Subgroups — C₁₃×#61649 #15747988

Order 3328.

2042 conjugacy classes of subgroups.

The subgroup lattice has 730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3538	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3485	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3323	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3315	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3276	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3266	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3223	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3202	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3196	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3123	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3009	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3007	C₂	1	2	yes	maximal, complemented
13	C₁₃×#2978	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
15	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×#137	C₂²	1	4	yes	complemented
17	C₂×C₁₃×#137	C₂²	1	2	yes	complemented
18	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
19	C₁₃×#563	—	2	2	no	—
20	C₁₃×#552	C₂²	1	4	yes	complemented
21	C₁₃×#551	—	2	2	no	—
22	D₄×Q₈×C₁₃	C₂²	1	4	yes	complemented
23	C₁₃×#547	—	2	2	no	—
24	C₁₃×#547	C₂²	1	4	yes	—
25	C₁₃×#546	—	2	2	no	—
26	C₁₃×#546	C₂²	1	4	yes	—
27	C₁₃×#544	—	2	2	no	—
28	C₁₃×#541	C₂²	1	2	yes	complemented
29	C₁₃×#539	—	2	2	no	—
30	C₁₃×#536	C₂²	1	1	yes	characteristic
31	C₁₃×#536	C₂²	1	2	yes	—
32	C₁₃×#536	C₂²	1	1	yes	characteristic
33	C₁₃×#534	—	2	2	no	—
34	C₁₃×#525	C₂²	1	1	yes	characteristic
35	C₁₃×#525	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×#123	—	2	2	no	—
37	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
38	C₁₃×#518	C₂²	1	1	yes	characteristic
39	C₁₃×#497	C₂²	1	2	yes	complemented
40	C₁₃×#494	C₂²	1	2	yes	complemented
41	C₁₃×#491	C₂²	1	2	yes	complemented
42	C₁₃×#488	C₂²	1	2	yes	complemented
43	C₁₃×#485	C₂²	1	4	yes	complemented
44	C₁₃×#485	C₂²	1	4	yes	complemented
45	C₁₃×#484	C₂²	1	2	yes	complemented
46	C₁₃×#481	C₂²	1	2	yes	complemented
47	C₁₃×#478	C₂²	1	4	yes	complemented
48	C₁₃×#470	C₂²	1	4	yes	complemented
49	C₁₃×#470	C₂²	1	4	yes	complemented
50	C₁₃×#468	C₂²	1	4	yes	complemented
51	C₁₃×#467	C₂²	1	4	yes	complemented
52	C₁₃×#464	C₂²	1	4	yes	complemented
53	C₁₃×#462	C₂²	1	4	yes	complemented
54	C₁₃×#461	C₂²	1	4	yes	complemented
55	C₁₃×#452	C₂²	1	4	yes	—
56	C₁₃×#452	C₂²	1	4	yes	complemented
57	C₁₃×#452	C₂²	1	4	yes	complemented
58	C₁₃×#452	C₂²	1	4	yes	complemented
59	C₁₃×#451	C₂²	1	4	yes	complemented
60	C₁₃×#451	C₂²	1	4	yes	complemented
61	C₁₃×#451	C₂²	1	2	yes	complemented
62	C₁₃×#450	C₂²	1	4	yes	—
63	C₁₃×#450	C₂²	1	4	yes	complemented
64	C₁₃×#448	C₂²	1	2	yes	complemented
65	C₁₃×#440	C₂²	1	4	yes	complemented
66	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
67	C₁₃×#436	C₂²	1	4	yes	complemented
68	C₁₃×#435	C₂²	1	4	yes	complemented
69	C₁₃×#433	C₂²	1	2	yes	complemented
70	C₁₃×#418	C₂²	1	2	yes	complemented
71	C₁₃×#417	C₂²	1	4	yes	complemented
72	C₁₃×#416	C₂²	1	2	yes	complemented
73	C₁₃×#408	C₂²	1	2	yes	—
74	C₁₃×#407	C₂²	1	2	yes	complemented
75	C₁₃×H(5,𝔽₂)	—	4	4	no	—
76	C₂×C₁₃×#41	—	2	1	no	—
77	C₂×C₁₃×#41	—	2	2	no	—
78	C₂×C₁₃×#41	—	4	4	no	—
79	C₂×C₁₃×#41	C₂³	1	2	yes	—
80	C₂×C₁₃×#41	C₂³	1	4	yes	—
81	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
82	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
83	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
