Subgroups — C₁₃×#61091 #15747430

Order 3328.

2650 conjugacy classes of subgroups.

The subgroup lattice has 484 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	C₁₃×#3499	C₂	1	2	yes	maximal, complemented
3	D₄×C₁₃×Q₁₆	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3283	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3276	C₂	1	8	yes	maximal, complemented
6	C₂×C₁₃×#494	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#3059	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3039	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3011	C₂	1	4	yes	maximal, complemented
10	C₄×C₁₃×#135	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2931	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	4	yes	—
13	C₁₃×#578	—	2	16	no	—
14	C₂×C₁₃×#137	C₂²	1	4	yes	—
15	C₂×C₁₃×#137	C₂²	1	8	yes	—
16	C₂×C₁₃×#135	C₂²	1	4	yes	—
17	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
18	C₂²×C₁₃×Q₁₆	C₂²	1	4	yes	—
19	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	—
20	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	—
21	C₂×C₁₃×#131	C₂²	1	2	yes	—
22	D₄×Q₈×C₁₃	C₂²	1	8	yes	—
23	C₁₃×#547	—	2	8	no	—
24	C₁₃×#547	C₂²	1	8	yes	—
25	C₁₃×#536	—	2	4	no	—
26	C₁₃×#536	C₂²	1	4	yes	—
27	C₁₃×#532	—	2	2	no	—
28	C₁₃×#532	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×C₄⋊Q₈	—	2	2	no	—
30	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
31	C₄×C₁₃×#41	C₂²	1	2	yes	—
32	C₁₃×#494	C₂²	1	4	yes	—
33	C₁₃×#494	C₂²	1	4	yes	—
34	C₁₃×#470	C₂²	1	8	yes	—
35	C₁₃×#467	C₂²	1	8	yes	—
36	C₁₃×#462	C₂²	1	8	yes	—
37	C₁₃×#461	C₂²	1	8	yes	—
38	C₁₃×#452	C₂²	1	16	yes	—
39	C₁₃×#451	C₂²	1	16	yes	—
40	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
41	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	—
42	C₄×C₁₃×D₈	C₂²	1	2	yes	—
43	C₁₃×#436	C₂²	1	4	yes	—
44	C₈×D₄×C₁₃	C₂²	1	4	yes	—
45	C₁₃×#427	C₂²	1	1	yes	characteristic
46	C₁₃×#423	C₂²	1	1	yes	characteristic
47	C₁₃×#419	C₂²	1	4	yes	—
48	C₁₃×#416	C₂²	1	2	yes	—
49	C₁₃×#408	C₂²	1	2	yes	—
50	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
51	C₁₃×2₋¹⁺⁴	—	2	16	no	—
52	C₁₃×2₋¹⁺⁴	—	4	8	no	—
53	C₂×C₁₃×#41	—	2	4	no	—
54	C₂×C₁₃×#41	—	2	8	no	—
55	C₂×C₁₃×#41	C₂³	1	8	yes	—
56	C₂×C₁₃×#41	C₂³	1	2	yes	—
57	C₂×C₁₃×#41	C₂³	1	2	yes	—
58	C₂²×Q₈×C₁₃	—	2	4	no	—
59	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
60	C₂²×Q₈×C₁₃	C₂³	1	8	yes	—
61	C₁₃×#137	—	2	16	no	—
62	C₁₃×#137	—	2	32	no	—
63	C₁₃×#135	—	2	16	no	—
64	C₁₃×#135	D₄	1	8	yes	complemented
65	C₂×C₁₃×Q₁₆	—	2	16	no	—
66	C₂×C₁₃×Q₁₆	—	2	8	no	—
67	C₂×C₁₃×Q₁₆	—	4	4	no	—
68	C₂×C₁₃×Q₁₆	C₂³	1	8	yes	—
69	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
70	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
71	C₂×C₁₃×Q₁₆	C₂³	1	8	yes	—
72	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
73	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
74	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
75	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
76	C₁₃×#131	—	2	8	no	—
77	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
