Subgroups — C₁₃×#61697 #15748036

Order 3328.

2082 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3496	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#554	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3335	C₂	1	8	yes	maximal, complemented
4	C₁₃×#3295	C₂	1	8	yes	maximal, complemented
5	C₁₃×#3227	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3187	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3103	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×#481	C₂	1	4	yes	maximal, complemented
9	C₁₃×#2972	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×H(5,𝔽₂)	—	2	1	no	—
11	C₁₃×#554	—	2	4	no	—
12	C₁₃×#554	C₂²	1	8	yes	complemented
13	C₁₃×#547	C₂²	1	4	yes	—
14	C₁₃×#546	—	2	4	no	—
15	D₄²×C₁₃	C₂²	1	4	yes	—
16	C₁₃×#537	—	2	1	no	—
17	C₁₃×#534	—	2	2	no	—
18	C₁₃×#532	C₂²	1	2	yes	—
19	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
20	C₂×C₁₃×#125	—	2	1	no	—
21	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
22	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
23	C₂×C₁₃×#121	C₂²	1	4	yes	—
24	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₄×D₄×C₁₃	—	2	1	no	—
26	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
27	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
28	C₁₃×#498	C₂²	1	4	yes	complemented
29	C₁₃×#486	C₂²	1	4	yes	complemented
30	C₁₃×#483	C₂²	1	8	yes	complemented
31	C₁₃×#481	C₂²	1	16	yes	complemented
32	C₁₃×#481	C₂²	1	4	yes	complemented
33	C₁₃×#481	C₂²	1	8	yes	complemented
34	C₁₃×#476	C₂²	1	8	yes	complemented
35	C₁₃×#475	C₂²	1	4	yes	complemented
36	C₁₃×#465	C₂²	1	16	yes	complemented
37	C₁₃×#460	C₂²	1	4	yes	complemented
38	C₁₃×#450	C₂²	1	8	yes	complemented
39	C₁₃×#448	C₂²	1	4	yes	complemented
40	C₄×C₁₃×SD₁₆	C₂²	1	8	yes	complemented
41	C₈×D₄×C₁₃	C₂²	1	8	yes	complemented
42	C₁₃×#431	C₂²	1	2	yes	complemented
43	C₂×C₁₃×#106	C₂²	1	8	yes	complemented
44	C₂×C₁₃×#102	C₂²	1	8	yes	complemented
45	C₂×C₁₃×C₂²⋊C₈	C₂²	1	4	yes	complemented
46	C₁₃×H(5,𝔽₂)	—	4	8	no	—
47	C₂×C₁₃×#41	—	2	4	no	—
48	C₂×C₁₃×#41	—	2	2	no	—
49	C₂²×Q₈×C₁₃	—	2	1	no	—
50	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
51	C₂²×D₄×C₁₃	—	2	4	no	—
52	C₂²×D₄×C₁₃	—	2	4	no	—
53	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
54	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
55	C₂³×C₄×C₁₃	—	2	2	no	—
56	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
57	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
58	C₂²×C₈×C₁₃	C₂³	1	8	yes	—
59	C₁₃×C₄⋊Q₈	—	2	2	no	—
60	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
61	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
62	C₁₃×#127	C₂³	1	2	yes	—
63	C₁₃×#125	—	2	8	no	—
64	C₁₃×#124	—	2	2	no	—
65	C₁₃×#123	—	2	8	no	—
66	C₁₃×C₂²⋊Q₈	—	2	4	no	—
67	C₁₃×C₂²⋊Q₈	—	2	4	no	—
68	C₁₃×C₂²⋊Q₈	—	2	16	no	—
69	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
70	C₁₃×#121	—	2	4	no	—
71	C₁₃×#121	—	2	4	no	—
72	C₁₃×#121	—	2	2	no	—
73	C₁₃×#121	—	2	4	no	—
74	C₁₃×#121	C₂³	1	4	yes	—
75	C₁₃×#121	C₂³	1	8	yes	—
76	C₁₃×#120	—	2	8	no	—
77	C₄×Q₈×C₁₃	—	2	2	no	—
78	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
79	C₄×D₄×C₁₃	—	2	8	no	—