84	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
85	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
86	C₂²×D₄×C₁₃	—	2	1	no	—
87	C₂²×D₄×C₁₃	—	2	2	no	—
88	C₂²×D₄×C₁₃	—	2	1	no	—
89	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
90	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
91	C₂³×C₄×C₁₃	—	2	1	no	—
92	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
93	C₁₃×#137	—	4	8	no	—
94	C₁₃×#137	—	4	4	no	—
95	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
96	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
97	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
98	C₂×C₁₃×SD₁₆	—	4	4	no	—
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×M₁₆	C₂³	1	4	yes	—
103	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
104	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
105	C₁₃×C₄⋊Q₈	—	2	2	no	—
106	C₁₃×C₄⋊Q₈	—	2	1	no	—
107	C₁₃×C₄⋊Q₈	—	2	4	no	—
108	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
109	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
110	C₁₃×#126	—	2	4	no	—
111	C₁₃×#126	—	2	4	no	—
112	C₁₃×#125	—	2	4	no	—
113	C₁₃×#125	—	2	4	no	—
114	C₁₃×#125	C₂³	1	2	yes	—
115	C₁₃×#124	—	2	1	no	—
116	C₁₃×#124	—	2	2	no	—
117	C₁₃×#124	C₂³	1	2	yes	—
118	C₁₃×#123	—	2	2	no	—
119	C₁₃×#123	—	2	2	no	—
120	C₁₃×#123	—	2	2	no	—
121	C₁₃×#123	—	2	4	no	—
122	C₁₃×#123	—	2	1	no	—
123	C₁₃×#123	—	2	4	no	—
124	C₁₃×#123	—	2	2	no	—
125	C₁₃×#123	—	2	4	no	—
126	C₁₃×#123	—	2	4	no	—
127	C₁₃×#123	D₄	1	2	yes	—
128	C₁₃×C₂²⋊Q₈	—	2	2	no	—
129	C₁₃×C₂²⋊Q₈	—	2	2	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	D₄	1	2	yes	—
134	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
135	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
136	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
137	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
138	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
139	C₁₃×#121	—	2	4	no	—
140	C₁₃×#121	—	2	4	no	—
141	C₁₃×#121	D₄	1	2	yes	—
142	C₁₃×#121	C₂³	1	2	yes	—
143	C₁₃×#120	—	2	1	no	—
144	C₁₃×#120	—	2	4	no	—
145	C₁₃×#120	D₄	1	2	yes	—
146	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
147	C₄×D₄×C₁₃	—	2	4	no	—
148	C₄×D₄×C₁₃	—	2	2	no	—
149	C₄×D₄×C₁₃	—	2	2	no	—
150	C₄×D₄×C₁₃	C₂³	1	4	yes	—
151	C₄×D₄×C₁₃	C₂³	1	4	yes	—
152	C₁₃×#117	—	2	4	no	—
153	C₁₃×#117	C₂³	1	2	yes	—
154	C₁₃×#117	C₂³	1	1	yes	characteristic
155	C₁₃×#117	C₂³	1	1	yes	characteristic
156	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
157	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
158	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
159	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
160	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
161	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
162	C₁₃×#107	C₂³	1	4	yes	—
163	C₁₃×#106	C₂³	1	4	yes	—
164	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
165	C₁₃×#103	C₂³	1	4	yes	—
166	C₁₃×#103	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×#102	C₂³	1	4	yes	—
171	C₁₃×#102	C₂³	1	4	yes	—
172	C₁₃×#102	C₂³	1	4	yes	—
173	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
174	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
175	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
176	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
177	C₁₃×#97	C₂³	1	2	yes	—
178	C₄×C₈×C₁₃	C₂³	1	2	yes	—
179	#61649	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
180	C₂⁴×C₁₃	—	2	1	no	—
181	C₂⁴×C₁₃	—	2	2	no	—
182	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