78	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
79	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
81	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
82	C₁₃×C₄⋊Q₈	—	2	4	no	—
83	C₁₃×C₄⋊Q₈	—	2	8	no	—
84	C₁₃×C₄⋊Q₈	—	2	2	no	—
85	C₁₃×C₄⋊Q₈	—	2	2	no	—
86	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
87	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
88	C₁₃×#127	D₄	1	1	yes	characteristic
89	C₁₃×#124	—	2	4	no	—
90	C₁₃×#124	D₄	1	2	yes	—
91	C₁₃×#123	—	2	8	no	—
92	C₁₃×#123	—	2	16	no	—
93	C₁₃×C₂²⋊Q₈	—	2	16	no	—
94	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
95	C₁₃×#121	—	2	8	no	—
96	C₁₃×#121	D₄	1	4	yes	—
97	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
98	C₄×D₄×C₁₃	—	2	8	no	—
99	C₄×D₄×C₁₃	—	2	4	no	—
100	C₄×D₄×C₁₃	C₂³	1	4	yes	—
101	C₄×D₄×C₁₃	C₂³	1	4	yes	—
102	C₁₃×#117	—	2	2	no	—
103	C₁₃×#117	C₂³	1	2	yes	—
104	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
105	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
106	C₂×C₄²×C₁₃	—	2	2	no	—
107	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
108	C₁₃×#107	C₂³	1	2	yes	—
109	C₁₃×#106	C₂³	1	2	yes	—
110	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
111	C₁₃×#103	C₂³	1	4	yes	—
112	C₁₃×#103	C₂³	1	16	yes	—
113	C₁₃×#102	C₂³	1	4	yes	—
114	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	—
115	C₄×C₈×C₁₃	C₂³	1	2	yes	—
116	C₄×C₈×C₁₃	C₂³	1	2	yes	—
117	#61091	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
118	C₁₃×#41	—	2	4	no	—
119	C₁₃×#41	—	2	4	no	—
120	C₁₃×#41	—	2	4	no	—
121	C₁₃×#41	—	2	16	no	—
122	C₁₃×#41	—	4	8	no	—
123	C₁₃×#41	—	4	16	no	—
124	C₁₃×#41	—	4	32	no	—
125	C₁₃×#41	C₂×D₄	1	8	yes	—
126	C₂×Q₈×C₁₃	—	2	8	no	—
127	C₂×Q₈×C₁₃	—	2	4	no	—
128	C₂×Q₈×C₁₃	—	2	16	no	—
129	C₂×Q₈×C₁₃	—	2	8	no	—
130	C₂×Q₈×C₁₃	—	2	8	no	—
131	C₂×Q₈×C₁₃	—	4	8	no	—
132	C₂×Q₈×C₁₃	—	4	16	no	—
133	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
134	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
135	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
136	C₂×D₄×C₁₃	—	2	2	no	—
137	C₂×D₄×C₁₃	—	2	8	no	—
138	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
139	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
140	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
141	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
142	C₂²×C₄×C₁₃	—	2	2	no	—
143	C₂²×C₄×C₁₃	—	2	4	no	—
144	C₂²×C₄×C₁₃	—	2	8	no	—
145	C₂²×C₄×C₁₃	—	2	4	no	—
146	C₂²×C₄×C₁₃	—	2	8	no	—
147	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
148	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
149	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
150	C₁₃×Q₁₆	—	2	16	no	—
151	C₁₃×Q₁₆	—	2	8	no	—
152	C₁₃×Q₁₆	—	2	8	no	—
153	C₁₃×Q₁₆	—	4	8	no	—
154	C₁₃×Q₁₆	C₂×D₄	1	4	yes	—
155	C₁₃×SD₁₆	—	2	16	no	—
156	C₁₃×SD₁₆	C₂×D₄	1	8	yes	—
157	C₁₃×D₈	C₂×D₄	1	4	yes	—
158	C₁₃×M₁₆	—	2	4	no	—
159	C₁₃×M₁₆	—	2	8	no	—
160	C₂×C₈×C₁₃	—	2	2	no	—
161	C₂×C₈×C₁₃	—	2	8	no	—
162	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
