Subgroups — C₁₃×#23614 #15709953

Order 3328.

1214 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#428	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#424	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#418	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₁₃×#102	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2316	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2309	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#2067	C₂	1	4	yes	maximal, complemented
8	C₁₃×#2065	C₂	1	4	yes	maximal, complemented
9	C₁₃×#1735	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
11	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
12	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
16	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₁₃×#428	—	2	4	no	—
18	C₂×C₁₃×#107	C₂²	1	2	yes	complemented
19	C₂×C₁₃×#106	C₂²	1	2	yes	complemented
20	C₁₃×#424	—	2	4	no	—
21	C₂×C₁₃×C₄⋊C₈	C₂²	1	4	yes	complemented
22	C₁₃×#418	—	2	4	no	—
23	C₂×C₁₃×#102	—	2	4	no	—
24	C₂×C₁₃×#102	C₂²	1	4	yes	—
25	C₂×C₁₃×#102	C₂²	1	4	yes	—
26	C₁₃×#390	—	2	2	no	—
27	C₁₃×#390	C₂²	1	2	yes	—
28	C₁₃×#390	C₂²	1	2	yes	—
29	C₁₃×#389	—	2	2	no	—
30	C₁₃×#389	C₂²	1	4	yes	complemented
31	C₁₃×#380	—	2	2	no	—
32	C₁₃×#379	—	2	2	no	—
33	C₁₃×#340	C₂²	1	2	yes	complemented
34	C₁₃×#340	C₂²	1	2	yes	complemented
35	C₂⁵×C₁₃	—	2	1	no	—
36	C₂²×D₄×C₁₃	—	2	2	no	—
37	C₂²×D₄×C₁₃	—	2	2	no	—
38	C₂²×D₄×C₁₃	—	2	1	no	—
39	C₂²×D₄×C₁₃	—	2	2	no	—
40	C₂²×D₄×C₁₃	—	2	2	no	—
41	C₂²×D₄×C₁₃	—	2	2	no	—
42	C₂²×D₄×C₁₃	Q₈	1	4	yes	—
43	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
44	C₂³×C₄×C₁₃	—	2	1	no	—
45	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
46	C₂×C₁₃×M₁₆	—	2	2	no	—
47	C₂×C₁₃×M₁₆	—	2	2	no	—
48	C₂×C₁₃×M₁₆	D₄	1	4	yes	—
49	C₂²×C₈×C₁₃	—	2	2	no	—
50	C₂²×C₈×C₁₃	—	2	2	no	—
51	C₂²×C₈×C₁₃	—	2	2	no	—
52	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
53	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
54	C₁₃×#117	—	2	2	no	—
55	C₁₃×#117	—	2	2	no	—
56	C₁₃×#117	—	2	2	no	—
57	C₁₃×#117	—	2	2	no	—
58	C₁₃×#117	—	2	2	no	—
59	C₁₃×#117	—	2	2	no	—
60	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
61	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
62	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
63	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
64	C₂×C₁₃×C₄⋊C₄	D₄	1	4	yes	—
65	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
66	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
67	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
68	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
69	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
70	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
71	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
72	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
73	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
74	C₂×C₄²×C₁₃	—	2	1	no	—
75	C₂×C₄²×C₁₃	—	2	1	no	—
76	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
77	C₁₃×#107	—	2	4	no	—
78	C₁₃×#106	—	2	4	no	—
79	C₁₃×C₄⋊C₈	—	2	8	no	—
80	C₁₃×#102	—	2	8	no	—
81	C₁₃×#102	—	2	8	no	—