183	C₁₃×#41	—	2	8	no	—
184	C₁₃×#41	—	2	4	no	—
185	C₁₃×#41	—	4	2	no	—
186	C₁₃×#41	—	4	4	no	—
187	C₁₃×#41	—	4	2	no	—
188	C₁₃×#41	—	4	2	no	—
189	C₁₃×#41	—	4	8	no	—
190	C₁₃×#41	—	4	4	no	—
191	C₂×Q₈×C₁₃	—	2	1	no	—
192	C₂×Q₈×C₁₃	—	2	2	no	—
193	C₂×Q₈×C₁₃	—	2	2	no	—
194	C₂×Q₈×C₁₃	—	4	2	no	—
195	C₂×Q₈×C₁₃	—	4	2	no	—
196	C₂×Q₈×C₁₃	—	4	4	no	—
197	C₂×Q₈×C₁₃	—	4	2	no	—
198	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
199	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
200	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
201	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
202	C₂×D₄×C₁₃	—	2	4	no	—
203	C₂×D₄×C₁₃	—	2	4	no	—
204	C₂×D₄×C₁₃	—	2	4	no	—
205	C₂×D₄×C₁₃	—	2	1	no	—
206	C₂×D₄×C₁₃	—	2	2	no	—
207	C₂×D₄×C₁₃	—	2	2	no	—
208	C₂×D₄×C₁₃	—	2	1	no	—
209	C₂×D₄×C₁₃	—	2	2	no	—
210	C₂×D₄×C₁₃	—	4	2	no	—
211	C₂×D₄×C₁₃	—	4	4	no	—
212	C₂×D₄×C₁₃	—	4	4	no	—
213	C₂×D₄×C₁₃	—	4	8	no	—
214	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
215	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
216	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
217	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
218	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
219	C₂²×C₄×C₁₃	—	2	2	no	—
220	C₂²×C₄×C₁₃	—	2	1	no	—
221	C₂²×C₄×C₁₃	—	2	2	no	—
222	C₂²×C₄×C₁₃	—	2	2	no	—
223	C₂²×C₄×C₁₃	—	2	4	no	—
224	C₂²×C₄×C₁₃	—	2	2	no	—
225	C₂²×C₄×C₁₃	—	2	1	no	—
226	C₂²×C₄×C₁₃	—	2	4	no	—
227	C₂²×C₄×C₁₃	—	4	2	no	—
228	C₂²×C₄×C₁₃	—	4	4	no	—
229	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
230	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
231	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
232	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
233	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
234	C₁₃×Q₁₆	—	4	4	no	—
235	C₁₃×Q₁₆	—	4	4	no	—
236	C₁₃×Q₁₆	—	4	4	no	—
237	C₁₃×SD₁₆	—	2	8	no	—
238	C₁₃×SD₁₆	—	2	8	no	—
239	C₁₃×SD₁₆	—	4	4	no	—
240	C₁₃×M₁₆	—	4	4	no	—
241	C₁₃×M₁₆	—	4	2	no	—
242	C₂×C₈×C₁₃	—	4	2	no	—
243	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
244	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
245	C₁₃×C₄⋊C₄	—	2	2	no	—
246	C₁₃×C₄⋊C₄	—	2	4	no	—
247	C₁₃×C₄⋊C₄	—	2	4	no	—
248	C₁₃×C₄⋊C₄	—	2	4	no	—
249	C₁₃×C₄⋊C₄	—	2	4	no	—
250	C₁₃×C₄⋊C₄	—	2	2	no	—
251	C₁₃×C₄⋊C₄	—	2	4	no	—
252	C₁₃×C₄⋊C₄	—	2	4	no	—
253	C₁₃×C₄⋊C₄	—	2	4	no	—
254	C₁₃×C₄⋊C₄	—	2	4	no	—
255	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
256	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
257	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
258	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
259	C₁₃×C₂²⋊C₄	—	2	1	no	—
260	C₁₃×C₂²⋊C₄	—	2	4	no	—
261	C₁₃×C₂²⋊C₄	—	2	4	no	—
262	C₁₃×C₂²⋊C₄	—	2	4	no	—
263	C₁₃×C₂²⋊C₄	—	2	2	no	—
264	C₁₃×C₂²⋊C₄	—	2	2	no	—
265	C₁₃×C₂²⋊C₄	—	2	4	no	—
266	C₁₃×C₂²⋊C₄	—	2	2	no	—
267	C₁₃×C₂²⋊C₄	—	2	4	no	—
268	C₁₃×C₂²⋊C₄	—	2	4	no	—
269	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
270	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
271	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
272	C₄²×C₁₃	—	2	2	no	—
273	C₄²×C₁₃	—	2	4	no	—
274	C₄²×C₁₃	—	2	1	no	—
275	C₄²×C₁₃	C₂⁴	1	2	yes	—
276	#3538	C₂×C₁₃	1	1	yes	characteristic, complemented
277	#3485	C₂×C₁₃	1	1	yes	characteristic
278	#3323	C₂×C₁₃	1	4	yes	complemented
279	#3315	C₂×C₁₃	1	4	yes	complemented
280	#3276	C₂×C₁₃	1	4	yes	complemented
281	#3266	C₂×C₁₃	1	4	yes	complemented
282	#3223	C₂×C₁₃	1	2	yes	complemented
283	#3202	C₂×C₁₃	1	2	yes	complemented
284	#3196	C₂×C₁₃	1	2	yes	complemented
