Subgroups — C₁₃×#60649 #15746988

Order 3328.

3178 conjugacy classes of subgroups.

The subgroup lattice has 466 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	C₂×C₁₃×#577	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₃×#576	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3500	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3156	C₂	1	3	yes	maximal, complemented
6	C₁₃×#3155	C₂	1	3	yes	maximal, complemented
7	C₁₃×#3154	C₂	1	6	yes	maximal, complemented
8	C₁₃×#3153	C₂	1	6	yes	maximal, complemented
9	C₁₃×#3147	C₂	1	3	yes	maximal, complemented
10	C₂×C₁₃×#495	C₂	1	3	yes	maximal, complemented
11	C₄×C₁₃×#131	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	2	yes	—
13	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	2	yes	—
14	C₁₃×#578	—	2	8	no	—
15	C₁₃×#577	—	2	16	no	—
16	C₁₃×#576	—	2	8	no	—
17	C₂×C₁₃×#137	C₂²	1	6	yes	complemented
18	C₂×C₁₃×#137	C₂²	1	6	yes	complemented
19	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	6	yes	—
20	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	6	yes	complemented
21	C₂×C₁₃×#135	C₂²	1	3	yes	—
22	C₂×C₁₃×#135	C₂²	1	6	yes	complemented
23	C₂×C₁₃×#135	C₂²	1	3	yes	complemented
24	C₂²×C₁₃×Q₁₆	C₂²	1	3	yes	complemented
25	C₂²×C₁₃×SD₁₆	C₂²	1	6	yes	complemented
26	C₂²×C₁₃×D₈	C₂²	1	3	yes	—
27	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
29	C₁₃×#548	—	2	4	no	—
30	C₁₃×#546	—	2	12	no	—
31	C₁₃×#536	C₂²	1	6	yes	complemented
32	C₁₃×#535	C₂²	1	6	yes	complemented
33	C₁₃×#532	C₂²	1	6	yes	complemented
34	C₂×C₁₃×#124	C₂²	1	6	yes	complemented
35	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
36	C₁₃×#497	C₂²	1	12	yes	complemented
37	C₁₃×#496	C₂²	1	12	yes	complemented
38	C₁₃×#495	C₂²	1	3	yes	complemented
39	C₁₃×#495	C₂²	1	6	yes	complemented
40	C₁₃×#495	C₂²	1	6	yes	complemented
41	C₁₃×#495	C₂²	1	6	yes	complemented
42	C₁₃×#495	C₂²	1	1	yes	characteristic, complemented
43	C₁₃×#495	C₂²	1	6	yes	complemented
44	C₁₃×#494	C₂²	1	3	yes	complemented
45	C₁₃×#493	C₂²	1	3	yes	complemented
46	C₁₃×#492	C₂²	1	6	yes	complemented
47	C₁₃×#405	C₂²	1	3	yes	complemented
48	C₁₃×#405	C₂²	1	3	yes	complemented
49	C₄×C₁₃×M₁₆	C₂²	1	3	yes	complemented
50	C₂×C₄×C₈×C₁₃	C₂²	1	3	yes	complemented
