Subgroups — C₁₃×#32945 #15719284

Order 3328.

1346 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#568	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#472	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₃×#469	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×#1815	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1811	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	C₁₃×#568	—	2	8	no	—
13	C₂×C₁₃×#131	—	2	2	no	—
14	C₂×C₁₃×#131	C₂²	1	2	yes	—
15	C₂×C₁₃×#131	C₂²	1	2	yes	—
16	C₂²×C₁₃×M₁₆	—	2	2	no	—
17	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#121	C₂²	1	2	yes	—
20	C₁₃×#472	—	2	8	no	—
21	C₁₃×#469	—	2	2	no	—
22	C₁₃×#469	—	2	2	no	—
23	C₁₃×#449	—	2	4	no	—
24	C₁₃×#448	—	2	2	no	—
25	C₁₃×#447	—	2	2	no	—
26	C₂×C₁₃×#108	C₂²	1	2	yes	complemented
27	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic, complemented
28	C₁₃×#417	C₂²	1	4	yes	—
29	C₂×C₁₃×#102	C₂²	1	2	yes	complemented
30	C₂×C₁₃×#100	C₂²	1	4	yes	complemented
31	C₁₃×#407	C₂²	1	2	yes	—
32	C₁₃×#343	C₂²	1	4	yes	complemented
33	C₁₃×#341	C₂²	1	2	yes	complemented
34	C₂×C₁₃×#41	—	2	4	no	—
35	C₂×C₁₃×#41	—	2	4	no	—
36	C₂×C₁₃×#41	—	2	1	no	—
37	C₂×C₁₃×#41	—	2	1	no	—
38	C₂×C₁₃×#41	D₄	1	2	yes	—
39	C₂×C₁₃×#41	C₂³	1	2	yes	—
40	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
41	C₂²×D₄×C₁₃	—	2	1	no	—
42	C₂²×D₄×C₁₃	—	2	2	no	—
43	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
44	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
45	C₂³×C₄×C₁₃	—	2	1	no	—
46	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
47	C₁₃×AGL(1,ℤ/8)	—	2	8	no	—
48	C₁₃×AGL(1,ℤ/8)	—	2	8	no	—
49	C₂×C₁₃×SD₁₆	—	2	4	no	—
50	C₂×C₁₃×D₈	—	2	4	no	—
51	C₂×C₁₃×D₈	—	2	2	no	—
52	C₂×C₁₃×D₈	—	2	4	no	—
53	C₁₃×#131	—	2	16	no	—
54	C₁₃×#131	—	2	4	no	—
55	C₁₃×#131	—	2	4	no	—
56	C₁₃×#131	—	2	4	no	—
57	C₁₃×#131	D₄	1	8	yes	complemented
58	C₂×C₁₃×M₁₆	—	2	16	no	—
59	C₂×C₁₃×M₁₆	—	2	1	no	—
60	C₂×C₁₃×M₁₆	—	2	4	no	—
61	C₂×C₁₃×M₁₆	—	2	2	no	—
62	C₂×C₁₃×M₁₆	—	2	2	no	—
63	C₂×C₁₃×M₁₆	—	2	4	no	—
64	C₂×C₁₃×M₁₆	D₄	1	2	yes	—
65	C₂×C₁₃×M₁₆	D₄	1	2	yes	—
66	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
67	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
68	C₂²×C₈×C₁₃	—	2	1	no	—
69	C₂²×C₈×C₁₃	—	2	2	no	—
70	C₂²×C₈×C₁₃	—	2	2	no	—
71	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
73	C₁₃×#121	—	2	2	no	—
74	C₁₃×#121	—	2	2	no	—
75	C₁₃×#121	—	2	2	no	—
76	C₁₃×#121	—	2	2	no	—
77	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
