Subgroups — C₁₃×#23602 #15709941

Order 3328.

1098 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#430	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#2911	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2905	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₃×#418	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₃×#418	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₁₃×#100	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#2063	C₂	1	8	yes	maximal, complemented
8	C₁₃×#1742	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
10	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
11	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
12	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
13	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
16	C₁₃×#430	—	2	4	no	—
17	C₂×C₁₃×#108	C₂²	1	4	yes	complemented
18	C₁₃×#428	—	2	2	no	—
19	C₁₃×#428	C₂²	1	4	yes	complemented
20	C₁₃×#427	—	2	2	no	—
21	C₁₃×#424	—	2	2	no	—
22	C₁₃×#424	C₂²	1	4	yes	complemented
23	C₁₃×#423	—	2	2	no	—
24	C₁₃×#418	—	2	2	no	—
25	C₁₃×#418	—	2	2	no	—
26	C₁₃×#418	—	2	2	no	—
27	C₁₃×#418	C₂²	1	4	yes	—
28	C₂×C₁₃×#102	—	2	2	no	—
29	C₂×C₁₃×#102	C₂²	1	4	yes	—
30	C₂×C₁₃×#100	—	2	4	no	—
31	C₂×C₁₃×#100	C₂²	1	4	yes	—
32	C₁₃×#343	C₂²	1	4	yes	complemented
33	C₂⁵×C₁₃	—	2	1	no	—
34	C₂²×D₄×C₁₃	—	2	1	no	—
35	C₂²×D₄×C₁₃	—	2	1	no	—
36	C₂²×D₄×C₁₃	—	2	1	no	—
37	C₂²×D₄×C₁₃	—	2	1	no	—
38	C₂²×D₄×C₁₃	—	2	2	no	—
39	C₂²×D₄×C₁₃	—	2	2	no	—
40	C₂²×D₄×C₁₃	—	2	2	no	—
41	C₂²×D₄×C₁₃	—	2	1	no	—
42	C₂²×D₄×C₁₃	Q₈	1	4	yes	—
43	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
44	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
45	C₂×C₁₃×M₁₆	—	2	1	no	—
46	C₂×C₁₃×M₁₆	—	2	2	no	—
47	C₂×C₁₃×M₁₆	—	2	2	no	—
48	C₂×C₁₃×M₁₆	—	2	2	no	—
49	C₂×C₁₃×M₁₆	—	2	1	no	—
50	C₂×C₁₃×M₁₆	—	2	1	no	—
51	C₂×C₁₃×M₁₆	—	2	2	no	—
52	C₂×C₁₃×M₁₆	—	2	2	no	—
53	C₂×C₁₃×M₁₆	—	2	2	no	—
54	C₂×C₁₃×M₁₆	—	2	2	no	—
55	C₂×C₁₃×M₁₆	D₄	1	4	yes	—
56	C₂×C₁₃×M₁₆	D₄	1	2	yes	—
57	C₂×C₁₃×M₁₆	D₄	1	2	yes	—
58	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
59	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
60	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
61	C₂²×C₈×C₁₃	—	2	1	no	—
62	C₂²×C₈×C₁₃	—	2	1	no	—
63	C₂²×C₈×C₁₃	—	2	1	no	—
64	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
65	C₁₃×#117	—	2	1	no	—
66	C₁₃×#117	—	2	1	no	—
67	C₁₃×#117	—	2	1	no	—
68	C₁₃×#117	—	2	1	no	—
69	C₁₃×#117	—	2	1	no	—
70	C₁₃×#117	—	2	1	no	—
71	C₁₃×#117	D₄	1	2	yes	—
72	C₁₃×#117	C₂³	1	2	yes	—
73	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
74	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
75	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
76	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
77	C₂×C₄²×C₁₃	—	2	1	no	—
78	C₂×C₄²×C₁₃	—	2	1	no	—
79	C₁₃×#108	—	2	8	no	—
80	C₁₃×#107	—	2	4	no	—
81	C₁₃×#106	—	2	4	no	—
82	C₁₃×C₄⋊C₈	—	2	8	no	—
83	C₁₃×#102	—	2	8	no	—
84	C₁₃×#102	—	2	8	no	—
85	C₁₃×#100	—	2	8	no	—
86	#23602	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
87	C₂⁴×C₁₃	—	2	4	no	—
88	C₂⁴×C₁₃	—	2	2	no	—
89	C₂⁴×C₁₃	—	4	1	no	—
90	C₂⁴×C₁₃	—	4	1	no	—
