Subgroups — C₁₃×#61393 #15747732

Order 3328.

1958 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3480	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3396	C₂	1	3	yes	maximal, complemented
3	C₁₃×#3395	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3394	C₂	1	6	yes	maximal, complemented
5	C₁₃×#3393	C₂	1	3	yes	maximal, complemented
6	C₁₃×#3392	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3391	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#3147	C₂	1	3	yes	maximal, complemented
9	C₁₃×#3035	C₂	1	6	yes	maximal, complemented
10	C₂×C₈×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₁₃×#135	C₂	1	3	yes	maximal, complemented
12	C₂×C₁₃×#135	C₂²	1	3	yes	—
13	C₂×C₁₃×#135	C₂²	1	6	yes	—
14	C₁₃×#559	C₂²	1	6	yes	—
15	C₁₃×#557	C₂²	1	2	yes	—
16	C₁₃×#556	C₂²	1	6	yes	—
17	C₁₃×#553	—	2	6	no	—
18	C₁₃×#550	C₂²	1	2	yes	—
19	C₁₃×#548	—	2	2	no	—
20	C₁₃×#532	C₂²	1	6	yes	—
21	C₁₃×#529	—	2	6	no	—
22	C₄×C₁₃×#41	—	2	2	no	—
23	C₄×C₁₃×#41	C₂²	1	6	yes	—
24	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
25	C₁₃×#495	C₂²	1	6	yes	—
26	C₁₃×#495	C₂²	1	6	yes	—
27	C₁₃×#494	C₂²	1	3	yes	—
28	C₁₃×#493	C₂²	1	3	yes	—
29	C₁₃×#492	C₂²	1	6	yes	—
30	C₁₃×#464	C₂²	1	12	yes	—
31	C₁₃×#463	C₂²	1	12	yes	—
32	C₁₃×#462	C₂²	1	6	yes	—
33	C₁₃×#461	C₂²	1	6	yes	—
34	C₁₃×#460	C₂²	1	6	yes	—
35	C₁₃×#459	C₂²	1	6	yes	—
36	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
37	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
38	C₈×Q₈×C₁₃	C₂²	1	3	yes	—
39	C₈×Q₈×C₁₃	C₂²	1	3	yes	—
40	C₄×C₁₃×Q₁₆	C₂²	1	3	yes	—
41	C₄×C₁₃×Q₁₆	C₂²	1	3	yes	—
42	C₄×C₁₃×SD₁₆	C₂²	1	6	yes	—
43	C₄×C₁₃×SD₁₆	C₂²	1	6	yes	—
44	C₄×C₁₃×D₈	C₂²	1	3	yes	—
45	C₄×C₁₃×D₈	C₂²	1	3	yes	—
46	C₁₃×#427	C₂²	1	1	yes	characteristic
47	C₂×C₁₃×C₄⋊C₈	C₂²	1	3	yes	—
48	C₁₃×#416	C₂²	1	6	yes	—
49	C₂×C₄×C₈×C₁₃	C₂²	1	3	yes	—
50	C₂×C₁₃×#41	—	2	2	no	—
51	C₂×C₁₃×#41	C₂³	1	6	yes	—
52	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
53	C₁₃×#135	—	2	12	no	—
54	C₁₃×#135	—	4	12	no	—
55	C₂×C₁₃×Q₁₆	C₂³	1	3	yes	—
56	C₂×C₁₃×Q₁₆	C₂³	1	6	yes	—
57	C₂×C₁₃×SD₁₆	C₂³	1	6	yes	—
58	C₂×C₁₃×SD₁₆	C₂³	1	12	yes	—
59	C₂×C₁₃×D₈	C₂³	1	3	yes	—
60	C₂×C₁₃×D₈	C₂³	1	6	yes	—
61	C₂²×C₈×C₁₃	C₂³	1	3	yes	—
62	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
63	C₁₃×C₄⋊Q₈	C₂³	1	6	yes	—
64	C₁₃×#127	C₂³	1	6	yes	—
65	C₁₃×#126	—	2	12	no	—
66	C₁₃×#125	—	2	6	no	—
67	C₁₃×#124	—	2	6	no	—
68	C₁₃×#124	C₂³	1	12	yes	—
69	C₁₃×#123	—	2	12	no	—
70	C₁₃×C₂²⋊Q₈	—	2	6	no	—
71	C₁₃×#121	—	2	6	no	—
72	C₁₃×#121	—	2	6	no	—
73	C₁₃×#121	—	2	6	no	—
74	C₄×Q₈×C₁₃	—	2	2	no	—
