Subgroups — C₁₃×#60797 #15747136

Order 3328.

2062 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3455	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3449	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3225	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3224	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3223	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3222	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3221	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3220	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3150	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3147	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3135	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3131	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3035	C₂	1	4	yes	maximal, complemented
14	C₁₃×#3002	C₂	1	4	yes	maximal, complemented
15	C₂×C₁₃×#433	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×#41	C₂²	1	2	yes	—
17	C₂×C₁₃×#135	C₂²	1	4	yes	complemented
18	C₂×C₁₃×#135	C₂²	1	4	yes	complemented
19	C₁₃×#542	C₂²	1	4	yes	complemented
20	C₁₃×#541	C₂²	1	2	yes	complemented
21	C₁₃×#540	C₂²	1	2	yes	complemented
22	C₁₃×#539	—	2	2	no	—
23	C₁₃×#538	—	2	2	no	—
24	C₁₃×#537	—	2	2	no	—
25	C₁₃×#536	C₂²	1	2	yes	—
26	C₁₃×#536	C₂²	1	2	yes	—
27	C₁₃×#535	C₂²	1	2	yes	—
28	C₁₃×#535	C₂²	1	2	yes	—
29	C₁₃×#534	—	2	2	no	—
30	C₁₃×#533	C₂²	1	1	yes	characteristic, complemented
31	C₁₃×#532	C₂²	1	2	yes	—
32	C₁₃×#532	C₂²	1	1	yes	characteristic
33	C₁₃×#532	C₂²	1	1	yes	characteristic
34	C₁₃×#532	C₂²	1	1	yes	characteristic, complemented
35	C₁₃×#529	—	2	4	no	—
36	C₁₃×#525	—	2	4	no	—
37	C₁₃×#525	C₂²	1	2	yes	—
38	C₄×C₁₃×#41	C₂²	1	2	yes	complemented
39	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
40	C₁₃×#497	C₂²	1	2	yes	complemented
41	C₁₃×#497	C₂²	1	2	yes	complemented
42	C₁₃×#496	C₂²	1	2	yes	complemented
43	C₁₃×#496	C₂²	1	2	yes	complemented
44	C₁₃×#495	C₂²	1	4	yes	complemented
45	C₁₃×#494	C₂²	1	1	yes	characteristic, complemented
46	C₁₃×#493	C₂²	1	1	yes	characteristic, complemented
47	C₁₃×#492	C₂²	1	1	yes	characteristic, complemented
48	C₁₃×#492	C₂²	1	1	yes	characteristic, complemented
49	C₁₃×#491	C₂²	1	2	yes	complemented
50	C₁₃×#490	C₂²	1	2	yes	complemented
51	C₁₃×#489	C₂²	1	4	yes	complemented
52	C₁₃×#488	C₂²	1	2	yes	complemented
53	C₁₃×#488	C₂²	1	2	yes	complemented
54	C₁₃×#487	C₂²	1	2	yes	complemented
55	C₁₃×#486	C₂²	1	2	yes	complemented
56	C₁₃×#464	C₂²	1	4	yes	complemented
57	C₁₃×#464	C₂²	1	4	yes	complemented
58	C₁₃×#463	C₂²	1	4	yes	complemented
59	C₁₃×#463	C₂²	1	4	yes	complemented
60	C₁₃×#462	C₂²	1	4	yes	complemented
61	C₁₃×#461	C₂²	1	4	yes	complemented
62	C₁₃×#460	C₂²	1	4	yes	complemented
63	C₁₃×#459	C₂²	1	4	yes	complemented
64	C₁₃×#452	C₂²	1	4	yes	—
65	C₁₃×#452	C₂²	1	4	yes	—
66	C₁₃×#451	C₂²	1	4	yes	complemented
67	C₁₃×#450	C₂²	1	4	yes	complemented
68	C₁₃×#449	C₂²	1	4	yes	—
69	C₁₃×#449	C₂²	1	4	yes	—
70	C₁₃×#448	C₂²	1	4	yes	complemented
71	C₁₃×#447	C₂²	1	4	yes	complemented
72	C₁₃×#433	C₂²	1	2	yes	complemented
73	C₁₃×#433	C₂²	1	2	yes	complemented
74	C₁₃×#433	C₂²	1	4	yes	complemented
75	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	complemented
76	C₁₃×#416	C₂²	1	4	yes	complemented
77	C₁₃×#416	C₂²	1	4	yes	complemented
78	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
79	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic, complemented
80	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
81	C₂×C₁₃×#41	—	2	2	no	—
82	C₂×C₁₃×#41	—	2	2	no	—
83	C₂×C₁₃×#41	—	4	8	no	—