51	C₁₃×2₋¹⁺⁴	—	2	8	no	—
52	C₁₃×2₋¹⁺⁴	—	2	8	no	—
53	C₁₃×H(5,𝔽₂)	—	2	8	no	—
54	C₁₃×H(5,𝔽₂)	—	2	8	no	—
55	C₂×C₁₃×#41	—	2	2	no	—
56	C₂×C₁₃×#41	—	2	6	no	—
57	C₂×C₁₃×#41	C₂³	1	6	yes	—
58	C₂×C₁₃×#41	C₂³	1	6	yes	—
59	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
60	C₂²×Q₈×C₁₃	—	2	2	no	—
61	C₂²×Q₈×C₁₃	C₂³	1	6	yes	—
62	C₂²×D₄×C₁₃	—	2	6	no	—
63	C₂²×D₄×C₁₃	C₂³	1	6	yes	—
64	C₁₃×#137	—	2	24	no	—
65	C₁₃×#137	—	2	24	no	—
66	C₁₃×AGL(1,ℤ/8)	—	2	24	no	—
67	C₁₃×AGL(1,ℤ/8)	—	2	24	no	—
68	C₁₃×#135	—	2	12	no	—
69	C₁₃×#135	—	2	24	no	—
70	C₁₃×#135	—	2	12	no	—
71	C₂×C₁₃×Q₁₆	—	2	12	no	—
72	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
73	C₂×C₁₃×Q₁₆	C₂³	1	3	yes	—
74	C₂×C₁₃×Q₁₆	C₂³	1	6	yes	—
75	C₂×C₁₃×Q₁₆	C₂³	1	6	yes	—
76	C₂×C₁₃×SD₁₆	—	2	24	no	—
77	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
78	C₂×C₁₃×SD₁₆	C₂³	1	6	yes	—
79	C₂×C₁₃×SD₁₆	C₂³	1	6	yes	—
80	C₂×C₁₃×SD₁₆	C₂³	1	6	yes	—
81	C₂×C₁₃×SD₁₆	C₂³	1	12	yes	—
82	C₂×C₁₃×D₈	—	2	12	no	—
83	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
84	C₂×C₁₃×D₈	C₂³	1	3	yes	—
85	C₂×C₁₃×D₈	C₂³	1	6	yes	—
86	C₂×C₁₃×D₈	C₂³	1	6	yes	—
87	C₁₃×#131	D₄	1	8	yes	complemented
88	C₁₃×#131	D₄	1	8	yes	complemented
89	C₂×C₁₃×M₁₆	C₂³	1	3	yes	—
90	C₂×C₁₃×M₁₆	C₂³	1	3	yes	—
91	C₂²×C₈×C₁₃	C₂³	1	3	yes	—
92	C₂²×C₈×C₁₃	C₂³	1	3	yes	—
93	C₁₃×C₄⋊Q₈	C₂³	1	6	yes	—
94	C₁₃×#127	C₂³	1	6	yes	—
95	C₁₃×#124	—	2	12	no	—
96	C₁₃×#124	C₂³	1	6	yes	—
97	C₁₃×#124	C₂³	1	2	yes	—
98	C₁₃×#124	C₂³	1	12	yes	—
99	C₁₃×#123	—	2	12	no	—
100	C₁₃×C₂²⋊Q₈	—	2	12	no	—
101	C₁₃×#121	—	2	12	no	—
102	C₁₃×#121	—	2	12	no	—
103	C₁₃×#120	—	2	12	no	—
104	C₄×Q₈×C₁₃	D₄	1	2	yes	—
105	C₄×D₄×C₁₃	—	2	12	no	—
106	C₄×D₄×C₁₃	D₄	1	6	yes	—
107	C₁₃×#117	C₂³	1	3	yes	—
108	C₂×C₁₃×C₂²⋊C₄	—	2	12	no	—
109	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
110	C₁₃×#97	C₂³	1	6	yes	—
111	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
112	C₄×C₈×C₁₃	C₂³	1	3	yes	—
113	C₄×C₈×C₁₃	C₂³	1	3	yes	—
114	C₄×C₈×C₁₃	C₂³	1	3	yes	—
115	#60649	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
116	C₂⁴×C₁₃	—	2	6	no	—
117	C₁₃×#41	—	2	12	no	—
118	C₁₃×#41	—	2	12	no	—
119	C₁₃×#41	—	2	12	no	—
120	C₁₃×#41	—	2	12	no	—
121	C₁₃×#41	—	4	8	no	—
122	C₁₃×#41	—	4	24	no	—
123	C₁₃×#41	C₂×D₄	1	4	yes	—
