Subgroups — C₁₃×#61054 #15747393

Order 3328.

2710 conjugacy classes of subgroups.

The subgroup lattice has 682 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	C₂²×C₁₃×#135	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3487	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3287	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3285	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3271	C₂	1	8	yes	maximal, complemented
7	C₁₃×#3155	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#3058	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3050	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3043	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3010	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3005	C₂	1	2	yes	maximal, complemented
13	C₁₃×#2950	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#2929	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	2	yes	—
16	C₂²×C₁₃×#41	C₂²	1	2	yes	—
17	C₁₃×#578	—	2	8	no	—
18	C₂×C₁₃×#137	C₂²	1	2	yes	—
19	C₂×C₁₃×#137	C₂²	1	4	yes	complemented
20	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
21	C₂×C₁₃×#135	—	2	8	no	—
22	C₂×C₁₃×#135	C₂²	1	4	yes	—
23	C₂×C₁₃×#135	C₂²	1	4	yes	—
24	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#135	C₂²	1	2	yes	complemented
26	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
27	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
28	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
29	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
31	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
32	C₁₃×#550	—	2	4	no	—
33	C₁₃×#550	C₂²	1	8	yes	complemented
34	C₁₃×#548	—	2	4	no	—
35	C₁₃×#548	C₂²	1	8	yes	complemented
36	C₁₃×#535	—	2	4	no	—
37	C₁₃×#535	C₂²	1	2	yes	—
38	C₁₃×#535	C₂²	1	2	yes	—
39	C₁₃×#525	—	2	4	no	—
40	C₁₃×#525	C₂²	1	2	yes	—
41	C₁₃×#525	C₂²	1	1	yes	characteristic
42	C₁₃×#519	C₂²	1	2	yes	—
43	C₁₃×#496	C₂²	1	4	yes	complemented
44	C₁₃×#495	C₂²	1	2	yes	complemented
45	C₁₃×#493	C₂²	1	2	yes	complemented
46	C₁₃×#469	C₂²	1	4	yes	complemented
47	C₁₃×#467	C₂²	1	2	yes	complemented
48	C₁₃×#466	C₂²	1	4	yes	complemented
49	C₁₃×#466	C₂²	1	2	yes	complemented
50	C₁₃×#465	C₂²	1	4	yes	complemented
51	C₁₃×#464	C₂²	1	8	yes	complemented
52	C₁₃×#460	C₂²	1	8	yes	complemented
53	C₁₃×#452	C₂²	1	8	yes	complemented
54	C₁₃×#449	C₂²	1	8	yes	complemented
55	C₁₃×#449	C₂²	1	8	yes	complemented
56	C₁₃×#448	C₂²	1	8	yes	complemented
57	C₁₃×#441	C₂²	1	4	yes	complemented
58	C₄×C₁₃×Q₁₆	C₂²	1	4	yes	complemented
59	C₁₃×#435	C₂²	1	4	yes	complemented
60	C₈×D₄×C₁₃	C₂²	1	4	yes	complemented
61	C₁₃×#427	C₂²	1	1	yes	characteristic
62	C₁₃×#424	C₂²	1	1	yes	characteristic
63	C₁₃×#419	C₂²	1	2	yes	—
64	C₁₃×#418	C₂²	1	2	yes	—
65	C₁₃×#416	C₂²	1	2	yes	—
66	C₁₃×#408	C₂²	1	1	yes	characteristic
67	C₁₃×#407	C₂²	1	1	yes	characteristic
68	C₁₃×#405	C₂²	1	1	yes	characteristic
69	C₁₃×2₋¹⁺⁴	—	2	8	no	—
70	C₁₃×2₋¹⁺⁴	—	4	4	no	—
71	C₂×C₁₃×#41	—	2	4	no	—
72	C₂×C₁₃×#41	—	2	2	no	—
73	C₂×C₁₃×#41	—	2	4	no	—
74	C₂×C₁₃×#41	—	2	8	no	—
75	C₂×C₁₃×#41	—	4	4	no	—
76	C₂×C₁₃×#41	C₂³	1	2	yes	—
77	C₂×C₁₃×#41	C₂³	1	4	yes	—
78	C₂×C₁₃×#41	C₂³	1	8	yes	—
79	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
80	C₂²×Q₈×C₁₃	—	2	2	no	—
81	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