78	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
79	C₁₃×#108	—	2	4	no	—
80	C₁₃×#106	—	2	2	no	—
81	C₁₃×#103	—	2	4	no	—
82	C₁₃×#102	—	2	4	no	—
83	C₁₃×#102	—	2	4	no	—
84	C₁₃×#100	—	2	8	no	—
85	C₁₃×C₂²⋊C₈	—	2	2	no	—
86	C₁₃×C₂²⋊C₈	—	2	2	no	—
87	#32945	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
88	C₂⁴×C₁₃	—	2	1	no	—
89	C₂⁴×C₁₃	—	2	2	no	—
90	C₂⁴×C₁₃	#41	1	1	yes	characteristic
91	C₁₃×#41	—	2	4	no	—
92	C₁₃×#41	—	2	8	no	—
93	C₁₃×#41	—	2	4	no	—
94	C₁₃×#41	—	2	4	no	—
95	C₁₃×#41	—	2	4	no	—
96	C₁₃×#41	—	2	2	no	—
97	C₁₃×#41	—	2	2	no	—
98	C₁₃×#41	C₂×D₄	1	4	yes	—
99	C₁₃×#41	#41	1	4	yes	—
100	C₂×Q₈×C₁₃	—	2	4	no	—
101	C₂×Q₈×C₁₃	—	2	1	no	—
102	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
103	C₂×D₄×C₁₃	—	2	8	no	—
104	C₂×D₄×C₁₃	—	2	2	no	—
105	C₂×D₄×C₁₃	—	2	2	no	—
106	C₂×D₄×C₁₃	—	2	4	no	—
107	C₂×D₄×C₁₃	—	2	1	no	—
108	C₂×D₄×C₁₃	—	2	4	no	—
109	C₂×D₄×C₁₃	—	2	2	no	—
110	C₂×D₄×C₁₃	—	2	2	no	—
111	C₂×D₄×C₁₃	—	2	4	no	—
112	C₂×D₄×C₁₃	—	4	2	no	—
113	C₂×D₄×C₁₃	—	4	2	no	—
114	C₂×D₄×C₁₃	—	8	4	no	—
115	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₁₃	—	2	4	no	—
117	C₂²×C₄×C₁₃	—	2	4	no	—
118	C₂²×C₄×C₁₃	—	2	1	no	—
119	C₂²×C₄×C₁₃	—	2	2	no	—
120	C₂²×C₄×C₁₃	—	2	2	no	—
121	C₂²×C₄×C₁₃	—	2	2	no	—
122	C₂²×C₄×C₁₃	—	2	2	no	—
123	C₂²×C₄×C₁₃	—	2	2	no	—
124	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
129	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
130	C₁₃×SD₁₆	—	4	8	no	—
131	C₁₃×D₈	—	4	8	no	—
132	C₁₃×D₈	—	4	4	no	—
133	C₁₃×M₁₆	—	2	4	no	—
134	C₁₃×M₁₆	—	2	8	no	—
135	C₁₃×M₁₆	—	2	2	no	—
136	C₁₃×M₁₆	—	2	4	no	—
137	C₁₃×M₁₆	—	2	8	no	—
138	C₁₃×M₁₆	—	2	4	no	—
139	C₁₃×M₁₆	—	2	4	no	—
140	C₁₃×M₁₆	—	2	4	no	—
141	C₁₃×M₁₆	C₂×D₄	1	4	yes	—
142	C₂×C₈×C₁₃	—	2	4	no	—
143	C₂×C₈×C₁₃	—	2	8	no	—
144	C₂×C₈×C₁₃	—	2	2	no	—
145	C₂×C₈×C₁₃	—	2	2	no	—
146	C₂×C₈×C₁₃	—	2	8	no	—
147	C₂×C₈×C₁₃	—	2	4	no	—
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	4	yes	—
151	C₁₃×C₄⋊C₄	—	2	2	no	—
152	C₁₃×C₄⋊C₄	—	2	2	no	—
153	C₁₃×C₂²⋊C₄	—	4	2	no	—
154	C₁₃×C₂²⋊C₄	—	4	2	no	—
155	C₂×#568	C₂×C₁₃	1	1	yes	characteristic, complemented
156	C₂×#472	C₂×C₁₃	1	2	yes	complemented
157	C₂×#469	C₂×C₁₃	1	1	yes	characteristic, complemented
158	#3006	C₂×C₁₃	1	2	yes	complemented
159	#1907	C₂×C₁₃	1	4	yes	complemented
160	#1900	C₂×C₁₃	1	2	yes	complemented
161	#1815	C₂×C₁₃	1	2	yes	complemented
162	#1811	C₂×C₁₃	1	1	yes	characteristic, complemented
163	C₂³×C₁₃	—	2	4	no	—
