Subgroups — C₁₃×#61686 #15748025

Order 3328.

2068 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3548	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3497	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3332	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3316	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3298	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3284	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3276	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3271	C₂	1	4	yes	maximal, complemented
9	C₁₃×#3214	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3210	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3204	C₂	1	4	yes	maximal, complemented
12	C₁₃×#3113	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3103	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3013	C₂	1	4	yes	maximal, complemented
15	C₁₃×#2981	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	2	yes	—
17	C₂×C₁₃×#137	C₂²	1	4	yes	—
18	C₂×C₁₃×#135	C₂²	1	4	yes	—
19	C₁₃×#562	—	2	2	no	—
20	C₁₃×#554	—	2	1	no	—
21	C₁₃×#554	C₂²	1	2	yes	—
22	C₁₃×#550	—	2	1	no	—
23	C₁₃×#550	—	2	1	no	—
24	C₁₃×#550	C₂²	1	2	yes	—
25	C₁₃×#550	C₂²	1	2	yes	—
26	D₄×Q₈×C₁₃	—	2	1	no	—
27	D₄×Q₈×C₁₃	C₂²	1	2	yes	—
28	C₁₃×#548	—	2	2	no	—
29	C₁₃×#548	C₂²	1	4	yes	—
30	C₁₃×#547	C₂²	1	2	yes	—
31	C₁₃×#547	C₂²	1	2	yes	—
32	C₁₃×#540	—	2	2	no	—
33	C₁₃×#537	—	2	2	no	—
34	C₁₃×#537	—	2	2	no	—
35	C₁₃×#537	C₂²	1	4	yes	—
36	C₁₃×#537	C₂²	1	2	yes	—
37	C₁₃×#533	C₂²	1	1	yes	characteristic
38	C₁₃×#532	—	2	2	no	—
39	C₁₃×#532	C₂²	1	1	yes	characteristic
40	C₁₃×#532	C₂²	1	1	yes	characteristic
41	C₁₃×#532	C₂²	1	1	yes	characteristic
42	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
43	C₁₃×#496	C₂²	1	2	yes	—
44	C₁₃×#494	C₂²	1	1	yes	characteristic
45	C₁₃×#492	C₂²	1	1	yes	characteristic
46	C₁₃×#489	C₂²	1	2	yes	—
47	C₁₃×#487	C₂²	1	1	yes	characteristic
48	C₁₃×#486	C₂²	1	1	yes	characteristic
49	C₁₃×#483	C₂²	1	4	yes	—
50	C₁₃×#483	C₂²	1	2	yes	—
51	C₁₃×#481	C₂²	1	4	yes	—
52	C₁₃×#481	C₂²	1	2	yes	—
53	C₁₃×#475	C₂²	1	2	yes	—
54	C₁₃×#475	C₂²	1	2	yes	—
55	C₁₃×#470	C₂²	1	4	yes	—
56	C₁₃×#469	C₂²	1	4	yes	—
57	C₁₃×#465	C₂²	1	4	yes	—
58	C₁₃×#465	C₂²	1	4	yes	—
59	C₁₃×#464	C₂²	1	4	yes	—
60	C₁₃×#462	C₂²	1	2	yes	—
61	C₁₃×#461	C₂²	1	2	yes	—
62	C₁₃×#460	C₂²	1	2	yes	—
63	C₁₃×#459	C₂²	1	2	yes	—
64	C₁₃×#452	C₂²	1	4	yes	—
65	C₁₃×#452	C₂²	1	4	yes	—
66	C₁₃×#452	C₂²	1	4	yes	—
67	C₁₃×#451	C₂²	1	2	yes	—
68	C₁₃×#451	C₂²	1	4	yes	—
69	C₁₃×#449	C₂²	1	4	yes	—
70	C₁₃×#449	C₂²	1	4	yes	—
71	C₁₃×#449	C₂²	1	4	yes	—
72	C₁₃×#448	C₂²	1	2	yes	—
73	C₁₃×#448	C₂²	1	4	yes	—
74	C₁₃×#441	C₂²	1	4	yes	—
75	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
76	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
77	C₁₃×#436	C₂²	1	2	yes	—
78	C₁₃×#435	C₂²	1	4	yes	—
79	C₈×D₄×C₁₃	C₂²	1	2	yes	—
80	C₁₃×#432	C₂²	1	1	yes	characteristic
81	C₁₃×#431	C₂²	1	1	yes	characteristic
82	C₁₃×#417	C₂²	1	4	yes	—
83	C₂×C₁₃×#103	C₂²	1	4	yes	—
84	C₁₃×#408	C₂²	1	4	yes	—
85	C₁₃×2₋¹⁺⁴	—	4	8	no	—
86	C₂×C₁₃×#41	—	2	4	no	—
87	C₂×C₁₃×#41	—	2	2	no	—
88	C₂×C₁₃×#41	—	2	2	no	—
89	C₂×C₁₃×#41	—	2	1	no	—
90	C₂×C₁₃×#41	C₂³	1	4	yes	—
91	C₂×C₁₃×#41	C₂³	1	2	yes	—
92	C₂×C₁₃×#41	C₂³	1	4	yes	—
93	C₂×C₁₃×#41	C₂³	1	2	yes	—
94	C₂²×Q₈×C₁₃	—	2	2	no	—
95	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
