Subgroups — C₁₃×#33520 #15719859

Order 3328.

1192 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×#135	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#509	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₃×#466	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2186	C₂	1	4	yes	maximal, complemented
5	C₁₃×#2185	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2184	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2139	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2112	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₁₃×#41	—	2	1	no	—
10	C₂×C₁₃×#135	—	2	8	no	—
11	C₂×C₁₃×#135	—	2	1	no	—
12	C₂×C₁₃×#135	—	2	1	no	—
13	C₂×C₁₃×#135	C₂²	1	2	yes	—
14	C₂×C₁₃×#135	C₂²	1	2	yes	complemented
15	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
16	C₂²×C₁₃×SD₁₆	—	2	1	no	—
17	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic, complemented
18	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic, complemented
19	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#121	—	2	1	no	—
21	C₁₃×#509	—	2	8	no	—
22	C₂×C₁₃×SD₃₂	C₂²	1	4	yes	complemented
23	C₂×C₁₃×D₁₆	C₂²	1	4	yes	complemented
24	C₂×C₁₃×M₃₂	C₂²	1	2	yes	complemented
25	C₁₃×#466	—	2	1	no	—
26	C₁₃×#466	—	2	1	no	—
27	C₁₃×#466	C₂²	1	2	yes	—
28	C₁₃×#466	C₂²	1	2	yes	complemented
29	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₁₃×#102	—	2	1	no	—
31	C₁₃×#358	C₂²	1	4	yes	complemented
32	C₁₃×#357	C₂²	1	4	yes	complemented
33	C₁₃×C₂²⋊C₁₆	C₂²	1	2	yes	complemented
34	C₁₃×C₂²⋊C₁₆	C₂²	1	2	yes	complemented
35	C₂×C₁₃×#41	—	2	8	no	—
36	C₂×C₁₃×#41	—	2	2	no	—
37	C₂×C₁₃×#41	—	2	2	no	—
38	C₂×C₁₃×#41	—	4	4	no	—
39	C₂×C₁₃×#41	—	4	1	no	—
40	C₂×C₁₃×#41	—	4	1	no	—
41	C₂²×Q₈×C₁₃	—	2	1	no	—
42	C₂²×D₄×C₁₃	—	2	1	no	—
43	C₂²×D₄×C₁₃	—	2	1	no	—
44	C₂²×D₄×C₁₃	—	4	1	no	—
45	C₂²×D₄×C₁₃	—	4	1	no	—
46	C₂³×C₄×C₁₃	—	4	1	no	—
47	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
48	C₁₃×#135	—	2	8	no	—
49	C₁₃×#135	—	2	8	no	—
50	C₁₃×#135	—	2	4	no	—
51	C₁₃×#135	—	2	4	no	—
52	C₁₃×#135	—	2	4	no	—
53	C₁₃×#135	D₄	1	8	yes	complemented
54	C₂×C₁₃×Q₁₆	—	2	4	no	—
55	C₂×C₁₃×Q₁₆	—	2	1	no	—
56	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
57	C₂×C₁₃×SD₁₆	—	2	8	no	—
58	C₂×C₁₃×SD₁₆	—	2	2	no	—
59	C₂×C₁₃×SD₁₆	—	2	2	no	—
60	C₂×C₁₃×D₈	—	2	4	no	—
61	C₂×C₁₃×D₈	—	2	1	no	—
62	C₂×C₁₃×D₈	—	2	4	no	—
63	C₂×C₁₃×D₈	—	2	1	no	—
64	C₂×C₁₃×D₈	C₂³	1	2	yes	—
65	C₂×C₁₃×D₈	C₂³	1	2	yes	—
66	C₂²×C₈×C₁₃	—	2	4	no	—
67	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
68	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
69	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
70	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
