Subgroups — C₁₃×#23604 #15709943

Order 3328.

1002 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#430	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#428	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2905	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2896	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₃×#417	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₃×#413	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#2064	C₂	1	4	yes	maximal, complemented
8	C₁₃×#2063	C₂	1	4	yes	maximal, complemented
9	C₂×C₁₃×#343	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
11	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
12	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
13	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
14	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
16	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₁₃×#430	—	2	4	no	—
18	C₂×C₁₃×#108	C₂²	1	4	yes	—
19	C₁₃×#428	—	2	2	no	—
20	C₁₃×#428	C₂²	1	4	yes	—
21	C₂×C₁₃×#107	—	2	1	no	—
22	C₂×C₁₃×#106	—	2	1	no	—
23	C₁₃×#424	—	2	2	no	—
24	C₁₃×#424	C₂²	1	4	yes	—
25	C₁₃×#423	—	2	2	no	—
26	C₁₃×#419	C₂²	1	2	yes	—
27	C₁₃×#418	C₂²	1	2	yes	—
28	C₁₃×#417	—	2	2	no	—
29	C₁₃×#417	—	2	2	no	—
30	C₁₃×#417	—	2	1	no	—
31	C₁₃×#417	—	2	1	no	—
32	C₁₃×#416	—	2	2	no	—
33	C₂×C₁₃×#103	C₂²	1	2	yes	—
34	C₂×C₁₃×#102	C₂²	1	2	yes	—
35	C₁₃×#413	—	2	4	no	—
36	C₂×C₁₃×#101	C₂²	1	2	yes	—
37	C₂×C₁₃×#100	C₂²	1	2	yes	—
38	C₁₃×#343	C₂²	1	4	yes	—
39	C₂×C₁₃×#41	—	2	2	no	—
40	C₂×C₁₃×#41	—	2	1	no	—
41	C₂×C₁₃×#41	—	2	1	no	—
42	C₂×C₁₃×#41	—	2	1	no	—
43	C₂×C₁₃×#41	—	2	1	no	—
44	C₂×C₁₃×#41	—	2	2	no	—
45	C₂×C₁₃×#41	—	2	2	no	—
46	C₂×C₁₃×#41	Q₈	1	4	yes	—
47	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
48	C₂²×D₄×C₁₃	—	2	1	no	—
49	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₁₃	—	2	1	no	—
51	C₂³×C₄×C₁₃	—	2	1	no	—
52	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
53	C₂×C₁₃×M₁₆	—	2	1	no	—
54	C₂×C₁₃×M₁₆	—	2	2	no	—
55	C₂×C₁₃×M₁₆	—	2	2	no	—
56	C₂×C₁₃×M₁₆	—	2	2	no	—
57	C₂×C₁₃×M₁₆	—	2	1	no	—
58	C₂×C₁₃×M₁₆	—	2	1	no	—
59	C₂×C₁₃×M₁₆	—	2	2	no	—
60	C₂×C₁₃×M₁₆	—	2	2	no	—
61	C₂×C₁₃×M₁₆	—	2	2	no	—
62	C₂×C₁₃×M₁₆	—	2	2	no	—
63	C₂×C₁₃×M₁₆	D₄	1	4	yes	—
64	C₂×C₁₃×M₁₆	D₄	1	2	yes	—
65	C₂×C₁₃×M₁₆	D₄	1	2	yes	—
66	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
67	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
68	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
69	C₂²×C₈×C₁₃	—	2	1	no	—
70	C₂²×C₈×C₁₃	—	2	1	no	—
71	C₂²×C₈×C₁₃	—	2	1	no	—
72	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
73	C₁₃×#117	—	2	1	no	—
74	C₁₃×#117	—	2	1	no	—
75	C₁₃×#117	D₄	1	2	yes	—
76	C₁₃×#117	C₂³	1	2	yes	—
77	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
78	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
79	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
80	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
81	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