75	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
76	C₄×Q₈×C₁₃	D₄	1	3	yes	—
77	C₄×Q₈×C₁₃	C₂³	1	6	yes	—
78	C₄×Q₈×C₁₃	C₂³	1	6	yes	—
79	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
80	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
81	C₄×D₄×C₁₃	—	2	6	no	—
82	C₄×D₄×C₁₃	—	2	6	no	—
83	C₄×D₄×C₁₃	—	2	6	no	—
84	C₄×D₄×C₁₃	—	2	6	no	—
85	C₄×D₄×C₁₃	—	2	6	no	—
86	C₄×D₄×C₁₃	C₂³	1	6	yes	—
87	C₄×D₄×C₁₃	C₂³	1	6	yes	—
88	C₁₃×#117	—	2	6	no	—
89	C₁₃×#117	—	2	6	no	—
90	C₁₃×#117	C₂³	1	2	yes	—
91	C₂×C₁₃×C₄⋊C₄	D₄	1	3	yes	—
92	C₂×C₄²×C₁₃	—	2	6	no	—
93	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
94	C₁₃×#107	C₂³	1	1	yes	characteristic
95	C₁₃×#107	C₂³	1	1	yes	characteristic
96	C₁₃×#106	C₂³	1	2	yes	—
97	C₁₃×C₄⋊C₈	C₂³	1	3	yes	—
98	C₁₃×C₄⋊C₈	C₂³	1	3	yes	—
99	C₁₃×C₄⋊C₈	C₂³	1	6	yes	—
100	C₁₃×#103	C₂³	1	6	yes	—
101	C₁₃×#103	C₂³	1	6	yes	—
102	C₁₃×#102	C₂³	1	6	yes	—
103	C₁₃×#102	C₂³	1	6	yes	—
104	C₄×C₈×C₁₃	C₂³	1	3	yes	—
105	C₄×C₈×C₁₃	C₂³	1	3	yes	—
106	C₄×C₈×C₁₃	C₂³	1	3	yes	—
107	C₄×C₈×C₁₃	C₂³	1	3	yes	—
108	#61393	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
109	C₁₃×#41	—	2	12	no	—
110	C₁₃×#41	—	2	12	no	—
111	C₁₃×#41	—	4	8	no	—
112	C₂×Q₈×C₁₃	—	2	4	no	—
113	C₂×Q₈×C₁₃	C₂×D₄	1	3	yes	—
114	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
115	C₂×Q₈×C₁₃	C₂⁴	1	6	yes	—
116	C₂×D₄×C₁₃	—	2	6	no	—
117	C₂×D₄×C₁₃	—	2	6	no	—
118	C₂×D₄×C₁₃	—	2	6	no	—
119	C₂×D₄×C₁₃	C₂⁴	1	6	yes	—
120	C₂²×C₄×C₁₃	—	2	6	no	—
121	C₂²×C₄×C₁₃	—	2	6	no	—
122	C₂²×C₄×C₁₃	—	2	6	no	—
123	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
124	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
125	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
126	C₁₃×Q₁₆	—	2	6	no	—
127	C₁₃×Q₁₆	—	4	6	no	—
128	C₁₃×SD₁₆	—	2	12	no	—
129	C₁₃×SD₁₆	—	4	12	no	—
130	C₁₃×D₈	—	2	6	no	—
131	C₁₃×D₈	—	4	6	no	—
132	C₂×C₈×C₁₃	—	2	6	no	—
133	C₂×C₈×C₁₃	#41	1	4	yes	complemented
134	C₂×C₈×C₁₃	C₂⁴	1	3	yes	—
135	C₂×C₈×C₁₃	C₂⁴	1	3	yes	—
136	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
137	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
138	C₁₃×C₄⋊C₄	—	2	6	no	—
139	C₁₃×C₄⋊C₄	—	2	6	no	—
140	C₁₃×C₄⋊C₄	—	2	6	no	—
141	C₁₃×C₄⋊C₄	—	2	6	no	—
142	C₁₃×C₄⋊C₄	C₂×D₄	1	3	yes	—
143	C₁₃×C₄⋊C₄	C₂×D₄	1	3	yes	—
144	C₁₃×C₄⋊C₄	C₂×D₄	1	6	yes	—
145	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
146	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
147	C₁₃×C₂²⋊C₄	—	2	2	no	—
148	C₁₃×C₂²⋊C₄	—	2	12	no	—
149	C₁₃×C₂²⋊C₄	—	2	6	no	—
150	C₁₃×C₂²⋊C₄	—	2	6	no	—
151	C₁₃×C₂²⋊C₄	—	2	12	no	—
152	C₄²×C₁₃	—	2	6	no	—
153	C₄²×C₁₃	—	2	6	no	—
