Subgroups — C₁₃×#33667 #15720006

Order 3328.

552 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3170	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×C₁₃×#135	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2237	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2225	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2224	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2209	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2208	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2189	C₂	1	2	yes	maximal
9	C₄×C₁₃×Q₃₂	C₂	1	2	yes	maximal, complemented
10	C₄×C₁₃×SD₃₂	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2162	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
13	C₁₃×#533	—	2	1	no	—
14	C₄×C₁₃×#41	—	2	1	no	—
15	C₂×C₁₃×Q₃₂	C₂²	1	2	yes	—
16	C₂×C₁₃×SD₃₂	C₂²	1	2	yes	—
17	C₁₃×#500	C₂²	1	1	yes	characteristic
18	C₁₃×#494	C₂²	1	1	yes	characteristic
19	C₁₃×#487	—	2	1	no	—
20	C₁₃×#467	—	2	1	no	—
21	C₁₃×#467	C₂²	1	2	yes	—
22	C₄×C₁₃×Q₁₆	—	2	1	no	—
23	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
24	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
25	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
26	C₄×C₁₃×SD₁₆	—	2	1	no	—
27	C₄×C₁₃×SD₁₆	—	2	1	no	—
28	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
29	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
30	C₁₃×#427	C₂²	1	1	yes	characteristic
31	C₁₃×#416	—	2	1	no	—
32	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
33	C₁₃×#367	C₂²	1	2	yes	—
34	C₁₃×#366	C₂²	1	2	yes	—
35	C₁₃×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
36	C₁₃×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
37	C₁₃×#358	C₂²	1	2	yes	—
38	C₁₃×#358	C₂²	1	2	yes	—
39	C₁₃×#358	C₂²	1	2	yes	—
40	C₁₃×#357	C₂²	1	2	yes	—
41	C₁₃×C₂²⋊C₁₆	C₂²	1	2	yes	—
42	C₄×C₁₃×C₁₆	C₂²	1	2	yes	—
43	C₂×C₁₃×#41	—	2	1	no	—
44	C₁₃×#135	—	2	2	no	—
45	C₁₃×#135	—	2	2	no	—
46	C₂×C₁₃×Q₁₆	—	2	1	no	—
47	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
48	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
49	C₂×C₁₃×SD₁₆	—	2	1	no	—
50	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
52	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
53	C₁₃×C₄⋊Q₈	—	2	1	no	—
54	C₁₃×C₄⋊Q₈	—	2	1	no	—
55	C₁₃×#125	—	4	1	no	—
56	C₁₃×C₂²⋊Q₈	—	2	2	no	—
57	C₁₃×C₂²⋊Q₈	—	4	1	no	—
58	C₄×Q₈×C₁₃	—	2	1	no	—
59	C₄×Q₈×C₁₃	—	2	1	no	—
60	C₄×Q₈×C₁₃	—	2	2	no	—
61	C₄×Q₈×C₁₃	—	4	1	no	—
62	C₄×D₄×C₁₃	—	2	1	no	—
63	C₄×D₄×C₁₃	—	2	1	no	—
64	C₄×D₄×C₁₃	—	4	1	no	—
65	C₄×D₄×C₁₃	—	4	1	no	—
66	C₁₃×#117	—	2	1	no	—
67	C₁₃×#117	—	4	1	no	—
68	C₁₃×#117	—	4	1	no	—
69	C₂×C₄²×C₁₃	—	4	1	no	—
70	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
71	C₁₃×Q₃₂	—	2	4	no	—
72	C₁₃×SD₃₂	—	2	4	no	—
73	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
74	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