82	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
83	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
84	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
85	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
86	C₂×C₄²×C₁₃	—	2	1	no	—
87	C₁₃×#108	—	2	8	no	—
88	C₁₃×#107	—	2	4	no	—
89	C₁₃×#106	—	2	4	no	—
90	C₁₃×C₄⋊C₈	—	2	8	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×#102	—	2	2	no	—
96	C₁₃×#102	—	2	2	no	—
97	C₁₃×#101	—	2	4	no	—
98	C₁₃×#100	—	2	4	no	—
99	#23604	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
100	C₂⁴×C₁₃	—	2	1	no	—
101	C₂⁴×C₁₃	#41	1	1	yes	characteristic
102	C₁₃×#41	—	2	4	no	—
103	C₁₃×#41	—	2	4	no	—
104	C₁₃×#41	—	2	4	no	—
105	C₁₃×#41	—	2	4	no	—
106	C₁₃×#41	—	4	2	no	—
107	C₁₃×#41	—	4	2	no	—
108	C₁₃×#41	—	4	2	no	—
109	C₁₃×#41	—	4	2	no	—
110	C₂×Q₈×C₁₃	—	2	1	no	—
111	C₂×Q₈×C₁₃	—	2	1	no	—
112	C₂×Q₈×C₁₃	—	2	1	no	—
113	C₂×Q₈×C₁₃	—	2	1	no	—
114	C₂×Q₈×C₁₃	—	2	1	no	—
115	C₂×Q₈×C₁₃	C₂×Q₈	1	2	yes	—
116	C₂×D₄×C₁₃	—	2	4	no	—
117	C₂×D₄×C₁₃	—	2	1	no	—
118	C₂×D₄×C₁₃	—	2	1	no	—
119	C₂×D₄×C₁₃	—	2	1	no	—
120	C₂×D₄×C₁₃	—	2	1	no	—
121	C₂×D₄×C₁₃	—	2	1	no	—
122	C₂×D₄×C₁₃	—	4	1	no	—
123	C₂×D₄×C₁₃	—	4	1	no	—
124	C₂×D₄×C₁₃	—	4	2	no	—
125	C₂×D₄×C₁₃	C₂×Q₈	1	2	yes	—
126	C₂²×C₄×C₁₃	—	2	1	no	—
127	C₂²×C₄×C₁₃	—	2	1	no	—
128	C₂²×C₄×C₁₃	—	2	1	no	—
129	C₂²×C₄×C₁₃	—	2	4	no	—
130	C₂²×C₄×C₁₃	—	2	2	no	—
131	C₂²×C₄×C₁₃	—	4	1	no	—
132	C₂²×C₄×C₁₃	—	4	1	no	—
133	C₂²×C₄×C₁₃	—	4	2	no	—
134	C₂²×C₄×C₁₃	—	4	1	no	—
135	C₂²×C₄×C₁₃	—	4	1	no	—
136	C₂²×C₄×C₁₃	—	8	2	no	—
137	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
138	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
143	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
144	C₂²×C₄×C₁₃	#41	1	2	yes	—
145	C₂²×C₄×C₁₃	#41	1	2	yes	—
146	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
147	C₁₃×M₁₆	—	2	4	no	—
148	C₁₃×M₁₆	—	2	4	no	—
149	C₁₃×M₁₆	—	2	4	no	—
150	C₁₃×M₁₆	—	2	2	no	—
151	C₁₃×M₁₆	—	2	2	no	—
152	C₁₃×M₁₆	—	2	2	no	—
153	C₁₃×M₁₆	—	2	2	no	—
154	C₁₃×M₁₆	—	2	2	no	—
155	C₁₃×M₁₆	—	4	2	no	—
156	C₁₃×M₁₆	—	4	2	no	—
157	C₁₃×M₁₆	C₂×D₄	1	4	yes	—
158	C₂×C₈×C₁₃	—	2	4	no	—
159	C₂×C₈×C₁₃	—	2	2	no	—
160	C₂×C₈×C₁₃	—	2	2	no	—
161	C₂×C₈×C₁₃	—	2	2	no	—
162	C₂×C₈×C₁₃	—	2	2	no	—
163	C₂×C₈×C₁₃	—	2	2	no	—
164	C₂×C₈×C₁₃	—	4	2	no	—
165	C₂×C₈×C₁₃	—	4	2	no	—
166	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
167	C₁₃×C₄⋊C₄	—	2	1	no	—
168	C₁₃×C₄⋊C₄	—	2	1	no	—
169	C₁₃×C₄⋊C₄	—	2	2	no	—
170	C₁₃×C₄⋊C₄	—	2	2	no	—
171	C₁₃×C₄⋊C₄	—	4	1	no	—
172	C₁₃×C₄⋊C₄	—	4	1	no	—
173	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
174	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
175	C₁₃×C₂²⋊C₄	—	2	2	no	—
176	C₁₃×C₂²⋊C₄	—	2	2	no	—
177	C₄²×C₁₃	—	2	2	no	—
178	C₄²×C₁₃	—	2	2	no	—
179	C₂×#430	C₂×C₁₃	1	1	yes	characteristic, complemented
180	C₂×#428	C₂×C₁₃	1	1	yes	characteristic, complemented
181	#2905	C₂×C₁₃	1	1	yes	characteristic, complemented
182	#2896	C₂×C₁₃	1	1	yes	characteristic