82	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
83	C₂²×D₄×C₁₃	—	2	2	no	—
84	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
85	C₂³×C₄×C₁₃	—	2	2	no	—
86	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
87	C₁₃×#137	—	2	8	no	—
88	C₁₃×#137	—	2	16	no	—
89	C₁₃×AGL(1,ℤ/8)	—	4	4	no	—
90	C₁₃×#135	—	2	16	no	—
91	C₁₃×#135	—	2	16	no	—
92	C₁₃×#135	—	2	8	no	—
93	C₁₃×#135	—	2	4	no	—
94	C₂×C₁₃×Q₁₆	—	2	8	no	—
95	C₂×C₁₃×Q₁₆	D₄	1	8	yes	complemented
96	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
97	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
98	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
99	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
100	C₂×C₁₃×SD₁₆	—	2	8	no	—
101	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
102	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
103	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
104	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
105	C₂×C₁₃×D₈	—	2	4	no	—
106	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
107	C₂×C₁₃×D₈	C₂³	1	2	yes	—
108	C₂×C₁₃×D₈	C₂³	1	2	yes	—
109	C₂×C₁₃×D₈	C₂³	1	4	yes	—
110	C₁₃×#131	—	2	4	no	—
111	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
112	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
113	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
114	C₂²×C₈×C₁₃	—	2	4	no	—
115	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
116	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
117	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
118	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
119	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
120	C₁₃×#127	—	2	8	no	—
121	C₁₃×#127	—	2	2	no	—
122	C₁₃×#127	C₂³	1	4	yes	—
123	C₁₃×#124	—	2	2	no	—
124	C₁₃×#124	—	2	8	no	—
125	C₁₃×#124	C₂³	1	4	yes	—
126	C₁₃×#123	—	2	2	no	—
127	C₁₃×#123	D₄	1	2	yes	—
128	C₁₃×C₂²⋊Q₈	—	2	8	no	—
129	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
130	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
131	C₁₃×#121	—	2	8	no	—
132	C₁₃×#121	—	2	4	no	—
133	C₁₃×#121	—	2	8	no	—
134	C₁₃×#121	—	2	8	no	—
135	C₁₃×#121	D₄	1	2	yes	—
136	C₁₃×#121	C₂³	1	8	yes	—
137	C₁₃×#121	C₂³	1	4	yes	—
138	C₁₃×#120	—	2	2	no	—
139	C₁₃×#120	—	2	4	no	—
140	C₁₃×#120	—	2	4	no	—
141	C₁₃×#120	D₄	1	2	yes	—
142	C₄×Q₈×C₁₃	—	2	4	no	—
143	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
144	C₄×D₄×C₁₃	—	2	4	no	—
145	C₄×D₄×C₁₃	—	2	8	no	—
146	C₄×D₄×C₁₃	—	2	8	no	—
147	C₄×D₄×C₁₃	C₂³	1	4	yes	—
148	C₁₃×#117	—	2	4	no	—
149	C₁₃×#117	C₂³	1	2	yes	—
150	C₁₃×#117	C₂³	1	1	yes	characteristic
151	C₁₃×#107	C₂³	1	2	yes	—
152	C₁₃×#106	C₂³	1	2	yes	—
153	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
154	C₁₃×#103	C₂³	1	4	yes	—
155	C₁₃×#103	C₂³	1	8	yes	—
156	C₁₃×#102	C₂³	1	4	yes	—
157	C₁₃×#102	C₂³	1	8	yes	—
158	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
159	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
160	C₁₃×#97	C₂³	1	2	yes	—
161	C₄×C₈×C₁₃	C₂³	1	2	yes	—
162	#61054	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
163	C₂⁴×C₁₃	—	2	2	no	—
164	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
165	C₁₃×#41	—	2	2	no	—
166	C₁₃×#41	—	2	2	no	—
167	C₁₃×#41	—	2	16	no	—
168	C₁₃×#41	—	2	8	no	—
169	C₁₃×#41	—	2	4	no	—