96	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
97	C₁₃×#137	—	4	8	no	—
98	C₁₃×#135	—	4	8	no	—
99	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
100	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
101	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
102	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
103	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
104	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
105	C₂×C₁₃×D₈	C₂³	1	4	yes	—
106	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
107	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
108	C₁₃×C₄⋊Q₈	—	2	2	no	—
109	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
110	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
111	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
112	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
113	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
114	C₁₃×#127	—	2	2	no	—
115	C₁₃×#127	—	2	2	no	—
116	C₁₃×#127	D₄	1	1	yes	characteristic
117	C₁₃×#127	C₂³	1	1	yes	characteristic
118	C₁₃×#127	C₂³	1	1	yes	characteristic
119	C₁₃×#125	—	2	2	no	—
120	C₁₃×#125	—	2	1	no	—
121	C₁₃×#124	—	2	4	no	—
122	C₁₃×#124	—	2	1	no	—
123	C₁₃×#124	D₄	1	2	yes	—
124	C₁₃×#124	C₂³	1	2	yes	—
125	C₁₃×#123	—	2	4	no	—
126	C₁₃×#123	—	2	4	no	—
127	C₁₃×C₂²⋊Q₈	—	2	2	no	—
128	C₁₃×C₂²⋊Q₈	—	2	4	no	—
129	C₁₃×C₂²⋊Q₈	—	2	1	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	2	yes	—
135	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
136	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
137	C₁₃×#121	—	2	4	no	—
138	C₁₃×#121	—	2	4	no	—
139	C₁₃×#121	—	2	4	no	—
140	C₁₃×#121	—	2	2	no	—
141	C₁₃×#121	—	2	4	no	—
142	C₁₃×#121	—	2	2	no	—
143	C₁₃×#121	—	2	4	no	—
144	C₁₃×#121	—	2	1	no	—
145	C₁₃×#121	—	2	1	no	—
146	C₁₃×#121	—	2	1	no	—
147	C₁₃×#121	—	2	4	no	—
148	C₁₃×#121	—	2	4	no	—
149	C₁₃×#121	D₄	1	2	yes	—
150	C₁₃×#121	D₄	1	2	yes	—
151	C₁₃×#121	C₂³	1	2	yes	—
152	C₁₃×#121	C₂³	1	4	yes	—
153	C₁₃×#121	C₂³	1	4	yes	—
154	C₄×Q₈×C₁₃	—	2	1	no	—
155	C₄×Q₈×C₁₃	—	2	1	no	—
156	C₄×Q₈×C₁₃	—	2	1	no	—
157	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
158	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
159	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
160	C₄×D₄×C₁₃	—	2	2	no	—
161	C₄×D₄×C₁₃	—	2	2	no	—
162	C₄×D₄×C₁₃	—	2	2	no	—
163	C₄×D₄×C₁₃	—	2	2	no	—
164	C₄×D₄×C₁₃	—	2	4	no	—
165	C₄×D₄×C₁₃	—	2	1	no	—
166	C₄×D₄×C₁₃	—	2	1	no	—
167	C₄×D₄×C₁₃	—	2	1	no	—
168	C₄×D₄×C₁₃	C₂³	1	2	yes	—
169	C₄×D₄×C₁₃	C₂³	1	2	yes	—
170	C₄×D₄×C₁₃	C₂³	1	2	yes	—
171	C₁₃×#117	—	2	1	no	—
172	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
173	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
174	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
175	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
176	C₂×C₄²×C₁₃	—	2	1	no	—
177	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
178	C₁₃×#106	C₂³	1	2	yes	—
179	C₁₃×#106	C₂³	1	2	yes	—
180	C₁₃×#106	C₂³	1	4	yes	—
181	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
182	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
183	C₁₃×#103	C₂³	1	2	yes	—
184	C₁₃×#103	C₂³	1	4	yes	—
185	C₁₃×#103	C₂³	1	4	yes	—
186	C₁₃×#103	C₂³	1	4	yes	—
187	C₁₃×#103	C₂³	1	2	yes	—
188	C₁₃×#103	C₂³	1	4	yes	—
189	C₁₃×#102	C₂³	1	4	yes	—
190	C₁₃×#102	C₂³	1	4	yes	—
191	C₁₃×#102	C₂³	1	2	yes	—
192	C₁₃×#102	C₂³	1	2	yes	—
