Subgroups — C₁₃×#32942 #15719281

Order 3328.

1368 conjugacy classes of subgroups.

The subgroup lattice has 518 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, complemented
2	C₂×C₁₃×#472	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₃×#466	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3006	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1907	C₂	1	4	yes	maximal, complemented
6	C₁₃×#1900	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×AGL(1,ℤ/8)	C₂²	1	4	yes	—
11	C₂²×C₁₃×D₈	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×#121	C₂²	1	2	yes	—
22	C₁₃×#472	—	2	8	no	—
23	C₁₃×#466	—	2	1	no	—
24	C₁₃×#466	—	2	1	no	—
25	C₁₃×#466	—	2	1	no	—
26	C₁₃×#466	—	2	1	no	—
27	C₁₃×#449	—	2	4	no	—
28	C₁₃×#448	—	2	2	no	—
29	C₁₃×#447	—	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×#102	C₂²	1	2	yes	complemented
34	C₂×C₁₃×#100	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×D₄×C₁₃	—	2	1	no	—
46	C₂²×D₄×C₁₃	—	2	2	no	—
47	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
48	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
49	C₂³×C₄×C₁₃	—	2	1	no	—
50	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
51	C₁₃×AGL(1,ℤ/8)	—	2	8	no	—
52	C₁₃×AGL(1,ℤ/8)	—	2	8	no	—
53	C₂×C₁₃×SD₁₆	—	2	4	no	—
54	C₂×C₁₃×D₈	—	2	4	no	—
55	C₂×C₁₃×D₈	—	2	1	no	—
56	C₂×C₁₃×D₈	—	2	1	no	—
57	C₂×C₁₃×D₈	—	2	4	no	—
58	C₁₃×#131	—	2	8	no	—
59	C₁₃×#131	—	2	8	no	—
60	C₁₃×#131	—	2	4	no	—
61	C₁₃×#131	—	2	4	no	—
62	C₁₃×#131	—	2	4	no	—
63	C₁₃×#131	D₄	1	8	yes	complemented
64	C₂×C₁₃×M₁₆	—	2	8	no	—
65	C₂×C₁₃×M₁₆	—	2	1	no	—
66	C₂×C₁₃×M₁₆	—	2	4	no	—
67	C₂×C₁₃×M₁₆	—	2	2	no	—
68	C₂×C₁₃×M₁₆	—	2	2	no	—
69	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
70	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
71	C₂²×C₈×C₁₃	—	2	8	no	—
72	C₂²×C₈×C₁₃	—	2	1	no	—
73	C₂²×C₈×C₁₃	—	2	2	no	—
74	C₂²×C₈×C₁₃	—	2	2	no	—
75	C₂²×C₈×C₁₃	—	2	4	no	—
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	D₄	1	1	yes	characteristic
80	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
81	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
82	C₁₃×#121	—	2	2	no	—
83	C₁₃×#121	—	2	2	no	—
84	C₁₃×#121	—	2	2	no	—
85	C₁₃×#121	—	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×#102	—	2	4	no	—
93	C₁₃×#102	—	2	2	no	—
94	C₁₃×#102	—	2	2	no	—
95	C₁₃×#100	—	2	8	no	—
96	C₁₃×C₂²⋊C₈	—	2	2	no	—
97	C₁₃×C₂²⋊C₈	—	2	2	no	—
98	#32942	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
99	C₂⁴×C₁₃	—	2	1	no	—
100	C₂⁴×C₁₃	—	2	2	no	—
101	C₂⁴×C₁₃	#41	1	1	yes	characteristic
102	C₁₃×#41	—	2	4	no	—
103	C₁₃×#41	—	2	8	no	—
104	C₁₃×#41	—	2	4	no	—
105	C₁₃×#41	—	2	4	no	—
106	C₁₃×#41	—	2	4	no	—
107	C₁₃×#41	—	2	2	no	—