84	C₂×C₁₃×#41	C₂³	1	2	yes	—
85	C₂×C₁₃×#41	C₂³	1	2	yes	—
86	C₂×C₁₃×#41	C₂³	1	2	yes	—
87	C₂×C₁₃×#41	C₂³	1	2	yes	—
88	C₂×C₁₃×#41	C₂³	1	2	yes	—
89	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
90	C₂²×D₄×C₁₃	—	2	2	no	—
91	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
92	C₂³×C₄×C₁₃	—	2	2	no	—
93	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
94	C₁₃×#135	—	4	8	no	—
95	C₁₃×#135	—	4	8	no	—
96	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
97	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
98	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
99	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
100	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
101	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
102	C₂×C₁₃×D₈	C₂³	1	4	yes	—
103	C₂×C₁₃×D₈	C₂³	1	4	yes	—
104	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
105	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
106	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
107	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
108	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
109	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
110	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
111	C₁₃×#127	C₂³	1	2	yes	—
112	C₁₃×#127	C₂³	1	1	yes	characteristic
113	C₁₃×#127	C₂³	1	1	yes	characteristic
114	C₁₃×#127	C₂³	1	1	yes	characteristic
115	C₁₃×#126	—	2	4	no	—
116	C₁₃×#126	—	2	4	no	—
117	C₁₃×#125	—	2	4	no	—
118	C₁₃×#125	C₂³	1	2	yes	—
119	C₁₃×#124	—	2	4	no	—
120	C₁₃×#124	C₂³	1	2	yes	—
121	C₁₃×#124	C₂³	1	2	yes	—
122	C₁₃×#124	C₂³	1	2	yes	—
123	C₁₃×#124	C₂³	1	2	yes	—
124	C₁₃×#124	C₂³	1	2	yes	—
125	C₁₃×#123	—	2	2	no	—
126	C₁₃×#123	—	2	4	no	—
127	C₁₃×#123	—	2	4	no	—
128	C₁₃×#123	—	2	4	no	—
129	C₁₃×#123	—	2	4	no	—
130	C₁₃×C₂²⋊Q₈	—	2	2	no	—
131	C₁₃×C₂²⋊Q₈	—	2	4	no	—
132	C₁₃×C₂²⋊Q₈	—	2	4	no	—
133	C₁₃×C₂²⋊Q₈	—	2	4	no	—
134	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
135	C₁₃×#121	—	2	4	no	—
136	C₁₃×#121	—	2	2	no	—
137	C₁₃×#121	—	2	2	no	—
138	C₁₃×#121	—	2	2	no	—
139	C₁₃×#121	—	2	4	no	—
140	C₁₃×#121	—	2	4	no	—
141	C₁₃×#121	—	2	4	no	—
142	C₁₃×#121	C₂³	1	4	yes	—
143	C₁₃×#120	—	2	2	no	—
144	C₁₃×#120	—	2	4	no	—
145	C₁₃×#120	—	2	4	no	—
146	C₄×Q₈×C₁₃	—	2	2	no	—
147	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
148	C₄×D₄×C₁₃	—	2	4	no	—
149	C₄×D₄×C₁₃	—	2	4	no	—
150	C₄×D₄×C₁₃	—	2	4	no	—
151	C₄×D₄×C₁₃	—	2	2	no	—
152	C₄×D₄×C₁₃	—	2	2	no	—
153	C₄×D₄×C₁₃	—	2	2	no	—
154	C₄×D₄×C₁₃	C₂³	1	4	yes	—
155	C₁₃×#117	—	2	2	no	—
156	C₁₃×#117	D₄	1	4	yes	—
157	C₁₃×#117	C₂³	1	2	yes	—
158	C₁₃×#117	C₂³	1	2	yes	—
159	C₁₃×#117	C₂³	1	2	yes	—
160	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
161	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
162	C₂×C₄²×C₁₃	—	2	2	no	—
163	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
164	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
165	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
166	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
167	C₁₃×#103	C₂³	1	4	yes	—
168	C₁₃×#103	C₂³	1	4	yes	—
169	C₁₃×#103	C₂³	1	4	yes	—
170	C₁₃×#103	C₂³	1	4	yes	—
171	C₁₃×#102	C₂³	1	4	yes	—
172	C₁₃×#102	C₂³	1	4	yes	—
173	C₁₃×#102	C₂³	1	4	yes	—
174	C₁₃×#102	C₂³	1	4	yes	—
175	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
176	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
177	C₁₃×#97	C₂³	1	2	yes	—
178	C₁₃×#97	C₂³	1	2	yes	—
179	C₄×C₈×C₁₃	C₂³	1	2	yes	—
180	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
181	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
