Subgroups — C₁₃×#33590 #15719929

Order 3328.

694 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#510	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#508	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3156	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2951	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2211	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2210	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2209	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2208	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2151	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2139	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×#358	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#137	—	2	1	no	—
13	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
15	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
16	C₁₃×#536	—	2	1	no	—
17	C₁₃×#520	—	2	1	no	—
18	C₁₃×#510	—	2	4	no	—
19	C₁₃×#508	—	2	4	no	—
20	C₂×C₁₃×Q₃₂	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×Q₃₂	C₂²	1	2	yes	—
22	C₂×C₁₃×SD₃₂	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×SD₃₂	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×SD₃₂	C₂²	1	2	yes	—
25	C₂×C₁₃×D₁₆	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×M₃₂	C₂²	1	1	yes	characteristic
27	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
28	C₁₃×#497	—	2	2	no	—
29	C₁₃×#495	C₂²	1	2	yes	—
30	C₁₃×#494	C₂²	1	2	yes	—
31	C₁₃×#440	—	2	2	no	—
32	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
33	C₄×C₁₃×D₈	C₂²	1	2	yes	—
34	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
35	C₁₃×#417	—	2	1	no	—
36	C₁₃×#405	C₂²	1	1	yes	characteristic
37	C₁₃×C₄⋊C₁₆	C₂²	1	2	yes	—
38	C₁₃×C₄⋊C₁₆	C₂²	1	2	yes	—
39	C₁₃×#358	C₂²	1	2	yes	—
40	C₁₃×#358	C₂²	1	2	yes	—
41	C₁₃×#358	C₂²	1	2	yes	—
42	C₁₃×#357	C₂²	1	2	yes	—
43	C₂×C₁₃×#41	—	2	1	no	—
44	C₂×C₁₃×#41	—	2	1	no	—
45	C₂²×Q₈×C₁₃	—	2	1	no	—
46	C₁₃×#137	—	4	4	no	—
47	C₁₃×#135	—	2	2	no	—
48	C₁₃×#135	—	2	2	no	—
49	C₁₃×#135	—	2	2	no	—
50	C₁₃×#135	D₄	1	4	yes	—
51	C₂×C₁₃×Q₁₆	—	2	2	no	—
52	C₂×C₁₃×Q₁₆	—	2	2	no	—
53	C₂×C₁₃×Q₁₆	—	2	1	no	—
54	C₂×C₁₃×Q₁₆	—	2	2	no	—
55	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
56	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
57	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
58	C₂×C₁₃×SD₁₆	—	2	1	no	—
59	C₂×C₁₃×SD₁₆	—	2	2	no	—
60	C₂×C₁₃×SD₁₆	—	2	1	no	—
61	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
62	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
63	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
64	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
65	C₁₃×C₄⋊Q₈	—	2	2	no	—
66	C₁₃×#124	—	2	2	no	—
67	C₁₃×#123	—	4	2	no	—
68	C₁₃×C₂²⋊Q₈	—	4	1	no	—
69	C₁₃×C₂²⋊Q₈	—	4	1	no	—
70	C₄×Q₈×C₁₃	—	2	2	no	—
71	C₄×D₄×C₁₃	—	2	2	no	—
72	C₄×D₄×C₁₃	—	4	2	no	—
73	C₁₃×#117	—	4	1	no	—
74	C₁₃×#117	D₄	1	1	yes	characteristic
