Subgroups — C₁₃×#23717 #15710056

Order 3328.

752 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₃×#137	C₂	1	2	yes	maximal
2	C₂×C₄×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2922	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2089	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2078	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#2064	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2052	C₂	1	2	yes	maximal
8	C₁₃×#2047	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2020	C₂	1	1	yes	maximal, characteristic
10	C₄×C₁₃×#108	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₁₃×#101	C₂	1	2	yes	maximal, complemented
12	C₂×C₁₃×#137	C₂²	1	2	yes	—
13	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
14	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
15	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
16	C₁₃×#441	—	2	2	no	—
17	C₁₃×#440	—	2	2	no	—
18	C₄×C₁₃×Q₁₆	—	2	2	no	—
19	C₄×C₁₃×Q₁₆	—	2	2	no	—
20	C₄×C₁₃×Q₁₆	—	2	2	no	—
21	C₄×C₁₃×SD₁₆	—	2	2	no	—
22	C₁₃×#433	—	2	2	no	—
23	C₁₃×#431	—	2	2	no	—
24	C₂×C₁₃×#108	C₂²	1	2	yes	—
25	C₁₃×#428	C₂²	1	2	yes	—
26	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
27	C₁₃×#424	C₂²	1	1	yes	characteristic
28	C₁₃×#424	C₂²	1	1	yes	characteristic
29	C₁₃×#419	C₂²	1	2	yes	—
30	C₁₃×#417	C₂²	1	2	yes	—
31	C₂×C₁₃×#103	C₂²	1	2	yes	—
32	C₂×C₁₃×#101	C₂²	1	2	yes	—
33	C₂×C₁₃×#101	C₂²	1	2	yes	—
34	C₁₃×#408	C₂²	1	1	yes	characteristic
35	C₁₃×#408	C₂²	1	1	yes	characteristic
36	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
37	C₄×C₁₃×M₁₆	C₂²	1	2	yes	—
38	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
39	C₁₃×#343	C₂²	1	2	yes	—
40	C₁₃×#343	C₂²	1	2	yes	—
41	C₁₃×#341	C₂²	1	1	yes	characteristic
42	C₁₃×#341	C₂²	1	1	yes	characteristic
43	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
44	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
45	C₁₃×#137	—	2	4	no	—
46	C₁₃×#137	—	2	4	no	—
47	C₂×C₁₃×Q₁₆	—	2	2	no	—
48	C₂×C₁₃×Q₁₆	—	2	4	no	—
49	C₂×C₁₃×Q₁₆	—	2	2	no	—
50	C₂×C₁₃×SD₁₆	—	2	2	no	—
51	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
52	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
53	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
54	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
55	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
57	C₄×Q₈×C₁₃	—	2	2	no	—
58	C₄×Q₈×C₁₃	—	2	2	no	—
59	C₄×Q₈×C₁₃	—	2	2	no	—
60	C₄×Q₈×C₁₃	—	2	2	no	—
61	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
62	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
63	C₄×D₄×C₁₃	—	2	1	no	—
64	C₄×D₄×C₁₃	—	2	1	no	—
65	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
66	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
67	C₁₃×#117	—	2	1	no	—
68	C₁₃×#117	C₂³	1	1	yes	characteristic
69	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
70	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
71	C₂×C₄²×C₁₃	—	2	1	no	—
72	C₂×C₄²×C₁₃	—	2	2	no	—