75	C₁₃×#107	—	2	1	no	—
76	C₁₃×#107	C₂³	1	1	yes	characteristic
77	C₁₃×#107	C₂³	1	1	yes	characteristic
78	C₁₃×#107	C₂³	1	2	yes	—
79	C₁₃×#106	—	2	1	no	—
80	C₁₃×#103	—	2	1	no	—
81	C₁₃×#103	—	2	1	no	—
82	C₁₃×#103	—	2	2	no	—
83	C₁₃×#103	—	2	2	no	—
84	C₁₃×#102	—	2	1	no	—
85	C₁₃×#102	—	2	1	no	—
86	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
87	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
88	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
89	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
90	#33667	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
91	C₁₃×#41	—	2	4	no	—
92	C₁₃×#41	—	4	2	no	—
93	C₂×Q₈×C₁₃	—	2	1	no	—
94	C₂×Q₈×C₁₃	—	2	2	no	—
95	C₂×Q₈×C₁₃	—	4	1	no	—
96	C₂×D₄×C₁₃	—	2	1	no	—
97	C₂×D₄×C₁₃	—	4	1	no	—
98	C₂²×C₄×C₁₃	—	4	1	no	—
99	C₂²×C₄×C₁₃	—	4	1	no	—
100	C₂²×C₄×C₁₃	—	4	1	no	—
101	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
102	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
103	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
104	C₁₃×Q₁₆	—	2	1	no	—
105	C₁₃×Q₁₆	—	2	2	no	—
106	C₁₃×Q₁₆	—	2	2	no	—
107	C₁₃×Q₁₆	—	4	2	no	—
108	C₁₃×Q₁₆	#41	1	2	yes	—
109	C₁₃×SD₁₆	—	2	4	no	—
110	C₁₃×D₈	—	2	1	no	—
111	C₁₃×D₈	#41	1	2	yes	—
112	C₂×C₈×C₁₃	—	2	1	no	—
113	C₂×C₈×C₁₃	—	2	1	no	—
114	C₂×C₈×C₁₃	—	4	1	no	—
115	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
116	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
117	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
118	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
119	C₁₃×C₄⋊C₄	—	2	1	no	—
120	C₁₃×C₄⋊C₄	—	2	1	no	—
121	C₁₃×C₄⋊C₄	—	2	2	no	—
122	C₁₃×C₄⋊C₄	—	4	1	no	—
123	C₁₃×C₄⋊C₄	—	4	1	no	—
124	C₁₃×C₄⋊C₄	—	4	1	no	—
125	C₁₃×C₄⋊C₄	—	4	1	no	—
126	C₁₃×C₄⋊C₄	—	4	2	no	—
127	C₁₃×C₄⋊C₄	—	4	2	no	—
128	C₁₃×C₄⋊C₄	—	4	1	no	—
129	C₁₃×C₂²⋊C₄	—	4	1	no	—
130	C₁₃×C₂²⋊C₄	—	4	2	no	—
131	C₁₃×C₂²⋊C₄	—	4	1	no	—
132	C₁₃×C₂²⋊C₄	—	4	1	no	—
133	C₄²×C₁₃	—	4	1	no	—
134	C₄²×C₁₃	—	4	1	no	—
135	C₄²×C₁₃	—	4	1	no	—
136	C₄²×C₁₃	—	4	2	no	—
137	C₄²×C₁₃	D₈	1	1	yes	characteristic
138	C₄²×C₁₃	D₈	1	1	yes	characteristic
139	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
140	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
141	C₁₃×C₁₆	—	2	2	no	—
142	C₁₃×C₁₆	—	2	2	no	—
143	#3170	C₂×C₁₃	1	1	yes	characteristic, complemented
144	C₄×#135	C₂×C₁₃	1	1	yes	characteristic
145	#2237	C₂×C₁₃	1	2	yes	complemented
146	#2225	C₂×C₁₃	1	1	yes	characteristic, complemented
147	#2224	C₂×C₁₃	1	1	yes	characteristic, complemented
148	#2209	C₂×C₁₃	1	1	yes	characteristic, complemented
149	#2208	C₂×C₁₃	1	1	yes	characteristic, complemented
150	#2189	C₂×C₁₃	1	2	yes	—
151	C₄×Q₃₂	C₂×C₁₃	1	2	yes	complemented
152	C₄×SD₃₂	C₂×C₁₃	1	2	yes	complemented
153	#2162	C₂×C₁₃	1	1	yes	characteristic, complemented
154	C₂³×C₁₃	—	4	1	no	—
155	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
