Subgroups — C₁₃×#23730 #15710069

Order 3328.

1126 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#427	C₂	1	2	yes	maximal, complemented
2	C₂×C₁₃×#416	C₂	1	2	yes	maximal
3	C₁₃×#2297	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2285	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2097	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2096	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2095	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2094	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2093	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2092	C₂	1	2	yes	maximal, complemented
11	C₂×C₁₃×#336	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₁₃	C₂²	1	2	yes	—
14	C₂×C₁₃×#117	C₂²	1	2	yes	—
15	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
17	C₁₃×#427	—	2	8	no	—
18	C₂×C₁₃×#107	C₂²	1	2	yes	—
19	C₂×C₁₃×#107	C₂²	1	2	yes	—
20	C₂×C₁₃×#106	C₂²	1	2	yes	—
21	C₂×C₁₃×#106	C₂²	1	2	yes	—
22	C₁₃×#416	—	2	8	no	—
23	C₂×C₁₃×#103	C₂²	1	2	yes	—
24	C₂×C₁₃×#103	C₂²	1	2	yes	—
25	C₂×C₁₃×#102	C₂²	1	2	yes	—
26	C₂×C₁₃×#102	C₂²	1	2	yes	—
27	C₁₃×#391	C₂²	1	1	yes	characteristic
28	C₁₃×#391	C₂²	1	1	yes	characteristic
29	C₁₃×#390	C₂²	1	1	yes	characteristic
30	C₁₃×#390	C₂²	1	1	yes	characteristic
31	C₁₃×#386	—	2	2	no	—
32	C₁₃×#384	C₂²	1	1	yes	characteristic
33	C₁₃×#384	C₂²	1	1	yes	characteristic
34	C₁₃×#382	C₂²	1	2	yes	—
35	C₁₃×#380	—	2	2	no	—
36	C₄×C₁₃×C₄⋊C₄	—	2	2	no	—
37	C₄×C₁₃×C₂²⋊C₄	—	2	2	no	—
38	C₁₃×#336	C₂²	1	2	yes	—
39	C₁₃×#336	C₂²	1	1	yes	characteristic
40	C₁₃×#336	C₂²	1	1	yes	characteristic
41	C₂×C₁₃×#41	—	2	2	no	—
42	C₂×C₁₃×#41	—	2	4	no	—
43	C₂×C₁₃×#41	—	2	4	no	—
44	C₂×C₁₃×#41	Q₈	1	4	yes	—
45	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
46	C₂²×D₄×C₁₃	—	2	1	no	—
47	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
48	C₂³×C₄×C₁₃	—	2	1	no	—
49	C₂³×C₄×C₁₃	D₄	1	2	yes	—
50	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₁₃	—	2	4	no	—
52	C₂²×C₈×C₁₃	—	2	4	no	—
53	C₂²×C₈×C₁₃	D₄	1	8	yes	—
54	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
55	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
56	C₁₃×#117	—	2	4	no	—
57	C₁₃×#117	—	2	4	no	—
58	C₁₃×#117	—	2	4	no	—
59	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
60	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
61	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
62	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
63	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
64	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
65	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
66	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
67	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
68	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
69	C₂×C₄²×C₁₃	—	2	4	no	—
70	C₂×C₄²×C₁₃	—	2	1	no	—
71	C₂×C₄²×C₁₃	—	2	2	no	—
72	C₂×C₄²×C₁₃	D₄	1	2	yes	—
73	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
