Subgroups — C₁₃×#61053 #15747392

Order 3328.

2666 conjugacy classes of subgroups.

The subgroup lattice has 670 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	C₂³×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3486	C₂	1	2	yes	maximal, complemented
4	D₄×C₁₃×Q₁₆	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3285	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3270	C₂	1	8	yes	maximal, complemented
7	C₁₃×#3156	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#3059	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3050	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3044	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3011	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3004	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	C₂³×Q₈×C₁₃	C₂²	1	2	yes	—
17	C₁₃×#578	—	2	8	no	—
18	C₂×C₁₃×#137	C₂²	1	2	yes	—
19	C₂×C₁₃×#137	C₂²	1	2	yes	—
20	C₂×C₁₃×#137	C₂²	1	4	yes	complemented
21	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#135	C₂²	1	2	yes	complemented
23	C₂²×C₁₃×Q₁₆	—	2	8	no	—
24	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	—
25	C₂²×C₁₃×Q₁₆	C₂²	1	4	yes	—
26	C₂²×C₁₃×Q₁₆	C₂²	1	4	yes	—
27	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
28	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
29	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
30	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
31	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
32	D₄×Q₈×C₁₃	—	2	4	no	—
33	D₄×Q₈×C₁₃	C₂²	1	8	yes	—
34	C₁₃×#548	—	2	4	no	—
35	C₁₃×#548	C₂²	1	8	yes	—
36	C₁₃×#536	—	2	4	no	—
37	C₁₃×#536	C₂²	1	2	yes	—
38	C₁₃×#536	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×#497	C₂²	1	4	yes	complemented
44	C₁₃×#495	C₂²	1	2	yes	complemented
45	C₁₃×#494	C₂²	1	2	yes	complemented
46	C₁₃×#470	C₂²	1	4	yes	complemented
47	C₁₃×#467	C₂²	1	2	yes	—
48	C₁₃×#467	C₂²	1	4	yes	complemented
49	C₁₃×#466	C₂²	1	2	yes	—
50	C₁₃×#465	C₂²	1	4	yes	—
51	C₁₃×#464	C₂²	1	8	yes	complemented
52	C₁₃×#462	C₂²	1	8	yes	complemented
53	C₁₃×#452	C₂²	1	8	yes	complemented
54	C₁₃×#451	C₂²	1	8	yes	—
55	C₁₃×#451	C₂²	1	8	yes	complemented
56	C₁₃×#448	C₂²	1	8	yes	—
57	C₁₃×#441	C₂²	1	4	yes	complemented
58	C₄×C₁₃×Q₁₆	C₂²	1	4	yes	complemented
59	C₁₃×#435	C₂²	1	4	yes	—
60	C₈×D₄×C₁₃	C₂²	1	4	yes	—
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×#419	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	C₂³	1	2	yes	—
74	C₂×C₁₃×#41	C₂³	1	4	yes	—
75	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
76	C₂²×Q₈×C₁₃	—	2	2	no	—
77	C₂²×Q₈×C₁₃	—	2	2	no	—
78	C₂²×Q₈×C₁₃	—	2	4	no	—
79	C₂²×Q₈×C₁₃	—	2	8	no	—
80	C₂²×Q₈×C₁₃	—	4	4	no	—
81	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
82	C₂²×Q₈×C₁₃	C₂³	1	8	yes	—
83	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
84	C₂²×Q₈×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×#137	—	4	4	no	—