91	C₂⁴×C₁₃	—	4	2	no	—
92	C₂⁴×C₁₃	—	8	4	no	—
93	C₂⁴×C₁₃	#41	1	1	yes	characteristic
94	C₂×D₄×C₁₃	—	2	4	no	—
95	C₂×D₄×C₁₃	—	2	4	no	—
96	C₂×D₄×C₁₃	—	2	4	no	—
97	C₂×D₄×C₁₃	—	2	4	no	—
98	C₂×D₄×C₁₃	—	2	4	no	—
99	C₂×D₄×C₁₃	—	2	2	no	—
100	C₂×D₄×C₁₃	—	2	2	no	—
101	C₂×D₄×C₁₃	—	2	2	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	2	no	—
106	C₂×D₄×C₁₃	—	4	2	no	—
107	C₂×D₄×C₁₃	—	4	2	no	—
108	C₂×D₄×C₁₃	—	4	1	no	—
109	C₂×D₄×C₁₃	—	4	1	no	—
110	C₂×D₄×C₁₃	—	4	2	no	—
111	C₂×D₄×C₁₃	C₂×Q₈	1	4	yes	—
112	C₂²×C₄×C₁₃	—	2	2	no	—
113	C₂²×C₄×C₁₃	—	2	2	no	—
114	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
120	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
121	C₂²×C₄×C₁₃	#41	1	2	yes	—
122	C₂²×C₄×C₁₃	#41	1	2	yes	—
123	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
124	C₁₃×M₁₆	—	2	4	no	—
125	C₁₃×M₁₆	—	2	4	no	—
126	C₁₃×M₁₆	—	2	4	no	—
127	C₁₃×M₁₆	—	2	2	no	—
128	C₁₃×M₁₆	—	2	2	no	—
129	C₁₃×M₁₆	—	2	2	no	—
130	C₁₃×M₁₆	—	2	2	no	—
131	C₁₃×M₁₆	—	2	2	no	—
132	C₁₃×M₁₆	—	4	2	no	—
133	C₁₃×M₁₆	—	4	2	no	—
134	C₁₃×M₁₆	C₂×D₄	1	4	yes	—
135	C₂×C₈×C₁₃	—	2	4	no	—
136	C₂×C₈×C₁₃	—	2	2	no	—
137	C₂×C₈×C₁₃	—	2	2	no	—
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	—	4	2	no	—
142	C₂×C₈×C₁₃	—	4	2	no	—
143	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
144	C₁₃×C₄⋊C₄	—	2	2	no	—
145	C₁₃×C₄⋊C₄	—	2	2	no	—
146	C₁₃×C₄⋊C₄	—	2	2	no	—
147	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
148	C₁₃×C₂²⋊C₄	—	2	2	no	—
149	C₁₃×C₂²⋊C₄	—	2	2	no	—
150	C₁₃×C₂²⋊C₄	—	4	1	no	—
151	C₁₃×C₂²⋊C₄	—	4	1	no	—
152	C₄²×C₁₃	—	2	2	no	—
153	C₄²×C₁₃	—	2	2	no	—
154	C₄²×C₁₃	—	4	1	no	—
155	C₄²×C₁₃	—	4	1	no	—
156	C₂×#430	C₂×C₁₃	1	1	yes	characteristic, complemented
157	#2911	C₂×C₁₃	1	1	yes	characteristic, complemented
158	#2905	C₂×C₁₃	1	1	yes	characteristic, complemented
159	C₂×#418	C₂×C₁₃	1	1	yes	characteristic
160	C₂×#418	C₂×C₁₃	1	1	yes	characteristic
161	C₂²×#100	C₂×C₁₃	1	1	yes	characteristic
162	#2063	C₂×C₁₃	1	8	yes	complemented
163	#1742	C₂×C₁₃	1	1	yes	characteristic, complemented
164	C₂³×C₁₃	—	2	4	no	—
165	C₂³×C₁₃	—	4	2	no	—
166	C₂³×C₁₃	—	4	2	no	—
167	C₂³×C₁₃	—	4	2	no	—
168	C₂³×C₁₃	—	4	4	no	—
169	C₂³×C₁₃	—	4	4	no	—
170	C₂³×C₁₃	—	8	4	no	—
171	C₂³×C₁₃	—	8	4	no	—
172	C₂³×C₁₃	—	8	4	no	—
173	C₂³×C₁₃	—	8	8	no	—
174	C₂³×C₁₃	—	8	8	no	—
175	C₂³×C₁₃	#121	1	1	yes	characteristic
176	C₂³×C₁₃	#121	1	1	yes	characteristic
177	C₂³×C₁₃	C₂²⋊Q₈	1	2	yes	—
178	C₂³×C₁₃	#126	1	2	yes	—
179	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
180	D₄×C₁₃	—	2	4	no	—
181	D₄×C₁₃	—	2	4	no	—
182	D₄×C₁₃	—	4	2	no	—
183	D₄×C₁₃	—	4	2	no	—
184	D₄×C₁₃	—	4	4	no	—
185	D₄×C₁₃	—	4	4	no	—
186	C₂×C₄×C₁₃	—	2	4	no	—
187	C₂×C₄×C₁₃	—	4	2	no	—
188	C₂×C₄×C₁₃	—	8	2	no	—
189	C₂×C₄×C₁₃	—	8	2	no	—
190	C₂×C₄×C₁₃	#121	1	2	yes	—
191	C₂×C₄×C₁₃	#121	1	2	yes	—
192	C₂×C₄×C₁₃	#121	1	2	yes	—
193	C₂×C₄×C₁₃	#121	1	2	yes	—
194	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
195	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
196	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
197	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
198	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
