Subgroups — C₁₃×#33540 #15719879

Order 3328.

1078 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#578	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3414	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#510	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3067	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2195	C₂	1	4	yes	maximal, complemented
6	C₁₃×#2193	C₂	1	4	yes	maximal, complemented
7	C₂×C₁₃×#362	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2143	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2117	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×2₋¹⁺⁴	—	2	1	no	—
11	C₁₃×#578	—	2	2	no	—
12	C₁₃×#578	—	2	2	no	—
13	C₁₃×#578	—	2	2	no	—
14	C₁₃×#578	C₂²	1	4	yes	—
15	C₁₃×#575	—	2	1	no	—
16	C₂×C₁₃×#137	—	2	2	no	—
17	C₂×C₁₃×#137	—	2	1	no	—
18	C₂×C₁₃×#135	—	2	1	no	—
19	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
21	C₂²×C₁₃×Q₁₆	—	2	1	no	—
22	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
24	C₁₃×#510	—	2	2	no	—
25	C₁₃×#510	—	2	2	no	—
26	C₁₃×#510	—	2	1	no	—
27	C₁₃×#510	C₂²	1	2	yes	complemented
28	C₁₃×#509	—	2	1	no	—
29	C₁₃×#509	C₂²	1	2	yes	complemented
30	C₁₃×#508	—	2	2	no	—
31	C₂×C₁₃×Q₃₂	C₂²	1	2	yes	complemented
32	C₂×C₁₃×SD₃₂	C₂²	1	2	yes	complemented
33	C₂×C₁₃×M₃₂	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×M₃₂	C₂²	1	1	yes	characteristic
35	C₁₃×#473	C₂²	1	2	yes	complemented
36	C₁₃×#472	C₂²	1	2	yes	complemented
37	C₁₃×#471	—	2	2	no	—
38	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
39	C₁₃×#413	—	2	1	no	—
40	C₁₃×#362	C₂²	1	4	yes	complemented
41	C₁₃×#359	C₂²	1	4	yes	complemented
42	C₁₃×#350	C₂²	1	4	yes	complemented
43	C₁₃×2₋¹⁺⁴	—	2	4	no	—
44	C₁₃×2₋¹⁺⁴	—	2	4	no	—
45	C₁₃×2₋¹⁺⁴	—	4	2	no	—
46	C₁₃×2₋¹⁺⁴	—	4	2	no	—
47	C₂×C₁₃×#41	—	2	2	no	—
48	C₂×C₁₃×#41	—	2	1	no	—
49	C₂×C₁₃×#41	—	2	1	no	—
50	C₂×C₁₃×#41	—	4	2	no	—
51	C₂×C₁₃×#41	—	4	1	no	—
52	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
53	C₂²×Q₈×C₁₃	—	2	2	no	—
54	C₂²×Q₈×C₁₃	—	2	1	no	—
55	C₂²×Q₈×C₁₃	—	4	1	no	—
56	C₁₃×#137	—	2	4	no	—
57	C₁₃×#137	—	2	8	no	—
58	C₁₃×#137	—	2	8	no	—
59	C₁₃×#137	—	2	2	no	—
60	C₁₃×#137	—	2	4	no	—
61	C₁₃×#137	—	4	1	no	—
62	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
63	C₁₃×AGL(1,ℤ/8)	—	4	1	no	—