285	#3123	C₂×C₁₃	1	2	yes	complemented
286	#3009	C₂×C₁₃	1	2	yes	complemented
287	#3007	C₂×C₁₃	1	2	yes	complemented
288	#2978	C₂×C₁₃	1	1	yes	characteristic, complemented
289	C₂³×C₁₃	—	2	4	no	—
290	C₂³×C₁₃	—	2	2	no	—
291	C₂³×C₁₃	—	2	1	no	—
292	C₂³×C₁₃	—	4	1	no	—
293	C₂³×C₁₃	—	4	2	no	—
294	C₂³×C₁₃	—	4	4	no	—
295	C₂³×C₁₃	—	8	2	no	—
296	C₂³×C₁₃	—	8	4	no	—
297	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
298	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
299	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
300	Q₈×C₁₃	—	2	4	no	—
301	Q₈×C₁₃	—	2	4	no	—
302	Q₈×C₁₃	—	2	4	no	—
303	Q₈×C₁₃	—	2	2	no	—
304	Q₈×C₁₃	—	4	1	no	—
305	Q₈×C₁₃	—	4	2	no	—
306	Q₈×C₁₃	—	8	2	no	—
307	Q₈×C₁₃	—	8	2	no	—
308	D₄×C₁₃	—	2	4	no	—
309	D₄×C₁₃	—	2	2	no	—
310	D₄×C₁₃	—	2	2	no	—
311	D₄×C₁₃	—	4	1	no	—
312	D₄×C₁₃	—	4	2	no	—
313	D₄×C₁₃	—	4	4	no	—
314	D₄×C₁₃	—	4	4	no	—
315	D₄×C₁₃	—	4	4	no	—
316	D₄×C₁₃	—	4	8	no	—
317	D₄×C₁₃	—	4	2	no	—
318	D₄×C₁₃	—	8	2	no	—
319	D₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
320	C₂×C₄×C₁₃	—	2	2	no	—
321	C₂×C₄×C₁₃	—	2	4	no	—
322	C₂×C₄×C₁₃	—	2	2	no	—
323	C₂×C₄×C₁₃	—	2	2	no	—
324	C₂×C₄×C₁₃	—	2	4	no	—
325	C₂×C₄×C₁₃	—	2	2	no	—
326	C₂×C₄×C₁₃	—	2	4	no	—
327	C₂×C₄×C₁₃	—	2	2	no	—
328	C₂×C₄×C₁₃	—	2	1	no	—
329	C₂×C₄×C₁₃	—	4	1	no	—
330	C₂×C₄×C₁₃	—	4	2	no	—
331	C₂×C₄×C₁₃	—	4	8	no	—
332	C₂×C₄×C₁₃	—	4	4	no	—
333	C₂×C₄×C₁₃	—	4	2	no	—
334	C₂×C₄×C₁₃	—	4	4	no	—
335	C₂×C₄×C₁₃	—	4	2	no	—
336	C₂×C₄×C₁₃	—	8	4	no	—
337	C₂×C₄×C₁₃	—	8	2	no	—
338	C₂×C₄×C₁₃	—	8	2	no	—
339	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
340	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
341	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
342	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
343	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
344	C₈×C₁₃	—	2	4	no	—
345	C₈×C₁₃	—	2	4	no	—
346	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	1	yes	characteristic
347	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
348	C₂×#137	C₂²×C₁₃	1	4	yes	complemented
349	C₂×#137	C₂²×C₁₃	1	2	yes	complemented
350	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
351	#563	—	2	2	no	—
352	#552	C₂²×C₁₃	1	4	yes	complemented
353	#551	—	2	2	no	—
354	D₄×Q₈	C₂²×C₁₃	1	4	yes	complemented
355	#547	—	2	2	no	—
356	#547	C₂²×C₁₃	1	4	yes	—
357	#546	—	2	2	no	—
358	#546	C₂²×C₁₃	1	4	yes	—
359	#544	—	2	2	no	—
360	#541	C₂²×C₁₃	1	2	yes	complemented
361	#539	—	2	2	no	—
362	#536	C₂²×C₁₃	1	1	yes	characteristic
363	#536	C₂²×C₁₃	1	1	yes	characteristic
364	#536	C₂²×C₁₃	1	2	yes	—
365	#534	—	2	2	no	—
366	#525	C₂²×C₁₃	1	1	yes	characteristic
367	#525	C₂²×C₁₃	1	1	yes	characteristic
368	C₂×#123	—	2	2	no	—
369	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
370	#518	C₂²×C₁₃	1	1	yes	characteristic
371	#497	C₂²×C₁₃	1	2	yes	complemented
372	#494	C₂²×C₁₃	1	2	yes	complemented
373	#491	C₂²×C₁₃	1	2	yes	complemented
374	#488	C₂²×C₁₃	1	2	yes	complemented
375	#485	C₂²×C₁₃	1	4	yes	complemented
376	#485	C₂²×C₁₃	1	4	yes	complemented
377	#484	C₂²×C₁₃	1	2	yes	complemented
378	#481	C₂²×C₁₃	1	2	yes	complemented
379	#478	C₂²×C₁₃	1	4	yes	complemented
380	#470	C₂²×C₁₃	1	4	yes	complemented
381	#470	C₂²×C₁₃	1	4	yes	complemented
382	#468	C₂²×C₁₃	1	4	yes	complemented
383	#467	C₂²×C₁₃	1	4	yes	complemented
384	#464	C₂²×C₁₃	1	4	yes	complemented
385	#462	C₂²×C₁₃	1	4	yes	complemented
386	#461	C₂²×C₁₃	1	4	yes	complemented
387	#452	C₂²×C₁₃	1	4	yes	—
388	#452	C₂²×C₁₃	1	4	yes	complemented
389	#452	C₂²×C₁₃	1	4	yes	complemented