154	C₄²×C₁₃	—	2	2	no	—
155	C₄²×C₁₃	C₂×D₄	1	3	yes	—
156	C₄²×C₁₃	C₂×D₄	1	3	yes	—
157	C₄²×C₁₃	C₂⁴	1	3	yes	—
158	C₄²×C₁₃	C₂⁴	1	3	yes	—
159	#3480	C₂×C₁₃	1	2	yes	complemented
160	#3396	C₂×C₁₃	1	3	yes	complemented
161	#3395	C₂×C₁₃	1	1	yes	characteristic, complemented
162	#3394	C₂×C₁₃	1	6	yes	complemented
163	#3393	C₂×C₁₃	1	3	yes	complemented
164	#3392	C₂×C₁₃	1	2	yes	complemented
165	#3391	C₂×C₁₃	1	1	yes	characteristic, complemented
166	#3147	C₂×C₁₃	1	3	yes	complemented
167	#3035	C₂×C₁₃	1	6	yes	complemented
168	C₂×C₈×Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
169	C₄×#135	C₂×C₁₃	1	3	yes	complemented
170	C₂³×C₁₃	—	2	6	no	—
171	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
172	Q₈×C₁₃	—	2	6	no	—
173	Q₈×C₁₃	—	2	6	no	—
174	Q₈×C₁₃	—	2	6	no	—
175	Q₈×C₁₃	#135	1	4	yes	complemented
176	D₄×C₁₃	—	2	6	no	—
177	D₄×C₁₃	—	2	6	no	—
178	D₄×C₁₃	—	4	12	no	—
179	D₄×C₁₃	—	4	12	no	—
180	D₄×C₁₃	—	8	6	no	—
181	C₂×C₄×C₁₃	—	2	6	no	—
182	C₂×C₄×C₁₃	—	2	2	no	—
183	C₂×C₄×C₁₃	—	2	2	no	—
184	C₂×C₄×C₁₃	—	2	6	no	—
185	C₂×C₄×C₁₃	—	4	3	no	—
186	C₂×C₄×C₁₃	—	4	12	no	—
187	C₂×C₄×C₁₃	—	4	12	no	—
188	C₂×C₄×C₁₃	—	8	6	no	—
189	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
190	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
191	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
192	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
193	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
194	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
195	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
196	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
197	C₈×C₁₃	—	2	3	no	—
198	C₈×C₁₃	—	2	3	no	—
199	C₈×C₁₃	C₂×#41	1	2	yes	—
200	C₈×C₁₃	C₂×#41	1	2	yes	—
201	C₂×#135	C₂²×C₁₃	1	3	yes	—
202	C₂×#135	C₂²×C₁₃	1	6	yes	—
203	#559	C₂²×C₁₃	1	6	yes	—
204	#557	C₂²×C₁₃	1	2	yes	—
205	#556	C₂²×C₁₃	1	6	yes	—
206	#553	—	2	6	no	—
207	#550	C₂²×C₁₃	1	2	yes	—
208	#548	—	2	2	no	—
209	#532	C₂²×C₁₃	1	6	yes	—
210	#529	—	2	6	no	—
211	C₄×#41	—	2	2	no	—
212	C₄×#41	C₂²×C₁₃	1	6	yes	—
213	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
214	#495	C₂²×C₁₃	1	6	yes	—
215	#495	C₂²×C₁₃	1	6	yes	—
216	#494	C₂²×C₁₃	1	3	yes	—
217	#493	C₂²×C₁₃	1	3	yes	—
218	#492	C₂²×C₁₃	1	6	yes	—
219	#464	C₂²×C₁₃	1	12	yes	—
220	#463	C₂²×C₁₃	1	12	yes	—
221	#462	C₂²×C₁₃	1	6	yes	—
222	#461	C₂²×C₁₃	1	6	yes	—
223	#460	C₂²×C₁₃	1	6	yes	—
224	#459	C₂²×C₁₃	1	6	yes	—
225	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
226	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
227	C₈×Q₈	C₂²×C₁₃	1	3	yes	—