64	C₁₃×#135	—	2	4	no	—
65	C₁₃×#135	—	2	4	no	—
66	C₁₃×#135	—	2	1	no	—
67	C₁₃×#135	—	2	1	no	—
68	C₁₃×#135	—	2	1	no	—
69	C₁₃×#135	—	2	1	no	—
70	C₁₃×#135	—	2	1	no	—
71	C₁₃×#135	—	2	1	no	—
72	C₁₃×#135	—	4	2	no	—
73	C₁₃×#135	D₄	1	2	yes	—
74	C₁₃×#135	C₂³	1	2	yes	—
75	C₂×C₁₃×Q₁₆	—	2	2	no	—
76	C₂×C₁₃×Q₁₆	—	2	4	no	—
77	C₂×C₁₃×Q₁₆	—	2	4	no	—
78	C₂×C₁₃×Q₁₆	—	2	1	no	—
79	C₂×C₁₃×Q₁₆	—	2	1	no	—
80	C₂×C₁₃×Q₁₆	—	2	1	no	—
81	C₂×C₁₃×Q₁₆	D₄	1	1	yes	characteristic
82	C₂×C₁₃×Q₁₆	D₄	1	2	yes	—
83	C₂×C₁₃×Q₁₆	D₄	1	2	yes	—
84	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
85	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
86	C₂×C₁₃×SD₁₆	—	2	2	no	—
87	C₂×C₁₃×SD₁₆	—	2	1	no	—
88	C₂×C₁₃×SD₁₆	—	2	1	no	—
89	C₂×C₁₃×D₈	D₄	1	1	yes	characteristic
90	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
91	C₁₃×#131	—	2	1	no	—
92	C₁₃×#131	—	2	1	no	—
93	C₁₃×#131	D₄	1	2	yes	—
94	C₁₃×#131	C₂³	1	2	yes	—
95	C₂×C₁₃×M₁₆	—	2	1	no	—
96	C₂×C₁₃×M₁₆	—	2	1	no	—
97	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
98	C₂²×C₈×C₁₃	—	2	1	no	—
99	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
100	C₁₃×Q₃₂	—	2	4	no	—
101	C₁₃×Q₃₂	—	2	2	no	—
102	C₁₃×SD₃₂	—	2	4	no	—
103	C₁₃×SD₃₂	—	2	2	no	—
104	C₁₃×SD₃₂	—	2	2	no	—
105	C₁₃×D₁₆	—	2	2	no	—
106	C₁₃×M₃₂	—	2	1	no	—
107	C₁₃×M₃₂	—	2	1	no	—
108	C₁₃×M₃₂	—	2	1	no	—
109	C₁₃×M₃₂	C₂³	1	2	yes	—
110	C₂×C₁₃×C₁₆	—	2	1	no	—
111	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
112	C₁₃×#108	—	2	1	no	—
113	C₁₃×#108	C₂³	1	2	yes	—
114	C₁₃×#101	—	2	2	no	—
115	C₁₃×#100	—	2	2	no	—
116	#33540	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
117	C₁₃×#41	—	2	1	no	—
118	C₁₃×#41	—	2	1	no	—
119	C₁₃×#41	—	2	8	no	—
120	C₁₃×#41	—	2	2	no	—
121	C₁₃×#41	—	2	2	no	—
122	C₁₃×#41	—	4	4	no	—
123	C₁₃×#41	—	4	8	no	—
124	C₁₃×#41	—	4	8	no	—
125	C₁₃×#41	—	4	4	no	—
126	C₁₃×#41	—	4	4	no	—
127	C₁₃×#41	—	4	1	no	—
128	C₁₃×#41	—	4	1	no	—
129	C₁₃×#41	—	4	1	no	—
130	C₁₃×#41	—	4	1	no	—
131	C₁₃×#41	—	4	1	no	—
132	C₁₃×#41	—	4	1	no	—
133	C₁₃×#41	D₈	1	2	yes	—
134	C₁₃×#41	C₂×D₄	1	2	yes	—
135	C₂×Q₈×C₁₃	—	2	8	no	—
136	C₂×Q₈×C₁₃	—	2	2	no	—
137	C₂×Q₈×C₁₃	—	2	1	no	—
138	C₂×Q₈×C₁₃	—	2	2	no	—
139	C₂×Q₈×C₁₃	—	2	2	no	—
140	C₂×Q₈×C₁₃	—	2	1	no	—
141	C₂×Q₈×C₁₃	—	4	2	no	—
142	C₂×Q₈×C₁₃	—	4	4	no	—
143	C₂×Q₈×C₁₃	—	4	4	no	—