124	C₁₃×#41	C₂×D₄	1	4	yes	—
125	C₂×Q₈×C₁₃	—	2	6	no	—
126	C₂×Q₈×C₁₃	—	2	12	no	—
127	C₂×Q₈×C₁₃	—	2	12	no	—
128	C₂×Q₈×C₁₃	—	4	8	no	—
129	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
130	C₂×Q₈×C₁₃	C₂⁴	1	6	yes	—
131	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
132	C₂×D₄×C₁₃	—	2	6	no	—
133	C₂×D₄×C₁₃	—	2	6	no	—
134	C₂×D₄×C₁₃	—	2	12	no	—
135	C₂×D₄×C₁₃	—	2	12	no	—
136	C₂×D₄×C₁₃	—	2	6	no	—
137	C₂×D₄×C₁₃	—	2	12	no	—
138	C₂×D₄×C₁₃	—	4	24	no	—
139	C₂×D₄×C₁₃	C₂×D₄	1	3	yes	—
140	C₂×D₄×C₁₃	C₂⁴	1	6	yes	—
141	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
142	C₂²×C₄×C₁₃	—	2	6	no	—
143	C₂²×C₄×C₁₃	—	2	6	no	—
144	C₂²×C₄×C₁₃	—	2	6	no	—
145	C₂²×C₄×C₁₃	C₂×D₄	1	6	yes	—
146	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
147	C₁₃×Q₁₆	—	2	6	no	—
148	C₁₃×Q₁₆	—	2	12	no	—
149	C₁₃×Q₁₆	—	2	2	no	—
150	C₁₃×Q₁₆	—	2	12	no	—
151	C₁₃×SD₁₆	—	2	12	no	—
152	C₁₃×SD₁₆	—	2	24	no	—
153	C₁₃×SD₁₆	—	2	4	no	—
154	C₁₃×SD₁₆	—	2	12	no	—
155	C₁₃×SD₁₆	—	2	12	no	—
156	C₁₃×D₈	—	2	6	no	—
157	C₁₃×D₈	—	2	12	no	—
158	C₁₃×D₈	—	2	2	no	—
159	C₁₃×D₈	—	2	12	no	—
160	C₁₃×M₁₆	C₂×D₄	1	12	yes	—
161	C₁₃×M₁₆	C₂×D₄	1	12	yes	—
162	C₂×C₈×C₁₃	C₂×D₄	1	12	yes	—
163	C₂×C₈×C₁₃	C₂×D₄	1	12	yes	—
164	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
165	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
166	C₂×C₈×C₁₃	C₂⁴	1	3	yes	—
167	C₂×C₈×C₁₃	C₂⁴	1	3	yes	—
168	C₁₃×C₄⋊C₄	—	2	12	no	—
169	C₁₃×C₄⋊C₄	C₂×D₄	1	6	yes	—
170	C₁₃×C₂²⋊C₄	—	2	12	no	—
171	C₁₃×C₂²⋊C₄	—	2	24	no	—
172	C₁₃×C₂²⋊C₄	—	2	4	no	—
173	C₁₃×C₂²⋊C₄	C₂×D₄	1	6	yes	—
174	C₄²×C₁₃	C₂×D₄	1	6	yes	—
175	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
176	C₄²×C₁₃	C₂⁴	1	3	yes	—
177	C₂×#578	C₂×C₁₃	1	1	yes	characteristic, complemented
178	C₂×#577	C₂×C₁₃	1	2	yes	complemented
179	C₂×#576	C₂×C₁₃	1	1	yes	characteristic, complemented
180	#3500	C₂×C₁₃	1	2	yes	complemented
181	#3156	C₂×C₁₃	1	3	yes	complemented
182	#3155	C₂×C₁₃	1	3	yes	complemented
183	#3154	C₂×C₁₃	1	6	yes	complemented
184	#3153	C₂×C₁₃	1	6	yes	complemented
185	#3147	C₂×C₁₃	1	3	yes	complemented
186	C₂×#495	C₂×C₁₃	1	3	yes	complemented
187	C₄×#131	C₂×C₁₃	1	1	yes	characteristic, complemented
188	C₂³×C₁₃	—	2	6	no	—
189	C₂³×C₁₃	—	2	2	no	—
