Subgroups — C₁₃×#60809 #15747148

Order 3328.

2034 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#541	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3449	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3223	C₂	1	8	yes	maximal, complemented
4	C₁₃×#3222	C₂	1	8	yes	maximal, complemented
5	C₁₃×#3152	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3142	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3037	C₂	1	4	yes	maximal, complemented
8	C₁₃×#3007	C₂	1	4	yes	maximal, complemented
9	C₁₃×#2921	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₁₃×#41	C₂²	1	2	yes	—
11	C₂×C₁₃×#137	C₂²	1	8	yes	complemented
12	C₁₃×#541	—	2	4	no	—
13	C₁₃×#541	C₂²	1	8	yes	complemented
14	C₁₃×#537	—	2	2	no	—
15	C₁₃×#536	C₂²	1	4	yes	—
16	C₁₃×#535	C₂²	1	4	yes	—
17	C₁₃×#534	—	2	2	no	—
18	C₁₃×#532	C₂²	1	2	yes	—
19	C₁₃×#532	C₂²	1	2	yes	—
20	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₁₃×#126	—	2	2	no	—
22	C₂×C₁₃×#125	—	2	2	no	—
23	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic, complemented
24	C₁₃×#525	—	2	4	no	—
25	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
26	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
27	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
28	C₁₃×#497	C₂²	1	8	yes	complemented
29	C₁₃×#494	C₂²	1	4	yes	complemented
30	C₁₃×#492	C₂²	1	4	yes	complemented
31	C₁₃×#491	C₂²	1	4	yes	complemented
32	C₁₃×#490	C₂²	1	4	yes	complemented
33	C₁₃×#488	C₂²	1	8	yes	complemented
34	C₁₃×#464	C₂²	1	16	yes	complemented
35	C₁₃×#462	C₂²	1	8	yes	complemented
36	C₁₃×#460	C₂²	1	8	yes	complemented
37	C₁₃×#452	C₂²	1	16	yes	—
38	C₁₃×#451	C₂²	1	8	yes	complemented
39	C₁₃×#450	C₂²	1	8	yes	complemented
40	C₁₃×#433	C₂²	1	8	yes	complemented
41	C₁₃×#423	C₂²	1	2	yes	complemented
42	C₁₃×#417	C₂²	1	8	yes	complemented
43	C₁₃×#407	C₂²	1	2	yes	—
44	C₄×C₁₃×M₁₆	C₂²	1	2	yes	complemented
45	C₂×C₁₃×#41	—	2	2	no	—
46	C₂×C₁₃×#41	—	2	2	no	—
47	C₂×C₁₃×#41	—	4	8	no	—
48	C₂×C₁₃×#41	C₂³	1	4	yes	—
49	C₂×C₁₃×#41	C₂³	1	4	yes	—
50	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
51	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
52	C₂²×D₄×C₁₃	—	2	2	no	—
53	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
54	C₂³×C₄×C₁₃	—	2	2	no	—
55	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
56	C₁₃×#137	—	4	16	no	—
57	C₂×C₁₃×Q₁₆	C₂³	1	16	yes	—
58	C₂×C₁₃×SD₁₆	C₂³	1	16	yes	—
59	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
60	C₁₃×C₄⋊Q₈	—	2	2	no	—
61	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
62	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
63	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
64	C₁₃×#127	C₂³	1	2	yes	—
65	C₁₃×#127	C₂³	1	2	yes	—
66	C₁₃×#126	—	2	16	no	—
67	C₁₃×#125	—	2	16	no	—
68	C₁₃×#125	—	2	2	no	—
69	C₁₃×#125	C₂³	1	4	yes	—
70	C₁₃×#124	C₂³	1	4	yes	—
71	C₁₃×#124	C₂³	1	4	yes	—