390	#452	C₂²×C₁₃	1	4	yes	complemented
391	#451	C₂²×C₁₃	1	2	yes	complemented
392	#451	C₂²×C₁₃	1	4	yes	complemented
393	#451	C₂²×C₁₃	1	4	yes	complemented
394	#450	C₂²×C₁₃	1	4	yes	—
395	#450	C₂²×C₁₃	1	4	yes	complemented
396	#448	C₂²×C₁₃	1	2	yes	complemented
397	#440	C₂²×C₁₃	1	4	yes	complemented
398	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
399	#436	C₂²×C₁₃	1	4	yes	complemented
400	#435	C₂²×C₁₃	1	4	yes	complemented
401	#433	C₂²×C₁₃	1	2	yes	complemented
402	#418	C₂²×C₁₃	1	2	yes	complemented
403	#417	C₂²×C₁₃	1	4	yes	complemented
404	#416	C₂²×C₁₃	1	2	yes	complemented
405	#408	C₂²×C₁₃	1	2	yes	—
406	#407	C₂²×C₁₃	1	2	yes	complemented
407	C₂²×C₁₃	—	2	2	no	—
408	C₂²×C₁₃	—	2	4	no	—
409	C₂²×C₁₃	—	2	2	no	—
410	C₂²×C₁₃	—	2	2	no	—
411	C₂²×C₁₃	—	2	1	no	—
412	C₂²×C₁₃	—	2	2	no	—
413	C₂²×C₁₃	—	2	2	no	—
414	C₂²×C₁₃	—	2	4	no	—
415	C₂²×C₁₃	—	4	4	no	—
416	C₂²×C₁₃	—	4	2	no	—
417	C₂²×C₁₃	—	4	1	no	—
418	C₂²×C₁₃	—	8	4	no	—
419	C₂²×C₁₃	—	8	2	no	—
420	C₂²×C₁₃	—	16	4	no	—
421	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
422	C₄×C₁₃	—	2	4	no	—
423	C₄×C₁₃	—	2	2	no	—
424	C₄×C₁₃	—	2	1	no	—
425	C₄×C₁₃	—	2	2	no	—
426	C₄×C₁₃	—	4	4	no	—
427	C₄×C₁₃	—	4	2	no	—
428	C₄×C₁₃	—	4	1	no	—
429	C₄×C₁₃	—	4	2	no	—
430	C₄×C₁₃	—	4	4	no	—
431	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
432	H(5,𝔽₂)	—	4	4	no	—
433	C₂×#41	—	2	1	no	—
434	C₂×#41	—	2	2	no	—
435	C₂×#41	—	4	4	no	—
436	C₂×#41	C₂³×C₁₃	1	4	yes	—
437	C₂×#41	C₂³×C₁₃	1	2	yes	—
438	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
439	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
440	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
441	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
442	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
443	C₂²×D₄	—	2	1	no	—
444	C₂²×D₄	—	2	2	no	—
445	C₂²×D₄	—	2	1	no	—
446	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
447	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
448	C₂³×C₄	—	2	1	no	—
449	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
450	#137	—	4	8	no	—
451	#137	—	4	4	no	—
452	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
453	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
454	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
455	C₂×SD₁₆	—	4	4	no	—
456	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
457	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
458	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
459	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
460	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
461	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
462	C₄⋊Q₈	—	2	2	no	—
463	C₄⋊Q₈	—	2	1	no	—
464	C₄⋊Q₈	—	2	4	no	—
465	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
466	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
467	#126	—	2	4	no	—
468	#126	—	2	4	no	—
469	#125	—	2	4	no	—
470	#125	—	2	4	no	—
471	#125	C₂³×C₁₃	1	2	yes	—
472	#124	—	2	1	no	—
473	#124	—	2	2	no	—
474	#124	C₂³×C₁₃	1	2	yes	—
475	#123	—	2	2	no	—
476	#123	—	2	2	no	—
477	#123	—	2	2	no	—
478	#123	—	2	4	no	—
479	#123	—	2	1	no	—
480	#123	—	2	4	no	—
481	#123	—	2	2	no	—
482	#123	—	2	4	no	—
483	#123	—	2	4	no	—
484	#123	D₄×C₁₃	1	2	yes	—
485	C₂²⋊Q₈	—	2	2	no	—
486	C₂²⋊Q₈	—	2	2	no	—
487	C₂²⋊Q₈	—	2	2	no	—
488	C₂²⋊Q₈	—	2	4	no	—
489	C₂²⋊Q₈	—	2	4	no	—
490	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
491	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
492	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