75	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
76	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
77	C₁₃×Q₃₂	—	2	2	no	—
78	C₁₃×Q₃₂	—	2	4	no	—
79	C₁₃×SD₃₂	—	2	2	no	—
80	C₁₃×SD₃₂	—	2	2	no	—
81	C₁₃×SD₃₂	—	2	4	no	—
82	C₁₃×D₁₆	—	2	2	no	—
83	C₁₃×M₃₂	—	2	2	no	—
84	C₂×C₁₃×C₁₆	—	2	2	no	—
85	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
86	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
87	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
88	C₁₃×#107	—	2	1	no	—
89	C₁₃×#107	C₂³	1	2	yes	—
90	C₁₃×#103	—	2	2	no	—
91	C₁₃×#102	—	2	2	no	—
92	C₁₃×#97	D₄	1	2	yes	—
93	C₄×C₈×C₁₃	C₂³	1	2	yes	—
94	#33590	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
95	C₁₃×#41	—	2	4	no	—
96	C₁₃×#41	—	4	2	no	—
97	C₁₃×#41	—	4	2	no	—
98	C₁₃×#41	—	4	2	no	—
99	C₂×Q₈×C₁₃	—	2	1	no	—
100	C₂×Q₈×C₁₃	—	2	2	no	—
101	C₂×Q₈×C₁₃	—	2	1	no	—
102	C₂×Q₈×C₁₃	—	4	1	no	—
103	C₂×Q₈×C₁₃	—	4	2	no	—
104	C₂×Q₈×C₁₃	—	4	2	no	—
105	C₂×D₄×C₁₃	—	2	1	no	—
106	C₂×D₄×C₁₃	—	2	1	no	—
107	C₂×D₄×C₁₃	—	4	1	no	—
108	C₂×D₄×C₁₃	—	4	1	no	—
109	C₂²×C₄×C₁₃	—	4	1	no	—
110	C₂²×C₄×C₁₃	—	4	1	no	—
111	C₂²×C₄×C₁₃	—	4	1	no	—
112	C₂²×C₄×C₁₃	—	4	1	no	—
113	C₂²×C₄×C₁₃	—	4	2	no	—
114	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
115	C₁₃×Q₁₆	—	2	2	no	—
116	C₁₃×Q₁₆	—	2	1	no	—
117	C₁₃×Q₁₆	—	2	1	no	—
118	C₁₃×Q₁₆	—	2	2	no	—
119	C₁₃×Q₁₆	—	2	1	no	—
120	C₁₃×Q₁₆	—	4	4	no	—
121	C₁₃×Q₁₆	—	4	2	no	—
122	C₁₃×Q₁₆	C₂×D₄	1	2	yes	—
123	C₁₃×SD₁₆	—	2	4	no	—
124	C₁₃×SD₁₆	—	4	4	no	—
125	C₁₃×SD₁₆	—	4	2	no	—
126	C₁₃×D₈	—	2	1	no	—
127	C₁₃×D₈	—	2	1	no	—
128	C₁₃×D₈	—	2	1	no	—
129	C₁₃×D₈	C₂×D₄	1	2	yes	—
130	C₁₃×M₁₆	—	2	2	no	—
131	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
132	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
133	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
134	C₂×C₈×C₁₃	#41	1	2	yes	—
135	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
136	C₁₃×C₄⋊C₄	—	2	2	no	—
137	C₁₃×C₄⋊C₄	—	4	1	no	—
138	C₁₃×C₄⋊C₄	—	4	2	no	—
139	C₁₃×C₄⋊C₄	—	4	2	no	—
140	C₁₃×C₄⋊C₄	—	4	2	no	—
141	C₁₃×C₄⋊C₄	D₈	1	1	yes	characteristic
142	C₁₃×C₄⋊C₄	D₈	1	1	yes	characteristic
143	C₁₃×C₂²⋊C₄	—	4	2	no	—
144	C₁₃×C₂²⋊C₄	—	4	2	no	—
145	C₁₃×C₂²⋊C₄	—	4	2	no	—
146	C₁₃×C₂²⋊C₄	D₈	1	2	yes	—
147	C₄²×C₁₃	—	4	2	no	—
148	C₄²×C₁₃	C₂×D₄	1	2	yes	—
149	C₁₃×C₁₆	—	2	1	no	—
150	C₁₃×C₁₆	—	2	1	no	—
151	C₁₃×C₁₆	—	2	2	no	—
152	C₂×#510	C₂×C₁₃	1	1	yes	characteristic, complemented
153	C₂×#508	C₂×C₁₃	1	1	yes	characteristic
154	#3156	C₂×C₁₃	1	1	yes	characteristic, complemented
155	#2951	C₂×C₁₃	1	1	yes	characteristic, complemented
156	#2211	C₂×C₁₃	1	2	yes	complemented
157	#2210	C₂×C₁₃	1	2	yes	complemented
158	#2209	C₂×C₁₃	1	2	yes	complemented
159	#2208	C₂×C₁₃	1	2	yes	complemented
160	#2151	C₂×C₁₃	1	1	yes	characteristic, complemented
161	#2139	C₂×C₁₃	1	1	yes	characteristic, complemented
162	C₂×#358	C₂×C₁₃	1	1	yes	characteristic, complemented
163	C₂³×C₁₃	—	4	1	no	—