82	C₁₃×#95	—	2	4	no	—
83	#23614	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
84	C₂⁴×C₁₃	—	2	2	no	—
85	C₂⁴×C₁₃	—	2	4	no	—
86	C₂⁴×C₁₃	—	4	2	no	—
87	C₂⁴×C₁₃	—	4	2	no	—
88	C₂⁴×C₁₃	—	8	2	no	—
89	C₂⁴×C₁₃	—	8	2	no	—
90	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
91	C₂×D₄×C₁₃	—	2	8	no	—
92	C₂×D₄×C₁₃	—	2	8	no	—
93	C₂×D₄×C₁₃	—	2	4	no	—
94	C₂×D₄×C₁₃	—	2	2	no	—
95	C₂×D₄×C₁₃	—	2	2	no	—
96	C₂×D₄×C₁₃	—	2	2	no	—
97	C₂×D₄×C₁₃	—	2	2	no	—
98	C₂×D₄×C₁₃	—	2	2	no	—
99	C₂×D₄×C₁₃	—	4	4	no	—
100	C₂×D₄×C₁₃	—	4	2	no	—
101	C₂×D₄×C₁₃	—	4	2	no	—
102	C₂×D₄×C₁₃	—	4	4	no	—
103	C₂×D₄×C₁₃	C₂×Q₈	1	4	yes	—
104	C₂²×C₄×C₁₃	—	2	2	no	—
105	C₂²×C₄×C₁₃	—	2	4	no	—
106	C₂²×C₄×C₁₃	—	2	2	no	—
107	C₂²×C₄×C₁₃	—	2	1	no	—
108	C₂²×C₄×C₁₃	—	2	1	no	—
109	C₂²×C₄×C₁₃	—	8	2	no	—
110	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
111	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
115	C₂²×C₄×C₁₃	#41	1	2	yes	—
116	C₂²×C₄×C₁₃	#41	1	2	yes	—
117	C₂²×C₄×C₁₃	#41	1	2	yes	—
118	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
119	C₁₃×M₁₆	—	2	8	no	—
120	C₂×C₈×C₁₃	—	2	2	no	—
121	C₂×C₈×C₁₃	—	2	2	no	—
122	C₂×C₈×C₁₃	—	2	2	no	—
123	C₂×C₈×C₁₃	—	2	2	no	—
124	C₂×C₈×C₁₃	—	2	2	no	—
125	C₂×C₈×C₁₃	—	4	4	no	—
126	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
127	C₁₃×C₄⋊C₄	—	2	4	no	—
128	C₁₃×C₄⋊C₄	—	2	4	no	—
129	C₁₃×C₄⋊C₄	—	2	2	no	—
130	C₁₃×C₄⋊C₄	—	2	2	no	—
131	C₁₃×C₄⋊C₄	—	2	1	no	—
132	C₁₃×C₄⋊C₄	—	2	1	no	—
133	C₁₃×C₄⋊C₄	—	2	2	no	—
134	C₁₃×C₄⋊C₄	—	2	1	no	—
135	C₁₃×C₄⋊C₄	—	2	1	no	—
136	C₁₃×C₄⋊C₄	—	8	4	no	—
137	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
138	C₁₃×C₂²⋊C₄	—	2	4	no	—
139	C₁₃×C₂²⋊C₄	—	4	2	no	—
140	C₁₃×C₂²⋊C₄	—	4	2	no	—
141	C₁₃×C₂²⋊C₄	—	8	4	no	—
142	C₁₃×C₂²⋊C₄	—	8	4	no	—
143	C₄²×C₁₃	—	2	2	no	—
144	C₄²×C₁₃	—	2	2	no	—
145	C₄²×C₁₃	—	4	2	no	—
146	C₄²×C₁₃	—	4	2	no	—
147	C₂×#428	C₂×C₁₃	1	1	yes	characteristic, complemented
148	C₂×#424	C₂×C₁₃	1	1	yes	characteristic, complemented
149	C₂×#418	C₂×C₁₃	1	1	yes	characteristic
150	C₂²×#102	C₂×C₁₃	1	1	yes	characteristic
151	#2316	C₂×C₁₃	1	1	yes	characteristic, complemented
152	#2309	C₂×C₁₃	1	1	yes	characteristic
153	#2067	C₂×C₁₃	1	4	yes	complemented
154	#2065	C₂×C₁₃	1	4	yes	complemented
155	#1735	C₂×C₁₃	1	1	yes	characteristic, complemented
156	C₂³×C₁₃	—	2	2	no	—
157	C₂³×C₁₃	—	2	2	no	—
158	C₂³×C₁₃	—	2	4	no	—
159	C₂³×C₁₃	—	4	2	no	—
160	C₂³×C₁₃	—	4	2	no	—
161	C₂³×C₁₃	—	4	4	no	—
162	C₂³×C₁₃	—	4	4	no	—
163	C₂³×C₁₃	—	4	8	no	—
164	C₂³×C₁₃	—	8	8	no	—
165	C₂³×C₁₃	—	8	4	no	—
166	C₂³×C₁₃	—	8	4	no	—
167	C₂³×C₁₃	—	8	8	no	—
168	C₂³×C₁₃	#121	1	2	yes	—
169	C₂³×C₁₃	#121	1	2	yes	—
170	C₂³×C₁₃	C₂²⋊Q₈	1	2	yes	—
171	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
172	D₄×C₁₃	—	2	4	no	—
173	D₄×C₁₃	—	2	4	no	—
174	D₄×C₁₃	—	4	2	no	—
175	D₄×C₁₃	—	4	2	no	—
176	D₄×C₁₃	—	4	8	no	—
177	C₂×C₄×C₁₃	—	2	4	no	—
178	C₂×C₄×C₁₃	—	2	4	no	—
179	C₂×C₄×C₁₃	—	2	4	no	—
180	C₂×C₄×C₁₃	—	2	4	no	—
181	C₂×C₄×C₁₃	—	4	4	no	—
182	C₂×C₄×C₁₃	—	4	1	no	—
183	C₂×C₄×C₁₃	—	4	1	no	—
184	C₂×C₄×C₁₃	—	4	2	no	—
185	C₂×C₄×C₁₃	—	4	2	no	—
186	C₂×C₄×C₁₃	—	4	2	no	—
187	C₂×C₄×C₁₃	—	4	2	no	—
188	C₂×C₄×C₁₃	—	4	2	no	—