73	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
74	C₁₃×#108	—	2	4	no	—
75	C₁₃×#107	—	2	2	no	—
76	C₁₃×#107	—	2	2	no	—
77	C₁₃×#106	—	2	2	no	—
78	C₁₃×C₄⋊C₈	—	2	2	no	—
79	C₁₃×C₄⋊C₈	—	2	2	no	—
80	C₁₃×#103	—	2	2	no	—
81	C₁₃×#103	—	2	4	no	—
82	C₁₃×#103	—	2	2	no	—
83	C₁₃×#103	—	2	2	no	—
84	C₁₃×#102	—	2	2	no	—
85	C₁₃×#101	—	2	4	no	—
86	C₁₃×#101	—	2	4	no	—
87	C₁₃×C₂²⋊C₈	—	2	2	no	—
88	C₁₃×C₂²⋊C₈	—	2	2	no	—
89	C₁₃×#97	—	2	1	no	—
90	C₁₃×#97	—	2	2	no	—
91	C₄×C₈×C₁₃	—	2	1	no	—
92	C₄×C₈×C₁₃	—	2	2	no	—
93	C₄×C₈×C₁₃	D₄	1	2	yes	—
94	C₄×C₈×C₁₃	D₄	1	2	yes	—
95	#23717	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
96	C₁₃×#41	—	2	2	no	—
97	C₁₃×#41	—	2	2	no	—
98	C₂×Q₈×C₁₃	—	2	2	no	—
99	C₂×Q₈×C₁₃	—	2	2	no	—
100	C₂×Q₈×C₁₃	—	2	2	no	—
101	C₂×Q₈×C₁₃	—	2	2	no	—
102	C₂×Q₈×C₁₃	—	2	2	no	—
103	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
104	C₂×Q₈×C₁₃	#41	1	4	yes	—
105	C₂×D₄×C₁₃	—	2	1	no	—
106	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₃	—	2	2	no	—
108	C₂²×C₄×C₁₃	—	2	1	no	—
109	C₂²×C₄×C₁₃	—	2	1	no	—
110	C₂²×C₄×C₁₃	—	2	1	no	—
111	C₂²×C₄×C₁₃	—	2	2	no	—
112	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
113	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
114	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
115	C₁₃×Q₁₆	—	2	8	no	—
116	C₁₃×Q₁₆	—	2	8	no	—
117	C₁₃×SD₁₆	—	2	8	no	—
118	C₁₃×M₁₆	—	2	2	no	—
119	C₁₃×M₁₆	—	2	2	no	—
120	C₁₃×M₁₆	—	2	2	no	—
121	C₁₃×M₁₆	—	2	2	no	—
122	C₁₃×M₁₆	—	2	2	no	—
123	C₁₃×M₁₆	#41	1	4	yes	—
124	C₂×C₈×C₁₃	—	2	2	no	—
125	C₂×C₈×C₁₃	—	2	2	no	—
126	C₂×C₈×C₁₃	—	2	2	no	—
127	C₂×C₈×C₁₃	—	2	1	no	—
128	C₂×C₈×C₁₃	—	2	1	no	—
129	C₂×C₈×C₁₃	—	2	2	no	—
130	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
131	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
132	C₁₃×C₄⋊C₄	—	2	1	no	—
133	C₁₃×C₄⋊C₄	—	2	1	no	—
134	C₁₃×C₄⋊C₄	—	2	2	no	—
135	C₁₃×C₄⋊C₄	—	2	2	no	—
136	C₁₃×C₄⋊C₄	—	4	2	no	—
137	C₁₃×C₄⋊C₄	—	4	2	no	—
138	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
139	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
140	C₁₃×C₂²⋊C₄	—	2	1	no	—
141	C₁₃×C₂²⋊C₄	—	2	1	no	—
142	C₁₃×C₂²⋊C₄	—	2	1	no	—
143	C₄²×C₁₃	—	2	1	no	—
144	C₄²×C₁₃	—	2	1	no	—
145	C₄²×C₁₃	—	2	1	no	—
146	C₄²×C₁₃	—	4	2	no	—
147	C₄²×C₁₃	—	4	2	no	—
148	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
149	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
150	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
151	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
152	C₄×#137	C₂×C₁₃	1	2	yes	—
153	C₂×C₄×Q₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
154	#2922	C₂×C₁₃	1	1	yes	characteristic
155	#2089	C₂×C₁₃	1	1	yes	characteristic, complemented
156	#2078	C₂×C₁₃	1	1	yes	characteristic
157	#2064	C₂×C₁₃	1	2	yes	complemented
158	#2052	C₂×C₁₃	1	2	yes	—
159	#2047	C₂×C₁₃	1	1	yes	characteristic, complemented
160	#2020	C₂×C₁₃	1	1	yes	characteristic
161	C₄×#108	C₂×C₁₃	1	1	yes	characteristic, complemented