73	C₁₃×#121	—	2	2	no	—
74	C₁₃×#121	—	2	2	no	—
75	C₁₃×#121	—	4	1	no	—
76	C₁₃×#121	—	4	1	no	—
77	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
78	C₂×C₁₃×C₂²⋊C₄	—	4	1	no	—
79	C₁₃×SD₃₂	—	2	8	no	—
80	C₁₃×D₁₆	—	2	8	no	—
81	C₁₃×M₃₂	—	2	4	no	—
82	C₂×C₁₃×C₁₆	C₂³	1	4	yes	—
83	C₁₃×#107	—	2	1	no	—
84	C₁₃×#107	C₂³	1	2	yes	—
85	C₁₃×#102	—	2	2	no	—
86	C₁₃×#102	—	2	2	no	—
87	#33520	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
88	C₂⁴×C₁₃	—	4	1	no	—
89	C₂⁴×C₁₃	—	4	1	no	—
90	C₂⁴×C₁₃	D₈	1	1	yes	characteristic
91	C₁₃×#41	—	2	8	no	—
92	C₁₃×#41	—	2	8	no	—
93	C₁₃×#41	—	4	8	no	—
94	C₁₃×#41	—	4	4	no	—
95	C₁₃×#41	—	4	8	no	—
96	C₁₃×#41	—	4	4	no	—
97	C₂×Q₈×C₁₃	—	2	4	no	—
98	C₂×Q₈×C₁₃	—	2	2	no	—
99	C₂×Q₈×C₁₃	—	4	2	no	—
100	C₂×Q₈×C₁₃	—	4	1	no	—
101	C₂×D₄×C₁₃	—	2	4	no	—
102	C₂×D₄×C₁₃	—	2	2	no	—
103	C₂×D₄×C₁₃	—	2	2	no	—
104	C₂×D₄×C₁₃	—	4	2	no	—
105	C₂×D₄×C₁₃	—	4	8	no	—
106	C₂×D₄×C₁₃	—	4	2	no	—
107	C₂×D₄×C₁₃	—	4	2	no	—
108	C₂×D₄×C₁₃	—	4	2	no	—
109	C₂×D₄×C₁₃	—	4	2	no	—
110	C₂×D₄×C₁₃	—	4	2	no	—
111	C₂×D₄×C₁₃	—	4	1	no	—
112	C₂×D₄×C₁₃	—	4	1	no	—
113	C₂×D₄×C₁₃	—	4	2	no	—
114	C₂×D₄×C₁₃	—	8	4	no	—
115	C₂²×C₄×C₁₃	—	2	2	no	—
116	C₂²×C₄×C₁₃	—	2	2	no	—
117	C₂²×C₄×C₁₃	—	4	8	no	—
118	C₂²×C₄×C₁₃	—	4	1	no	—
119	C₂²×C₄×C₁₃	—	4	2	no	—
120	C₂²×C₄×C₁₃	—	4	2	no	—
121	C₂²×C₄×C₁₃	—	4	1	no	—
122	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
123	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
124	C₂²×C₄×C₁₃	D₈	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	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
128	C₁₃×Q₁₆	—	2	4	no	—
129	C₁₃×Q₁₆	—	2	2	no	—
130	C₁₃×Q₁₆	C₂×D₄	1	4	yes	complemented
131	C₁₃×SD₁₆	—	2	8	no	—
132	C₁₃×SD₁₆	—	2	8	no	—
133	C₁₃×D₈	—	2	4	no	—
134	C₁₃×D₈	—	2	2	no	—
135	C₁₃×D₈	—	2	4	no	—
136	C₁₃×D₈	—	4	2	no	—
137	C₁₃×D₈	C₂×D₄	1	4	yes	complemented
138	C₂×C₈×C₁₃	—	2	2	no	—
139	C₂×C₈×C₁₃	—	2	2	no	—
140	C₂×C₈×C₁₃	—	2	2	no	—
141	C₂×C₈×C₁₃	—	2	2	no	—
142	C₂×C₈×C₁₃	—	2	2	no	—
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	1	yes	characteristic
146	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
147	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
148	C₁₃×C₄⋊C₄	—	2	2	no	—
149	C₁₃×C₄⋊C₄	—	4	1	no	—
150	C₁₃×C₂²⋊C₄	—	4	2	no	—
151	C₁₃×C₂²⋊C₄	—	4	2	no	—
152	C₁₃×C₁₆	—	2	4	no	—
153	C₂²×#135	C₂×C₁₃	1	1	yes	characteristic, complemented
154	C₂×#509	C₂×C₁₃	1	2	yes	complemented
155	C₂×#466	C₂×C₁₃	1	1	yes	characteristic, complemented
156	#2186	C₂×C₁₃	1	4	yes	complemented
157	#2185	C₂×C₁₃	1	2	yes	complemented
158	#2184	C₂×C₁₃	1	2	yes	complemented
159	#2139	C₂×C₁₃	1	2	yes	complemented
160	#2112	C₂×C₁₃	1	1	yes	characteristic, complemented