170	C₁₃×#41	—	2	4	no	—
171	C₁₃×#41	—	4	8	no	—
172	C₁₃×#41	—	4	4	no	—
173	C₁₃×#41	—	4	16	no	—
174	C₁₃×#41	—	4	16	no	—
175	C₁₃×#41	—	4	8	no	—
176	C₂×Q₈×C₁₃	—	2	2	no	—
177	C₂×Q₈×C₁₃	—	2	4	no	—
178	C₂×Q₈×C₁₃	—	2	4	no	—
179	C₂×Q₈×C₁₃	—	2	8	no	—
180	C₂×Q₈×C₁₃	—	4	4	no	—
181	C₂×Q₈×C₁₃	—	4	8	no	—
182	C₂×Q₈×C₁₃	C₂×D₄	1	8	yes	—
183	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
184	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
185	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
186	C₂×D₄×C₁₃	—	2	2	no	—
187	C₂×D₄×C₁₃	—	2	8	no	—
188	C₂×D₄×C₁₃	—	2	4	no	—
189	C₂×D₄×C₁₃	—	2	8	no	—
190	C₂×D₄×C₁₃	—	2	4	no	—
191	C₂×D₄×C₁₃	—	2	4	no	—
192	C₂×D₄×C₁₃	—	2	2	no	—
193	C₂×D₄×C₁₃	—	2	8	no	—
194	C₂×D₄×C₁₃	—	2	4	no	—
195	C₂×D₄×C₁₃	—	4	8	no	—
196	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
197	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
198	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
199	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
200	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
201	C₂²×C₄×C₁₃	—	2	2	no	—
202	C₂²×C₄×C₁₃	—	2	2	no	—
203	C₂²×C₄×C₁₃	—	2	2	no	—
204	C₂²×C₄×C₁₃	—	2	4	no	—
205	C₂²×C₄×C₁₃	—	2	4	no	—
206	C₂²×C₄×C₁₃	—	2	2	no	—
207	C₂²×C₄×C₁₃	—	2	8	no	—
208	C₂²×C₄×C₁₃	—	4	8	no	—
209	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
210	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
211	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
212	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
213	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
214	C₁₃×Q₁₆	—	2	8	no	—
215	C₁₃×Q₁₆	—	2	2	no	—
216	C₁₃×Q₁₆	C₂×D₄	1	8	yes	—
217	C₁₃×Q₁₆	C₂×D₄	1	8	yes	—
218	C₁₃×SD₁₆	—	2	16	no	—
219	C₁₃×SD₁₆	—	2	8	no	—
220	C₁₃×SD₁₆	—	2	4	no	—
221	C₁₃×SD₁₆	—	4	4	no	—
222	C₁₃×D₈	—	2	4	no	—
223	C₁₃×D₈	—	2	4	no	—
224	C₁₃×D₈	—	2	2	no	—
225	C₁₃×D₈	—	4	4	no	—
226	C₁₃×M₁₆	—	2	2	no	—
227	C₁₃×M₁₆	—	2	2	no	—
228	C₁₃×M₁₆	—	2	4	no	—
229	C₂×C₈×C₁₃	—	2	2	no	—
230	C₂×C₈×C₁₃	—	2	4	no	—
231	C₂×C₈×C₁₃	—	2	4	no	—
232	C₂×C₈×C₁₃	—	2	4	no	—
233	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
234	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
235	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
236	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
237	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
238	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
239	C₁₃×C₄⋊C₄	—	2	8	no	—
240	C₁₃×C₄⋊C₄	—	2	4	no	—
241	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
242	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
243	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
244	C₁₃×C₂²⋊C₄	—	2	2	no	—
245	C₁₃×C₂²⋊C₄	—	2	4	no	—
246	C₁₃×C₂²⋊C₄	—	2	4	no	—
247	C₁₃×C₂²⋊C₄	—	2	8	no	—
248	C₁₃×C₂²⋊C₄	—	2	8	no	—
249	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
250	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
251	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
252	C₄²×C₁₃	—	2	8	no	—
253	C₄²×C₁₃	—	2	2	no	—
254	C₄²×C₁₃	C₂⁴	1	2	yes	—
255	C₂×#578	C₂×C₁₃	1	1	yes	characteristic, complemented
256	C₂²×#135	C₂×C₁₃	1	1	yes	characteristic, complemented
257	#3487	C₂×C₁₃	1	2	yes	complemented
258	#3287	C₂×C₁₃	1	4	yes	complemented
259	#3285	C₂×C₁₃	1	4	yes	complemented