493	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
494	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
495	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
496	#121	—	2	4	no	—
497	#121	—	2	4	no	—
498	#121	D₄×C₁₃	1	2	yes	—
499	#121	C₂³×C₁₃	1	2	yes	—
500	#120	—	2	1	no	—
501	#120	—	2	4	no	—
502	#120	D₄×C₁₃	1	2	yes	—
503	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
504	C₄×D₄	—	2	4	no	—
505	C₄×D₄	—	2	2	no	—
506	C₄×D₄	—	2	2	no	—
507	C₄×D₄	C₂³×C₁₃	1	4	yes	—
508	C₄×D₄	C₂³×C₁₃	1	4	yes	—
509	#117	—	2	4	no	—
510	#117	C₂³×C₁₃	1	1	yes	characteristic
511	#117	C₂³×C₁₃	1	2	yes	—
512	#117	C₂³×C₁₃	1	1	yes	characteristic
513	C₂×C₄⋊C₄	—	2	2	no	—
514	C₂×C₄⋊C₄	—	2	4	no	—
515	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
516	C₂×C₂²⋊C₄	—	2	2	no	—
517	C₂×C₂²⋊C₄	—	2	2	no	—
518	C₂×C₂²⋊C₄	—	2	4	no	—
519	#107	C₂³×C₁₃	1	4	yes	—
520	#106	C₂³×C₁₃	1	4	yes	—
521	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
522	#103	C₂³×C₁₃	1	4	yes	—
523	#103	C₂³×C₁₃	1	4	yes	—
524	#103	C₂³×C₁₃	1	4	yes	—
525	#103	C₂³×C₁₃	1	4	yes	—
526	#103	C₂³×C₁₃	1	4	yes	—
527	#102	C₂³×C₁₃	1	4	yes	—
528	#102	C₂³×C₁₃	1	4	yes	—
529	#102	C₂³×C₁₃	1	4	yes	—
530	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
531	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
532	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
533	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
534	#97	C₂³×C₁₃	1	2	yes	—
535	C₄×C₈	C₂³×C₁₃	1	2	yes	—
536	C₂×C₁₃	—	4	2	no	—
537	C₂×C₁₃	—	4	1	no	—
538	C₂×C₁₃	—	4	2	no	—
539	C₂×C₁₃	—	4	4	no	—
540	C₂×C₁₃	—	8	1	no	—
541	C₂×C₁₃	#3484	1	1	yes	characteristic
542	C₂×C₁₃	#3586	1	2	yes	—
543	C₂⁴	—	2	1	no	—
544	C₂⁴	—	2	2	no	—
545	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
546	#41	—	2	8	no	—
547	#41	—	2	4	no	—
548	#41	—	4	2	no	—
549	#41	—	4	4	no	—
550	#41	—	4	2	no	—
551	#41	—	4	2	no	—
552	#41	—	4	8	no	—
553	#41	—	4	4	no	—
554	C₂×Q₈	—	2	1	no	—
555	C₂×Q₈	—	2	2	no	—
556	C₂×Q₈	—	2	2	no	—
557	C₂×Q₈	—	4	2	no	—
558	C₂×Q₈	—	4	2	no	—
559	C₂×Q₈	—	4	4	no	—
560	C₂×Q₈	—	4	2	no	—
561	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
562	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
563	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
564	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
565	C₂×D₄	—	2	4	no	—
566	C₂×D₄	—	2	4	no	—
567	C₂×D₄	—	2	4	no	—
568	C₂×D₄	—	2	1	no	—
569	C₂×D₄	—	2	2	no	—
570	C₂×D₄	—	2	2	no	—
571	C₂×D₄	—	2	1	no	—
572	C₂×D₄	—	2	2	no	—
573	C₂×D₄	—	4	2	no	—
574	C₂×D₄	—	4	4	no	—
575	C₂×D₄	—	4	4	no	—
576	C₂×D₄	—	4	8	no	—
577	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
578	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
579	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
580	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
581	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
582	C₂²×C₄	—	2	2	no	—
583	C₂²×C₄	—	2	1	no	—
584	C₂²×C₄	—	2	2	no	—
585	C₂²×C₄	—	2	2	no	—
586	C₂²×C₄	—	2	4	no	—
587	C₂²×C₄	—	2	2	no	—
588	C₂²×C₄	—	2	1	no	—
589	C₂²×C₄	—	2	4	no	—
590	C₂²×C₄	—	4	2	no	—
591	C₂²×C₄	—	4	4	no	—
592	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
593	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
594	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
595	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
596	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
597	Q₁₆	—	4	4	no	—
598	Q₁₆	—	4	4	no	—
599	Q₁₆	—	4	4	no	—
600	SD₁₆	—	2	8	no	—
601	SD₁₆	—	2	8	no	—
602	SD₁₆	—	4	4	no	—