90	C₁₃×#135	—	2	8	no	—
91	C₁₃×#135	—	2	4	no	—
92	C₂×C₁₃×Q₁₆	—	2	8	no	—
93	C₂×C₁₃×Q₁₆	—	2	16	no	—
94	C₂×C₁₃×Q₁₆	—	2	16	no	—
95	C₂×C₁₃×Q₁₆	—	2	8	no	—
96	C₂×C₁₃×Q₁₆	—	2	4	no	—
97	C₂×C₁₃×Q₁₆	D₄	1	8	yes	complemented
98	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
99	C₂×C₁₃×Q₁₆	C₂³	1	8	yes	—
100	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
101	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
102	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
103	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
104	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
105	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
106	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
107	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
108	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
109	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
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×C₄⋊Q₈	—	2	2	no	—
121	C₁₃×C₄⋊Q₈	—	2	8	no	—
122	C₁₃×C₄⋊Q₈	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	4	no	—
127	C₁₃×#123	—	2	2	no	—
128	C₁₃×#123	—	2	4	no	—
129	C₁₃×#123	D₄	1	2	yes	—
130	C₁₃×C₂²⋊Q₈	—	2	8	no	—
131	C₁₃×C₂²⋊Q₈	—	2	4	no	—
132	C₁₃×C₂²⋊Q₈	—	2	8	no	—
133	C₁₃×C₂²⋊Q₈	—	2	8	no	—
134	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
135	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
136	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
137	C₁₃×#121	—	2	8	no	—
138	C₁₃×#121	D₄	1	2	yes	—
139	C₁₃×#121	C₂³	1	4	yes	—
140	C₁₃×#120	—	2	2	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	8	no	—
145	C₄×D₄×C₁₃	—	2	4	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×#103	C₂³	1	8	yes	—
157	C₁₃×#102	C₂³	1	4	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	#61053	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
163	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
164	C₁₃×#41	—	2	2	no	—
165	C₁₃×#41	—	2	2	no	—
166	C₁₃×#41	—	2	8	no	—
167	C₁₃×#41	—	2	4	no	—
168	C₁₃×#41	—	2	4	no	—
169	C₁₃×#41	—	4	4	no	—
170	C₁₃×#41	—	4	16	no	—
171	C₁₃×#41	—	4	8	no	—
172	C₂×Q₈×C₁₃	—	2	2	no	—
173	C₂×Q₈×C₁₃	—	2	8	no	—
174	C₂×Q₈×C₁₃	—	2	2	no	—
175	C₂×Q₈×C₁₃	—	2	4	no	—
176	C₂×Q₈×C₁₃	—	2	4	no	—
177	C₂×Q₈×C₁₃	—	2	16	no	—
178	C₂×Q₈×C₁₃	—	2	8	no	—
179	C₂×Q₈×C₁₃	—	2	4	no	—
180	C₂×Q₈×C₁₃	—	2	4	no	—
181	C₂×Q₈×C₁₃	—	4	8	no	—
182	C₂×Q₈×C₁₃	—	4	8	no	—
183	C₂×Q₈×C₁₃	—	4	4	no	—
184	C₂×Q₈×C₁₃	—	4	16	no	—
185	C₂×Q₈×C₁₃	—	4	8	no	—
186	C₂×Q₈×C₁₃	C₂×D₄	1	8	yes	—
187	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
188	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
189	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
190	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
191	C₂×D₄×C₁₃	—	2	4	no	—
192	C₂×D₄×C₁₃	—	2	2	no	—
193	C₂×D₄×C₁₃	—	2	4	no	—
194	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
195	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