190	C₂³×C₁₃	—	4	12	no	—
191	C₂³×C₁₃	—	8	12	no	—
192	C₂³×C₁₃	C₂²×D₄	1	3	yes	—
193	Q₈×C₁₃	—	2	6	no	—
194	Q₈×C₁₃	—	2	2	no	—
195	Q₈×C₁₃	—	2	6	no	—
196	Q₈×C₁₃	—	2	2	no	—
197	Q₈×C₁₃	—	4	12	no	—
198	Q₈×C₁₃	#127	1	4	yes	—
199	D₄×C₁₃	—	2	6	no	—
200	D₄×C₁₃	—	2	2	no	—
201	D₄×C₁₃	—	2	6	no	—
202	D₄×C₁₃	—	2	2	no	—
203	D₄×C₁₃	—	4	12	no	—
204	D₄×C₁₃	—	4	12	no	—
205	D₄×C₁₃	—	4	12	no	—
206	D₄×C₁₃	—	8	12	no	—
207	D₄×C₁₃	#127	1	12	yes	—
208	C₂×C₄×C₁₃	—	2	6	no	—
209	C₂×C₄×C₁₃	—	2	2	no	—
210	C₂×C₄×C₁₃	—	4	6	no	—
211	C₂×C₄×C₁₃	—	4	12	no	—
212	C₂×C₄×C₁₃	—	4	12	no	—
213	C₂×C₄×C₁₃	—	4	12	no	—
214	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
215	C₂×C₄×C₁₃	C₂²×D₄	1	6	yes	—
216	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
217	C₂×C₄×C₁₃	C₂²×D₄	1	6	yes	—
218	C₂×C₄×C₁₃	C₂²×D₄	1	6	yes	—
219	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
220	C₈×C₁₃	C₂²×D₄	1	2	yes	—
221	C₈×C₁₃	C₂²×D₄	1	2	yes	—
222	C₈×C₁₃	C₂²×D₄	1	6	yes	—
223	C₈×C₁₃	C₂²×D₄	1	6	yes	—
224	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	2	yes	—
225	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	2	yes	—
226	#578	—	2	8	no	—
227	#577	—	2	16	no	—
228	#576	—	2	8	no	—
229	C₂×#137	C₂²×C₁₃	1	6	yes	complemented
230	C₂×#137	C₂²×C₁₃	1	6	yes	complemented
231	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	6	yes	—
232	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	6	yes	complemented
233	C₂×#135	C₂²×C₁₃	1	3	yes	—
234	C₂×#135	C₂²×C₁₃	1	6	yes	complemented
235	C₂×#135	C₂²×C₁₃	1	3	yes	complemented
236	C₂²×Q₁₆	C₂²×C₁₃	1	3	yes	complemented
237	C₂²×SD₁₆	C₂²×C₁₃	1	6	yes	complemented
238	C₂²×D₈	C₂²×C₁₃	1	3	yes	—
239	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
240	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
241	#548	—	2	4	no	—
242	#546	—	2	12	no	—
243	#536	C₂²×C₁₃	1	6	yes	complemented
244	#535	C₂²×C₁₃	1	6	yes	complemented
245	#532	C₂²×C₁₃	1	6	yes	complemented
246	C₂×#124	C₂²×C₁₃	1	6	yes	complemented
247	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
248	#497	C₂²×C₁₃	1	12	yes	complemented
249	#496	C₂²×C₁₃	1	12	yes	complemented
250	#495	C₂²×C₁₃	1	3	yes	complemented
251	#495	C₂²×C₁₃	1	6	yes	complemented
252	#495	C₂²×C₁₃	1	6	yes	complemented