183	C₂×#417	C₂×C₁₃	1	1	yes	characteristic
184	C₂×#413	C₂×C₁₃	1	1	yes	characteristic
185	#2064	C₂×C₁₃	1	4	yes	complemented
186	#2063	C₂×C₁₃	1	4	yes	complemented
187	C₂×#343	C₂×C₁₃	1	1	yes	characteristic, complemented
188	C₂³×C₁₃	—	2	2	no	—
189	C₂³×C₁₃	—	4	1	no	—
190	C₂³×C₁₃	—	4	1	no	—
191	C₂³×C₁₃	—	4	1	no	—
192	C₂³×C₁₃	—	4	1	no	—
193	C₂³×C₁₃	—	8	1	no	—
194	C₂³×C₁₃	—	8	1	no	—
195	C₂³×C₁₃	#121	1	1	yes	characteristic
196	C₂³×C₁₃	#121	1	1	yes	characteristic
197	C₂³×C₁₃	C₂²⋊Q₈	1	2	yes	—
198	C₂³×C₁₃	#126	1	2	yes	—
199	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
200	Q₈×C₁₃	—	2	2	no	—
201	Q₈×C₁₃	—	2	2	no	—
202	Q₈×C₁₃	—	4	1	no	—
203	Q₈×C₁₃	—	4	1	no	—
204	D₄×C₁₃	—	2	2	no	—
205	D₄×C₁₃	—	2	2	no	—
206	D₄×C₁₃	—	4	4	no	—
207	D₄×C₁₃	—	4	4	no	—
208	D₄×C₁₃	—	4	1	no	—
209	D₄×C₁₃	—	4	1	no	—
210	C₂×C₄×C₁₃	—	2	2	no	—
211	C₂×C₄×C₁₃	—	2	2	no	—
212	C₂×C₄×C₁₃	—	2	2	no	—
213	C₂×C₄×C₁₃	—	4	1	no	—
214	C₂×C₄×C₁₃	—	4	1	no	—
215	C₂×C₄×C₁₃	—	4	4	no	—
216	C₂×C₄×C₁₃	—	4	4	no	—
217	C₂×C₄×C₁₃	—	4	2	no	—
218	C₂×C₄×C₁₃	—	8	1	no	—
219	C₂×C₄×C₁₃	—	8	1	no	—
220	C₂×C₄×C₁₃	—	8	2	no	—
221	C₂×C₄×C₁₃	—	8	2	no	—
222	C₂×C₄×C₁₃	—	8	2	no	—
223	C₂×C₄×C₁₃	#121	1	2	yes	—
224	C₂×C₄×C₁₃	#121	1	2	yes	—
225	C₂×C₄×C₁₃	#121	1	2	yes	—
226	C₂×C₄×C₁₃	#121	1	2	yes	—
227	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
228	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
229	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
230	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
231	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
232	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
233	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
234	C₂×C₄×C₁₃	#126	1	2	yes	—
235	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
236	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
237	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
238	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
239	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
240	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
241	C₈×C₁₃	—	2	4	no	—
242	C₈×C₁₃	—	2	4	no	—
243	C₈×C₁₃	—	4	2	no	—
244	C₈×C₁₃	—	4	2	no	—
245	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
246	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
247	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
248	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
249	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
250	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
251	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
252	#430	—	2	4	no	—
253	C₂×#108	C₂²×C₁₃	1	4	yes	—
254	#428	—	2	2	no	—
255	#428	C₂²×C₁₃	1	4	yes	—
256	C₂×#107	—	2	1	no	—
257	C₂×#106	—	2	1	no	—
258	#424	—	2	2	no	—
259	#424	C₂²×C₁₃	1	4	yes	—
260	#423	—	2	2	no	—
261	#419	C₂²×C₁₃	1	2	yes	—
262	#418	C₂²×C₁₃	1	2	yes	—
263	#417	—	2	2	no	—
264	#417	—	2	2	no	—
265	#417	—	2	1	no	—
266	#417	—	2	1	no	—