80	C₄×D₄×C₁₃	—	2	2	no	—
81	C₄×D₄×C₁₃	D₄	1	4	yes	—
82	C₄×D₄×C₁₃	C₂³	1	4	yes	—
83	C₄×D₄×C₁₃	C₂³	1	4	yes	—
84	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
85	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
86	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
87	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
88	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
89	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
90	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
91	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
92	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
93	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
94	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
95	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
96	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
97	C₂×C₄²×C₁₃	—	2	1	no	—
98	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
99	C₁₃×#106	C₂³	1	8	yes	—
100	C₁₃×#106	C₂³	1	16	yes	—
101	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
102	C₁₃×#103	C₂³	1	8	yes	—
103	C₁₃×#102	C₂³	1	8	yes	—
104	C₁₃×#102	C₂³	1	16	yes	—
105	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
106	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	—
107	C₄×C₈×C₁₃	C₂³	1	4	yes	—
108	#61697	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
109	C₂⁴×C₁₃	—	2	4	no	—
110	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
111	C₁₃×#41	—	4	16	no	—
112	C₁₃×#41	—	4	8	no	—
113	C₂×Q₈×C₁₃	—	2	1	no	—
114	C₂×Q₈×C₁₃	—	2	2	no	—
115	C₂×Q₈×C₁₃	—	2	4	no	—
116	C₂×Q₈×C₁₃	—	4	2	no	—
117	C₂×Q₈×C₁₃	—	8	2	no	—
118	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
119	C₂×D₄×C₁₃	—	2	8	no	—
120	C₂×D₄×C₁₃	—	2	4	no	—
121	C₂×D₄×C₁₃	—	2	2	no	—
122	C₂×D₄×C₁₃	—	2	2	no	—
123	C₂×D₄×C₁₃	—	2	4	no	—
124	C₂×D₄×C₁₃	—	4	8	no	—
125	C₂×D₄×C₁₃	—	4	16	no	—
126	C₂×D₄×C₁₃	—	4	16	no	—
127	C₂×D₄×C₁₃	SD₁₆	1	8	yes	complemented
128	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
129	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
130	C₂²×C₄×C₁₃	—	2	1	no	—
131	C₂²×C₄×C₁₃	—	2	1	no	—
132	C₂²×C₄×C₁₃	—	2	2	no	—
133	C₂²×C₄×C₁₃	—	2	4	no	—
134	C₂²×C₄×C₁₃	—	2	8	no	—
135	C₂²×C₄×C₁₃	—	2	4	no	—
136	C₂²×C₄×C₁₃	—	4	4	no	—
137	C₂²×C₄×C₁₃	—	8	4	no	—
138	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
140	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
141	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
143	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
144	C₁₃×SD₁₆	—	4	8	no	—
145	C₂×C₈×C₁₃	—	4	8	no	—
146	C₂×C₈×C₁₃	C₂⁴	1	8	yes	—
147	C₁₃×C₄⋊C₄	—	2	1	no	—
148	C₁₃×C₄⋊C₄	—	2	8	no	—
149	C₁₃×C₄⋊C₄	—	2	2	no	—
150	C₁₃×C₄⋊C₄	—	2	4	no	—
151	C₁₃×C₄⋊C₄	—	2	4	no	—
152	C₁₃×C₄⋊C₄	—	2	8	no	—
153	C₁₃×C₄⋊C₄	—	2	4	no	—
154	C₁₃×C₄⋊C₄	—	2	2	no	—
155	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
156	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
157	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
158	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
159	C₁₃×C₂²⋊C₄	—	2	8	no	—
160	C₁₃×C₂²⋊C₄	—	2	4	no	—
161	C₁₃×C₂²⋊C₄	—	2	8	no	—