164	C₂³×C₁₃	—	4	1	no	—
165	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
166	Q₈×C₁₃	—	2	2	no	—
167	Q₈×C₁₃	—	4	1	no	—
168	Q₈×C₁₃	—	4	1	no	—
169	Q₈×C₁₃	—	4	2	no	—
170	Q₈×C₁₃	—	4	2	no	—
171	Q₈×C₁₃	—	4	1	no	—
172	Q₈×C₁₃	—	8	2	no	—
173	D₄×C₁₃	—	2	2	no	—
174	D₄×C₁₃	—	4	4	no	—
175	D₄×C₁₃	—	4	1	no	—
176	D₄×C₁₃	—	4	1	no	—
177	D₄×C₁₃	—	4	1	no	—
178	D₄×C₁₃	—	8	2	no	—
179	C₂×C₄×C₁₃	—	4	1	no	—
180	C₂×C₄×C₁₃	—	4	4	no	—
181	C₂×C₄×C₁₃	—	4	2	no	—
182	C₂×C₄×C₁₃	—	4	2	no	—
183	C₂×C₄×C₁₃	—	4	1	no	—
184	C₂×C₄×C₁₃	—	8	2	no	—
185	C₂×C₄×C₁₃	—	8	2	no	—
186	C₂×C₄×C₁₃	—	16	2	no	—
187	C₂×C₄×C₁₃	—	16	1	no	—
188	C₂×C₄×C₁₃	#121	1	2	yes	—
189	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
190	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
191	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
192	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
193	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
194	C₈×C₁₃	—	2	2	no	—
195	C₈×C₁₃	#121	1	2	yes	—
196	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
197	C₈×C₁₃	C₂×#41	1	1	yes	characteristic
198	C₂×#137	—	2	1	no	—
199	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
200	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
201	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
202	#536	—	2	1	no	—
203	#520	—	2	1	no	—
204	#510	—	2	4	no	—
205	#508	—	2	4	no	—
206	C₂×Q₃₂	C₂²×C₁₃	1	1	yes	characteristic
207	C₂×Q₃₂	C₂²×C₁₃	1	2	yes	—
208	C₂×SD₃₂	C₂²×C₁₃	1	1	yes	characteristic
209	C₂×SD₃₂	C₂²×C₁₃	1	1	yes	characteristic
210	C₂×SD₃₂	C₂²×C₁₃	1	2	yes	—
211	C₂×D₁₆	C₂²×C₁₃	1	1	yes	characteristic
212	C₂×M₃₂	C₂²×C₁₃	1	1	yes	characteristic
213	C₂²×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
214	#497	—	2	2	no	—
215	#495	C₂²×C₁₃	1	2	yes	—
216	#494	C₂²×C₁₃	1	2	yes	—
217	#440	—	2	2	no	—
218	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
219	C₄×D₈	C₂²×C₁₃	1	2	yes	—
220	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
221	#417	—	2	1	no	—
222	#405	C₂²×C₁₃	1	1	yes	characteristic
223	C₄⋊C₁₆	C₂²×C₁₃	1	2	yes	—
224	C₄⋊C₁₆	C₂²×C₁₃	1	2	yes	—
225	#358	C₂²×C₁₃	1	2	yes	—
226	#358	C₂²×C₁₃	1	2	yes	—
227	#358	C₂²×C₁₃	1	2	yes	—
228	#357	C₂²×C₁₃	1	2	yes	—
229	C₂²×C₁₃	—	2	1	no	—
230	C₂²×C₁₃	—	2	1	no	—
231	C₂²×C₁₃	—	4	2	no	—
232	C₂²×C₁₃	—	8	1	no	—
233	C₂²×C₁₃	—	8	1	no	—
234	C₂²×C₁₃	—	8	1	no	—
235	C₂²×C₁₃	—	8	1	no	—
236	C₂²×C₁₃	—	8	1	no	—
237	C₂²×C₁₃	#459	1	2	yes	—
238	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
239	C₄×C₁₃	—	2	2	no	—
240	C₄×C₁₃	—	2	2	no	—
241	C₄×C₁₃	—	4	2	no	—
242	C₄×C₁₃	—	8	2	no	—
243	C₄×C₁₃	—	8	1	no	—
244	C₄×C₁₃	—	8	2	no	—
245	C₄×C₁₃	#459	1	2	yes	—
246	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
247	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
248	C₂×#41	—	2	1	no	—
249	C₂×#41	—	2	1	no	—
250	C₂²×Q₈	—	2	1	no	—
251	#137	—	4	4	no	—
252	#135	—	2	2	no	—
253	#135	—	2	2	no	—
254	#135	—	2	2	no	—