199	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
200	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
201	C₂×C₄×C₁₃	#126	1	2	yes	—
202	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
203	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
204	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
205	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
206	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
207	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
208	C₈×C₁₃	—	2	4	no	—
209	C₈×C₁₃	—	2	4	no	—
210	C₈×C₁₃	—	4	2	no	—
211	C₈×C₁₃	—	4	2	no	—
212	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
213	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
214	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
215	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
216	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
217	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
218	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
219	#430	—	2	4	no	—
220	C₂×#108	C₂²×C₁₃	1	4	yes	complemented
221	#428	—	2	2	no	—
222	#428	C₂²×C₁₃	1	4	yes	complemented
223	#427	—	2	2	no	—
224	#424	—	2	2	no	—
225	#424	C₂²×C₁₃	1	4	yes	complemented
226	#423	—	2	2	no	—
227	#418	—	2	2	no	—
228	#418	—	2	2	no	—
229	#418	—	2	2	no	—
230	#418	C₂²×C₁₃	1	4	yes	—
231	C₂×#102	—	2	2	no	—
232	C₂×#102	C₂²×C₁₃	1	4	yes	—
233	C₂×#100	—	2	4	no	—
234	C₂×#100	C₂²×C₁₃	1	4	yes	—
235	#343	C₂²×C₁₃	1	4	yes	complemented
236	C₂²×C₁₃	—	2	2	no	—
237	C₂²×C₁₃	—	2	2	no	—
238	C₂²×C₁₃	—	2	2	no	—
239	C₂²×C₁₃	—	4	2	no	—
240	C₂²×C₁₃	—	4	2	no	—
241	C₂²×C₁₃	—	4	4	no	—
242	C₂²×C₁₃	—	8	4	no	—
243	C₂²×C₁₃	—	8	8	no	—
244	C₂²×C₁₃	—	8	4	no	—
245	C₂²×C₁₃	—	8	8	no	—
246	C₂²×C₁₃	—	8	4	no	—
247	C₂²×C₁₃	#396	1	2	yes	—
248	C₂²×C₁₃	#396	1	2	yes	—
249	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
250	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
251	C₂²×C₁₃	C₂×#126	1	1	yes	characteristic
252	C₄×C₁₃	—	4	4	no	—
253	C₄×C₁₃	—	8	2	no	—
254	C₄×C₁₃	#396	1	2	yes	—
255	C₄×C₁₃	#396	1	2	yes	—
256	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
257	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
258	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
259	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
260	C₂⁵	—	2	1	no	—
261	C₂²×D₄	—	2	1	no	—
262	C₂²×D₄	—	2	1	no	—
263	C₂²×D₄	—	2	1	no	—
264	C₂²×D₄	—	2	1	no	—
265	C₂²×D₄	—	2	2	no	—
266	C₂²×D₄	—	2	2	no	—
267	C₂²×D₄	—	2	2	no	—
268	C₂²×D₄	—	2	1	no	—
269	C₂²×D₄	Q₈×C₁₃	1	4	yes	—
270	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
271	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
272	C₂×M₁₆	—	2	1	no	—
273	C₂×M₁₆	—	2	2	no	—
274	C₂×M₁₆	—	2	2	no	—
275	C₂×M₁₆	—	2	2	no	—
276	C₂×M₁₆	—	2	1	no	—
277	C₂×M₁₆	—	2	1	no	—
278	C₂×M₁₆	—	2	2	no	—
279	C₂×M₁₆	—	2	2	no	—
280	C₂×M₁₆	—	2	2	no	—
281	C₂×M₁₆	—	2	2	no	—
282	C₂×M₁₆	D₄×C₁₃	1	4	yes	—
283	C₂×M₁₆	D₄×C₁₃	1	2	yes	—
284	C₂×M₁₆	D₄×C₁₃	1	2	yes	—
285	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
286	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
