Subgroups — C₁₃×#33605 #15719944

Order 3328.

738 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#509	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₃×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3050	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₃×#466	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2220	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2218	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2217	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2215	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2159	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2140	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2139	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
13	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
15	C₁₃×#525	—	2	1	no	—
16	C₂×C₁₃×#121	—	2	1	no	—
17	C₁₃×#509	—	2	4	no	—
18	C₂×C₁₃×SD₃₂	C₂²	1	2	yes	complemented
19	C₂×C₁₃×D₁₆	C₂²	1	2	yes	complemented
20	C₂×C₁₃×M₃₂	—	2	4	no	—
21	C₂×C₁₃×M₃₂	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×M₃₂	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×M₃₂	C₂²	1	2	yes	complemented
24	C₂²×C₁₃×C₁₆	C₂²	1	2	yes	complemented
25	C₁₃×#467	C₂²	1	1	yes	characteristic, complemented
26	C₁₃×#467	C₂²	1	1	yes	characteristic, complemented
27	C₁₃×#466	—	2	1	no	—
28	C₁₃×#466	—	2	1	no	—
29	C₁₃×#466	C₂²	1	2	yes	—
30	C₁₃×#466	C₂²	1	2	yes	—
31	C₁₃×#466	C₂²	1	1	yes	characteristic, complemented
32	C₁₃×#466	C₂²	1	1	yes	characteristic, complemented
33	C₁₃×#465	—	2	1	no	—
34	C₁₃×#465	—	2	1	no	—
35	C₁₃×#427	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
37	C₁₃×#416	—	2	1	no	—
38	C₂×C₁₃×#102	—	2	1	no	—
39	C₁₃×#367	C₂²	1	2	yes	complemented
40	C₁₃×#366	C₂²	1	2	yes	complemented
41	C₁₃×#358	C₂²	1	2	yes	complemented
42	C₁₃×#357	C₂²	1	2	yes	complemented
43	C₁₃×#357	C₂²	1	2	yes	complemented
44	C₁₃×#357	C₂²	1	2	yes	complemented
45	C₂×C₁₃×#41	—	2	1	no	—
46	C₂²×D₄×C₁₃	—	2	1	no	—
47	C₂²×D₄×C₁₃	—	4	1	no	—
48	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
49	C₁₃×#135	—	2	2	no	—
50	C₁₃×#135	—	2	2	no	—
51	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
52	C₂×C₁₃×SD₁₆	—	2	1	no	—
53	C₂×C₁₃×D₈	—	2	2	no	—
54	C₂×C₁₃×D₈	—	2	1	no	—
55	C₂×C₁₃×D₈	—	2	2	no	—
56	C₂×C₁₃×D₈	C₂³	1	2	yes	—
57	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
58	C₂²×C₈×C₁₃	—	2	2	no	—
59	C₂²×C₈×C₁₃	—	2	2	no	—
60	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
61	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