267	#416	—	2	2	no	—
268	C₂×#103	C₂²×C₁₃	1	2	yes	—
269	C₂×#102	C₂²×C₁₃	1	2	yes	—
270	#413	—	2	4	no	—
271	C₂×#101	C₂²×C₁₃	1	2	yes	—
272	C₂×#100	C₂²×C₁₃	1	2	yes	—
273	#343	C₂²×C₁₃	1	4	yes	—
274	C₂²×C₁₃	—	2	1	no	—
275	C₂²×C₁₃	—	2	1	no	—
276	C₂²×C₁₃	—	2	1	no	—
277	C₂²×C₁₃	—	2	1	no	—
278	C₂²×C₁₃	—	2	1	no	—
279	C₂²×C₁₃	—	2	1	no	—
280	C₂²×C₁₃	—	4	2	no	—
281	C₂²×C₁₃	—	4	2	no	—
282	C₂²×C₁₃	—	4	2	no	—
283	C₂²×C₁₃	—	8	2	no	—
284	C₂²×C₁₃	—	8	2	no	—
285	C₂²×C₁₃	—	8	1	no	—
286	C₂²×C₁₃	—	8	1	no	—
287	C₂²×C₁₃	#396	1	2	yes	—
288	C₂²×C₁₃	#396	1	2	yes	—
289	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
290	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
291	C₂²×C₁₃	C₂×#126	1	1	yes	characteristic
292	C₄×C₁₃	—	4	2	no	—
293	C₄×C₁₃	—	4	2	no	—
294	C₄×C₁₃	—	4	2	no	—
295	C₄×C₁₃	—	8	2	no	—
296	C₄×C₁₃	#396	1	2	yes	—
297	C₄×C₁₃	#396	1	2	yes	—
298	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
299	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
300	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
301	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
302	C₂×#41	—	2	2	no	—
303	C₂×#41	—	2	1	no	—
304	C₂×#41	—	2	1	no	—
305	C₂×#41	—	2	1	no	—
306	C₂×#41	—	2	1	no	—
307	C₂×#41	—	2	2	no	—
308	C₂×#41	—	2	2	no	—
309	C₂×#41	Q₈×C₁₃	1	4	yes	—
310	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
311	C₂²×D₄	—	2	1	no	—
312	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
313	C₂³×C₄	—	2	1	no	—
314	C₂³×C₄	—	2	1	no	—
315	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
316	C₂×M₁₆	—	2	1	no	—
317	C₂×M₁₆	—	2	2	no	—
318	C₂×M₁₆	—	2	2	no	—
319	C₂×M₁₆	—	2	2	no	—
320	C₂×M₁₆	—	2	1	no	—
321	C₂×M₁₆	—	2	1	no	—
322	C₂×M₁₆	—	2	2	no	—
323	C₂×M₁₆	—	2	2	no	—
324	C₂×M₁₆	—	2	2	no	—
325	C₂×M₁₆	—	2	2	no	—
326	C₂×M₁₆	D₄×C₁₃	1	4	yes	—
327	C₂×M₁₆	D₄×C₁₃	1	2	yes	—
328	C₂×M₁₆	D₄×C₁₃	1	2	yes	—
329	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
330	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
331	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
332	C₂²×C₈	—	2	1	no	—
333	C₂²×C₈	—	2	1	no	—
334	C₂²×C₈	—	2	1	no	—
335	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
336	#117	—	2	1	no	—
337	#117	—	2	1	no	—
338	#117	D₄×C₁₃	1	2	yes	—
339	#117	C₂³×C₁₃	1	2	yes	—
340	C₂×C₄⋊C₄	—	2	1	no	—
341	C₂×C₄⋊C₄	—	2	1	no	—
342	C₂×C₄⋊C₄	—	2	1	no	—
343	C₂×C₄⋊C₄	—	2	1	no	—
344	C₂×C₄⋊C₄	—	2	1	no	—
345	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
346	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
347	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
348	C₂×C₂²⋊C₄	—	2	1	no	—
349	C₂×C₄²	—	2	1	no	—
350	#108	—	2	8	no	—
351	#107	—	2	4	no	—
352	#106	—	2	4	no	—
353	C₄⋊C₈	—	2	8	no	—
354	#103	—	2	4	no	—
355	#103	—	2	2	no	—
356	#103	—	2	2	no	—
357	#102	—	2	4	no	—
358	#102	—	2	2	no	—
359	#102	—	2	2	no	—
360	#101	—	2	4	no	—
361	#100	—	2	4	no	—
362	C₂×C₁₃	—	2	1	no	—
363	C₂×C₁₃	—	2	1	no	—
364	C₂×C₁₃	—	2	2	no	—
365	C₂×C₁₃	—	2	2	no	—