287	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
288	C₂²×C₈	—	2	1	no	—
289	C₂²×C₈	—	2	1	no	—
290	C₂²×C₈	—	2	1	no	—
291	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
292	#117	—	2	1	no	—
293	#117	—	2	1	no	—
294	#117	—	2	1	no	—
295	#117	—	2	1	no	—
296	#117	—	2	1	no	—
297	#117	—	2	1	no	—
298	#117	D₄×C₁₃	1	2	yes	—
299	#117	C₂³×C₁₃	1	2	yes	—
300	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
301	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
302	C₂×C₂²⋊C₄	—	2	1	no	—
303	C₂×C₂²⋊C₄	—	2	1	no	—
304	C₂×C₄²	—	2	1	no	—
305	C₂×C₄²	—	2	1	no	—
306	#108	—	2	8	no	—
307	#107	—	2	4	no	—
308	#106	—	2	4	no	—
309	C₄⋊C₈	—	2	8	no	—
310	#102	—	2	8	no	—
311	#102	—	2	8	no	—
312	#100	—	2	8	no	—
313	C₂×C₁₃	—	2	1	no	—
314	C₂×C₁₃	—	2	1	no	—
315	C₂×C₁₃	—	2	2	no	—
316	C₂×C₁₃	—	2	2	no	—
317	C₂×C₁₃	—	8	4	no	—
318	C₂×C₁₃	C₂×#396	1	1	yes	characteristic
319	C₂×C₁₃	#3068	1	2	yes	—
320	C₂⁴	—	2	4	no	—
321	C₂⁴	—	2	2	no	—
322	C₂⁴	—	4	1	no	—
323	C₂⁴	—	4	1	no	—
324	C₂⁴	—	4	2	no	—
325	C₂⁴	—	8	4	no	—
326	C₂⁴	C₁₃×#41	1	1	yes	characteristic
327	C₂×D₄	—	2	4	no	—
328	C₂×D₄	—	2	4	no	—
329	C₂×D₄	—	2	4	no	—
330	C₂×D₄	—	2	4	no	—
331	C₂×D₄	—	2	4	no	—
332	C₂×D₄	—	2	2	no	—
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	—	2	2	no	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	—	2	2	no	—
337	C₂×D₄	—	4	1	no	—
338	C₂×D₄	—	4	1	no	—
339	C₂×D₄	—	4	2	no	—
340	C₂×D₄	—	4	2	no	—
341	C₂×D₄	—	4	2	no	—
342	C₂×D₄	—	4	2	no	—
343	C₂×D₄	—	4	2	no	—
344	C₂×D₄	C₂×Q₈×C₁₃	1	4	yes	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
348	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
349	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
350	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
351	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
352	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
353	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
354	C₂²×C₄	C₁₃×#41	1	2	yes	—
355	C₂²×C₄	C₁₃×#41	1	2	yes	—
356	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
357	M₁₆	—	2	4	no	—
358	M₁₆	—	2	4	no	—
359	M₁₆	—	2	4	no	—
360	M₁₆	—	2	2	no	—
361	M₁₆	—	2	2	no	—
362	M₁₆	—	2	2	no	—
363	M₁₆	—	2	2	no	—
364	M₁₆	—	2	2	no	—
365	M₁₆	—	4	2	no	—
366	M₁₆	—	4	2	no	—
367	M₁₆	C₂×D₄×C₁₃	1	4	yes	—
368	C₂×C₈	—	2	4	no	—
369	C₂×C₈	—	2	2	no	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	—	2	2	no	—
372	C₂×C₈	—	2	2	no	—
373	C₂×C₈	—	2	2	no	—
374	C₂×C₈	—	4	2	no	—
375	C₂×C₈	—	4	2	no	—
376	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
381	C₂²⋊C₄	—	2	2	no	—
382	C₂²⋊C₄	—	2	2	no	—
383	C₂²⋊C₄	—	4	1	no	—
384	C₂²⋊C₄	—	4	1	no	—
385	C₄²	—	2	2	no	—
386	C₄²	—	2	2	no	—
387	C₄²	—	4	1	no	—
388	C₄²	—	4	1	no	—
389	C₁₃	#23602	1	1	yes	characteristic, direct product factor, Sylow
390	C₂³	—	2	4	no	—
391	C₂³	—	4	2	no	—
392	C₂³	—	4	4	no	—
393	C₂³	—	4	4	no	—
394	C₂³	—	4	2	no	—
395	C₂³	—	4	2	no	—
396	C₂³	—	8	4	no	—
397	C₂³	—	8	4	no	—
398	C₂³	—	8	4	no	—
399	C₂³	—	8	8	no	—
400	C₂³	—	8	8	no	—
401	C₂³	C₁₃×#121	1	1	yes	characteristic
402	C₂³	C₁₃×#121	1	1	yes	characteristic
403	C₂³	C₁₃×C₂²⋊Q₈	1	2	yes	—
404	C₂³	C₁₃×#126	1	2	yes	—
405	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