253	#495	C₂²×C₁₃	1	6	yes	complemented
254	#495	C₂²×C₁₃	1	1	yes	characteristic, complemented
255	#495	C₂²×C₁₃	1	6	yes	complemented
256	#494	C₂²×C₁₃	1	3	yes	complemented
257	#493	C₂²×C₁₃	1	3	yes	complemented
258	#492	C₂²×C₁₃	1	6	yes	complemented
259	#405	C₂²×C₁₃	1	3	yes	complemented
260	#405	C₂²×C₁₃	1	3	yes	complemented
261	C₄×M₁₆	C₂²×C₁₃	1	3	yes	complemented
262	C₂×C₄×C₈	C₂²×C₁₃	1	3	yes	complemented
263	C₂²×C₁₃	—	2	6	no	—
264	C₂²×C₁₃	—	4	4	no	—
265	C₂²×C₁₃	—	4	12	no	—
266	C₂²×C₁₃	—	4	2	no	—
267	C₂²×C₁₃	—	4	6	no	—
268	C₂²×C₁₃	—	16	12	no	—
269	C₂²×C₁₃	C₂×#127	1	6	yes	—
270	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
271	C₄×C₁₃	—	2	2	no	—
272	C₄×C₁₃	—	2	6	no	—
273	C₄×C₁₃	—	4	2	no	—
274	C₄×C₁₃	—	4	6	no	—
275	C₄×C₁₃	C₂×#127	1	6	yes	—
276	C₄×C₁₃	C₂³×D₄	1	1	yes	characteristic
277	C₄×C₁₃	C₂³×D₄	1	1	yes	characteristic
278	2₋¹⁺⁴	—	2	8	no	—
279	2₋¹⁺⁴	—	2	8	no	—
280	H(5,𝔽₂)	—	2	8	no	—
281	H(5,𝔽₂)	—	2	8	no	—
282	C₂×#41	—	2	2	no	—
283	C₂×#41	—	2	6	no	—
284	C₂×#41	C₂³×C₁₃	1	6	yes	—
285	C₂×#41	C₂³×C₁₃	1	6	yes	—
286	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
287	C₂²×Q₈	—	2	2	no	—
288	C₂²×Q₈	C₂³×C₁₃	1	6	yes	—
289	C₂²×D₄	—	2	6	no	—
290	C₂²×D₄	C₂³×C₁₃	1	6	yes	—
291	#137	—	2	24	no	—
292	#137	—	2	24	no	—
293	AGL(1,ℤ/8)	—	2	24	no	—
294	AGL(1,ℤ/8)	—	2	24	no	—
295	#135	—	2	12	no	—
296	#135	—	2	24	no	—
297	#135	—	2	12	no	—
298	C₂×Q₁₆	—	2	12	no	—
299	C₂×Q₁₆	C₂³×C₁₃	1	3	yes	—
300	C₂×Q₁₆	C₂³×C₁₃	1	6	yes	—
301	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
302	C₂×Q₁₆	C₂³×C₁₃	1	6	yes	—
303	C₂×SD₁₆	—	2	24	no	—
304	C₂×SD₁₆	C₂³×C₁₃	1	6	yes	—
305	C₂×SD₁₆	C₂³×C₁₃	1	12	yes	—
306	C₂×SD₁₆	C₂³×C₁₃	1	6	yes	—
307	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
308	C₂×SD₁₆	C₂³×C₁₃	1	6	yes	—
309	C₂×D₈	—	2	12	no	—
310	C₂×D₈	C₂³×C₁₃	1	3	yes	—
311	C₂×D₈	C₂³×C₁₃	1	6	yes	—
312	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
313	C₂×D₈	C₂³×C₁₃	1	6	yes	—
314	#131	D₄×C₁₃	1	8	yes	complemented
315	#131	D₄×C₁₃	1	8	yes	complemented
316	C₂×M₁₆	C₂³×C₁₃	1	3	yes	—
317	C₂×M₁₆	C₂³×C₁₃	1	3	yes	—
318	C₂²×C₈	C₂³×C₁₃	1	3	yes	—
319	C₂²×C₈	C₂³×C₁₃	1	3	yes	—
320	C₄⋊Q₈	C₂³×C₁₃	1	6	yes	—
321	#127	C₂³×C₁₃	1	6	yes	—
322	#124	—	2	12	no	—
323	#124	C₂³×C₁₃	1	6	yes	—
