Subgroups — C₁₃×#23740 #15710079

Order 3328.

988 conjugacy classes of subgroups.

The subgroup lattice has 408 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×#2905	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₃×#421	C₂	1	2	yes	maximal
4	C₁₃×#2879	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2098	C₂	1	8	yes	maximal, complemented
6	C₂×C₁₃×H(3,ℤ/4)	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
8	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	—
9	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
10	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
11	C₂×C₁₃×#117	C₂²	1	2	yes	—
12	C₁₃×#430	—	2	2	no	—
13	C₁₃×#430	C₂²	1	4	yes	complemented
14	C₂×C₁₃×#108	—	2	2	no	—
15	C₁₃×#424	—	2	4	no	—
16	C₁₃×#424	C₂²	1	8	yes	complemented
17	C₁₃×#423	—	2	4	no	—
18	C₁₃×#421	—	2	4	no	—
19	C₁₃×#421	C₂²	1	8	yes	—
20	C₂×C₁₃×#104	—	2	4	no	—
21	C₁₃×#408	—	2	2	no	—
22	C₁₃×#408	C₂²	1	4	yes	—
23	C₁₃×#407	—	2	2	no	—
24	C₁₃×H(3,ℤ/4)	C₂²	1	4	yes	complemented
25	C₂×C₁₃×#41	—	2	1	no	—
26	C₂×C₁₃×#41	—	2	1	no	—
27	C₂×C₁₃×#41	—	2	2	no	—
28	C₂×C₁₃×#41	—	2	2	no	—
29	C₂×C₁₃×#41	—	2	2	no	—
30	C₂×C₁₃×#41	—	2	2	no	—
31	C₂×C₁₃×#41	Q₈	1	2	yes	—
32	C₂×C₁₃×#41	C₂³	1	2	yes	—
33	C₂²×Q₈×C₁₃	Q₈	1	1	yes	characteristic
34	C₂²×D₄×C₁₃	—	2	1	no	—
35	C₂²×D₄×C₁₃	Q₈	1	1	yes	characteristic
36	C₂³×C₄×C₁₃	—	2	1	no	—
37	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
38	C₂×C₁₃×M₁₆	—	2	2	no	—
39	C₂×C₁₃×M₁₆	—	2	2	no	—
40	C₂×C₁₃×M₁₆	—	2	1	no	—
41	C₂×C₁₃×M₁₆	—	2	1	no	—
42	C₂×C₁₃×M₁₆	—	2	2	no	—
43	C₂×C₁₃×M₁₆	—	2	2	no	—
44	C₂×C₁₃×M₁₆	—	2	2	no	—
45	C₂×C₁₃×M₁₆	—	2	2	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	D₄	1	2	yes	—
50	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
51	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
52	C₂²×C₈×C₁₃	—	2	2	no	—
53	C₂²×C₈×C₁₃	D₄	1	2	yes	—
54	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
55	C₁₃×#117	—	2	2	no	—
56	C₁₃×#117	—	2	2	no	—
57	C₁₃×#117	D₄	1	4	yes	—
58	C₁₃×#117	C₂³	1	4	yes	—
59	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
60	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
61	C₂×C₄²×C₁₃	D₄	1	4	yes	—
62	C₁₃×#108	—	2	8	no	—
63	C₁₃×C₄⋊C₈	—	2	16	no	—
64	C₁₃×#104	—	2	16	no	—
65	C₁₃×C₂²⋊C₈	—	2	8	no	—
66	#23740	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
67	C₂⁴×C₁₃	—	2	1	no	—
68	C₂⁴×C₁₃	#41	1	1	yes	characteristic
69	C₁₃×#41	—	2	4	no	—
70	C₁₃×#41	—	2	4	no	—
71	C₁₃×#41	—	2	4	no	—
72	C₁₃×#41	—	2	4	no	—
73	C₁₃×#41	—	4	1	no	—
74	C₁₃×#41	—	4	1	no	—
75	C₁₃×#41	—	4	2	no	—
76	C₁₃×#41	—	4	2	no	—
77	C₁₃×#41	—	4	1	no	—
78	C₁₃×#41	—	4	1	no	—
79	C₂×Q₈×C₁₃	—	2	1	no	—
80	C₂×Q₈×C₁₃	—	2	2	no	—
81	C₂×Q₈×C₁₃	—	2	2	no	—
82	C₂×Q₈×C₁₃	C₂×Q₈	1	2	yes	—
83	C₂×D₄×C₁₃	—	2	2	no	—
84	C₂×D₄×C₁₃	—	2	2	no	—