189	C₂×C₄×C₁₃	—	8	4	no	—
190	C₂×C₄×C₁₃	#121	1	4	yes	—
191	C₂×C₄×C₁₃	#121	1	2	yes	—
192	C₂×C₄×C₁₃	#121	1	2	yes	—
193	C₂×C₄×C₁₃	C₂²⋊Q₈	1	4	yes	—
194	C₂×C₄×C₁₃	C₂²⋊Q₈	1	4	yes	—
195	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
196	C₂×C₄×C₁₃	#126	1	4	yes	—
197	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
198	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
199	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
200	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
201	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
202	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
203	C₈×C₁₃	—	2	4	no	—
204	C₈×C₁₃	—	4	2	no	—
205	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
206	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
207	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
208	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
209	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
210	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
211	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
212	#428	—	2	4	no	—
213	C₂×#107	C₂²×C₁₃	1	2	yes	complemented
214	C₂×#106	C₂²×C₁₃	1	2	yes	complemented
215	#424	—	2	4	no	—
216	C₂×C₄⋊C₈	C₂²×C₁₃	1	4	yes	complemented
217	#418	—	2	4	no	—
218	C₂×#102	—	2	4	no	—
219	C₂×#102	C₂²×C₁₃	1	4	yes	—
220	C₂×#102	C₂²×C₁₃	1	4	yes	—
221	#390	—	2	2	no	—
222	#390	C₂²×C₁₃	1	2	yes	—
223	#390	C₂²×C₁₃	1	2	yes	—
224	#389	—	2	2	no	—
225	#389	C₂²×C₁₃	1	4	yes	complemented
226	#380	—	2	2	no	—
227	#379	—	2	2	no	—
228	#340	C₂²×C₁₃	1	2	yes	complemented
229	#340	C₂²×C₁₃	1	2	yes	complemented
230	C₂²×C₁₃	—	2	4	no	—
231	C₂²×C₁₃	—	2	2	no	—
232	C₂²×C₁₃	—	2	2	no	—
233	C₂²×C₁₃	—	2	4	no	—
234	C₂²×C₁₃	—	4	8	no	—
235	C₂²×C₁₃	—	4	4	no	—
236	C₂²×C₁₃	—	8	16	no	—
237	C₂²×C₁₃	—	8	2	no	—
238	C₂²×C₁₃	—	8	2	no	—
239	C₂²×C₁₃	—	8	4	no	—
240	C₂²×C₁₃	#396	1	4	yes	—
241	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
242	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
243	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
244	C₂²×C₁₃	#576	1	2	yes	—
245	C₂²×C₁₃	#577	1	2	yes	—
246	C₄×C₁₃	—	4	4	no	—
247	C₄×C₁₃	—	4	4	no	—
248	C₄×C₁₃	—	8	1	no	—
249	C₄×C₁₃	—	8	1	no	—
250	C₄×C₁₃	—	8	2	no	—
251	C₄×C₁₃	#396	1	4	yes	—
252	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
253	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
254	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
255	C₄×C₁₃	C₂×#126	1	1	yes	characteristic
256	C₂⁵	—	2	1	no	—
257	C₂²×D₄	—	2	2	no	—
258	C₂²×D₄	—	2	2	no	—
259	C₂²×D₄	—	2	1	no	—
260	C₂²×D₄	—	2	2	no	—
261	C₂²×D₄	—	2	2	no	—
262	C₂²×D₄	—	2	2	no	—
263	C₂²×D₄	Q₈×C₁₃	1	4	yes	—
264	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
265	C₂³×C₄	—	2	1	no	—
266	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
267	C₂×M₁₆	—	2	2	no	—
268	C₂×M₁₆	—	2	2	no	—
269	C₂×M₁₆	D₄×C₁₃	1	4	yes	—
270	C₂²×C₈	—	2	2	no	—
271	C₂²×C₈	—	2	2	no	—
272	C₂²×C₈	—	2	2	no	—
273	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
274	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
275	#117	—	2	2	no	—
276	#117	—	2	2	no	—
277	#117	—	2	2	no	—