62	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
63	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
65	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
66	C₁₃×#123	—	4	1	no	—
67	C₁₃×C₂²⋊Q₈	—	2	1	no	—
68	C₁₃×C₂²⋊Q₈	—	2	1	no	—
69	C₁₃×#121	—	2	1	no	—
70	C₁₃×#121	—	2	1	no	—
71	C₁₃×#121	—	2	2	no	—
72	C₁₃×#121	—	2	2	no	—
73	C₁₃×#121	—	4	1	no	—
74	C₁₃×#121	—	4	1	no	—
75	C₁₃×#120	—	4	1	no	—
76	C₄×D₄×C₁₃	—	4	1	no	—
77	C₄×D₄×C₁₃	—	4	1	no	—
78	C₁₃×#117	—	2	1	no	—
79	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
80	C₂×C₁₃×C₂²⋊C₄	—	4	1	no	—
81	C₁₃×SD₃₂	—	2	4	no	—
82	C₁₃×D₁₆	—	2	4	no	—
83	C₁₃×M₃₂	—	2	2	no	—
84	C₁₃×M₃₂	—	2	4	no	—
85	C₁₃×M₃₂	D₄	1	4	yes	complemented
86	C₂×C₁₃×C₁₆	—	2	4	no	—
87	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
88	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
89	C₁₃×#107	—	2	1	no	—
90	C₁₃×#107	C₂³	1	2	yes	—
91	C₁₃×#107	C₂³	1	1	yes	characteristic
92	C₁₃×#107	C₂³	1	1	yes	characteristic
93	C₁₃×#106	—	2	1	no	—
94	C₁₃×#103	—	2	1	no	—
95	C₁₃×#103	—	2	1	no	—
96	C₁₃×#102	—	2	2	no	—
97	C₁₃×#102	—	2	2	no	—
98	C₁₃×#102	—	2	1	no	—
99	C₁₃×#102	—	2	1	no	—
100	#33605	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
101	C₂⁴×C₁₃	—	4	1	no	—
102	C₂⁴×C₁₃	D₈	1	1	yes	characteristic
103	C₁₃×#41	—	4	2	no	—
104	C₁₃×#41	—	4	2	no	—
105	C₂×Q₈×C₁₃	—	2	1	no	—
106	C₂×D₄×C₁₃	—	2	2	no	—
107	C₂×D₄×C₁₃	—	2	1	no	—
108	C₂×D₄×C₁₃	—	4	1	no	—
109	C₂×D₄×C₁₃	—	4	1	no	—
110	C₂×D₄×C₁₃	—	4	1	no	—
111	C₂×D₄×C₁₃	—	4	2	no	—
112	C₂×D₄×C₁₃	—	4	2	no	—
113	C₂×D₄×C₁₃	—	4	2	no	—
114	C₂×D₄×C₁₃	—	4	1	no	—
115	C₂×D₄×C₁₃	—	4	2	no	—
116	C₂×D₄×C₁₃	—	8	4	no	—
117	C₂²×C₄×C₁₃	—	2	2	no	—
118	C₂²×C₄×C₁₃	—	2	2	no	—
119	C₂²×C₄×C₁₃	—	4	1	no	—
120	C₂²×C₄×C₁₃	—	4	1	no	—
121	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
122	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
123	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
124	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
127	C₁₃×Q₁₆	—	2	1	no	—
128	C₁₃×Q₁₆	—	2	1	no	—
129	C₁₃×SD₁₆	—	4	2	no	—
130	C₁₃×D₈	—	2	1	no	—
131	C₁₃×D₈	—	2	2	no	—
132	C₁₃×D₈	—	2	2	no	—
133	C₁₃×D₈	—	2	1	no	—
134	C₁₃×D₈	—	4	2	no	—
135	C₂×C₈×C₁₃	—	2	2	no	—
136	C₂×C₈×C₁₃	—	2	2	no	—
137	C₂×C₈×C₁₃	—	2	2	no	—
138	C₂×C₈×C₁₃	—	2	1	no	—
139	C₂×C₈×C₁₃	—	2	1	no	—
140	C₂×C₈×C₁₃	—	2	1	no	—
141	C₂×C₈×C₁₃	—	2	1	no	—
142	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
143	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