156	Q₈×C₁₃	—	2	2	no	—
157	Q₈×C₁₃	—	4	1	no	—
158	Q₈×C₁₃	—	4	2	no	—
159	Q₈×C₁₃	—	4	2	no	—
160	Q₈×C₁₃	—	8	2	no	—
161	D₄×C₁₃	—	2	2	no	—
162	D₄×C₁₃	—	4	4	no	—
163	D₄×C₁₃	—	4	1	no	—
164	C₂×C₄×C₁₃	—	2	1	no	—
165	C₂×C₄×C₁₃	—	2	1	no	—
166	C₂×C₄×C₁₃	—	2	2	no	—
167	C₂×C₄×C₁₃	—	2	2	no	—
168	C₂×C₄×C₁₃	—	4	4	no	—
169	C₂×C₄×C₁₃	—	4	1	no	—
170	C₂×C₄×C₁₃	—	4	1	no	—
171	C₂×C₄×C₁₃	—	4	1	no	—
172	C₂×C₄×C₁₃	—	4	2	no	—
173	C₂×C₄×C₁₃	—	4	2	no	—
174	C₂×C₄×C₁₃	—	8	2	no	—
175	C₂×C₄×C₁₃	—	8	2	no	—
176	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
177	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
178	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
179	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
180	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
181	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
182	C₈×C₁₃	—	2	1	no	—
183	C₈×C₁₃	—	2	1	no	—
184	C₈×C₁₃	—	2	1	no	—
185	C₈×C₁₃	C₂×#41	1	1	yes	characteristic
186	C₈×C₁₃	C₂×#41	1	1	yes	characteristic
187	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
188	#533	—	2	1	no	—
189	C₄×#41	—	2	1	no	—
190	C₂×Q₃₂	C₂²×C₁₃	1	2	yes	—
191	C₂×SD₃₂	C₂²×C₁₃	1	2	yes	—
192	#500	C₂²×C₁₃	1	1	yes	characteristic
193	#494	C₂²×C₁₃	1	1	yes	characteristic
194	#487	—	2	1	no	—
195	#467	—	2	1	no	—
196	#467	C₂²×C₁₃	1	2	yes	—
197	C₄×Q₁₆	—	2	1	no	—
198	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
199	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
200	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
201	C₄×SD₁₆	—	2	1	no	—
202	C₄×SD₁₆	—	2	1	no	—
203	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
204	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
205	#427	C₂²×C₁₃	1	1	yes	characteristic
206	#416	—	2	1	no	—
207	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
208	#367	C₂²×C₁₃	1	2	yes	—
209	#366	C₂²×C₁₃	1	2	yes	—
210	C₄⋊C₁₆	C₂²×C₁₃	1	1	yes	characteristic
211	C₄⋊C₁₆	C₂²×C₁₃	1	1	yes	characteristic
212	#358	C₂²×C₁₃	1	2	yes	—
213	#358	C₂²×C₁₃	1	2	yes	—
214	#358	C₂²×C₁₃	1	2	yes	—
215	#357	C₂²×C₁₃	1	2	yes	—
216	C₂²⋊C₁₆	C₂²×C₁₃	1	2	yes	—
217	C₄×C₁₆	C₂²×C₁₃	1	2	yes	—
218	C₂²×C₁₃	—	2	1	no	—
219	C₂²×C₁₃	—	2	1	no	—
220	C₂²×C₁₃	—	2	1	no	—
221	C₂²×C₁₃	—	4	2	no	—
222	C₂²×C₁₃	—	8	1	no	—
223	C₂²×C₁₃	—	8	1	no	—
224	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
225	C₄×C₁₃	—	2	1	no	—
226	C₄×C₁₃	—	2	1	no	—
227	C₄×C₁₃	—	2	1	no	—
228	C₄×C₁₃	—	4	2	no	—
229	C₄×C₁₃	—	8	2	no	—
230	C₄×C₁₃	—	8	1	no	—
231	C₄×C₁₃	—	8	2	no	—
232	C₄×C₁₃	—	8	1	no	—
233	C₄×C₁₃	#508	1	2	yes	—
234	C₄×C₁₃	#510	1	2	yes	—
235	C₄×C₁₃	#525	1	1	yes	characteristic
236	C₄×C₁₃	#575	1	1	yes	characteristic
237	C₂×#41	—	2	1	no	—
238	#135	—	2	2	no	—
239	#135	—	2	2	no	—
240	C₂×Q₁₆	—	2	1	no	—
241	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
242	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