108	C₁₃×#41	—	2	2	no	—
109	C₁₃×#41	C₂×D₄	1	4	yes	—
110	C₁₃×#41	#41	1	4	yes	—
111	C₂×Q₈×C₁₃	—	2	4	no	—
112	C₂×Q₈×C₁₃	—	2	1	no	—
113	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
114	C₂×D₄×C₁₃	—	2	8	no	—
115	C₂×D₄×C₁₃	—	2	2	no	—
116	C₂×D₄×C₁₃	—	2	2	no	—
117	C₂×D₄×C₁₃	—	2	4	no	—
118	C₂×D₄×C₁₃	—	2	1	no	—
119	C₂×D₄×C₁₃	—	2	4	no	—
120	C₂×D₄×C₁₃	—	2	2	no	—
121	C₂×D₄×C₁₃	—	2	2	no	—
122	C₂×D₄×C₁₃	—	2	4	no	—
123	C₂×D₄×C₁₃	—	4	2	no	—
124	C₂×D₄×C₁₃	—	4	2	no	—
125	C₂×D₄×C₁₃	—	8	4	no	—
126	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₁₃	—	2	4	no	—
128	C₂²×C₄×C₁₃	—	2	4	no	—
129	C₂²×C₄×C₁₃	—	2	1	no	—
130	C₂²×C₄×C₁₃	—	2	2	no	—
131	C₂²×C₄×C₁₃	—	2	2	no	—
132	C₂²×C₄×C₁₃	—	2	2	no	—
133	C₂²×C₄×C₁₃	—	2	2	no	—
134	C₂²×C₄×C₁₃	—	2	2	no	—
135	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
140	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
141	C₁₃×SD₁₆	—	4	8	no	—
142	C₁₃×D₈	—	4	8	no	—
143	C₁₃×D₈	—	4	2	no	—
144	C₁₃×D₈	—	4	2	no	—
145	C₁₃×M₁₆	—	2	4	no	—
146	C₁₃×M₁₆	—	2	8	no	—
147	C₁₃×M₁₆	—	2	2	no	—
148	C₁₃×M₁₆	—	2	8	no	—
149	C₁₃×M₁₆	—	2	4	no	—
150	C₁₃×M₁₆	—	2	4	no	—
151	C₁₃×M₁₆	C₂×D₄	1	4	yes	—
152	C₂×C₈×C₁₃	—	2	4	no	—
153	C₂×C₈×C₁₃	—	2	8	no	—
154	C₂×C₈×C₁₃	—	2	2	no	—
155	C₂×C₈×C₁₃	—	2	2	no	—
156	C₂×C₈×C₁₃	—	2	2	no	—
157	C₂×C₈×C₁₃	—	2	8	no	—
158	C₂×C₈×C₁₃	—	2	2	no	—
159	C₂×C₈×C₁₃	—	2	2	no	—
160	C₂×C₈×C₁₃	—	2	2	no	—
161	C₂×C₈×C₁₃	—	2	4	no	—
162	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
163	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
164	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
165	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
166	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
167	C₁₃×C₄⋊C₄	—	2	2	no	—
168	C₁₃×C₄⋊C₄	—	2	2	no	—
169	C₁₃×C₂²⋊C₄	—	4	2	no	—
170	C₁₃×C₂²⋊C₄	—	4	2	no	—
171	C₂²×#131	C₂×C₁₃	1	1	yes	characteristic, complemented
172	C₂×#472	C₂×C₁₃	1	2	yes	complemented
173	C₂×#466	C₂×C₁₃	1	1	yes	characteristic, complemented
174	#3006	C₂×C₁₃	1	2	yes	complemented
175	#1907	C₂×C₁₃	1	4	yes	complemented
176	#1900	C₂×C₁₃	1	2	yes	complemented
177	#1816	C₂×C₁₃	1	2	yes	complemented
178	#1810	C₂×C₁₃	1	1	yes	characteristic, complemented
179	C₂³×C₁₃	—	2	4	no	—
180	C₂³×C₁₃	—	2	2	no	—
181	C₂³×C₁₃	—	2	2	no	—
182	C₂³×C₁₃	—	2	2	no	—
183	C₂³×C₁₃	—	4	1	no	—
184	C₂³×C₁₃	—	4	2	no	—
185	C₂³×C₁₃	—	4	2	no	—
186	C₂³×C₁₃	—	4	2	no	—
187	C₂³×C₁₃	—	4	4	no	—
188	C₂³×C₁₃	—	8	2	no	—
189	C₂³×C₁₃	—	8	2	no	—
190	C₂³×C₁₃	#121	1	1	yes	characteristic
191	C₂³×C₁₃	#121	1	1	yes	characteristic
192	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
193	Q₈×C₁₃	—	2	4	no	—
194	Q₈×C₁₃	—	2	2	no	—
195	Q₈×C₁₃	#121	1	4	yes	—