144	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
145	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
146	C₂×C₈×C₁₃	#41	1	2	yes	—
147	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
148	C₁₃×C₄⋊C₄	—	2	2	no	—
149	C₁₃×C₄⋊C₄	—	2	1	no	—
150	C₁₃×C₄⋊C₄	—	2	1	no	—
151	C₁₃×C₄⋊C₄	—	4	1	no	—
152	C₁₃×C₄⋊C₄	—	4	1	no	—
153	C₁₃×C₄⋊C₄	—	4	1	no	—
154	C₁₃×C₂²⋊C₄	—	4	1	no	—
155	C₁₃×C₂²⋊C₄	—	4	1	no	—
156	C₁₃×C₂²⋊C₄	—	4	1	no	—
157	C₁₃×C₂²⋊C₄	—	4	2	no	—
158	C₁₃×C₂²⋊C₄	—	4	2	no	—
159	C₁₃×C₂²⋊C₄	—	4	1	no	—
160	C₁₃×C₂²⋊C₄	—	4	1	no	—
161	C₄²×C₁₃	—	4	1	no	—
162	C₁₃×C₁₆	—	2	2	no	—
163	C₁₃×C₁₆	C₂×D₄	1	4	yes	complemented
164	C₂×#509	C₂×C₁₃	1	1	yes	characteristic, complemented
165	C₂²×M₃₂	C₂×C₁₃	1	1	yes	characteristic, complemented
166	#3050	C₂×C₁₃	1	1	yes	characteristic, complemented
167	C₂×#466	C₂×C₁₃	1	1	yes	characteristic, complemented
168	#2220	C₂×C₁₃	1	2	yes	complemented
169	#2218	C₂×C₁₃	1	2	yes	complemented
170	#2217	C₂×C₁₃	1	2	yes	complemented
171	#2215	C₂×C₁₃	1	2	yes	complemented
172	#2159	C₂×C₁₃	1	1	yes	characteristic, complemented
173	#2140	C₂×C₁₃	1	1	yes	characteristic, complemented
174	#2139	C₂×C₁₃	1	1	yes	characteristic, complemented
175	C₂³×C₁₃	—	2	2	no	—
176	C₂³×C₁₃	—	2	2	no	—
177	C₂³×C₁₃	—	4	1	no	—
178	C₂³×C₁₃	—	4	1	no	—
179	C₂³×C₁₃	—	4	2	no	—
180	C₂³×C₁₃	—	8	2	no	—
181	C₂³×C₁₃	—	8	2	no	—
182	C₂³×C₁₃	—	8	2	no	—
183	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
184	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
185	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
186	Q₈×C₁₃	—	4	1	no	—
187	Q₈×C₁₃	—	4	1	no	—
188	D₄×C₁₃	—	4	2	no	—
189	D₄×C₁₃	—	4	1	no	—
190	D₄×C₁₃	—	4	2	no	—
191	D₄×C₁₃	—	4	1	no	—
192	D₄×C₁₃	—	8	2	no	—
193	D₄×C₁₃	—	8	4	no	—
194	D₄×C₁₃	—	8	2	no	—
195	D₄×C₁₃	—	8	2	no	—
196	D₄×C₁₃	—	8	4	no	—
197	D₄×C₁₃	—	8	2	no	—
198	C₂×C₄×C₁₃	—	2	2	no	—
199	C₂×C₄×C₁₃	—	2	1	no	—
200	C₂×C₄×C₁₃	—	2	1	no	—
201	C₂×C₄×C₁₃	—	2	1	no	—
202	C₂×C₄×C₁₃	—	2	1	no	—
203	C₂×C₄×C₁₃	—	2	2	no	—
204	C₂×C₄×C₁₃	—	2	2	no	—
205	C₂×C₄×C₁₃	—	4	1	no	—
206	C₂×C₄×C₁₃	—	4	1	no	—
207	C₂×C₄×C₁₃	—	4	2	no	—
208	C₂×C₄×C₁₃	—	4	1	no	—
209	C₂×C₄×C₁₃	—	8	2	no	—
210	C₂×C₄×C₁₃	—	8	2	no	—
211	C₂×C₄×C₁₃	#121	1	2	yes	—
212	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
213	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
214	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
215	C₂×C₄×C₁₃	#135	1	2	yes	—
216	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
217	C₈×C₁₃	—	2	1	no	—