72	C₁₃×#123	—	2	8	no	—
73	C₁₃×C₂²⋊Q₈	—	2	4	no	—
74	C₁₃×C₂²⋊Q₈	—	2	8	no	—
75	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
76	C₁₃×#121	—	2	4	no	—
77	C₁₃×#121	—	2	4	no	—
78	C₁₃×#121	—	2	8	no	—
79	C₁₃×#120	—	2	8	no	—
80	C₄×Q₈×C₁₃	—	2	4	no	—
81	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
82	C₄×D₄×C₁₃	—	2	4	no	—
83	C₄×D₄×C₁₃	—	2	4	no	—
84	C₁₃×#117	D₄	1	4	yes	—
85	C₁₃×#117	C₂³	1	4	yes	—
86	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
87	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
88	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
89	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
90	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
91	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
92	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
93	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
94	C₂×C₄²×C₁₃	—	2	2	no	—
95	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
96	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
97	C₁₃×C₄⋊C₈	C₂³	1	8	yes	—
98	C₁₃×#103	C₂³	1	16	yes	—
99	C₁₃×#102	C₂³	1	16	yes	—
100	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	—
101	C₁₃×#97	C₂³	1	4	yes	—
102	C₄×C₈×C₁₃	C₂³	1	4	yes	—
103	#60809	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
104	C₂⁴×C₁₃	—	2	2	no	—
105	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
106	C₁₃×#41	—	2	16	no	—
107	C₁₃×#41	—	4	8	no	—
108	C₁₃×#41	—	4	8	no	—
109	C₁₃×#41	—	4	8	no	—
110	C₂×Q₈×C₁₃	—	2	2	no	—
111	C₂×Q₈×C₁₃	—	2	2	no	—
112	C₂×Q₈×C₁₃	—	2	8	no	—
113	C₂×Q₈×C₁₃	—	4	4	no	—
114	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
115	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
116	C₂×D₄×C₁₃	—	2	4	no	—
117	C₂×D₄×C₁₃	—	2	4	no	—
118	C₂×D₄×C₁₃	—	2	2	no	—
119	C₂×D₄×C₁₃	—	2	4	no	—
120	C₂×D₄×C₁₃	—	2	4	no	—
121	C₂×D₄×C₁₃	—	4	4	no	—
122	C₂×D₄×C₁₃	—	4	8	no	—
123	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
124	C₂²×C₄×C₁₃	—	2	4	no	—
125	C₂²×C₄×C₁₃	—	2	2	no	—
126	C₂²×C₄×C₁₃	—	2	2	no	—
127	C₂²×C₄×C₁₃	—	2	2	no	—
128	C₂²×C₄×C₁₃	—	2	4	no	—
129	C₂²×C₄×C₁₃	—	2	4	no	—
130	C₂²×C₄×C₁₃	—	4	8	no	—
131	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
133	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
134	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
135	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
136	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
137	C₁₃×Q₁₆	—	4	16	no	—
138	C₁₃×SD₁₆	—	4	16	no	—
139	C₁₃×M₁₆	—	2	8	no	—
140	C₂×C₈×C₁₃	C₂⁴	1	8	yes	—
141	C₁₃×C₄⋊C₄	—	2	8	no	—
142	C₁₃×C₄⋊C₄	—	2	8	no	—
143	C₁₃×C₄⋊C₄	—	2	8	no	—
144	C₁₃×C₄⋊C₄	—	2	8	no	—
145	C₁₃×C₄⋊C₄	—	2	2	no	—
146	C₁₃×C₄⋊C₄	—	2	4	no	—
147	C₁₃×C₄⋊C₄	—	2	4	no	—
148	C₁₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
149	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
150	C₁₃×C₂²⋊C₄	—	2	8	no	—