144	C₂×Q₈×C₁₃	—	4	4	no	—
145	C₂×Q₈×C₁₃	—	4	1	no	—
146	C₂×Q₈×C₁₃	—	4	1	no	—
147	C₂×Q₈×C₁₃	—	4	1	no	—
148	C₂×Q₈×C₁₃	D₈	1	1	yes	characteristic
149	C₂×D₄×C₁₃	—	2	1	no	—
150	C₂×D₄×C₁₃	—	2	1	no	—
151	C₂×D₄×C₁₃	—	2	1	no	—
152	C₂×D₄×C₁₃	—	4	2	no	—
153	C₂×D₄×C₁₃	—	4	1	no	—
154	C₂×D₄×C₁₃	—	4	1	no	—
155	C₂×D₄×C₁₃	D₈	1	1	yes	characteristic
156	C₂²×C₄×C₁₃	—	2	1	no	—
157	C₂²×C₄×C₁₃	—	4	2	no	—
158	C₂²×C₄×C₁₃	—	4	2	no	—
159	C₂²×C₄×C₁₃	—	4	1	no	—
160	C₂²×C₄×C₁₃	—	4	1	no	—
161	C₂²×C₄×C₁₃	—	4	1	no	—
162	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
163	C₁₃×Q₁₆	—	2	8	no	—
164	C₁₃×Q₁₆	—	2	1	no	—
165	C₁₃×Q₁₆	—	2	2	no	—
166	C₁₃×Q₁₆	—	2	2	no	—
167	C₁₃×Q₁₆	—	2	2	no	—
168	C₁₃×Q₁₆	—	2	1	no	—
169	C₁₃×Q₁₆	—	2	1	no	—
170	C₁₃×Q₁₆	—	4	2	no	—
171	C₁₃×Q₁₆	C₂×D₄	1	2	yes	—
172	C₁₃×Q₁₆	C₂×D₄	1	4	yes	—
173	C₁₃×SD₁₆	—	2	8	no	—
174	C₁₃×SD₁₆	—	2	2	no	—
175	C₁₃×SD₁₆	—	2	2	no	—
176	C₁₃×SD₁₆	—	4	2	no	—
177	C₁₃×SD₁₆	—	4	2	no	—
178	C₁₃×SD₁₆	—	4	1	no	—
179	C₁₃×SD₁₆	—	4	1	no	—
180	C₁₃×D₈	—	2	1	no	—
181	C₁₃×D₈	—	2	1	no	—
182	C₁₃×D₈	—	2	1	no	—
183	C₁₃×D₈	—	4	2	no	—
184	C₁₃×D₈	C₂×D₄	1	2	yes	—
185	C₁₃×M₁₆	—	2	1	no	—
186	C₁₃×M₁₆	—	2	2	no	—
187	C₁₃×M₁₆	—	2	2	no	—
188	C₁₃×M₁₆	—	2	2	no	—
189	C₁₃×M₁₆	—	4	1	no	—
190	C₁₃×M₁₆	C₂×D₄	1	2	yes	—
191	C₂×C₈×C₁₃	—	2	1	no	—
192	C₂×C₈×C₁₃	—	2	2	no	—
193	C₂×C₈×C₁₃	—	2	2	no	—
194	C₂×C₈×C₁₃	—	4	1	no	—
195	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
196	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
197	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
198	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
199	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
200	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
201	C₁₃×C₁₆	—	2	2	no	—
202	C₁₃×C₁₆	—	2	2	no	—
203	C₂×#578	C₂×C₁₃	1	1	yes	characteristic, complemented
204	#3414	C₂×C₁₃	1	1	yes	characteristic, complemented
205	C₂×#510	C₂×C₁₃	1	1	yes	characteristic, complemented
206	#3067	C₂×C₁₃	1	1	yes	characteristic, complemented
207	#2195	C₂×C₁₃	1	4	yes	complemented
208	#2193	C₂×C₁₃	1	4	yes	complemented
209	C₂×#362	C₂×C₁₃	1	1	yes	characteristic, complemented
210	#2143	C₂×C₁₃	1	1	yes	characteristic, complemented
211	#2117	C₂×C₁₃	1	1	yes	characteristic, complemented
212	C₂³×C₁₃	—	2	1	no	—