196	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
197	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
198	C₂²×C₄×C₁₃	—	2	2	no	—
199	C₂²×C₄×C₁₃	—	2	2	no	—
200	C₂²×C₄×C₁₃	—	2	2	no	—
201	C₂²×C₄×C₁₃	—	2	8	no	—
202	C₂²×C₄×C₁₃	—	2	4	no	—
203	C₂²×C₄×C₁₃	—	2	2	no	—
204	C₂²×C₄×C₁₃	—	2	4	no	—
205	C₂²×C₄×C₁₃	—	2	2	no	—
206	C₂²×C₄×C₁₃	—	4	8	no	—
207	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
208	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
209	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
210	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
211	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
212	C₁₃×Q₁₆	—	2	16	no	—
213	C₁₃×Q₁₆	—	2	8	no	—
214	C₁₃×Q₁₆	—	2	4	no	—
215	C₁₃×Q₁₆	—	2	4	no	—
216	C₁₃×Q₁₆	—	2	2	no	—
217	C₁₃×Q₁₆	—	4	4	no	—
218	C₁₃×Q₁₆	C₂×D₄	1	8	yes	—
219	C₁₃×Q₁₆	C₂×D₄	1	8	yes	—
220	C₁₃×SD₁₆	—	2	8	no	—
221	C₁₃×SD₁₆	—	2	4	no	—
222	C₁₃×SD₁₆	—	4	4	no	—
223	C₁₃×D₈	—	2	2	no	—
224	C₁₃×M₁₆	—	2	2	no	—
225	C₁₃×M₁₆	—	2	2	no	—
226	C₁₃×M₁₆	—	2	4	no	—
227	C₂×C₈×C₁₃	—	2	2	no	—
228	C₂×C₈×C₁₃	—	2	4	no	—
229	C₂×C₈×C₁₃	—	2	4	no	—
230	C₂×C₈×C₁₃	—	2	4	no	—
231	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
232	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
233	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
234	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
235	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
236	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
237	C₁₃×C₄⋊C₄	—	2	8	no	—
238	C₁₃×C₄⋊C₄	—	2	8	no	—
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	8	no	—
247	C₁₃×C₂²⋊C₄	—	2	8	no	—
248	C₁₃×C₂²⋊C₄	—	2	4	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	C₂³×Q₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
257	#3486	C₂×C₁₃	1	2	yes	complemented
258	D₄×Q₁₆	C₂×C₁₃	1	4	yes	complemented
259	#3285	C₂×C₁₃	1	4	yes	complemented
260	#3270	C₂×C₁₃	1	8	yes	complemented
261	#3156	C₂×C₁₃	1	1	yes	characteristic, complemented
262	#3059	C₂×C₁₃	1	1	yes	characteristic, complemented
263	#3050	C₂×C₁₃	1	1	yes	characteristic, complemented
264	#3044	C₂×C₁₃	1	2	yes	complemented
265	#3011	C₂×C₁₃	1	2	yes	complemented
266	#3004	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	C₂²×D₄	1	2	yes	—
273	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
274	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
275	Q₈×C₁₃	—	2	8	no	—
276	Q₈×C₁₃	—	2	2	no	—
277	Q₈×C₁₃	—	2	4	no	—
278	Q₈×C₁₃	—	2	2	no	—
279	Q₈×C₁₃	—	2	4	no	—
280	Q₈×C₁₃	—	2	4	no	—
281	Q₈×C₁₃	—	2	2	no	—
282	Q₈×C₁₃	—	4	16	no	—
283	Q₈×C₁₃	—	4	8	no	—
284	Q₈×C₁₃	—	4	4	no	—
285	Q₈×C₁₃	C₂²×D₄	1	8	yes	—
286	D₄×C₁₃	—	2	4	no	—
287	D₄×C₁₃	—	2	8	no	—
288	D₄×C₁₃	—	2	2	no	—
289	D₄×C₁₃	—	2	2	no	—
290	D₄×C₁₃	—	2	2	no	—
291	D₄×C₁₃	—	4	8	no	—
292	D₄×C₁₃	—	4	4	no	—
293	D₄×C₁₃	—	4	8	no	—
294	C₂×C₄×C₁₃	—	2	2	no	—
295	C₂×C₄×C₁₃	—	2	8	no	—
296	C₂×C₄×C₁₃	—	2	4	no	—