182	#60797	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
183	C₂⁴×C₁₃	—	2	2	no	—
184	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
185	C₁₃×#41	—	2	8	no	—
186	C₁₃×#41	—	2	8	no	—
187	C₁₃×#41	—	2	8	no	—
188	C₁₃×#41	—	4	4	no	—
189	C₁₃×#41	—	4	4	no	—
190	C₁₃×#41	—	4	8	no	—
191	C₁₃×#41	—	4	8	no	—
192	C₂×Q₈×C₁₃	—	2	2	no	—
193	C₂×Q₈×C₁₃	—	2	2	no	—
194	C₂×Q₈×C₁₃	—	4	4	no	—
195	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
196	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
197	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
198	C₂×D₄×C₁₃	—	2	2	no	—
199	C₂×D₄×C₁₃	—	2	2	no	—
200	C₂×D₄×C₁₃	—	2	2	no	—
201	C₂×D₄×C₁₃	—	2	2	no	—
202	C₂×D₄×C₁₃	—	2	2	no	—
203	C₂×D₄×C₁₃	—	2	4	no	—
204	C₂×D₄×C₁₃	—	2	2	no	—
205	C₂×D₄×C₁₃	—	2	4	no	—
206	C₂×D₄×C₁₃	—	2	2	no	—
207	C₂×D₄×C₁₃	—	2	2	no	—
208	C₂×D₄×C₁₃	—	2	2	no	—
209	C₂×D₄×C₁₃	—	4	4	no	—
210	C₂×D₄×C₁₃	—	4	8	no	—
211	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
212	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
213	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
214	C₂²×C₄×C₁₃	—	2	4	no	—
215	C₂²×C₄×C₁₃	—	2	2	no	—
216	C₂²×C₄×C₁₃	—	2	2	no	—
217	C₂²×C₄×C₁₃	—	2	2	no	—
218	C₂²×C₄×C₁₃	—	2	2	no	—
219	C₂²×C₄×C₁₃	—	2	2	no	—
220	C₂²×C₄×C₁₃	—	2	2	no	—
221	C₂²×C₄×C₁₃	—	2	4	no	—
222	C₂²×C₄×C₁₃	—	4	8	no	—
223	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
224	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
225	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
226	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
227	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
228	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
229	C₁₃×Q₁₆	—	4	4	no	—
230	C₁₃×Q₁₆	—	4	4	no	—
231	C₁₃×SD₁₆	—	4	4	no	—
232	C₁₃×SD₁₆	—	4	4	no	—
233	C₁₃×SD₁₆	—	4	4	no	—
234	C₁₃×SD₁₆	—	4	4	no	—
235	C₁₃×D₈	—	4	4	no	—
236	C₁₃×D₈	—	4	4	no	—
237	C₂×C₈×C₁₃	—	2	4	no	—
238	C₂×C₈×C₁₃	—	2	4	no	—
239	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
240	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
241	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
242	C₁₃×C₄⋊C₄	—	2	4	no	—
243	C₁₃×C₄⋊C₄	—	2	4	no	—
244	C₁₃×C₄⋊C₄	—	2	2	no	—
245	C₁₃×C₄⋊C₄	—	2	2	no	—
246	C₁₃×C₄⋊C₄	—	2	2	no	—
247	C₁₃×C₄⋊C₄	—	2	4	no	—
248	C₁₃×C₄⋊C₄	—	2	4	no	—
249	C₁₃×C₄⋊C₄	—	2	2	no	—
250	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
251	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
252	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
253	C₁₃×C₂²⋊C₄	—	2	2	no	—
254	C₁₃×C₂²⋊C₄	—	2	4	no	—
255	C₁₃×C₂²⋊C₄	—	2	4	no	—
256	C₁₃×C₂²⋊C₄	—	2	4	no	—
257	C₁₃×C₂²⋊C₄	—	2	4	no	—
258	C₁₃×C₂²⋊C₄	—	2	4	no	—
259	C₁₃×C₂²⋊C₄	—	2	4	no	—
260	C₁₃×C₂²⋊C₄	—	2	4	no	—
261	C₁₃×C₂²⋊C₄	—	2	4	no	—
262	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
263	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
264	C₄²×C₁₃	—	2	4	no	—
265	C₄²×C₁₃	—	2	2	no	—
266	C₄²×C₁₃	C₂×D₄	1	2	yes	—
267	C₄²×C₁₃	C₂×D₄	1	2	yes	—
268	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
269	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
270	C₄²×C₁₃	C₂⁴	1	2	yes	—
271	#3455	C₂×C₁₃	1	1	yes	characteristic, complemented
272	#3449	C₂×C₁₃	1	1	yes	characteristic, complemented
273	#3225	C₂×C₁₃	1	4	yes	complemented
274	#3224	C₂×C₁₃	1	4	yes	complemented
275	#3223	C₂×C₁₃	1	2	yes	complemented
276	#3222	C₂×C₁₃	1	2	yes	complemented
277	#3221	C₂×C₁₃	1	2	yes	complemented
278	#3220	C₂×C₁₃	1	2	yes	complemented
279	#3150	C₂×C₁₃	1	1	yes	characteristic, complemented
280	#3147	C₂×C₁₃	1	1	yes	characteristic, complemented