255	#135	D₄×C₁₃	1	4	yes	—
256	C₂×Q₁₆	—	2	2	no	—
257	C₂×Q₁₆	—	2	1	no	—
258	C₂×Q₁₆	—	2	2	no	—
259	C₂×Q₁₆	—	2	2	no	—
260	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
261	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
262	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
263	C₂×SD₁₆	—	2	1	no	—
264	C₂×SD₁₆	—	2	1	no	—
265	C₂×SD₁₆	—	2	2	no	—
266	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
267	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
268	C₂×M₁₆	D₄×C₁₃	1	1	yes	characteristic
269	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
270	C₄⋊Q₈	—	2	2	no	—
271	#124	—	2	2	no	—
272	#123	—	4	2	no	—
273	C₂²⋊Q₈	—	4	1	no	—
274	C₂²⋊Q₈	—	4	1	no	—
275	C₄×Q₈	—	2	2	no	—
276	C₄×D₄	—	2	2	no	—
277	C₄×D₄	—	4	2	no	—
278	#117	—	4	1	no	—
279	#117	D₄×C₁₃	1	1	yes	characteristic
280	C₂×C₄⋊C₄	—	2	1	no	—
281	C₂×C₄⋊C₄	—	4	1	no	—
282	Q₃₂	—	2	2	no	—
283	Q₃₂	—	2	4	no	—
284	SD₃₂	—	2	2	no	—
285	SD₃₂	—	2	2	no	—
286	SD₃₂	—	2	4	no	—
287	D₁₆	—	2	2	no	—
288	M₃₂	—	2	2	no	—
289	C₂×C₁₆	—	2	2	no	—
290	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
291	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
292	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
293	#107	—	2	1	no	—
294	#107	C₂³×C₁₃	1	2	yes	—
295	#103	—	2	2	no	—
296	#102	—	2	2	no	—
297	#97	D₄×C₁₃	1	2	yes	—
298	C₄×C₈	C₂³×C₁₃	1	2	yes	—
299	C₂×C₁₃	—	2	2	no	—
300	C₂×C₁₃	—	8	2	no	—
301	C₂×C₁₃	—	16	1	no	—
302	C₂×C₁₃	C₂×#459	1	1	yes	characteristic
303	C₂×C₁₃	#3416	1	1	yes	characteristic
304	C₂×C₁₃	#3417	1	1	yes	characteristic
305	#41	—	2	4	no	—
306	#41	—	4	2	no	—
307	#41	—	4	2	no	—
308	#41	—	4	2	no	—
309	C₂×Q₈	—	2	1	no	—
310	C₂×Q₈	—	2	2	no	—
311	C₂×Q₈	—	2	1	no	—
312	C₂×Q₈	—	4	1	no	—
313	C₂×Q₈	—	4	2	no	—
314	C₂×Q₈	—	4	2	no	—
315	C₂×D₄	—	2	1	no	—
316	C₂×D₄	—	2	1	no	—
317	C₂×D₄	—	4	1	no	—
318	C₂×D₄	—	4	1	no	—
319	C₂²×C₄	—	4	1	no	—
320	C₂²×C₄	—	4	1	no	—
321	C₂²×C₄	—	4	1	no	—
322	C₂²×C₄	—	4	1	no	—
323	C₂²×C₄	—	4	2	no	—
324	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
325	Q₁₆	—	2	2	no	—
326	Q₁₆	—	2	1	no	—
327	Q₁₆	—	2	1	no	—
328	Q₁₆	—	2	2	no	—
329	Q₁₆	—	2	1	no	—
330	Q₁₆	—	4	4	no	—
331	Q₁₆	—	4	2	no	—
332	Q₁₆	C₂×D₄×C₁₃	1	2	yes	—
333	SD₁₆	—	2	4	no	—
334	SD₁₆	—	4	4	no	—
335	SD₁₆	—	4	2	no	—
336	D₈	—	2	1	no	—
337	D₈	—	2	1	no	—
338	D₈	—	2	1	no	—
339	D₈	C₂×D₄×C₁₃	1	2	yes	—
340	M₁₆	—	2	2	no	—
341	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
342	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
343	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
344	C₂×C₈	C₁₃×#41	1	2	yes	—
345	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	4	1	no	—
348	C₄⋊C₄	—	4	2	no	—
349	C₄⋊C₄	—	4	2	no	—
350	C₄⋊C₄	—	4	2	no	—
351	C₄⋊C₄	C₁₃×D₈	1	1	yes	characteristic
352	C₄⋊C₄	C₁₃×D₈	1	1	yes	characteristic
353	C₂²⋊C₄	—	4	2	no	—
354	C₂²⋊C₄	—	4	2	no	—
355	C₂²⋊C₄	—	4	2	no	—
356	C₂²⋊C₄	C₁₃×D₈	1	2	yes	—
357	C₄²	—	4	2	no	—
358	C₄²	C₂×D₄×C₁₃	1	2	yes	—