74	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
75	C₁₃×#107	—	2	4	no	—
76	C₁₃×#107	—	2	4	no	—
77	C₁₃×#106	—	2	4	no	—
78	C₁₃×#106	—	2	4	no	—
79	C₁₃×#103	—	2	4	no	—
80	C₁₃×#103	—	2	4	no	—
81	C₁₃×#102	—	2	4	no	—
82	C₁₃×#102	—	2	4	no	—
83	C₁₃×#95	—	2	2	no	—
84	C₁₃×#95	—	2	2	no	—
85	C₁₃×#95	—	2	4	no	—
86	#23730	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
87	C₂⁴×C₁₃	—	2	1	no	—
88	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
89	C₁₃×#41	—	2	16	no	—
90	C₁₃×#41	—	4	8	no	—
91	C₂×Q₈×C₁₃	—	2	1	no	—
92	C₂×Q₈×C₁₃	—	2	2	no	—
93	C₂×Q₈×C₁₃	—	2	2	no	—
94	C₂×Q₈×C₁₃	C₂×Q₈	1	2	yes	—
95	C₂×D₄×C₁₃	—	2	4	no	—
96	C₂×D₄×C₁₃	—	2	2	no	—
97	C₂×D₄×C₁₃	—	2	2	no	—
98	C₂×D₄×C₁₃	—	2	1	no	—
99	C₂×D₄×C₁₃	—	4	2	no	—
100	C₂×D₄×C₁₃	—	4	2	no	—
101	C₂×D₄×C₁₃	C₂×Q₈	1	2	yes	—
102	C₂²×C₄×C₁₃	—	2	4	no	—
103	C₂²×C₄×C₁₃	—	2	1	no	—
104	C₂²×C₄×C₁₃	—	2	4	no	—
105	C₂²×C₄×C₁₃	—	2	4	no	—
106	C₂²×C₄×C₁₃	—	2	1	no	—
107	C₂²×C₄×C₁₃	—	2	1	no	—
108	C₂²×C₄×C₁₃	—	2	2	no	—
109	C₂²×C₄×C₁₃	—	2	2	no	—
110	C₂²×C₄×C₁₃	—	4	2	no	—
111	C₂²×C₄×C₁₃	—	4	2	no	—
112	C₂²×C₄×C₁₃	—	4	2	no	—
113	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
116	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
118	C₂²×C₄×C₁₃	#41	1	4	yes	—
119	C₂²×C₄×C₁₃	#41	1	2	yes	—
120	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
121	C₂×C₈×C₁₃	—	2	16	no	—
122	C₂×C₈×C₁₃	—	2	2	no	—
123	C₂×C₈×C₁₃	—	2	2	no	—
124	C₂×C₈×C₁₃	—	2	2	no	—
125	C₂×C₈×C₁₃	—	2	2	no	—
126	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
127	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
128	C₁₃×C₄⋊C₄	—	2	2	no	—
129	C₁₃×C₄⋊C₄	—	2	2	no	—
130	C₁₃×C₄⋊C₄	—	2	2	no	—
131	C₁₃×C₄⋊C₄	—	2	2	no	—
132	C₁₃×C₄⋊C₄	—	2	2	no	—
133	C₁₃×C₄⋊C₄	—	2	2	no	—
134	C₁₃×C₄⋊C₄	—	4	4	no	—
135	C₁₃×C₄⋊C₄	—	4	4	no	—
136	C₁₃×C₂²⋊C₄	—	4	4	no	—
137	C₁₃×C₂²⋊C₄	—	4	4	no	—
138	C₁₃×C₂²⋊C₄	—	4	2	no	—
139	C₁₃×C₂²⋊C₄	—	4	4	no	—
140	C₄²×C₁₃	—	2	4	no	—
141	C₄²×C₁₃	—	2	2	no	—
142	C₄²×C₁₃	—	2	2	no	—
143	C₄²×C₁₃	—	4	2	no	—
144	C₄²×C₁₃	—	4	4	no	—
145	C₂×#427	C₂×C₁₃	1	2	yes	complemented
146	C₂×#416	C₂×C₁₃	1	2	yes	—
147	#2297	C₂×C₁₃	1	1	yes	characteristic
148	#2285	C₂×C₁₃	1	1	yes	characteristic, complemented
149	#2097	C₂×C₁₃	1	2	yes	complemented
150	#2096	C₂×C₁₃	1	1	yes	characteristic, complemented
151	#2095	C₂×C₁₃	1	1	yes	characteristic, complemented
152	#2094	C₂×C₁₃	1	1	yes	characteristic, complemented
153	#2093	C₂×C₁₃	1	1	yes	characteristic, complemented
154	#2092	C₂×C₁₃	1	2	yes	complemented
155	C₂×#336	C₂×C₁₃	1	1	yes	characteristic, complemented
156	C₂³×C₁₃	—	2	2	no	—
157	C₂³×C₁₃	—	2	2	no	—
158	C₂³×C₁₃	—	2	2	no	—
159	C₂³×C₁₃	—	4	1	no	—
160	C₂³×C₁₃	—	4	1	no	—
161	C₂³×C₁₃	—	4	2	no	—
162	C₂³×C₁₃	—	4	2	no	—
163	C₂³×C₁₃	C₂²⋊Q₈	1	2	yes	—
164	C₂³×C₁₃	#123	1	2	yes	—
165	C₂³×C₁₃	#127	1	2	yes	—
166	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
167	Q₈×C₁₃	—	2	4	no	—
168	Q₈×C₁₃	—	4	2	no	—
169	D₄×C₁₃	—	2	4	no	—
170	D₄×C₁₃	—	4	8	no	—
171	D₄×C₁₃	—	4	2	no	—