406	D₄	—	2	4	no	—
407	D₄	—	2	4	no	—
408	D₄	—	4	4	no	—
409	D₄	—	4	4	no	—
410	D₄	—	4	2	no	—
411	D₄	—	4	2	no	—
412	C₂×C₄	—	2	4	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	8	2	no	—
415	C₂×C₄	—	8	2	no	—
416	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
417	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
418	C₂×C₄	C₁₃×#121	1	2	yes	—
419	C₂×C₄	C₁₃×#121	1	2	yes	—
420	C₂×C₄	C₁₃×#121	1	2	yes	—
421	C₂×C₄	C₁₃×#121	1	2	yes	—
422	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
423	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
424	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
425	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
426	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
427	C₂×C₄	C₁₃×#126	1	2	yes	—
428	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
429	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
430	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
431	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
432	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
433	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
434	C₈	—	2	4	no	—
435	C₈	—	2	4	no	—
436	C₈	—	4	2	no	—
437	C₈	—	4	2	no	—
438	C₂²	—	2	2	no	—
439	C₂²	—	2	2	no	—
440	C₂²	—	2	2	no	—
441	C₂²	—	4	2	no	—
442	C₂²	—	4	2	no	—
443	C₂²	—	4	4	no	—
444	C₂²	—	8	4	no	—
445	C₂²	—	8	8	no	—
446	C₂²	—	8	8	no	—
447	C₂²	—	8	4	no	—
448	C₂²	—	8	4	no	—
449	C₂²	C₁₃×#396	1	2	yes	—
450	C₂²	C₁₃×#396	1	2	yes	—
451	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
452	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
453	C₂²	C₂×C₁₃×#126	1	1	yes	characteristic
454	C₄	—	4	4	no	—
455	C₄	—	8	2	no	—
456	C₄	C₁₃×#396	1	2	yes	—
457	C₄	C₁₃×#396	1	2	yes	—
458	C₄	C₂×C₁₃×#121	1	1	yes	characteristic
459	C₄	C₂×C₁₃×#121	1	1	yes	characteristic
460	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
461	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
462	C₂	—	2	2	no	—
463	C₂	—	2	2	no	—
464	C₂	—	2	1	no	—
465	C₂	—	2	1	no	—
466	C₂	—	8	4	no	—
467	C₂	C₂×C₁₃×#396	1	1	yes	characteristic
468	C₂	C₁₃×#3068	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂³×D₄×C₁₃	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂³×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#430	C₂	semidirect
2. C₁₃×#2911	C₂	semidirect
3. C₁₃×#2905	C₂	semidirect
7. C₁₃×#2063	C₂	semidirect
8. C₁₃×#1742	C₂	semidirect
17. C₂×C₁₃×#108	C₂²	semidirect
19. C₁₃×#428	C₂²	semidirect
22. C₁₃×#424	C₂²	semidirect
32. C₁₃×#343	C₂²	semidirect
86. #23602	C₁₃	direct (N × H)
156. C₂×#430	C₂×C₁₃	semidirect
157. #2911	C₂×C₁₃	semidirect
158. #2905	C₂×C₁₃	semidirect
162. #2063	C₂×C₁₃	semidirect
163. #1742	C₂×C₁₃	semidirect
220. C₂×#108	C₂²×C₁₃	semidirect
222. #428	C₂²×C₁₃	semidirect
225. #424	C₂²×C₁₃	semidirect
235. #343	C₂²×C₁₃	semidirect
389. C₁₃	#23602	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×#430	2
C₁₃×#2911	2
C₁₃×#2905	2
C₂×C₁₃×#418	2
C₂²×C₁₃×#100	2
C₁₃×#2063	2
C₁₃×#1742	2
#23602	13

Subgroups — C13×#23602 #15709941

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#23602 #15709941