193	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
194	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
195	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
196	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
197	C₁₃×#97	C₂³	1	2	yes	—
198	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
199	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
200	#61686	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
201	C₁₃×#41	—	2	8	no	—
202	C₁₃×#41	—	4	4	no	—
203	C₁₃×#41	—	4	4	no	—
204	C₁₃×#41	—	4	4	no	—
205	C₁₃×#41	—	4	16	no	—
206	C₁₃×#41	—	4	4	no	—
207	C₁₃×#41	—	4	4	no	—
208	C₁₃×#41	—	4	8	no	—
209	C₁₃×#41	—	8	2	no	—
210	C₁₃×#41	—	8	4	no	—
211	C₂×Q₈×C₁₃	—	2	4	no	—
212	C₂×Q₈×C₁₃	—	2	1	no	—
213	C₂×Q₈×C₁₃	—	2	1	no	—
214	C₂×Q₈×C₁₃	—	2	4	no	—
215	C₂×Q₈×C₁₃	—	2	1	no	—
216	C₂×Q₈×C₁₃	—	2	8	no	—
217	C₂×Q₈×C₁₃	—	4	4	no	—
218	C₂×Q₈×C₁₃	—	4	8	no	—
219	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
220	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
221	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
222	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
223	C₂×D₄×C₁₃	—	2	2	no	—
224	C₂×D₄×C₁₃	—	2	4	no	—
225	C₂×D₄×C₁₃	—	2	4	no	—
226	C₂×D₄×C₁₃	—	2	2	no	—
227	C₂×D₄×C₁₃	—	2	4	no	—
228	C₂×D₄×C₁₃	—	2	4	no	—
229	C₂×D₄×C₁₃	—	2	1	no	—
230	C₂×D₄×C₁₃	—	2	1	no	—
231	C₂×D₄×C₁₃	—	2	1	no	—
232	C₂×D₄×C₁₃	—	2	1	no	—
233	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
234	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
235	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
236	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
237	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
238	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₁₃	—	2	1	no	—
240	C₂²×C₄×C₁₃	—	2	4	no	—
241	C₂²×C₄×C₁₃	—	2	1	no	—
242	C₂²×C₄×C₁₃	—	2	4	no	—
243	C₂²×C₄×C₁₃	—	2	2	no	—
244	C₂²×C₄×C₁₃	—	2	4	no	—
245	C₂²×C₄×C₁₃	—	2	2	no	—
246	C₂²×C₄×C₁₃	—	2	4	no	—
247	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
248	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
249	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
250	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
251	C₁₃×Q₁₆	—	2	8	no	—
252	C₁₃×Q₁₆	—	4	4	no	—
253	C₁₃×SD₁₆	—	2	4	no	—
254	C₁₃×SD₁₆	—	2	4	no	—
255	C₁₃×SD₁₆	—	4	4	no	—
256	C₁₃×SD₁₆	—	4	4	no	—
257	C₁₃×D₈	—	4	4	no	—
258	C₁₃×M₁₆	—	4	4	no	—
259	C₂×C₈×C₁₃	—	4	4	no	—
260	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
261	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
262	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
263	C₁₃×C₄⋊C₄	—	2	1	no	—
264	C₁₃×C₄⋊C₄	—	2	2	no	—
265	C₁₃×C₄⋊C₄	—	2	2	no	—
266	C₁₃×C₄⋊C₄	—	2	4	no	—
267	C₁₃×C₄⋊C₄	—	2	1	no	—
268	C₁₃×C₄⋊C₄	—	2	4	no	—
269	C₁₃×C₄⋊C₄	—	2	1	no	—
270	C₁₃×C₄⋊C₄	—	2	1	no	—
271	C₁₃×C₄⋊C₄	—	2	1	no	—
272	C₁₃×C₄⋊C₄	—	2	1	no	—
273	C₁₃×C₄⋊C₄	—	2	1	no	—
274	C₁₃×C₄⋊C₄	—	2	4	no	—
275	C₁₃×C₄⋊C₄	—	2	2	no	—
276	C₁₃×C₄⋊C₄	—	2	2	no	—
277	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
278	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
279	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
280	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
281	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
282	C₁₃×C₂²⋊C₄	—	2	2	no	—
283	C₁₃×C₂²⋊C₄	—	2	4	no	—
284	C₁₃×C₂²⋊C₄	—	2	4	no	—
285	C₁₃×C₂²⋊C₄	—	2	2	no	—
