Subgroups — C₁₃×#61586 #15747925

Order 3328.

2098 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3501	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#547	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3331	C₂	1	8	yes	maximal, complemented
4	C₁₃×#3276	C₂	1	8	yes	maximal, complemented
5	C₁₃×#3209	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3195	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3101	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3007	C₂	1	4	yes	maximal, complemented
9	C₁₃×#2975	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₁₃×#41	C₂²	1	2	yes	—
11	C₂×C₁₃×#137	C₂²	1	8	yes	complemented
12	C₁₃×#554	—	2	4	no	—
13	C₁₃×#554	C₂²	1	4	yes	complemented
14	D₄×Q₈×C₁₃	C₂²	1	4	yes	complemented
15	C₁₃×#547	—	2	4	no	—
16	C₁₃×#547	C₂²	1	8	yes	—
17	C₁₃×#544	—	2	1	no	—
18	C₁₃×#543	—	2	2	no	—
19	C₁₃×#533	C₂²	1	2	yes	—
20	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#123	—	2	2	no	—
22	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
23	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
24	C₂×C₁₃×#121	—	2	1	no	—
25	C₁₃×#518	—	2	1	no	—
26	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
28	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
29	C₁₃×#494	C₂²	1	4	yes	complemented
30	C₁₃×#487	C₂²	1	4	yes	complemented
31	C₁₃×#483	C₂²	1	4	yes	—
32	C₁₃×#483	C₂²	1	8	yes	complemented
33	C₁₃×#476	C₂²	1	4	yes	complemented
34	C₁₃×#470	C₂²	1	16	yes	complemented
35	C₁₃×#462	C₂²	1	8	yes	complemented
36	C₁₃×#461	C₂²	1	4	yes	complemented
37	C₁₃×#452	C₂²	1	16	yes	complemented
38	C₁₃×#451	C₂²	1	8	yes	—
39	C₁₃×#451	C₂²	1	8	yes	complemented
40	C₁₃×#450	C₂²	1	4	yes	—
41	C₄×C₁₃×SD₁₆	C₂²	1	8	yes	complemented
42	C₁₃×#436	C₂²	1	8	yes	complemented
43	C₁₃×#431	C₂²	1	2	yes	—
44	C₁₃×#417	C₂²	1	8	yes	complemented
45	C₁₃×#407	C₂²	1	4	yes	—
46	C₂×C₁₃×#41	—	2	4	no	—
47	C₂×C₁₃×#41	—	4	8	no	—
48	C₂×C₁₃×#41	C₂³	1	8	yes	—
49	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
50	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
51	C₂²×D₄×C₁₃	—	2	2	no	—
52	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
53	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
54	C₂³×C₄×C₁₃	—	2	1	no	—
55	C₂³×C₄×C₁₃	—	2	2	no	—
56	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
57	C₁₃×#137	—	4	16	no	—
58	C₂×C₁₃×Q₁₆	C₂³	1	16	yes	—
59	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
60	C₂×C₁₃×M₁₆	C₂³	1	8	yes	—
61	C₁₃×C₄⋊Q₈	—	2	4	no	—
62	C₁₃×C₄⋊Q₈	—	2	2	no	—
63	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
64	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
65	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
66	C₁₃×#125	—	2	4	no	—
67	C₁₃×#125	—	2	2	no	—
68	C₁₃×#123	—	2	16	no	—
69	C₁₃×C₂²⋊Q₈	—	2	4	no	—
70	C₁₃×C₂²⋊Q₈	—	2	4	no	—
71	C₁₃×C₂²⋊Q₈	—	2	4	no	—
72	C₁₃×C₂²⋊Q₈	—	2	2	no	—
73	C₁₃×C₂²⋊Q₈	—	2	8	no	—
74	C₁₃×C₂²⋊Q₈	—	2	8	no	—
75	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
76	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