164	C₂³×C₁₃	—	2	2	no	—
165	C₂³×C₁₃	—	2	2	no	—
166	C₂³×C₁₃	—	4	2	no	—
167	C₂³×C₁₃	—	4	2	no	—
168	C₂³×C₁₃	—	4	4	no	—
169	C₂³×C₁₃	—	8	2	no	—
170	C₂³×C₁₃	—	8	2	no	—
171	C₂³×C₁₃	—	8	2	no	—
172	C₂³×C₁₃	#121	1	1	yes	characteristic
173	C₂³×C₁₃	#121	1	1	yes	characteristic
174	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
175	Q₈×C₁₃	—	2	4	no	—
176	Q₈×C₁₃	—	2	2	no	—
177	Q₈×C₁₃	#121	1	4	yes	—
178	D₄×C₁₃	—	2	8	no	—
179	D₄×C₁₃	—	2	4	no	—
180	D₄×C₁₃	—	2	4	no	—
181	D₄×C₁₃	—	2	4	no	—
182	D₄×C₁₃	—	2	2	no	—
183	D₄×C₁₃	—	4	2	no	—
184	D₄×C₁₃	—	4	4	no	—
185	D₄×C₁₃	—	4	2	no	—
186	D₄×C₁₃	—	8	4	no	—
187	D₄×C₁₃	—	8	4	no	—
188	D₄×C₁₃	#121	1	4	yes	—
189	C₂×C₄×C₁₃	—	2	4	no	—
190	C₂×C₄×C₁₃	—	2	8	no	—
191	C₂×C₄×C₁₃	—	2	2	no	—
192	C₂×C₄×C₁₃	—	2	2	no	—
193	C₂×C₄×C₁₃	—	2	4	no	—
194	C₂×C₄×C₁₃	—	2	1	no	—
195	C₂×C₄×C₁₃	—	2	1	no	—
196	C₂×C₄×C₁₃	—	2	2	no	—
197	C₂×C₄×C₁₃	—	2	2	no	—
198	C₂×C₄×C₁₃	—	2	1	no	—
199	C₂×C₄×C₁₃	—	2	4	no	—
200	C₂×C₄×C₁₃	—	2	1	no	—
201	C₂×C₄×C₁₃	—	4	2	no	—
202	C₂×C₄×C₁₃	—	8	2	no	—
203	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
204	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
205	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
206	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
207	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
208	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
209	C₈×C₁₃	—	2	4	no	—
210	C₈×C₁₃	—	2	2	no	—
211	C₈×C₁₃	—	4	4	no	—
212	C₈×C₁₃	#120	1	4	yes	—
213	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
214	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	4	yes	—
215	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
216	#568	—	2	8	no	—
217	C₂×#131	—	2	2	no	—
218	C₂×#131	C₂²×C₁₃	1	2	yes	—
219	C₂×#131	C₂²×C₁₃	1	2	yes	—
220	C₂²×M₁₆	—	2	2	no	—
221	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
222	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
223	C₂×#121	C₂²×C₁₃	1	2	yes	—
224	#472	—	2	8	no	—
225	#469	—	2	2	no	—
226	#469	—	2	2	no	—
227	#449	—	2	4	no	—
228	#448	—	2	2	no	—
229	#447	—	2	2	no	—
230	C₂×#108	C₂²×C₁₃	1	2	yes	complemented
231	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic, complemented
232	#417	C₂²×C₁₃	1	4	yes	—
233	C₂×#102	C₂²×C₁₃	1	2	yes	complemented
234	C₂×#100	C₂²×C₁₃	1	4	yes	complemented
235	#407	C₂²×C₁₃	1	2	yes	—
236	#343	C₂²×C₁₃	1	4	yes	complemented
237	#341	C₂²×C₁₃	1	2	yes	complemented
238	C₂²×C₁₃	—	2	2	no	—
239	C₂²×C₁₃	—	2	1	no	—
240	C₂²×C₁₃	—	2	1	no	—