260	#3271	C₂×C₁₃	1	8	yes	complemented
261	#3155	C₂×C₁₃	1	1	yes	characteristic, complemented
262	#3058	C₂×C₁₃	1	1	yes	characteristic, complemented
263	#3050	C₂×C₁₃	1	1	yes	characteristic, complemented
264	#3043	C₂×C₁₃	1	2	yes	complemented
265	#3010	C₂×C₁₃	1	2	yes	complemented
266	#3005	C₂×C₁₃	1	2	yes	complemented
267	#2950	C₂×C₁₃	1	1	yes	characteristic, complemented
268	#2929	C₂×C₁₃	1	1	yes	characteristic, complemented
269	C₂³×C₁₃	—	2	2	no	—
270	C₂³×C₁₃	—	2	4	no	—
271	C₂³×C₁₃	—	2	2	no	—
272	C₂³×C₁₃	—	4	2	no	—
273	C₂³×C₁₃	—	4	4	no	—
274	C₂³×C₁₃	—	8	4	no	—
275	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
276	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
277	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
278	Q₈×C₁₃	—	2	8	no	—
279	Q₈×C₁₃	—	2	2	no	—
280	Q₈×C₁₃	—	2	4	no	—
281	Q₈×C₁₃	—	2	2	no	—
282	Q₈×C₁₃	—	2	2	no	—
283	Q₈×C₁₃	—	4	8	no	—
284	Q₈×C₁₃	C₂²×D₄	1	8	yes	—
285	D₄×C₁₃	—	2	4	no	—
286	D₄×C₁₃	—	2	2	no	—
287	D₄×C₁₃	—	2	4	no	—
288	D₄×C₁₃	—	2	2	no	—
289	D₄×C₁₃	—	2	2	no	—
290	D₄×C₁₃	—	2	4	no	—
291	D₄×C₁₃	—	4	4	no	—
292	D₄×C₁₃	—	4	16	no	—
293	D₄×C₁₃	—	4	8	no	—
294	D₄×C₁₃	—	4	4	no	—
295	D₄×C₁₃	—	4	4	no	—
296	D₄×C₁₃	—	8	8	no	—
297	D₄×C₁₃	—	8	8	no	—
298	D₄×C₁₃	—	8	4	no	—
299	C₂×C₄×C₁₃	—	2	2	no	—
300	C₂×C₄×C₁₃	—	2	8	no	—
301	C₂×C₄×C₁₃	—	2	4	no	—
302	C₂×C₄×C₁₃	—	2	4	no	—
303	C₂×C₄×C₁₃	—	2	2	no	—
304	C₂×C₄×C₁₃	—	2	2	no	—
305	C₂×C₄×C₁₃	—	2	2	no	—
306	C₂×C₄×C₁₃	—	2	2	no	—
307	C₂×C₄×C₁₃	—	2	4	no	—
308	C₂×C₄×C₁₃	—	2	2	no	—
309	C₂×C₄×C₁₃	—	4	16	no	—
310	C₂×C₄×C₁₃	—	4	8	no	—
311	C₂×C₄×C₁₃	—	4	8	no	—
312	C₂×C₄×C₁₃	—	4	4	no	—
313	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
314	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
315	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
316	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
317	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
318	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
319	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
320	C₈×C₁₃	—	2	2	no	—
321	C₈×C₁₃	—	2	2	no	—
322	C₈×C₁₃	—	2	2	no	—
323	C₈×C₁₃	C₂²×D₄	1	2	yes	—
324	C₈×C₁₃	C₂²×D₄	1	2	yes	—
325	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	2	yes	—
326	C₂²×#41	C₂²×C₁₃	1	2	yes	—
327	#578	—	2	8	no	—
328	C₂×#137	C₂²×C₁₃	1	2	yes	—
329	C₂×#137	C₂²×C₁₃	1	4	yes	complemented
330	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	—
331	C₂×#135	—	2	8	no	—
332	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
333	C₂×#135	C₂²×C₁₃	1	4	yes	—
334	C₂×#135	C₂²×C₁₃	1	4	yes	—
335	C₂×#135	C₂²×C₁₃	1	2	yes	complemented
336	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
337	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
338	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
339	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
340	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
341	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
342	#550	—	2	4	no	—
343	#550	C₂²×C₁₃	1	8	yes	complemented
344	#548	—	2	4	no	—
345	#548	C₂²×C₁₃	1	8	yes	complemented
346	#535	—	2	4	no	—
347	#535	C₂²×C₁₃	1	2	yes	—
348	#535	C₂²×C₁₃	1	2	yes	—
349	#525	—	2	4	no	—
350	#525	C₂²×C₁₃	1	2	yes	—
351	#525	C₂²×C₁₃	1	1	yes	characteristic
352	#519	C₂²×C₁₃	1	2	yes	—
353	#496	C₂²×C₁₃	1	4	yes	complemented