77	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
78	C₁₃×#121	—	2	8	no	—
79	C₄×Q₈×C₁₃	—	2	2	no	—
80	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
81	C₄×D₄×C₁₃	—	2	4	no	—
82	C₄×D₄×C₁₃	—	2	4	no	—
83	C₄×D₄×C₁₃	—	2	2	no	—
84	C₄×D₄×C₁₃	D₄	1	4	yes	—
85	C₄×D₄×C₁₃	C₂³	1	4	yes	—
86	C₄×D₄×C₁₃	C₂³	1	4	yes	—
87	C₁₃×#117	—	2	2	no	—
88	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
89	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
90	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
91	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
92	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
93	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
94	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
95	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
96	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
97	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
98	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
99	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
100	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
101	C₁₃×#106	C₂³	1	8	yes	—
102	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
103	C₁₃×#103	C₂³	1	16	yes	—
104	C₁₃×#103	C₂³	1	8	yes	—
105	C₁₃×#102	C₂³	1	8	yes	—
106	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
107	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	—
108	C₄×C₈×C₁₃	C₂³	1	4	yes	—
109	#61586	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
110	C₂⁴×C₁₃	—	2	1	no	—
111	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
112	C₁₃×#41	—	2	16	no	—
113	C₁₃×#41	—	4	8	no	—
114	C₁₃×#41	—	4	16	no	—
115	C₂×Q₈×C₁₃	—	2	2	no	—
116	C₂×Q₈×C₁₃	—	2	2	no	—
117	C₂×Q₈×C₁₃	—	2	4	no	—
118	C₂×Q₈×C₁₃	—	4	4	no	—
119	C₂×Q₈×C₁₃	—	4	8	no	—
120	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
121	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
122	C₂×D₄×C₁₃	—	2	4	no	—
123	C₂×D₄×C₁₃	—	2	8	no	—
124	C₂×D₄×C₁₃	—	2	4	no	—
125	C₂×D₄×C₁₃	—	2	1	no	—
126	C₂×D₄×C₁₃	—	4	8	no	—
127	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
128	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
129	C₂²×C₄×C₁₃	—	2	1	no	—
130	C₂²×C₄×C₁₃	—	2	2	no	—
131	C₂²×C₄×C₁₃	—	2	4	no	—
132	C₂²×C₄×C₁₃	—	2	4	no	—
133	C₂²×C₄×C₁₃	—	2	4	no	—
134	C₂²×C₄×C₁₃	—	2	8	no	—
135	C₂²×C₄×C₁₃	—	4	4	no	—
136	C₂²×C₄×C₁₃	—	4	8	no	—
137	C₂²×C₄×C₁₃	—	4	4	no	—
138	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
140	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
141	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
143	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
144	C₁₃×Q₁₆	—	4	16	no	—
145	C₁₃×SD₁₆	—	2	16	no	—
146	C₁₃×M₁₆	—	4	8	no	—
147	C₂×C₈×C₁₃	C₂⁴	1	8	yes	—
148	C₁₃×C₄⋊C₄	—	2	4	no	—
149	C₁₃×C₄⋊C₄	—	2	8	no	—
150	C₁₃×C₄⋊C₄	—	2	4	no	—
151	C₁₃×C₄⋊C₄	—	2	8	no	—
152	C₁₃×C₄⋊C₄	—	2	4	no	—
153	C₁₃×C₄⋊C₄	—	2	1	no	—
154	C₁₃×C₄⋊C₄	—	2	4	no	—
155	C₁₃×C₄⋊C₄	—	2	2	no	—
156	C₁₃×C₄⋊C₄	—	2	2	no	—
157	C₁₃×C₄⋊C₄	—	2	2	no	—
158	C₁₃×C₄⋊C₄	—	2	4	no	—