241	C₂²×C₁₃	—	2	4	no	—
242	C₂²×C₁₃	—	2	2	no	—
243	C₂²×C₁₃	—	2	2	no	—
244	C₂²×C₁₃	—	4	4	no	—
245	C₂²×C₁₃	—	8	2	no	—
246	C₂²×C₁₃	—	8	4	no	—
247	C₂²×C₁₃	—	8	2	no	—
248	C₂²×C₁₃	—	8	2	no	—
249	C₂²×C₁₃	—	8	2	no	—
250	C₂²×C₁₃	—	16	4	no	—
251	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
252	C₂²×C₁₃	#525	1	2	yes	—
253	C₄×C₁₃	—	2	1	no	—
254	C₄×C₁₃	—	2	4	no	—
255	C₄×C₁₃	—	2	1	no	—
256	C₄×C₁₃	—	8	2	no	—
257	C₄×C₁₃	C₂×#120	1	1	yes	characteristic
258	C₄×C₁₃	C₂×#121	1	2	yes	—
259	C₄×C₁₃	#525	1	1	yes	characteristic
260	C₂×#41	—	2	4	no	—
261	C₂×#41	—	2	4	no	—
262	C₂×#41	—	2	1	no	—
263	C₂×#41	—	2	1	no	—
264	C₂×#41	D₄×C₁₃	1	2	yes	—
265	C₂×#41	C₂³×C₁₃	1	2	yes	—
266	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
267	C₂²×D₄	—	2	1	no	—
268	C₂²×D₄	—	2	2	no	—
269	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
270	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
271	C₂³×C₄	—	2	1	no	—
272	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
273	AGL(1,ℤ/8)	—	2	8	no	—
274	AGL(1,ℤ/8)	—	2	8	no	—
275	C₂×SD₁₆	—	2	4	no	—
276	C₂×D₈	—	2	4	no	—
277	C₂×D₈	—	2	2	no	—
278	C₂×D₈	—	2	4	no	—
279	#131	—	2	16	no	—
280	#131	—	2	4	no	—
281	#131	—	2	4	no	—
282	#131	—	2	4	no	—
283	#131	D₄×C₁₃	1	8	yes	complemented
284	C₂×M₁₆	—	2	16	no	—
285	C₂×M₁₆	—	2	1	no	—
286	C₂×M₁₆	—	2	4	no	—
287	C₂×M₁₆	—	2	2	no	—
288	C₂×M₁₆	—	2	2	no	—
289	C₂×M₁₆	—	2	4	no	—
290	C₂×M₁₆	D₄×C₁₃	1	2	yes	—
291	C₂×M₁₆	D₄×C₁₃	1	2	yes	—
292	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
293	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
294	C₂²×C₈	—	2	1	no	—
295	C₂²×C₈	—	2	2	no	—
296	C₂²×C₈	—	2	2	no	—
297	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
298	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
299	#121	—	2	2	no	—
300	#121	—	2	2	no	—
301	#121	—	2	2	no	—
302	#121	—	2	2	no	—
303	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
304	C₂×C₂²⋊C₄	—	2	2	no	—
305	#108	—	2	4	no	—
306	#106	—	2	2	no	—
307	#103	—	2	4	no	—
308	#102	—	2	4	no	—
309	#102	—	2	4	no	—
310	#100	—	2	8	no	—
311	C₂²⋊C₈	—	2	2	no	—
312	C₂²⋊C₈	—	2	2	no	—
313	C₂×C₁₃	—	2	2	no	—
314	C₂×C₁₃	—	4	1	no	—
315	C₂×C₁₃	—	4	1	no	—
316	C₂×C₁₃	—	4	4	no	—
317	C₂×C₁₃	—	16	2	no	—
318	C₂×C₁₃	#2847	1	1	yes	characteristic
319	C₂×C₁₃	#3068	1	2	yes	—
320	C₂⁴	—	2	1	no	—
321	C₂⁴	—	2	2	no	—
322	C₂⁴	C₁₃×#41	1	1	yes	characteristic
323	#41	—	2	4	no	—
324	#41	—	2	8	no	—
325	#41	—	2	4	no	—
326	#41	—	2	4	no	—
327	#41	—	2	4	no	—