213	C₂³×C₁₃	—	4	1	no	—
214	C₂³×C₁₃	—	4	1	no	—
215	C₂³×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
216	Q₈×C₁₃	—	2	1	no	—
217	Q₈×C₁₃	—	2	4	no	—
218	Q₈×C₁₃	—	2	2	no	—
219	Q₈×C₁₃	—	4	8	no	—
220	Q₈×C₁₃	—	4	2	no	—
221	Q₈×C₁₃	—	4	1	no	—
222	Q₈×C₁₃	—	4	2	no	—
223	Q₈×C₁₃	—	4	2	no	—
224	Q₈×C₁₃	—	4	1	no	—
225	Q₈×C₁₃	—	4	1	no	—
226	Q₈×C₁₃	C₂×D₈	1	2	yes	—
227	D₄×C₁₃	—	2	2	no	—
228	D₄×C₁₃	—	2	2	no	—
229	D₄×C₁₃	—	2	2	no	—
230	D₄×C₁₃	—	2	1	no	—
231	D₄×C₁₃	—	4	8	no	—
232	D₄×C₁₃	—	4	2	no	—
233	D₄×C₁₃	—	4	2	no	—
234	D₄×C₁₃	—	4	1	no	—
235	D₄×C₁₃	—	4	1	no	—
236	D₄×C₁₃	—	4	1	no	—
237	D₄×C₁₃	—	8	1	no	—
238	D₄×C₁₃	—	8	1	no	—
239	D₄×C₁₃	C₂×D₈	1	2	yes	—
240	C₂×C₄×C₁₃	—	2	1	no	—
241	C₂×C₄×C₁₃	—	2	2	no	—
242	C₂×C₄×C₁₃	—	2	2	no	—
243	C₂×C₄×C₁₃	—	4	8	no	—
244	C₂×C₄×C₁₃	—	4	8	no	—
245	C₂×C₄×C₁₃	—	4	2	no	—
246	C₂×C₄×C₁₃	—	4	2	no	—
247	C₂×C₄×C₁₃	—	4	1	no	—
248	C₂×C₄×C₁₃	—	4	2	no	—
249	C₂×C₄×C₁₃	—	4	2	no	—
250	C₂×C₄×C₁₃	—	4	2	no	—
251	C₂×C₄×C₁₃	—	4	1	no	—
252	C₂×C₄×C₁₃	—	8	1	no	—
253	C₂×C₄×C₁₃	—	8	1	no	—
254	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
255	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
256	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
257	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
258	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
259	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
260	C₈×C₁₃	—	2	2	no	—
261	C₈×C₁₃	—	4	2	no	—
262	C₈×C₁₃	#120	1	1	yes	characteristic
263	C₈×C₁₃	#120	1	1	yes	characteristic
264	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
265	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
266	C₂×2₋¹⁺⁴	—	2	1	no	—
267	#578	—	2	2	no	—
268	#578	—	2	2	no	—
269	#578	—	2	2	no	—
270	#578	C₂²×C₁₃	1	4	yes	—
271	#575	—	2	1	no	—
272	C₂×#137	—	2	2	no	—
273	C₂×#137	—	2	1	no	—
274	C₂×#135	—	2	1	no	—
275	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
276	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
277	C₂²×Q₁₆	—	2	1	no	—
278	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
279	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
280	#510	—	2	2	no	—
281	#510	—	2	2	no	—
282	#510	—	2	1	no	—
283	#510	C₂²×C₁₃	1	2	yes	complemented
284	#509	—	2	1	no	—
285	#509	C₂²×C₁₃	1	2	yes	complemented