218	C₈×C₁₃	—	2	1	no	—
219	C₈×C₁₃	#121	1	2	yes	—
220	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
221	C₈×C₁₃	C₂×#41	1	1	yes	characteristic
222	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
223	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
224	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
225	#525	—	2	1	no	—
226	C₂×#121	—	2	1	no	—
227	#509	—	2	4	no	—
228	C₂×SD₃₂	C₂²×C₁₃	1	2	yes	complemented
229	C₂×D₁₆	C₂²×C₁₃	1	2	yes	complemented
230	C₂×M₃₂	—	2	4	no	—
231	C₂×M₃₂	C₂²×C₁₃	1	1	yes	characteristic
232	C₂×M₃₂	C₂²×C₁₃	1	1	yes	characteristic
233	C₂×M₃₂	C₂²×C₁₃	1	2	yes	complemented
234	C₂²×C₁₆	C₂²×C₁₃	1	2	yes	complemented
235	#467	C₂²×C₁₃	1	1	yes	characteristic, complemented
236	#467	C₂²×C₁₃	1	1	yes	characteristic, complemented
237	#466	—	2	1	no	—
238	#466	—	2	1	no	—
239	#466	C₂²×C₁₃	1	2	yes	—
240	#466	C₂²×C₁₃	1	2	yes	—
241	#466	C₂²×C₁₃	1	1	yes	characteristic, complemented
242	#466	C₂²×C₁₃	1	1	yes	characteristic, complemented
243	#465	—	2	1	no	—
244	#465	—	2	1	no	—
245	#427	C₂²×C₁₃	1	1	yes	characteristic
246	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
247	#416	—	2	1	no	—
248	C₂×#102	—	2	1	no	—
249	#367	C₂²×C₁₃	1	2	yes	complemented
250	#366	C₂²×C₁₃	1	2	yes	complemented
251	#358	C₂²×C₁₃	1	2	yes	complemented
252	#357	C₂²×C₁₃	1	2	yes	complemented
253	#357	C₂²×C₁₃	1	2	yes	complemented
254	#357	C₂²×C₁₃	1	2	yes	complemented
255	C₂²×C₁₃	—	2	1	no	—
256	C₂²×C₁₃	—	2	1	no	—
257	C₂²×C₁₃	—	2	1	no	—
258	C₂²×C₁₃	—	2	1	no	—
259	C₂²×C₁₃	—	2	1	no	—
260	C₂²×C₁₃	—	2	1	no	—
261	C₂²×C₁₃	—	2	1	no	—
262	C₂²×C₁₃	—	4	4	no	—
263	C₂²×C₁₃	—	8	2	no	—
264	C₂²×C₁₃	—	8	1	no	—
265	C₂²×C₁₃	—	8	1	no	—
266	C₂²×C₁₃	—	8	2	no	—
267	C₂²×C₁₃	—	8	1	no	—
268	C₂²×C₁₃	—	8	2	no	—
269	C₂²×C₁₃	—	16	4	no	—
270	C₂²×C₁₃	#466	1	2	yes	—
271	C₂²×C₁₃	#509	1	2	yes	complemented
272	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
273	C₄×C₁₃	—	2	1	no	—
274	C₄×C₁₃	—	2	1	no	—
275	C₄×C₁₃	—	8	2	no	—
276	C₄×C₁₃	—	8	1	no	—
277	C₄×C₁₃	—	8	1	no	—
278	C₄×C₁₃	—	8	1	no	—
279	C₄×C₁₃	#466	1	2	yes	—
280	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
281	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
282	C₂×#41	—	2	1	no	—
283	C₂²×D₄	—	2	1	no	—
284	C₂²×D₄	—	4	1	no	—
285	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
286	#135	—	2	2	no	—
287	#135	—	2	2	no	—
288	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
289	C₂×SD₁₆	—	2	1	no	—
290	C₂×D₈	—	2	2	no	—
291	C₂×D₈	—	2	1	no	—
292	C₂×D₈	—	2	2	no	—