196	D₄×C₁₃	—	2	8	no	—
197	D₄×C₁₃	—	2	4	no	—
198	D₄×C₁₃	—	2	4	no	—
199	D₄×C₁₃	—	2	4	no	—
200	D₄×C₁₃	—	2	2	no	—
201	D₄×C₁₃	—	4	2	no	—
202	D₄×C₁₃	—	4	4	no	—
203	D₄×C₁₃	—	4	2	no	—
204	D₄×C₁₃	—	8	4	no	—
205	D₄×C₁₃	—	8	4	no	—
206	D₄×C₁₃	#121	1	4	yes	—
207	C₂×C₄×C₁₃	—	2	4	no	—
208	C₂×C₄×C₁₃	—	2	8	no	—
209	C₂×C₄×C₁₃	—	2	2	no	—
210	C₂×C₄×C₁₃	—	2	2	no	—
211	C₂×C₄×C₁₃	—	2	1	no	—
212	C₂×C₄×C₁₃	—	2	4	no	—
213	C₂×C₄×C₁₃	—	2	1	no	—
214	C₂×C₄×C₁₃	—	2	2	no	—
215	C₂×C₄×C₁₃	—	2	2	no	—
216	C₂×C₄×C₁₃	—	2	1	no	—
217	C₂×C₄×C₁₃	—	2	4	no	—
218	C₂×C₄×C₁₃	—	2	1	no	—
219	C₂×C₄×C₁₃	—	4	2	no	—
220	C₂×C₄×C₁₃	—	8	2	no	—
221	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
222	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
223	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
224	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
225	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
226	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
227	C₈×C₁₃	—	2	1	no	—
228	C₈×C₁₃	—	2	4	no	—
229	C₈×C₁₃	—	2	1	no	—
230	C₈×C₁₃	—	4	4	no	—
231	C₈×C₁₃	#120	1	2	yes	—
232	C₈×C₁₃	#120	1	2	yes	—
233	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
234	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	4	yes	—
235	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
236	C₂×#131	—	2	8	no	—
237	C₂×#131	—	2	1	no	—
238	C₂×#131	—	2	1	no	—
239	C₂×#131	C₂²×C₁₃	1	2	yes	—
240	C₂×#131	C₂²×C₁₃	1	2	yes	—
241	C₂²×M₁₆	—	2	1	no	—
242	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
243	C₂³×C₈	—	2	1	no	—
244	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
245	C₂×#121	C₂²×C₁₃	1	2	yes	—
246	#472	—	2	8	no	—
247	#466	—	2	1	no	—
248	#466	—	2	1	no	—
249	#466	—	2	1	no	—
250	#466	—	2	1	no	—
251	#449	—	2	4	no	—
252	#448	—	2	2	no	—
253	#447	—	2	2	no	—
254	C₂×#108	C₂²×C₁₃	1	2	yes	complemented
255	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic, complemented
256	#417	C₂²×C₁₃	1	4	yes	—
257	C₂×#102	C₂²×C₁₃	1	2	yes	complemented
258	C₂×#100	C₂²×C₁₃	1	4	yes	complemented
259	#407	C₂²×C₁₃	1	2	yes	—
260	#343	C₂²×C₁₃	1	4	yes	complemented
261	#341	C₂²×C₁₃	1	2	yes	complemented
262	C₂²×C₁₃	—	2	1	no	—
263	C₂²×C₁₃	—	2	1	no	—
264	C₂²×C₁₃	—	2	1	no	—
265	C₂²×C₁₃	—	2	1	no	—
266	C₂²×C₁₃	—	2	1	no	—
267	C₂²×C₁₃	—	2	4	no	—
268	C₂²×C₁₃	—	2	1	no	—
269	C₂²×C₁₃	—	2	1	no	—
270	C₂²×C₁₃	—	4	4	no	—
271	C₂²×C₁₃	—	4	8	no	—
272	C₂²×C₁₃	—	4	2	no	—
273	C₂²×C₁₃	—	4	2	no	—
274	C₂²×C₁₃	—	8	2	no	—
275	C₂²×C₁₃	—	8	2	no	—
276	C₂²×C₁₃	—	8	2	no	—
277	C₂²×C₁₃	—	16	4	no	—
278	C₂²×C₁₃	#472	1	2	yes	complemented
279	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
280	C₂²×C₁₃	#525	1	2	yes	—
281	C₄×C₁₃	—	2	1	no	—