281	#3135	C₂×C₁₃	1	1	yes	characteristic, complemented
282	#3131	C₂×C₁₃	1	1	yes	characteristic, complemented
283	#3035	C₂×C₁₃	1	4	yes	complemented
284	#3002	C₂×C₁₃	1	4	yes	complemented
285	C₂×#433	C₂×C₁₃	1	1	yes	characteristic, complemented
286	C₂³×C₁₃	—	2	2	no	—
287	C₂³×C₁₃	—	2	2	no	—
288	C₂³×C₁₃	—	2	2	no	—
289	C₂³×C₁₃	—	2	2	no	—
290	C₂³×C₁₃	—	4	2	no	—
291	C₂³×C₁₃	—	4	4	no	—
292	C₂³×C₁₃	—	8	4	no	—
293	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
294	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
295	Q₈×C₁₃	—	2	4	no	—
296	Q₈×C₁₃	—	2	4	no	—
297	Q₈×C₁₃	—	2	4	no	—
298	Q₈×C₁₃	—	4	4	no	—
299	Q₈×C₁₃	—	8	2	no	—
300	D₄×C₁₃	—	2	4	no	—
301	D₄×C₁₃	—	2	4	no	—
302	D₄×C₁₃	—	2	4	no	—
303	D₄×C₁₃	—	4	4	no	—
304	D₄×C₁₃	—	4	4	no	—
305	D₄×C₁₃	—	4	4	no	—
306	D₄×C₁₃	—	4	4	no	—
307	D₄×C₁₃	—	4	4	no	—
308	D₄×C₁₃	—	4	4	no	—
309	D₄×C₁₃	—	8	4	no	—
310	D₄×C₁₃	—	8	2	no	—
311	D₄×C₁₃	—	8	2	no	—
312	D₄×C₁₃	—	8	2	no	—
313	D₄×C₁₃	—	8	4	no	—
314	C₂×C₄×C₁₃	—	2	2	no	—
315	C₂×C₄×C₁₃	—	2	4	no	—
316	C₂×C₄×C₁₃	—	2	4	no	—
317	C₂×C₄×C₁₃	—	2	2	no	—
318	C₂×C₄×C₁₃	—	2	4	no	—
319	C₂×C₄×C₁₃	—	2	2	no	—
320	C₂×C₄×C₁₃	—	2	2	no	—
321	C₂×C₄×C₁₃	—	4	2	no	—
322	C₂×C₄×C₁₃	—	4	2	no	—
323	C₂×C₄×C₁₃	—	4	4	no	—
324	C₂×C₄×C₁₃	—	4	4	no	—
325	C₂×C₄×C₁₃	—	4	4	no	—
326	C₂×C₄×C₁₃	—	4	4	no	—
327	C₂×C₄×C₁₃	—	4	4	no	—
328	C₂×C₄×C₁₃	—	4	4	no	—
329	C₂×C₄×C₁₃	—	8	4	no	—
330	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
331	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
332	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
333	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
334	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
335	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
336	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
337	C₈×C₁₃	—	2	2	no	—
338	C₈×C₁₃	—	2	4	no	—
339	C₈×C₁₃	—	2	2	no	—
340	C₂²×#41	C₂²×C₁₃	1	2	yes	—
341	C₂×#135	C₂²×C₁₃	1	4	yes	complemented
342	C₂×#135	C₂²×C₁₃	1	4	yes	complemented
343	#542	C₂²×C₁₃	1	4	yes	complemented
344	#541	C₂²×C₁₃	1	2	yes	complemented
345	#540	C₂²×C₁₃	1	2	yes	complemented
346	#539	—	2	2	no	—
347	#538	—	2	2	no	—
348	#537	—	2	2	no	—
349	#536	C₂²×C₁₃	1	2	yes	—
350	#536	C₂²×C₁₃	1	2	yes	—
351	#535	C₂²×C₁₃	1	2	yes	—
352	#535	C₂²×C₁₃	1	2	yes	—
353	#534	—	2	2	no	—
354	#533	C₂²×C₁₃	1	1	yes	characteristic, complemented
355	#532	C₂²×C₁₃	1	1	yes	characteristic
356	#532	C₂²×C₁₃	1	1	yes	characteristic
357	#532	C₂²×C₁₃	1	2	yes	—
358	#532	C₂²×C₁₃	1	1	yes	characteristic, complemented
359	#529	—	2	4	no	—
360	#525	—	2	4	no	—
361	#525	C₂²×C₁₃	1	2	yes	—
362	C₄×#41	C₂²×C₁₃	1	2	yes	complemented
363	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
364	#497	C₂²×C₁₃	1	2	yes	complemented
365	#497	C₂²×C₁₃	1	2	yes	complemented
366	#496	C₂²×C₁₃	1	2	yes	complemented
367	#496	C₂²×C₁₃	1	2	yes	complemented
368	#495	C₂²×C₁₃	1	4	yes	complemented
369	#494	C₂²×C₁₃	1	1	yes	characteristic, complemented
370	#493	C₂²×C₁₃	1	1	yes	characteristic, complemented
371	#492	C₂²×C₁₃	1	1	yes	characteristic, complemented
372	#492	C₂²×C₁₃	1	1	yes	characteristic, complemented
373	#491	C₂²×C₁₃	1	2	yes	complemented
374	#490	C₂²×C₁₃	1	2	yes	complemented
375	#489	C₂²×C₁₃	1	4	yes	complemented
376	#488	C₂²×C₁₃	1	2	yes	complemented
377	#488	C₂²×C₁₃	1	2	yes	complemented
378	#487	C₂²×C₁₃	1	2	yes	complemented
379	#486	C₂²×C₁₃	1	2	yes	complemented
380	#464	C₂²×C₁₃	1	4	yes	complemented
381	#464	C₂²×C₁₃	1	4	yes	complemented
382	#463	C₂²×C₁₃	1	4	yes	complemented
383	#463	C₂²×C₁₃	1	4	yes	complemented
384	#462	C₂²×C₁₃	1	4	yes	complemented
