Subgroups — C₁₃×#61086 #15747425

Order 3328.

2666 conjugacy classes of subgroups.

The subgroup lattice has 604 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×#3497	C₂	1	2	yes	maximal, complemented
3	C₁₃×#3287	C₂	1	2	yes	maximal, complemented
4	D₄×C₁₃×Q₁₆	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3285	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3278	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3277	C₂	1	4	yes	maximal, complemented
8	C₁₃×#3147	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3061	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3037	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3013	C₂	1	4	yes	maximal, complemented
12	C₂×C₄×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#2931	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	4	yes	—
15	C₁₃×#578	—	2	16	no	—
16	C₂×C₁₃×#137	C₂²	1	4	yes	—
17	C₂×C₁₃×#137	C₂²	1	8	yes	—
18	C₂×C₁₃×#135	C₂²	1	4	yes	—
19	C₂×C₁₃×#135	C₂²	1	2	yes	—
20	C₂×C₁₃×#135	C₂²	1	2	yes	—
21	C₂²×C₁₃×Q₁₆	C₂²	1	4	yes	—
22	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#131	C₂²	1	2	yes	—
24	C₁₃×#550	—	2	2	no	—
25	C₁₃×#550	C₂²	1	4	yes	—
26	D₄×Q₈×C₁₃	—	2	2	no	—
27	D₄×Q₈×C₁₃	C₂²	1	4	yes	—
28	C₁₃×#548	—	2	4	no	—
29	C₁₃×#548	C₂²	1	8	yes	—
30	C₁₃×#537	—	2	4	no	—
31	C₁₃×#537	C₂²	1	4	yes	—
32	C₁₃×#532	—	2	4	no	—
33	C₁₃×#532	C₂²	1	2	yes	—
34	C₁₃×#532	C₂²	1	1	yes	characteristic
35	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
36	C₁₃×#495	C₂²	1	2	yes	—
37	C₁₃×#495	C₂²	1	2	yes	—
38	C₁₃×#494	C₂²	1	1	yes	characteristic
39	C₁₃×#493	C₂²	1	1	yes	characteristic
40	C₁₃×#492	C₂²	1	2	yes	—
41	C₁₃×#468	C₂²	1	8	yes	—
42	C₁₃×#467	C₂²	1	4	yes	—
43	C₁₃×#466	C₂²	1	4	yes	—
44	C₁₃×#464	C₂²	1	8	yes	—
45	C₁₃×#462	C₂²	1	4	yes	—
46	C₁₃×#460	C₂²	1	4	yes	—
47	C₁₃×#452	C₂²	1	8	yes	—
48	C₁₃×#451	C₂²	1	8	yes	—
49	C₁₃×#449	C₂²	1	8	yes	—
50	C₁₃×#448	C₂²	1	8	yes	—
51	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
52	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
53	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
54	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
55	C₁₃×#436	C₂²	1	2	yes	—
56	C₁₃×#436	C₂²	1	2	yes	—
57	C₈×D₄×C₁₃	C₂²	1	2	yes	—
58	C₈×D₄×C₁₃	C₂²	1	2	yes	—
59	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
60	C₁₃×#423	C₂²	1	1	yes	characteristic
61	C₁₃×#417	C₂²	1	4	yes	—
62	C₂×C₁₃×#103	C₂²	1	2	yes	—
63	C₁₃×#408	C₂²	1	2	yes	—
64	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
65	C₁₃×2₋¹⁺⁴	—	2	16	no	—
66	C₁₃×2₋¹⁺⁴	—	4	8	no	—
67	C₂×C₁₃×#41	—	2	8	no	—
68	C₂×C₁₃×#41	—	2	4	no	—
69	C₂×C₁₃×#41	C₂³	1	4	yes	—
70	C₂×C₁₃×#41	C₂³	1	8	yes	—
71	C₂×C₁₃×#41	C₂³	1	2	yes	—
72	C₂²×Q₈×C₁₃	—	2	4	no	—
73	C₂²×Q₈×C₁₃	C₂³	1	8	yes	—
74	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
75	C₁₃×#137	—	2	16	no	—
76	C₁₃×#137	—	2	32	no	—
77	C₁₃×#135	—	2	16	no	—
78	C₁₃×#135	—	2	8	no	—
79	C₁₃×#135	—	4	4	no	—
80	C₂×C₁₃×Q₁₆	—	2	16	no	—
81	C₂×C₁₃×Q₁₆	D₄	1	8	yes	complemented
82	C₂×C₁₃×Q₁₆	C₂³	1	8	yes	—
83	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
84	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
85	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
86	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