366	C₂×C₁₃	—	8	2	no	—
367	C₂×C₁₃	C₂×#396	1	1	yes	characteristic
368	C₂×C₁₃	#3068	1	1	yes	characteristic
369	C₂×C₁₃	#3069	1	1	yes	characteristic
370	C₂⁴	—	2	1	no	—
371	C₂⁴	C₁₃×#41	1	1	yes	characteristic
372	#41	—	2	4	no	—
373	#41	—	2	4	no	—
374	#41	—	2	4	no	—
375	#41	—	2	4	no	—
376	#41	—	4	2	no	—
377	#41	—	4	2	no	—
378	#41	—	4	2	no	—
379	#41	—	4	2	no	—
380	C₂×Q₈	—	2	1	no	—
381	C₂×Q₈	—	2	1	no	—
382	C₂×Q₈	—	2	1	no	—
383	C₂×Q₈	—	2	1	no	—
384	C₂×Q₈	—	2	1	no	—
385	C₂×Q₈	C₂×Q₈×C₁₃	1	2	yes	—
386	C₂×D₄	—	2	4	no	—
387	C₂×D₄	—	2	1	no	—
388	C₂×D₄	—	2	1	no	—
389	C₂×D₄	—	2	1	no	—
390	C₂×D₄	—	2	1	no	—
391	C₂×D₄	—	2	1	no	—
392	C₂×D₄	—	4	1	no	—
393	C₂×D₄	—	4	1	no	—
394	C₂×D₄	—	4	2	no	—
395	C₂×D₄	C₂×Q₈×C₁₃	1	2	yes	—
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	2	1	no	—
398	C₂²×C₄	—	2	1	no	—
399	C₂²×C₄	—	2	4	no	—
400	C₂²×C₄	—	2	2	no	—
401	C₂²×C₄	—	4	1	no	—
402	C₂²×C₄	—	4	1	no	—
403	C₂²×C₄	—	4	2	no	—
404	C₂²×C₄	—	4	1	no	—
405	C₂²×C₄	—	4	1	no	—
406	C₂²×C₄	—	8	2	no	—
407	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
408	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
409	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
410	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
411	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
412	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
413	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
414	C₂²×C₄	C₁₃×#41	1	2	yes	—
415	C₂²×C₄	C₁₃×#41	1	2	yes	—
416	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
417	M₁₆	—	2	4	no	—
418	M₁₆	—	2	4	no	—
419	M₁₆	—	2	4	no	—
420	M₁₆	—	2	2	no	—
421	M₁₆	—	2	2	no	—
422	M₁₆	—	2	2	no	—
423	M₁₆	—	2	2	no	—
424	M₁₆	—	2	2	no	—
425	M₁₆	—	4	2	no	—
426	M₁₆	—	4	2	no	—
427	M₁₆	C₂×D₄×C₁₃	1	4	yes	—
428	C₂×C₈	—	2	4	no	—
429	C₂×C₈	—	2	2	no	—
430	C₂×C₈	—	2	2	no	—
431	C₂×C₈	—	2	2	no	—
432	C₂×C₈	—	2	2	no	—
433	C₂×C₈	—	2	2	no	—
434	C₂×C₈	—	4	2	no	—
435	C₂×C₈	—	4	2	no	—
436	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
437	C₄⋊C₄	—	2	1	no	—
438	C₄⋊C₄	—	2	1	no	—
439	C₄⋊C₄	—	2	2	no	—
440	C₄⋊C₄	—	2	2	no	—
441	C₄⋊C₄	—	4	1	no	—
442	C₄⋊C₄	—	4	1	no	—
443	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
444	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
445	C₂²⋊C₄	—	2	2	no	—
446	C₂²⋊C₄	—	2	2	no	—
447	C₄²	—	2	2	no	—
448	C₄²	—	2	2	no	—
449	C₁₃	#23604	1	1	yes	characteristic, direct product factor, Sylow
450	C₂³	—	2	2	no	—
451	C₂³	—	4	1	no	—
452	C₂³	—	4	1	no	—
453	C₂³	—	4	1	no	—
454	C₂³	—	4	1	no	—
455	C₂³	—	8	1	no	—
456	C₂³	—	8	1	no	—
457	C₂³	C₁₃×#121	1	1	yes	characteristic
458	C₂³	C₁₃×#121	1	1	yes	characteristic
459	C₂³	C₁₃×C₂²⋊Q₈	1	2	yes	—
460	C₂³	C₁₃×#126	1	2	yes	—
461	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
462	Q₈	—	2	2	no	—
463	Q₈	—	2	2	no	—
464	Q₈	—	4	1	no	—
465	Q₈	—	4	1	no	—
466	D₄	—	2	2	no	—
467	D₄	—	2	2	no	—
468	D₄	—	4	4	no	—
469	D₄	—	4	4	no	—
470	D₄	—	4	1	no	—
471	D₄	—	4	1	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	4	1	no	—