297	C₂×C₄×C₁₃	—	2	4	no	—
298	C₂×C₄×C₁₃	—	2	2	no	—
299	C₂×C₄×C₁₃	—	2	2	no	—
300	C₂×C₄×C₁₃	—	2	2	no	—
301	C₂×C₄×C₁₃	—	2	2	no	—
302	C₂×C₄×C₁₃	—	2	4	no	—
303	C₂×C₄×C₁₃	—	2	4	no	—
304	C₂×C₄×C₁₃	—	2	2	no	—
305	C₂×C₄×C₁₃	—	4	8	no	—
306	C₂×C₄×C₁₃	—	4	16	no	—
307	C₂×C₄×C₁₃	—	4	8	no	—
308	C₂×C₄×C₁₃	—	4	4	no	—
309	C₂×C₄×C₁₃	—	4	4	no	—
310	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
311	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
312	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
313	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
314	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
315	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
316	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
317	C₈×C₁₃	—	2	2	no	—
318	C₈×C₁₃	—	2	2	no	—
319	C₈×C₁₃	—	2	2	no	—
320	C₈×C₁₃	C₂²×D₄	1	2	yes	—
321	C₈×C₁₃	C₂²×D₄	1	2	yes	—
322	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	2	yes	—
323	C₂³×Q₈	C₂²×C₁₃	1	2	yes	—
324	#578	—	2	8	no	—
325	C₂×#137	C₂²×C₁₃	1	2	yes	—
326	C₂×#137	C₂²×C₁₃	1	2	yes	—
327	C₂×#137	C₂²×C₁₃	1	4	yes	complemented
328	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
329	C₂×#135	C₂²×C₁₃	1	2	yes	complemented
330	C₂²×Q₁₆	—	2	8	no	—
331	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
332	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	—
333	C₂²×Q₁₆	C₂²×C₁₃	1	4	yes	—
334	C₂²×Q₁₆	C₂²×C₁₃	1	4	yes	—
335	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
336	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
337	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
338	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
339	D₄×Q₈	—	2	4	no	—
340	D₄×Q₈	C₂²×C₁₃	1	8	yes	—
341	#548	—	2	4	no	—
342	#548	C₂²×C₁₃	1	8	yes	—
343	#536	—	2	4	no	—
344	#536	C₂²×C₁₃	1	2	yes	—
345	#536	C₂²×C₁₃	1	2	yes	—
346	#525	—	2	4	no	—
347	#525	C₂²×C₁₃	1	2	yes	—
348	#525	C₂²×C₁₃	1	1	yes	characteristic
349	#519	C₂²×C₁₃	1	2	yes	—
350	#497	C₂²×C₁₃	1	4	yes	complemented
351	#495	C₂²×C₁₃	1	2	yes	complemented
352	#494	C₂²×C₁₃	1	2	yes	complemented
353	#470	C₂²×C₁₃	1	4	yes	complemented
354	#467	C₂²×C₁₃	1	2	yes	—
355	#467	C₂²×C₁₃	1	4	yes	complemented
356	#466	C₂²×C₁₃	1	2	yes	—
357	#465	C₂²×C₁₃	1	4	yes	—
358	#464	C₂²×C₁₃	1	8	yes	complemented
359	#462	C₂²×C₁₃	1	8	yes	complemented
360	#452	C₂²×C₁₃	1	8	yes	complemented
361	#451	C₂²×C₁₃	1	8	yes	—
362	#451	C₂²×C₁₃	1	8	yes	complemented
363	#448	C₂²×C₁₃	1	8	yes	—
364	#441	C₂²×C₁₃	1	4	yes	complemented
365	C₄×Q₁₆	C₂²×C₁₃	1	4	yes	complemented
366	#435	C₂²×C₁₃	1	4	yes	—
367	C₈×D₄	C₂²×C₁₃	1	4	yes	—
368	#427	C₂²×C₁₃	1	1	yes	characteristic
369	#424	C₂²×C₁₃	1	1	yes	characteristic
370	#419	C₂²×C₁₃	1	2	yes	—
371	#419	C₂²×C₁₃	1	2	yes	—
372	#416	C₂²×C₁₃	1	2	yes	—
373	#408	C₂²×C₁₃	1	1	yes	characteristic
374	#407	C₂²×C₁₃	1	1	yes	characteristic
375	#405	C₂²×C₁₃	1	1	yes	characteristic
376	C₂²×C₁₃	—	2	8	no	—