293	C₂×D₈	C₂³×C₁₃	1	2	yes	—
294	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
295	C₂²×C₈	—	2	2	no	—
296	C₂²×C₈	—	2	2	no	—
297	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
298	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
299	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
300	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
301	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
302	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
303	#123	—	4	1	no	—
304	C₂²⋊Q₈	—	2	1	no	—
305	C₂²⋊Q₈	—	2	1	no	—
306	#121	—	2	2	no	—
307	#121	—	2	2	no	—
308	#121	—	2	1	no	—
309	#121	—	2	1	no	—
310	#121	—	4	1	no	—
311	#121	—	4	1	no	—
312	#120	—	4	1	no	—
313	C₄×D₄	—	4	1	no	—
314	C₄×D₄	—	4	1	no	—
315	#117	—	2	1	no	—
316	C₂×C₄⋊C₄	—	2	1	no	—
317	C₂×C₂²⋊C₄	—	4	1	no	—
318	SD₃₂	—	2	4	no	—
319	D₁₆	—	2	4	no	—
320	M₃₂	—	2	2	no	—
321	M₃₂	—	2	4	no	—
322	M₃₂	D₄×C₁₃	1	4	yes	complemented
323	C₂×C₁₆	—	2	4	no	—
324	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
325	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
326	#107	—	2	1	no	—
327	#107	C₂³×C₁₃	1	1	yes	characteristic
328	#107	C₂³×C₁₃	1	1	yes	characteristic
329	#107	C₂³×C₁₃	1	2	yes	—
330	#106	—	2	1	no	—
331	#103	—	2	1	no	—
332	#103	—	2	1	no	—
333	#102	—	2	2	no	—
334	#102	—	2	2	no	—
335	#102	—	2	1	no	—
336	#102	—	2	1	no	—
337	C₂×C₁₃	—	2	2	no	—
338	C₂×C₁₃	—	2	2	no	—
339	C₂×C₁₃	—	4	1	no	—
340	C₂×C₁₃	—	16	1	no	—
341	C₂×C₁₃	—	16	2	no	—
342	C₂×C₁₃	C₂×#466	1	1	yes	characteristic
343	C₂×C₁₃	C₂×#509	1	1	yes	characteristic
344	C₂×C₁₃	#3414	1	1	yes	characteristic
345	C₂⁴	—	4	1	no	—
346	C₂⁴	C₁₃×D₈	1	1	yes	characteristic
347	#41	—	4	2	no	—
348	#41	—	4	2	no	—
349	C₂×Q₈	—	2	1	no	—
350	C₂×D₄	—	2	2	no	—
351	C₂×D₄	—	2	1	no	—
352	C₂×D₄	—	4	1	no	—
353	C₂×D₄	—	4	1	no	—
354	C₂×D₄	—	4	1	no	—
355	C₂×D₄	—	4	2	no	—
356	C₂×D₄	—	4	2	no	—
357	C₂×D₄	—	4	2	no	—
358	C₂×D₄	—	4	1	no	—
359	C₂×D₄	—	4	2	no	—
360	C₂×D₄	—	8	4	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	4	1	no	—
364	C₂²×C₄	—	4	1	no	—
365	C₂²×C₄	C₁₃×D₈	1	1	yes	characteristic
366	C₂²×C₄	C₁₃×D₈	1	1	yes	characteristic
367	C₂²×C₄	C₁₃×D₈	1	1	yes	characteristic
368	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
369	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
370	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
371	Q₁₆	—	2	1	no	—
372	Q₁₆	—	2	1	no	—
373	SD₁₆	—	4	2	no	—
374	D₈	—	2	1	no	—
375	D₈	—	2	2	no	—
376	D₈	—	2	2	no	—
377	D₈	—	2	1	no	—
378	D₈	—	4	2	no	—