172	C₂×C₄×C₁₃	—	2	2	no	—
173	C₂×C₄×C₁₃	—	2	2	no	—
174	C₂×C₄×C₁₃	—	2	2	no	—
175	C₂×C₄×C₁₃	—	2	2	no	—
176	C₂×C₄×C₁₃	—	2	2	no	—
177	C₂×C₄×C₁₃	—	2	2	no	—
178	C₂×C₄×C₁₃	—	4	8	no	—
179	C₂×C₄×C₁₃	—	4	1	no	—
180	C₂×C₄×C₁₃	—	4	1	no	—
181	C₂×C₄×C₁₃	—	4	8	no	—
182	C₂×C₄×C₁₃	—	4	2	no	—
183	C₂×C₄×C₁₃	—	4	1	no	—
184	C₂×C₄×C₁₃	—	4	2	no	—
185	C₂×C₄×C₁₃	—	4	1	no	—
186	C₂×C₄×C₁₃	—	4	2	no	—
187	C₂×C₄×C₁₃	—	4	4	no	—
188	C₂×C₄×C₁₃	—	4	2	no	—
189	C₂×C₄×C₁₃	—	4	4	no	—
190	C₂×C₄×C₁₃	C₂²⋊Q₈	1	8	yes	—
191	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
192	C₂×C₄×C₁₃	#123	1	8	yes	—
193	C₂×C₄×C₁₃	#123	1	2	yes	—
194	C₂×C₄×C₁₃	#127	1	2	yes	—
195	C₂×C₄×C₁₃	#135	1	4	yes	—
196	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
197	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
198	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
199	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
200	C₈×C₁₃	—	2	4	no	—
201	C₈×C₁₃	—	2	4	no	—
202	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
203	C₂³×C₈	C₂²×C₁₃	1	2	yes	—
204	C₂×#117	C₂²×C₁₃	1	2	yes	—
205	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
206	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
207	#427	—	2	8	no	—
208	C₂×#107	C₂²×C₁₃	1	2	yes	—
209	C₂×#107	C₂²×C₁₃	1	2	yes	—
210	C₂×#106	C₂²×C₁₃	1	2	yes	—
211	C₂×#106	C₂²×C₁₃	1	2	yes	—
212	#416	—	2	8	no	—
213	C₂×#103	C₂²×C₁₃	1	2	yes	—
214	C₂×#103	C₂²×C₁₃	1	2	yes	—
215	C₂×#102	C₂²×C₁₃	1	2	yes	—
216	C₂×#102	C₂²×C₁₃	1	2	yes	—
217	#391	C₂²×C₁₃	1	1	yes	characteristic
218	#391	C₂²×C₁₃	1	1	yes	characteristic
219	#390	C₂²×C₁₃	1	1	yes	characteristic
220	#390	C₂²×C₁₃	1	1	yes	characteristic
221	#386	—	2	2	no	—
222	#384	C₂²×C₁₃	1	1	yes	characteristic
223	#384	C₂²×C₁₃	1	1	yes	characteristic
224	#382	C₂²×C₁₃	1	2	yes	—
225	#380	—	2	2	no	—
226	C₄×C₄⋊C₄	—	2	2	no	—
227	C₄×C₂²⋊C₄	—	2	2	no	—
228	#336	C₂²×C₁₃	1	2	yes	—
229	#336	C₂²×C₁₃	1	1	yes	characteristic
230	#336	C₂²×C₁₃	1	1	yes	characteristic
231	C₂²×C₁₃	—	2	4	no	—
232	C₂²×C₁₃	—	2	4	no	—
233	C₂²×C₁₃	—	2	2	no	—
234	C₂²×C₁₃	—	2	2	no	—
235	C₂²×C₁₃	—	4	4	no	—
236	C₂²×C₁₃	—	4	2	no	—
237	C₂²×C₁₃	—	8	2	no	—
238	C₂²×C₁₃	—	8	1	no	—
239	C₂²×C₁₃	—	8	1	no	—
240	C₂²×C₁₃	#399	1	4	yes	—
241	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
242	C₂²×C₁₃	C₂×#123	1	1	yes	characteristic
243	C₂²×C₁₃	C₂×#127	1	1	yes	characteristic
244	C₂²×C₁₃	C₂×#135	1	2	yes	—
245	C₂²×C₁₃	#575	1	2	yes	—
246	C₄×C₁₃	—	2	4	no	—
247	C₄×C₁₃	—	4	2	no	—
248	C₄×C₁₃	—	4	2	no	—
249	C₄×C₁₃	—	8	1	no	—
250	C₄×C₁₃	—	8	2	no	—
251	C₄×C₁₃	—	8	1	no	—
252	C₄×C₁₃	—	8	2	no	—
253	C₄×C₁₃	#399	1	4	yes	—
254	C₄×C₁₃	C₂×C₂²⋊Q₈	1	2	yes	—
255	C₄×C₁₃	C₂×#123	1	2	yes	—
256	C₂×#41	—	2	2	no	—
257	C₂×#41	—	2	4	no	—
258	C₂×#41	—	2	4	no	—
259	C₂×#41	Q₈×C₁₃	1	4	yes	—
260	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
261	C₂²×D₄	—	2	1	no	—
262	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
263	C₂³×C₄	—	2	1	no	—
264	C₂³×C₄	D₄×C₁₃	1	2	yes	—