151	C₁₃×C₂²⋊C₄	—	2	8	no	—
152	C₁₃×C₂²⋊C₄	—	2	8	no	—
153	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
154	C₄²×C₁₃	—	2	8	no	—
155	C₄²×C₁₃	C₂×D₄	1	2	yes	—
156	C₄²×C₁₃	C₂×D₄	1	2	yes	—
157	C₄²×C₁₃	C₂⁴	1	2	yes	—
158	C₄²×C₁₃	C₂⁴	1	2	yes	—
159	C₂×#541	C₂×C₁₃	1	1	yes	characteristic, complemented
160	#3449	C₂×C₁₃	1	1	yes	characteristic
161	#3223	C₂×C₁₃	1	8	yes	complemented
162	#3222	C₂×C₁₃	1	8	yes	complemented
163	#3152	C₂×C₁₃	1	2	yes	complemented
164	#3142	C₂×C₁₃	1	2	yes	complemented
165	#3037	C₂×C₁₃	1	4	yes	complemented
166	#3007	C₂×C₁₃	1	4	yes	complemented
167	#2921	C₂×C₁₃	1	1	yes	characteristic, complemented
168	C₂³×C₁₃	—	2	2	no	—
169	C₂³×C₁₃	—	2	4	no	—
170	C₂³×C₁₃	—	4	2	no	—
171	C₂³×C₁₃	—	4	4	no	—
172	C₂³×C₁₃	—	8	4	no	—
173	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
174	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
175	Q₈×C₁₃	—	2	8	no	—
176	Q₈×C₁₃	—	2	8	no	—
177	Q₈×C₁₃	—	4	4	no	—
178	Q₈×C₁₃	—	4	4	no	—
179	D₄×C₁₃	—	2	8	no	—
180	D₄×C₁₃	—	4	4	no	—
181	D₄×C₁₃	—	4	8	no	—
182	D₄×C₁₃	—	4	8	no	—
183	D₄×C₁₃	—	8	4	no	—
184	D₄×C₁₃	—	8	4	no	—
185	C₂×C₄×C₁₃	—	2	2	no	—
186	C₂×C₄×C₁₃	—	2	4	no	—
187	C₂×C₄×C₁₃	—	2	4	no	—
188	C₂×C₄×C₁₃	—	2	4	no	—
189	C₂×C₄×C₁₃	—	2	4	no	—
190	C₂×C₄×C₁₃	—	2	4	no	—
191	C₂×C₄×C₁₃	—	4	2	no	—
192	C₂×C₄×C₁₃	—	4	2	no	—
193	C₂×C₄×C₁₃	—	4	8	no	—
194	C₂×C₄×C₁₃	—	4	4	no	—
195	C₂×C₄×C₁₃	—	4	4	no	—
196	C₂×C₄×C₁₃	—	4	4	no	—
197	C₂×C₄×C₁₃	—	4	8	no	—
198	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
199	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
200	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
201	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
202	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
203	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
204	C₈×C₁₃	—	2	8	no	—
205	C₂²×#41	C₂²×C₁₃	1	2	yes	—
206	C₂×#137	C₂²×C₁₃	1	8	yes	complemented
207	#541	—	2	4	no	—
208	#541	C₂²×C₁₃	1	8	yes	complemented
209	#537	—	2	2	no	—
210	#536	C₂²×C₁₃	1	4	yes	—
211	#535	C₂²×C₁₃	1	4	yes	—
212	#534	—	2	2	no	—
213	#532	C₂²×C₁₃	1	2	yes	—
214	#532	C₂²×C₁₃	1	2	yes	—
215	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
216	C₂×#126	—	2	2	no	—
217	C₂×#125	—	2	2	no	—
218	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic, complemented
219	#525	—	2	4	no	—
220	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
221	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
222	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
223	#497	C₂²×C₁₃	1	8	yes	complemented
224	#494	C₂²×C₁₃	1	4	yes	complemented
225	#492	C₂²×C₁₃	1	4	yes	complemented
226	#491	C₂²×C₁₃	1	4	yes	complemented
227	#490	C₂²×C₁₃	1	4	yes	complemented
228	#488	C₂²×C₁₃	1	8	yes	complemented
229	#464	C₂²×C₁₃	1	16	yes	complemented
230	#462	C₂²×C₁₃	1	8	yes	complemented
231	#460	C₂²×C₁₃	1	8	yes	complemented