161	C₂³×C₁₃	—	2	2	no	—
162	C₂³×C₁₃	—	2	2	no	—
163	C₂³×C₁₃	—	4	1	no	—
164	C₂³×C₁₃	—	4	4	no	—
165	C₂³×C₁₃	—	4	2	no	—
166	C₂³×C₁₃	—	4	2	no	—
167	C₂³×C₁₃	—	8	2	no	—
168	C₂³×C₁₃	—	8	2	no	—
169	C₂³×C₁₃	—	8	2	no	—
170	C₂³×C₁₃	—	8	2	no	—
171	C₂³×C₁₃	—	8	2	no	—
172	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
173	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
174	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
175	Q₈×C₁₃	—	2	4	no	—
176	Q₈×C₁₃	—	4	4	no	—
177	Q₈×C₁₃	—	4	2	no	—
178	D₄×C₁₃	—	2	4	no	—
179	D₄×C₁₃	—	4	4	no	—
180	D₄×C₁₃	—	4	8	no	—
181	D₄×C₁₃	—	4	8	no	—
182	D₄×C₁₃	—	4	2	no	—
183	D₄×C₁₃	—	4	2	no	—
184	D₄×C₁₃	—	4	2	no	—
185	D₄×C₁₃	—	8	4	no	—
186	D₄×C₁₃	—	8	4	no	—
187	D₄×C₁₃	—	8	2	no	—
188	C₂×C₄×C₁₃	—	2	2	no	—
189	C₂×C₄×C₁₃	—	2	1	no	—
190	C₂×C₄×C₁₃	—	2	1	no	—
191	C₂×C₄×C₁₃	—	2	1	no	—
192	C₂×C₄×C₁₃	—	2	1	no	—
193	C₂×C₄×C₁₃	—	2	2	no	—
194	C₂×C₄×C₁₃	—	2	2	no	—
195	C₂×C₄×C₁₃	—	4	8	no	—
196	C₂×C₄×C₁₃	—	4	4	no	—
197	C₂×C₄×C₁₃	—	4	2	no	—
198	C₂×C₄×C₁₃	—	4	8	no	—
199	C₂×C₄×C₁₃	—	4	2	no	—
200	C₂×C₄×C₁₃	—	8	2	no	—
201	C₂×C₄×C₁₃	#120	1	2	yes	—
202	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
203	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
204	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
205	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
206	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
207	C₈×C₁₃	—	2	1	no	—
208	C₈×C₁₃	—	2	1	no	—
209	C₈×C₁₃	#120	1	2	yes	—
210	C₈×C₁₃	C₂²×D₄	1	2	yes	—
211	C₂²×#41	—	2	1	no	—
212	C₂×#135	—	2	8	no	—
213	C₂×#135	—	2	1	no	—
214	C₂×#135	—	2	1	no	—
215	C₂×#135	C₂²×C₁₃	1	2	yes	—
216	C₂×#135	C₂²×C₁₃	1	2	yes	complemented
217	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
218	C₂²×SD₁₆	—	2	1	no	—
219	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
220	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
221	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
222	C₂×#121	—	2	1	no	—
223	#509	—	2	8	no	—
224	C₂×SD₃₂	C₂²×C₁₃	1	4	yes	complemented
225	C₂×D₁₆	C₂²×C₁₃	1	4	yes	complemented
226	C₂×M₃₂	C₂²×C₁₃	1	2	yes	complemented
227	#466	—	2	1	no	—
228	#466	—	2	1	no	—
229	#466	C₂²×C₁₃	1	2	yes	—
230	#466	C₂²×C₁₃	1	2	yes	complemented
231	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic, complemented
232	C₂×#102	—	2	1	no	—
233	#358	C₂²×C₁₃	1	4	yes	complemented
234	#357	C₂²×C₁₃	1	4	yes	complemented
235	C₂²⋊C₁₆	C₂²×C₁₃	1	2	yes	complemented
236	C₂²⋊C₁₆	C₂²×C₁₃	1	2	yes	complemented
237	C₂²×C₁₃	—	2	1	no	—
238	C₂²×C₁₃	—	2	1	no	—
239	C₂²×C₁₃	—	2	1	no	—
240	C₂²×C₁₃	—	2	1	no	—
241	C₂²×C₁₃	—	2	1	no	—
242	C₂²×C₁₃	—	2	1	no	—
243	C₂²×C₁₃	—	2	1	no	—
244	C₂²×C₁₃	—	4	4	no	—
245	C₂²×C₁₃	—	4	4	no	—
