Subgroups — C₁₃×#62096 #15748435

Order 3328.

2030 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3503	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×C₁₃×#41	C₂	1	1	yes	maximal, characteristic
3	Q₈×C₁₃×SD₁₆	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3362	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3335	C₂	1	6	yes	maximal, complemented
6	C₁₃×#3295	C₂	1	6	yes	maximal, complemented
7	C₁₃×#3246	C₂	1	3	yes	maximal, complemented
8	C₁₃×#3227	C₂	1	3	yes	maximal, complemented
9	C₁₃×#3101	C₂	1	3	yes	maximal, complemented
10	C₂×C₁₃×#476	C₂	1	3	yes	maximal, complemented
11	C₁₃×#2988	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×#41	—	2	1	no	—
13	Q₈²×C₁₃	C₂²	1	2	yes	complemented
14	C₁₃×#557	—	2	1	no	—
15	C₁₃×#554	C₂²	1	6	yes	complemented
16	C₁₃×#550	C₂²	1	1	yes	characteristic
17	D₄×Q₈×C₁₃	—	2	3	no	—
18	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
19	C₁₃×#548	—	2	1	no	—
20	C₁₃×#547	C₂²	1	3	yes	—
21	C₁₃×#546	—	2	3	no	—
22	D₄²×C₁₃	C₂²	1	3	yes	—
23	C₁₃×#544	—	2	3	no	—
24	C₁₃×#533	C₂²	1	3	yes	complemented
25	C₁₃×#532	C₂²	1	3	yes	—
26	C₂×C₁₃×C₄⋊Q₈	C₂²	1	3	yes	complemented
27	C₁₃×#525	—	2	3	no	—
28	C₁₃×#520	—	2	1	no	—
29	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₁₃	C₂²	1	3	yes	—
31	C₁₃×#498	C₂²	1	6	yes	complemented
32	C₁₃×#486	C₂²	1	6	yes	complemented
33	C₁₃×#483	C₂²	1	6	yes	complemented
34	C₁₃×#481	C₂²	1	12	yes	complemented
35	C₁₃×#476	C₂²	1	6	yes	—
36	C₁₃×#476	C₂²	1	3	yes	—
37	C₁₃×#476	C₂²	1	6	yes	complemented
38	C₁₃×#476	C₂²	1	6	yes	complemented
39	C₁₃×#476	C₂²	1	3	yes	complemented
40	C₁₃×#475	C₂²	1	6	yes	complemented
41	C₁₃×#465	C₂²	1	12	yes	complemented
42	C₁₃×#461	C₂²	1	1	yes	characteristic
43	C₁₃×#461	C₂²	1	3	yes	complemented
44	C₁₃×#460	C₂²	1	6	yes	complemented
45	C₁₃×#450	C₂²	1	6	yes	—
46	C₈×Q₈×C₁₃	C₂²	1	2	yes	complemented
47	C₄×C₁₃×SD₁₆	C₂²	1	6	yes	—
48	C₄×C₁₃×SD₁₆	C₂²	1	6	yes	complemented
49	C₈×D₄×C₁₃	C₂²	1	6	yes	complemented
50	C₁₃×#431	C₂²	1	3	yes	complemented
51	C₂×C₁₃×#106	C₂²	1	6	yes	complemented
52	C₂×C₁₃×C₄⋊C₈	C₂²	1	3	yes	complemented
53	C₂×C₁₃×#102	C₂²	1	6	yes	—
54	C₂×C₁₃×#41	—	2	1	no	—
55	C₂×C₁₃×#41	—	2	3	no	—
56	C₂×C₁₃×#41	—	2	3	no	—
57	C₂×C₁₃×#41	—	4	8	no	—
58	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
59	C₂²×Q₈×C₁₃	—	2	1	no	—
60	C₂²×Q₈×C₁₃	—	2	3	no	—
61	C₂²×D₄×C₁₃	—	2	3	no	—