354	#495	C₂²×C₁₃	1	2	yes	complemented
355	#493	C₂²×C₁₃	1	2	yes	complemented
356	#469	C₂²×C₁₃	1	4	yes	complemented
357	#467	C₂²×C₁₃	1	2	yes	complemented
358	#466	C₂²×C₁₃	1	4	yes	complemented
359	#466	C₂²×C₁₃	1	2	yes	complemented
360	#465	C₂²×C₁₃	1	4	yes	complemented
361	#464	C₂²×C₁₃	1	8	yes	complemented
362	#460	C₂²×C₁₃	1	8	yes	complemented
363	#452	C₂²×C₁₃	1	8	yes	complemented
364	#449	C₂²×C₁₃	1	8	yes	complemented
365	#449	C₂²×C₁₃	1	8	yes	complemented
366	#448	C₂²×C₁₃	1	8	yes	complemented
367	#441	C₂²×C₁₃	1	4	yes	complemented
368	C₄×Q₁₆	C₂²×C₁₃	1	4	yes	complemented
369	#435	C₂²×C₁₃	1	4	yes	complemented
370	C₈×D₄	C₂²×C₁₃	1	4	yes	complemented
371	#427	C₂²×C₁₃	1	1	yes	characteristic
372	#424	C₂²×C₁₃	1	1	yes	characteristic
373	#419	C₂²×C₁₃	1	2	yes	—
374	#418	C₂²×C₁₃	1	2	yes	—
375	#416	C₂²×C₁₃	1	2	yes	—
376	#408	C₂²×C₁₃	1	1	yes	characteristic
377	#407	C₂²×C₁₃	1	1	yes	characteristic
378	#405	C₂²×C₁₃	1	1	yes	characteristic
379	C₂²×C₁₃	—	2	2	no	—
380	C₂²×C₁₃	—	2	2	no	—
381	C₂²×C₁₃	—	2	4	no	—
382	C₂²×C₁₃	—	2	2	no	—
383	C₂²×C₁₃	—	2	2	no	—
384	C₂²×C₁₃	—	2	2	no	—
385	C₂²×C₁₃	—	4	4	no	—
386	C₂²×C₁₃	—	4	4	no	—
387	C₂²×C₁₃	—	4	8	no	—
388	C₂²×C₁₃	—	4	2	no	—
389	C₂²×C₁₃	—	4	4	no	—
390	C₂²×C₁₃	—	8	8	no	—
391	C₂²×C₁₃	D₄²	1	2	yes	—
392	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
393	C₄×C₁₃	—	2	4	no	—
394	C₄×C₁₃	—	2	2	no	—
395	C₄×C₁₃	—	2	8	no	—
396	C₄×C₁₃	—	2	2	no	—
397	C₄×C₁₃	—	4	4	no	—
398	C₄×C₁₃	—	4	2	no	—
399	C₄×C₁₃	D₄²	1	2	yes	—
400	C₄×C₁₃	C₂³×D₄	1	1	yes	characteristic
401	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
402	2₋¹⁺⁴	—	2	8	no	—
403	2₋¹⁺⁴	—	4	4	no	—
404	C₂×#41	—	2	4	no	—
405	C₂×#41	—	2	2	no	—
406	C₂×#41	—	2	4	no	—
407	C₂×#41	—	2	8	no	—
408	C₂×#41	—	4	4	no	—
409	C₂×#41	C₂³×C₁₃	1	2	yes	—
410	C₂×#41	C₂³×C₁₃	1	8	yes	—
411	C₂×#41	C₂³×C₁₃	1	4	yes	—
412	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
413	C₂²×Q₈	—	2	2	no	—
414	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
415	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
416	C₂²×D₄	—	2	2	no	—
417	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
418	C₂³×C₄	—	2	2	no	—
419	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
420	#137	—	2	8	no	—
421	#137	—	2	16	no	—
422	AGL(1,ℤ/8)	—	4	4	no	—
423	#135	—	2	16	no	—
424	#135	—	2	16	no	—
425	#135	—	2	8	no	—
426	#135	—	2	4	no	—
427	C₂×Q₁₆	—	2	8	no	—
428	C₂×Q₁₆	D₄×C₁₃	1	8	yes	complemented
429	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
430	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
431	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
432	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
433	C₂×SD₁₆	—	2	8	no	—
434	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
435	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
436	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
437	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
438	C₂×D₈	—	2	4	no	—
439	C₂×D₈	C₂³×C₁₃	1	2	yes	—
440	C₂×D₈	C₂³×C₁₃	1	2	yes	—
441	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
442	C₂×D₈	C₂³×C₁₃	1	4	yes	—
443	#131	—	2	4	no	—
444	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
445	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