286	#508	—	2	2	no	—
287	C₂×Q₃₂	C₂²×C₁₃	1	2	yes	complemented
288	C₂×SD₃₂	C₂²×C₁₃	1	2	yes	complemented
289	C₂×M₃₂	C₂²×C₁₃	1	1	yes	characteristic
290	C₂×M₃₂	C₂²×C₁₃	1	1	yes	characteristic
291	#473	C₂²×C₁₃	1	2	yes	complemented
292	#472	C₂²×C₁₃	1	2	yes	complemented
293	#471	—	2	2	no	—
294	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
295	#413	—	2	1	no	—
296	#362	C₂²×C₁₃	1	4	yes	complemented
297	#359	C₂²×C₁₃	1	4	yes	complemented
298	#350	C₂²×C₁₃	1	4	yes	complemented
299	C₂²×C₁₃	—	2	2	no	—
300	C₂²×C₁₃	—	4	1	no	—
301	C₂²×C₁₃	—	4	2	no	—
302	C₂²×C₁₃	—	4	2	no	—
303	C₂²×C₁₃	—	8	2	no	—
304	C₂²×C₁₃	—	8	1	no	—
305	C₂²×C₁₃	—	16	1	no	—
306	C₂²×C₁₃	#447	1	1	yes	characteristic
307	C₂²×C₁₃	#447	1	1	yes	characteristic
308	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
309	C₄×C₁₃	—	2	2	no	—
310	C₄×C₁₃	—	4	4	no	—
311	C₄×C₁₃	—	4	2	no	—
312	C₄×C₁₃	—	8	1	no	—
313	C₄×C₁₃	#447	1	1	yes	characteristic
314	C₄×C₁₃	#447	1	1	yes	characteristic
315	C₄×C₁₃	C₂×#120	1	1	yes	characteristic
316	C₄×C₁₃	C₂²×D₈	1	1	yes	characteristic
317	2₋¹⁺⁴	—	2	4	no	—
318	2₋¹⁺⁴	—	2	4	no	—
319	2₋¹⁺⁴	—	4	2	no	—
320	2₋¹⁺⁴	—	4	2	no	—
321	C₂×#41	—	2	2	no	—
322	C₂×#41	—	2	1	no	—
323	C₂×#41	—	2	1	no	—
324	C₂×#41	—	4	2	no	—
325	C₂×#41	—	4	1	no	—
326	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
327	C₂²×Q₈	—	2	2	no	—
328	C₂²×Q₈	—	2	1	no	—
329	C₂²×Q₈	—	4	1	no	—
330	#137	—	2	4	no	—
331	#137	—	2	8	no	—
332	#137	—	2	8	no	—
333	#137	—	2	2	no	—
334	#137	—	2	4	no	—
335	#137	—	4	1	no	—
336	AGL(1,ℤ/8)	—	2	2	no	—
337	AGL(1,ℤ/8)	—	4	1	no	—
338	#135	—	2	4	no	—
339	#135	—	2	4	no	—
340	#135	—	2	1	no	—
341	#135	—	2	1	no	—
342	#135	—	2	1	no	—
343	#135	—	2	1	no	—
344	#135	—	2	1	no	—
345	#135	—	2	1	no	—
346	#135	—	4	2	no	—
347	#135	D₄×C₁₃	1	2	yes	—
348	#135	C₂³×C₁₃	1	2	yes	—
349	C₂×Q₁₆	—	2	2	no	—
350	C₂×Q₁₆	—	2	4	no	—
351	C₂×Q₁₆	—	2	4	no	—
352	C₂×Q₁₆	—	2	1	no	—
353	C₂×Q₁₆	—	2	1	no	—
354	C₂×Q₁₆	—	2	1	no	—
355	C₂×Q₁₆	D₄×C₁₃	1	1	yes	characteristic
356	C₂×Q₁₆	D₄×C₁₃	1	2	yes	—
357	C₂×Q₁₆	D₄×C₁₃	1	2	yes	—
358	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
359	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
360	C₂×SD₁₆	—	2	2	no	—
361	C₂×SD₁₆	—	2	1	no	—
362	C₂×SD₁₆	—	2	1	no	—
363	C₂×D₈	D₄×C₁₃	1	1	yes	characteristic