324	#124	C₂³×C₁₃	1	12	yes	—
325	#124	C₂³×C₁₃	1	2	yes	—
326	#123	—	2	12	no	—
327	C₂²⋊Q₈	—	2	12	no	—
328	#121	—	2	12	no	—
329	#121	—	2	12	no	—
330	#120	—	2	12	no	—
331	C₄×Q₈	D₄×C₁₃	1	2	yes	—
332	C₄×D₄	—	2	12	no	—
333	C₄×D₄	D₄×C₁₃	1	6	yes	—
334	#117	C₂³×C₁₃	1	3	yes	—
335	C₂×C₂²⋊C₄	—	2	12	no	—
336	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
337	#97	C₂³×C₁₃	1	6	yes	—
338	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
339	C₄×C₈	C₂³×C₁₃	1	3	yes	—
340	C₄×C₈	C₂³×C₁₃	1	3	yes	—
341	C₄×C₈	C₂³×C₁₃	1	3	yes	—
342	C₂×C₁₃	—	2	6	no	—
343	C₂×C₁₃	—	8	2	no	—
344	C₂×C₁₃	—	8	6	no	—
345	C₂×C₁₃	C₂²×#127	1	1	yes	characteristic
346	C₂×C₁₃	#3584	1	2	yes	—
347	C₂⁴	—	2	6	no	—
348	#41	—	2	12	no	—
349	#41	—	2	12	no	—
350	#41	—	2	12	no	—
351	#41	—	2	12	no	—
352	#41	—	4	8	no	—
353	#41	—	4	24	no	—
354	#41	C₂×D₄×C₁₃	1	4	yes	—
355	#41	C₂×D₄×C₁₃	1	4	yes	—
356	C₂×Q₈	—	2	6	no	—
357	C₂×Q₈	—	2	12	no	—
358	C₂×Q₈	—	2	12	no	—
359	C₂×Q₈	—	4	8	no	—
360	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
361	C₂×Q₈	C₂⁴×C₁₃	1	6	yes	—
362	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
363	C₂×D₄	—	2	6	no	—
364	C₂×D₄	—	2	6	no	—
365	C₂×D₄	—	2	12	no	—
366	C₂×D₄	—	2	12	no	—
367	C₂×D₄	—	2	6	no	—
368	C₂×D₄	—	2	12	no	—
369	C₂×D₄	—	4	24	no	—
370	C₂×D₄	C₂×D₄×C₁₃	1	3	yes	—
371	C₂×D₄	C₂⁴×C₁₃	1	6	yes	—
372	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
373	C₂²×C₄	—	2	6	no	—
374	C₂²×C₄	—	2	6	no	—
375	C₂²×C₄	—	2	6	no	—
376	C₂²×C₄	C₂×D₄×C₁₃	1	6	yes	—
377	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
378	Q₁₆	—	2	6	no	—
379	Q₁₆	—	2	12	no	—
380	Q₁₆	—	2	2	no	—
381	Q₁₆	—	2	12	no	—
382	SD₁₆	—	2	12	no	—
383	SD₁₆	—	2	24	no	—
384	SD₁₆	—	2	4	no	—
385	SD₁₆	—	2	12	no	—
386	SD₁₆	—	2	12	no	—
387	D₈	—	2	6	no	—
388	D₈	—	2	12	no	—
389	D₈	—	2	2	no	—
390	D₈	—	2	12	no	—
391	M₁₆	C₂×D₄×C₁₃	1	12	yes	—
392	M₁₆	C₂×D₄×C₁₃	1	12	yes	—
393	C₂×C₈	C₂×D₄×C₁₃	1	12	yes	—
394	C₂×C₈	C₂×D₄×C₁₃	1	12	yes	—
395	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
396	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
397	C₂×C₈	C₂⁴×C₁₃	1	3	yes	—
398	C₂×C₈	C₂⁴×C₁₃	1	3	yes	—
399	C₄⋊C₄	—	2	12	no	—
400	C₄⋊C₄	C₂×D₄×C₁₃	1	6	yes	—
401	C₂²⋊C₄	—	2	12	no	—
402	C₂²⋊C₄	—	2	24	no	—