162	C₄×#101	C₂×C₁₃	1	2	yes	complemented
163	C₂³×C₁₃	—	2	1	no	—
164	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
165	Q₈×C₁₃	—	2	4	no	—
166	Q₈×C₁₃	—	2	4	no	—
167	Q₈×C₁₃	—	2	2	no	—
168	Q₈×C₁₃	—	4	2	no	—
169	Q₈×C₁₃	—	4	2	no	—
170	D₄×C₁₃	—	2	2	no	—
171	D₄×C₁₃	—	4	2	no	—
172	C₂×C₄×C₁₃	—	2	2	no	—
173	C₂×C₄×C₁₃	—	2	1	no	—
174	C₂×C₄×C₁₃	—	2	1	no	—
175	C₂×C₄×C₁₃	—	2	1	no	—
176	C₂×C₄×C₁₃	—	2	4	no	—
177	C₂×C₄×C₁₃	—	4	1	no	—
178	C₂×C₄×C₁₃	—	4	2	no	—
179	C₂×C₄×C₁₃	—	4	2	no	—
180	C₂×C₄×C₁₃	—	4	2	no	—
181	C₂×C₄×C₁₃	—	4	1	no	—
182	C₂×C₄×C₁₃	—	4	1	no	—
183	C₂×C₄×C₁₃	—	4	2	no	—
184	C₂×C₄×C₁₃	—	4	2	no	—
185	C₂×C₄×C₁₃	—	8	2	no	—
186	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
187	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
188	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
189	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
190	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
191	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
192	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
193	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
194	C₈×C₁₃	—	2	2	no	—
195	C₈×C₁₃	—	2	4	no	—
196	C₈×C₁₃	—	2	2	no	—
197	C₈×C₁₃	—	4	1	no	—
198	C₈×C₁₃	—	4	2	no	—
199	C₈×C₁₃	—	4	1	no	—
200	C₂×#137	C₂²×C₁₃	1	2	yes	—
201	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
202	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
203	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
204	#441	—	2	2	no	—
205	#440	—	2	2	no	—
206	C₄×Q₁₆	—	2	2	no	—
207	C₄×Q₁₆	—	2	2	no	—
208	C₄×Q₁₆	—	2	2	no	—
209	C₄×SD₁₆	—	2	2	no	—
210	#433	—	2	2	no	—
211	#431	—	2	2	no	—
212	C₂×#108	C₂²×C₁₃	1	2	yes	—
213	#428	C₂²×C₁₃	1	2	yes	—
214	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
215	#424	C₂²×C₁₃	1	1	yes	characteristic
216	#424	C₂²×C₁₃	1	1	yes	characteristic
217	#419	C₂²×C₁₃	1	2	yes	—
218	#417	C₂²×C₁₃	1	2	yes	—
219	C₂×#103	C₂²×C₁₃	1	2	yes	—
220	C₂×#101	C₂²×C₁₃	1	2	yes	—
221	C₂×#101	C₂²×C₁₃	1	2	yes	—
222	#408	C₂²×C₁₃	1	1	yes	characteristic
223	#408	C₂²×C₁₃	1	1	yes	characteristic
224	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
225	C₄×M₁₆	C₂²×C₁₃	1	2	yes	—
226	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
227	#343	C₂²×C₁₃	1	2	yes	—
228	#343	C₂²×C₁₃	1	2	yes	—
229	#341	C₂²×C₁₃	1	1	yes	characteristic
230	#341	C₂²×C₁₃	1	1	yes	characteristic
231	C₂²×C₁₃	—	2	1	no	—
232	C₂²×C₁₃	—	2	1	no	—
233	C₂²×C₁₃	—	4	1	no	—
234	C₂²×C₁₃	—	4	1	no	—
235	C₂²×C₁₃	—	4	1	no	—
236	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
237	C₂²×C₁₃	#529	1	2	yes	—
238	C₄×C₁₃	—	2	1	no	—
239	C₄×C₁₃	—	2	1	no	—
240	C₄×C₁₃	—	2	1	no	—
241	C₄×C₁₃	—	4	1	no	—
242	C₄×C₁₃	—	4	4	no	—
243	C₄×C₁₃	—	4	1	no	—
244	C₄×C₁₃	—	4	1	no	—
245	C₄×C₁₃	—	8	2	no	—
246	C₄×C₁₃	#473	1	2	yes	—
247	C₄×C₁₃	#525	1	1	yes	characteristic
248	C₄×C₁₃	#525	1	2	yes	—
249	C₄×C₁₃	#532	1	1	yes	characteristic
250	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