163	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
164	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
165	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
166	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
167	C₁₃×C₄⋊C₄	—	2	8	no	—
168	C₁₃×C₄⋊C₄	—	2	8	no	—
169	C₁₃×C₄⋊C₄	—	2	16	no	—
170	C₁₃×C₄⋊C₄	—	2	4	no	—
171	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
172	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
173	C₁₃×C₂²⋊C₄	—	2	2	no	—
174	C₁₃×C₂²⋊C₄	—	2	16	no	—
175	C₁₃×C₂²⋊C₄	—	2	4	no	—
176	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
177	C₄²×C₁₃	—	2	2	no	—
178	C₄²×C₁₃	—	2	4	no	—
179	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
180	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
181	C₄²×C₁₃	C₂⁴	1	2	yes	—
182	C₂×#578	C₂×C₁₃	1	2	yes	complemented
183	#3499	C₂×C₁₃	1	2	yes	complemented
184	D₄×Q₁₆	C₂×C₁₃	1	4	yes	complemented
185	#3283	C₂×C₁₃	1	4	yes	complemented
186	#3276	C₂×C₁₃	1	8	yes	complemented
187	C₂×#494	C₂×C₁₃	1	1	yes	characteristic, complemented
188	#3059	C₂×C₁₃	1	2	yes	complemented
189	#3039	C₂×C₁₃	1	2	yes	complemented
190	#3011	C₂×C₁₃	1	4	yes	complemented
191	C₄×#135	C₂×C₁₃	1	1	yes	characteristic, complemented
192	#2931	C₂×C₁₃	1	1	yes	characteristic, complemented
193	C₂³×C₁₃	—	2	2	no	—
194	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
195	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
196	Q₈×C₁₃	—	2	4	no	—
197	Q₈×C₁₃	—	2	2	no	—
198	Q₈×C₁₃	—	2	8	no	—
199	Q₈×C₁₃	—	2	8	no	—
200	Q₈×C₁₃	—	4	16	no	—
201	Q₈×C₁₃	—	4	8	no	—
202	Q₈×C₁₃	C₂²×D₄	1	4	yes	—
203	D₄×C₁₃	—	2	8	no	—
204	D₄×C₁₃	—	2	8	no	—
205	D₄×C₁₃	—	2	4	no	—
206	D₄×C₁₃	—	2	8	no	—
207	D₄×C₁₃	—	2	2	no	—
208	D₄×C₁₃	—	4	16	no	—
209	D₄×C₁₃	C₂²×D₄	1	4	yes	—
210	C₂×C₄×C₁₃	—	2	2	no	—
211	C₂×C₄×C₁₃	—	2	8	no	—
212	C₂×C₄×C₁₃	—	2	4	no	—
213	C₂×C₄×C₁₃	—	2	4	no	—
214	C₂×C₄×C₁₃	—	2	4	no	—
215	C₂×C₄×C₁₃	—	2	4	no	—
216	C₂×C₄×C₁₃	—	2	8	no	—
217	C₂×C₄×C₁₃	—	4	16	no	—
218	C₂×C₄×C₁₃	—	4	16	no	—
219	C₂×C₄×C₁₃	—	4	8	no	—
220	C₂×C₄×C₁₃	—	4	8	no	—
221	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
222	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
223	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
224	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
225	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
226	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
227	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
228	C₈×C₁₃	—	2	4	no	—
229	C₈×C₁₃	—	2	2	no	—
230	C₈×C₁₃	C₂²×D₄	1	2	yes	—
231	C₈×C₁₃	C₂²×D₄	1	2	yes	—
232	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	4	yes	—
233	#578	—	2	16	no	—
234	C₂×#137	C₂²×C₁₃	1	4	yes	—
235	C₂×#137	C₂²×C₁₃	1	8	yes	—
236	C₂×#135	C₂²×C₁₃	1	4	yes	—
237	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
238	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	—
239	C₂²×Q₁₆	C₂²×C₁₃	1	4	yes	—
240	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	—
241	C₂×#131	C₂²×C₁₃	1	2	yes	—
242	D₄×Q₈	C₂²×C₁₃	1	8	yes	—