232	#452	C₂²×C₁₃	1	16	yes	—
233	#451	C₂²×C₁₃	1	8	yes	complemented
234	#450	C₂²×C₁₃	1	8	yes	complemented
235	#433	C₂²×C₁₃	1	8	yes	complemented
236	#423	C₂²×C₁₃	1	2	yes	complemented
237	#417	C₂²×C₁₃	1	8	yes	complemented
238	#407	C₂²×C₁₃	1	2	yes	—
239	C₄×M₁₆	C₂²×C₁₃	1	2	yes	complemented
240	C₂²×C₁₃	—	2	2	no	—
241	C₂²×C₁₃	—	2	4	no	—
242	C₂²×C₁₃	—	2	2	no	—
243	C₂²×C₁₃	—	4	8	no	—
244	C₂²×C₁₃	—	4	4	no	—
245	C₂²×C₁₃	—	8	2	no	—
246	C₂²×C₁₃	—	8	8	no	—
247	C₂²×C₁₃	#535	1	2	yes	—
248	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
249	C₄×C₁₃	—	2	4	no	—
250	C₄×C₁₃	—	2	4	no	—
251	C₄×C₁₃	—	2	2	no	—
252	C₄×C₁₃	—	4	4	no	—
253	C₄×C₁₃	—	4	4	no	—
254	C₄×C₁₃	—	4	4	no	—
255	C₄×C₁₃	#535	1	2	yes	—
256	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
257	C₂×#41	—	2	2	no	—
258	C₂×#41	—	2	2	no	—
259	C₂×#41	—	4	8	no	—
260	C₂×#41	C₂³×C₁₃	1	4	yes	—
261	C₂×#41	C₂³×C₁₃	1	4	yes	—
262	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
263	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
264	C₂²×D₄	—	2	2	no	—
265	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
266	C₂³×C₄	—	2	2	no	—
267	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
268	#137	—	4	16	no	—
269	C₂×Q₁₆	C₂³×C₁₃	1	16	yes	—
270	C₂×SD₁₆	C₂³×C₁₃	1	16	yes	—
271	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
272	C₄⋊Q₈	—	2	2	no	—
273	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
274	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
275	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
276	#127	C₂³×C₁₃	1	2	yes	—
277	#127	C₂³×C₁₃	1	2	yes	—
278	#126	—	2	16	no	—
279	#125	—	2	16	no	—
280	#125	—	2	2	no	—
281	#125	C₂³×C₁₃	1	4	yes	—
282	#124	C₂³×C₁₃	1	4	yes	—
283	#124	C₂³×C₁₃	1	4	yes	—
284	#123	—	2	8	no	—
285	C₂²⋊Q₈	—	2	4	no	—
286	C₂²⋊Q₈	—	2	8	no	—
287	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
288	#121	—	2	4	no	—
289	#121	—	2	4	no	—
290	#121	—	2	8	no	—
291	#120	—	2	8	no	—
292	C₄×Q₈	—	2	4	no	—
293	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
294	C₄×D₄	—	2	4	no	—
295	C₄×D₄	—	2	4	no	—
296	#117	D₄×C₁₃	1	4	yes	—
297	#117	C₂³×C₁₃	1	4	yes	—
298	C₂×C₄⋊C₄	—	2	2	no	—
299	C₂×C₄⋊C₄	—	2	2	no	—
300	C₂×C₄⋊C₄	—	2	2	no	—
301	C₂×C₄⋊C₄	—	2	2	no	—
302	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
303	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
304	C₂×C₂²⋊C₄	—	2	2	no	—
305	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
306	C₂×C₄²	—	2	2	no	—
307	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
308	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
309	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
310	#103	C₂³×C₁₃	1	16	yes	—
311	#102	C₂³×C₁₃	1	16	yes	—
312	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
313	#97	C₂³×C₁₃	1	4	yes	—
314	C₄×C₈	C₂³×C₁₃	1	4	yes	—
315	C₂×C₁₃	—	2	2	no	—
316	C₂×C₁₃	—	4	2	no	—
317	C₂×C₁₃	—	8	4	no	—