159	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
160	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
161	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
162	C₁₃×C₂²⋊C₄	—	2	4	no	—
163	C₁₃×C₂²⋊C₄	—	2	8	no	—
164	C₁₃×C₂²⋊C₄	—	2	8	no	—
165	C₁₃×C₂²⋊C₄	—	2	4	no	—
166	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
167	C₄²×C₁₃	—	2	4	no	—
168	C₄²×C₁₃	C₂×D₄	1	2	yes	—
169	C₄²×C₁₃	C₂⁴	1	2	yes	—
170	#3501	C₂×C₁₃	1	1	yes	characteristic, complemented
171	C₂×#547	C₂×C₁₃	1	1	yes	characteristic
172	#3331	C₂×C₁₃	1	8	yes	complemented
173	#3276	C₂×C₁₃	1	8	yes	complemented
174	#3209	C₂×C₁₃	1	2	yes	complemented
175	#3195	C₂×C₁₃	1	4	yes	complemented
176	#3101	C₂×C₁₃	1	2	yes	complemented
177	#3007	C₂×C₁₃	1	4	yes	complemented
178	#2975	C₂×C₁₃	1	1	yes	characteristic, complemented
179	C₂³×C₁₃	—	2	4	no	—
180	C₂³×C₁₃	—	2	2	no	—
181	C₂³×C₁₃	—	2	4	no	—
182	C₂³×C₁₃	—	4	2	no	—
183	C₂³×C₁₃	—	4	2	no	—
184	C₂³×C₁₃	—	4	2	no	—
185	C₂³×C₁₃	—	4	2	no	—
186	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
187	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
188	Q₈×C₁₃	—	2	8	no	—
189	Q₈×C₁₃	—	2	8	no	—
190	Q₈×C₁₃	—	4	4	no	—
191	Q₈×C₁₃	—	8	2	no	—
192	Q₈×C₁₃	—	8	4	no	—
193	D₄×C₁₃	—	2	4	no	—
194	D₄×C₁₃	—	2	8	no	—
195	D₄×C₁₃	—	2	2	no	—
196	D₄×C₁₃	—	4	16	no	—
197	D₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
198	C₂×C₄×C₁₃	—	2	8	no	—
199	C₂×C₄×C₁₃	—	2	2	no	—
200	C₂×C₄×C₁₃	—	2	4	no	—
201	C₂×C₄×C₁₃	—	2	4	no	—
202	C₂×C₄×C₁₃	—	2	2	no	—
203	C₂×C₄×C₁₃	—	2	4	no	—
204	C₂×C₄×C₁₃	—	4	2	no	—
205	C₂×C₄×C₁₃	—	4	4	no	—
206	C₂×C₄×C₁₃	—	4	1	no	—
207	C₂×C₄×C₁₃	—	4	16	no	—
208	C₂×C₄×C₁₃	—	4	4	no	—
209	C₂×C₄×C₁₃	—	4	2	no	—
210	C₂×C₄×C₁₃	—	4	8	no	—
211	C₂×C₄×C₁₃	—	8	4	no	—
212	C₂×C₄×C₁₃	—	8	4	no	—
213	C₂×C₄×C₁₃	#137	1	4	yes	complemented
214	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
215	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
216	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
217	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
218	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
219	C₈×C₁₃	—	2	8	no	—
220	C₂²×#41	C₂²×C₁₃	1	2	yes	—
221	C₂×#137	C₂²×C₁₃	1	8	yes	complemented
222	#554	—	2	4	no	—
223	#554	C₂²×C₁₃	1	4	yes	complemented
224	D₄×Q₈	C₂²×C₁₃	1	4	yes	complemented
225	#547	—	2	4	no	—
226	#547	C₂²×C₁₃	1	8	yes	—
227	#544	—	2	1	no	—
228	#543	—	2	2	no	—
229	#533	C₂²×C₁₃	1	2	yes	—
230	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
231	C₂×#123	—	2	2	no	—
232	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
233	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
234	C₂×#121	—	2	1	no	—
235	#518	—	2	1	no	—
236	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
237	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
238	C₂²×C₄⋊C₄	—	2	1	no	—
239	#494	C₂²×C₁₃	1	4	yes	complemented
240	#487	C₂²×C₁₃	1	4	yes	complemented
241	#483	C₂²×C₁₃	1	4	yes	—
242	#483	C₂²×C₁₃	1	8	yes	complemented
243	#476	C₂²×C₁₃	1	4	yes	complemented
244	#470	C₂²×C₁₃	1	16	yes	complemented
245	#462	C₂²×C₁₃	1	8	yes	complemented