243	#547	—	2	8	no	—
244	#547	C₂²×C₁₃	1	8	yes	—
245	#536	—	2	4	no	—
246	#536	C₂²×C₁₃	1	4	yes	—
247	#532	—	2	2	no	—
248	#532	C₂²×C₁₃	1	1	yes	characteristic
249	C₂×C₄⋊Q₈	—	2	2	no	—
250	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
251	C₄×#41	C₂²×C₁₃	1	2	yes	—
252	#494	C₂²×C₁₃	1	4	yes	—
253	#494	C₂²×C₁₃	1	4	yes	—
254	#470	C₂²×C₁₃	1	8	yes	—
255	#467	C₂²×C₁₃	1	8	yes	—
256	#462	C₂²×C₁₃	1	8	yes	—
257	#461	C₂²×C₁₃	1	8	yes	—
258	#452	C₂²×C₁₃	1	16	yes	—
259	#451	C₂²×C₁₃	1	16	yes	—
260	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
261	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	—
262	C₄×D₈	C₂²×C₁₃	1	2	yes	—
263	#436	C₂²×C₁₃	1	4	yes	—
264	C₈×D₄	C₂²×C₁₃	1	4	yes	—
265	#427	C₂²×C₁₃	1	1	yes	characteristic
266	#423	C₂²×C₁₃	1	1	yes	characteristic
267	#419	C₂²×C₁₃	1	4	yes	—
268	#416	C₂²×C₁₃	1	2	yes	—
269	#408	C₂²×C₁₃	1	2	yes	—
270	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
271	C₂²×C₁₃	—	2	2	no	—
272	C₂²×C₁₃	—	2	4	no	—
273	C₂²×C₁₃	—	2	4	no	—
274	C₂²×C₁₃	—	2	8	no	—
275	C₂²×C₁₃	—	4	4	no	—
276	C₂²×C₁₃	D₄²	1	2	yes	—
277	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
278	C₄×C₁₃	—	2	4	no	—
279	C₄×C₁₃	—	2	4	no	—
280	C₄×C₁₃	—	2	2	no	—
281	C₄×C₁₃	—	4	8	no	—
282	C₄×C₁₃	—	4	4	no	—
283	C₄×C₁₃	D₄²	1	2	yes	—
284	C₄×C₁₃	#578	1	4	yes	complemented
285	C₄×C₁₃	C₂³×D₄	1	1	yes	characteristic
286	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
287	2₋¹⁺⁴	—	2	16	no	—
288	2₋¹⁺⁴	—	4	8	no	—
289	C₂×#41	—	2	4	no	—
290	C₂×#41	—	2	8	no	—
291	C₂×#41	C₂³×C₁₃	1	8	yes	—
292	C₂×#41	C₂³×C₁₃	1	2	yes	—
293	C₂×#41	C₂³×C₁₃	1	2	yes	—
294	C₂²×Q₈	—	2	4	no	—
295	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
296	C₂²×Q₈	C₂³×C₁₃	1	8	yes	—
297	#137	—	2	16	no	—
298	#137	—	2	32	no	—
299	#135	—	2	16	no	—
300	#135	D₄×C₁₃	1	8	yes	complemented
301	C₂×Q₁₆	—	2	16	no	—
302	C₂×Q₁₆	—	2	8	no	—
303	C₂×Q₁₆	—	4	4	no	—
304	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
305	C₂×Q₁₆	C₂³×C₁₃	1	8	yes	—
306	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
307	C₂×Q₁₆	C₂³×C₁₃	1	8	yes	—
308	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
309	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
310	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
311	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
312	#131	—	2	8	no	—
313	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
314	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
315	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
316	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
317	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
318	C₄⋊Q₈	—	2	4	no	—
319	C₄⋊Q₈	—	2	8	no	—
320	C₄⋊Q₈	—	2	2	no	—
321	C₄⋊Q₈	—	2	2	no	—
322	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
323	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
324	#127	D₄×C₁₃	1	1	yes	characteristic
325	#124	—	2	4	no	—
326	#124	D₄×C₁₃	1	2	yes	—
327	#123	—	2	8	no	—
328	#123	—	2	16	no	—
329	C₂²⋊Q₈	—	2	16	no	—
330	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
