Subgroups — C₁₃×#60651 #15746990

Order 3328.

3138 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	C₂×C₁₃×#578	C₂	1	2	yes	maximal, complemented
2	C₂×C₁₃×#577	C₂	1	2	yes	maximal, complemented
3	C₁₃×#3500	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3499	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#3156	C₂	1	6	yes	maximal, complemented
6	C₁₃×#3154	C₂	1	6	yes	maximal, complemented
7	C₁₃×#3153	C₂	1	3	yes	maximal, complemented
8	C₁₃×#3152	C₂	1	3	yes	maximal, complemented
9	C₁₃×#3150	C₂	1	3	yes	maximal, complemented
10	C₂×C₁₃×#497	C₂	1	3	yes	maximal, complemented
11	C₁₃×#2875	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	2	yes	—
13	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
15	C₁₃×#578	—	2	16	no	—
16	C₁₃×#577	—	2	16	no	—
17	C₂×C₁₃×#137	C₂²	1	6	yes	—
18	C₂×C₁₃×#137	C₂²	1	6	yes	complemented
19	C₂×C₁₃×#137	C₂²	1	6	yes	complemented
20	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	6	yes	—
21	C₂×C₁₃×#135	C₂²	1	6	yes	—
22	C₂×C₁₃×#135	C₂²	1	6	yes	complemented
23	C₂²×C₁₃×Q₁₆	C₂²	1	6	yes	complemented
24	C₂²×C₁₃×SD₁₆	C₂²	1	6	yes	—
25	C₂×C₁₃×#131	C₂²	1	2	yes	—
26	D₄×Q₈×C₁₃	—	2	2	no	—
27	C₁₃×#548	—	2	2	no	—
28	C₁₃×#547	—	2	6	no	—
29	C₁₃×#546	—	2	6	no	—
30	C₁₃×#536	C₂²	1	3	yes	—
31	C₁₃×#536	C₂²	1	6	yes	complemented
32	C₁₃×#535	C₂²	1	3	yes	—
33	C₁₃×#532	C₂²	1	3	yes	—
34	C₁₃×#532	C₂²	1	3	yes	complemented
35	C₂×C₁₃×C₄⋊Q₈	C₂²	1	3	yes	complemented
36	C₂×C₁₃×#124	C₂²	1	3	yes	—
37	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
38	C₁₃×#497	C₂²	1	3	yes	complemented
39	C₁₃×#497	C₂²	1	6	yes	complemented
40	C₁₃×#497	C₂²	1	12	yes	complemented
41	C₁₃×#497	C₂²	1	3	yes	complemented
42	C₁₃×#497	C₂²	1	6	yes	complemented
43	C₁₃×#496	C₂²	1	1	yes	characteristic, complemented
44	C₁₃×#496	C₂²	1	3	yes	complemented
45	C₁₃×#496	C₂²	1	6	yes	complemented
46	C₁₃×#495	C₂²	1	12	yes	complemented
47	C₁₃×#494	C₂²	1	6	yes	complemented
48	C₁₃×#492	C₂²	1	6	yes	complemented
49	C₁₃×#405	C₂²	1	6	yes	complemented
50	C₄×C₁₃×M₁₆	C₂²	1	3	yes	complemented
51	C₂×C₁₃×#97	C₂²	1	3	yes	complemented
52	C₁₃×2₋¹⁺⁴	—	2	8	no	—
53	C₁₃×2₋¹⁺⁴	—	2	8	no	—
54	C₁₃×2₋¹⁺⁴	—	2	8	no	—
55	C₁₃×H(5,𝔽₂)	—	2	8	no	—
56	C₂×C₁₃×#41	—	2	1	no	—
57	C₂×C₁₃×#41	—	2	3	no	—