246	#461	C₂²×C₁₃	1	4	yes	complemented
247	#452	C₂²×C₁₃	1	16	yes	complemented
248	#451	C₂²×C₁₃	1	8	yes	—
249	#451	C₂²×C₁₃	1	8	yes	complemented
250	#450	C₂²×C₁₃	1	4	yes	—
251	C₄×SD₁₆	C₂²×C₁₃	1	8	yes	complemented
252	#436	C₂²×C₁₃	1	8	yes	complemented
253	#431	C₂²×C₁₃	1	2	yes	—
254	#417	C₂²×C₁₃	1	8	yes	complemented
255	#407	C₂²×C₁₃	1	4	yes	—
256	C₂²×C₁₃	—	2	1	no	—
257	C₂²×C₁₃	—	2	1	no	—
258	C₂²×C₁₃	—	2	4	no	—
259	C₂²×C₁₃	—	2	4	no	—
260	C₂²×C₁₃	—	2	4	no	—
261	C₂²×C₁₃	—	2	4	no	—
262	C₂²×C₁₃	—	4	8	no	—
263	C₂²×C₁₃	—	4	2	no	—
264	C₂²×C₁₃	—	4	2	no	—
265	C₂²×C₁₃	—	8	4	no	—
266	C₂²×C₁₃	C₂×#137	1	2	yes	—
267	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
268	C₄×C₁₃	—	2	2	no	—
269	C₄×C₁₃	—	2	4	no	—
270	C₄×C₁₃	—	2	1	no	—
271	C₄×C₁₃	—	4	4	no	—
272	C₄×C₁₃	—	4	4	no	—
273	C₄×C₁₃	—	4	4	no	—
274	C₄×C₁₃	—	4	2	no	—
275	C₄×C₁₃	C₂×#137	1	4	yes	—
276	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
277	C₂×#41	—	2	4	no	—
278	C₂×#41	—	4	8	no	—
279	C₂×#41	C₂³×C₁₃	1	8	yes	—
280	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
281	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
282	C₂²×D₄	—	2	2	no	—
283	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
284	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
285	C₂³×C₄	—	2	1	no	—
286	C₂³×C₄	—	2	2	no	—
287	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
288	#137	—	4	16	no	—
289	C₂×Q₁₆	C₂³×C₁₃	1	16	yes	—
290	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
291	C₂×M₁₆	C₂³×C₁₃	1	8	yes	—
292	C₄⋊Q₈	—	2	4	no	—
293	C₄⋊Q₈	—	2	2	no	—
294	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
295	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
296	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
297	#125	—	2	4	no	—
298	#125	—	2	2	no	—
299	#123	—	2	16	no	—
300	C₂²⋊Q₈	—	2	4	no	—
301	C₂²⋊Q₈	—	2	4	no	—
302	C₂²⋊Q₈	—	2	4	no	—
303	C₂²⋊Q₈	—	2	2	no	—
304	C₂²⋊Q₈	—	2	8	no	—
305	C₂²⋊Q₈	—	2	8	no	—
306	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
307	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
308	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
309	#121	—	2	8	no	—
310	C₄×Q₈	—	2	2	no	—
311	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
312	C₄×D₄	—	2	4	no	—
313	C₄×D₄	—	2	4	no	—
314	C₄×D₄	—	2	2	no	—
315	C₄×D₄	D₄×C₁₃	1	4	yes	—
316	C₄×D₄	C₂³×C₁₃	1	4	yes	—
317	C₄×D₄	C₂³×C₁₃	1	4	yes	—
318	#117	—	2	2	no	—
319	C₂×C₄⋊C₄	—	2	1	no	—
320	C₂×C₄⋊C₄	—	2	2	no	—
321	C₂×C₄⋊C₄	—	2	4	no	—
322	C₂×C₄⋊C₄	—	2	1	no	—
323	C₂×C₄⋊C₄	—	2	8	no	—
324	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
325	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
326	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
327	C₂×C₂²⋊C₄	—	2	4	no	—
328	C₂×C₂²⋊C₄	—	2	2	no	—
329	C₂×C₂²⋊C₄	—	2	1	no	—
330	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
331	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
332	#106	C₂³×C₁₃	1	8	yes	—
333	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
334	#103	C₂³×C₁₃	1	16	yes	—