243	C₂×SD₁₆	—	2	1	no	—
244	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
245	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
246	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
247	C₄⋊Q₈	—	2	1	no	—
248	C₄⋊Q₈	—	2	1	no	—
249	#125	—	4	1	no	—
250	C₂²⋊Q₈	—	2	2	no	—
251	C₂²⋊Q₈	—	4	1	no	—
252	C₄×Q₈	—	2	1	no	—
253	C₄×Q₈	—	2	1	no	—
254	C₄×Q₈	—	2	2	no	—
255	C₄×Q₈	—	4	1	no	—
256	C₄×D₄	—	2	1	no	—
257	C₄×D₄	—	2	1	no	—
258	C₄×D₄	—	4	1	no	—
259	C₄×D₄	—	4	1	no	—
260	#117	—	2	1	no	—
261	#117	—	4	1	no	—
262	#117	—	4	1	no	—
263	C₂×C₄²	—	4	1	no	—
264	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
265	Q₃₂	—	2	4	no	—
266	SD₃₂	—	2	4	no	—
267	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
268	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
269	#107	—	2	1	no	—
270	#107	C₂³×C₁₃	1	2	yes	—
271	#107	C₂³×C₁₃	1	1	yes	characteristic
272	#107	C₂³×C₁₃	1	1	yes	characteristic
273	#106	—	2	1	no	—
274	#103	—	2	1	no	—
275	#103	—	2	1	no	—
276	#103	—	2	2	no	—
277	#103	—	2	2	no	—
278	#102	—	2	1	no	—
279	#102	—	2	1	no	—
280	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
281	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
282	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
283	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
284	C₂×C₁₃	—	4	1	no	—
285	C₂×C₁₃	—	8	2	no	—
286	C₂×C₁₃	#3100	1	1	yes	characteristic
287	C₂×C₁₃	C₂×#508	1	1	yes	characteristic
288	C₂×C₁₃	C₂×#510	1	1	yes	characteristic
289	#41	—	2	4	no	—
290	#41	—	4	2	no	—
291	C₂×Q₈	—	2	1	no	—
292	C₂×Q₈	—	2	2	no	—
293	C₂×Q₈	—	4	1	no	—
294	C₂×D₄	—	2	1	no	—
295	C₂×D₄	—	4	1	no	—
296	C₂²×C₄	—	4	1	no	—
297	C₂²×C₄	—	4	1	no	—
298	C₂²×C₄	—	4	1	no	—
299	C₂²×C₄	C₁₃×D₈	1	1	yes	characteristic
300	C₂²×C₄	C₁₃×D₈	1	1	yes	characteristic
301	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
302	Q₁₆	—	2	1	no	—
303	Q₁₆	—	2	2	no	—
304	Q₁₆	—	2	2	no	—
305	Q₁₆	—	4	2	no	—
306	Q₁₆	C₁₃×#41	1	2	yes	—
307	SD₁₆	—	2	4	no	—
308	D₈	—	2	1	no	—
309	D₈	C₁₃×#41	1	2	yes	—
310	C₂×C₈	—	2	1	no	—
311	C₂×C₈	—	2	1	no	—
312	C₂×C₈	—	4	1	no	—
313	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
314	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
315	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
316	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
317	C₄⋊C₄	—	2	1	no	—
318	C₄⋊C₄	—	2	1	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	—	4	1	no	—
321	C₄⋊C₄	—	4	1	no	—
322	C₄⋊C₄	—	4	1	no	—
323	C₄⋊C₄	—	4	1	no	—
324	C₄⋊C₄	—	4	2	no	—
325	C₄⋊C₄	—	4	2	no	—
326	C₄⋊C₄	—	4	1	no	—
327	C₂²⋊C₄	—	4	1	no	—
328	C₂²⋊C₄	—	4	2	no	—
329	C₂²⋊C₄	—	4	1	no	—
330	C₂²⋊C₄	—	4	1	no	—
331	C₄²	—	4	1	no	—
332	C₄²	—	4	1	no	—
333	C₄²	—	4	1	no	—
334	C₄²	—	4	2	no	—
335	C₄²	C₁₃×D₈	1	1	yes	characteristic
336	C₄²	C₁₃×D₈	1	1	yes	characteristic