328	#41	—	2	2	no	—
329	#41	—	2	2	no	—
330	#41	C₂×D₄×C₁₃	1	4	yes	—
331	#41	C₁₃×#41	1	4	yes	—
332	C₂×Q₈	—	2	4	no	—
333	C₂×Q₈	—	2	1	no	—
334	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
335	C₂×D₄	—	2	8	no	—
336	C₂×D₄	—	2	2	no	—
337	C₂×D₄	—	2	2	no	—
338	C₂×D₄	—	2	4	no	—
339	C₂×D₄	—	2	1	no	—
340	C₂×D₄	—	2	4	no	—
341	C₂×D₄	—	2	2	no	—
342	C₂×D₄	—	2	2	no	—
343	C₂×D₄	—	2	4	no	—
344	C₂×D₄	—	4	2	no	—
345	C₂×D₄	—	4	2	no	—
346	C₂×D₄	—	8	4	no	—
347	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
348	C₂²×C₄	—	2	4	no	—
349	C₂²×C₄	—	2	4	no	—
350	C₂²×C₄	—	2	1	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
357	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
358	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
359	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
360	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
361	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
362	SD₁₆	—	4	8	no	—
363	D₈	—	4	8	no	—
364	D₈	—	4	4	no	—
365	M₁₆	—	2	4	no	—
366	M₁₆	—	2	8	no	—
367	M₁₆	—	2	2	no	—
368	M₁₆	—	2	4	no	—
369	M₁₆	—	2	8	no	—
370	M₁₆	—	2	4	no	—
371	M₁₆	—	2	4	no	—
372	M₁₆	—	2	4	no	—
373	M₁₆	C₂×D₄×C₁₃	1	4	yes	—
374	C₂×C₈	—	2	4	no	—
375	C₂×C₈	—	2	8	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	2	8	no	—
379	C₂×C₈	—	2	4	no	—
380	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
381	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
382	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	—	2	2	no	—
385	C₂²⋊C₄	—	4	2	no	—
386	C₂²⋊C₄	—	4	2	no	—
387	C₁₃	#32945	1	1	yes	characteristic, direct product factor, Sylow
388	C₂³	—	2	4	no	—
389	C₂³	—	2	2	no	—
390	C₂³	—	2	2	no	—
391	C₂³	—	4	2	no	—
392	C₂³	—	4	2	no	—
393	C₂³	—	4	4	no	—
394	C₂³	—	8	2	no	—
395	C₂³	—	8	2	no	—
396	C₂³	—	8	2	no	—
397	C₂³	C₁₃×#121	1	1	yes	characteristic
398	C₂³	C₁₃×#121	1	1	yes	characteristic
399	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
400	Q₈	—	2	4	no	—
401	Q₈	—	2	2	no	—
402	Q₈	C₁₃×#121	1	4	yes	—
403	D₄	—	2	8	no	—
404	D₄	—	2	4	no	—
405	D₄	—	2	4	no	—
406	D₄	—	2	4	no	—
407	D₄	—	2	2	no	—
408	D₄	—	4	2	no	—
409	D₄	—	4	4	no	—
410	D₄	—	4	2	no	—
411	D₄	—	8	4	no	—
412	D₄	—	8	4	no	—
413	D₄	C₁₃×#121	1	4	yes	—
414	C₂×C₄	—	2	4	no	—
415	C₂×C₄	—	2	8	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	4	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	4	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	8	2	no	—