62	C₂²×D₄×C₁₃	C₂³	1	3	yes	—
63	C₂³×C₄×C₁₃	—	2	3	no	—
64	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
65	C₂×C₁₃×SD₁₆	C₂³	1	6	yes	—
66	C₂²×C₈×C₁₃	C₂³	1	6	yes	—
67	C₁₃×C₄⋊Q₈	—	2	6	no	—
68	C₁₃×C₄⋊Q₈	—	2	3	no	—
69	C₁₃×C₄⋊Q₈	—	2	3	no	—
70	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
71	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
72	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
73	C₁₃×C₄⋊Q₈	C₂³	1	6	yes	—
74	C₁₃×#127	C₂³	1	3	yes	—
75	C₁₃×#125	—	2	6	no	—
76	C₁₃×#125	—	2	3	no	—
77	C₁₃×#124	—	2	3	no	—
78	C₁₃×#123	—	2	6	no	—
79	C₁₃×C₂²⋊Q₈	—	2	3	no	—
80	C₁₃×C₂²⋊Q₈	—	2	3	no	—
81	C₁₃×C₂²⋊Q₈	—	2	3	no	—
82	C₁₃×C₂²⋊Q₈	—	2	12	no	—
83	C₁₃×C₂²⋊Q₈	C₂³	1	6	yes	—
84	C₁₃×#121	—	2	3	no	—
85	C₁₃×#121	—	2	3	no	—
86	C₁₃×#121	—	2	3	no	—
87	C₁₃×#121	C₂³	1	6	yes	—
88	C₁₃×#120	—	2	6	no	—
89	C₄×Q₈×C₁₃	—	2	2	no	—
90	C₄×Q₈×C₁₃	—	2	3	no	—
91	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
92	C₄×Q₈×C₁₃	C₂³	1	6	yes	—
93	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
94	C₄×D₄×C₁₃	—	2	6	no	—
95	C₄×D₄×C₁₃	—	2	3	no	—
96	C₄×D₄×C₁₃	—	2	3	no	—
97	C₄×D₄×C₁₃	—	2	3	no	—
98	C₄×D₄×C₁₃	D₄	1	3	yes	—
99	C₄×D₄×C₁₃	C₂³	1	3	yes	—
100	C₄×D₄×C₁₃	C₂³	1	3	yes	—
101	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
102	C₄×D₄×C₁₃	C₂³	1	3	yes	—
103	C₄×D₄×C₁₃	C₂³	1	3	yes	—
104	C₁₃×#117	—	2	3	no	—
105	C₁₃×#117	D₄	1	3	yes	—
106	C₂×C₁₃×C₄⋊C₄	—	2	3	no	—
107	C₂×C₁₃×C₄⋊C₄	C₂³	1	6	yes	—
108	C₂×C₁₃×C₄⋊C₄	C₂³	1	3	yes	—
109	C₂×C₁₃×C₂²⋊C₄	—	2	3	no	—
110	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
111	C₁₃×#106	C₂³	1	6	yes	—
112	C₁₃×#106	C₂³	1	12	yes	—
113	C₁₃×#106	C₂³	1	6	yes	—
114	C₁₃×C₄⋊C₈	C₂³	1	3	yes	—
115	C₁₃×C₄⋊C₈	C₂³	1	6	yes	—
116	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
117	C₁₃×#103	C₂³	1	6	yes	—
118	C₁₃×#103	C₂³	1	2	yes	—
119	C₁₃×#102	C₂³	1	6	yes	—
120	C₁₃×#102	C₂³	1	12	yes	—
121	C₁₃×#102	C₂³	1	6	yes	—
122	C₁₃×C₂²⋊C₈	C₂³	1	6	yes	—
123	C₄×C₈×C₁₃	C₂³	1	6	yes	—
124	#62096	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
125	C₂⁴×C₁₃	—	2	3	no	—
126	C₁₃×#41	—	4	4	no	—
127	C₁₃×#41	—	4	12	no	—
128	C₁₃×#41	—	4	12	no	—
129	C₁₃×#41	SD₁₆	1	8	yes	complemented
130	C₂×Q₈×C₁₃	—	2	3	no	—
131	C₂×Q₈×C₁₃	—	2	3	no	—
132	C₂×Q₈×C₁₃	—	2	6	no	—
133	C₂×Q₈×C₁₃	—	4	4	no	—
134	C₂×Q₈×C₁₃	—	8	6	no	—
135	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