246	C₂²×C₁₃	—	8	8	no	—
247	C₂²×C₁₃	—	8	2	no	—
248	C₂²×C₁₃	—	8	2	no	—
249	C₂²×C₁₃	—	8	2	no	—
250	C₂²×C₁₃	—	8	2	no	—
251	C₂²×C₁₃	—	8	2	no	—
252	C₂²×C₁₃	—	16	4	no	—
253	C₂²×C₁₃	#447	1	2	yes	—
254	C₂²×C₁₃	#509	1	2	yes	complemented
255	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
256	C₄×C₁₃	—	2	1	no	—
257	C₄×C₁₃	—	2	1	no	—
258	C₄×C₁₃	—	4	4	no	—
259	C₄×C₁₃	—	8	2	no	—
260	C₄×C₁₃	#447	1	2	yes	—
261	C₄×C₁₃	C₂×#120	1	1	yes	characteristic
262	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
263	C₂×#41	—	2	8	no	—
264	C₂×#41	—	2	2	no	—
265	C₂×#41	—	2	2	no	—
266	C₂×#41	—	4	4	no	—
267	C₂×#41	—	4	1	no	—
268	C₂×#41	—	4	1	no	—
269	C₂²×Q₈	—	2	1	no	—
270	C₂²×D₄	—	2	1	no	—
271	C₂²×D₄	—	2	1	no	—
272	C₂²×D₄	—	4	1	no	—
273	C₂²×D₄	—	4	1	no	—
274	C₂³×C₄	—	4	1	no	—
275	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
276	#135	—	2	8	no	—
277	#135	—	2	8	no	—
278	#135	—	2	4	no	—
279	#135	—	2	4	no	—
280	#135	—	2	4	no	—
281	#135	D₄×C₁₃	1	8	yes	complemented
282	C₂×Q₁₆	—	2	4	no	—
283	C₂×Q₁₆	—	2	1	no	—
284	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
285	C₂×SD₁₆	—	2	8	no	—
286	C₂×SD₁₆	—	2	2	no	—
287	C₂×SD₁₆	—	2	2	no	—
288	C₂×D₈	—	2	4	no	—
289	C₂×D₈	—	2	1	no	—
290	C₂×D₈	—	2	4	no	—
291	C₂×D₈	—	2	1	no	—
292	C₂×D₈	C₂³×C₁₃	1	2	yes	—
293	C₂×D₈	C₂³×C₁₃	1	2	yes	—
294	C₂²×C₈	—	2	4	no	—
295	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
296	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
297	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
298	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
299	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
300	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
301	#121	—	2	2	no	—
302	#121	—	2	2	no	—
303	#121	—	4	1	no	—
304	#121	—	4	1	no	—
305	C₂×C₄⋊C₄	—	2	1	no	—
306	C₂×C₂²⋊C₄	—	4	1	no	—
307	SD₃₂	—	2	8	no	—
308	D₁₆	—	2	8	no	—
309	M₃₂	—	2	4	no	—
310	C₂×C₁₆	C₂³×C₁₃	1	4	yes	—
311	#107	—	2	1	no	—
312	#107	C₂³×C₁₃	1	2	yes	—
313	#102	—	2	2	no	—
314	#102	—	2	2	no	—
315	C₂×C₁₃	—	2	2	no	—
316	C₂×C₁₃	—	2	2	no	—
317	C₂×C₁₃	—	4	1	no	—
318	C₂×C₁₃	—	8	4	no	—
319	C₂×C₁₃	—	16	2	no	—
320	C₂×C₁₃	C₂×#447	1	1	yes	characteristic
321	C₂×C₁₃	C₂×#509	1	1	yes	characteristic
322	C₂×C₁₃	#3414	1	1	yes	characteristic
323	C₂⁴	—	4	1	no	—
324	C₂⁴	—	4	1	no	—
325	C₂⁴	C₁₃×D₈	1	1	yes	characteristic
326	#41	—	2	8	no	—
327	#41	—	2	8	no	—
328	#41	—	4	8	no	—
329	#41	—	4	8	no	—
330	#41	—	4	4	no	—
331	#41	—	4	4	no	—
332	C₂×Q₈	—	2	4	no	—
333	C₂×Q₈	—	2	2	no	—
334	C₂×Q₈	—	4	2	no	—
335	C₂×Q₈	—	4	1	no	—
336	C₂×D₄	—	2	4	no	—
337	C₂×D₄	—	2	2	no	—
338	C₂×D₄	—	2	2	no	—
339	C₂×D₄	—	4	2	no	—
340	C₂×D₄	—	4	8	no	—
341	C₂×D₄	—	4	2	no	—