377	C₂²×C₁₃	—	2	2	no	—
378	C₂²×C₁₃	—	2	2	no	—
379	C₂²×C₁₃	—	2	2	no	—
380	C₂²×C₁₃	—	2	2	no	—
381	C₂²×C₁₃	—	2	4	no	—
382	C₂²×C₁₃	—	4	2	no	—
383	C₂²×C₁₃	—	4	4	no	—
384	C₂²×C₁₃	D₄²	1	2	yes	—
385	C₂²×C₁₃	#578	1	4	yes	complemented
386	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
387	C₄×C₁₃	—	2	2	no	—
388	C₄×C₁₃	—	2	8	no	—
389	C₄×C₁₃	—	2	2	no	—
390	C₄×C₁₃	—	2	4	no	—
391	C₄×C₁₃	—	4	2	no	—
392	C₄×C₁₃	—	4	4	no	—
393	C₄×C₁₃	—	4	4	no	—
394	C₄×C₁₃	D₄²	1	2	yes	—
395	C₄×C₁₃	C₂³×D₄	1	1	yes	characteristic
396	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
397	2₋¹⁺⁴	—	2	8	no	—
398	2₋¹⁺⁴	—	4	4	no	—
399	C₂×#41	—	2	4	no	—
400	C₂×#41	—	2	2	no	—
401	C₂×#41	C₂³×C₁₃	1	2	yes	—
402	C₂×#41	C₂³×C₁₃	1	4	yes	—
403	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
404	C₂²×Q₈	—	2	2	no	—
405	C₂²×Q₈	—	2	2	no	—
406	C₂²×Q₈	—	2	4	no	—
407	C₂²×Q₈	—	2	8	no	—
408	C₂²×Q₈	—	4	4	no	—
409	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
410	C₂²×Q₈	C₂³×C₁₃	1	8	yes	—
411	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
412	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
413	C₂³×C₄	—	2	2	no	—
414	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
415	#137	—	2	8	no	—
416	#137	—	2	16	no	—
417	#137	—	4	4	no	—
418	#135	—	2	8	no	—
419	#135	—	2	4	no	—
420	C₂×Q₁₆	—	2	8	no	—
421	C₂×Q₁₆	—	2	16	no	—
422	C₂×Q₁₆	—	2	16	no	—
423	C₂×Q₁₆	—	2	8	no	—
424	C₂×Q₁₆	—	2	4	no	—
425	C₂×Q₁₆	D₄×C₁₃	1	8	yes	complemented
426	C₂×Q₁₆	C₂³×C₁₃	1	8	yes	—
427	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
428	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
429	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
430	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
431	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
432	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
433	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
434	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
435	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
436	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
437	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
438	#131	—	2	4	no	—
439	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
440	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
441	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
442	C₂²×C₈	—	2	4	no	—
443	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
444	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
445	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
446	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
447	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
448	C₄⋊Q₈	—	2	2	no	—
449	C₄⋊Q₈	—	2	8	no	—
450	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
451	#124	—	2	2	no	—
452	#124	—	2	8	no	—
453	#124	C₂³×C₁₃	1	4	yes	—
454	#123	—	2	4	no	—
455	#123	—	2	2	no	—
456	#123	—	2	4	no	—
457	#123	D₄×C₁₃	1	2	yes	—