136	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
137	C₂×D₄×C₁₃	—	2	6	no	—
138	C₂×D₄×C₁₃	—	2	6	no	—
139	C₂×D₄×C₁₃	—	2	3	no	—
140	C₂×D₄×C₁₃	—	2	3	no	—
141	C₂×D₄×C₁₃	—	2	3	no	—
142	C₂×D₄×C₁₃	—	4	3	no	—
143	C₂×D₄×C₁₃	—	4	12	no	—
144	C₂×D₄×C₁₃	C₂×D₄	1	3	yes	—
145	C₂×D₄×C₁₃	C₂⁴	1	3	yes	—
146	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
147	C₂²×C₄×C₁₃	—	2	3	no	—
148	C₂²×C₄×C₁₃	—	2	6	no	—
149	C₂²×C₄×C₁₃	—	2	1	no	—
150	C₂²×C₄×C₁₃	—	2	3	no	—
151	C₂²×C₄×C₁₃	—	2	3	no	—
152	C₂²×C₄×C₁₃	—	2	3	no	—
153	C₂²×C₄×C₁₃	—	4	12	no	—
154	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
155	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
156	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
157	C₁₃×SD₁₆	—	2	4	no	—
158	C₁₃×SD₁₆	—	4	6	no	—
159	C₂×C₈×C₁₃	—	4	6	no	—
160	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
161	C₂×C₈×C₁₃	C₂⁴	1	6	yes	—
162	C₁₃×C₄⋊C₄	—	2	3	no	—
163	C₁₃×C₄⋊C₄	—	2	6	no	—
164	C₁₃×C₄⋊C₄	—	2	3	no	—
165	C₁₃×C₄⋊C₄	—	2	6	no	—
166	C₁₃×C₄⋊C₄	—	2	1	no	—
167	C₁₃×C₄⋊C₄	—	2	3	no	—
168	C₁₃×C₄⋊C₄	—	2	1	no	—
169	C₁₃×C₄⋊C₄	—	2	6	no	—
170	C₁₃×C₄⋊C₄	—	2	6	no	—
171	C₁₃×C₄⋊C₄	C₂×D₄	1	3	yes	—
172	C₁₃×C₄⋊C₄	C₂×D₄	1	3	yes	—
173	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
174	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
175	C₁₃×C₄⋊C₄	C₂⁴	1	3	yes	—
176	C₁₃×C₂²⋊C₄	—	2	6	no	—
177	C₁₃×C₂²⋊C₄	—	2	1	no	—
178	C₁₃×C₂²⋊C₄	—	2	3	no	—
179	C₁₃×C₂²⋊C₄	—	2	3	no	—
180	C₁₃×C₂²⋊C₄	—	2	3	no	—
181	C₁₃×C₂²⋊C₄	—	2	6	no	—
182	C₁₃×C₂²⋊C₄	C₂×D₄	1	6	yes	—
183	C₄²×C₁₃	—	2	6	no	—
184	C₄²×C₁₃	C₂×D₄	1	3	yes	—
185	C₄²×C₁₃	C₂×D₄	1	3	yes	—
186	C₄²×C₁₃	C₂⁴	1	3	yes	—
187	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
188	#3503	C₂×C₁₃	1	1	yes	characteristic, complemented
189	D₄×#41	C₂×C₁₃	1	1	yes	characteristic
190	Q₈×SD₁₆	C₂×C₁₃	1	2	yes	complemented
191	#3362	C₂×C₁₃	1	2	yes	complemented
192	#3335	C₂×C₁₃	1	6	yes	complemented
193	#3295	C₂×C₁₃	1	6	yes	complemented
194	#3246	C₂×C₁₃	1	3	yes	complemented
195	#3227	C₂×C₁₃	1	3	yes	complemented
196	#3101	C₂×C₁₃	1	3	yes	complemented
197	C₂×#476	C₂×C₁₃	1	3	yes	complemented
198	#2988	C₂×C₁₃	1	1	yes	characteristic, complemented
199	C₂³×C₁₃	—	2	1	no	—
200	C₂³×C₁₃	—	2	3	no	—
201	C₂³×C₁₃	—	4	6	no	—
202	C₂³×C₁₃	—	4	6	no	—
203	C₂³×C₁₃	—	8	3	no	—
204	C₂³×C₁₃	C₂²×D₄	1	3	yes	—
205	Q₈×C₁₃	—	2	2	no	—
206	Q₈×C₁₃	—	2	2	no	—
207	Q₈×C₁₃	—	4	6	no	—