162	C₁₃×C₂²⋊C₄	—	2	4	no	—
163	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
164	C₄²×C₁₃	—	2	4	no	—
165	C₄²×C₁₃	C₂×D₄	1	2	yes	—
166	C₄²×C₁₃	C₂⁴	1	2	yes	—
167	#3496	C₂×C₁₃	1	1	yes	characteristic
168	C₂×#554	C₂×C₁₃	1	1	yes	characteristic, complemented
169	#3335	C₂×C₁₃	1	8	yes	complemented
170	#3295	C₂×C₁₃	1	8	yes	complemented
171	#3227	C₂×C₁₃	1	2	yes	complemented
172	#3187	C₂×C₁₃	1	4	yes	complemented
173	#3103	C₂×C₁₃	1	2	yes	complemented
174	C₂×#481	C₂×C₁₃	1	4	yes	complemented
175	#2972	C₂×C₁₃	1	1	yes	characteristic, complemented
176	C₂³×C₁₃	—	2	4	no	—
177	C₂³×C₁₃	—	4	2	no	—
178	C₂³×C₁₃	—	4	2	no	—
179	C₂³×C₁₃	—	4	8	no	—
180	C₂³×C₁₃	—	8	4	no	—
181	C₂³×C₁₃	—	8	4	no	—
182	C₂³×C₁₃	C₂×SD₁₆	1	8	yes	—
183	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
184	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
185	Q₈×C₁₃	—	2	4	no	—
186	Q₈×C₁₃	—	4	2	no	—
187	Q₈×C₁₃	—	4	4	no	—
188	Q₈×C₁₃	—	8	4	no	—
189	D₄×C₁₃	—	2	8	no	—
190	D₄×C₁₃	—	4	16	no	—
191	D₄×C₁₃	—	4	8	no	—
192	D₄×C₁₃	—	4	4	no	—
193	D₄×C₁₃	—	8	2	no	—
194	D₄×C₁₃	—	8	4	no	—
195	D₄×C₁₃	C₂×SD₁₆	1	16	yes	—
196	C₂×C₄×C₁₃	—	2	8	no	—
197	C₂×C₄×C₁₃	—	2	2	no	—
198	C₂×C₄×C₁₃	—	2	2	no	—
199	C₂×C₄×C₁₃	—	2	2	no	—
200	C₂×C₄×C₁₃	—	2	4	no	—
201	C₂×C₄×C₁₃	—	2	4	no	—
202	C₂×C₄×C₁₃	—	4	4	no	—
203	C₂×C₄×C₁₃	—	4	2	no	—
204	C₂×C₄×C₁₃	—	4	1	no	—
205	C₂×C₄×C₁₃	—	4	2	no	—
206	C₂×C₄×C₁₃	—	4	4	no	—
207	C₂×C₄×C₁₃	—	4	2	no	—
208	C₂×C₄×C₁₃	—	4	8	no	—
209	C₂×C₄×C₁₃	—	4	8	no	—
210	C₂×C₄×C₁₃	—	8	8	no	—
211	C₂×C₄×C₁₃	C₂×SD₁₆	1	4	yes	—
212	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
213	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
214	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
215	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
216	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
217	C₈×C₁₃	—	2	8	no	—
218	C₂×H(5,𝔽₂)	—	2	1	no	—
219	#554	—	2	4	no	—
220	#554	C₂²×C₁₃	1	8	yes	complemented
221	#547	C₂²×C₁₃	1	4	yes	—
222	#546	—	2	4	no	—
223	D₄²	C₂²×C₁₃	1	4	yes	—
224	#537	—	2	1	no	—
225	#534	—	2	2	no	—
226	#532	C₂²×C₁₃	1	2	yes	—
227	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
228	C₂×#125	—	2	1	no	—
229	C₂×C₂²⋊Q₈	—	2	2	no	—
230	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
231	C₂×#121	C₂²×C₁₃	1	4	yes	—
232	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
233	C₂×C₄×D₄	—	2	1	no	—
234	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
235	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
236	#498	C₂²×C₁₃	1	4	yes	complemented
237	#486	C₂²×C₁₃	1	4	yes	complemented
238	#483	C₂²×C₁₃	1	8	yes	complemented
239	#481	C₂²×C₁₃	1	16	yes	complemented
240	#481	C₂²×C₁₃	1	4	yes	complemented
241	#481	C₂²×C₁₃	1	8	yes	complemented
242	#476	C₂²×C₁₃	1	8	yes	complemented
243	#475	C₂²×C₁₃	1	4	yes	complemented
244	#465	C₂²×C₁₃	1	16	yes	complemented
245	#460	C₂²×C₁₃	1	4	yes	complemented
246	#450	C₂²×C₁₃	1	8	yes	complemented
247	#448	C₂²×C₁₃	1	4	yes	complemented
248	C₄×SD₁₆	C₂²×C₁₃	1	8	yes	complemented
249	C₈×D₄	C₂²×C₁₃	1	8	yes	complemented
250	#431	C₂²×C₁₃	1	2	yes	complemented
251	C₂×#106	C₂²×C₁₃	1	8	yes	complemented