286	C₁₃×C₂²⋊C₄	—	2	2	no	—
287	C₁₃×C₂²⋊C₄	—	2	4	no	—
288	C₁₃×C₂²⋊C₄	—	2	4	no	—
289	C₁₃×C₂²⋊C₄	—	2	2	no	—
290	C₁₃×C₂²⋊C₄	—	2	2	no	—
291	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
292	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
293	C₄²×C₁₃	—	2	2	no	—
294	C₄²×C₁₃	—	2	2	no	—
295	C₄²×C₁₃	—	2	2	no	—
296	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
297	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
298	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
299	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
300	#3548	C₂×C₁₃	1	1	yes	characteristic, complemented
301	#3497	C₂×C₁₃	1	1	yes	characteristic, complemented
302	#3332	C₂×C₁₃	1	2	yes	complemented
303	#3316	C₂×C₁₃	1	4	yes	complemented
304	#3298	C₂×C₁₃	1	2	yes	complemented
305	#3284	C₂×C₁₃	1	2	yes	complemented
306	#3276	C₂×C₁₃	1	2	yes	complemented
307	#3271	C₂×C₁₃	1	4	yes	complemented
308	#3214	C₂×C₁₃	1	1	yes	characteristic, complemented
309	#3210	C₂×C₁₃	1	1	yes	characteristic, complemented
310	#3204	C₂×C₁₃	1	4	yes	complemented
311	#3113	C₂×C₁₃	1	1	yes	characteristic, complemented
312	#3103	C₂×C₁₃	1	1	yes	characteristic, complemented
313	#3013	C₂×C₁₃	1	4	yes	complemented
314	#2981	C₂×C₁₃	1	1	yes	characteristic, complemented
315	C₂³×C₁₃	—	2	2	no	—
316	C₂³×C₁₃	—	2	2	no	—
317	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
318	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
319	Q₈×C₁₃	—	2	4	no	—
320	Q₈×C₁₃	—	2	2	no	—
321	Q₈×C₁₃	—	2	4	no	—
322	Q₈×C₁₃	—	2	4	no	—
323	Q₈×C₁₃	—	4	2	no	—
324	Q₈×C₁₃	—	4	8	no	—
325	Q₈×C₁₃	—	4	2	no	—
326	Q₈×C₁₃	—	8	1	no	—
327	Q₈×C₁₃	H(5,𝔽₂)	1	4	yes	—
328	D₄×C₁₃	—	2	4	no	—
329	D₄×C₁₃	—	2	2	no	—
330	D₄×C₁₃	—	2	4	no	—
331	D₄×C₁₃	—	2	2	no	—
332	D₄×C₁₃	—	4	2	no	—
333	D₄×C₁₃	—	4	2	no	—
334	D₄×C₁₃	—	4	4	no	—
335	D₄×C₁₃	—	4	8	no	—
336	D₄×C₁₃	—	4	2	no	—
337	D₄×C₁₃	—	4	4	no	—
338	D₄×C₁₃	—	4	2	no	—
339	D₄×C₁₃	—	8	1	no	—
340	D₄×C₁₃	—	8	1	no	—
341	D₄×C₁₃	—	8	4	no	—
342	D₄×C₁₃	—	8	4	no	—
343	D₄×C₁₃	—	8	2	no	—
344	D₄×C₁₃	—	8	4	no	—
345	C₂×C₄×C₁₃	—	2	4	no	—
346	C₂×C₄×C₁₃	—	2	2	no	—
347	C₂×C₄×C₁₃	—	2	2	no	—
348	C₂×C₄×C₁₃	—	2	4	no	—
349	C₂×C₄×C₁₃	—	2	4	no	—
350	C₂×C₄×C₁₃	—	2	2	no	—
351	C₂×C₄×C₁₃	—	2	2	no	—
352	C₂×C₄×C₁₃	—	2	2	no	—
353	C₂×C₄×C₁₃	—	2	2	no	—
354	C₂×C₄×C₁₃	—	2	2	no	—
355	C₂×C₄×C₁₃	—	2	2	no	—
356	C₂×C₄×C₁₃	—	4	1	no	—
357	C₂×C₄×C₁₃	—	4	8	no	—
358	C₂×C₄×C₁₃	—	4	8	no	—
359	C₂×C₄×C₁₃	—	4	4	no	—
360	C₂×C₄×C₁₃	—	4	4	no	—
361	C₂×C₄×C₁₃	—	8	4	no	—
362	C₂×C₄×C₁₃	—	8	1	no	—
363	C₂×C₄×C₁₃	—	8	4	no	—
364	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
365	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
366	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
367	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
368	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
369	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
370	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
371	C₈×C₁₃	—	2	2	no	—
372	C₈×C₁₃	—	2	4	no	—
373	C₈×C₁₃	—	2	2	no	—
374	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	2	yes	—
375	C₂×#137	C₂²×C₁₃	1	4	yes	—
376	C₂×#135	C₂²×C₁₃	1	4	yes	—
377	#562	—	2	2	no	—
378	#554	—	2	1	no	—
379	#554	C₂²×C₁₃	1	2	yes	—
380	#550	—	2	1	no	—
381	#550	—	2	1	no	—
382	#550	C₂²×C₁₃	1	2	yes	—
383	#550	C₂²×C₁₃	1	2	yes	—
384	D₄×Q₈	—	2	1	no	—
385	D₄×Q₈	C₂²×C₁₃	1	2	yes	—