208	Q₈×C₁₃	—	4	6	no	—
209	Q₈×C₁₃	—	8	6	no	—
210	Q₈×C₁₃	C₂×SD₁₆	1	4	yes	—
211	D₄×C₁₃	—	2	3	no	—
212	D₄×C₁₃	—	2	1	no	—
213	D₄×C₁₃	—	2	3	no	—
214	D₄×C₁₃	—	4	6	no	—
215	D₄×C₁₃	—	4	12	no	—
216	D₄×C₁₃	—	4	6	no	—
217	D₄×C₁₃	—	8	3	no	—
218	D₄×C₁₃	C₂×SD₁₆	1	12	yes	—
219	D₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
220	C₂×C₄×C₁₃	—	2	3	no	—
221	C₂×C₄×C₁₃	—	2	3	no	—
222	C₂×C₄×C₁₃	—	2	2	no	—
223	C₂×C₄×C₁₃	—	2	6	no	—
224	C₂×C₄×C₁₃	—	2	1	no	—
225	C₂×C₄×C₁₃	—	2	3	no	—
226	C₂×C₄×C₁₃	—	4	3	no	—
227	C₂×C₄×C₁₃	—	4	6	no	—
228	C₂×C₄×C₁₃	—	4	2	no	—
229	C₂×C₄×C₁₃	—	4	6	no	—
230	C₂×C₄×C₁₃	—	4	6	no	—
231	C₂×C₄×C₁₃	—	4	6	no	—
232	C₂×C₄×C₁₃	—	8	6	no	—
233	C₂×C₄×C₁₃	C₂×SD₁₆	1	12	yes	—
234	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
235	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
236	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
237	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
238	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
239	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
240	C₈×C₁₃	—	2	2	no	—
241	C₈×C₁₃	—	2	6	no	—
242	C₂²×#41	—	2	1	no	—
243	Q₈²	C₂²×C₁₃	1	2	yes	complemented
244	#557	—	2	1	no	—
245	#554	C₂²×C₁₃	1	6	yes	complemented
246	#550	C₂²×C₁₃	1	1	yes	characteristic
247	D₄×Q₈	—	2	3	no	—
248	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
249	#548	—	2	1	no	—
250	#547	C₂²×C₁₃	1	3	yes	—
251	#546	—	2	3	no	—
252	D₄²	C₂²×C₁₃	1	3	yes	—
253	#544	—	2	3	no	—
254	#533	C₂²×C₁₃	1	3	yes	complemented
255	#532	C₂²×C₁₃	1	3	yes	—
256	C₂×C₄⋊Q₈	C₂²×C₁₃	1	3	yes	complemented
257	#525	—	2	3	no	—
258	#520	—	2	1	no	—
259	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
260	C₂×C₄×D₄	C₂²×C₁₃	1	3	yes	—
261	#498	C₂²×C₁₃	1	6	yes	complemented
262	#486	C₂²×C₁₃	1	6	yes	complemented
263	#483	C₂²×C₁₃	1	6	yes	complemented
264	#481	C₂²×C₁₃	1	12	yes	complemented
265	#476	C₂²×C₁₃	1	3	yes	—
266	#476	C₂²×C₁₃	1	6	yes	—
267	#476	C₂²×C₁₃	1	6	yes	complemented
268	#476	C₂²×C₁₃	1	3	yes	complemented
269	#476	C₂²×C₁₃	1	6	yes	complemented
270	#475	C₂²×C₁₃	1	6	yes	complemented
271	#465	C₂²×C₁₃	1	12	yes	complemented
272	#461	C₂²×C₁₃	1	1	yes	characteristic
273	#461	C₂²×C₁₃	1	3	yes	complemented
274	#460	C₂²×C₁₃	1	6	yes	complemented
275	#450	C₂²×C₁₃	1	6	yes	—
276	C₈×Q₈	C₂²×C₁₃	1	2	yes	complemented
277	C₄×SD₁₆	C₂²×C₁₃	1	6	yes	—
278	C₄×SD₁₆	C₂²×C₁₃	1	6	yes	complemented