87	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
88	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
89	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
90	C₂×C₁₃×D₈	C₂³	1	2	yes	—
91	C₂×C₁₃×D₈	C₂³	1	2	yes	—
92	C₁₃×#131	—	2	8	no	—
93	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
94	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
95	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
96	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
97	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
98	C₁₃×C₄⋊Q₈	—	2	4	no	—
99	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
100	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
101	C₁₃×#127	—	2	4	no	—
102	C₁₃×#127	D₄	1	1	yes	characteristic
103	C₁₃×#127	C₂³	1	2	yes	—
104	C₁₃×#124	—	2	8	no	—
105	C₁₃×#124	D₄	1	2	yes	—
106	C₁₃×#124	C₂³	1	4	yes	—
107	C₁₃×C₂²⋊Q₈	—	2	4	no	—
108	C₁₃×C₂²⋊Q₈	—	2	8	no	—
109	C₁₃×C₂²⋊Q₈	—	2	8	no	—
110	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
111	C₁₃×#121	—	2	8	no	—
112	C₁₃×#121	—	2	8	no	—
113	C₁₃×#121	—	2	4	no	—
114	C₁₃×#121	—	2	2	no	—
115	C₁₃×#121	—	2	2	no	—
116	C₁₃×#121	—	2	8	no	—
117	C₁₃×#121	D₄	1	2	yes	—
118	C₁₃×#121	D₄	1	2	yes	—
119	C₁₃×#121	C₂³	1	8	yes	—
120	C₄×Q₈×C₁₃	—	2	2	no	—
121	C₄×Q₈×C₁₃	—	2	2	no	—
122	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
123	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
124	C₄×D₄×C₁₃	—	2	4	no	—
125	C₄×D₄×C₁₃	—	2	4	no	—
126	C₄×D₄×C₁₃	—	2	8	no	—
127	C₄×D₄×C₁₃	—	2	2	no	—
128	C₄×D₄×C₁₃	—	2	2	no	—
129	C₄×D₄×C₁₃	C₂³	1	2	yes	—
130	C₄×D₄×C₁₃	C₂³	1	2	yes	—
131	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
132	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
133	C₂×C₄²×C₁₃	—	2	2	no	—
134	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
135	C₁₃×#107	C₂³	1	2	yes	—
136	C₁₃×#107	C₂³	1	2	yes	—
137	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
138	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
139	C₁₃×#103	C₂³	1	4	yes	—
140	C₁₃×#103	C₂³	1	4	yes	—
141	C₁₃×#103	C₂³	1	8	yes	—
142	C₁₃×#102	C₂³	1	8	yes	—
143	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
144	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
145	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
146	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
147	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
148	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
149	#61086	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
150	C₁₃×#41	—	2	4	no	—
151	C₁₃×#41	—	2	4	no	—
152	C₁₃×#41	—	2	16	no	—
153	C₁₃×#41	—	2	8	no	—
154	C₁₃×#41	—	2	8	no	—
155	C₁₃×#41	—	4	8	no	—
156	C₁₃×#41	—	4	32	no	—
157	C₁₃×#41	—	4	16	no	—
158	C₂×Q₈×C₁₃	—	2	2	no	—
159	C₂×Q₈×C₁₃	—	2	8	no	—
160	C₂×Q₈×C₁₃	—	2	4	no	—
161	C₂×Q₈×C₁₃	—	2	16	no	—
162	C₂×Q₈×C₁₃	—	4	8	no	—
163	C₂×Q₈×C₁₃	—	4	16	no	—
164	C₂×Q₈×C₁₃	C₂×D₄	1	8	yes	—
165	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
166	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
167	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
168	C₂×D₄×C₁₃	—	2	4	no	—
169	C₂×D₄×C₁₃	—	2	8	no	—
170	C₂×D₄×C₁₃	—	2	8	no	—
171	C₂×D₄×C₁₃	—	2	2	no	—
172	C₂×D₄×C₁₃	—	2	2	no	—