386	#548	—	2	2	no	—
387	#548	C₂²×C₁₃	1	4	yes	—
388	#547	C₂²×C₁₃	1	2	yes	—
389	#547	C₂²×C₁₃	1	2	yes	—
390	#540	—	2	2	no	—
391	#537	—	2	2	no	—
392	#537	—	2	2	no	—
393	#537	C₂²×C₁₃	1	2	yes	—
394	#537	C₂²×C₁₃	1	4	yes	—
395	#533	C₂²×C₁₃	1	1	yes	characteristic
396	#532	—	2	2	no	—
397	#532	C₂²×C₁₃	1	1	yes	characteristic
398	#532	C₂²×C₁₃	1	1	yes	characteristic
399	#532	C₂²×C₁₃	1	1	yes	characteristic
400	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
401	#496	C₂²×C₁₃	1	2	yes	—
402	#494	C₂²×C₁₃	1	1	yes	characteristic
403	#492	C₂²×C₁₃	1	1	yes	characteristic
404	#489	C₂²×C₁₃	1	2	yes	—
405	#487	C₂²×C₁₃	1	1	yes	characteristic
406	#486	C₂²×C₁₃	1	1	yes	characteristic
407	#483	C₂²×C₁₃	1	2	yes	—
408	#483	C₂²×C₁₃	1	4	yes	—
409	#481	C₂²×C₁₃	1	4	yes	—
410	#481	C₂²×C₁₃	1	2	yes	—
411	#475	C₂²×C₁₃	1	2	yes	—
412	#475	C₂²×C₁₃	1	2	yes	—
413	#470	C₂²×C₁₃	1	4	yes	—
414	#469	C₂²×C₁₃	1	4	yes	—
415	#465	C₂²×C₁₃	1	4	yes	—
416	#465	C₂²×C₁₃	1	4	yes	—
417	#464	C₂²×C₁₃	1	4	yes	—
418	#462	C₂²×C₁₃	1	2	yes	—
419	#461	C₂²×C₁₃	1	2	yes	—
420	#460	C₂²×C₁₃	1	2	yes	—
421	#459	C₂²×C₁₃	1	2	yes	—
422	#452	C₂²×C₁₃	1	4	yes	—
423	#452	C₂²×C₁₃	1	4	yes	—
424	#452	C₂²×C₁₃	1	4	yes	—
425	#451	C₂²×C₁₃	1	2	yes	—
426	#451	C₂²×C₁₃	1	4	yes	—
427	#449	C₂²×C₁₃	1	4	yes	—
428	#449	C₂²×C₁₃	1	4	yes	—
429	#449	C₂²×C₁₃	1	4	yes	—
430	#448	C₂²×C₁₃	1	2	yes	—
431	#448	C₂²×C₁₃	1	4	yes	—
432	#441	C₂²×C₁₃	1	4	yes	—
433	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
434	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
435	#436	C₂²×C₁₃	1	2	yes	—
436	#435	C₂²×C₁₃	1	4	yes	—
437	C₈×D₄	C₂²×C₁₃	1	2	yes	—
438	#432	C₂²×C₁₃	1	1	yes	characteristic
439	#431	C₂²×C₁₃	1	1	yes	characteristic
440	#417	C₂²×C₁₃	1	4	yes	—
441	C₂×#103	C₂²×C₁₃	1	4	yes	—
442	#408	C₂²×C₁₃	1	4	yes	—
443	C₂²×C₁₃	—	2	1	no	—
444	C₂²×C₁₃	—	2	4	no	—
445	C₂²×C₁₃	—	2	1	no	—
446	C₂²×C₁₃	—	2	4	no	—
447	C₂²×C₁₃	—	2	1	no	—
448	C₂²×C₁₃	—	2	4	no	—
449	C₂²×C₁₃	—	4	2	no	—
450	C₂²×C₁₃	—	4	2	no	—
451	C₂²×C₁₃	—	4	2	no	—
452	C₂²×C₁₃	—	4	2	no	—
453	C₂²×C₁₃	—	4	2	no	—
454	C₂²×C₁₃	—	4	2	no	—
455	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
456	C₄×C₁₃	—	2	1	no	—
457	C₄×C₁₃	—	2	1	no	—
458	C₄×C₁₃	—	2	4	no	—
459	C₄×C₁₃	—	2	1	no	—
460	C₄×C₁₃	—	2	4	no	—
461	C₄×C₁₃	—	2	1	no	—
462	C₄×C₁₃	—	4	2	no	—
463	C₄×C₁₃	—	4	2	no	—
464	C₄×C₁₃	—	4	2	no	—
465	C₄×C₁₃	—	4	2	no	—
466	C₄×C₁₃	—	4	2	no	—
467	C₄×C₁₃	#577	1	2	yes	—
468	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
469	2₋¹⁺⁴	—	4	8	no	—
470	C₂×#41	—	2	4	no	—
471	C₂×#41	—	2	2	no	—
472	C₂×#41	—	2	2	no	—
473	C₂×#41	—	2	1	no	—
474	C₂×#41	C₂³×C₁₃	1	4	yes	—
475	C₂×#41	C₂³×C₁₃	1	2	yes	—
476	C₂×#41	C₂³×C₁₃	1	4	yes	—
477	C₂×#41	C₂³×C₁₃	1	2	yes	—
478	C₂²×Q₈	—	2	2	no	—
479	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
480	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
481	#137	—	4	8	no	—
482	#135	—	4	8	no	—
483	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
484	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
485	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
486	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
487	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
488	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
489	C₂×D₈	C₂³×C₁₃	1	4	yes	—
490	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
491	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