58	C₂×C₁₃×#41	—	2	6	no	—
59	C₂×C₁₃×#41	C₂³	1	3	yes	—
60	C₂×C₁₃×#41	C₂³	1	3	yes	—
61	C₂×C₁₃×#41	C₂³	1	6	yes	—
62	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
63	C₂²×Q₈×C₁₃	—	2	1	no	—
64	C₂²×Q₈×C₁₃	—	2	2	no	—
65	C₂²×Q₈×C₁₃	C₂³	1	3	yes	—
66	C₂²×Q₈×C₁₃	C₂³	1	6	yes	—
67	C₂²×D₄×C₁₃	—	2	3	no	—
68	C₂²×D₄×C₁₃	C₂³	1	3	yes	—
69	C₁₃×#137	—	2	24	no	—
70	C₁₃×#137	—	2	24	no	—
71	C₁₃×#137	—	2	24	no	—
72	C₁₃×AGL(1,ℤ/8)	—	2	24	no	—
73	C₁₃×#135	—	2	24	no	—
74	C₁₃×#135	—	2	24	no	—
75	C₂×C₁₃×Q₁₆	—	2	24	no	—
76	C₂×C₁₃×Q₁₆	C₂³	1	6	yes	—
77	C₂×C₁₃×Q₁₆	C₂³	1	12	yes	—
78	C₂×C₁₃×Q₁₆	C₂³	1	6	yes	—
79	C₂×C₁₃×SD₁₆	—	2	24	no	—
80	C₂×C₁₃×SD₁₆	C₂³	1	6	yes	—
81	C₂×C₁₃×SD₁₆	C₂³	1	12	yes	—
82	C₂×C₁₃×SD₁₆	C₂³	1	6	yes	—
83	C₂×C₁₃×SD₁₆	C₂³	1	6	yes	—
84	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
85	C₂×C₁₃×D₈	C₂³	1	6	yes	—
86	C₂×C₁₃×D₈	C₂³	1	2	yes	—
87	C₁₃×#131	D₄	1	16	yes	complemented
88	C₂×C₁₃×M₁₆	C₂³	1	6	yes	—
89	C₂²×C₈×C₁₃	C₂³	1	6	yes	—
90	C₁₃×C₄⋊Q₈	—	2	6	no	—
91	C₁₃×C₄⋊Q₈	C₂³	1	6	yes	—
92	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
93	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
94	C₁₃×#127	C₂³	1	3	yes	—
95	C₁₃×#127	C₂³	1	1	yes	characteristic
96	C₁₃×#124	—	2	6	no	—
97	C₁₃×#124	C₂³	1	6	yes	—
98	C₁₃×#124	C₂³	1	6	yes	—
99	C₁₃×#124	C₂³	1	3	yes	—
100	C₁₃×#124	C₂³	1	1	yes	characteristic
101	C₁₃×#123	—	2	6	no	—
102	C₁₃×#123	—	2	12	no	—
103	C₁₃×C₂²⋊Q₈	—	2	6	no	—
104	C₁₃×C₂²⋊Q₈	—	2	12	no	—
105	C₁₃×#121	—	2	6	no	—
106	C₁₃×#121	—	2	6	no	—
107	C₁₃×#121	—	2	6	no	—
108	C₁₃×#120	—	2	6	no	—
109	C₄×Q₈×C₁₃	D₄	1	2	yes	—
110	C₄×D₄×C₁₃	—	2	6	no	—
111	C₄×D₄×C₁₃	—	2	6	no	—
112	C₄×D₄×C₁₃	D₄	1	6	yes	—
113	C₁₃×#117	C₂³	1	3	yes	—
114	C₂×C₁₃×C₄⋊C₄	—	2	6	no	—
115	C₂×C₁₃×C₂²⋊C₄	—	2	6	no	—
116	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
117	C₁₃×#97	C₂³	1	1	yes	characteristic
118	C₁₃×#97	C₂³	1	3	yes	—
119	C₁₃×#97	C₂³	1	6	yes	—
120	C₄×C₈×C₁₃	C₂³	1	6	yes	—
121	#60651	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
122	C₂⁴×C₁₃	—	2	3	no	—
123	C₁₃×#41	—	2	12	no	—
124	C₁₃×#41	—	2	12	no	—
125	C₁₃×#41	—	2	12	no	—
126	C₁₃×#41	—	2	12	no	—
127	C₁₃×#41	—	4	4	no	—
128	C₁₃×#41	—	4	12	no	—
129	C₁₃×#41	—	4	24	no	—
130	C₁₃×#41	C₂×D₄	1	8	yes	—