173	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
174	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
175	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
176	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
177	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
178	C₂²×C₄×C₁₃	—	2	2	no	—
179	C₂²×C₄×C₁₃	—	2	8	no	—
180	C₂²×C₄×C₁₃	—	2	2	no	—
181	C₂²×C₄×C₁₃	—	2	8	no	—
182	C₂²×C₄×C₁₃	—	2	4	no	—
183	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
184	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
185	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
186	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
187	C₁₃×Q₁₆	—	2	16	no	—
188	C₁₃×Q₁₆	—	2	4	no	—
189	C₁₃×Q₁₆	—	4	2	no	—
190	C₁₃×Q₁₆	C₂×D₄	1	8	yes	—
191	C₁₃×Q₁₆	C₂×D₄	1	8	yes	—
192	C₁₃×SD₁₆	—	2	16	no	—
193	C₁₃×SD₁₆	—	2	8	no	—
194	C₁₃×SD₁₆	—	4	4	no	—
195	C₁₃×D₈	—	2	4	no	—
196	C₁₃×D₈	—	4	2	no	—
197	C₁₃×M₁₆	—	2	4	no	—
198	C₁₃×M₁₆	—	2	8	no	—
199	C₂×C₈×C₁₃	—	2	2	no	—
200	C₂×C₈×C₁₃	—	2	8	no	—
201	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
202	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
203	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
204	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
205	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
206	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
207	C₁₃×C₄⋊C₄	—	2	4	no	—
208	C₁₃×C₄⋊C₄	—	2	4	no	—
209	C₁₃×C₄⋊C₄	—	2	2	no	—
210	C₁₃×C₄⋊C₄	—	2	2	no	—
211	C₁₃×C₄⋊C₄	—	2	2	no	—
212	C₁₃×C₄⋊C₄	—	2	8	no	—
213	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
214	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
215	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
216	C₁₃×C₂²⋊C₄	—	2	8	no	—
217	C₁₃×C₂²⋊C₄	—	2	4	no	—
218	C₁₃×C₂²⋊C₄	—	2	4	no	—
219	C₁₃×C₂²⋊C₄	—	2	8	no	—
220	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
221	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
222	C₄²×C₁₃	—	2	4	no	—
223	C₄²×C₁₃	—	2	4	no	—
224	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
225	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
226	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
227	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
228	C₂×#578	C₂×C₁₃	1	2	yes	complemented
229	#3497	C₂×C₁₃	1	2	yes	complemented
230	#3287	C₂×C₁₃	1	2	yes	complemented
231	D₄×Q₁₆	C₂×C₁₃	1	2	yes	complemented
232	#3285	C₂×C₁₃	1	4	yes	complemented
233	#3278	C₂×C₁₃	1	4	yes	complemented
234	#3277	C₂×C₁₃	1	4	yes	complemented
235	#3147	C₂×C₁₃	1	1	yes	characteristic, complemented
236	#3061	C₂×C₁₃	1	2	yes	complemented
237	#3037	C₂×C₁₃	1	2	yes	complemented
238	#3013	C₂×C₁₃	1	4	yes	complemented
239	C₂×C₄×Q₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
240	#2931	C₂×C₁₃	1	1	yes	characteristic, complemented
241	C₂³×C₁₃	—	2	4	no	—
242	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
243	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
244	Q₈×C₁₃	—	2	8	no	—
245	Q₈×C₁₃	—	2	4	no	—
246	Q₈×C₁₃	—	2	4	no	—
247	Q₈×C₁₃	—	2	4	no	—
248	Q₈×C₁₃	—	2	4	no	—
249	Q₈×C₁₃	—	4	16	no	—
250	Q₈×C₁₃	C₂²×D₄	1	8	yes	—
251	D₄×C₁₃	—	2	8	no	—
252	D₄×C₁₃	—	2	4	no	—
253	D₄×C₁₃	—	2	4	no	—
254	D₄×C₁₃	—	2	4	no	—
255	D₄×C₁₃	—	2	4	no	—
256	D₄×C₁₃	—	4	2	no	—