379	C₂×C₈	—	2	2	no	—
380	C₂×C₈	—	2	2	no	—
381	C₂×C₈	—	2	2	no	—
382	C₂×C₈	—	2	1	no	—
383	C₂×C₈	—	2	1	no	—
384	C₂×C₈	—	2	1	no	—
385	C₂×C₈	—	2	1	no	—
386	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
387	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
388	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
389	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
390	C₂×C₈	C₁₃×#41	1	2	yes	—
391	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
392	C₄⋊C₄	—	2	2	no	—
393	C₄⋊C₄	—	2	1	no	—
394	C₄⋊C₄	—	2	1	no	—
395	C₄⋊C₄	—	4	1	no	—
396	C₄⋊C₄	—	4	1	no	—
397	C₄⋊C₄	—	4	1	no	—
398	C₂²⋊C₄	—	4	1	no	—
399	C₂²⋊C₄	—	4	1	no	—
400	C₂²⋊C₄	—	4	1	no	—
401	C₂²⋊C₄	—	4	2	no	—
402	C₂²⋊C₄	—	4	2	no	—
403	C₂²⋊C₄	—	4	1	no	—
404	C₂²⋊C₄	—	4	1	no	—
405	C₄²	—	4	1	no	—
406	C₁₆	—	2	2	no	—
407	C₁₆	C₂×D₄×C₁₃	1	4	yes	complemented
408	C₁₃	#33605	1	1	yes	characteristic, direct product factor, Sylow
409	C₂³	—	2	2	no	—
410	C₂³	—	2	2	no	—
411	C₂³	—	4	1	no	—
412	C₂³	—	4	1	no	—
413	C₂³	—	4	2	no	—
414	C₂³	—	8	2	no	—
415	C₂³	—	8	2	no	—
416	C₂³	—	8	2	no	—
417	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
418	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
419	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
420	Q₈	—	4	1	no	—
421	Q₈	—	4	1	no	—
422	D₄	—	4	2	no	—
423	D₄	—	4	1	no	—
424	D₄	—	4	2	no	—
425	D₄	—	4	1	no	—
426	D₄	—	8	4	no	—
427	D₄	—	8	2	no	—
428	D₄	—	8	2	no	—
429	D₄	—	8	4	no	—
430	D₄	—	8	2	no	—
431	D₄	—	8	2	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	—	8	2	no	—
444	C₂×C₄	—	8	2	no	—
445	C₂×C₄	C₁₃×#121	1	2	yes	—
446	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
447	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
448	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
449	C₂×C₄	C₁₃×#135	1	2	yes	—
450	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
451	C₈	—	2	1	no	—
452	C₈	—	2	1	no	—
453	C₈	C₁₃×#121	1	2	yes	—
454	C₈	C₂²×D₄×C₁₃	1	1	yes	characteristic
455	C₈	C₂×C₁₃×#41	1	1	yes	characteristic
456	C₂²	—	2	1	no	—
457	C₂²	—	2	1	no	—
458	C₂²	—	2	1	no	—
459	C₂²	—	2	1	no	—
460	C₂²	—	2	1	no	—
461	C₂²	—	2	1	no	—
462	C₂²	—	2	1	no	—
463	C₂²	—	4	4	no	—
464	C₂²	—	8	1	no	—
465	C₂²	—	8	2	no	—
466	C₂²	—	8	2	no	—
467	C₂²	—	8	1	no	—
468	C₂²	—	8	1	no	—
469	C₂²	—	8	2	no	—
470	C₂²	—	16	4	no	—
471	C₂²	C₁₃×#466	1	2	yes	—
472	C₂²	C₁₃×#509	1	2	yes	complemented
473	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
474	C₄	—	2	1	no	—
475	C₄	—	2	1	no	—
476	C₄	—	8	1	no	—
477	C₄	—	8	2	no	—