85	C₂×D₄×C₁₃	—	2	2	no	—
86	C₂×D₄×C₁₃	—	2	2	no	—
87	C₂×D₄×C₁₃	—	2	1	no	—
88	C₂×D₄×C₁₃	—	4	2	no	—
89	C₂×D₄×C₁₃	—	4	2	no	—
90	C₂×D₄×C₁₃	C₂×Q₈	1	2	yes	—
91	C₂²×C₄×C₁₃	—	2	1	no	—
92	C₂²×C₄×C₁₃	—	2	4	no	—
93	C₂²×C₄×C₁₃	—	2	2	no	—
94	C₂²×C₄×C₁₃	—	2	2	no	—
95	C₂²×C₄×C₁₃	—	4	2	no	—
96	C₂²×C₄×C₁₃	—	4	2	no	—
97	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
98	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
99	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
102	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
103	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
104	C₂²×C₄×C₁₃	#41	1	2	yes	—
105	C₂²×C₄×C₁₃	#41	1	2	yes	—
106	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
107	C₁₃×M₁₆	—	2	4	no	—
108	C₁₃×M₁₆	—	2	4	no	—
109	C₁₃×M₁₆	—	2	4	no	—
110	C₁₃×M₁₆	—	2	4	no	—
111	C₁₃×M₁₆	—	4	1	no	—
112	C₁₃×M₁₆	—	4	2	no	—
113	C₁₃×M₁₆	—	4	1	no	—
114	C₁₃×M₁₆	—	4	2	no	—
115	C₁₃×M₁₆	—	4	2	no	—
116	C₂×C₈×C₁₃	—	2	2	no	—
117	C₂×C₈×C₁₃	—	2	2	no	—
118	C₂×C₈×C₁₃	—	2	2	no	—
119	C₂×C₈×C₁₃	—	2	4	no	—
120	C₂×C₈×C₁₃	—	2	4	no	—
121	C₂×C₈×C₁₃	—	4	2	no	—
122	C₂×C₈×C₁₃	—	4	2	no	—
123	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
124	C₁₃×C₄⋊C₄	—	2	4	no	—
125	C₁₃×C₄⋊C₄	—	2	4	no	—
126	C₁₃×C₂²⋊C₄	—	2	4	no	—
127	C₁₃×C₂²⋊C₄	—	2	4	no	—
128	C₄²×C₁₃	—	2	4	no	—
129	C₄²×C₁₃	C₂×D₄	1	8	yes	—
130	C₂×#430	C₂×C₁₃	1	1	yes	characteristic, complemented
131	#2905	C₂×C₁₃	1	2	yes	complemented
132	C₂×#421	C₂×C₁₃	1	2	yes	—
133	#2879	C₂×C₁₃	1	1	yes	characteristic
134	#2098	C₂×C₁₃	1	8	yes	complemented
135	C₂×H(3,ℤ/4)	C₂×C₁₃	1	1	yes	characteristic, complemented
136	C₂³×C₁₃	—	2	2	no	—
137	C₂³×C₁₃	—	4	2	no	—
138	C₂³×C₁₃	—	8	1	no	—
139	C₂³×C₁₃	—	8	2	no	—
140	C₂³×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
141	C₂³×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
142	C₂³×C₁₃	#123	1	2	yes	—
143	C₂³×C₁₃	#123	1	2	yes	—
144	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
145	Q₈×C₁₃	—	2	4	no	—
146	Q₈×C₁₃	—	4	1	no	—
147	Q₈×C₁₃	—	4	1	no	—
148	D₄×C₁₃	—	2	4	no	—
149	D₄×C₁₃	—	4	4	no	—
150	D₄×C₁₃	—	4	2	no	—
151	D₄×C₁₃	—	4	2	no	—
152	D₄×C₁₃	—	4	1	no	—
153	D₄×C₁₃	—	4	1	no	—
154	C₂×C₄×C₁₃	—	2	2	no	—
155	C₂×C₄×C₁₃	—	2	8	no	—
156	C₂×C₄×C₁₃	—	4	2	no	—
157	C₂×C₄×C₁₃	—	4	2	no	—
158	C₂×C₄×C₁₃	—	4	2	no	—
159	C₂×C₄×C₁₃	—	4	4	no	—
160	C₂×C₄×C₁₃	—	8	4	no	—
161	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
162	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
163	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
164	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
165	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
166	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
167	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