131	C₂×Q₈×C₁₃	—	2	3	no	—
132	C₂×Q₈×C₁₃	—	2	6	no	—
133	C₂×Q₈×C₁₃	—	2	12	no	—
134	C₂×Q₈×C₁₃	—	2	12	no	—
135	C₂×Q₈×C₁₃	—	2	12	no	—
136	C₂×Q₈×C₁₃	—	4	4	no	—
137	C₂×Q₈×C₁₃	—	4	8	no	—
138	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
139	C₂×Q₈×C₁₃	C₂⁴	1	3	yes	—
140	C₂×Q₈×C₁₃	C₂⁴	1	6	yes	—
141	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
142	C₂×D₄×C₁₃	—	2	3	no	—
143	C₂×D₄×C₁₃	—	2	3	no	—
144	C₂×D₄×C₁₃	—	2	6	no	—
145	C₂×D₄×C₁₃	—	2	12	no	—
146	C₂×D₄×C₁₃	—	2	2	no	—
147	C₂×D₄×C₁₃	—	2	3	no	—
148	C₂×D₄×C₁₃	—	2	6	no	—
149	C₂×D₄×C₁₃	—	4	12	no	—
150	C₂×D₄×C₁₃	C₂×D₄	1	3	yes	—
151	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
152	C₂×D₄×C₁₃	C₂⁴	1	3	yes	—
153	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
154	C₂²×C₄×C₁₃	—	2	3	no	—
155	C₂²×C₄×C₁₃	—	2	6	no	—
156	C₂²×C₄×C₁₃	—	2	3	no	—
157	C₂²×C₄×C₁₃	—	2	3	no	—
158	C₂²×C₄×C₁₃	—	2	6	no	—
159	C₂²×C₄×C₁₃	C₂×D₄	1	6	yes	—
160	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
161	C₁₃×Q₁₆	—	2	12	no	—
162	C₁₃×Q₁₆	—	2	24	no	—
163	C₁₃×Q₁₆	—	2	12	no	—
164	C₁₃×SD₁₆	—	2	12	no	—
165	C₁₃×SD₁₆	—	2	24	no	—
166	C₁₃×SD₁₆	—	2	4	no	—
167	C₁₃×SD₁₆	—	2	12	no	—
168	C₁₃×SD₁₆	—	2	12	no	—
169	C₁₃×D₈	—	2	4	no	—
170	C₁₃×D₈	—	2	12	no	—
171	C₁₃×M₁₆	C₂×D₄	1	24	yes	—
172	C₂×C₈×C₁₃	C₂×D₄	1	24	yes	—
173	C₂×C₈×C₁₃	C₂⁴	1	6	yes	—
174	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
175	C₁₃×C₄⋊C₄	—	2	6	no	—
176	C₁₃×C₄⋊C₄	—	2	12	no	—
177	C₁₃×C₄⋊C₄	—	2	6	no	—
178	C₁₃×C₄⋊C₄	C₂×D₄	1	6	yes	—
179	C₁₃×C₂²⋊C₄	—	2	6	no	—
180	C₁₃×C₂²⋊C₄	—	2	12	no	—
181	C₁₃×C₂²⋊C₄	—	2	2	no	—
182	C₁₃×C₂²⋊C₄	—	2	12	no	—
183	C₁₃×C₂²⋊C₄	C₂×D₄	1	6	yes	—
184	C₄²×C₁₃	C₂×D₄	1	6	yes	—
185	C₄²×C₁₃	C₂⁴	1	3	yes	—
186	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
187	C₂×#578	C₂×C₁₃	1	2	yes	complemented
188	C₂×#577	C₂×C₁₃	1	2	yes	complemented
189	#3500	C₂×C₁₃	1	1	yes	characteristic, complemented
190	#3499	C₂×C₁₃	1	1	yes	characteristic, complemented
191	#3156	C₂×C₁₃	1	6	yes	complemented
192	#3154	C₂×C₁₃	1	6	yes	complemented
193	#3153	C₂×C₁₃	1	3	yes	complemented
194	#3152	C₂×C₁₃	1	3	yes	complemented
195	#3150	C₂×C₁₃	1	3	yes	complemented
196	C₂×#497	C₂×C₁₃	1	3	yes	complemented
197	#2875	C₂×C₁₃	1	1	yes	characteristic, complemented
198	C₂³×C₁₃	—	2	2	no	—