446	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
447	C₂²×C₈	—	2	4	no	—
448	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
449	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
450	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
451	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
452	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
453	#127	—	2	8	no	—
454	#127	—	2	2	no	—
455	#127	C₂³×C₁₃	1	4	yes	—
456	#124	—	2	2	no	—
457	#124	—	2	8	no	—
458	#124	C₂³×C₁₃	1	4	yes	—
459	#123	—	2	2	no	—
460	#123	D₄×C₁₃	1	2	yes	—
461	C₂²⋊Q₈	—	2	8	no	—
462	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
463	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
464	#121	—	2	8	no	—
465	#121	—	2	4	no	—
466	#121	—	2	8	no	—
467	#121	—	2	8	no	—
468	#121	D₄×C₁₃	1	2	yes	—
469	#121	C₂³×C₁₃	1	4	yes	—
470	#121	C₂³×C₁₃	1	8	yes	—
471	#120	—	2	2	no	—
472	#120	—	2	4	no	—
473	#120	—	2	4	no	—
474	#120	D₄×C₁₃	1	2	yes	—
475	C₄×Q₈	—	2	4	no	—
476	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
477	C₄×D₄	—	2	4	no	—
478	C₄×D₄	—	2	8	no	—
479	C₄×D₄	—	2	8	no	—
480	C₄×D₄	C₂³×C₁₃	1	4	yes	—
481	#117	—	2	4	no	—
482	#117	C₂³×C₁₃	1	2	yes	—
483	#117	C₂³×C₁₃	1	1	yes	characteristic
484	#107	C₂³×C₁₃	1	2	yes	—
485	#106	C₂³×C₁₃	1	2	yes	—
486	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
487	#103	C₂³×C₁₃	1	4	yes	—
488	#103	C₂³×C₁₃	1	8	yes	—
489	#102	C₂³×C₁₃	1	4	yes	—
490	#102	C₂³×C₁₃	1	8	yes	—
491	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
492	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
493	#97	C₂³×C₁₃	1	2	yes	—
494	C₄×C₈	C₂³×C₁₃	1	2	yes	—
495	C₂×C₁₃	—	2	2	no	—
496	C₂×C₁₃	—	4	2	no	—
497	C₂×C₁₃	—	4	2	no	—
498	C₂×C₁₃	—	8	2	no	—
499	C₂×C₁₃	—	8	4	no	—
500	C₂×C₁₃	C₂×D₄²	1	1	yes	characteristic
501	C₂×C₁₃	#3584	1	2	yes	—
502	C₂⁴	—	2	2	no	—
503	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
504	#41	—	2	2	no	—
505	#41	—	2	2	no	—
506	#41	—	2	16	no	—
507	#41	—	2	8	no	—
508	#41	—	2	4	no	—
509	#41	—	2	4	no	—
510	#41	—	4	8	no	—
511	#41	—	4	4	no	—
512	#41	—	4	16	no	—
513	#41	—	4	16	no	—
514	#41	—	4	8	no	—
515	C₂×Q₈	—	2	2	no	—
516	C₂×Q₈	—	2	4	no	—
517	C₂×Q₈	—	2	4	no	—
518	C₂×Q₈	—	2	8	no	—
519	C₂×Q₈	—	4	4	no	—
520	C₂×Q₈	—	4	8	no	—
521	C₂×Q₈	C₂×D₄×C₁₃	1	8	yes	—
522	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
523	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
524	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
525	C₂×D₄	—	2	2	no	—
526	C₂×D₄	—	2	8	no	—
527	C₂×D₄	—	2	4	no	—
528	C₂×D₄	—	2	8	no	—
529	C₂×D₄	—	2	4	no	—
530	C₂×D₄	—	2	4	no	—
531	C₂×D₄	—	2	2	no	—
532	C₂×D₄	—	2	8	no	—
533	C₂×D₄	—	2	4	no	—
534	C₂×D₄	—	4	8	no	—
535	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
536	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
537	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
538	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
539	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
540	C₂²×C₄	—	2	2	no	—
541	C₂²×C₄	—	2	2	no	—
542	C₂²×C₄	—	2	2	no	—
543	C₂²×C₄	—	2	4	no	—
544	C₂²×C₄	—	2	4	no	—
545	C₂²×C₄	—	2	2	no	—
546	C₂²×C₄	—	2	8	no	—
547	C₂²×C₄	—	4	8	no	—
548	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
549	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
550	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