342	C₂×D₄	—	4	2	no	—
343	C₂×D₄	—	4	2	no	—
344	C₂×D₄	—	4	2	no	—
345	C₂×D₄	—	4	2	no	—
346	C₂×D₄	—	4	1	no	—
347	C₂×D₄	—	4	1	no	—
348	C₂×D₄	—	4	2	no	—
349	C₂×D₄	—	8	4	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	4	8	no	—
353	C₂²×C₄	—	4	1	no	—
354	C₂²×C₄	—	4	2	no	—
355	C₂²×C₄	—	4	2	no	—
356	C₂²×C₄	—	4	1	no	—
357	C₂²×C₄	C₁₃×D₈	1	1	yes	characteristic
358	C₂²×C₄	C₁₃×D₈	1	1	yes	characteristic
359	C₂²×C₄	C₁₃×D₈	1	1	yes	characteristic
360	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
361	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
362	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
363	Q₁₆	—	2	4	no	—
364	Q₁₆	—	2	2	no	—
365	Q₁₆	C₂×D₄×C₁₃	1	4	yes	complemented
366	SD₁₆	—	2	8	no	—
367	SD₁₆	—	2	8	no	—
368	D₈	—	2	4	no	—
369	D₈	—	2	2	no	—
370	D₈	—	2	4	no	—
371	D₈	—	4	2	no	—
372	D₈	C₂×D₄×C₁₃	1	4	yes	complemented
373	C₂×C₈	—	2	2	no	—
374	C₂×C₈	—	2	2	no	—
375	C₂×C₈	—	2	2	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
379	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
380	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
381	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
382	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	—	4	1	no	—
385	C₂²⋊C₄	—	4	2	no	—
386	C₂²⋊C₄	—	4	2	no	—
387	C₁₆	—	2	4	no	—
388	C₁₃	#33520	1	1	yes	characteristic, direct product factor, Sylow
389	C₂³	—	2	2	no	—
390	C₂³	—	2	2	no	—
391	C₂³	—	4	1	no	—
392	C₂³	—	4	4	no	—
393	C₂³	—	4	2	no	—
394	C₂³	—	4	2	no	—
395	C₂³	—	8	2	no	—
396	C₂³	—	8	2	no	—
397	C₂³	—	8	2	no	—
398	C₂³	—	8	2	no	—
399	C₂³	—	8	2	no	—
400	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
401	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
402	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
403	Q₈	—	2	4	no	—
404	Q₈	—	4	4	no	—
405	Q₈	—	4	2	no	—
406	D₄	—	2	4	no	—
407	D₄	—	4	4	no	—
408	D₄	—	4	8	no	—
409	D₄	—	4	8	no	—
410	D₄	—	4	2	no	—
411	D₄	—	4	2	no	—
412	D₄	—	4	2	no	—
413	D₄	—	8	4	no	—
414	D₄	—	8	4	no	—
415	D₄	—	8	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	4	8	no	—
424	C₂×C₄	—	4	4	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	8	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	8	2	no	—
429	C₂×C₄	C₁₃×#120	1	2	yes	—
430	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
431	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
432	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
433	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
434	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
435	C₈	—	2	1	no	—
436	C₈	—	2	1	no	—
437	C₈	C₁₃×#120	1	2	yes	—
438	C₈	C₂²×D₄×C₁₃	1	2	yes	—
439	C₂²	—	2	1	no	—
440	C₂²	—	2	1	no	—
441	C₂²	—	2	1	no	—