364	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
365	#131	—	2	1	no	—
366	#131	—	2	1	no	—
367	#131	D₄×C₁₃	1	2	yes	—
368	#131	C₂³×C₁₃	1	2	yes	—
369	C₂×M₁₆	—	2	1	no	—
370	C₂×M₁₆	—	2	1	no	—
371	C₂×M₁₆	D₄×C₁₃	1	1	yes	characteristic
372	C₂²×C₈	—	2	1	no	—
373	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
374	Q₃₂	—	2	4	no	—
375	Q₃₂	—	2	2	no	—
376	SD₃₂	—	2	4	no	—
377	SD₃₂	—	2	2	no	—
378	SD₃₂	—	2	2	no	—
379	D₁₆	—	2	2	no	—
380	M₃₂	—	2	1	no	—
381	M₃₂	—	2	1	no	—
382	M₃₂	—	2	1	no	—
383	M₃₂	C₂³×C₁₃	1	2	yes	—
384	C₂×C₁₆	—	2	1	no	—
385	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
386	#108	—	2	1	no	—
387	#108	C₂³×C₁₃	1	2	yes	—
388	#101	—	2	2	no	—
389	#100	—	2	2	no	—
390	C₂×C₁₃	—	2	1	no	—
391	C₂×C₁₃	—	2	1	no	—
392	C₂×C₁₃	—	2	1	no	—
393	C₂×C₁₃	—	4	2	no	—
394	C₂×C₁₃	—	8	2	no	—
395	C₂×C₁₃	—	16	1	no	—
396	C₂×C₁₃	C₂×#447	1	1	yes	characteristic
397	#41	—	2	1	no	—
398	#41	—	2	1	no	—
399	#41	—	2	8	no	—
400	#41	—	2	2	no	—
401	#41	—	2	2	no	—
402	#41	—	4	4	no	—
403	#41	—	4	8	no	—
404	#41	—	4	8	no	—
405	#41	—	4	4	no	—
406	#41	—	4	4	no	—
407	#41	—	4	1	no	—
408	#41	—	4	1	no	—
409	#41	—	4	1	no	—
410	#41	—	4	1	no	—
411	#41	—	4	1	no	—
412	#41	—	4	1	no	—
413	#41	C₁₃×D₈	1	2	yes	—
414	#41	C₂×D₄×C₁₃	1	2	yes	—
415	C₂×Q₈	—	2	8	no	—
416	C₂×Q₈	—	2	2	no	—
417	C₂×Q₈	—	2	1	no	—
418	C₂×Q₈	—	2	2	no	—
419	C₂×Q₈	—	2	2	no	—
420	C₂×Q₈	—	2	1	no	—
421	C₂×Q₈	—	4	2	no	—
422	C₂×Q₈	—	4	4	no	—
423	C₂×Q₈	—	4	4	no	—
424	C₂×Q₈	—	4	4	no	—
425	C₂×Q₈	—	4	1	no	—
426	C₂×Q₈	—	4	1	no	—
427	C₂×Q₈	—	4	1	no	—
428	C₂×Q₈	C₁₃×D₈	1	1	yes	characteristic
429	C₂×D₄	—	2	1	no	—
430	C₂×D₄	—	2	1	no	—
431	C₂×D₄	—	2	1	no	—
432	C₂×D₄	—	4	2	no	—
433	C₂×D₄	—	4	1	no	—
434	C₂×D₄	—	4	1	no	—
435	C₂×D₄	C₁₃×D₈	1	1	yes	characteristic
436	C₂²×C₄	—	2	1	no	—
437	C₂²×C₄	—	4	2	no	—
438	C₂²×C₄	—	4	2	no	—
439	C₂²×C₄	—	4	1	no	—
440	C₂²×C₄	—	4	1	no	—
441	C₂²×C₄	—	4	1	no	—
442	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
443	Q₁₆	—	2	8	no	—
444	Q₁₆	—	2	1	no	—
445	Q₁₆	—	2	2	no	—
446	Q₁₆	—	2	2	no	—
447	Q₁₆	—	2	2	no	—
448	Q₁₆	—	2	1	no	—
449	Q₁₆	—	2	1	no	—
450	Q₁₆	—	4	2	no	—
451	Q₁₆	C₂×D₄×C₁₃	1	2	yes	—
452	Q₁₆	C₂×D₄×C₁₃	1	4	yes	—
453	SD₁₆	—	2	8	no	—
454	SD₁₆	—	2	2	no	—
455	SD₁₆	—	2	2	no	—
456	SD₁₆	—	4	2	no	—
457	SD₁₆	—	4	2	no	—