458	C₂²⋊Q₈	—	2	8	no	—
459	C₂²⋊Q₈	—	2	4	no	—
460	C₂²⋊Q₈	—	2	8	no	—
461	C₂²⋊Q₈	—	2	8	no	—
462	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
463	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
464	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
465	#121	—	2	8	no	—
466	#121	D₄×C₁₃	1	2	yes	—
467	#121	C₂³×C₁₃	1	4	yes	—
468	#120	—	2	2	no	—
469	#120	D₄×C₁₃	1	2	yes	—
470	C₄×Q₈	—	2	4	no	—
471	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
472	C₄×D₄	—	2	8	no	—
473	C₄×D₄	—	2	4	no	—
474	C₄×D₄	—	2	8	no	—
475	C₄×D₄	C₂³×C₁₃	1	4	yes	—
476	#117	—	2	4	no	—
477	#117	C₂³×C₁₃	1	2	yes	—
478	#117	C₂³×C₁₃	1	1	yes	characteristic
479	#107	C₂³×C₁₃	1	2	yes	—
480	#106	C₂³×C₁₃	1	2	yes	—
481	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
482	#103	C₂³×C₁₃	1	4	yes	—
483	#103	C₂³×C₁₃	1	8	yes	—
484	#103	C₂³×C₁₃	1	8	yes	—
485	#102	C₂³×C₁₃	1	4	yes	—
486	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
487	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
488	#97	C₂³×C₁₃	1	2	yes	—
489	C₄×C₈	C₂³×C₁₃	1	2	yes	—
490	C₂×C₁₃	—	2	2	no	—
491	C₂×C₁₃	—	2	4	no	—
492	C₂×C₁₃	—	4	2	no	—
493	C₂×C₁₃	—	8	2	no	—
494	C₂×C₁₃	C₂×D₄²	1	1	yes	characteristic
495	C₂×C₁₃	C₂×#578	1	2	yes	—
496	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
497	#41	—	2	2	no	—
498	#41	—	2	2	no	—
499	#41	—	2	8	no	—
500	#41	—	2	4	no	—
501	#41	—	2	4	no	—
502	#41	—	4	4	no	—
503	#41	—	4	16	no	—
504	#41	—	4	8	no	—
505	C₂×Q₈	—	2	2	no	—
506	C₂×Q₈	—	2	8	no	—
507	C₂×Q₈	—	2	2	no	—
508	C₂×Q₈	—	2	4	no	—
509	C₂×Q₈	—	2	4	no	—
510	C₂×Q₈	—	2	16	no	—
511	C₂×Q₈	—	2	8	no	—
512	C₂×Q₈	—	2	4	no	—
513	C₂×Q₈	—	2	4	no	—
514	C₂×Q₈	—	4	8	no	—
515	C₂×Q₈	—	4	8	no	—
516	C₂×Q₈	—	4	4	no	—
517	C₂×Q₈	—	4	16	no	—
518	C₂×Q₈	—	4	8	no	—
519	C₂×Q₈	C₂×D₄×C₁₃	1	8	yes	—
520	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
521	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
522	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
523	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
524	C₂×D₄	—	2	4	no	—
525	C₂×D₄	—	2	2	no	—
526	C₂×D₄	—	2	4	no	—
527	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
528	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
529	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
530	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
531	C₂²×C₄	—	2	2	no	—
532	C₂²×C₄	—	2	2	no	—
533	C₂²×C₄	—	2	2	no	—
534	C₂²×C₄	—	2	8	no	—
535	C₂²×C₄	—	2	4	no	—
536	C₂²×C₄	—	2	2	no	—
537	C₂²×C₄	—	2	4	no	—
538	C₂²×C₄	—	2	2	no	—
539	C₂²×C₄	—	4	8	no	—
540	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
541	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
542	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
543	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
544	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
545	Q₁₆	—	2	16	no	—
546	Q₁₆	—	2	8	no	—
547	Q₁₆	—	2	4	no	—