318	C₂×C₁₃	C₂×#535	1	1	yes	characteristic
319	C₂×C₁₃	#3586	1	2	yes	—
320	C₂⁴	—	2	2	no	—
321	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
322	#41	—	2	16	no	—
323	#41	—	4	8	no	—
324	#41	—	4	8	no	—
325	#41	—	4	8	no	—
326	C₂×Q₈	—	2	2	no	—
327	C₂×Q₈	—	2	2	no	—
328	C₂×Q₈	—	2	8	no	—
329	C₂×Q₈	—	4	4	no	—
330	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
331	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
332	C₂×D₄	—	2	4	no	—
333	C₂×D₄	—	2	4	no	—
334	C₂×D₄	—	2	2	no	—
335	C₂×D₄	—	2	4	no	—
336	C₂×D₄	—	2	4	no	—
337	C₂×D₄	—	4	4	no	—
338	C₂×D₄	—	4	8	no	—
339	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
340	C₂²×C₄	—	2	4	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	4	no	—
345	C₂²×C₄	—	2	4	no	—
346	C₂²×C₄	—	4	8	no	—
347	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
348	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
349	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
350	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
351	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
352	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
353	Q₁₆	—	4	16	no	—
354	SD₁₆	—	4	16	no	—
355	M₁₆	—	2	8	no	—
356	C₂×C₈	C₂⁴×C₁₃	1	8	yes	—
357	C₄⋊C₄	—	2	8	no	—
358	C₄⋊C₄	—	2	8	no	—
359	C₄⋊C₄	—	2	8	no	—
360	C₄⋊C₄	—	2	8	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	2	4	no	—
363	C₄⋊C₄	—	2	4	no	—
364	C₄⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
365	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
366	C₂²⋊C₄	—	2	8	no	—
367	C₂²⋊C₄	—	2	8	no	—
368	C₂²⋊C₄	—	2	8	no	—
369	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
370	C₄²	—	2	8	no	—
371	C₄²	C₂×D₄×C₁₃	1	2	yes	—
372	C₄²	C₂×D₄×C₁₃	1	2	yes	—
373	C₄²	C₂⁴×C₁₃	1	2	yes	—
374	C₄²	C₂⁴×C₁₃	1	2	yes	—
375	C₁₃	#60809	1	1	yes	characteristic, direct product factor, Sylow
376	C₂³	—	2	2	no	—
377	C₂³	—	2	4	no	—
378	C₂³	—	4	2	no	—
379	C₂³	—	4	4	no	—
380	C₂³	—	8	4	no	—
381	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
382	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
383	Q₈	—	2	8	no	—
384	Q₈	—	2	8	no	—
385	Q₈	—	4	4	no	—
386	Q₈	—	4	4	no	—
387	D₄	—	2	8	no	—
388	D₄	—	4	4	no	—
389	D₄	—	4	8	no	—
390	D₄	—	4	8	no	—
391	D₄	—	8	4	no	—
392	D₄	—	8	4	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	4	no	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	2	4	no	—
397	C₂×C₄	—	2	4	no	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	8	no	—
402	C₂×C₄	—	4	4	no	—
403	C₂×C₄	—	4	4	no	—
404	C₂×C₄	—	4	4	no	—
405	C₂×C₄	—	4	8	no	—
406	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
407	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
408	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
409	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
410	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