252	C₂×#102	C₂²×C₁₃	1	8	yes	complemented
253	C₂×C₂²⋊C₈	C₂²×C₁₃	1	4	yes	complemented
254	C₂²×C₁₃	—	2	1	no	—
255	C₂²×C₁₃	—	2	4	no	—
256	C₂²×C₁₃	—	2	1	no	—
257	C₂²×C₁₃	—	2	4	no	—
258	C₂²×C₁₃	—	4	8	no	—
259	C₂²×C₁₃	—	4	4	no	—
260	C₂²×C₁₃	—	4	4	no	—
261	C₂²×C₁₃	—	4	4	no	—
262	C₂²×C₁₃	—	16	8	no	—
263	C₂²×C₁₃	C₂²×SD₁₆	1	8	yes	—
264	C₂²×C₁₃	C₂²×SD₁₆	1	2	yes	—
265	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
266	C₄×C₁₃	—	2	2	no	—
267	C₄×C₁₃	—	2	1	no	—
268	C₄×C₁₃	—	2	4	no	—
269	C₄×C₁₃	—	4	2	no	—
270	C₄×C₁₃	—	4	4	no	—
271	C₄×C₁₃	—	4	2	no	—
272	C₄×C₁₃	—	4	4	no	—
273	C₄×C₁₃	C₂²×SD₁₆	1	4	yes	—
274	C₄×C₁₃	#585	1	2	yes	—
275	H(5,𝔽₂)	—	4	8	no	—
276	C₂×#41	—	2	4	no	—
277	C₂×#41	—	2	2	no	—
278	C₂²×Q₈	—	2	1	no	—
279	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
280	C₂²×D₄	—	2	4	no	—
281	C₂²×D₄	—	2	4	no	—
282	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
283	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
284	C₂³×C₄	—	2	2	no	—
285	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
286	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
287	C₂²×C₈	C₂³×C₁₃	1	8	yes	—
288	C₄⋊Q₈	—	2	2	no	—
289	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
290	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
291	#127	C₂³×C₁₃	1	2	yes	—
292	#125	—	2	8	no	—
293	#124	—	2	2	no	—
294	#123	—	2	8	no	—
295	C₂²⋊Q₈	—	2	4	no	—
296	C₂²⋊Q₈	—	2	4	no	—
297	C₂²⋊Q₈	—	2	16	no	—
298	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
299	#121	—	2	4	no	—
300	#121	—	2	4	no	—
301	#121	—	2	2	no	—
302	#121	—	2	4	no	—
303	#121	C₂³×C₁₃	1	4	yes	—
304	#121	C₂³×C₁₃	1	8	yes	—
305	#120	—	2	8	no	—
306	C₄×Q₈	—	2	2	no	—
307	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
308	C₄×D₄	—	2	8	no	—
309	C₄×D₄	—	2	2	no	—
310	C₄×D₄	D₄×C₁₃	1	4	yes	—
311	C₄×D₄	C₂³×C₁₃	1	4	yes	—
312	C₄×D₄	C₂³×C₁₃	1	4	yes	—
313	C₂×C₄⋊C₄	—	2	2	no	—
314	C₂×C₄⋊C₄	—	2	4	no	—
315	C₂×C₄⋊C₄	—	2	1	no	—
316	C₂×C₄⋊C₄	—	2	1	no	—
317	C₂×C₄⋊C₄	—	2	2	no	—
318	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
319	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
320	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
321	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
322	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
323	C₂×C₂²⋊C₄	—	2	2	no	—
324	C₂×C₂²⋊C₄	—	2	4	no	—
325	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
326	C₂×C₄²	—	2	1	no	—
327	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
328	#106	C₂³×C₁₃	1	8	yes	—
329	#106	C₂³×C₁₃	1	16	yes	—
330	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
331	#103	C₂³×C₁₃	1	8	yes	—
332	#102	C₂³×C₁₃	1	8	yes	—
333	#102	C₂³×C₁₃	1	16	yes	—
334	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
335	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
336	C₄×C₈	C₂³×C₁₃	1	4	yes	—
337	C₂×C₁₃	—	2	2	no	—
338	C₂×C₁₃	—	2	8	no	—
339	C₂×C₁₃	—	8	4	no	—
340	C₂×C₁₃	#3485	1	1	yes	characteristic
341	C₂×C₁₃	C₂³×SD₁₆	1	1	yes	characteristic
342	C₂×C₁₃	#3585	1	1	yes	characteristic
343	C₂⁴	—	2	4	no	—
344	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
345	#41	—	4	16	no	—