492	C₄⋊Q₈	—	2	2	no	—
493	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
494	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
495	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
496	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
497	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
498	#127	—	2	2	no	—
499	#127	—	2	2	no	—
500	#127	D₄×C₁₃	1	1	yes	characteristic
501	#127	C₂³×C₁₃	1	1	yes	characteristic
502	#127	C₂³×C₁₃	1	1	yes	characteristic
503	#125	—	2	2	no	—
504	#125	—	2	1	no	—
505	#124	—	2	4	no	—
506	#124	—	2	1	no	—
507	#124	D₄×C₁₃	1	2	yes	—
508	#124	C₂³×C₁₃	1	2	yes	—
509	#123	—	2	4	no	—
510	#123	—	2	4	no	—
511	C₂²⋊Q₈	—	2	2	no	—
512	C₂²⋊Q₈	—	2	4	no	—
513	C₂²⋊Q₈	—	2	1	no	—
514	C₂²⋊Q₈	—	2	2	no	—
515	C₂²⋊Q₈	—	2	4	no	—
516	C₂²⋊Q₈	—	2	4	no	—
517	C₂²⋊Q₈	—	2	4	no	—
518	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
519	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
520	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
521	#121	—	2	4	no	—
522	#121	—	2	4	no	—
523	#121	—	2	4	no	—
524	#121	—	2	2	no	—
525	#121	—	2	4	no	—
526	#121	—	2	2	no	—
527	#121	—	2	4	no	—
528	#121	—	2	1	no	—
529	#121	—	2	1	no	—
530	#121	—	2	1	no	—
531	#121	—	2	4	no	—
532	#121	—	2	4	no	—
533	#121	D₄×C₁₃	1	2	yes	—
534	#121	D₄×C₁₃	1	2	yes	—
535	#121	C₂³×C₁₃	1	2	yes	—
536	#121	C₂³×C₁₃	1	4	yes	—
537	#121	C₂³×C₁₃	1	4	yes	—
538	C₄×Q₈	—	2	1	no	—
539	C₄×Q₈	—	2	1	no	—
540	C₄×Q₈	—	2	1	no	—
541	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
542	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
543	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
544	C₄×D₄	—	2	2	no	—
545	C₄×D₄	—	2	2	no	—
546	C₄×D₄	—	2	2	no	—
547	C₄×D₄	—	2	2	no	—
548	C₄×D₄	—	2	4	no	—
549	C₄×D₄	—	2	1	no	—
550	C₄×D₄	—	2	1	no	—
551	C₄×D₄	—	2	1	no	—
552	C₄×D₄	C₂³×C₁₃	1	2	yes	—
553	C₄×D₄	C₂³×C₁₃	1	2	yes	—
554	C₄×D₄	C₂³×C₁₃	1	2	yes	—
555	#117	—	2	1	no	—
556	C₂×C₄⋊C₄	—	2	1	no	—
557	C₂×C₄⋊C₄	—	2	2	no	—
558	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
559	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
560	C₂×C₄²	—	2	1	no	—
561	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
562	#106	C₂³×C₁₃	1	2	yes	—
563	#106	C₂³×C₁₃	1	2	yes	—
564	#106	C₂³×C₁₃	1	4	yes	—
565	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
566	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
567	#103	C₂³×C₁₃	1	2	yes	—
568	#103	C₂³×C₁₃	1	4	yes	—
569	#103	C₂³×C₁₃	1	4	yes	—
570	#103	C₂³×C₁₃	1	4	yes	—
571	#103	C₂³×C₁₃	1	2	yes	—
572	#103	C₂³×C₁₃	1	4	yes	—
573	#102	C₂³×C₁₃	1	4	yes	—
574	#102	C₂³×C₁₃	1	4	yes	—
575	#102	C₂³×C₁₃	1	2	yes	—
576	#102	C₂³×C₁₃	1	2	yes	—
577	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
578	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
579	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
580	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
581	#97	C₂³×C₁₃	1	2	yes	—
582	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
583	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
584	C₂×C₁₃	—	4	1	no	—
585	C₂×C₁₃	—	4	4	no	—
586	C₂×C₁₃	—	8	2	no	—
587	C₂×C₁₃	—	8	2	no	—
588	C₂×C₁₃	#3484	1	1	yes	characteristic
589	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
590	C₂×C₁₃	#3586	1	1	yes	characteristic
591	#41	—	2	8	no	—
592	#41	—	4	4	no	—
593	#41	—	4	4	no	—
594	#41	—	4	4	no	—