279	C₈×D₄	C₂²×C₁₃	1	6	yes	complemented
280	#431	C₂²×C₁₃	1	3	yes	complemented
281	C₂×#106	C₂²×C₁₃	1	6	yes	complemented
282	C₂×C₄⋊C₈	C₂²×C₁₃	1	3	yes	complemented
283	C₂×#102	C₂²×C₁₃	1	6	yes	—
284	C₂²×C₁₃	—	2	3	no	—
285	C₂²×C₁₃	—	2	3	no	—
286	C₂²×C₁₃	—	2	2	no	—
287	C₂²×C₁₃	—	4	1	no	—
288	C₂²×C₁₃	—	4	1	no	—
289	C₂²×C₁₃	—	4	3	no	—
290	C₂²×C₁₃	—	4	3	no	—
291	C₂²×C₁₃	—	4	3	no	—
292	C₂²×C₁₃	—	8	12	no	—
293	C₂²×C₁₃	C₂²×SD₁₆	1	6	yes	—
294	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
295	C₄×C₁₃	—	2	1	no	—
296	C₄×C₁₃	—	2	3	no	—
297	C₄×C₁₃	—	2	3	no	—
298	C₄×C₁₃	—	4	6	no	—
299	C₄×C₁₃	—	4	2	no	—
300	C₄×C₁₃	—	4	1	no	—
301	C₄×C₁₃	—	4	3	no	—
302	C₄×C₁₃	C₂²×SD₁₆	1	2	yes	—
303	C₄×C₁₃	C₂²×SD₁₆	1	6	yes	—
304	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
305	C₄×C₁₃	#585	1	1	yes	characteristic
306	C₂×#41	—	2	1	no	—
307	C₂×#41	—	2	3	no	—
308	C₂×#41	—	2	3	no	—
309	C₂×#41	—	4	8	no	—
310	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
311	C₂²×Q₈	—	2	1	no	—
312	C₂²×Q₈	—	2	3	no	—
313	C₂²×D₄	—	2	3	no	—
314	C₂²×D₄	C₂³×C₁₃	1	3	yes	—
315	C₂³×C₄	—	2	3	no	—
316	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
317	C₂×SD₁₆	C₂³×C₁₃	1	6	yes	—
318	C₂²×C₈	C₂³×C₁₃	1	6	yes	—
319	C₄⋊Q₈	—	2	6	no	—
320	C₄⋊Q₈	—	2	3	no	—
321	C₄⋊Q₈	—	2	3	no	—
322	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
323	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
324	C₄⋊Q₈	C₂³×C₁₃	1	6	yes	—
325	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
326	#127	C₂³×C₁₃	1	3	yes	—
327	#125	—	2	6	no	—
328	#125	—	2	3	no	—
329	#124	—	2	3	no	—
330	#123	—	2	6	no	—
331	C₂²⋊Q₈	—	2	3	no	—
332	C₂²⋊Q₈	—	2	3	no	—
333	C₂²⋊Q₈	—	2	3	no	—
334	C₂²⋊Q₈	—	2	12	no	—
335	C₂²⋊Q₈	C₂³×C₁₃	1	6	yes	—
336	#121	—	2	3	no	—
337	#121	—	2	3	no	—
338	#121	—	2	3	no	—
339	#121	C₂³×C₁₃	1	6	yes	—
340	#120	—	2	6	no	—
341	C₄×Q₈	—	2	2	no	—
342	C₄×Q₈	—	2	3	no	—
343	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
344	C₄×Q₈	C₂³×C₁₃	1	6	yes	—
345	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
346	C₄×D₄	—	2	6	no	—
347	C₄×D₄	—	2	3	no	—
348	C₄×D₄	—	2	3	no	—
349	C₄×D₄	—	2	3	no	—
350	C₄×D₄	D₄×C₁₃	1	3	yes	—
351	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
352	C₄×D₄	C₂³×C₁₃	1	3	yes	—
353	C₄×D₄	C₂³×C₁₃	1	3	yes	—
354	C₄×D₄	C₂³×C₁₃	1	3	yes	—
355	C₄×D₄	C₂³×C₁₃	1	3	yes	—
356	#117	—	2	3	no	—
357	#117	D₄×C₁₃	1	3	yes	—