282	C₄×C₁₃	—	2	4	no	—
283	C₄×C₁₃	—	2	1	no	—
284	C₄×C₁₃	—	8	2	no	—
285	C₄×C₁₃	C₂×#120	1	1	yes	characteristic
286	C₄×C₁₃	C₂×#121	1	2	yes	—
287	C₄×C₁₃	#525	1	1	yes	characteristic
288	C₂×#41	—	2	4	no	—
289	C₂×#41	—	2	4	no	—
290	C₂×#41	—	2	1	no	—
291	C₂×#41	—	2	1	no	—
292	C₂×#41	D₄×C₁₃	1	2	yes	—
293	C₂×#41	C₂³×C₁₃	1	2	yes	—
294	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
295	C₂²×D₄	—	2	1	no	—
296	C₂²×D₄	—	2	2	no	—
297	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
298	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
299	C₂³×C₄	—	2	1	no	—
300	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
301	AGL(1,ℤ/8)	—	2	8	no	—
302	AGL(1,ℤ/8)	—	2	8	no	—
303	C₂×SD₁₆	—	2	4	no	—
304	C₂×D₈	—	2	4	no	—
305	C₂×D₈	—	2	1	no	—
306	C₂×D₈	—	2	1	no	—
307	C₂×D₈	—	2	4	no	—
308	#131	—	2	8	no	—
309	#131	—	2	8	no	—
310	#131	—	2	4	no	—
311	#131	—	2	4	no	—
312	#131	—	2	4	no	—
313	#131	D₄×C₁₃	1	8	yes	complemented
314	C₂×M₁₆	—	2	8	no	—
315	C₂×M₁₆	—	2	1	no	—
316	C₂×M₁₆	—	2	4	no	—
317	C₂×M₁₆	—	2	2	no	—
318	C₂×M₁₆	—	2	2	no	—
319	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
320	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
321	C₂²×C₈	—	2	8	no	—
322	C₂²×C₈	—	2	1	no	—
323	C₂²×C₈	—	2	2	no	—
324	C₂²×C₈	—	2	2	no	—
325	C₂²×C₈	—	2	4	no	—
326	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
327	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
328	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
329	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
330	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
331	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
332	#121	—	2	2	no	—
333	#121	—	2	2	no	—
334	#121	—	2	2	no	—
335	#121	—	2	2	no	—
336	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
337	C₂×C₂²⋊C₄	—	2	2	no	—
338	#108	—	2	4	no	—
339	#107	—	2	1	no	—
340	#107	—	2	1	no	—
341	#103	—	2	4	no	—
342	#102	—	2	4	no	—
343	#102	—	2	2	no	—
344	#102	—	2	2	no	—
345	#100	—	2	8	no	—
346	C₂²⋊C₈	—	2	2	no	—
347	C₂²⋊C₈	—	2	2	no	—
348	C₂×C₁₃	—	2	2	no	—
349	C₂×C₁₃	—	2	2	no	—
350	C₂×C₁₃	—	4	1	no	—
351	C₂×C₁₃	—	4	4	no	—
352	C₂×C₁₃	—	16	2	no	—
353	C₂×C₁₃	#2847	1	1	yes	characteristic
354	C₂×C₁₃	C₂×#472	1	1	yes	characteristic
355	C₂×C₁₃	#3067	1	1	yes	characteristic
356	C₂⁴	—	2	1	no	—
357	C₂⁴	—	2	2	no	—
358	C₂⁴	C₁₃×#41	1	1	yes	characteristic
359	#41	—	2	4	no	—
360	#41	—	2	8	no	—
361	#41	—	2	4	no	—
362	#41	—	2	4	no	—
363	#41	—	2	4	no	—
364	#41	—	2	2	no	—
365	#41	—	2	2	no	—
366	#41	C₂×D₄×C₁₃	1	4	yes	—
367	#41	C₁₃×#41	1	4	yes	—
368	C₂×Q₈	—	2	4	no	—
369	C₂×Q₈	—	2	1	no	—
370	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
371	C₂×D₄	—	2	8	no	—