278	#117	—	2	2	no	—
279	#117	—	2	2	no	—
280	#117	—	2	2	no	—
281	C₂×C₄⋊C₄	—	2	1	no	—
282	C₂×C₄⋊C₄	—	2	2	no	—
283	C₂×C₄⋊C₄	—	2	4	no	—
284	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
285	C₂×C₄⋊C₄	D₄×C₁₃	1	4	yes	—
286	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
287	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
288	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
289	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
290	C₂×C₂²⋊C₄	—	2	1	no	—
291	C₂×C₂²⋊C₄	—	2	1	no	—
292	C₂×C₂²⋊C₄	—	2	4	no	—
293	C₂×C₂²⋊C₄	—	2	4	no	—
294	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
295	C₂×C₄²	—	2	1	no	—
296	C₂×C₄²	—	2	1	no	—
297	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
298	#107	—	2	4	no	—
299	#106	—	2	4	no	—
300	C₄⋊C₈	—	2	8	no	—
301	#102	—	2	8	no	—
302	#102	—	2	8	no	—
303	#95	—	2	4	no	—
304	C₂×C₁₃	—	2	4	no	—
305	C₂×C₁₃	—	8	4	no	—
306	C₂×C₁₃	C₂×#396	1	1	yes	characteristic
307	C₂×C₁₃	#3041	1	1	yes	characteristic
308	C₂×C₁₃	#3043	1	1	yes	characteristic
309	C₂×C₁₃	#3062	1	2	yes	—
310	C₂×C₁₃	#3081	1	2	yes	—
311	C₂⁴	—	2	2	no	—
312	C₂⁴	—	2	4	no	—
313	C₂⁴	—	4	2	no	—
314	C₂⁴	—	4	2	no	—
315	C₂⁴	—	8	2	no	—
316	C₂⁴	—	8	2	no	—
317	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
318	C₂×D₄	—	2	8	no	—
319	C₂×D₄	—	2	8	no	—
320	C₂×D₄	—	2	4	no	—
321	C₂×D₄	—	2	2	no	—
322	C₂×D₄	—	2	2	no	—
323	C₂×D₄	—	2	2	no	—
324	C₂×D₄	—	2	2	no	—
325	C₂×D₄	—	2	2	no	—
326	C₂×D₄	—	4	2	no	—
327	C₂×D₄	—	4	2	no	—
328	C₂×D₄	—	4	4	no	—
329	C₂×D₄	—	4	4	no	—
330	C₂×D₄	C₂×Q₈×C₁₃	1	4	yes	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	2	4	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	8	2	no	—
337	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
338	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
339	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
340	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
341	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
342	C₂²×C₄	C₁₃×#41	1	2	yes	—
343	C₂²×C₄	C₁₃×#41	1	2	yes	—
344	C₂²×C₄	C₁₃×#41	1	2	yes	—
345	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
346	M₁₆	—	2	8	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	4	4	no	—
353	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
354	C₄⋊C₄	—	2	4	no	—
355	C₄⋊C₄	—	2	4	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	8	4	no	—
364	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
365	C₂²⋊C₄	—	2	4	no	—
366	C₂²⋊C₄	—	4	2	no	—
367	C₂²⋊C₄	—	4	2	no	—
368	C₂²⋊C₄	—	8	4	no	—
369	C₂²⋊C₄	—	8	4	no	—
370	C₄²	—	2	2	no	—
371	C₄²	—	2	2	no	—
372	C₄²	—	4	2	no	—
373	C₄²	—	4	2	no	—
374	C₁₃	#23614	1	1	yes	characteristic, direct product factor, Sylow
375	C₂³	—	2	2	no	—
376	C₂³	—	2	2	no	—
377	C₂³	—	2	4	no	—
378	C₂³	—	4	8	no	—
379	C₂³	—	4	2	no	—
380	C₂³	—	4	2	no	—
381	C₂³	—	4	4	no	—
382	C₂³	—	4	4	no	—
383	C₂³	—	8	8	no	—
384	C₂³	—	8	4	no	—
385	C₂³	—	8	4	no	—
386	C₂³	—	8	8	no	—
387	C₂³	C₁₃×#121	1	2	yes	—
388	C₂³	C₁₃×#121	1	2	yes	—
389	C₂³	C₁₃×C₂²⋊Q₈	1	2	yes	—
390	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
391	D₄	—	2	4	no	—
392	D₄	—	2	4	no	—
393	D₄	—	4	8	no	—