358	C₂×C₄⋊C₄	—	2	3	no	—
359	C₂×C₄⋊C₄	C₂³×C₁₃	1	3	yes	—
360	C₂×C₄⋊C₄	C₂³×C₁₃	1	6	yes	—
361	C₂×C₂²⋊C₄	—	2	3	no	—
362	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
363	#106	C₂³×C₁₃	1	6	yes	—
364	#106	C₂³×C₁₃	1	12	yes	—
365	#106	C₂³×C₁₃	1	6	yes	—
366	C₄⋊C₈	C₂³×C₁₃	1	3	yes	—
367	C₄⋊C₈	C₂³×C₁₃	1	6	yes	—
368	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
369	#103	C₂³×C₁₃	1	6	yes	—
370	#103	C₂³×C₁₃	1	2	yes	—
371	#102	C₂³×C₁₃	1	6	yes	—
372	#102	C₂³×C₁₃	1	12	yes	—
373	#102	C₂³×C₁₃	1	6	yes	—
374	C₂²⋊C₈	C₂³×C₁₃	1	6	yes	—
375	C₄×C₈	C₂³×C₁₃	1	6	yes	—
376	C₂×C₁₃	—	2	6	no	—
377	C₂×C₁₃	—	4	2	no	—
378	C₂×C₁₃	—	8	3	no	—
379	C₂×C₁₃	#3489	1	1	yes	characteristic
380	C₂×C₁₃	C₂³×SD₁₆	1	1	yes	characteristic
381	C₂×C₁₃	#3585	1	1	yes	characteristic
382	C₂⁴	—	2	3	no	—
383	#41	—	4	4	no	—
384	#41	—	4	12	no	—
385	#41	—	4	12	no	—
386	#41	C₁₃×SD₁₆	1	8	yes	complemented
387	C₂×Q₈	—	2	3	no	—
388	C₂×Q₈	—	2	3	no	—
389	C₂×Q₈	—	2	6	no	—
390	C₂×Q₈	—	4	4	no	—
391	C₂×Q₈	—	8	6	no	—
392	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
393	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
394	C₂×D₄	—	2	6	no	—
395	C₂×D₄	—	2	6	no	—
396	C₂×D₄	—	2	3	no	—
397	C₂×D₄	—	2	3	no	—
398	C₂×D₄	—	2	3	no	—
399	C₂×D₄	—	4	3	no	—
400	C₂×D₄	—	4	12	no	—
401	C₂×D₄	C₂×D₄×C₁₃	1	3	yes	—
402	C₂×D₄	C₂⁴×C₁₃	1	3	yes	—
403	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
404	C₂²×C₄	—	2	3	no	—
405	C₂²×C₄	—	2	6	no	—
406	C₂²×C₄	—	2	1	no	—
407	C₂²×C₄	—	2	3	no	—
408	C₂²×C₄	—	2	3	no	—
409	C₂²×C₄	—	2	3	no	—
410	C₂²×C₄	—	4	12	no	—
411	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
412	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
413	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
414	SD₁₆	—	2	4	no	—
415	SD₁₆	—	4	6	no	—
416	C₂×C₈	—	4	6	no	—
417	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
418	C₂×C₈	C₂⁴×C₁₃	1	6	yes	—
419	C₄⋊C₄	—	2	3	no	—
420	C₄⋊C₄	—	2	6	no	—
421	C₄⋊C₄	—	2	3	no	—
422	C₄⋊C₄	—	2	6	no	—
423	C₄⋊C₄	—	2	1	no	—
424	C₄⋊C₄	—	2	3	no	—
425	C₄⋊C₄	—	2	1	no	—
426	C₄⋊C₄	—	2	6	no	—
427	C₄⋊C₄	—	2	6	no	—
428	C₄⋊C₄	C₂×D₄×C₁₃	1	3	yes	—
429	C₄⋊C₄	C₂×D₄×C₁₃	1	3	yes	—
430	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
431	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
432	C₄⋊C₄	C₂⁴×C₁₃	1	3	yes	—
433	C₂²⋊C₄	—	2	6	no	—
434	C₂²⋊C₄	—	2	1	no	—
435	C₂²⋊C₄	—	2	3	no	—
436	C₂²⋊C₄	—	2	3	no	—