199	C₂³×C₁₃	—	2	3	no	—
200	C₂³×C₁₃	—	2	1	no	—
201	C₂³×C₁₃	—	4	6	no	—
202	C₂³×C₁₃	—	8	6	no	—
203	C₂³×C₁₃	C₂²×D₄	1	3	yes	—
204	Q₈×C₁₃	—	2	6	no	—
205	Q₈×C₁₃	—	2	6	no	—
206	Q₈×C₁₃	—	2	6	no	—
207	Q₈×C₁₃	—	2	2	no	—
208	Q₈×C₁₃	—	4	6	no	—
209	Q₈×C₁₃	—	4	12	no	—
210	Q₈×C₁₃	#127	1	4	yes	—
211	D₄×C₁₃	—	2	2	no	—
212	D₄×C₁₃	—	2	6	no	—
213	D₄×C₁₃	—	2	2	no	—
214	D₄×C₁₃	—	2	2	no	—
215	D₄×C₁₃	—	4	4	no	—
216	D₄×C₁₃	—	4	6	no	—
217	D₄×C₁₃	—	4	6	no	—
218	D₄×C₁₃	—	4	12	no	—
219	D₄×C₁₃	—	4	6	no	—
220	D₄×C₁₃	—	8	6	no	—
221	D₄×C₁₃	#127	1	12	yes	—
222	C₂×C₄×C₁₃	—	2	3	no	—
223	C₂×C₄×C₁₃	—	2	1	no	—
224	C₂×C₄×C₁₃	—	2	6	no	—
225	C₂×C₄×C₁₃	—	4	6	no	—
226	C₂×C₄×C₁₃	—	4	6	no	—
227	C₂×C₄×C₁₃	—	4	12	no	—
228	C₂×C₄×C₁₃	—	4	6	no	—
229	C₂×C₄×C₁₃	—	4	6	no	—
230	C₂×C₄×C₁₃	—	4	12	no	—
231	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
232	C₂×C₄×C₁₃	C₂²×D₄	1	6	yes	—
233	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
234	C₂×C₄×C₁₃	C₂²×D₄	1	12	yes	—
235	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
236	C₈×C₁₃	C₂²×D₄	1	4	yes	—
237	C₈×C₁₃	C₂²×D₄	1	12	yes	—
238	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	2	yes	—
239	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	1	yes	characteristic
240	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	1	yes	characteristic
241	#578	—	2	16	no	—
242	#577	—	2	16	no	—
243	C₂×#137	C₂²×C₁₃	1	6	yes	—
244	C₂×#137	C₂²×C₁₃	1	6	yes	complemented
245	C₂×#137	C₂²×C₁₃	1	6	yes	complemented
246	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	6	yes	—
247	C₂×#135	C₂²×C₁₃	1	6	yes	—
248	C₂×#135	C₂²×C₁₃	1	6	yes	complemented
249	C₂²×Q₁₆	C₂²×C₁₃	1	6	yes	complemented
250	C₂²×SD₁₆	C₂²×C₁₃	1	6	yes	—
251	C₂×#131	C₂²×C₁₃	1	2	yes	—
252	D₄×Q₈	—	2	2	no	—
253	#548	—	2	2	no	—
254	#547	—	2	6	no	—
255	#546	—	2	6	no	—
256	#536	C₂²×C₁₃	1	3	yes	—
257	#536	C₂²×C₁₃	1	6	yes	complemented
258	#535	C₂²×C₁₃	1	3	yes	—
259	#532	C₂²×C₁₃	1	3	yes	—
260	#532	C₂²×C₁₃	1	3	yes	complemented
261	C₂×C₄⋊Q₈	C₂²×C₁₃	1	3	yes	complemented
262	C₂×#124	C₂²×C₁₃	1	3	yes	—
263	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
264	#497	C₂²×C₁₃	1	3	yes	complemented
265	#497	C₂²×C₁₃	1	6	yes	complemented
266	#497	C₂²×C₁₃	1	12	yes	complemented