411	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
412	C₈	—	2	8	no	—
413	C₂²	—	2	2	no	—
414	C₂²	—	2	4	no	—
415	C₂²	—	2	2	no	—
416	C₂²	—	4	8	no	—
417	C₂²	—	4	4	no	—
418	C₂²	—	8	2	no	—
419	C₂²	—	8	8	no	—
420	C₂²	C₁₃×#535	1	2	yes	—
421	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
422	C₄	—	2	4	no	—
423	C₄	—	2	4	no	—
424	C₄	—	2	2	no	—
425	C₄	—	4	4	no	—
426	C₄	—	4	4	no	—
427	C₄	—	4	4	no	—
428	C₄	C₁₃×#535	1	2	yes	—
429	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
430	C₂	—	2	2	no	—
431	C₂	—	4	2	no	—
432	C₂	—	8	4	no	—
433	C₂	C₂×C₁₃×#535	1	1	yes	characteristic
434	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×#3449	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₁₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#541	C₂	semidirect
3. C₁₃×#3223	C₂	semidirect
4. C₁₃×#3222	C₂	semidirect
5. C₁₃×#3152	C₂	semidirect
6. C₁₃×#3142	C₂	semidirect
7. C₁₃×#3037	C₂	semidirect
8. C₁₃×#3007	C₂	semidirect
9. C₁₃×#2921	C₂	semidirect
11. C₂×C₁₃×#137	C₂²	semidirect
13. C₁₃×#541	C₂²	semidirect
20. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
23. C₂×C₁₃×#125	C₂²	semidirect
26. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
28. C₁₃×#497	C₂²	semidirect
29. C₁₃×#494	C₂²	semidirect
30. C₁₃×#492	C₂²	semidirect
31. C₁₃×#491	C₂²	semidirect
32. C₁₃×#490	C₂²	semidirect
33. C₁₃×#488	C₂²	semidirect
34. C₁₃×#464	C₂²	semidirect
35. C₁₃×#462	C₂²	semidirect
36. C₁₃×#460	C₂²	semidirect
38. C₁₃×#451	C₂²	semidirect
39. C₁₃×#450	C₂²	semidirect
40. C₁₃×#433	C₂²	semidirect
41. C₁₃×#423	C₂²	semidirect
42. C₁₃×#417	C₂²	semidirect
44. C₄×C₁₃×M₁₆	C₂²	semidirect
103. #60809	C₁₃	direct (N × H)
159. C₂×#541	C₂×C₁₃	semidirect
161. #3223	C₂×C₁₃	semidirect
162. #3222	C₂×C₁₃	semidirect
163. #3152	C₂×C₁₃	semidirect
164. #3142	C₂×C₁₃	semidirect
165. #3037	C₂×C₁₃	semidirect
166. #3007	C₂×C₁₃	semidirect
167. #2921	C₂×C₁₃	semidirect
206. C₂×#137	C₂²×C₁₃	semidirect
208. #541	C₂²×C₁₃	semidirect
215. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
218. C₂×#125	C₂²×C₁₃	semidirect
221. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
223. #497	C₂²×C₁₃	semidirect
224. #494	C₂²×C₁₃	semidirect
225. #492	C₂²×C₁₃	semidirect
226. #491	C₂²×C₁₃	semidirect
227. #490	C₂²×C₁₃	semidirect
228. #488	C₂²×C₁₃	semidirect
229. #464	C₂²×C₁₃	semidirect
230. #462	C₂²×C₁₃	semidirect
231. #460	C₂²×C₁₃	semidirect
233. #451	C₂²×C₁₃	semidirect
234. #450	C₂²×C₁₃	semidirect
235. #433	C₂²×C₁₃	semidirect
236. #423	C₂²×C₁₃	semidirect
237. #417	C₂²×C₁₃	semidirect
239. C₄×M₁₆	C₂²×C₁₃	semidirect
375. C₁₃	#60809	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×#541	2
C₁₃×#3449	2
C₁₃×#3223	2
C₁₃×#3222	2
C₁₃×#3152	2
C₁₃×#3142	2
C₁₃×#3037	2
C₁₃×#3007	2
C₁₃×#2921	2
#60809	13

Subgroups — C13×#60809 #15747148

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60809 #15747148