437	C₂²⋊C₄	—	2	3	no	—
438	C₂²⋊C₄	—	2	6	no	—
439	C₂²⋊C₄	C₂×D₄×C₁₃	1	6	yes	—
440	C₄²	—	2	6	no	—
441	C₄²	C₂×D₄×C₁₃	1	3	yes	—
442	C₄²	C₂×D₄×C₁₃	1	3	yes	—
443	C₄²	C₂⁴×C₁₃	1	3	yes	—
444	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
445	C₁₃	#62096	1	1	yes	characteristic, direct product factor, Sylow
446	C₂³	—	2	1	no	—
447	C₂³	—	2	3	no	—
448	C₂³	—	4	6	no	—
449	C₂³	—	4	6	no	—
450	C₂³	—	8	3	no	—
451	C₂³	C₂²×D₄×C₁₃	1	3	yes	—
452	Q₈	—	2	2	no	—
453	Q₈	—	2	2	no	—
454	Q₈	—	4	6	no	—
455	Q₈	—	4	6	no	—
456	Q₈	—	8	6	no	—
457	Q₈	C₂×C₁₃×SD₁₆	1	4	yes	—
458	D₄	—	2	3	no	—
459	D₄	—	2	1	no	—
460	D₄	—	2	3	no	—
461	D₄	—	4	6	no	—
462	D₄	—	4	12	no	—
463	D₄	—	4	6	no	—
464	D₄	—	8	3	no	—
465	D₄	C₂×C₁₃×SD₁₆	1	12	yes	—
466	D₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
467	C₂×C₄	—	2	3	no	—
468	C₂×C₄	—	2	3	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	6	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	3	no	—
473	C₂×C₄	—	4	3	no	—
474	C₂×C₄	—	4	6	no	—
475	C₂×C₄	—	4	2	no	—
476	C₂×C₄	—	4	6	no	—
477	C₂×C₄	—	4	6	no	—
478	C₂×C₄	—	4	6	no	—
479	C₂×C₄	—	8	6	no	—
480	C₂×C₄	C₂×C₁₃×SD₁₆	1	12	yes	—
481	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
482	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
483	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
484	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
485	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
486	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
487	C₈	—	2	2	no	—
488	C₈	—	2	6	no	—
489	C₂²	—	2	3	no	—
490	C₂²	—	2	3	no	—
491	C₂²	—	2	2	no	—
492	C₂²	—	4	1	no	—
493	C₂²	—	4	1	no	—
494	C₂²	—	4	3	no	—
495	C₂²	—	4	3	no	—
496	C₂²	—	4	3	no	—
497	C₂²	—	8	12	no	—
498	C₂²	C₂²×C₁₃×SD₁₆	1	6	yes	—
499	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
500	C₄	—	2	1	no	—
501	C₄	—	2	3	no	—
502	C₄	—	2	3	no	—
503	C₄	—	4	1	no	—
504	C₄	—	4	3	no	—
505	C₄	—	4	6	no	—
506	C₄	—	4	2	no	—
507	C₄	C₂²×C₁₃×SD₁₆	1	2	yes	—
508	C₄	C₂²×C₁₃×SD₁₆	1	6	yes	—
509	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
510	C₄	C₁₃×#585	1	1	yes	characteristic
511	C₂	—	2	6	no	—
512	C₂	—	4	2	no	—
513	C₂	—	8	3	no	—
514	C₂	C₁₃×#3489	1	1	yes	characteristic
515	C₂	C₂³×C₁₃×SD₁₆	1	1	yes	characteristic
516	C₂	C₁₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	D₄×C₁₃×#41	C₂
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. C₁₃×#3503	C₂	semidirect