394	D₄	—	4	2	no	—
395	D₄	—	4	2	no	—
396	C₂×C₄	—	2	4	no	—
397	C₂×C₄	—	2	4	no	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	4	4	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	8	4	no	—
409	C₂×C₄	C₁₃×#121	1	2	yes	—
410	C₂×C₄	C₁₃×#121	1	2	yes	—
411	C₂×C₄	C₁₃×#121	1	4	yes	—
412	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
413	C₂×C₄	C₁₃×C₂²⋊Q₈	1	4	yes	—
414	C₂×C₄	C₁₃×C₂²⋊Q₈	1	4	yes	—
415	C₂×C₄	C₁₃×#126	1	4	yes	—
416	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
417	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
418	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
419	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
420	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
421	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
422	C₈	—	2	4	no	—
423	C₈	—	4	2	no	—
424	C₂²	—	2	2	no	—
425	C₂²	—	2	2	no	—
426	C₂²	—	2	4	no	—
427	C₂²	—	2	4	no	—
428	C₂²	—	4	8	no	—
429	C₂²	—	4	4	no	—
430	C₂²	—	8	16	no	—
431	C₂²	—	8	2	no	—
432	C₂²	—	8	2	no	—
433	C₂²	—	8	4	no	—
434	C₂²	C₁₃×#396	1	4	yes	—
435	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
436	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
437	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
438	C₂²	C₁₃×#576	1	2	yes	—
439	C₂²	C₁₃×#577	1	2	yes	—
440	C₄	—	4	4	no	—
441	C₄	—	4	4	no	—
442	C₄	—	8	1	no	—
443	C₄	—	8	1	no	—
444	C₄	—	8	2	no	—
445	C₄	C₁₃×#396	1	4	yes	—
446	C₄	C₂×C₁₃×#121	1	1	yes	characteristic
447	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
448	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
449	C₄	C₂×C₁₃×#126	1	1	yes	characteristic
450	C₂	—	2	4	no	—
451	C₂	—	8	4	no	—
452	C₂	C₂×C₁₃×#396	1	1	yes	characteristic
453	C₂	C₁₃×#3041	1	1	yes	characteristic
454	C₂	C₁₃×#3043	1	1	yes	characteristic
455	C₂	C₁₃×#3062	1	2	yes	—
456	C₂	C₁₃×#3081	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂³×D₄×C₁₃	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₁₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#428	C₂	semidirect
2. C₂×C₁₃×#424	C₂	semidirect
5. C₁₃×#2316	C₂	semidirect
7. C₁₃×#2067	C₂	semidirect
8. C₁₃×#2065	C₂	semidirect
9. C₁₃×#1735	C₂	semidirect
18. C₂×C₁₃×#107	C₂²	semidirect
19. C₂×C₁₃×#106	C₂²	semidirect
21. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
30. C₁₃×#389	C₂²	semidirect
33. C₁₃×#340	C₂²	semidirect
34. C₁₃×#340	C₂²	semidirect
83. #23614	C₁₃	direct (N × H)
147. C₂×#428	C₂×C₁₃	semidirect
148. C₂×#424	C₂×C₁₃	semidirect
151. #2316	C₂×C₁₃	semidirect
153. #2067	C₂×C₁₃	semidirect
154. #2065	C₂×C₁₃	semidirect
155. #1735	C₂×C₁₃	semidirect
213. C₂×#107	C₂²×C₁₃	semidirect
214. C₂×#106	C₂²×C₁₃	semidirect
216. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
225. #389	C₂²×C₁₃	semidirect
228. #340	C₂²×C₁₃	semidirect
229. #340	C₂²×C₁₃	semidirect
374. C₁₃	#23614	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×#428	2
C₂×C₁₃×#424	2
C₂×C₁₃×#418	2
C₂²×C₁₃×#102	2
C₁₃×#2316	2
C₁₃×#2309	2
C₁₃×#2067	2
C₁₃×#2065	2
C₁₃×#1735	2
#23614	13

Subgroups — C13×#23614 #15709953

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#23614 #15709953