×C₁₃	semidirect
177. #1810	C₂×C₁₃	semidirect
230. C₂²×Q₁₆	C₂²×C₁₃	semidirect
249. C₂×#108	C₂²×C₁₃	semidirect
250. C₂×#107	C₂²×C₁₃	semidirect
252. C₂×#103	C₂²×C₁₃	semidirect
253. C₂×#101	C₂²×C₁₃	semidirect
255. #343	C₂²×C₁₃	semidirect
256. #341	C₂²×C₁₃	semidirect
269. C₂²×C₁₃	#473	semidirect
418. C₁₃	#32943	direct (N × H)
481. C₂²	C₁₃×#473	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₁₃×#131	2
C₂×C₁₃×#473	2
C₂×C₁₃×#467	2
C₁₃×#3007	2
C₁₃×#1908	2
C₁₃×#1901	2
C₁₃×#1816	2
C₁₃×#1810	2
#32943	13

Subgroups — C13×#32943 #15719282

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#32943 #15719282