3. Q₈×C₁₃×SD₁₆	C₂	semidirect
4. C₁₃×#3362	C₂	semidirect
5. C₁₃×#3335	C₂	semidirect
6. C₁₃×#3295	C₂	semidirect
7. C₁₃×#3246	C₂	semidirect
8. C₁₃×#3227	C₂	semidirect
9. C₁₃×#3101	C₂	semidirect
10. C₂×C₁₃×#476	C₂	semidirect
11. C₁₃×#2988	C₂	semidirect
13. Q₈²×C₁₃	C₂²	semidirect
15. C₁₃×#554	C₂²	semidirect
24. C₁₃×#533	C₂²	semidirect
26. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
31. C₁₃×#498	C₂²	semidirect
32. C₁₃×#486	C₂²	semidirect
33. C₁₃×#483	C₂²	semidirect
34. C₁₃×#481	C₂²	semidirect
37. C₁₃×#476	C₂²	semidirect
38. C₁₃×#476	C₂²	semidirect
39. C₁₃×#476	C₂²	semidirect
40. C₁₃×#475	C₂²	semidirect
41. C₁₃×#465	C₂²	semidirect
43. C₁₃×#461	C₂²	semidirect
44. C₁₃×#460	C₂²	semidirect
46. C₈×Q₈×C₁₃	C₂²	semidirect
48. C₄×C₁₃×SD₁₆	C₂²	semidirect
49. C₈×D₄×C₁₃	C₂²	semidirect
50. C₁₃×#431	C₂²	semidirect
51. C₂×C₁₃×#106	C₂²	semidirect
52. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
124. #62096	C₁₃	direct (N × H)
129. C₁₃×#41	SD₁₆	semidirect
188. #3503	C₂×C₁₃	semidirect
190. Q₈×SD₁₆	C₂×C₁₃	semidirect
191. #3362	C₂×C₁₃	semidirect
192. #3335	C₂×C₁₃	semidirect
193. #3295	C₂×C₁₃	semidirect
194. #3246	C₂×C₁₃	semidirect
195. #3227	C₂×C₁₃	semidirect
196. #3101	C₂×C₁₃	semidirect
197. C₂×#476	C₂×C₁₃	semidirect
198. #2988	C₂×C₁₃	semidirect
243. Q₈²	C₂²×C₁₃	semidirect
245. #554	C₂²×C₁₃	semidirect
254. #533	C₂²×C₁₃	semidirect
256. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
261. #498	C₂²×C₁₃	semidirect
262. #486	C₂²×C₁₃	semidirect
263. #483	C₂²×C₁₃	semidirect
264. #481	C₂²×C₁₃	semidirect
267. #476	C₂²×C₁₃	semidirect
268. #476	C₂²×C₁₃	semidirect
269. #476	C₂²×C₁₃	semidirect
270. #475	C₂²×C₁₃	semidirect
271. #465	C₂²×C₁₃	semidirect
273. #461	C₂²×C₁₃	semidirect
274. #460	C₂²×C₁₃	semidirect
276. C₈×Q₈	C₂²×C₁₃	semidirect
278. C₄×SD₁₆	C₂²×C₁₃	semidirect
279. C₈×D₄	C₂²×C₁₃	semidirect
280. #431	C₂²×C₁₃	semidirect
281. C₂×#106	C₂²×C₁₃	semidirect
282. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
386. #41	C₁₃×SD₁₆	semidirect
445. C₁₃	#62096	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₃×#3503	2
D₄×C₁₃×#41	2
Q₈×C₁₃×SD₁₆	2
C₁₃×#3362	2
C₁₃×#3335	2
C₁₃×#3295	2
C₁₃×#3246	2
C₁₃×#3227	2
C₁₃×#3101	2
C₂×C₁₃×#476	2
C₁₃×#2988	2
#62096	13

Subgroups — C13×#62096 #15748435

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62096 #15748435