265	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
266	C₂²×C₈	—	2	4	no	—
267	C₂²×C₈	—	2	4	no	—
268	C₂²×C₈	D₄×C₁₃	1	8	yes	—
269	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
270	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
271	#117	—	2	4	no	—
272	#117	—	2	4	no	—
273	#117	—	2	4	no	—
274	C₂×C₄⋊C₄	—	2	2	no	—
275	C₂×C₄⋊C₄	—	2	2	no	—
276	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
277	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
278	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
279	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
280	C₂×C₂²⋊C₄	—	2	2	no	—
281	C₂×C₂²⋊C₄	—	2	1	no	—
282	C₂×C₂²⋊C₄	—	2	2	no	—
283	C₂×C₂²⋊C₄	—	2	2	no	—
284	C₂×C₄²	—	2	4	no	—
285	C₂×C₄²	—	2	1	no	—
286	C₂×C₄²	—	2	2	no	—
287	C₂×C₄²	D₄×C₁₃	1	2	yes	—
288	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
289	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
290	#107	—	2	4	no	—
291	#107	—	2	4	no	—
292	#106	—	2	4	no	—
293	#106	—	2	4	no	—
294	#103	—	2	4	no	—
295	#103	—	2	4	no	—
296	#102	—	2	4	no	—
297	#102	—	2	4	no	—
298	#95	—	2	2	no	—
299	#95	—	2	2	no	—
300	#95	—	2	4	no	—
301	C₂×C₁₃	—	2	4	no	—
302	C₂×C₁₃	—	8	2	no	—
303	C₂×C₁₃	C₂×#399	1	1	yes	characteristic
304	C₂×C₁₃	#3076	1	2	yes	—
305	C₂×C₁₃	#3091	1	2	yes	—
306	C₂×C₁₃	#3147	1	1	yes	characteristic
307	C₂×C₁₃	#3150	1	1	yes	characteristic
308	C₂⁴	—	2	1	no	—
309	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
310	#41	—	2	16	no	—
311	#41	—	4	8	no	—
312	C₂×Q₈	—	2	1	no	—
313	C₂×Q₈	—	2	2	no	—
314	C₂×Q₈	—	2	2	no	—
315	C₂×Q₈	C₂×Q₈×C₁₃	1	2	yes	—
316	C₂×D₄	—	2	4	no	—
317	C₂×D₄	—	2	2	no	—
318	C₂×D₄	—	2	2	no	—
319	C₂×D₄	—	2	1	no	—
320	C₂×D₄	—	4	2	no	—
321	C₂×D₄	—	4	2	no	—
322	C₂×D₄	C₂×Q₈×C₁₃	1	2	yes	—
323	C₂²×C₄	—	2	4	no	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	4	no	—
326	C₂²×C₄	—	2	4	no	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	—	4	2	no	—
332	C₂²×C₄	—	4	2	no	—
333	C₂²×C₄	—	4	2	no	—
334	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
335	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
336	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
337	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
338	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
339	C₂²×C₄	C₁₃×#41	1	4	yes	—
340	C₂²×C₄	C₁₃×#41	1	2	yes	—
341	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
342	C₂×C₈	—	2	16	no	—
343	C₂×C₈	—	2	2	no	—
344	C₂×C₈	—	2	2	no	—
345	C₂×C₈	—	2	2	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
348	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	2	2	no	—
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	—	2	2	no	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	4	4	no	—
356	C₄⋊C₄	—	4	4	no	—
357	C₂²⋊C₄	—	4	4	no	—
358	C₂²⋊C₄	—	4	4	no	—
359	C₂²⋊C₄	—	4	2	no	—
360	C₂²⋊C₄	—	4	4	no	—
361	C₄²	—	2	4	no	—
362	C₄²	—	2	2	no	—
363	C₄²	—	2	2	no	—
364	C₄²	—	4	2	no	—
365	C₄²	—	4	4	no	—
366	C₁₃	#23730	1	1	yes	characteristic, direct product factor, Sylow