267	#497	C₂²×C₁₃	1	3	yes	complemented
268	#497	C₂²×C₁₃	1	6	yes	complemented
269	#496	C₂²×C₁₃	1	1	yes	characteristic, complemented
270	#496	C₂²×C₁₃	1	3	yes	complemented
271	#496	C₂²×C₁₃	1	6	yes	complemented
272	#495	C₂²×C₁₃	1	12	yes	complemented
273	#494	C₂²×C₁₃	1	6	yes	complemented
274	#492	C₂²×C₁₃	1	6	yes	complemented
275	#405	C₂²×C₁₃	1	6	yes	complemented
276	C₄×M₁₆	C₂²×C₁₃	1	3	yes	complemented
277	C₂×#97	C₂²×C₁₃	1	3	yes	complemented
278	C₂²×C₁₃	—	2	6	no	—
279	C₂²×C₁₃	—	4	4	no	—
280	C₂²×C₁₃	—	4	2	no	—
281	C₂²×C₁₃	—	4	6	no	—
282	C₂²×C₁₃	—	4	2	no	—
283	C₂²×C₁₃	—	4	1	no	—
284	C₂²×C₁₃	—	4	3	no	—
285	C₂²×C₁₃	—	16	6	no	—
286	C₂²×C₁₃	C₂×#127	1	6	yes	—
287	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
288	C₄×C₁₃	—	2	2	no	—
289	C₄×C₁₃	—	2	6	no	—
290	C₄×C₁₃	—	4	1	no	—
291	C₄×C₁₃	—	4	3	no	—
292	C₄×C₁₃	—	4	6	no	—
293	C₄×C₁₃	C₂×#127	1	6	yes	—
294	C₄×C₁₃	C₂³×D₄	1	2	yes	—
295	2₋¹⁺⁴	—	2	8	no	—
296	2₋¹⁺⁴	—	2	8	no	—
297	2₋¹⁺⁴	—	2	8	no	—
298	H(5,𝔽₂)	—	2	8	no	—
299	C₂×#41	—	2	1	no	—
300	C₂×#41	—	2	3	no	—
301	C₂×#41	—	2	6	no	—
302	C₂×#41	C₂³×C₁₃	1	3	yes	—
303	C₂×#41	C₂³×C₁₃	1	3	yes	—
304	C₂×#41	C₂³×C₁₃	1	6	yes	—
305	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
306	C₂²×Q₈	—	2	1	no	—
307	C₂²×Q₈	—	2	2	no	—
308	C₂²×Q₈	C₂³×C₁₃	1	3	yes	—
309	C₂²×Q₈	C₂³×C₁₃	1	6	yes	—
310	C₂²×D₄	—	2	3	no	—
311	C₂²×D₄	C₂³×C₁₃	1	3	yes	—
312	#137	—	2	24	no	—
313	#137	—	2	24	no	—
314	#137	—	2	24	no	—
315	AGL(1,ℤ/8)	—	2	24	no	—
316	#135	—	2	24	no	—
317	#135	—	2	24	no	—
318	C₂×Q₁₆	—	2	24	no	—
319	C₂×Q₁₆	C₂³×C₁₃	1	6	yes	—
320	C₂×Q₁₆	C₂³×C₁₃	1	12	yes	—
321	C₂×Q₁₆	C₂³×C₁₃	1	6	yes	—
322	C₂×SD₁₆	—	2	24	no	—
323	C₂×SD₁₆	C₂³×C₁₃	1	6	yes	—
324	C₂×SD₁₆	C₂³×C₁₃	1	12	yes	—
325	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
326	C₂×SD₁₆	C₂³×C₁₃	1	6	yes	—
327	C₂×SD₁₆	C₂³×C₁₃	1	6	yes	—
328	C₂×D₈	C₂³×C₁₃	1	6	yes	—
329	C₂×D₈	C₂³×C₁₃	1	2	yes	—
330	#131	D₄×C₁₃	1	16	yes	complemented
331	C₂×M₁₆	C₂³×C₁₃	1	6	yes	—
332	C₂²×C₈	C₂³×C₁₃	1	6	yes	—
333	C₄⋊Q₈	—	2	6	no	—
334	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
335	C₄⋊Q₈	C₂³×C₁₃	1	6	yes	—
336	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
337	#127	C₂³×C₁₃	1	3	yes	—
338	#127	C₂³×C₁₃	1	1	yes	characteristic
339	#124	—	2	6	no	—