458	SD₁₆	—	4	1	no	—
459	SD₁₆	—	4	1	no	—
460	D₈	—	2	1	no	—
461	D₈	—	2	1	no	—
462	D₈	—	2	1	no	—
463	D₈	—	4	2	no	—
464	D₈	C₂×D₄×C₁₃	1	2	yes	—
465	M₁₆	—	2	1	no	—
466	M₁₆	—	2	2	no	—
467	M₁₆	—	2	2	no	—
468	M₁₆	—	2	2	no	—
469	M₁₆	—	4	1	no	—
470	M₁₆	C₂×D₄×C₁₃	1	2	yes	—
471	C₂×C₈	—	2	1	no	—
472	C₂×C₈	—	2	2	no	—
473	C₂×C₈	—	2	2	no	—
474	C₂×C₈	—	4	1	no	—
475	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
476	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
477	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
478	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
479	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
480	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
481	C₁₆	—	2	2	no	—
482	C₁₆	—	2	2	no	—
483	C₁₃	#33540	1	1	yes	characteristic, direct product factor, Sylow
484	C₂³	—	2	1	no	—
485	C₂³	—	4	1	no	—
486	C₂³	—	4	1	no	—
487	C₂³	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
488	Q₈	—	2	1	no	—
489	Q₈	—	2	4	no	—
490	Q₈	—	2	2	no	—
491	Q₈	—	4	8	no	—
492	Q₈	—	4	1	no	—
493	Q₈	—	4	2	no	—
494	Q₈	—	4	2	no	—
495	Q₈	—	4	2	no	—
496	Q₈	—	4	1	no	—
497	Q₈	—	4	1	no	—
498	Q₈	C₂×C₁₃×D₈	1	2	yes	—
499	D₄	—	2	2	no	—
500	D₄	—	2	2	no	—
501	D₄	—	2	1	no	—
502	D₄	—	2	2	no	—
503	D₄	—	4	8	no	—
504	D₄	—	4	2	no	—
505	D₄	—	4	2	no	—
506	D₄	—	4	1	no	—
507	D₄	—	4	1	no	—
508	D₄	—	4	1	no	—
509	D₄	—	8	1	no	—
510	D₄	—	8	1	no	—
511	D₄	C₂×C₁₃×D₈	1	2	yes	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	2	no	—
515	C₂×C₄	—	4	8	no	—
516	C₂×C₄	—	4	8	no	—
517	C₂×C₄	—	4	2	no	—
518	C₂×C₄	—	4	1	no	—
519	C₂×C₄	—	4	2	no	—
520	C₂×C₄	—	4	2	no	—
521	C₂×C₄	—	4	2	no	—
522	C₂×C₄	—	4	2	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	8	1	no	—
525	C₂×C₄	—	8	1	no	—
526	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
527	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
528	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
529	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
530	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
531	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
532	C₈	—	2	2	no	—
533	C₈	—	4	2	no	—
534	C₈	C₁₃×#120	1	1	yes	characteristic
535	C₈	C₁₃×#120	1	1	yes	characteristic
536	C₈	C₂²×D₄×C₁₃	1	1	yes	characteristic