385	#461	C₂²×C₁₃	1	4	yes	complemented
386	#460	C₂²×C₁₃	1	4	yes	complemented
387	#459	C₂²×C₁₃	1	4	yes	complemented
388	#452	C₂²×C₁₃	1	4	yes	—
389	#452	C₂²×C₁₃	1	4	yes	—
390	#451	C₂²×C₁₃	1	4	yes	complemented
391	#450	C₂²×C₁₃	1	4	yes	complemented
392	#449	C₂²×C₁₃	1	4	yes	—
393	#449	C₂²×C₁₃	1	4	yes	—
394	#448	C₂²×C₁₃	1	4	yes	complemented
395	#447	C₂²×C₁₃	1	4	yes	complemented
396	#433	C₂²×C₁₃	1	2	yes	complemented
397	#433	C₂²×C₁₃	1	2	yes	complemented
398	#433	C₂²×C₁₃	1	4	yes	complemented
399	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	complemented
400	#416	C₂²×C₁₃	1	4	yes	complemented
401	#416	C₂²×C₁₃	1	4	yes	complemented
402	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
403	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic, complemented
404	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
405	C₂²×C₁₃	—	2	2	no	—
406	C₂²×C₁₃	—	2	4	no	—
407	C₂²×C₁₃	—	2	2	no	—
408	C₂²×C₁₃	—	4	4	no	—
409	C₂²×C₁₃	—	4	4	no	—
410	C₂²×C₁₃	—	4	4	no	—
411	C₂²×C₁₃	—	4	2	no	—
412	C₂²×C₁₃	—	4	2	no	—
413	C₂²×C₁₃	—	4	2	no	—
414	C₂²×C₁₃	—	8	2	no	—
415	C₂²×C₁₃	—	8	8	no	—
416	C₂²×C₁₃	#535	1	2	yes	—
417	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
418	C₄×C₁₃	—	2	4	no	—
419	C₄×C₁₃	—	2	2	no	—
420	C₄×C₁₃	—	2	2	no	—
421	C₄×C₁₃	—	2	2	no	—
422	C₄×C₁₃	—	4	4	no	—
423	C₄×C₁₃	—	4	2	no	—
424	C₄×C₁₃	—	4	2	no	—
425	C₄×C₁₃	—	4	2	no	—
426	C₄×C₁₃	#535	1	2	yes	—
427	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
428	C₂×#41	—	2	2	no	—
429	C₂×#41	—	2	2	no	—
430	C₂×#41	—	4	8	no	—
431	C₂×#41	C₂³×C₁₃	1	2	yes	—
432	C₂×#41	C₂³×C₁₃	1	2	yes	—
433	C₂×#41	C₂³×C₁₃	1	2	yes	—
434	C₂×#41	C₂³×C₁₃	1	2	yes	—
435	C₂×#41	C₂³×C₁₃	1	2	yes	—
436	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
437	C₂²×D₄	—	2	2	no	—
438	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
439	C₂³×C₄	—	2	2	no	—
440	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
441	#135	—	4	8	no	—
442	#135	—	4	8	no	—
443	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
444	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
445	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
446	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
447	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
448	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
449	C₂×D₈	C₂³×C₁₃	1	4	yes	—
450	C₂×D₈	C₂³×C₁₃	1	4	yes	—
451	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
452	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
453	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
454	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
455	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
456	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
457	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
458	#127	C₂³×C₁₃	1	2	yes	—
459	#127	C₂³×C₁₃	1	1	yes	characteristic
460	#127	C₂³×C₁₃	1	1	yes	characteristic
461	#127	C₂³×C₁₃	1	1	yes	characteristic
462	#126	—	2	4	no	—
463	#126	—	2	4	no	—
464	#125	—	2	4	no	—
465	#125	C₂³×C₁₃	1	2	yes	—
466	#124	—	2	4	no	—
467	#124	C₂³×C₁₃	1	2	yes	—
468	#124	C₂³×C₁₃	1	2	yes	—
469	#124	C₂³×C₁₃	1	2	yes	—
470	#124	C₂³×C₁₃	1	2	yes	—
471	#124	C₂³×C₁₃	1	2	yes	—
472	#123	—	2	2	no	—
473	#123	—	2	4	no	—
474	#123	—	2	4	no	—
475	#123	—	2	4	no	—
476	#123	—	2	4	no	—
477	C₂²⋊Q₈	—	2	2	no	—
478	C₂²⋊Q₈	—	2	4	no	—
479	C₂²⋊Q₈	—	2	4	no	—
480	C₂²⋊Q₈	—	2	4	no	—
481	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
482	#121	—	2	4	no	—
483	#121	—	2	2	no	—
484	#121	—	2	2	no	—
485	#121	—	2	2	no	—
486	#121	—	2	4	no	—
487	#121	—	2	4	no	—
488	#121	—	2	4	no	—