257	D₄×C₁₃	—	4	16	no	—
258	D₄×C₁₃	—	4	8	no	—
259	D₄×C₁₃	—	4	4	no	—
260	D₄×C₁₃	—	8	2	no	—
261	D₄×C₁₃	—	8	8	no	—
262	C₂×C₄×C₁₃	—	2	8	no	—
263	C₂×C₄×C₁₃	—	2	4	no	—
264	C₂×C₄×C₁₃	—	2	2	no	—
265	C₂×C₄×C₁₃	—	2	4	no	—
266	C₂×C₄×C₁₃	—	2	4	no	—
267	C₂×C₄×C₁₃	—	2	4	no	—
268	C₂×C₄×C₁₃	—	2	4	no	—
269	C₂×C₄×C₁₃	—	4	1	no	—
270	C₂×C₄×C₁₃	—	4	16	no	—
271	C₂×C₄×C₁₃	—	4	16	no	—
272	C₂×C₄×C₁₃	—	4	8	no	—
273	C₂×C₄×C₁₃	—	8	2	no	—
274	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
275	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
276	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
277	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
278	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
279	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
280	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
281	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
282	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
283	C₈×C₁₃	—	2	4	no	—
284	C₈×C₁₃	—	2	1	no	—
285	C₈×C₁₃	—	2	1	no	—
286	C₈×C₁₃	C₂²×D₄	1	2	yes	—
287	C₈×C₁₃	C₂²×D₄	1	2	yes	—
288	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	4	yes	—
289	#578	—	2	16	no	—
290	C₂×#137	C₂²×C₁₃	1	4	yes	—
291	C₂×#137	C₂²×C₁₃	1	8	yes	—
292	C₂×#135	C₂²×C₁₃	1	2	yes	—
293	C₂×#135	C₂²×C₁₃	1	4	yes	—
294	C₂×#135	C₂²×C₁₃	1	2	yes	—
295	C₂²×Q₁₆	C₂²×C₁₃	1	4	yes	—
296	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
297	C₂×#131	C₂²×C₁₃	1	2	yes	—
298	#550	—	2	2	no	—
299	#550	C₂²×C₁₃	1	4	yes	—
300	D₄×Q₈	—	2	2	no	—
301	D₄×Q₈	C₂²×C₁₃	1	4	yes	—
302	#548	—	2	4	no	—
303	#548	C₂²×C₁₃	1	8	yes	—
304	#537	—	2	4	no	—
305	#537	C₂²×C₁₃	1	4	yes	—
306	#532	—	2	4	no	—
307	#532	C₂²×C₁₃	1	2	yes	—
308	#532	C₂²×C₁₃	1	1	yes	characteristic
309	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
310	#495	C₂²×C₁₃	1	2	yes	—
311	#495	C₂²×C₁₃	1	2	yes	—
312	#494	C₂²×C₁₃	1	1	yes	characteristic
313	#493	C₂²×C₁₃	1	1	yes	characteristic
314	#492	C₂²×C₁₃	1	2	yes	—
315	#468	C₂²×C₁₃	1	8	yes	—
316	#467	C₂²×C₁₃	1	4	yes	—
317	#466	C₂²×C₁₃	1	4	yes	—
318	#464	C₂²×C₁₃	1	8	yes	—
319	#462	C₂²×C₁₃	1	4	yes	—
320	#460	C₂²×C₁₃	1	4	yes	—
321	#452	C₂²×C₁₃	1	8	yes	—
322	#451	C₂²×C₁₃	1	8	yes	—
323	#449	C₂²×C₁₃	1	8	yes	—
324	#448	C₂²×C₁₃	1	8	yes	—
325	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
326	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
327	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
328	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
329	#436	C₂²×C₁₃	1	2	yes	—
330	#436	C₂²×C₁₃	1	2	yes	—
331	C₈×D₄	C₂²×C₁₃	1	2	yes	—
332	C₈×D₄	C₂²×C₁₃	1	2	yes	—
333	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
334	#423	C₂²×C₁₃	1	1	yes	characteristic
335	#417	C₂²×C₁₃	1	4	yes	—
336	C₂×#103	C₂²×C₁₃	1	2	yes	—
337	#408	C₂²×C₁₃	1	2	yes	—
338	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
339	C₂²×C₁₃	—	2	1	no	—
340	C₂²×C₁₃	—	2	1	no	—
341	C₂²×C₁₃	—	2	4	no	—
342	C₂²×C₁₃	—	2	4	no	—
343	C₂²×C₁₃	—	2	4	no	—
344	C₂²×C₁₃	—	4	4	no	—
345	C₂²×C₁₃	—	4	4	no	—
346	C₂²×C₁₃	—	4	4	no	—
347	C₂²×C₁₃	D₄²	1	2	yes	—
348	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
349	C₄×C₁₃	—	2	1	no	—
350	C₄×C₁₃	—	2	1	no	—
351	C₄×C₁₃	—	2	8	no	—
352	C₄×C₁₃	—	2	4	no	—