603	M₁₆	—	4	4	no	—
604	M₁₆	—	4	2	no	—
605	C₂×C₈	—	4	2	no	—
606	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
607	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
608	C₄⋊C₄	—	2	2	no	—
609	C₄⋊C₄	—	2	4	no	—
610	C₄⋊C₄	—	2	4	no	—
611	C₄⋊C₄	—	2	4	no	—
612	C₄⋊C₄	—	2	4	no	—
613	C₄⋊C₄	—	2	2	no	—
614	C₄⋊C₄	—	2	4	no	—
615	C₄⋊C₄	—	2	4	no	—
616	C₄⋊C₄	—	2	4	no	—
617	C₄⋊C₄	—	2	4	no	—
618	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
619	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
620	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
621	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
622	C₂²⋊C₄	—	2	1	no	—
623	C₂²⋊C₄	—	2	4	no	—
624	C₂²⋊C₄	—	2	4	no	—
625	C₂²⋊C₄	—	2	4	no	—
626	C₂²⋊C₄	—	2	2	no	—
627	C₂²⋊C₄	—	2	2	no	—
628	C₂²⋊C₄	—	2	4	no	—
629	C₂²⋊C₄	—	2	2	no	—
630	C₂²⋊C₄	—	2	4	no	—
631	C₂²⋊C₄	—	2	4	no	—
632	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
633	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
634	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
635	C₄²	—	2	2	no	—
636	C₄²	—	2	4	no	—
637	C₄²	—	2	1	no	—
638	C₄²	C₂⁴×C₁₃	1	2	yes	—
639	C₁₃	#61649	1	1	yes	characteristic, direct product factor, Sylow
640	C₂³	—	2	4	no	—
641	C₂³	—	2	2	no	—
642	C₂³	—	2	1	no	—
643	C₂³	—	4	1	no	—
644	C₂³	—	4	2	no	—
645	C₂³	—	4	4	no	—
646	C₂³	—	8	2	no	—
647	C₂³	—	8	4	no	—
648	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
649	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
650	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
651	Q₈	—	2	4	no	—
652	Q₈	—	2	4	no	—
653	Q₈	—	2	4	no	—
654	Q₈	—	2	2	no	—
655	Q₈	—	4	1	no	—
656	Q₈	—	4	2	no	—
657	Q₈	—	8	2	no	—
658	Q₈	—	8	2	no	—
659	D₄	—	2	4	no	—
660	D₄	—	2	2	no	—
661	D₄	—	2	2	no	—
662	D₄	—	4	1	no	—
663	D₄	—	4	2	no	—
664	D₄	—	4	4	no	—
665	D₄	—	4	4	no	—
666	D₄	—	4	4	no	—
667	D₄	—	4	8	no	—
668	D₄	—	4	2	no	—
669	D₄	—	8	2	no	—
670	D₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	4	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	4	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	4	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	1	no	—
680	C₂×C₄	—	4	1	no	—
681	C₂×C₄	—	4	2	no	—
682	C₂×C₄	—	4	8	no	—
683	C₂×C₄	—	4	4	no	—
684	C₂×C₄	—	4	2	no	—
685	C₂×C₄	—	4	2	no	—
686	C₂×C₄	—	4	4	no	—
687	C₂×C₄	—	8	4	no	—
688	C₂×C₄	—	8	2	no	—
689	C₂×C₄	—	8	2	no	—
690	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
691	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
692	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
693	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
694	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
695	C₈	—	2	4	no	—
696	C₈	—	2	4	no	—
697	C₂²	—	2	2	no	—
698	C₂²	—	2	4	no	—
699	C₂²	—	2	2	no	—
700	C₂²	—	2	2	no	—
701	C₂²	—	2	1	no	—
702	C₂²	—	2	2	no	—
703	C₂²	—	2	2	no	—
704	C₂²	—	2	4	no	—
705	C₂²	—	4	4	no	—
706	C₂²	—	4	2	no	—
707	C₂²	—	4	1	no	—
708	C₂²	—	8	4	no	—
709	C₂²	—	8	2	no	—
710	C₂²	—	16	4	no	—
711	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
712	C₄	—	2	4	no	—
713	C₄	—	2	2	no	—
714	C₄	—	2	1	no	—
715	C₄	—	2	2	no	—
716	C₄	—	4	4	no	—
717	C₄	—	4	2	no	—
718	C₄	—	4	1	no	—
719	C₄	—	4	2	no	—
720	C₄	—	4	4	no	—
721	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
722	C₂	—	4	1	no	—
723	C₂	—	4	2	no	—
724	C₂	—	4	2	no	—
725	C₂	—	4	4	no	—
726	C₂	—	8	1	no	—
727	C₂	C₁₃×#3484	1	1	yes	characteristic
728	C₂	C₁₃×#3586	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3485	C₂
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. C₁₃×#3538	C₂	semidirect