403	C₂²⋊C₄	—	2	4	no	—
404	C₂²⋊C₄	C₂×D₄×C₁₃	1	6	yes	—
405	C₄²	C₂×D₄×C₁₃	1	6	yes	—
406	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
407	C₄²	C₂⁴×C₁₃	1	3	yes	—
408	C₁₃	#60649	1	1	yes	characteristic, direct product factor, Sylow
409	C₂³	—	2	6	no	—
410	C₂³	—	2	2	no	—
411	C₂³	—	4	12	no	—
412	C₂³	—	8	12	no	—
413	C₂³	C₂²×D₄×C₁₃	1	3	yes	—
414	Q₈	—	2	6	no	—
415	Q₈	—	2	2	no	—
416	Q₈	—	2	6	no	—
417	Q₈	—	2	2	no	—
418	Q₈	—	4	12	no	—
419	Q₈	C₁₃×#127	1	4	yes	—
420	D₄	—	2	6	no	—
421	D₄	—	2	2	no	—
422	D₄	—	2	6	no	—
423	D₄	—	2	2	no	—
424	D₄	—	4	12	no	—
425	D₄	—	4	12	no	—
426	D₄	—	4	12	no	—
427	D₄	—	8	12	no	—
428	D₄	C₁₃×#127	1	12	yes	—
429	C₂×C₄	—	2	6	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	4	6	no	—
432	C₂×C₄	—	4	12	no	—
433	C₂×C₄	—	4	12	no	—
434	C₂×C₄	—	4	12	no	—
435	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
436	C₂×C₄	C₂²×D₄×C₁₃	1	6	yes	—
437	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
438	C₂×C₄	C₂²×D₄×C₁₃	1	6	yes	—
439	C₂×C₄	C₂²×D₄×C₁₃	1	6	yes	—
440	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
441	C₈	C₂²×D₄×C₁₃	1	2	yes	—
442	C₈	C₂²×D₄×C₁₃	1	2	yes	—
443	C₈	C₂²×D₄×C₁₃	1	6	yes	—
444	C₈	C₂²×D₄×C₁₃	1	6	yes	—
445	C₂²	—	2	6	no	—
446	C₂²	—	4	4	no	—
447	C₂²	—	4	12	no	—
448	C₂²	—	4	2	no	—
449	C₂²	—	4	6	no	—
450	C₂²	—	16	12	no	—
451	C₂²	C₂×C₁₃×#127	1	6	yes	—
452	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
453	C₄	—	2	2	no	—
454	C₄	—	2	6	no	—
455	C₄	—	4	2	no	—
456	C₄	—	4	6	no	—
457	C₄	C₂×C₁₃×#127	1	6	yes	—
458	C₄	C₂³×D₄×C₁₃	1	1	yes	characteristic
459	C₄	C₂³×D₄×C₁₃	1	1	yes	characteristic
460	C₂	—	2	6	no	—
461	C₂	—	8	6	no	—
462	C₂	—	8	2	no	—
463	C₂	C₂²×C₁₃×#127	1	1	yes	characteristic
464	C₂	C₁₃×#3584	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. C₂×C₁₃×#576	C₂	semidirect
4. C₁₃×#3500	C₂	semidirect
5. C₁₃×#3156	C₂	semidirect
6. C₁₃×#3155	C₂	semidirect
7. C₁₃×#3154	C₂	semidirect
8. C₁₃×#3153	C₂	semidirect
9. C₁₃×#3147	C₂	semidirect
10. C₂×C₁₃×#495	C₂	semidirect
11. C₄×C₁₃×#131	C₂	semidirect
17. C₂×C₁₃×#137	C₂²	semidirect
18. C₂×C₁₃×#137	C₂²	semidirect
20. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
22. C₂×C₁₃×#135	C₂²	semidirect
23. C₂×C₁₃×#135	C₂²	semidirect
24. C₂²×C₁₃×Q₁₆	C₂²	semidirect