353	C₄×C₁₃	—	2	1	no	—
354	C₄×C₁₃	—	4	4	no	—
355	C₄×C₁₃	—	4	4	no	—
356	C₄×C₁₃	D₄²	1	2	yes	—
357	C₄×C₁₃	#578	1	2	yes	complemented
358	C₄×C₁₃	C₂³×D₄	1	1	yes	characteristic
359	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
360	2₋¹⁺⁴	—	2	16	no	—
361	2₋¹⁺⁴	—	4	8	no	—
362	C₂×#41	—	2	8	no	—
363	C₂×#41	—	2	4	no	—
364	C₂×#41	C₂³×C₁₃	1	4	yes	—
365	C₂×#41	C₂³×C₁₃	1	8	yes	—
366	C₂×#41	C₂³×C₁₃	1	2	yes	—
367	C₂²×Q₈	—	2	4	no	—
368	C₂²×Q₈	C₂³×C₁₃	1	8	yes	—
369	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
370	#137	—	2	16	no	—
371	#137	—	2	32	no	—
372	#135	—	2	16	no	—
373	#135	—	2	8	no	—
374	#135	—	4	4	no	—
375	C₂×Q₁₆	—	2	16	no	—
376	C₂×Q₁₆	D₄×C₁₃	1	8	yes	complemented
377	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
378	C₂×Q₁₆	C₂³×C₁₃	1	8	yes	—
379	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
380	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
381	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
382	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
383	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
384	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
385	C₂×D₈	C₂³×C₁₃	1	2	yes	—
386	C₂×D₈	C₂³×C₁₃	1	2	yes	—
387	#131	—	2	8	no	—
388	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
389	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
390	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
391	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
392	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
393	C₄⋊Q₈	—	2	4	no	—
394	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
395	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
396	#127	—	2	4	no	—
397	#127	D₄×C₁₃	1	1	yes	characteristic
398	#127	C₂³×C₁₃	1	2	yes	—
399	#124	—	2	8	no	—
400	#124	D₄×C₁₃	1	2	yes	—
401	#124	C₂³×C₁₃	1	4	yes	—
402	C₂²⋊Q₈	—	2	4	no	—
403	C₂²⋊Q₈	—	2	8	no	—
404	C₂²⋊Q₈	—	2	8	no	—
405	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
406	#121	—	2	8	no	—
407	#121	—	2	8	no	—
408	#121	—	2	4	no	—
409	#121	—	2	2	no	—
410	#121	—	2	2	no	—
411	#121	—	2	8	no	—
412	#121	D₄×C₁₃	1	2	yes	—
413	#121	D₄×C₁₃	1	2	yes	—
414	#121	C₂³×C₁₃	1	8	yes	—
415	C₄×Q₈	—	2	2	no	—
416	C₄×Q₈	—	2	2	no	—
417	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
418	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
419	C₄×D₄	—	2	4	no	—
420	C₄×D₄	—	2	4	no	—
421	C₄×D₄	—	2	8	no	—
422	C₄×D₄	—	2	2	no	—
423	C₄×D₄	—	2	2	no	—
424	C₄×D₄	C₂³×C₁₃	1	2	yes	—
425	C₄×D₄	C₂³×C₁₃	1	2	yes	—
426	C₂×C₄⋊C₄	—	2	2	no	—
427	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
428	C₂×C₄²	—	2	2	no	—
429	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
430	#107	C₂³×C₁₃	1	2	yes	—
431	#107	C₂³×C₁₃	1	2	yes	—
432	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
433	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
434	#103	C₂³×C₁₃	1	4	yes	—
435	#103	C₂³×C₁₃	1	4	yes	—
436	#103	C₂³×C₁₃	1	8	yes	—
437	#102	C₂³×C₁₃	1	8	yes	—
438	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
439	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
440	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
441	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
442	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