3. C₁₃×#3323	C₂	semidirect
4. C₁₃×#3315	C₂	semidirect
5. C₁₃×#3276	C₂	semidirect
6. C₁₃×#3266	C₂	semidirect
7. C₁₃×#3223	C₂	semidirect
8. C₁₃×#3202	C₂	semidirect
9. C₁₃×#3196	C₂	semidirect
10. C₁₃×#3123	C₂	semidirect
11. C₁₃×#3009	C₂	semidirect
12. C₁₃×#3007	C₂	semidirect
13. C₁₃×#2978	C₂	semidirect
16. C₂×C₁₃×#137	C₂²	semidirect
17. C₂×C₁₃×#137	C₂²	semidirect
18. C₂²×C₁₃×SD₁₆	C₂²	semidirect
20. C₁₃×#552	C₂²	semidirect
22. D₄×Q₈×C₁₃	C₂²	semidirect
28. C₁₃×#541	C₂²	semidirect
37. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
39. C₁₃×#497	C₂²	semidirect
40. C₁₃×#494	C₂²	semidirect
41. C₁₃×#491	C₂²	semidirect
42. C₁₃×#488	C₂²	semidirect
43. C₁₃×#485	C₂²	semidirect
44. C₁₃×#485	C₂²	semidirect
45. C₁₃×#484	C₂²	semidirect
46. C₁₃×#481	C₂²	semidirect
47. C₁₃×#478	C₂²	semidirect
48. C₁₃×#470	C₂²	semidirect
49. C₁₃×#470	C₂²	semidirect
50. C₁₃×#468	C₂²	semidirect
51. C₁₃×#467	C₂²	semidirect
52. C₁₃×#464	C₂²	semidirect
53. C₁₃×#462	C₂²	semidirect
54. C₁₃×#461	C₂²	semidirect
56. C₁₃×#452	C₂²	semidirect
57. C₁₃×#452	C₂²	semidirect
58. C₁₃×#452	C₂²	semidirect
59. C₁₃×#451	C₂²	semidirect
60. C₁₃×#451	C₂²	semidirect
61. C₁₃×#451	C₂²	semidirect
63. C₁₃×#450	C₂²	semidirect
64. C₁₃×#448	C₂²	semidirect
65. C₁₃×#440	C₂²	semidirect
66. C₄×C₁₃×SD₁₆	C₂²	semidirect
67. C₁₃×#436	C₂²	semidirect
68. C₁₃×#435	C₂²	semidirect
69. C₁₃×#433	C₂²	semidirect
70. C₁₃×#418	C₂²	semidirect
71. C₁₃×#417	C₂²	semidirect
72. C₁₃×#416	C₂²	semidirect
74. C₁₃×#407	C₂²	semidirect
179. #61649	C₁₃	direct (N × H)
276. #3538	C₂×C₁₃	semidirect
278. #3323	C₂×C₁₃	semidirect
279. #3315	C₂×C₁₃	semidirect
280. #3276	C₂×C₁₃	semidirect
281. #3266	C₂×C₁₃	semidirect
282. #3223	C₂×C₁₃	semidirect
283. #3202	C₂×C₁₃	semidirect
284. #3196	C₂×C₁₃	semidirect
285. #3123	C₂×C₁₃	semidirect
286. #3009	C₂×C₁₃	semidirect
287. #3007	C₂×C₁₃	semidirect
288. #2978	C₂×C₁₃	semidirect
348. C₂×#137	C₂²×C₁₃	semidirect
349. C₂×#137	C₂²×C₁₃	semidirect
350. C₂²×SD₁₆	C₂²×C₁₃	semidirect
352. #552	C₂²×C₁₃	semidirect
354. D₄×Q₈	C₂²×C₁₃	semidirect
360. #541	C₂²×C₁₃	semidirect
369. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
371. #497	C₂²×C₁₃	semidirect
372. #494	C₂²×C₁₃	semidirect
373. #491	C₂²×C₁₃	semidirect
374. #488	C₂²×C₁₃	semidirect
375. #485	C₂²×C₁₃	semidirect
376. #485	C₂²×C₁₃	semidirect
377. #484	C₂²×C₁₃	semidirect
378. #481	C₂²×C₁₃	semidirect
379. #478	C₂²×C₁₃	semidirect
380. #470	C₂²×C₁₃	semidirect
381. #470	C₂²×C₁₃	semidirect
382. #468	C₂²×C₁₃	semidirect
383. #467	C₂²×C₁₃	semidirect
384. #464	C₂²×C₁₃	semidirect
385. #462	C₂²×C₁₃	semidirect
386. #461	C₂²×C₁₃	semidirect
388. #452	C₂²×C₁₃	semidirect
389. #452	C₂²×C₁₃	semidirect
390. #452	C₂²×C₁₃	semidirect
391. #451	C₂²×C₁₃	semidirect
392. #451	C₂²×C₁₃	semidirect
393. #451	C₂²×C₁₃	semidirect
395. #450	C₂²×C₁₃	semidirect
396. #448	C₂²×C₁₃	semidirect
397. #440	C₂²×C₁₃	semidirect
398. C₄×SD₁₆	C₂²×C₁₃	semidirect
399. #436	C₂²×C₁₃	semidirect
400. #435	C₂²×C₁₃	semidirect
401. #433	C₂²×C₁₃	semidirect
402. #418	C₂²×C₁₃	semidirect
403. #417	C₂²×C₁₃	semidirect
404. #416	C₂²×C₁₃	semidirect
406. #407	C₂²×C₁₃	semidirect
639. C₁₃	#61649	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×#3538	2
C₁₃×#3485	2
C₁₃×#3323	2
C₁₃×#3315	2
C₁₃×#3276	2
C₁₃×#3266	2
C₁₃×#3223	2
C₁₃×#3202	2
C₁₃×#3196	2
C₁₃×#3123	2
C₁₃×#3009	2
C₁₃×#3007	2
C₁₃×#2978	2
#61649	13

Subgroups — C13×#61649 #15747988

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61649 #15747988