442	C₂²	—	2	1	no	—
443	C₂²	—	2	1	no	—
444	C₂²	—	2	1	no	—
445	C₂²	—	2	1	no	—
446	C₂²	—	4	4	no	—
447	C₂²	—	4	4	no	—
448	C₂²	—	8	8	no	—
449	C₂²	—	8	2	no	—
450	C₂²	—	8	2	no	—
451	C₂²	—	8	2	no	—
452	C₂²	—	8	2	no	—
453	C₂²	—	8	2	no	—
454	C₂²	—	16	4	no	—
455	C₂²	C₁₃×#447	1	2	yes	—
456	C₂²	C₁₃×#509	1	2	yes	complemented
457	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
458	C₄	—	2	1	no	—
459	C₄	—	2	1	no	—
460	C₄	—	4	4	no	—
461	C₄	—	8	2	no	—
462	C₄	C₁₃×#447	1	2	yes	—
463	C₄	C₂×C₁₃×#120	1	1	yes	characteristic
464	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
465	C₂	—	2	2	no	—
466	C₂	—	2	2	no	—
467	C₂	—	4	1	no	—
468	C₂	—	8	4	no	—
469	C₂	—	16	2	no	—
470	C₂	C₂×C₁₃×#447	1	1	yes	characteristic
471	C₂	C₂×C₁₃×#509	1	1	yes	characteristic
472	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. C₂²×C₁₃×#135	C₂	semidirect
2. C₂×C₁₃×#509	C₂	semidirect
3. C₂×C₁₃×#466	C₂	semidirect
4. C₁₃×#2186	C₂	semidirect
5. C₁₃×#2185	C₂	semidirect
6. C₁₃×#2184	C₂	semidirect
7. C₁₃×#2139	C₂	semidirect
8. C₁₃×#2112	C₂	semidirect
14. C₂×C₁₃×#135	C₂²	semidirect
15. C₂²×C₁₃×Q₁₆	C₂²	semidirect
17. C₂²×C₁₃×D₈	C₂²	semidirect
18. C₂²×C₁₃×D₈	C₂²	semidirect
22. C₂×C₁₃×SD₃₂	C₂²	semidirect
23. C₂×C₁₃×D₁₆	C₂²	semidirect
24. C₂×C₁₃×M₃₂	C₂²	semidirect
28. C₁₃×#466	C₂²	semidirect
29. C₂×C₁₃×#107	C₂²	semidirect
31. C₁₃×#358	C₂²	semidirect
32. C₁₃×#357	C₂²	semidirect
33. C₁₃×C₂²⋊C₁₆	C₂²	semidirect
34. C₁₃×C₂²⋊C₁₆	C₂²	semidirect
53. C₁₃×#135	D₄	semidirect
87. #33520	C₁₃	direct (N × H)
130. C₁₃×Q₁₆	C₂×D₄	semidirect
137. C₁₃×D₈	C₂×D₄	semidirect
153. C₂²×#135	C₂×C₁₃	semidirect
154. C₂×#509	C₂×C₁₃	semidirect
155. C₂×#466	C₂×C₁₃	semidirect
156. #2186	C₂×C₁₃	semidirect
157. #2185	C₂×C₁₃	semidirect
158. #2184	C₂×C₁₃	semidirect
159. #2139	C₂×C₁₃	semidirect
160. #2112	C₂×C₁₃	semidirect
216. C₂×#135	C₂²×C₁₃	semidirect
217. C₂²×Q₁₆	C₂²×C₁₃	semidirect
219. C₂²×D₈	C₂²×C₁₃	semidirect
220. C₂²×D₈	C₂²×C₁₃	semidirect
224. C₂×SD₃₂	C₂²×C₁₃	semidirect
225. C₂×D₁₆	C₂²×C₁₃	semidirect
226. C₂×M₃₂	C₂²×C₁₃	semidirect
230. #466	C₂²×C₁₃	semidirect
231. C₂×#107	C₂²×C₁₃	semidirect
233. #358	C₂²×C₁₃	semidirect
234. #357	C₂²×C₁₃	semidirect
235. C₂²⋊C₁₆	C₂²×C₁₃	semidirect
236. C₂²⋊C₁₆	C₂²×C₁₃	semidirect
254. C₂²×C₁₃	#509	semidirect
281. #135	D₄×C₁₃	semidirect
365. Q₁₆	C₂×D₄×C₁₃	semidirect
372. D₈	C₂×D₄×C₁₃	semidirect
388. C₁₃	#33520	direct (N × H)
456. 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
C₂²×C₁₃×#135	2
C₂×C₁₃×#509	2
C₂×C₁₃×#466	2
C₁₃×#2186	2
C₁₃×#2185	2
C₁₃×#2184	2
C₁₃×#2139	2
C₁₃×#2112	2
#33520	13

Subgroups — C13×#33520 #15719859

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33520 #15719859