551	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
552	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
553	Q₁₆	—	2	8	no	—
554	Q₁₆	—	2	2	no	—
555	Q₁₆	C₂×D₄×C₁₃	1	8	yes	—
556	Q₁₆	C₂×D₄×C₁₃	1	8	yes	—
557	SD₁₆	—	2	16	no	—
558	SD₁₆	—	2	8	no	—
559	SD₁₆	—	2	4	no	—
560	SD₁₆	—	4	4	no	—
561	D₈	—	2	4	no	—
562	D₈	—	2	4	no	—
563	D₈	—	2	2	no	—
564	D₈	—	4	4	no	—
565	M₁₆	—	2	2	no	—
566	M₁₆	—	2	2	no	—
567	M₁₆	—	2	4	no	—
568	C₂×C₈	—	2	2	no	—
569	C₂×C₈	—	2	4	no	—
570	C₂×C₈	—	2	4	no	—
571	C₂×C₈	—	2	4	no	—
572	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
573	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
574	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
575	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
576	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
577	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
578	C₄⋊C₄	—	2	8	no	—
579	C₄⋊C₄	—	2	4	no	—
580	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
581	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
582	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
583	C₂²⋊C₄	—	2	2	no	—
584	C₂²⋊C₄	—	2	4	no	—
585	C₂²⋊C₄	—	2	4	no	—
586	C₂²⋊C₄	—	2	8	no	—
587	C₂²⋊C₄	—	2	8	no	—
588	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
589	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
590	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
591	C₄²	—	2	8	no	—
592	C₄²	—	2	2	no	—
593	C₄²	C₂⁴×C₁₃	1	2	yes	—
594	C₁₃	#61054	1	1	yes	characteristic, direct product factor, Sylow
595	C₂³	—	2	2	no	—
596	C₂³	—	2	4	no	—
597	C₂³	—	2	2	no	—
598	C₂³	—	4	2	no	—
599	C₂³	—	4	4	no	—
600	C₂³	—	8	4	no	—
601	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
602	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
603	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
604	Q₈	—	2	8	no	—
605	Q₈	—	2	2	no	—
606	Q₈	—	2	4	no	—
607	Q₈	—	2	2	no	—
608	Q₈	—	2	2	no	—
609	Q₈	—	4	8	no	—
610	Q₈	C₂²×D₄×C₁₃	1	8	yes	—
611	D₄	—	2	4	no	—
612	D₄	—	2	2	no	—
613	D₄	—	2	4	no	—
614	D₄	—	2	2	no	—
615	D₄	—	2	2	no	—
616	D₄	—	2	4	no	—
617	D₄	—	4	4	no	—
618	D₄	—	4	16	no	—
619	D₄	—	4	8	no	—
620	D₄	—	4	4	no	—
621	D₄	—	4	4	no	—
622	D₄	—	8	8	no	—
623	D₄	—	8	8	no	—
624	D₄	—	8	4	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	2	8	no	—
627	C₂×C₄	—	2	4	no	—
628	C₂×C₄	—	2	4	no	—
629	C₂×C₄	—	2	2	no	—
630	C₂×C₄	—	2	2	no	—
631	C₂×C₄	—	2	2	no	—
632	C₂×C₄	—	2	2	no	—
633	C₂×C₄	—	2	4	no	—
634	C₂×C₄	—	2	2	no	—
635	C₂×C₄	—	4	16	no	—
636	C₂×C₄	—	4	8	no	—
637	C₂×C₄	—	4	8	no	—
638	C₂×C₄	—	4	4	no	—
639	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
640	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
641	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
642	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
643	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
644	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
645	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
646	C₈	—	2	2	no	—
647	C₈	—	2	2	no	—
648	C₈	—	2	2	no	—
649	C₈	C₂²×D₄×C₁₃	1	2	yes	—
650	C₈	C₂²×D₄×C₁₃	1	2	yes	—
651	C₂²	—	2	2	no	—
652	C₂²	—	2	2	no	—
653	C₂²	—	2	4	no	—
654	C₂²	—	2	2	no	—
655	C₂²	—	2	2	no	—
656	C₂²	—	2	2	no	—
657	C₂²	—	4	4	no	—
658	C₂²	—	4	4	no	—
659	C₂²	—	4	8	no	—