443	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
444	C₂×C₁₃	—	2	2	no	—
445	C₂×C₁₃	—	4	4	no	—
446	C₂×C₁₃	—	8	4	no	—
447	C₂×C₁₃	C₂×D₄²	1	1	yes	characteristic
448	C₂×C₁₃	C₂×#578	1	1	yes	characteristic
449	C₂×C₁₃	#3584	1	1	yes	characteristic
450	#41	—	2	4	no	—
451	#41	—	2	4	no	—
452	#41	—	2	16	no	—
453	#41	—	2	8	no	—
454	#41	—	2	8	no	—
455	#41	—	4	8	no	—
456	#41	—	4	32	no	—
457	#41	—	4	16	no	—
458	C₂×Q₈	—	2	2	no	—
459	C₂×Q₈	—	2	8	no	—
460	C₂×Q₈	—	2	4	no	—
461	C₂×Q₈	—	2	16	no	—
462	C₂×Q₈	—	4	8	no	—
463	C₂×Q₈	—	4	16	no	—
464	C₂×Q₈	C₂×D₄×C₁₃	1	8	yes	—
465	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
466	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
467	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
468	C₂×D₄	—	2	4	no	—
469	C₂×D₄	—	2	8	no	—
470	C₂×D₄	—	2	8	no	—
471	C₂×D₄	—	2	2	no	—
472	C₂×D₄	—	2	2	no	—
473	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
474	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
475	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
476	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
477	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
478	C₂²×C₄	—	2	2	no	—
479	C₂²×C₄	—	2	8	no	—
480	C₂²×C₄	—	2	2	no	—
481	C₂²×C₄	—	2	8	no	—
482	C₂²×C₄	—	2	4	no	—
483	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
484	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
485	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
486	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
487	Q₁₆	—	2	16	no	—
488	Q₁₆	—	2	4	no	—
489	Q₁₆	—	4	2	no	—
490	Q₁₆	C₂×D₄×C₁₃	1	8	yes	—
491	Q₁₆	C₂×D₄×C₁₃	1	8	yes	—
492	SD₁₆	—	2	16	no	—
493	SD₁₆	—	2	8	no	—
494	SD₁₆	—	4	4	no	—
495	D₈	—	2	4	no	—
496	D₈	—	4	2	no	—
497	M₁₆	—	2	4	no	—
498	M₁₆	—	2	8	no	—
499	C₂×C₈	—	2	2	no	—
500	C₂×C₈	—	2	8	no	—
501	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
502	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
503	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
504	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
505	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
506	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
507	C₄⋊C₄	—	2	4	no	—
508	C₄⋊C₄	—	2	4	no	—
509	C₄⋊C₄	—	2	2	no	—
510	C₄⋊C₄	—	2	2	no	—
511	C₄⋊C₄	—	2	2	no	—
512	C₄⋊C₄	—	2	8	no	—
513	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
514	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
515	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
516	C₂²⋊C₄	—	2	8	no	—
517	C₂²⋊C₄	—	2	4	no	—
518	C₂²⋊C₄	—	2	4	no	—
519	C₂²⋊C₄	—	2	8	no	—
520	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
521	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
522	C₄²	—	2	4	no	—
523	C₄²	—	2	4	no	—
524	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
525	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
526	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
527	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
528	C₁₃	#61086	1	1	yes	characteristic, direct product factor, Sylow
529	C₂³	—	2	4	no	—
530	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
531	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
532	Q₈	—	2	8	no	—
533	Q₈	—	2	4	no	—