340	#124	C₂³×C₁₃	1	3	yes	—
341	#124	C₂³×C₁₃	1	6	yes	—
342	#124	C₂³×C₁₃	1	1	yes	characteristic
343	#124	C₂³×C₁₃	1	6	yes	—
344	#123	—	2	6	no	—
345	#123	—	2	12	no	—
346	C₂²⋊Q₈	—	2	6	no	—
347	C₂²⋊Q₈	—	2	12	no	—
348	#121	—	2	6	no	—
349	#121	—	2	6	no	—
350	#121	—	2	6	no	—
351	#120	—	2	6	no	—
352	C₄×Q₈	D₄×C₁₃	1	2	yes	—
353	C₄×D₄	—	2	6	no	—
354	C₄×D₄	—	2	6	no	—
355	C₄×D₄	D₄×C₁₃	1	6	yes	—
356	#117	C₂³×C₁₃	1	3	yes	—
357	C₂×C₄⋊C₄	—	2	6	no	—
358	C₂×C₂²⋊C₄	—	2	6	no	—
359	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
360	#97	C₂³×C₁₃	1	1	yes	characteristic
361	#97	C₂³×C₁₃	1	3	yes	—
362	#97	C₂³×C₁₃	1	6	yes	—
363	C₄×C₈	C₂³×C₁₃	1	6	yes	—
364	C₂×C₁₃	—	2	6	no	—
365	C₂×C₁₃	—	8	2	no	—
366	C₂×C₁₃	—	8	1	no	—
367	C₂×C₁₃	—	8	3	no	—
368	C₂×C₁₃	C₂²×#127	1	1	yes	characteristic
369	C₂×C₁₃	#3586	1	2	yes	—
370	C₂⁴	—	2	3	no	—
371	#41	—	2	12	no	—
372	#41	—	2	12	no	—
373	#41	—	2	12	no	—
374	#41	—	2	12	no	—
375	#41	—	4	4	no	—
376	#41	—	4	12	no	—
377	#41	—	4	24	no	—
378	#41	C₂×D₄×C₁₃	1	8	yes	—
379	C₂×Q₈	—	2	3	no	—
380	C₂×Q₈	—	2	6	no	—
381	C₂×Q₈	—	2	12	no	—
382	C₂×Q₈	—	2	12	no	—
383	C₂×Q₈	—	2	12	no	—
384	C₂×Q₈	—	4	4	no	—
385	C₂×Q₈	—	4	8	no	—
386	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
387	C₂×Q₈	C₂⁴×C₁₃	1	3	yes	—
388	C₂×Q₈	C₂⁴×C₁₃	1	6	yes	—
389	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
390	C₂×D₄	—	2	3	no	—
391	C₂×D₄	—	2	3	no	—
392	C₂×D₄	—	2	6	no	—
393	C₂×D₄	—	2	12	no	—
394	C₂×D₄	—	2	2	no	—
395	C₂×D₄	—	2	3	no	—
396	C₂×D₄	—	2	6	no	—
397	C₂×D₄	—	4	12	no	—
398	C₂×D₄	C₂×D₄×C₁₃	1	3	yes	—
399	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
400	C₂×D₄	C₂⁴×C₁₃	1	3	yes	—
401	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
402	C₂²×C₄	—	2	3	no	—
403	C₂²×C₄	—	2	6	no	—
404	C₂²×C₄	—	2	3	no	—
405	C₂²×C₄	—	2	3	no	—
406	C₂²×C₄	—	2	6	no	—
407	C₂²×C₄	C₂×D₄×C₁₃	1	6	yes	—
408	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
409	Q₁₆	—	2	12	no	—
410	Q₁₆	—	2	24	no	—
411	Q₁₆	—	2	12	no	—
412	SD₁₆	—	2	12	no	—
413	SD₁₆	—	2	24	no	—
414	SD₁₆	—	2	4	no	—
415	SD₁₆	—	2	12	no	—
416	SD₁₆	—	2	12	no	—
417	D₈	—	2	4	no	—
418	D₈	—	2	12	no	—
419	M₁₆	C₂×D₄×C₁₃	1	24	yes	—
420	C₂×C₈	C₂×D₄×C₁₃	1	24	yes	—
421	C₂×C₈	C₂⁴×C₁₃	1	6	yes	—