359	C₁₆	—	2	1	no	—
360	C₁₆	—	2	1	no	—
361	C₁₆	—	2	2	no	—
362	C₁₃	#33590	1	1	yes	characteristic, direct product factor, Sylow
363	C₂³	—	4	1	no	—
364	C₂³	—	4	1	no	—
365	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
366	Q₈	—	2	2	no	—
367	Q₈	—	4	1	no	—
368	Q₈	—	4	1	no	—
369	Q₈	—	4	2	no	—
370	Q₈	—	4	2	no	—
371	Q₈	—	4	1	no	—
372	Q₈	—	8	2	no	—
373	D₄	—	2	2	no	—
374	D₄	—	4	4	no	—
375	D₄	—	4	1	no	—
376	D₄	—	4	1	no	—
377	D₄	—	4	1	no	—
378	D₄	—	8	2	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	4	4	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	1	no	—
384	C₂×C₄	—	8	2	no	—
385	C₂×C₄	—	8	2	no	—
386	C₂×C₄	—	16	2	no	—
387	C₂×C₄	—	16	1	no	—
388	C₂×C₄	C₁₃×#121	1	2	yes	—
389	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
390	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
391	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
392	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
393	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
394	C₈	—	2	2	no	—
395	C₈	C₁₃×#121	1	2	yes	—
396	C₈	C₂²×D₄×C₁₃	1	1	yes	characteristic
397	C₈	C₂×C₁₃×#41	1	1	yes	characteristic
398	C₂²	—	2	1	no	—
399	C₂²	—	2	1	no	—
400	C₂²	—	4	2	no	—
401	C₂²	—	8	1	no	—
402	C₂²	—	8	1	no	—
403	C₂²	—	8	1	no	—
404	C₂²	—	8	1	no	—
405	C₂²	—	8	1	no	—
406	C₂²	C₁₃×#459	1	2	yes	—
407	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
408	C₄	—	2	2	no	—
409	C₄	—	2	2	no	—
410	C₄	—	4	2	no	—
411	C₄	—	8	1	no	—
412	C₄	—	8	2	no	—
413	C₄	—	8	2	no	—
414	C₄	C₁₃×#459	1	2	yes	—
415	C₄	C₂×C₁₃×#121	1	1	yes	characteristic
416	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
417	C₂	—	2	2	no	—
418	C₂	—	8	2	no	—
419	C₂	—	16	1	no	—
420	C₂	C₂×C₁₃×#459	1	1	yes	characteristic
421	C₂	C₁₃×#3416	1	1	yes	characteristic
422	C₂	C₁₃×#3417	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#508	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₁₃×#117 ◁ C₁₃×#405 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#510	C₂	semidirect
3. C₁₃×#3156	C₂	semidirect
4. C₁₃×#2951	C₂	semidirect
5. C₁₃×#2211	C₂	semidirect
6. C₁₃×#2210	C₂	semidirect
7. C₁₃×#2209	C₂	semidirect
8. C₁₃×#2208	C₂	semidirect
9. C₁₃×#2151	C₂	semidirect
10. C₁₃×#2139	C₂	semidirect
11. C₂×C₁₃×#358	C₂	semidirect
94. #33590	C₁₃	direct (N × H)
152. C₂×#510	C₂×C₁₃	semidirect
154. #3156	C₂×C₁₃	semidirect
155. #2951	C₂×C₁₃	semidirect
156. #2211	C₂×C₁₃	semidirect
157. #2210	C₂×C₁₃	semidirect
158. #2209	C₂×C₁₃	semidirect
159. #2208	C₂×C₁₃	semidirect
160. #2151	C₂×C₁₃	semidirect
161. #2139	C₂×C₁₃	semidirect
162. C₂×#358	C₂×C₁₃	semidirect
362. C₁₃	#33590	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×#510	2
C₂×C₁₃×#508	2
C₁₃×#3156	2
C₁₃×#2951	2
C₁₃×#2211	2
C₁₃×#2210	2
C₁₃×#2209	2
C₁₃×#2208	2
C₁₃×#2151	2
C₁₃×#2139	2
C₂×C₁₃×#358	2
#33590	13

Subgroups — C13×#33590 #15719929

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33590 #15719929