168	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
169	C₂×C₄×C₁₃	#123	1	2	yes	—
170	C₂×C₄×C₁₃	#123	1	2	yes	—
171	C₂×C₄×C₁₃	#123	1	2	yes	—
172	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
173	C₂×C₄×C₁₃	#127	1	2	yes	—
174	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
175	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
176	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
177	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
178	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
179	C₈×C₁₃	—	2	4	no	—
180	C₈×C₁₃	—	4	2	no	—
181	C₈×C₁₃	—	4	4	no	—
182	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
183	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	—
184	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
185	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
186	C₂×#117	C₂²×C₁₃	1	2	yes	—
187	#430	—	2	2	no	—
188	#430	C₂²×C₁₃	1	4	yes	complemented
189	C₂×#108	—	2	2	no	—
190	#424	—	2	4	no	—
191	#424	C₂²×C₁₃	1	8	yes	complemented
192	#423	—	2	4	no	—
193	#421	—	2	4	no	—
194	#421	C₂²×C₁₃	1	8	yes	—
195	C₂×#104	—	2	4	no	—
196	#408	—	2	2	no	—
197	#408	C₂²×C₁₃	1	4	yes	—
198	#407	—	2	2	no	—
199	H(3,ℤ/4)	C₂²×C₁₃	1	4	yes	complemented
200	C₂²×C₁₃	—	4	2	no	—
201	C₂²×C₁₃	—	4	1	no	—
202	C₂²×C₁₃	—	4	1	no	—
203	C₂²×C₁₃	—	4	2	no	—
204	C₂²×C₁₃	—	4	1	no	—
205	C₂²×C₁₃	—	4	4	no	—
206	C₂²×C₁₃	—	4	2	no	—
207	C₂²×C₁₃	—	8	4	no	—
208	C₂²×C₁₃	#399	1	2	yes	—
209	C₂²×C₁₃	#399	1	1	yes	characteristic
210	C₂²×C₁₃	#399	1	1	yes	characteristic
211	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
212	C₂²×C₁₃	C₂×#123	1	2	yes	—
213	C₄×C₁₃	—	4	8	no	—
214	C₄×C₁₃	—	4	2	no	—
215	C₄×C₁₃	#399	1	2	yes	—
216	C₄×C₁₃	#399	1	1	yes	characteristic
217	C₄×C₁₃	#399	1	1	yes	characteristic
218	C₄×C₁₃	C₂×C₂²⋊Q₈	1	2	yes	—
219	C₄×C₁₃	C₂×#123	1	1	yes	characteristic
220	C₄×C₁₃	C₂×#127	1	1	yes	characteristic
221	C₂×#41	—	2	1	no	—
222	C₂×#41	—	2	1	no	—
223	C₂×#41	—	2	2	no	—
224	C₂×#41	—	2	2	no	—
225	C₂×#41	—	2	2	no	—
226	C₂×#41	—	2	2	no	—
227	C₂×#41	Q₈×C₁₃	1	2	yes	—
228	C₂×#41	C₂³×C₁₃	1	2	yes	—
229	C₂²×Q₈	Q₈×C₁₃	1	1	yes	characteristic
230	C₂²×D₄	—	2	1	no	—
231	C₂²×D₄	Q₈×C₁₃	1	1	yes	characteristic
232	C₂³×C₄	—	2	1	no	—
233	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
234	C₂×M₁₆	—	2	2	no	—
235	C₂×M₁₆	—	2	2	no	—
236	C₂×M₁₆	—	2	1	no	—
237	C₂×M₁₆	—	2	1	no	—
238	C₂×M₁₆	—	2	2	no	—
239	C₂×M₁₆	—	2	2	no	—
240	C₂×M₁₆	—	2	2	no	—
241	C₂×M₁₆	—	2	2	no	—
242	C₂×M₁₆	—	2	2	no	—
243	C₂×M₁₆	—	2	2	no	—
244	C₂×M₁₆	—	2	2	no	—
245	C₂×M₁₆	D₄×C₁₃	1	2	yes	—
246	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
247	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
248	C₂²×C₈	—	2	2	no	—
249	C₂²×C₈	D₄×C₁₃	1	2	yes	—
250	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