422	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
423	C₄⋊C₄	—	2	6	no	—
424	C₄⋊C₄	—	2	12	no	—
425	C₄⋊C₄	—	2	6	no	—
426	C₄⋊C₄	C₂×D₄×C₁₃	1	6	yes	—
427	C₂²⋊C₄	—	2	6	no	—
428	C₂²⋊C₄	—	2	12	no	—
429	C₂²⋊C₄	—	2	2	no	—
430	C₂²⋊C₄	—	2	12	no	—
431	C₂²⋊C₄	C₂×D₄×C₁₃	1	6	yes	—
432	C₄²	C₂×D₄×C₁₃	1	6	yes	—
433	C₄²	C₂⁴×C₁₃	1	3	yes	—
434	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
435	C₁₃	#60651	1	1	yes	characteristic, direct product factor, Sylow
436	C₂³	—	2	2	no	—
437	C₂³	—	2	3	no	—
438	C₂³	—	2	1	no	—
439	C₂³	—	4	6	no	—
440	C₂³	—	8	6	no	—
441	C₂³	C₂²×D₄×C₁₃	1	3	yes	—
442	Q₈	—	2	6	no	—
443	Q₈	—	2	6	no	—
444	Q₈	—	2	6	no	—
445	Q₈	—	2	2	no	—
446	Q₈	—	4	6	no	—
447	Q₈	—	4	12	no	—
448	Q₈	C₁₃×#127	1	4	yes	—
449	D₄	—	2	2	no	—
450	D₄	—	2	6	no	—
451	D₄	—	2	2	no	—
452	D₄	—	2	2	no	—
453	D₄	—	4	4	no	—
454	D₄	—	4	6	no	—
455	D₄	—	4	6	no	—
456	D₄	—	4	12	no	—
457	D₄	—	4	6	no	—
458	D₄	—	8	6	no	—
459	D₄	C₁₃×#127	1	12	yes	—
460	C₂×C₄	—	2	3	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	6	no	—
463	C₂×C₄	—	4	6	no	—
464	C₂×C₄	—	4	6	no	—
465	C₂×C₄	—	4	12	no	—
466	C₂×C₄	—	4	6	no	—
467	C₂×C₄	—	4	6	no	—
468	C₂×C₄	—	4	12	no	—
469	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
470	C₂×C₄	C₂²×D₄×C₁₃	1	6	yes	—
471	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
472	C₂×C₄	C₂²×D₄×C₁₃	1	12	yes	—
473	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
474	C₈	C₂²×D₄×C₁₃	1	4	yes	—
475	C₈	C₂²×D₄×C₁₃	1	12	yes	—
476	C₂²	—	2	6	no	—
477	C₂²	—	4	4	no	—
478	C₂²	—	4	2	no	—
479	C₂²	—	4	6	no	—
480	C₂²	—	4	2	no	—
481	C₂²	—	4	1	no	—
482	C₂²	—	4	3	no	—
483	C₂²	—	16	6	no	—
484	C₂²	C₂×C₁₃×#127	1	6	yes	—
485	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
486	C₄	—	2	2	no	—
487	C₄	—	2	6	no	—
488	C₄	—	4	1	no	—
489	C₄	—	4	3	no	—
490	C₄	—	4	6	no	—
491	C₄	C₂×C₁₃×#127	1	6	yes	—
492	C₄	C₂³×D₄×C₁₃	1	2	yes	—
493	C₂	—	2	6	no	—
494	C₂	—	8	3	no	—
495	C₂	—	8	2	no	—
496	C₂	—	8	1	no	—
497	C₂	C₂²×C₁₃×#127	1	1	yes	characteristic
498	C₂	C₁₃×#3586	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₄×C₁₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#578	C₂	semidirect
2. C₂×C₁₃×#577	C₂	semidirect
3. C₁₃×#3500	C₂	semidirect
4. C₁₃×#3499	C₂	semidirect
5. C₁₃×#3156	C₂	semidirect