478	C₄	—	8	1	no	—
479	C₄	—	8	1	no	—
480	C₄	C₁₃×#466	1	2	yes	—
481	C₄	C₂×C₁₃×#121	1	1	yes	characteristic
482	C₄	C₂×C₁₃×#135	1	1	yes	characteristic
483	C₂	—	2	2	no	—
484	C₂	—	2	2	no	—
485	C₂	—	4	1	no	—
486	C₂	—	16	2	no	—
487	C₂	—	16	1	no	—
488	C₂	C₂×C₁₃×#466	1	1	yes	characteristic
489	C₂	C₂×C₁₃×#509	1	1	yes	characteristic
490	C₂	C₁₃×#3414	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂³×C₄×C₁₃ ◁ C₂³×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#509	C₂	semidirect
2. C₂²×C₁₃×M₃₂	C₂	semidirect
3. C₁₃×#3050	C₂	semidirect
4. C₂×C₁₃×#466	C₂	semidirect
5. C₁₃×#2220	C₂	semidirect
6. C₁₃×#2218	C₂	semidirect
7. C₁₃×#2217	C₂	semidirect
8. C₁₃×#2215	C₂	semidirect
9. C₁₃×#2159	C₂	semidirect
10. C₁₃×#2140	C₂	semidirect
11. C₁₃×#2139	C₂	semidirect
18. C₂×C₁₃×SD₃₂	C₂²	semidirect
19. C₂×C₁₃×D₁₆	C₂²	semidirect
23. C₂×C₁₃×M₃₂	C₂²	semidirect
24. C₂²×C₁₃×C₁₆	C₂²	semidirect
25. C₁₃×#467	C₂²	semidirect
26. C₁₃×#467	C₂²	semidirect
31. C₁₃×#466	C₂²	semidirect
32. C₁₃×#466	C₂²	semidirect
39. C₁₃×#367	C₂²	semidirect
40. C₁₃×#366	C₂²	semidirect
41. C₁₃×#358	C₂²	semidirect
42. C₁₃×#357	C₂²	semidirect
43. C₁₃×#357	C₂²	semidirect
44. C₁₃×#357	C₂²	semidirect
85. C₁₃×M₃₂	D₄	semidirect
100. #33605	C₁₃	direct (N × H)
163. C₁₃×C₁₆	C₂×D₄	semidirect
164. C₂×#509	C₂×C₁₃	semidirect
165. C₂²×M₃₂	C₂×C₁₃	semidirect
166. #3050	C₂×C₁₃	semidirect
167. C₂×#466	C₂×C₁₃	semidirect
168. #2220	C₂×C₁₃	semidirect
169. #2218	C₂×C₁₃	semidirect
170. #2217	C₂×C₁₃	semidirect
171. #2215	C₂×C₁₃	semidirect
172. #2159	C₂×C₁₃	semidirect
173. #2140	C₂×C₁₃	semidirect
174. #2139	C₂×C₁₃	semidirect
228. C₂×SD₃₂	C₂²×C₁₃	semidirect
229. C₂×D₁₆	C₂²×C₁₃	semidirect
233. C₂×M₃₂	C₂²×C₁₃	semidirect
234. C₂²×C₁₆	C₂²×C₁₃	semidirect
235. #467	C₂²×C₁₃	semidirect
236. #467	C₂²×C₁₃	semidirect
241. #466	C₂²×C₁₃	semidirect
242. #466	C₂²×C₁₃	semidirect
249. #367	C₂²×C₁₃	semidirect
250. #366	C₂²×C₁₃	semidirect
251. #358	C₂²×C₁₃	semidirect
252. #357	C₂²×C₁₃	semidirect
253. #357	C₂²×C₁₃	semidirect
254. #357	C₂²×C₁₃	semidirect
271. C₂²×C₁₃	#509	semidirect
322. M₃₂	D₄×C₁₃	semidirect
407. C₁₆	C₂×D₄×C₁₃	semidirect
408. C₁₃	#33605	direct (N × H)
472. C₂²	C₁₃×#509	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#509	2
C₂²×C₁₃×M₃₂	2
C₁₃×#3050	2
C₂×C₁₃×#466	2
C₁₃×#2220	2
C₁₃×#2218	2
C₁₃×#2217	2
C₁₃×#2215	2
C₁₃×#2159	2
C₁₃×#2140	2
C₁₃×#2139	2
#33605	13

Subgroups — C13×#33605 #15719944

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33605 #15719944