595	#41	—	4	16	no	—
596	#41	—	4	4	no	—
597	#41	—	4	4	no	—
598	#41	—	4	8	no	—
599	#41	—	8	2	no	—
600	#41	—	8	4	no	—
601	C₂×Q₈	—	2	4	no	—
602	C₂×Q₈	—	2	1	no	—
603	C₂×Q₈	—	2	1	no	—
604	C₂×Q₈	—	2	4	no	—
605	C₂×Q₈	—	2	1	no	—
606	C₂×Q₈	—	2	8	no	—
607	C₂×Q₈	—	4	4	no	—
608	C₂×Q₈	—	4	8	no	—
609	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
610	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
611	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
612	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
613	C₂×D₄	—	2	2	no	—
614	C₂×D₄	—	2	4	no	—
615	C₂×D₄	—	2	4	no	—
616	C₂×D₄	—	2	2	no	—
617	C₂×D₄	—	2	4	no	—
618	C₂×D₄	—	2	4	no	—
619	C₂×D₄	—	2	1	no	—
620	C₂×D₄	—	2	1	no	—
621	C₂×D₄	—	2	1	no	—
622	C₂×D₄	—	2	1	no	—
623	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
624	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
625	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
626	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
627	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
628	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
629	C₂²×C₄	—	2	1	no	—
630	C₂²×C₄	—	2	4	no	—
631	C₂²×C₄	—	2	1	no	—
632	C₂²×C₄	—	2	4	no	—
633	C₂²×C₄	—	2	2	no	—
634	C₂²×C₄	—	2	4	no	—
635	C₂²×C₄	—	2	2	no	—
636	C₂²×C₄	—	2	4	no	—
637	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
638	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
639	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
640	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
641	Q₁₆	—	2	8	no	—
642	Q₁₆	—	4	4	no	—
643	SD₁₆	—	2	4	no	—
644	SD₁₆	—	2	4	no	—
645	SD₁₆	—	4	4	no	—
646	SD₁₆	—	4	4	no	—
647	D₈	—	4	4	no	—
648	M₁₆	—	4	4	no	—
649	C₂×C₈	—	4	4	no	—
650	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
651	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
652	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
653	C₄⋊C₄	—	2	1	no	—
654	C₄⋊C₄	—	2	2	no	—
655	C₄⋊C₄	—	2	2	no	—
656	C₄⋊C₄	—	2	4	no	—
657	C₄⋊C₄	—	2	1	no	—
658	C₄⋊C₄	—	2	4	no	—
659	C₄⋊C₄	—	2	1	no	—
660	C₄⋊C₄	—	2	1	no	—
661	C₄⋊C₄	—	2	1	no	—
662	C₄⋊C₄	—	2	1	no	—
663	C₄⋊C₄	—	2	1	no	—
664	C₄⋊C₄	—	2	4	no	—
665	C₄⋊C₄	—	2	2	no	—
666	C₄⋊C₄	—	2	2	no	—
667	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
668	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
669	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
670	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
671	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
672	C₂²⋊C₄	—	2	2	no	—
673	C₂²⋊C₄	—	2	4	no	—
674	C₂²⋊C₄	—	2	4	no	—
675	C₂²⋊C₄	—	2	2	no	—
676	C₂²⋊C₄	—	2	2	no	—
677	C₂²⋊C₄	—	2	4	no	—
678	C₂²⋊C₄	—	2	4	no	—
679	C₂²⋊C₄	—	2	2	no	—
680	C₂²⋊C₄	—	2	2	no	—
681	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
682	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
683	C₄²	—	2	2	no	—
684	C₄²	—	2	2	no	—
685	C₄²	—	2	2	no	—
686	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
687	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
688	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
689	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
690	C₁₃	#61686	1	1	yes	characteristic, direct product factor, Sylow
691	C₂³	—	2	2	no	—
692	C₂³	—	2	2	no	—
693	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
694	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
695	Q₈	—	2	4	no	—