331	#121	—	2	8	no	—
332	#121	D₄×C₁₃	1	4	yes	—
333	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
334	C₄×D₄	—	2	8	no	—
335	C₄×D₄	—	2	4	no	—
336	C₄×D₄	C₂³×C₁₃	1	4	yes	—
337	C₄×D₄	C₂³×C₁₃	1	4	yes	—
338	#117	—	2	2	no	—
339	#117	C₂³×C₁₃	1	2	yes	—
340	C₂×C₄⋊C₄	—	2	4	no	—
341	C₂×C₄⋊C₄	—	2	8	no	—
342	C₂×C₄²	—	2	2	no	—
343	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
344	#107	C₂³×C₁₃	1	2	yes	—
345	#106	C₂³×C₁₃	1	2	yes	—
346	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
347	#103	C₂³×C₁₃	1	4	yes	—
348	#103	C₂³×C₁₃	1	16	yes	—
349	#102	C₂³×C₁₃	1	4	yes	—
350	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
351	C₄×C₈	C₂³×C₁₃	1	2	yes	—
352	C₄×C₈	C₂³×C₁₃	1	2	yes	—
353	C₂×C₁₃	—	2	2	no	—
354	C₂×C₁₃	—	4	4	no	—
355	C₂×C₁₃	—	4	4	no	—
356	C₂×C₁₃	C₂×D₄²	1	1	yes	characteristic
357	C₂×C₁₃	C₂×#578	1	2	yes	—
358	#41	—	2	4	no	—
359	#41	—	2	4	no	—
360	#41	—	2	4	no	—
361	#41	—	2	16	no	—
362	#41	—	4	8	no	—
363	#41	—	4	16	no	—
364	#41	—	4	32	no	—
365	#41	C₂×D₄×C₁₃	1	8	yes	—
366	C₂×Q₈	—	2	8	no	—
367	C₂×Q₈	—	2	4	no	—
368	C₂×Q₈	—	2	16	no	—
369	C₂×Q₈	—	2	8	no	—
370	C₂×Q₈	—	2	8	no	—
371	C₂×Q₈	—	4	8	no	—
372	C₂×Q₈	—	4	16	no	—
373	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
374	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
375	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
376	C₂×D₄	—	2	2	no	—
377	C₂×D₄	—	2	8	no	—
378	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
379	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
380	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
381	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	2	4	no	—
384	C₂²×C₄	—	2	8	no	—
385	C₂²×C₄	—	2	4	no	—
386	C₂²×C₄	—	2	8	no	—
387	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
388	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
389	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
390	Q₁₆	—	2	16	no	—
391	Q₁₆	—	2	8	no	—
392	Q₁₆	—	2	8	no	—
393	Q₁₆	—	4	8	no	—
394	Q₁₆	C₂×D₄×C₁₃	1	4	yes	—
395	SD₁₆	—	2	16	no	—
396	SD₁₆	C₂×D₄×C₁₃	1	8	yes	—
397	D₈	C₂×D₄×C₁₃	1	4	yes	—
398	M₁₆	—	2	4	no	—
399	M₁₆	—	2	8	no	—
400	C₂×C₈	—	2	2	no	—
401	C₂×C₈	—	2	8	no	—
402	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
403	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
404	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
405	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
406	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
407	C₄⋊C₄	—	2	8	no	—
408	C₄⋊C₄	—	2	8	no	—
409	C₄⋊C₄	—	2	16	no	—
410	C₄⋊C₄	—	2	4	no	—
411	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
412	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
413	C₂²⋊C₄	—	2	2	no	—
414	C₂²⋊C₄	—	2	16	no	—
415	C₂²⋊C₄	—	2	4	no	—
416	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
417	C₄²	—	2	2	no	—
418	C₄²	—	2	4	no	—
419	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
420	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
421	C₄²	C₂⁴×C₁₃	1	2	yes	—