251	#117	—	2	2	no	—
252	#117	—	2	2	no	—
253	#117	D₄×C₁₃	1	4	yes	—
254	#117	C₂³×C₁₃	1	4	yes	—
255	C₂×C₄⋊C₄	—	2	2	no	—
256	C₂×C₂²⋊C₄	—	2	2	no	—
257	C₂×C₄²	D₄×C₁₃	1	4	yes	—
258	#108	—	2	8	no	—
259	C₄⋊C₈	—	2	16	no	—
260	#104	—	2	16	no	—
261	C₂²⋊C₈	—	2	8	no	—
262	C₂×C₁₃	—	2	2	no	—
263	C₂×C₁₃	—	2	1	no	—
264	C₂×C₁₃	—	2	2	no	—
265	C₂×C₁₃	—	2	1	no	—
266	C₂×C₁₃	—	2	1	no	—
267	C₂×C₁₃	—	8	2	no	—
268	C₂×C₁₃	C₂×#399	1	1	yes	characteristic
269	C₂⁴	—	2	1	no	—
270	C₂⁴	C₁₃×#41	1	1	yes	characteristic
271	#41	—	2	4	no	—
272	#41	—	2	4	no	—
273	#41	—	2	4	no	—
274	#41	—	2	4	no	—
275	#41	—	4	2	no	—
276	#41	—	4	2	no	—
277	#41	—	4	1	no	—
278	#41	—	4	1	no	—
279	#41	—	4	1	no	—
280	#41	—	4	1	no	—
281	C₂×Q₈	—	2	1	no	—
282	C₂×Q₈	—	2	2	no	—
283	C₂×Q₈	—	2	2	no	—
284	C₂×Q₈	C₂×Q₈×C₁₃	1	2	yes	—
285	C₂×D₄	—	2	2	no	—
286	C₂×D₄	—	2	2	no	—
287	C₂×D₄	—	2	2	no	—
288	C₂×D₄	—	2	2	no	—
289	C₂×D₄	—	2	1	no	—
290	C₂×D₄	—	4	2	no	—
291	C₂×D₄	—	4	2	no	—
292	C₂×D₄	C₂×Q₈×C₁₃	1	2	yes	—
293	C₂²×C₄	—	2	1	no	—
294	C₂²×C₄	—	2	4	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	4	2	no	—
298	C₂²×C₄	—	4	2	no	—
299	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
300	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
301	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
302	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
303	C₂²×C₄	C₂×Q₈×C₁₃	1	1	yes	characteristic
304	C₂²×C₄	C₂×Q₈×C₁₃	1	1	yes	characteristic
305	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
306	C₂²×C₄	C₁₃×#41	1	2	yes	—
307	C₂²×C₄	C₁₃×#41	1	2	yes	—
308	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
309	M₁₆	—	2	4	no	—
310	M₁₆	—	2	4	no	—
311	M₁₆	—	2	4	no	—
312	M₁₆	—	2	4	no	—
313	M₁₆	—	4	1	no	—
314	M₁₆	—	4	2	no	—
315	M₁₆	—	4	1	no	—
316	M₁₆	—	4	2	no	—
317	M₁₆	—	4	2	no	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	4	no	—
322	C₂×C₈	—	2	4	no	—
323	C₂×C₈	—	4	2	no	—
324	C₂×C₈	—	4	2	no	—
325	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
326	C₄⋊C₄	—	2	4	no	—
327	C₄⋊C₄	—	2	4	no	—
328	C₂²⋊C₄	—	2	4	no	—
329	C₂²⋊C₄	—	2	4	no	—
330	C₄²	—	2	4	no	—
331	C₄²	C₂×D₄×C₁₃	1	8	yes	—
332	C₁₃	#23740	1	1	yes	characteristic, direct product factor, Sylow
333	C₂³	—	2	2	no	—
334	C₂³	—	4	2	no	—
335	C₂³	—	8	1	no	—
336	C₂³	—	8	2	no	—
337	C₂³	C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
338	C₂³	C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
339	C₂³	C₁₃×#123	1	2	yes	—
340	C₂³	C₁₃×#123	1	2	yes	—
341	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
342	Q₈	—	2	4	no	—
343	Q₈	—	4	1	no	—
344	Q₈	—	4	1	no	—
345	D₄	—	2	4	no	—
346	D₄	—	4	2	no	—
347	D₄	—	4	2	no	—
348	D₄	—	4	4	no	—
349	D₄	—	4	1	no	—
350	D₄	—	4	1	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	8	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	4	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	8	4	no	—