346	#41	—	4	8	no	—
347	C₂×Q₈	—	2	1	no	—
348	C₂×Q₈	—	2	2	no	—
349	C₂×Q₈	—	2	4	no	—
350	C₂×Q₈	—	4	2	no	—
351	C₂×Q₈	—	8	2	no	—
352	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
353	C₂×D₄	—	2	8	no	—
354	C₂×D₄	—	2	4	no	—
355	C₂×D₄	—	2	2	no	—
356	C₂×D₄	—	2	2	no	—
357	C₂×D₄	—	2	4	no	—
358	C₂×D₄	—	4	8	no	—
359	C₂×D₄	—	4	16	no	—
360	C₂×D₄	—	4	16	no	—
361	C₂×D₄	C₁₃×SD₁₆	1	8	yes	complemented
362	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
363	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
364	C₂²×C₄	—	2	1	no	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	4	no	—
368	C₂²×C₄	—	2	8	no	—
369	C₂²×C₄	—	2	4	no	—
370	C₂²×C₄	—	4	4	no	—
371	C₂²×C₄	—	8	4	no	—
372	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
373	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
374	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
375	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
376	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
377	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
378	SD₁₆	—	4	8	no	—
379	C₂×C₈	—	4	8	no	—
380	C₂×C₈	C₂⁴×C₁₃	1	8	yes	—
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	2	8	no	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	—	2	4	no	—
385	C₄⋊C₄	—	2	4	no	—
386	C₄⋊C₄	—	2	8	no	—
387	C₄⋊C₄	—	2	4	no	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
390	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
391	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
392	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
393	C₂²⋊C₄	—	2	8	no	—
394	C₂²⋊C₄	—	2	4	no	—
395	C₂²⋊C₄	—	2	8	no	—
396	C₂²⋊C₄	—	2	4	no	—
397	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
398	C₄²	—	2	4	no	—
399	C₄²	C₂×D₄×C₁₃	1	2	yes	—
400	C₄²	C₂⁴×C₁₃	1	2	yes	—
401	C₁₃	#61697	1	1	yes	characteristic, direct product factor, Sylow
402	C₂³	—	2	4	no	—
403	C₂³	—	4	2	no	—
404	C₂³	—	4	2	no	—
405	C₂³	—	4	8	no	—
406	C₂³	—	8	4	no	—
407	C₂³	—	8	4	no	—
408	C₂³	C₂×C₁₃×SD₁₆	1	8	yes	—
409	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
410	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
411	Q₈	—	2	4	no	—
412	Q₈	—	4	2	no	—
413	Q₈	—	4	4	no	—
414	Q₈	—	8	4	no	—
415	D₄	—	2	8	no	—
416	D₄	—	4	16	no	—
417	D₄	—	4	8	no	—
418	D₄	—	4	4	no	—
419	D₄	—	8	4	no	—
420	D₄	—	8	2	no	—
421	D₄	C₂×C₁₃×SD₁₆	1	16	yes	—
422	C₂×C₄	—	2	8	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	4	no	—
427	C₂×C₄	—	2	4	no	—
428	C₂×C₄	—	4	4	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	1	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	4	4	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	8	no	—
435	C₂×C₄	—	4	8	no	—
436	C₂×C₄	—	8	8	no	—
437	C₂×C₄	C₂×C₁₃×SD₁₆	1	4	yes	—
438	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
439	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
440	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
441	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
442	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
443	C₈	—	2	8	no	—
444	C₂²	—	2	1	no	—
445	C₂²	—	2	4	no	—
446	C₂²	—	2	1	no	—
447	C₂²	—	2	4	no	—
448	C₂²	—	4	8	no	—