548	Q₁₆	—	2	4	no	—
549	Q₁₆	—	2	2	no	—
550	Q₁₆	—	4	4	no	—
551	Q₁₆	C₂×D₄×C₁₃	1	8	yes	—
552	Q₁₆	C₂×D₄×C₁₃	1	8	yes	—
553	SD₁₆	—	2	8	no	—
554	SD₁₆	—	2	4	no	—
555	SD₁₆	—	4	4	no	—
556	D₈	—	2	2	no	—
557	M₁₆	—	2	2	no	—
558	M₁₆	—	2	2	no	—
559	M₁₆	—	2	4	no	—
560	C₂×C₈	—	2	2	no	—
561	C₂×C₈	—	2	4	no	—
562	C₂×C₈	—	2	4	no	—
563	C₂×C₈	—	2	4	no	—
564	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
565	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
566	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
567	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
568	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
569	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
570	C₄⋊C₄	—	2	8	no	—
571	C₄⋊C₄	—	2	8	no	—
572	C₄⋊C₄	—	2	8	no	—
573	C₄⋊C₄	—	2	4	no	—
574	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
575	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
576	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
577	C₂²⋊C₄	—	2	2	no	—
578	C₂²⋊C₄	—	2	4	no	—
579	C₂²⋊C₄	—	2	8	no	—
580	C₂²⋊C₄	—	2	8	no	—
581	C₂²⋊C₄	—	2	4	no	—
582	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
583	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
584	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
585	C₄²	—	2	8	no	—
586	C₄²	—	2	2	no	—
587	C₄²	C₂⁴×C₁₃	1	2	yes	—
588	C₁₃	#61053	1	1	yes	characteristic, direct product factor, Sylow
589	C₂³	—	2	2	no	—
590	C₂³	—	2	4	no	—
591	C₂³	—	2	2	no	—
592	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
593	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
594	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
595	Q₈	—	2	8	no	—
596	Q₈	—	2	2	no	—
597	Q₈	—	2	4	no	—
598	Q₈	—	2	2	no	—
599	Q₈	—	2	4	no	—
600	Q₈	—	2	4	no	—
601	Q₈	—	2	2	no	—
602	Q₈	—	4	16	no	—
603	Q₈	—	4	8	no	—
604	Q₈	—	4	4	no	—
605	Q₈	C₂²×D₄×C₁₃	1	8	yes	—
606	D₄	—	2	4	no	—
607	D₄	—	2	8	no	—
608	D₄	—	2	2	no	—
609	D₄	—	2	2	no	—
610	D₄	—	2	2	no	—
611	D₄	—	4	8	no	—
612	D₄	—	4	4	no	—
613	D₄	—	4	8	no	—
614	C₂×C₄	—	2	2	no	—
615	C₂×C₄	—	2	8	no	—
616	C₂×C₄	—	2	4	no	—
617	C₂×C₄	—	2	4	no	—
618	C₂×C₄	—	2	2	no	—
619	C₂×C₄	—	2	2	no	—
620	C₂×C₄	—	2	2	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	2	4	no	—
623	C₂×C₄	—	2	4	no	—
624	C₂×C₄	—	2	2	no	—
625	C₂×C₄	—	4	8	no	—
626	C₂×C₄	—	4	16	no	—
627	C₂×C₄	—	4	8	no	—
628	C₂×C₄	—	4	4	no	—
629	C₂×C₄	—	4	4	no	—
630	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
631	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
632	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
633	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
634	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
635	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
636	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
637	C₈	—	2	2	no	—
638	C₈	—	2	2	no	—
639	C₈	—	2	2	no	—
640	C₈	C₂²×D₄×C₁₃	1	2	yes	—
641	C₈	C₂²×D₄×C₁₃	1	2	yes	—
642	C₂²	—	2	8	no	—