489	#121	C₂³×C₁₃	1	4	yes	—
490	#120	—	2	2	no	—
491	#120	—	2	4	no	—
492	#120	—	2	4	no	—
493	C₄×Q₈	—	2	2	no	—
494	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
495	C₄×D₄	—	2	4	no	—
496	C₄×D₄	—	2	4	no	—
497	C₄×D₄	—	2	4	no	—
498	C₄×D₄	—	2	2	no	—
499	C₄×D₄	—	2	2	no	—
500	C₄×D₄	—	2	2	no	—
501	C₄×D₄	C₂³×C₁₃	1	4	yes	—
502	#117	—	2	2	no	—
503	#117	D₄×C₁₃	1	4	yes	—
504	#117	C₂³×C₁₃	1	2	yes	—
505	#117	C₂³×C₁₃	1	2	yes	—
506	#117	C₂³×C₁₃	1	2	yes	—
507	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
508	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
509	C₂×C₄²	—	2	2	no	—
510	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
511	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
512	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
513	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
514	#103	C₂³×C₁₃	1	4	yes	—
515	#103	C₂³×C₁₃	1	4	yes	—
516	#103	C₂³×C₁₃	1	4	yes	—
517	#103	C₂³×C₁₃	1	4	yes	—
518	#102	C₂³×C₁₃	1	4	yes	—
519	#102	C₂³×C₁₃	1	4	yes	—
520	#102	C₂³×C₁₃	1	4	yes	—
521	#102	C₂³×C₁₃	1	4	yes	—
522	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
523	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
524	#97	C₂³×C₁₃	1	2	yes	—
525	#97	C₂³×C₁₃	1	2	yes	—
526	C₄×C₈	C₂³×C₁₃	1	2	yes	—
527	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
528	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
529	C₂×C₁₃	—	2	2	no	—
530	C₂×C₁₃	—	4	2	no	—
531	C₂×C₁₃	—	8	2	no	—
532	C₂×C₁₃	—	8	2	no	—
533	C₂×C₁₃	—	8	2	no	—
534	C₂×C₁₃	C₂×#535	1	1	yes	characteristic
535	C₂×C₁₃	#3584	1	2	yes	—
536	C₂⁴	—	2	2	no	—
537	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
538	#41	—	2	8	no	—
539	#41	—	2	8	no	—
540	#41	—	2	8	no	—
541	#41	—	4	4	no	—
542	#41	—	4	4	no	—
543	#41	—	4	8	no	—
544	#41	—	4	8	no	—
545	C₂×Q₈	—	2	2	no	—
546	C₂×Q₈	—	2	2	no	—
547	C₂×Q₈	—	4	4	no	—
548	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
549	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
550	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
551	C₂×D₄	—	2	2	no	—
552	C₂×D₄	—	2	2	no	—
553	C₂×D₄	—	2	2	no	—
554	C₂×D₄	—	2	2	no	—
555	C₂×D₄	—	2	2	no	—
556	C₂×D₄	—	2	4	no	—
557	C₂×D₄	—	2	2	no	—
558	C₂×D₄	—	2	4	no	—
559	C₂×D₄	—	2	2	no	—
560	C₂×D₄	—	2	2	no	—
561	C₂×D₄	—	2	2	no	—
562	C₂×D₄	—	4	4	no	—
563	C₂×D₄	—	4	8	no	—
564	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
565	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
566	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
567	C₂²×C₄	—	2	4	no	—
568	C₂²×C₄	—	2	2	no	—
569	C₂²×C₄	—	2	2	no	—
570	C₂²×C₄	—	2	2	no	—
571	C₂²×C₄	—	2	2	no	—
572	C₂²×C₄	—	2	2	no	—
573	C₂²×C₄	—	2	2	no	—
574	C₂²×C₄	—	2	4	no	—
575	C₂²×C₄	—	4	8	no	—
576	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
577	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
578	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
579	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
580	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
581	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
582	Q₁₆	—	4	4	no	—
583	Q₁₆	—	4	4	no	—
584	SD₁₆	—	4	4	no	—
585	SD₁₆	—	4	4	no	—
586	SD₁₆	—	4	4	no	—
587	SD₁₆	—	4	4	no	—
588	D₈	—	4	4	no	—
589	D₈	—	4	4	no	—
590	C₂×C₈	—	2	4	no	—
591	C₂×C₈	—	2	4	no	—
592	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
593	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
594	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
595	C₄⋊C₄	—	2	4	no	—
596	C₄⋊C₄	—	2	4	no	—
597	C₄⋊C₄	—	2	2	no	—
598	C₄⋊C₄	—	2	2	no	—
599	C₄⋊C₄	—	2	2	no	—
600	C₄⋊C₄	—	2	4	no	—