372	C₂×D₄	—	2	2	no	—
373	C₂×D₄	—	2	2	no	—
374	C₂×D₄	—	2	4	no	—
375	C₂×D₄	—	2	1	no	—
376	C₂×D₄	—	2	4	no	—
377	C₂×D₄	—	2	2	no	—
378	C₂×D₄	—	2	2	no	—
379	C₂×D₄	—	2	4	no	—
380	C₂×D₄	—	4	2	no	—
381	C₂×D₄	—	4	2	no	—
382	C₂×D₄	—	8	4	no	—
383	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
384	C₂²×C₄	—	2	4	no	—
385	C₂²×C₄	—	2	4	no	—
386	C₂²×C₄	—	2	1	no	—
387	C₂²×C₄	—	2	2	no	—
388	C₂²×C₄	—	2	2	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	2	2	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
393	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
394	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
395	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
396	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
397	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
398	SD₁₆	—	4	8	no	—
399	D₈	—	4	8	no	—
400	D₈	—	4	2	no	—
401	D₈	—	4	2	no	—
402	M₁₆	—	2	4	no	—
403	M₁₆	—	2	8	no	—
404	M₁₆	—	2	2	no	—
405	M₁₆	—	2	8	no	—
406	M₁₆	—	2	4	no	—
407	M₁₆	—	2	4	no	—
408	M₁₆	C₂×D₄×C₁₃	1	4	yes	—
409	C₂×C₈	—	2	4	no	—
410	C₂×C₈	—	2	8	no	—
411	C₂×C₈	—	2	2	no	—
412	C₂×C₈	—	2	2	no	—
413	C₂×C₈	—	2	2	no	—
414	C₂×C₈	—	2	8	no	—
415	C₂×C₈	—	2	2	no	—
416	C₂×C₈	—	2	2	no	—
417	C₂×C₈	—	2	2	no	—
418	C₂×C₈	—	2	4	no	—
419	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
420	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
421	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
422	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
423	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
424	C₄⋊C₄	—	2	2	no	—
425	C₄⋊C₄	—	2	2	no	—
426	C₂²⋊C₄	—	4	2	no	—
427	C₂²⋊C₄	—	4	2	no	—
428	C₁₃	#32942	1	1	yes	characteristic, direct product factor, Sylow
429	C₂³	—	2	4	no	—
430	C₂³	—	2	2	no	—
431	C₂³	—	2	2	no	—
432	C₂³	—	2	2	no	—
433	C₂³	—	4	1	no	—
434	C₂³	—	4	2	no	—
435	C₂³	—	4	2	no	—
436	C₂³	—	4	2	no	—
437	C₂³	—	4	4	no	—
438	C₂³	—	8	2	no	—
439	C₂³	—	8	2	no	—
440	C₂³	C₁₃×#121	1	1	yes	characteristic
441	C₂³	C₁₃×#121	1	1	yes	characteristic
442	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
443	Q₈	—	2	4	no	—
444	Q₈	—	2	2	no	—
445	Q₈	C₁₃×#121	1	4	yes	—
446	D₄	—	2	8	no	—
447	D₄	—	2	4	no	—
448	D₄	—	2	4	no	—
449	D₄	—	2	4	no	—
450	D₄	—	2	2	no	—
451	D₄	—	4	2	no	—
452	D₄	—	4	4	no	—
453	D₄	—	4	2	no	—
454	D₄	—	8	4	no	—
455	D₄	—	8	4	no	—
456	D₄	C₁₃×#121	1	4	yes	—
457	C₂×C₄	—	2	4	no	—
458	C₂×C₄	—	2	8	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	4	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	2	4	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	—	8	2	no	—
471	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
472	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