696	Q₈	—	2	2	no	—
697	Q₈	—	2	4	no	—
698	Q₈	—	2	4	no	—
699	Q₈	—	4	2	no	—
700	Q₈	—	4	8	no	—
701	Q₈	—	4	2	no	—
702	Q₈	—	8	1	no	—
703	Q₈	C₁₃×H(5,𝔽₂)	1	4	yes	—
704	D₄	—	2	4	no	—
705	D₄	—	2	2	no	—
706	D₄	—	2	4	no	—
707	D₄	—	2	2	no	—
708	D₄	—	4	2	no	—
709	D₄	—	4	2	no	—
710	D₄	—	4	4	no	—
711	D₄	—	4	8	no	—
712	D₄	—	4	2	no	—
713	D₄	—	4	4	no	—
714	D₄	—	4	2	no	—
715	D₄	—	8	1	no	—
716	D₄	—	8	1	no	—
717	D₄	—	8	4	no	—
718	D₄	—	8	4	no	—
719	D₄	—	8	2	no	—
720	D₄	—	8	4	no	—
721	C₂×C₄	—	2	4	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	4	no	—
725	C₂×C₄	—	2	4	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	4	1	no	—
733	C₂×C₄	—	4	8	no	—
734	C₂×C₄	—	4	8	no	—
735	C₂×C₄	—	4	4	no	—
736	C₂×C₄	—	4	4	no	—
737	C₂×C₄	—	8	4	no	—
738	C₂×C₄	—	8	1	no	—
739	C₂×C₄	—	8	4	no	—
740	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
741	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
742	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
743	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
744	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
745	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
746	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
747	C₈	—	2	2	no	—
748	C₈	—	2	4	no	—
749	C₈	—	2	2	no	—
750	C₂²	—	2	1	no	—
751	C₂²	—	2	4	no	—
752	C₂²	—	2	1	no	—
753	C₂²	—	2	4	no	—
754	C₂²	—	2	1	no	—
755	C₂²	—	2	4	no	—
756	C₂²	—	4	2	no	—
757	C₂²	—	4	2	no	—
758	C₂²	—	4	2	no	—
759	C₂²	—	4	2	no	—
760	C₂²	—	4	2	no	—
761	C₂²	—	4	2	no	—
762	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
763	C₄	—	2	1	no	—
764	C₄	—	2	1	no	—
765	C₄	—	2	1	no	—
766	C₄	—	2	4	no	—
767	C₄	—	2	1	no	—
768	C₄	—	2	4	no	—
769	C₄	—	4	2	no	—
770	C₄	—	4	2	no	—
771	C₄	—	4	2	no	—
772	C₄	—	4	2	no	—
773	C₄	—	4	2	no	—
774	C₄	C₁₃×#577	1	2	yes	—
775	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
776	C₂	—	4	1	no	—
777	C₂	—	4	4	no	—
778	C₂	—	8	2	no	—
779	C₂	—	8	2	no	—
780	C₂	C₁₃×#3484	1	1	yes	characteristic
781	C₂	C₂×C₁₃×#577	1	1	yes	characteristic
782	C₂	C₁₃×#3586	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. C₁₃×#3548	C₂	semidirect
2. C₁₃×#3497	C₂	semidirect
3. C₁₃×#3332	C₂	semidirect
4. C₁₃×#3316	C₂	semidirect
5. C₁₃×#3298	C₂	semidirect
6. C₁₃×#3284	C₂	semidirect
7. C₁₃×#3276	C₂	semidirect
8. C₁₃×#3271	C₂	semidirect
9. C₁₃×#3214	C₂	semidirect
10. C₁₃×#3210	C₂	semidirect
11. C₁₃×#3204	C₂	semidirect
12. C₁₃×#3113	C₂	semidirect
13. C₁₃×#3103	C₂	semidirect
14. C₁₃×#3013	C₂	semidirect
15. C₁₃×#2981	C₂	semidirect
200. #61686	C₁₃	direct (N × H)
300. #3548	C₂×C₁₃	semidirect
301. #3497	C₂×C₁₃	semidirect
302. #3332	C₂×C₁₃	semidirect
303. #3316	C₂×C₁₃	semidirect
304. #3298	C₂×C₁₃	semidirect
305. #3284	C₂×C₁₃	semidirect
306. #3276	C₂×C₁₃	semidirect
307. #3271	C₂×C₁₃	semidirect
308. #3214	C₂×C₁₃	semidirect
309. #3210	C₂×C₁₃	semidirect
310. #3204	C₂×C₁₃	semidirect
311. #3113	C₂×C₁₃	semidirect
312. #3103	C₂×C₁₃	semidirect
313. #3013	C₂×C₁₃	semidirect
314. #2981	C₂×C₁₃	semidirect
690. C₁₃	#61686	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×#3548	2
C₁₃×#3497	2
C₁₃×#3332	2
C₁₃×#3316	2
C₁₃×#3298	2
C₁₃×#3284	2
C₁₃×#3276	2
C₁₃×#3271	2
C₁₃×#3214	2
C₁₃×#3210	2
C₁₃×#3204	2
C₁₃×#3113	2
C₁₃×#3103	2
C₁₃×#3013	2
C₁₃×#2981	2
#61686	13

Subgroups — C13×#61686 #15748025

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61686 #15748025