476	C₂×C₄	—	4	1	no	—
477	C₂×C₄	—	4	4	no	—
478	C₂×C₄	—	4	4	no	—
479	C₂×C₄	—	4	2	no	—
480	C₂×C₄	—	8	1	no	—
481	C₂×C₄	—	8	1	no	—
482	C₂×C₄	—	8	2	no	—
483	C₂×C₄	—	8	2	no	—
484	C₂×C₄	—	8	2	no	—
485	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
486	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
487	C₂×C₄	C₁₃×#121	1	2	yes	—
488	C₂×C₄	C₁₃×#121	1	2	yes	—
489	C₂×C₄	C₁₃×#121	1	2	yes	—
490	C₂×C₄	C₁₃×#121	1	2	yes	—
491	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
492	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
493	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
494	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
495	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
496	C₂×C₄	C₁₃×#126	1	2	yes	—
497	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
498	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
499	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
500	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
501	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
502	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
503	C₈	—	2	4	no	—
504	C₈	—	2	4	no	—
505	C₈	—	4	2	no	—
506	C₈	—	4	2	no	—
507	C₂²	—	2	1	no	—
508	C₂²	—	2	1	no	—
509	C₂²	—	2	1	no	—
510	C₂²	—	2	1	no	—
511	C₂²	—	2	1	no	—
512	C₂²	—	2	1	no	—
513	C₂²	—	4	2	no	—
514	C₂²	—	4	2	no	—
515	C₂²	—	4	2	no	—
516	C₂²	—	8	2	no	—
517	C₂²	—	8	2	no	—
518	C₂²	—	8	1	no	—
519	C₂²	—	8	1	no	—
520	C₂²	C₁₃×#396	1	2	yes	—
521	C₂²	C₁₃×#396	1	2	yes	—
522	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
523	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
524	C₂²	C₂×C₁₃×#126	1	1	yes	characteristic
525	C₄	—	4	2	no	—
526	C₄	—	4	2	no	—
527	C₄	—	4	2	no	—
528	C₄	—	8	2	no	—
529	C₄	C₁₃×#396	1	2	yes	—
530	C₄	C₁₃×#396	1	2	yes	—
531	C₄	C₂×C₁₃×#121	1	1	yes	characteristic
532	C₄	C₂×C₁₃×#121	1	1	yes	characteristic
533	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
534	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
535	C₂	—	2	1	no	—
536	C₂	—	2	1	no	—
537	C₂	—	2	2	no	—
538	C₂	—	2	2	no	—
539	C₂	—	8	2	no	—
540	C₂	C₂×C₁₃×#396	1	1	yes	characteristic
541	C₂	C₁₃×#3068	1	1	yes	characteristic
542	C₂	C₁₃×#3069	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
1. C₂×C₁₃×#430	C₂	semidirect
2. C₂×C₁₃×#428	C₂	semidirect
3. C₁₃×#2905	C₂	semidirect
7. C₁₃×#2064	C₂	semidirect
8. C₁₃×#2063	C₂	semidirect
9. C₂×C₁₃×#343	C₂	semidirect
99. #23604	C₁₃	direct (N × H)
179. C₂×#430	C₂×C₁₃	semidirect
180. C₂×#428	C₂×C₁₃	semidirect
181. #2905	C₂×C₁₃	semidirect
185. #2064	C₂×C₁₃	semidirect
186. #2063	C₂×C₁₃	semidirect
187. C₂×#343	C₂×C₁₃	semidirect
449. C₁₃	#23604	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×#430	2
C₂×C₁₃×#428	2
C₁₃×#2905	2
C₁₃×#2896	2
C₂×C₁₃×#417	2
C₂×C₁₃×#413	2
C₁₃×#2064	2
C₁₃×#2063	2
C₂×C₁₃×#343	2
#23604	13

Subgroups — C13×#23604 #15709943

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#23604 #15709943