337	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
338	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
339	C₁₆	—	2	2	no	—
340	C₁₆	—	2	2	no	—
341	C₁₃	#33667	1	1	yes	characteristic, direct product factor, Sylow
342	C₂³	—	4	1	no	—
343	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
344	Q₈	—	2	2	no	—
345	Q₈	—	4	1	no	—
346	Q₈	—	4	2	no	—
347	Q₈	—	4	2	no	—
348	Q₈	—	8	2	no	—
349	D₄	—	2	2	no	—
350	D₄	—	4	4	no	—
351	D₄	—	4	1	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	4	4	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	—	4	1	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	8	2	no	—
363	C₂×C₄	—	8	2	no	—
364	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
365	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
366	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
367	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
368	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
369	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
370	C₈	—	2	1	no	—
371	C₈	—	2	1	no	—
372	C₈	—	2	1	no	—
373	C₈	C₂×C₁₃×#41	1	1	yes	characteristic
374	C₈	C₂×C₁₃×#41	1	1	yes	characteristic
375	C₂²	—	2	1	no	—
376	C₂²	—	2	1	no	—
377	C₂²	—	2	1	no	—
378	C₂²	—	4	2	no	—
379	C₂²	—	8	1	no	—
380	C₂²	—	8	1	no	—
381	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
382	C₄	—	2	1	no	—
383	C₄	—	2	1	no	—
384	C₄	—	2	1	no	—
385	C₄	—	4	2	no	—
386	C₄	—	8	2	no	—
387	C₄	—	8	1	no	—
388	C₄	—	8	2	no	—
389	C₄	—	8	1	no	—
390	C₄	C₁₃×#508	1	2	yes	—
391	C₄	C₁₃×#510	1	2	yes	—
392	C₄	C₁₃×#525	1	1	yes	characteristic
393	C₄	C₁₃×#575	1	1	yes	characteristic
394	C₂	—	4	1	no	—
395	C₂	—	8	2	no	—
396	C₂	C₁₃×#3100	1	1	yes	characteristic
397	C₂	C₂×C₁₃×#508	1	1	yes	characteristic
398	C₂	C₂×C₁₃×#510	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
socle	C₂²×C₁₃	C₂²×D₈
prime radical	C₂×C₁₃×#135	C₂²
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ C₂×C₄×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3170	C₂	semidirect
3. C₁₃×#2237	C₂	semidirect
4. C₁₃×#2225	C₂	semidirect
5. C₁₃×#2224	C₂	semidirect
6. C₁₃×#2209	C₂	semidirect
7. C₁₃×#2208	C₂	semidirect
9. C₄×C₁₃×Q₃₂	C₂	semidirect
10. C₄×C₁₃×SD₃₂	C₂	semidirect
11. C₁₃×#2162	C₂	semidirect
90. #33667	C₁₃	direct (N × H)
143. #3170	C₂×C₁₃	semidirect
145. #2237	C₂×C₁₃	semidirect
146. #2225	C₂×C₁₃	semidirect
147. #2224	C₂×C₁₃	semidirect
148. #2209	C₂×C₁₃	semidirect
149. #2208	C₂×C₁₃	semidirect
151. C₄×Q₃₂	C₂×C₁₃	semidirect
152. C₄×SD₃₂	C₂×C₁₃	semidirect
153. #2162	C₂×C₁₃	semidirect
341. C₁₃	#33667	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#3170	2
C₄×C₁₃×#135	2
C₁₃×#2237	2
C₁₃×#2225	2
C₁₃×#2224	2
C₁₃×#2209	2
C₁₃×#2208	2
C₁₃×#2189	2
C₄×C₁₃×Q₃₂	2
C₄×C₁₃×SD₃₂	2
C₁₃×#2162	2
#33667	13

Subgroups — C13×#33667 #15720006

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33667 #15720006