422	C₁₃	#61091	1	1	yes	characteristic, direct product factor, Sylow
423	C₂³	—	2	2	no	—
424	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
425	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
426	Q₈	—	2	4	no	—
427	Q₈	—	2	2	no	—
428	Q₈	—	2	8	no	—
429	Q₈	—	2	8	no	—
430	Q₈	—	4	16	no	—
431	Q₈	—	4	8	no	—
432	Q₈	C₂²×D₄×C₁₃	1	4	yes	—
433	D₄	—	2	8	no	—
434	D₄	—	2	8	no	—
435	D₄	—	2	4	no	—
436	D₄	—	2	8	no	—
437	D₄	—	2	2	no	—
438	D₄	—	4	16	no	—
439	D₄	C₂²×D₄×C₁₃	1	4	yes	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	8	no	—
442	C₂×C₄	—	2	4	no	—
443	C₂×C₄	—	2	4	no	—
444	C₂×C₄	—	2	4	no	—
445	C₂×C₄	—	2	4	no	—
446	C₂×C₄	—	2	8	no	—
447	C₂×C₄	—	4	16	no	—
448	C₂×C₄	—	4	16	no	—
449	C₂×C₄	—	4	8	no	—
450	C₂×C₄	—	4	8	no	—
451	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
452	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
453	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
454	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
455	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
456	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
457	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
458	C₈	—	2	4	no	—
459	C₈	—	2	2	no	—
460	C₈	C₂²×D₄×C₁₃	1	2	yes	—
461	C₈	C₂²×D₄×C₁₃	1	2	yes	—
462	C₂²	—	2	2	no	—
463	C₂²	—	2	8	no	—
464	C₂²	—	2	4	no	—
465	C₂²	—	2	4	no	—
466	C₂²	—	4	4	no	—
467	C₂²	D₄²×C₁₃	1	2	yes	—
468	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
469	C₄	—	2	2	no	—
470	C₄	—	2	4	no	—
471	C₄	—	2	4	no	—
472	C₄	—	4	4	no	—
473	C₄	—	4	8	no	—
474	C₄	D₄²×C₁₃	1	2	yes	—
475	C₄	C₁₃×#578	1	4	yes	complemented
476	C₄	C₂³×D₄×C₁₃	1	1	yes	characteristic
477	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
478	C₂	—	2	2	no	—
479	C₂	—	4	4	no	—
480	C₂	—	4	4	no	—
481	C₂	C₂×D₄²×C₁₃	1	1	yes	characteristic
482	C₂	C₂×C₁₃×#578	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×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#578	C₂	semidirect
2. C₁₃×#3499	C₂	semidirect
3. D₄×C₁₃×Q₁₆	C₂	semidirect
4. C₁₃×#3283	C₂	semidirect
5. C₁₃×#3276	C₂	semidirect
6. C₂×C₁₃×#494	C₂	semidirect
7. C₁₃×#3059	C₂	semidirect
8. C₁₃×#3039	C₂	semidirect
9. C₁₃×#3011	C₂	semidirect
10. C₄×C₁₃×#135	C₂	semidirect
11. C₁₃×#2931	C₂	semidirect
64. C₁₃×#135	D₄	semidirect
117. #61091	C₁₃	direct (N × H)
182. C₂×#578	C₂×C₁₃	semidirect
183. #3499	C₂×C₁₃	semidirect
184. D₄×Q₁₆	C₂×C₁₃	semidirect
185. #3283	C₂×C₁₃	semidirect
186. #3276	C₂×C₁₃	semidirect
187. C₂×#494	C₂×C₁₃	semidirect
188. #3059	C₂×C₁₃	semidirect
189. #3039	C₂×C₁₃	semidirect
190. #3011	C₂×C₁₃	semidirect
191. C₄×#135	C₂×C₁₃	semidirect
192. #2931	C₂×C₁₃	semidirect
284. C₄×C₁₃	#578	semidirect
300. #135	D₄×C₁₃	semidirect
422. C₁₃	#61091	direct (N × H)
475. C₄	C₁₃×#578	semidirect

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
C₁₃×#3499	2
D₄×C₁₃×Q₁₆	2
C₁₃×#3283	2
C₁₃×#3276	2
C₂×C₁₃×#494	2
C₁₃×#3059	2
C₁₃×#3039	2
C₁₃×#3011	2
C₄×C₁₃×#135	2
C₁₃×#2931	2
#61091	13

Subgroups — C13×#61091 #15747430

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61091 #15747430