537	C₈	C₂²×D₄×C₁₃	1	1	yes	characteristic
538	C₂²	—	2	2	no	—
539	C₂²	—	4	1	no	—
540	C₂²	—	4	2	no	—
541	C₂²	—	4	2	no	—
542	C₂²	—	8	2	no	—
543	C₂²	—	8	1	no	—
544	C₂²	—	16	1	no	—
545	C₂²	C₁₃×#447	1	1	yes	characteristic
546	C₂²	C₁₃×#447	1	1	yes	characteristic
547	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
548	C₄	—	2	2	no	—
549	C₄	—	4	4	no	—
550	C₄	—	4	2	no	—
551	C₄	—	8	1	no	—
552	C₄	C₁₃×#447	1	1	yes	characteristic
553	C₄	C₁₃×#447	1	1	yes	characteristic
554	C₄	C₂×C₁₃×#120	1	1	yes	characteristic
555	C₄	C₂²×C₁₃×D₈	1	1	yes	characteristic
556	C₂	—	2	1	no	—
557	C₂	—	2	1	no	—
558	C₂	—	2	1	no	—
559	C₂	—	4	2	no	—
560	C₂	—	8	2	no	—
561	C₂	—	16	1	no	—
562	C₂	C₂×C₁₃×#447	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₃	C₂×#447
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₂×C₁₃×#131 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#578	C₂	semidirect
2. C₁₃×#3414	C₂	semidirect
3. C₂×C₁₃×#510	C₂	semidirect
4. C₁₃×#3067	C₂	semidirect
5. C₁₃×#2195	C₂	semidirect
6. C₁₃×#2193	C₂	semidirect
7. C₂×C₁₃×#362	C₂	semidirect
8. C₁₃×#2143	C₂	semidirect
9. C₁₃×#2117	C₂	semidirect
27. C₁₃×#510	C₂²	semidirect
29. C₁₃×#509	C₂²	semidirect
31. C₂×C₁₃×Q₃₂	C₂²	semidirect
32. C₂×C₁₃×SD₃₂	C₂²	semidirect
35. C₁₃×#473	C₂²	semidirect
36. C₁₃×#472	C₂²	semidirect
40. C₁₃×#362	C₂²	semidirect
41. C₁₃×#359	C₂²	semidirect
42. C₁₃×#350	C₂²	semidirect
116. #33540	C₁₃	direct (N × H)
203. C₂×#578	C₂×C₁₃	semidirect
204. #3414	C₂×C₁₃	semidirect
205. C₂×#510	C₂×C₁₃	semidirect
206. #3067	C₂×C₁₃	semidirect
207. #2195	C₂×C₁₃	semidirect
208. #2193	C₂×C₁₃	semidirect
209. C₂×#362	C₂×C₁₃	semidirect
210. #2143	C₂×C₁₃	semidirect
211. #2117	C₂×C₁₃	semidirect
283. #510	C₂²×C₁₃	semidirect
285. #509	C₂²×C₁₃	semidirect
287. C₂×Q₃₂	C₂²×C₁₃	semidirect
288. C₂×SD₃₂	C₂²×C₁₃	semidirect
291. #473	C₂²×C₁₃	semidirect
292. #472	C₂²×C₁₃	semidirect
296. #362	C₂²×C₁₃	semidirect
297. #359	C₂²×C₁₃	semidirect
298. #350	C₂²×C₁₃	semidirect
483. C₁₃	#33540	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×#578	2
C₁₃×#3414	2
C₂×C₁₃×#510	2
C₁₃×#3067	2
C₁₃×#2195	2
C₁₃×#2193	2
C₂×C₁₃×#362	2
C₁₃×#2143	2
C₁₃×#2117	2
#33540	13

Subgroups — C13×#33540 #15719879

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33540 #15719879