428	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
429	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
430	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
431	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
432	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
433	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
434	C₈	—	2	4	no	—
435	C₈	—	2	2	no	—
436	C₈	—	4	4	no	—
437	C₈	C₁₃×#120	1	4	yes	—
438	C₂²	—	2	2	no	—
439	C₂²	—	2	2	no	—
440	C₂²	—	2	2	no	—
441	C₂²	—	2	1	no	—
442	C₂²	—	2	1	no	—
443	C₂²	—	2	4	no	—
444	C₂²	—	4	4	no	—
445	C₂²	—	8	2	no	—
446	C₂²	—	8	4	no	—
447	C₂²	—	8	2	no	—
448	C₂²	—	8	2	no	—
449	C₂²	—	8	2	no	—
450	C₂²	—	16	4	no	—
451	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
452	C₂²	C₁₃×#525	1	2	yes	—
453	C₄	—	2	1	no	—
454	C₄	—	2	4	no	—
455	C₄	—	2	1	no	—
456	C₄	—	8	2	no	—
457	C₄	C₂×C₁₃×#120	1	1	yes	characteristic
458	C₄	C₂×C₁₃×#121	1	2	yes	—
459	C₄	C₁₃×#525	1	1	yes	characteristic
460	C₂	—	2	2	no	—
461	C₂	—	4	1	no	—
462	C₂	—	4	1	no	—
463	C₂	—	4	4	no	—
464	C₂	—	16	2	no	—
465	C₂	C₁₃×#2847	1	1	yes	characteristic
466	C₂	C₁₃×#3068	1	2	yes	—

	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. C₂×C₁₃×#568	C₂	semidirect
2. C₂×C₁₃×#472	C₂	semidirect
3. C₂×C₁₃×#469	C₂	semidirect
4. C₁₃×#3006	C₂	semidirect
5. C₁₃×#1907	C₂	semidirect
6. C₁₃×#1900	C₂	semidirect
7. C₁₃×#1815	C₂	semidirect
8. C₁₃×#1811	C₂	semidirect
11. C₂²×C₁₃×D₈	C₂²	semidirect
26. C₂×C₁₃×#108	C₂²	semidirect
27. C₂×C₁₃×#106	C₂²	semidirect
29. C₂×C₁₃×#102	C₂²	semidirect
30. C₂×C₁₃×#100	C₂²	semidirect
32. C₁₃×#343	C₂²	semidirect
33. C₁₃×#341	C₂²	semidirect
57. C₁₃×#131	D₄	semidirect
87. #32945	C₁₃	direct (N × H)
155. C₂×#568	C₂×C₁₃	semidirect
156. C₂×#472	C₂×C₁₃	semidirect
157. C₂×#469	C₂×C₁₃	semidirect
158. #3006	C₂×C₁₃	semidirect
159. #1907	C₂×C₁₃	semidirect
160. #1900	C₂×C₁₃	semidirect
161. #1815	C₂×C₁₃	semidirect
162. #1811	C₂×C₁₃	semidirect
215. C₂²×D₈	C₂²×C₁₃	semidirect
230. C₂×#108	C₂²×C₁₃	semidirect
231. C₂×#106	C₂²×C₁₃	semidirect
233. C₂×#102	C₂²×C₁₃	semidirect
234. C₂×#100	C₂²×C₁₃	semidirect
236. #343	C₂²×C₁₃	semidirect
237. #341	C₂²×C₁₃	semidirect
283. #131	D₄×C₁₃	semidirect
387. C₁₃	#32945	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×#568	2
C₂×C₁₃×#472	2
C₂×C₁₃×#469	2
C₁₃×#3006	2
C₁₃×#1907	2
C₁₃×#1900	2
C₁₃×#1815	2
C₁₃×#1811	2
#32945	13

Subgroups — C13×#32945 #15719284

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#32945 #15719284