601	C₄⋊C₄	—	2	4	no	—
602	C₄⋊C₄	—	2	2	no	—
603	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
604	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
605	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
606	C₂²⋊C₄	—	2	2	no	—
607	C₂²⋊C₄	—	2	4	no	—
608	C₂²⋊C₄	—	2	4	no	—
609	C₂²⋊C₄	—	2	4	no	—
610	C₂²⋊C₄	—	2	4	no	—
611	C₂²⋊C₄	—	2	4	no	—
612	C₂²⋊C₄	—	2	4	no	—
613	C₂²⋊C₄	—	2	4	no	—
614	C₂²⋊C₄	—	2	4	no	—
615	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
616	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
617	C₄²	—	2	2	no	—
618	C₄²	—	2	4	no	—
619	C₄²	C₂×D₄×C₁₃	1	2	yes	—
620	C₄²	C₂×D₄×C₁₃	1	2	yes	—
621	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
622	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
623	C₄²	C₂⁴×C₁₃	1	2	yes	—
624	C₁₃	#60797	1	1	yes	characteristic, direct product factor, Sylow
625	C₂³	—	2	2	no	—
626	C₂³	—	2	2	no	—
627	C₂³	—	2	2	no	—
628	C₂³	—	2	2	no	—
629	C₂³	—	4	2	no	—
630	C₂³	—	4	4	no	—
631	C₂³	—	8	4	no	—
632	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
633	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
634	Q₈	—	2	4	no	—
635	Q₈	—	2	4	no	—
636	Q₈	—	2	4	no	—
637	Q₈	—	4	4	no	—
638	Q₈	—	8	2	no	—
639	D₄	—	2	4	no	—
640	D₄	—	2	4	no	—
641	D₄	—	2	4	no	—
642	D₄	—	4	4	no	—
643	D₄	—	4	4	no	—
644	D₄	—	4	4	no	—
645	D₄	—	4	4	no	—
646	D₄	—	4	4	no	—
647	D₄	—	4	4	no	—
648	D₄	—	8	4	no	—
649	D₄	—	8	2	no	—
650	D₄	—	8	2	no	—
651	D₄	—	8	2	no	—
652	D₄	—	8	4	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	2	4	no	—
655	C₂×C₄	—	2	4	no	—
656	C₂×C₄	—	2	2	no	—
657	C₂×C₄	—	2	4	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	2	2	no	—
660	C₂×C₄	—	4	2	no	—
661	C₂×C₄	—	4	2	no	—
662	C₂×C₄	—	4	4	no	—
663	C₂×C₄	—	4	4	no	—
664	C₂×C₄	—	4	4	no	—
665	C₂×C₄	—	4	4	no	—
666	C₂×C₄	—	4	4	no	—
667	C₂×C₄	—	4	4	no	—
668	C₂×C₄	—	8	4	no	—
669	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
670	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
671	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
672	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
673	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
674	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
675	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
676	C₈	—	2	2	no	—
677	C₈	—	2	4	no	—
678	C₈	—	2	2	no	—
679	C₂²	—	2	2	no	—
680	C₂²	—	2	4	no	—
681	C₂²	—	2	2	no	—
682	C₂²	—	4	4	no	—
683	C₂²	—	4	4	no	—
684	C₂²	—	4	4	no	—
685	C₂²	—	4	2	no	—
686	C₂²	—	4	2	no	—
687	C₂²	—	4	2	no	—
688	C₂²	—	8	2	no	—
689	C₂²	—	8	8	no	—
690	C₂²	C₁₃×#535	1	2	yes	—
691	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
692	C₄	—	2	4	no	—
693	C₄	—	2	2	no	—
694	C₄	—	2	2	no	—
695	C₄	—	2	2	no	—
696	C₄	—	4	4	no	—
697	C₄	—	4	2	no	—
698	C₄	—	4	2	no	—
699	C₄	—	4	2	no	—
700	C₄	C₁₃×#535	1	2	yes	—
701	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
702	C₂	—	2	2	no	—
703	C₂	—	4	2	no	—
704	C₂	—	8	2	no	—
705	C₂	—	8	2	no	—
706	C₂	—	8	2	no	—
707	C₂	C₂×C₁₃×#535	1	1	yes	characteristic
708	C₂	C₁₃×#3584	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
socle	C₂²×C₁₃	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂×C₁₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3455	C₂	semidirect
2. C₁₃×#3449	C₂	semidirect
3. C₁₃×#3225	C₂	semidirect
4. C₁₃×#3224	C₂	semidirect
5. C₁₃×#3223	C₂	semidirect
6. C₁₃×#3222	C₂	semidirect
7. C₁₃×#3221	C₂	semidirect
8. C₁₃×#3220	C₂	semidirect
9. C₁₃×#3150	C₂	semidirect
10. C₁₃×#3147	C₂	semidirect
11. C₁₃×#3135	C₂	semidirect
12. C₁₃×#3131	C₂	semidirect
13. C₁₃×#3035	C₂	semidirect
14. C₁₃×#3002	C₂	semidirect