449	C₂²	—	4	4	no	—
450	C₂²	—	4	4	no	—
451	C₂²	—	4	4	no	—
452	C₂²	—	16	8	no	—
453	C₂²	C₂²×C₁₃×SD₁₆	1	8	yes	—
454	C₂²	C₂²×C₁₃×SD₁₆	1	2	yes	—
455	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
456	C₄	—	2	2	no	—
457	C₄	—	2	1	no	—
458	C₄	—	2	4	no	—
459	C₄	—	4	4	no	—
460	C₄	—	4	2	no	—
461	C₄	—	4	4	no	—
462	C₄	—	4	2	no	—
463	C₄	C₂²×C₁₃×SD₁₆	1	4	yes	—
464	C₄	C₁₃×#585	1	2	yes	—
465	C₂	—	2	2	no	—
466	C₂	—	2	8	no	—
467	C₂	—	8	4	no	—
468	C₂	C₁₃×#3485	1	1	yes	characteristic
469	C₂	C₂³×C₁₃×SD₁₆	1	1	yes	characteristic
470	C₂	C₁₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3496	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#554	C₂	semidirect
3. C₁₃×#3335	C₂	semidirect
4. C₁₃×#3295	C₂	semidirect
5. C₁₃×#3227	C₂	semidirect
6. C₁₃×#3187	C₂	semidirect
7. C₁₃×#3103	C₂	semidirect
8. C₂×C₁₃×#481	C₂	semidirect
9. C₁₃×#2972	C₂	semidirect
12. C₁₃×#554	C₂²	semidirect
19. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
22. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
24. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
27. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
28. C₁₃×#498	C₂²	semidirect
29. C₁₃×#486	C₂²	semidirect
30. C₁₃×#483	C₂²	semidirect
31. C₁₃×#481	C₂²	semidirect
32. C₁₃×#481	C₂²	semidirect
33. C₁₃×#481	C₂²	semidirect
34. C₁₃×#476	C₂²	semidirect
35. C₁₃×#475	C₂²	semidirect
36. C₁₃×#465	C₂²	semidirect
37. C₁₃×#460	C₂²	semidirect
38. C₁₃×#450	C₂²	semidirect
39. C₁₃×#448	C₂²	semidirect
40. C₄×C₁₃×SD₁₆	C₂²	semidirect
41. C₈×D₄×C₁₃	C₂²	semidirect
42. C₁₃×#431	C₂²	semidirect
43. C₂×C₁₃×#106	C₂²	semidirect
44. C₂×C₁₃×#102	C₂²	semidirect
45. C₂×C₁₃×C₂²⋊C₈	C₂²	semidirect
108. #61697	C₁₃	direct (N × H)
127. C₂×D₄×C₁₃	SD₁₆	semidirect
168. C₂×#554	C₂×C₁₃	semidirect
169. #3335	C₂×C₁₃	semidirect
170. #3295	C₂×C₁₃	semidirect
171. #3227	C₂×C₁₃	semidirect
172. #3187	C₂×C₁₃	semidirect
173. #3103	C₂×C₁₃	semidirect
174. C₂×#481	C₂×C₁₃	semidirect
175. #2972	C₂×C₁₃	semidirect
220. #554	C₂²×C₁₃	semidirect
227. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
230. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
232. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
235. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
236. #498	C₂²×C₁₃	semidirect
237. #486	C₂²×C₁₃	semidirect
238. #483	C₂²×C₁₃	semidirect
239. #481	C₂²×C₁₃	semidirect
240. #481	C₂²×C₁₃	semidirect
241. #481	C₂²×C₁₃	semidirect
242. #476	C₂²×C₁₃	semidirect
243. #475	C₂²×C₁₃	semidirect
244. #465	C₂²×C₁₃	semidirect
245. #460	C₂²×C₁₃	semidirect
246. #450	C₂²×C₁₃	semidirect
247. #448	C₂²×C₁₃	semidirect
248. C₄×SD₁₆	C₂²×C₁₃	semidirect
249. C₈×D₄	C₂²×C₁₃	semidirect
250. #431	C₂²×C₁₃	semidirect
251. C₂×#106	C₂²×C₁₃	semidirect
252. C₂×#102	C₂²×C₁₃	semidirect
253. C₂×C₂²⋊C₈	C₂²×C₁₃	semidirect
361. C₂×D₄	C₁₃×SD₁₆	semidirect
401. C₁₃	#61697	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×#3496	2
C₂×C₁₃×#554	2
C₁₃×#3335	2
C₁₃×#3295	2
C₁₃×#3227	2
C₁₃×#3187	2
C₁₃×#3103	2
C₂×C₁₃×#481	2
C₁₃×#2972	2
#61697	13

Subgroups — C13×#61697 #15748036

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61697 #15748036