643	C₂²	—	2	2	no	—
644	C₂²	—	2	2	no	—
645	C₂²	—	2	2	no	—
646	C₂²	—	2	4	no	—
647	C₂²	—	2	2	no	—
648	C₂²	—	4	4	no	—
649	C₂²	—	4	2	no	—
650	C₂²	D₄²×C₁₃	1	2	yes	—
651	C₂²	C₁₃×#578	1	4	yes	complemented
652	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
653	C₄	—	2	4	no	—
654	C₄	—	2	2	no	—
655	C₄	—	2	8	no	—
656	C₄	—	2	2	no	—
657	C₄	—	4	4	no	—
658	C₄	—	4	2	no	—
659	C₄	—	4	4	no	—
660	C₄	D₄²×C₁₃	1	2	yes	—
661	C₄	C₂³×D₄×C₁₃	1	1	yes	characteristic
662	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
663	C₂	—	2	2	no	—
664	C₂	—	2	4	no	—
665	C₂	—	4	2	no	—
666	C₂	—	8	2	no	—
667	C₂	C₂×D₄²×C₁₃	1	1	yes	characteristic
668	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×#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. C₂³×C₁₃×Q₁₆	C₂	semidirect
3. C₁₃×#3486	C₂	semidirect
4. D₄×C₁₃×Q₁₆	C₂	semidirect
5. C₁₃×#3285	C₂	semidirect
6. C₁₃×#3270	C₂	semidirect
7. C₁₃×#3156	C₂	semidirect
8. C₁₃×#3059	C₂	semidirect
9. C₁₃×#3050	C₂	semidirect
10. C₁₃×#3044	C₂	semidirect
11. C₁₃×#3011	C₂	semidirect
12. C₁₃×#3004	C₂	semidirect
13. C₁₃×#2950	C₂	semidirect
14. C₁₃×#2929	C₂	semidirect
20. C₂×C₁₃×#137	C₂²	semidirect
22. C₂×C₁₃×#135	C₂²	semidirect
29. C₂²×C₁₃×Q₁₆	C₂²	semidirect
43. C₁₃×#497	C₂²	semidirect
44. C₁₃×#495	C₂²	semidirect
45. C₁₃×#494	C₂²	semidirect
46. C₁₃×#470	C₂²	semidirect
48. C₁₃×#467	C₂²	semidirect
51. C₁₃×#464	C₂²	semidirect
52. C₁₃×#462	C₂²	semidirect
53. C₁₃×#452	C₂²	semidirect
55. C₁₃×#451	C₂²	semidirect
57. C₁₃×#441	C₂²	semidirect
58. C₄×C₁₃×Q₁₆	C₂²	semidirect
97. C₂×C₁₃×Q₁₆	D₄	semidirect
162. #61053	C₁₃	direct (N × H)
255. C₂×#578	C₂×C₁₃	semidirect
256. C₂³×Q₁₆	C₂×C₁₃	semidirect
257. #3486	C₂×C₁₃	semidirect
258. D₄×Q₁₆	C₂×C₁₃	semidirect
259. #3285	C₂×C₁₃	semidirect
260. #3270	C₂×C₁₃	semidirect
261. #3156	C₂×C₁₃	semidirect
262. #3059	C₂×C₁₃	semidirect
263. #3050	C₂×C₁₃	semidirect
264. #3044	C₂×C₁₃	semidirect
265. #3011	C₂×C₁₃	semidirect
266. #3004	C₂×C₁₃	semidirect
267. #2950	C₂×C₁₃	semidirect
268. #2929	C₂×C₁₃	semidirect
327. C₂×#137	C₂²×C₁₃	semidirect
329. C₂×#135	C₂²×C₁₃	semidirect
336. C₂²×Q₁₆	C₂²×C₁₃	semidirect
350. #497	C₂²×C₁₃	semidirect
351. #495	C₂²×C₁₃	semidirect
352. #494	C₂²×C₁₃	semidirect
353. #470	C₂²×C₁₃	semidirect
355. #467	C₂²×C₁₃	semidirect
358. #464	C₂²×C₁₃	semidirect
359. #462	C₂²×C₁₃	semidirect
360. #452	C₂²×C₁₃	semidirect
362. #451	C₂²×C₁₃	semidirect
364. #441	C₂²×C₁₃	semidirect
365. C₄×Q₁₆	C₂²×C₁₃	semidirect
385. C₂²×C₁₃	#578	semidirect
425. C₂×Q₁₆	D₄×C₁₃	semidirect
588. C₁₃	#61053	direct (N × H)
651. C₂²	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
C₂³×C₁₃×Q₁₆	2
C₁₃×#3486	2
D₄×C₁₃×Q₁₆	2
C₁₃×#3285	2
C₁₃×#3270	2
C₁₃×#3156	2
C₁₃×#3059	2
C₁₃×#3050	2
C₁₃×#3044	2
C₁₃×#3011	2
C₁₃×#3004	2
C₁₃×#2950	2
C₁₃×#2929	2
#61053	13

Subgroups — C13×#61053 #15747392

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61053 #15747392