251	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
252	#137	—	2	4	no	—
253	#137	—	2	4	no	—
254	C₂×Q₁₆	—	2	2	no	—
255	C₂×Q₁₆	—	2	4	no	—
256	C₂×Q₁₆	—	2	2	no	—
257	C₂×SD₁₆	—	2	2	no	—
258	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
259	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
260	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
261	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
262	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
263	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
264	C₄×Q₈	—	2	2	no	—
265	C₄×Q₈	—	2	2	no	—
266	C₄×Q₈	—	2	2	no	—
267	C₄×Q₈	—	2	2	no	—
268	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
269	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
270	C₄×D₄	—	2	1	no	—
271	C₄×D₄	—	2	1	no	—
272	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
273	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
274	#117	—	2	1	no	—
275	#117	C₂³×C₁₃	1	1	yes	characteristic
276	C₂×C₄⋊C₄	—	2	2	no	—
277	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
278	C₂×C₄²	—	2	1	no	—
279	C₂×C₄²	—	2	2	no	—
280	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
281	#108	—	2	4	no	—
282	#107	—	2	2	no	—
283	#107	—	2	2	no	—
284	#106	—	2	2	no	—
285	C₄⋊C₈	—	2	2	no	—
286	C₄⋊C₈	—	2	2	no	—
287	#103	—	2	2	no	—
288	#103	—	2	4	no	—
289	#103	—	2	2	no	—
290	#103	—	2	2	no	—
291	#102	—	2	2	no	—
292	#101	—	2	4	no	—
293	#101	—	2	4	no	—
294	C₂²⋊C₈	—	2	2	no	—
295	C₂²⋊C₈	—	2	2	no	—
296	#97	—	2	1	no	—
297	#97	—	2	2	no	—
298	C₄×C₈	—	2	1	no	—
299	C₄×C₈	—	2	2	no	—
300	C₄×C₈	D₄×C₁₃	1	2	yes	—
301	C₄×C₈	D₄×C₁₃	1	2	yes	—
302	C₂×C₁₃	—	2	2	no	—
303	C₂×C₁₃	—	8	1	no	—
304	C₂×C₁₃	#2392	1	1	yes	characteristic
305	C₂×C₁₃	C₂×#473	1	1	yes	characteristic
306	C₂×C₁₃	#3067	1	1	yes	characteristic
307	#41	—	2	2	no	—
308	#41	—	2	2	no	—
309	C₂×Q₈	—	2	2	no	—
310	C₂×Q₈	—	2	2	no	—
311	C₂×Q₈	—	2	2	no	—
312	C₂×Q₈	—	2	2	no	—
313	C₂×Q₈	—	2	2	no	—
314	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
315	C₂×Q₈	C₁₃×#41	1	4	yes	—
316	C₂×D₄	—	2	1	no	—
317	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	2	1	no	—
320	C₂²×C₄	—	2	1	no	—
321	C₂²×C₄	—	2	1	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
324	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
325	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
326	Q₁₆	—	2	8	no	—
327	Q₁₆	—	2	8	no	—
328	SD₁₆	—	2	8	no	—
329	M₁₆	—	2	2	no	—
330	M₁₆	—	2	2	no	—
331	M₁₆	—	2	2	no	—
332	M₁₆	—	2	2	no	—
333	M₁₆	—	2	2	no	—
334	M₁₆	C₁₃×#41	1	4	yes	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	2	1	no	—
339	C₂×C₈	—	2	1	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
342	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
343	C₄⋊C₄	—	2	1	no	—
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	4	2	no	—
348	C₄⋊C₄	—	4	2	no	—
349	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
350	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
351	C₂²⋊C₄	—	2	1	no	—