534	Q₈	—	2	4	no	—
535	Q₈	—	2	4	no	—
536	Q₈	—	2	4	no	—
537	Q₈	—	4	16	no	—
538	Q₈	C₂²×D₄×C₁₃	1	8	yes	—
539	D₄	—	2	8	no	—
540	D₄	—	2	4	no	—
541	D₄	—	2	4	no	—
542	D₄	—	2	4	no	—
543	D₄	—	2	4	no	—
544	D₄	—	4	2	no	—
545	D₄	—	4	16	no	—
546	D₄	—	4	8	no	—
547	D₄	—	4	4	no	—
548	D₄	—	8	2	no	—
549	D₄	—	8	8	no	—
550	C₂×C₄	—	2	8	no	—
551	C₂×C₄	—	2	4	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	2	4	no	—
554	C₂×C₄	—	2	4	no	—
555	C₂×C₄	—	2	4	no	—
556	C₂×C₄	—	2	4	no	—
557	C₂×C₄	—	4	1	no	—
558	C₂×C₄	—	4	16	no	—
559	C₂×C₄	—	4	16	no	—
560	C₂×C₄	—	4	8	no	—
561	C₂×C₄	—	8	2	no	—
562	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
563	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
564	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
565	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
566	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
567	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
568	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
569	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
570	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
571	C₈	—	2	4	no	—
572	C₈	—	2	1	no	—
573	C₈	—	2	1	no	—
574	C₈	C₂²×D₄×C₁₃	1	2	yes	—
575	C₈	C₂²×D₄×C₁₃	1	2	yes	—
576	C₂²	—	2	1	no	—
577	C₂²	—	2	1	no	—
578	C₂²	—	2	4	no	—
579	C₂²	—	2	4	no	—
580	C₂²	—	2	4	no	—
581	C₂²	—	4	4	no	—
582	C₂²	—	4	4	no	—
583	C₂²	—	4	4	no	—
584	C₂²	D₄²×C₁₃	1	2	yes	—
585	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
586	C₄	—	2	1	no	—
587	C₄	—	2	1	no	—
588	C₄	—	2	1	no	—
589	C₄	—	2	8	no	—
590	C₄	—	2	4	no	—
591	C₄	—	4	4	no	—
592	C₄	—	4	4	no	—
593	C₄	D₄²×C₁₃	1	2	yes	—
594	C₄	C₁₃×#578	1	2	yes	complemented
595	C₄	C₂³×D₄×C₁₃	1	1	yes	characteristic
596	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
597	C₂	—	2	2	no	—
598	C₂	—	4	4	no	—
599	C₂	—	8	4	no	—
600	C₂	C₂×D₄²×C₁₃	1	1	yes	characteristic
601	C₂	C₂×C₁₃×#578	1	1	yes	characteristic
602	C₂	C₁₃×#3584	1	1	yes	characteristic

	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×#3497	C₂	semidirect
3. C₁₃×#3287	C₂	semidirect
4. D₄×C₁₃×Q₁₆	C₂	semidirect
5. C₁₃×#3285	C₂	semidirect
6. C₁₃×#3278	C₂	semidirect
7. C₁₃×#3277	C₂	semidirect
8. C₁₃×#3147	C₂	semidirect
9. C₁₃×#3061	C₂	semidirect
10. C₁₃×#3037	C₂	semidirect
11. C₁₃×#3013	C₂	semidirect
12. C₂×C₄×C₁₃×Q₁₆	C₂	semidirect
13. C₁₃×#2931	C₂	semidirect
81. C₂×C₁₃×Q₁₆	D₄	semidirect
149. #61086	C₁₃	direct (N × H)
228. C₂×#578	C₂×C₁₃	semidirect
229. #3497	C₂×C₁₃	semidirect
230. #3287	C₂×C₁₃	semidirect
231. D₄×Q₁₆	C₂×C₁₃	semidirect
232. #3285	C₂×C₁₃	semidirect
233. #3278	C₂×C₁₃	semidirect
234. #3277	C₂×C₁₃	semidirect
235. #3147	C₂×C₁₃	semidirect
236. #3061	C₂×C₁₃	semidirect
237. #3037	C₂×C₁₃	semidirect
238. #3013	C₂×C₁₃	semidirect
239. C₂×C₄×Q₁₆	C₂×C₁₃	semidirect
240. #2931	C₂×C₁₃	semidirect
357. C₄×C₁₃	#578	semidirect
376. C₂×Q₁₆	D₄×C₁₃	semidirect
528. C₁₃	#61086	direct (N × H)
594. 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×#3497	2
C₁₃×#3287	2
D₄×C₁₃×Q₁₆	2
C₁₃×#3285	2
C₁₃×#3278	2
C₁₃×#3277	2
C₁₃×#3147	2
C₁₃×#3061	2
C₁₃×#3037	2
C₁₃×#3013	2
C₂×C₄×C₁₃×Q₁₆	2
C₁₃×#2931	2
#61086	13

Subgroups — C13×#61086 #15747425

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61086 #15747425