358	C₂×C₄	C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
359	C₂×C₄	C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
360	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
361	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
362	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
363	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
364	C₂×C₄	C₁₃×#123	1	2	yes	—
365	C₂×C₄	C₁₃×#123	1	2	yes	—
366	C₂×C₄	C₁₃×#123	1	1	yes	characteristic
367	C₂×C₄	C₁₃×#123	1	1	yes	characteristic
368	C₂×C₄	C₁₃×#123	1	2	yes	—
369	C₂×C₄	C₁₃×#127	1	1	yes	characteristic
370	C₂×C₄	C₁₃×#127	1	2	yes	—
371	C₂×C₄	C₁₃×#127	1	1	yes	characteristic
372	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
373	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
374	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
375	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
376	C₈	—	2	4	no	—
377	C₈	—	4	2	no	—
378	C₈	—	4	4	no	—
379	C₂²	—	4	2	no	—
380	C₂²	—	4	1	no	—
381	C₂²	—	4	1	no	—
382	C₂²	—	4	2	no	—
383	C₂²	—	4	1	no	—
384	C₂²	—	4	4	no	—
385	C₂²	—	4	2	no	—
386	C₂²	—	8	4	no	—
387	C₂²	C₁₃×#399	1	2	yes	—
388	C₂²	C₁₃×#399	1	1	yes	characteristic
389	C₂²	C₁₃×#399	1	1	yes	characteristic
390	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
391	C₂²	C₂×C₁₃×#123	1	2	yes	—
392	C₄	—	4	8	no	—
393	C₄	—	4	2	no	—
394	C₄	C₁₃×#399	1	2	yes	—
395	C₄	C₁₃×#399	1	1	yes	characteristic
396	C₄	C₁₃×#399	1	1	yes	characteristic
397	C₄	C₂×C₁₃×C₂²⋊Q₈	1	2	yes	—
398	C₄	C₂×C₁₃×#123	1	1	yes	characteristic
399	C₄	C₂×C₁₃×#127	1	1	yes	characteristic
400	C₂	—	2	2	no	—
401	C₂	—	2	1	no	—
402	C₂	—	2	2	no	—
403	C₂	—	2	1	no	—
404	C₂	—	2	1	no	—
405	C₂	—	8	2	no	—
406	C₂	C₂×C₁₃×#399	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₁₃	C₂×#127
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
socle	C₂×C₁₃	C₂×#399
prime radical	C₂²×C₁₃×#41	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×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×#2905	C₂	semidirect
5. C₁₃×#2098	C₂	semidirect
6. C₂×C₁₃×H(3,ℤ/4)	C₂	semidirect
13. C₁₃×#430	C₂²	semidirect
16. C₁₃×#424	C₂²	semidirect
24. C₁₃×H(3,ℤ/4)	C₂²	semidirect
66. #23740	C₁₃	direct (N × H)
130. C₂×#430	C₂×C₁₃	semidirect
131. #2905	C₂×C₁₃	semidirect
134. #2098	C₂×C₁₃	semidirect
135. C₂×H(3,ℤ/4)	C₂×C₁₃	semidirect
188. #430	C₂²×C₁₃	semidirect
191. #424	C₂²×C₁₃	semidirect
199. H(3,ℤ/4)	C₂²×C₁₃	semidirect
332. C₁₃	#23740	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×#2905	2
C₂×C₁₃×#421	2
C₁₃×#2879	2
C₁₃×#2098	2
C₂×C₁₃×H(3,ℤ/4)	2
#23740	13

Subgroups — C13×#23740 #15710079

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#23740 #15710079