335	#103	C₂³×C₁₃	1	8	yes	—
336	#102	C₂³×C₁₃	1	8	yes	—
337	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
338	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
339	C₄×C₈	C₂³×C₁₃	1	4	yes	—
340	C₂×C₁₃	—	2	2	no	—
341	C₂×C₁₃	—	4	4	no	—
342	C₂×C₁₃	—	4	4	no	—
343	C₂×C₁₃	#3484	1	1	yes	characteristic
344	C₂×C₁₃	C₂²×#137	1	1	yes	characteristic
345	C₂×C₁₃	#3586	1	1	yes	characteristic
346	C₂⁴	—	2	1	no	—
347	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
348	#41	—	2	16	no	—
349	#41	—	4	8	no	—
350	#41	—	4	16	no	—
351	C₂×Q₈	—	2	2	no	—
352	C₂×Q₈	—	2	2	no	—
353	C₂×Q₈	—	2	4	no	—
354	C₂×Q₈	—	4	4	no	—
355	C₂×Q₈	—	4	8	no	—
356	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
357	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
358	C₂×D₄	—	2	4	no	—
359	C₂×D₄	—	2	8	no	—
360	C₂×D₄	—	2	4	no	—
361	C₂×D₄	—	2	1	no	—
362	C₂×D₄	—	4	8	no	—
363	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
364	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	4	no	—
368	C₂²×C₄	—	2	4	no	—
369	C₂²×C₄	—	2	4	no	—
370	C₂²×C₄	—	2	8	no	—
371	C₂²×C₄	—	4	4	no	—
372	C₂²×C₄	—	4	8	no	—
373	C₂²×C₄	—	4	4	no	—
374	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
375	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
376	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
377	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
378	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
379	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
380	Q₁₆	—	4	16	no	—
381	SD₁₆	—	2	16	no	—
382	M₁₆	—	4	8	no	—
383	C₂×C₈	C₂⁴×C₁₃	1	8	yes	—
384	C₄⋊C₄	—	2	4	no	—
385	C₄⋊C₄	—	2	8	no	—
386	C₄⋊C₄	—	2	4	no	—
387	C₄⋊C₄	—	2	8	no	—
388	C₄⋊C₄	—	2	4	no	—
389	C₄⋊C₄	—	2	1	no	—
390	C₄⋊C₄	—	2	4	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	2	2	no	—
393	C₄⋊C₄	—	2	2	no	—
394	C₄⋊C₄	—	2	4	no	—
395	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
396	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
397	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
398	C₂²⋊C₄	—	2	4	no	—
399	C₂²⋊C₄	—	2	8	no	—
400	C₂²⋊C₄	—	2	8	no	—
401	C₂²⋊C₄	—	2	4	no	—
402	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
403	C₄²	—	2	4	no	—
404	C₄²	C₂×D₄×C₁₃	1	2	yes	—
405	C₄²	C₂⁴×C₁₃	1	2	yes	—
406	C₁₃	#61586	1	1	yes	characteristic, direct product factor, Sylow
407	C₂³	—	2	4	no	—
408	C₂³	—	2	2	no	—
409	C₂³	—	2	4	no	—
410	C₂³	—	4	2	no	—
411	C₂³	—	4	2	no	—
412	C₂³	—	4	2	no	—
413	C₂³	—	4	2	no	—
414	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
415	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
416	Q₈	—	2	8	no	—
417	Q₈	—	2	8	no	—
418	Q₈	—	4	4	no	—
419	Q₈	—	8	4	no	—
420	Q₈	—	8	2	no	—
421	D₄	—	2	4	no	—
422	D₄	—	2	8	no	—
423	D₄	—	2	2	no	—
424	D₄	—	4	16	no	—
425	D₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
426	C₂×C₄	—	2	8	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	4	no	—
429	C₂×C₄	—	2	4	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	4	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	4	no	—
434	C₂×C₄	—	4	1	no	—