15. C₂×C₁₃×#433	C₂	semidirect
17. C₂×C₁₃×#135	C₂²	semidirect
18. C₂×C₁₃×#135	C₂²	semidirect
19. C₁₃×#542	C₂²	semidirect
20. C₁₃×#541	C₂²	semidirect
21. C₁₃×#540	C₂²	semidirect
30. C₁₃×#533	C₂²	semidirect
34. C₁₃×#532	C₂²	semidirect
38. C₄×C₁₃×#41	C₂²	semidirect
40. C₁₃×#497	C₂²	semidirect
41. C₁₃×#497	C₂²	semidirect
42. C₁₃×#496	C₂²	semidirect
43. C₁₃×#496	C₂²	semidirect
44. C₁₃×#495	C₂²	semidirect
45. C₁₃×#494	C₂²	semidirect
46. C₁₃×#493	C₂²	semidirect
47. C₁₃×#492	C₂²	semidirect
48. C₁₃×#492	C₂²	semidirect
49. C₁₃×#491	C₂²	semidirect
50. C₁₃×#490	C₂²	semidirect
51. C₁₃×#489	C₂²	semidirect
52. C₁₃×#488	C₂²	semidirect
53. C₁₃×#488	C₂²	semidirect
54. C₁₃×#487	C₂²	semidirect
55. C₁₃×#486	C₂²	semidirect
56. C₁₃×#464	C₂²	semidirect
57. C₁₃×#464	C₂²	semidirect
58. C₁₃×#463	C₂²	semidirect
59. C₁₃×#463	C₂²	semidirect
60. C₁₃×#462	C₂²	semidirect
61. C₁₃×#461	C₂²	semidirect
62. C₁₃×#460	C₂²	semidirect
63. C₁₃×#459	C₂²	semidirect
66. C₁₃×#451	C₂²	semidirect
67. C₁₃×#450	C₂²	semidirect
70. C₁₃×#448	C₂²	semidirect
71. C₁₃×#447	C₂²	semidirect
72. C₁₃×#433	C₂²	semidirect
73. C₁₃×#433	C₂²	semidirect
74. C₁₃×#433	C₂²	semidirect
75. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
76. C₁₃×#416	C₂²	semidirect
77. C₁₃×#416	C₂²	semidirect
79. C₂×C₁₃×#97	C₂²	semidirect
80. C₂×C₄×C₈×C₁₃	C₂²	semidirect
182. #60797	C₁₃	direct (N × H)
271. #3455	C₂×C₁₃	semidirect
272. #3449	C₂×C₁₃	semidirect
273. #3225	C₂×C₁₃	semidirect
274. #3224	C₂×C₁₃	semidirect
275. #3223	C₂×C₁₃	semidirect
276. #3222	C₂×C₁₃	semidirect
277. #3221	C₂×C₁₃	semidirect
278. #3220	C₂×C₁₃	semidirect
279. #3150	C₂×C₁₃	semidirect
280. #3147	C₂×C₁₃	semidirect
281. #3135	C₂×C₁₃	semidirect
282. #3131	C₂×C₁₃	semidirect
283. #3035	C₂×C₁₃	semidirect
284. #3002	C₂×C₁₃	semidirect
285. C₂×#433	C₂×C₁₃	semidirect
341. C₂×#135	C₂²×C₁₃	semidirect
342. C₂×#135	C₂²×C₁₃	semidirect
343. #542	C₂²×C₁₃	semidirect
344. #541	C₂²×C₁₃	semidirect
345. #540	C₂²×C₁₃	semidirect
354. #533	C₂²×C₁₃	semidirect
358. #532	C₂²×C₁₃	semidirect
362. C₄×#41	C₂²×C₁₃	semidirect
364. #497	C₂²×C₁₃	semidirect
365. #497	C₂²×C₁₃	semidirect
366. #496	C₂²×C₁₃	semidirect
367. #496	C₂²×C₁₃	semidirect
368. #495	C₂²×C₁₃	semidirect
369. #494	C₂²×C₁₃	semidirect
370. #493	C₂²×C₁₃	semidirect
371. #492	C₂²×C₁₃	semidirect
372. #492	C₂²×C₁₃	semidirect
373. #491	C₂²×C₁₃	semidirect
374. #490	C₂²×C₁₃	semidirect
375. #489	C₂²×C₁₃	semidirect
376. #488	C₂²×C₁₃	semidirect
377. #488	C₂²×C₁₃	semidirect
378. #487	C₂²×C₁₃	semidirect
379. #486	C₂²×C₁₃	semidirect
380. #464	C₂²×C₁₃	semidirect
381. #464	C₂²×C₁₃	semidirect
382. #463	C₂²×C₁₃	semidirect
383. #463	C₂²×C₁₃	semidirect
384. #462	C₂²×C₁₃	semidirect
385. #461	C₂²×C₁₃	semidirect
386. #460	C₂²×C₁₃	semidirect
387. #459	C₂²×C₁₃	semidirect
390. #451	C₂²×C₁₃	semidirect
391. #450	C₂²×C₁₃	semidirect
394. #448	C₂²×C₁₃	semidirect
395. #447	C₂²×C₁₃	semidirect
396. #433	C₂²×C₁₃	semidirect
397. #433	C₂²×C₁₃	semidirect
398. #433	C₂²×C₁₃	semidirect
399. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
400. #416	C₂²×C₁₃	semidirect
401. #416	C₂²×C₁₃	semidirect
403. C₂×#97	C₂²×C₁₃	semidirect
404. C₂×C₄×C₈	C₂²×C₁₃	semidirect
624. C₁₃	#60797	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×#3455	2
C₁₃×#3449	2
C₁₃×#3225	2
C₁₃×#3224	2
C₁₃×#3223	2
C₁₃×#3222	2
C₁₃×#3221	2
C₁₃×#3220	2
C₁₃×#3150	2
C₁₃×#3147	2
C₁₃×#3135	2
C₁₃×#3131	2
C₁₃×#3035	2
C₁₃×#3002	2
C₂×C₁₃×#433	2
#60797	13

Subgroups — C13×#60797 #15747136

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60797 #15747136