473	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
474	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
475	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
476	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
477	C₈	—	2	1	no	—
478	C₈	—	2	4	no	—
479	C₈	—	2	1	no	—
480	C₈	—	4	4	no	—
481	C₈	C₁₃×#120	1	2	yes	—
482	C₈	C₁₃×#120	1	2	yes	—
483	C₂²	—	2	1	no	—
484	C₂²	—	2	1	no	—
485	C₂²	—	2	1	no	—
486	C₂²	—	2	1	no	—
487	C₂²	—	2	1	no	—
488	C₂²	—	2	1	no	—
489	C₂²	—	2	1	no	—
490	C₂²	—	2	4	no	—
491	C₂²	—	4	4	no	—
492	C₂²	—	4	8	no	—
493	C₂²	—	4	2	no	—
494	C₂²	—	4	2	no	—
495	C₂²	—	8	2	no	—
496	C₂²	—	8	2	no	—
497	C₂²	—	8	2	no	—
498	C₂²	—	16	4	no	—
499	C₂²	C₁₃×#472	1	2	yes	complemented
500	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
501	C₂²	C₁₃×#525	1	2	yes	—
502	C₄	—	2	1	no	—
503	C₄	—	2	4	no	—
504	C₄	—	2	1	no	—
505	C₄	—	8	2	no	—
506	C₄	C₂×C₁₃×#120	1	1	yes	characteristic
507	C₄	C₂×C₁₃×#121	1	2	yes	—
508	C₄	C₁₃×#525	1	1	yes	characteristic
509	C₂	—	2	2	no	—
510	C₂	—	2	2	no	—
511	C₂	—	4	1	no	—
512	C₂	—	4	4	no	—
513	C₂	—	16	2	no	—
514	C₂	C₁₃×#2847	1	1	yes	characteristic
515	C₂	C₂×C₁₃×#472	1	1	yes	characteristic
516	C₂	C₁₃×#3067	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
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
1. C₂²×C₁₃×#131	C₂	semidirect
2. C₂×C₁₃×#472	C₂	semidirect
3. C₂×C₁₃×#466	C₂	semidirect
4. C₁₃×#3006	C₂	semidirect
5. C₁₃×#1907	C₂	semidirect
6. C₁₃×#1900	C₂	semidirect
7. C₁₃×#1816	C₂	semidirect
8. C₁₃×#1810	C₂	semidirect
11. C₂²×C₁₃×D₈	C₂²	semidirect
30. C₂×C₁₃×#108	C₂²	semidirect
31. C₂×C₁₃×#107	C₂²	semidirect
33. C₂×C₁₃×#102	C₂²	semidirect
34. C₂×C₁₃×#100	C₂²	semidirect
36. C₁₃×#343	C₂²	semidirect
37. C₁₃×#341	C₂²	semidirect
63. C₁₃×#131	D₄	semidirect
98. #32942	C₁₃	direct (N × H)
171. C₂²×#131	C₂×C₁₃	semidirect
172. C₂×#472	C₂×C₁₃	semidirect
173. C₂×#466	C₂×C₁₃	semidirect
174. #3006	C₂×C₁₃	semidirect
175. #1907	C₂×C₁₃	semidirect
176. #1900	C₂×C₁₃	semidirect
177. #1816	C₂×C₁₃	semidirect
178. #1810	C₂×C₁₃	semidirect
235. C₂²×D₈	C₂²×C₁₃	semidirect
254. C₂×#108	C₂²×C₁₃	semidirect
255. C₂×#107	C₂²×C₁₃	semidirect
257. C₂×#102	C₂²×C₁₃	semidirect
258. C₂×#100	C₂²×C₁₃	semidirect
260. #343	C₂²×C₁₃	semidirect
261. #341	C₂²×C₁₃	semidirect
278. C₂²×C₁₃	#472	semidirect
313. #131	D₄×C₁₃	semidirect
428. C₁₃	#32942	direct (N × H)
499. C₂²	C₁₃×#472	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×#472	2
C₂×C₁₃×#466	2
C₁₃×#3006	2
C₁₃×#1907	2
C₁₃×#1900	2
C₁₃×#1816	2
C₁₃×#1810	2
#32942	13

Subgroups — C13×#32942 #15719281

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#32942 #15719281