435	C₂×C₄	—	4	16	no	—
436	C₂×C₄	—	4	4	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	4	8	no	—
439	C₂×C₄	—	8	4	no	—
440	C₂×C₄	—	8	4	no	—
441	C₂×C₄	C₁₃×#137	1	4	yes	complemented
442	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
443	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
444	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
445	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
446	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
447	C₈	—	2	8	no	—
448	C₂²	—	2	1	no	—
449	C₂²	—	2	1	no	—
450	C₂²	—	2	4	no	—
451	C₂²	—	2	4	no	—
452	C₂²	—	2	4	no	—
453	C₂²	—	2	4	no	—
454	C₂²	—	4	8	no	—
455	C₂²	—	4	2	no	—
456	C₂²	—	4	2	no	—
457	C₂²	—	8	4	no	—
458	C₂²	C₂×C₁₃×#137	1	2	yes	—
459	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
460	C₄	—	2	2	no	—
461	C₄	—	2	4	no	—
462	C₄	—	2	1	no	—
463	C₄	—	4	2	no	—
464	C₄	—	4	4	no	—
465	C₄	—	4	4	no	—
466	C₄	—	4	4	no	—
467	C₄	C₂×C₁₃×#137	1	4	yes	—
468	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
469	C₂	—	2	2	no	—
470	C₂	—	4	4	no	—
471	C₂	—	4	4	no	—
472	C₂	C₁₃×#3484	1	1	yes	characteristic
473	C₂	C₂²×C₁₃×#137	1	1	yes	characteristic
474	C₂	C₁₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₂×C₁₃×#547	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3501	C₂	semidirect
3. C₁₃×#3331	C₂	semidirect
4. C₁₃×#3276	C₂	semidirect
5. C₁₃×#3209	C₂	semidirect
6. C₁₃×#3195	C₂	semidirect
7. C₁₃×#3101	C₂	semidirect
8. C₁₃×#3007	C₂	semidirect
9. C₁₃×#2975	C₂	semidirect
11. C₂×C₁₃×#137	C₂²	semidirect
13. C₁₃×#554	C₂²	semidirect
14. D₄×Q₈×C₁₃	C₂²	semidirect
29. C₁₃×#494	C₂²	semidirect
30. C₁₃×#487	C₂²	semidirect
32. C₁₃×#483	C₂²	semidirect
33. C₁₃×#476	C₂²	semidirect
34. C₁₃×#470	C₂²	semidirect
35. C₁₃×#462	C₂²	semidirect
36. C₁₃×#461	C₂²	semidirect
37. C₁₃×#452	C₂²	semidirect
39. C₁₃×#451	C₂²	semidirect
41. C₄×C₁₃×SD₁₆	C₂²	semidirect
42. C₁₃×#436	C₂²	semidirect
44. C₁₃×#417	C₂²	semidirect
109. #61586	C₁₃	direct (N × H)
170. #3501	C₂×C₁₃	semidirect
172. #3331	C₂×C₁₃	semidirect
173. #3276	C₂×C₁₃	semidirect
174. #3209	C₂×C₁₃	semidirect
175. #3195	C₂×C₁₃	semidirect
176. #3101	C₂×C₁₃	semidirect
177. #3007	C₂×C₁₃	semidirect
178. #2975	C₂×C₁₃	semidirect
213. C₂×C₄×C₁₃	#137	semidirect
221. C₂×#137	C₂²×C₁₃	semidirect
223. #554	C₂²×C₁₃	semidirect
224. D₄×Q₈	C₂²×C₁₃	semidirect
239. #494	C₂²×C₁₃	semidirect
240. #487	C₂²×C₁₃	semidirect
242. #483	C₂²×C₁₃	semidirect
243. #476	C₂²×C₁₃	semidirect
244. #470	C₂²×C₁₃	semidirect
245. #462	C₂²×C₁₃	semidirect
246. #461	C₂²×C₁₃	semidirect
247. #452	C₂²×C₁₃	semidirect
249. #451	C₂²×C₁₃	semidirect
251. C₄×SD₁₆	C₂²×C₁₃	semidirect
252. #436	C₂²×C₁₃	semidirect
254. #417	C₂²×C₁₃	semidirect
406. C₁₃	#61586	direct (N × H)
441. C₂×C₄	C₁₃×#137	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#3501	2
C₂×C₁₃×#547	2
C₁₃×#3331	2
C₁₃×#3276	2
C₁₃×#3209	2
C₁₃×#3195	2
C₁₃×#3101	2
C₁₃×#3007	2
C₁₃×#2975	2
#61586	13

Subgroups — C13×#61586 #15747925

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61586 #15747925