352	C₂²⋊C₄	—	2	1	no	—
353	C₂²⋊C₄	—	2	1	no	—
354	C₄²	—	2	1	no	—
355	C₄²	—	2	1	no	—
356	C₄²	—	2	1	no	—
357	C₄²	—	4	2	no	—
358	C₄²	—	4	2	no	—
359	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
360	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
361	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
362	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
363	C₁₃	#23717	1	1	yes	characteristic, direct product factor, Sylow
364	C₂³	—	2	1	no	—
365	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
366	Q₈	—	2	4	no	—
367	Q₈	—	2	4	no	—
368	Q₈	—	2	2	no	—
369	Q₈	—	4	2	no	—
370	Q₈	—	4	2	no	—
371	D₄	—	2	2	no	—
372	D₄	—	4	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	4	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	1	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	8	2	no	—
387	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
388	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
389	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
390	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
391	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
392	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
393	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
394	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
395	C₈	—	2	2	no	—
396	C₈	—	2	4	no	—
397	C₈	—	2	2	no	—
398	C₈	—	4	1	no	—
399	C₈	—	4	2	no	—
400	C₈	—	4	1	no	—
401	C₂²	—	2	1	no	—
402	C₂²	—	2	1	no	—
403	C₂²	—	4	1	no	—
404	C₂²	—	4	1	no	—
405	C₂²	—	4	1	no	—
406	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
407	C₂²	C₁₃×#529	1	2	yes	—
408	C₄	—	2	1	no	—
409	C₄	—	2	1	no	—
410	C₄	—	2	1	no	—
411	C₄	—	4	1	no	—
412	C₄	—	4	1	no	—
413	C₄	—	4	1	no	—
414	C₄	—	4	4	no	—
415	C₄	—	8	2	no	—
416	C₄	C₁₃×#473	1	2	yes	—
417	C₄	C₁₃×#525	1	1	yes	characteristic
418	C₄	C₁₃×#525	1	2	yes	—
419	C₄	C₁₃×#532	1	1	yes	characteristic
420	C₂	—	2	2	no	—
421	C₂	—	8	1	no	—
422	C₂	C₁₃×#2392	1	1	yes	characteristic
423	C₂	C₂×C₁₃×#473	1	1	yes	characteristic
424	C₂	C₁₃×#3067	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃	#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
socle	C₂²×C₁₃	C₂×#121
prime radical	C₂×C₁₃×#41	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×C₁₃×Q₁₆	C₂	semidirect
4. C₁₃×#2089	C₂	semidirect
6. C₁₃×#2064	C₂	semidirect
8. C₁₃×#2047	C₂	semidirect
10. C₄×C₁₃×#108	C₂	semidirect
11. C₄×C₁₃×#101	C₂	semidirect
95. #23717	C₁₃	direct (N × H)
153. C₂×C₄×Q₁₆	C₂×C₁₃	semidirect
155. #2089	C₂×C₁₃	semidirect
157. #2064	C₂×C₁₃	semidirect
159. #2047	C₂×C₁₃	semidirect
161. C₄×#108	C₂×C₁₃	semidirect
162. C₄×#101	C₂×C₁₃	semidirect
363. C₁₃	#23717	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₁₃×#137	2
C₂×C₄×C₁₃×Q₁₆	2
C₁₃×#2922	2
C₁₃×#2089	2
C₁₃×#2078	2
C₁₃×#2064	2
C₁₃×#2052	2
C₁₃×#2047	2
C₁₃×#2020	2
C₄×C₁₃×#108	2
C₄×C₁₃×#101	2
#23717	13

Subgroups — C13×#23717 #15710056

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#23717 #15710056