367	C₂³	—	2	2	no	—
368	C₂³	—	2	2	no	—
369	C₂³	—	2	2	no	—
370	C₂³	—	4	1	no	—
371	C₂³	—	4	1	no	—
372	C₂³	—	4	2	no	—
373	C₂³	—	4	2	no	—
374	C₂³	C₁₃×C₂²⋊Q₈	1	2	yes	—
375	C₂³	C₁₃×#123	1	2	yes	—
376	C₂³	C₁₃×#127	1	2	yes	—
377	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
378	Q₈	—	2	4	no	—
379	Q₈	—	4	2	no	—
380	D₄	—	2	4	no	—
381	D₄	—	4	8	no	—
382	D₄	—	4	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	4	8	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	8	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	4	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	4	no	—
401	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
402	C₂×C₄	C₁₃×C₂²⋊Q₈	1	8	yes	—
403	C₂×C₄	C₁₃×#123	1	2	yes	—
404	C₂×C₄	C₁₃×#123	1	8	yes	—
405	C₂×C₄	C₁₃×#127	1	2	yes	—
406	C₂×C₄	C₁₃×#135	1	4	yes	—
407	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
408	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
409	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
410	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
411	C₈	—	2	4	no	—
412	C₈	—	2	4	no	—
413	C₂²	—	2	4	no	—
414	C₂²	—	2	4	no	—
415	C₂²	—	2	2	no	—
416	C₂²	—	2	2	no	—
417	C₂²	—	4	4	no	—
418	C₂²	—	4	2	no	—
419	C₂²	—	8	2	no	—
420	C₂²	—	8	1	no	—
421	C₂²	—	8	1	no	—
422	C₂²	C₁₃×#399	1	4	yes	—
423	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
424	C₂²	C₂×C₁₃×#123	1	1	yes	characteristic
425	C₂²	C₂×C₁₃×#127	1	1	yes	characteristic
426	C₂²	C₂×C₁₃×#135	1	2	yes	—
427	C₂²	C₁₃×#575	1	2	yes	—
428	C₄	—	2	4	no	—
429	C₄	—	4	2	no	—
430	C₄	—	4	2	no	—
431	C₄	—	8	1	no	—
432	C₄	—	8	2	no	—
433	C₄	—	8	1	no	—
434	C₄	—	8	2	no	—
435	C₄	C₁₃×#399	1	4	yes	—
436	C₄	C₂×C₁₃×C₂²⋊Q₈	1	2	yes	—
437	C₄	C₂×C₁₃×#123	1	2	yes	—
438	C₂	—	2	4	no	—
439	C₂	—	8	2	no	—
440	C₂	C₂×C₁₃×#399	1	1	yes	characteristic
441	C₂	C₁₃×#3076	1	2	yes	—
442	C₂	C₁₃×#3091	1	2	yes	—
443	C₂	C₁₃×#3147	1	1	yes	characteristic
444	C₂	C₁₃×#3150	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
socle	C₂³×C₁₃	C₂²×D₄
prime radical	C₂²×C₁₃×#41	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#427	C₂	semidirect
4. C₁₃×#2285	C₂	semidirect
5. C₁₃×#2097	C₂	semidirect
6. C₁₃×#2096	C₂	semidirect
7. C₁₃×#2095	C₂	semidirect
8. C₁₃×#2094	C₂	semidirect
9. C₁₃×#2093	C₂	semidirect
10. C₁₃×#2092	C₂	semidirect
11. C₂×C₁₃×#336	C₂	semidirect
86. #23730	C₁₃	direct (N × H)
145. C₂×#427	C₂×C₁₃	semidirect
148. #2285	C₂×C₁₃	semidirect
149. #2097	C₂×C₁₃	semidirect
150. #2096	C₂×C₁₃	semidirect
151. #2095	C₂×C₁₃	semidirect
152. #2094	C₂×C₁₃	semidirect
153. #2093	C₂×C₁₃	semidirect
154. #2092	C₂×C₁₃	semidirect
155. C₂×#336	C₂×C₁₃	semidirect
366. C₁₃	#23730	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₃×#427	2
C₂×C₁₃×#416	2
C₁₃×#2297	2
C₁₃×#2285	2
C₁₃×#2097	2
C₁₃×#2096	2
C₁₃×#2095	2
C₁₃×#2094	2
C₁₃×#2093	2
C₁₃×#2092	2
C₂×C₁₃×#336	2
#23730	13

Subgroups — C13×#23730 #15710069

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#23730 #15710069