25. C₂²×C₁₃×SD₁₆	C₂²	semidirect
31. C₁₃×#536	C₂²	semidirect
32. C₁₃×#535	C₂²	semidirect
33. C₁₃×#532	C₂²	semidirect
34. C₂×C₁₃×#124	C₂²	semidirect
36. C₁₃×#497	C₂²	semidirect
37. C₁₃×#496	C₂²	semidirect
38. C₁₃×#495	C₂²	semidirect
39. C₁₃×#495	C₂²	semidirect
40. C₁₃×#495	C₂²	semidirect
41. C₁₃×#495	C₂²	semidirect
42. C₁₃×#495	C₂²	semidirect
43. C₁₃×#495	C₂²	semidirect
44. C₁₃×#494	C₂²	semidirect
45. C₁₃×#493	C₂²	semidirect
46. C₁₃×#492	C₂²	semidirect
47. C₁₃×#405	C₂²	semidirect
48. C₁₃×#405	C₂²	semidirect
49. C₄×C₁₃×M₁₆	C₂²	semidirect
50. C₂×C₄×C₈×C₁₃	C₂²	semidirect
87. C₁₃×#131	D₄	semidirect
88. C₁₃×#131	D₄	semidirect
115. #60649	C₁₃	direct (N × H)
177. C₂×#578	C₂×C₁₃	semidirect
178. C₂×#577	C₂×C₁₃	semidirect
179. C₂×#576	C₂×C₁₃	semidirect
180. #3500	C₂×C₁₃	semidirect
181. #3156	C₂×C₁₃	semidirect
182. #3155	C₂×C₁₃	semidirect
183. #3154	C₂×C₁₃	semidirect
184. #3153	C₂×C₁₃	semidirect
185. #3147	C₂×C₁₃	semidirect
186. C₂×#495	C₂×C₁₃	semidirect
187. C₄×#131	C₂×C₁₃	semidirect
229. C₂×#137	C₂²×C₁₃	semidirect
230. C₂×#137	C₂²×C₁₃	semidirect
232. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
234. C₂×#135	C₂²×C₁₃	semidirect
235. C₂×#135	C₂²×C₁₃	semidirect
236. C₂²×Q₁₆	C₂²×C₁₃	semidirect
237. C₂²×SD₁₆	C₂²×C₁₃	semidirect
243. #536	C₂²×C₁₃	semidirect
244. #535	C₂²×C₁₃	semidirect
245. #532	C₂²×C₁₃	semidirect
246. C₂×#124	C₂²×C₁₃	semidirect
248. #497	C₂²×C₁₃	semidirect
249. #496	C₂²×C₁₃	semidirect
250. #495	C₂²×C₁₃	semidirect
251. #495	C₂²×C₁₃	semidirect
252. #495	C₂²×C₁₃	semidirect
253. #495	C₂²×C₁₃	semidirect
254. #495	C₂²×C₁₃	semidirect
255. #495	C₂²×C₁₃	semidirect
256. #494	C₂²×C₁₃	semidirect
257. #493	C₂²×C₁₃	semidirect
258. #492	C₂²×C₁₃	semidirect
259. #405	C₂²×C₁₃	semidirect
260. #405	C₂²×C₁₃	semidirect
261. C₄×M₁₆	C₂²×C₁₃	semidirect
262. C₂×C₄×C₈	C₂²×C₁₃	semidirect
314. #131	D₄×C₁₃	semidirect
315. #131	D₄×C₁₃	semidirect
408. C₁₃	#60649	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
C₂×C₁₃×#576	2
C₁₃×#3500	2
C₁₃×#3156	2
C₁₃×#3155	2
C₁₃×#3154	2
C₁₃×#3153	2
C₁₃×#3147	2
C₂×C₁₃×#495	2
C₄×C₁₃×#131	2
#60649	13

Subgroups — C13×#60649 #15746988

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60649 #15746988