660	C₂²	—	4	2	no	—
661	C₂²	—	4	4	no	—
662	C₂²	—	8	8	no	—
663	C₂²	D₄²×C₁₃	1	2	yes	—
664	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
665	C₄	—	2	4	no	—
666	C₄	—	2	2	no	—
667	C₄	—	2	8	no	—
668	C₄	—	2	2	no	—
669	C₄	—	4	4	no	—
670	C₄	—	4	2	no	—
671	C₄	D₄²×C₁₃	1	2	yes	—
672	C₄	C₂³×D₄×C₁₃	1	1	yes	characteristic
673	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
674	C₂	—	2	2	no	—
675	C₂	—	4	2	no	—
676	C₂	—	4	2	no	—
677	C₂	—	8	4	no	—
678	C₂	—	8	2	no	—
679	C₂	C₂×D₄²×C₁₃	1	1	yes	characteristic
680	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 ◁ C₁₃×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#578	C₂	semidirect
2. C₂²×C₁₃×#135	C₂	semidirect
3. C₁₃×#3487	C₂	semidirect
4. C₁₃×#3287	C₂	semidirect
5. C₁₃×#3285	C₂	semidirect
6. C₁₃×#3271	C₂	semidirect
7. C₁₃×#3155	C₂	semidirect
8. C₁₃×#3058	C₂	semidirect
9. C₁₃×#3050	C₂	semidirect
10. C₁₃×#3043	C₂	semidirect
11. C₁₃×#3010	C₂	semidirect
12. C₁₃×#3005	C₂	semidirect
13. C₁₃×#2950	C₂	semidirect
14. C₁₃×#2929	C₂	semidirect
19. C₂×C₁₃×#137	C₂²	semidirect
25. C₂×C₁₃×#135	C₂²	semidirect
27. C₂²×C₁₃×Q₁₆	C₂²	semidirect
33. C₁₃×#550	C₂²	semidirect
35. C₁₃×#548	C₂²	semidirect
43. C₁₃×#496	C₂²	semidirect
44. C₁₃×#495	C₂²	semidirect
45. C₁₃×#493	C₂²	semidirect
46. C₁₃×#469	C₂²	semidirect
47. C₁₃×#467	C₂²	semidirect
48. C₁₃×#466	C₂²	semidirect
49. C₁₃×#466	C₂²	semidirect
50. C₁₃×#465	C₂²	semidirect
51. C₁₃×#464	C₂²	semidirect
52. C₁₃×#460	C₂²	semidirect
53. C₁₃×#452	C₂²	semidirect
54. C₁₃×#449	C₂²	semidirect
55. C₁₃×#449	C₂²	semidirect
56. C₁₃×#448	C₂²	semidirect
57. C₁₃×#441	C₂²	semidirect
58. C₄×C₁₃×Q₁₆	C₂²	semidirect
59. C₁₃×#435	C₂²	semidirect
60. C₈×D₄×C₁₃	C₂²	semidirect
95. C₂×C₁₃×Q₁₆	D₄	semidirect
162. #61054	C₁₃	direct (N × H)
255. C₂×#578	C₂×C₁₃	semidirect
256. C₂²×#135	C₂×C₁₃	semidirect
257. #3487	C₂×C₁₃	semidirect
258. #3287	C₂×C₁₃	semidirect
259. #3285	C₂×C₁₃	semidirect
260. #3271	C₂×C₁₃	semidirect
261. #3155	C₂×C₁₃	semidirect
262. #3058	C₂×C₁₃	semidirect
263. #3050	C₂×C₁₃	semidirect
264. #3043	C₂×C₁₃	semidirect
265. #3010	C₂×C₁₃	semidirect
266. #3005	C₂×C₁₃	semidirect
267. #2950	C₂×C₁₃	semidirect
268. #2929	C₂×C₁₃	semidirect
329. C₂×#137	C₂²×C₁₃	semidirect
335. C₂×#135	C₂²×C₁₃	semidirect
337. C₂²×Q₁₆	C₂²×C₁₃	semidirect
343. #550	C₂²×C₁₃	semidirect
345. #548	C₂²×C₁₃	semidirect
353. #496	C₂²×C₁₃	semidirect
354. #495	C₂²×C₁₃	semidirect
355. #493	C₂²×C₁₃	semidirect
356. #469	C₂²×C₁₃	semidirect
357. #467	C₂²×C₁₃	semidirect
358. #466	C₂²×C₁₃	semidirect
359. #466	C₂²×C₁₃	semidirect
360. #465	C₂²×C₁₃	semidirect
361. #464	C₂²×C₁₃	semidirect
362. #460	C₂²×C₁₃	semidirect
363. #452	C₂²×C₁₃	semidirect
364. #449	C₂²×C₁₃	semidirect
365. #449	C₂²×C₁₃	semidirect
366. #448	C₂²×C₁₃	semidirect
367. #441	C₂²×C₁₃	semidirect
368. C₄×Q₁₆	C₂²×C₁₃	semidirect
369. #435	C₂²×C₁₃	semidirect
370. C₈×D₄	C₂²×C₁₃	semidirect
428. C₂×Q₁₆	D₄×C₁₃	semidirect
594. C₁₃	#61054	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
C₂²×C₁₃×#135	2
C₁₃×#3487	2
C₁₃×#3287	2
C₁₃×#3285	2
C₁₃×#3271	2
C₁₃×#3155	2
C₁₃×#3058	2
C₁₃×#3050	2
C₁₃×#3043	2
C₁₃×#3010	2
C₁₃×#3005	2
C₁₃×#2950	2
C₁₃×#2929	2
#61054	13

Subgroups — C13×#61054 #15747393

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61054 #15747393