6. C₁₃×#3154	C₂	semidirect
7. C₁₃×#3153	C₂	semidirect
8. C₁₃×#3152	C₂	semidirect
9. C₁₃×#3150	C₂	semidirect
10. C₂×C₁₃×#497	C₂	semidirect
11. C₁₃×#2875	C₂	semidirect
18. C₂×C₁₃×#137	C₂²	semidirect
19. C₂×C₁₃×#137	C₂²	semidirect
22. C₂×C₁₃×#135	C₂²	semidirect
23. C₂²×C₁₃×Q₁₆	C₂²	semidirect
31. C₁₃×#536	C₂²	semidirect
34. C₁₃×#532	C₂²	semidirect
35. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
38. C₁₃×#497	C₂²	semidirect
39. C₁₃×#497	C₂²	semidirect
40. C₁₃×#497	C₂²	semidirect
41. C₁₃×#497	C₂²	semidirect
42. C₁₃×#497	C₂²	semidirect
43. C₁₃×#496	C₂²	semidirect
44. C₁₃×#496	C₂²	semidirect
45. C₁₃×#496	C₂²	semidirect
46. C₁₃×#495	C₂²	semidirect
47. C₁₃×#494	C₂²	semidirect
48. C₁₃×#492	C₂²	semidirect
49. C₁₃×#405	C₂²	semidirect
50. C₄×C₁₃×M₁₆	C₂²	semidirect
51. C₂×C₁₃×#97	C₂²	semidirect
87. C₁₃×#131	D₄	semidirect
121. #60651	C₁₃	direct (N × H)
187. C₂×#578	C₂×C₁₃	semidirect
188. C₂×#577	C₂×C₁₃	semidirect
189. #3500	C₂×C₁₃	semidirect
190. #3499	C₂×C₁₃	semidirect
191. #3156	C₂×C₁₃	semidirect
192. #3154	C₂×C₁₃	semidirect
193. #3153	C₂×C₁₃	semidirect
194. #3152	C₂×C₁₃	semidirect
195. #3150	C₂×C₁₃	semidirect
196. C₂×#497	C₂×C₁₃	semidirect
197. #2875	C₂×C₁₃	semidirect
244. C₂×#137	C₂²×C₁₃	semidirect
245. C₂×#137	C₂²×C₁₃	semidirect
248. C₂×#135	C₂²×C₁₃	semidirect
249. C₂²×Q₁₆	C₂²×C₁₃	semidirect
257. #536	C₂²×C₁₃	semidirect
260. #532	C₂²×C₁₃	semidirect
261. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
264. #497	C₂²×C₁₃	semidirect
265. #497	C₂²×C₁₃	semidirect
266. #497	C₂²×C₁₃	semidirect
267. #497	C₂²×C₁₃	semidirect
268. #497	C₂²×C₁₃	semidirect
269. #496	C₂²×C₁₃	semidirect
270. #496	C₂²×C₁₃	semidirect
271. #496	C₂²×C₁₃	semidirect
272. #495	C₂²×C₁₃	semidirect
273. #494	C₂²×C₁₃	semidirect
274. #492	C₂²×C₁₃	semidirect
275. #405	C₂²×C₁₃	semidirect
276. C₄×M₁₆	C₂²×C₁₃	semidirect
277. C₂×#97	C₂²×C₁₃	semidirect
330. #131	D₄×C₁₃	semidirect
435. C₁₃	#60651	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
C₂×C₁₃×#577	2
C₁₃×#3500	2
C₁₃×#3499	2
C₁₃×#3156	2
C₁₃×#3154	2
C₁₃×#3153	2
C₁₃×#3152	2
C₁₃×#3150	2
C₂×C₁₃×#497	2
C₁₃×#2875	2
#60651	13

Subgroups — C13×#60651 #15746990

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60651 #15746990