228	C₈×Q₈	C₂²×C₁₃	1	3	yes	—
229	C₄×Q₁₆	C₂²×C₁₃	1	3	yes	—
230	C₄×Q₁₆	C₂²×C₁₃	1	3	yes	—
231	C₄×SD₁₆	C₂²×C₁₃	1	6	yes	—
232	C₄×SD₁₆	C₂²×C₁₃	1	6	yes	—
233	C₄×D₈	C₂²×C₁₃	1	3	yes	—
234	C₄×D₈	C₂²×C₁₃	1	3	yes	—
235	#427	C₂²×C₁₃	1	1	yes	characteristic
236	C₂×C₄⋊C₈	C₂²×C₁₃	1	3	yes	—
237	#416	C₂²×C₁₃	1	6	yes	—
238	C₂×C₄×C₈	C₂²×C₁₃	1	3	yes	—
239	C₂²×C₁₃	—	2	1	no	—
240	C₂²×C₁₃	—	2	1	no	—
241	C₂²×C₁₃	—	4	6	no	—
242	C₂²×C₁₃	—	4	6	no	—
243	C₂²×C₁₃	—	4	6	no	—
244	C₂²×C₁₃	#550	1	2	yes	—
245	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
246	C₄×C₁₃	—	2	3	no	—
247	C₄×C₁₃	—	2	3	no	—
248	C₄×C₁₃	—	2	3	no	—
249	C₄×C₁₃	—	4	2	no	—
250	C₄×C₁₃	—	4	6	no	—
251	C₄×C₁₃	—	4	2	no	—
252	C₄×C₁₃	#550	1	2	yes	—
253	C₄×C₁₃	C₂×#135	1	6	yes	—
254	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
255	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
256	C₂×#41	—	2	2	no	—
257	C₂×#41	C₂³×C₁₃	1	6	yes	—
258	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
259	#135	—	2	12	no	—
260	#135	—	4	12	no	—
261	C₂×Q₁₆	C₂³×C₁₃	1	3	yes	—
262	C₂×Q₁₆	C₂³×C₁₃	1	6	yes	—
263	C₂×SD₁₆	C₂³×C₁₃	1	6	yes	—
264	C₂×SD₁₆	C₂³×C₁₃	1	12	yes	—
265	C₂×D₈	C₂³×C₁₃	1	3	yes	—
266	C₂×D₈	C₂³×C₁₃	1	6	yes	—
267	C₂²×C₈	C₂³×C₁₃	1	3	yes	—
268	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
269	C₄⋊Q₈	C₂³×C₁₃	1	6	yes	—
270	#127	C₂³×C₁₃	1	6	yes	—
271	#126	—	2	12	no	—
272	#125	—	2	6	no	—
273	#124	—	2	6	no	—
274	#124	C₂³×C₁₃	1	12	yes	—
275	#123	—	2	12	no	—
276	C₂²⋊Q₈	—	2	6	no	—
277	#121	—	2	6	no	—
278	#121	—	2	6	no	—
279	#121	—	2	6	no	—
280	C₄×Q₈	—	2	2	no	—
281	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
282	C₄×Q₈	D₄×C₁₃	1	3	yes	—
283	C₄×Q₈	C₂³×C₁₃	1	6	yes	—
284	C₄×Q₈	C₂³×C₁₃	1	6	yes	—
285	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
286	C₄×Q₈	C₂³×C₁₃	1	3	yes	—
287	C₄×D₄	—	2	6	no	—
288	C₄×D₄	—	2	6	no	—
289	C₄×D₄	—	2	6	no	—
290	C₄×D₄	—	2	6	no	—
291	C₄×D₄	—	2	6	no	—
292	C₄×D₄	C₂³×C₁₃	1	6	yes	—
293	C₄×D₄	C₂³×C₁₃	1	6	yes	—
294	#117	—	2	6	no	—
295	#117	—	2	6	no	—
296	#117	C₂³×C₁₃	1	2	yes	—
297	C₂×C₄⋊C₄	D₄×C₁₃	1	3	yes	—
298	C₂×C₄²	—	2	6	no	—
299	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
300	#107	C₂³×C₁₃	1	1	yes	characteristic
301	#107	C₂³×C₁₃	1	1	yes	characteristic
302	#106	C₂³×C₁₃	1	2	yes	—
303	C₄⋊C₈	C₂³×C₁₃	1	3	yes	—
304	C₄⋊C₈	C₂³×C₁₃	1	3	yes	—
305	C₄⋊C₈	C₂³×C₁₃	1	6	yes	—
306	#103	C₂³×C₁₃	1	6	yes	—
307	#103	C₂³×C₁₃	1	6	yes	—
308	#102	C₂³×C₁₃	1	6	yes	—
309	#102	C₂³×C₁₃	1	6	yes	—
310	C₄×C₈	C₂³×C₁₃	1	3	yes	—
311	C₄×C₈	C₂³×C₁₃	1	3	yes	—
312	C₄×C₈	C₂³×C₁₃	1	3	yes	—
313	C₄×C₈	C₂³×C₁₃	1	3	yes	—
314	C₂×C₁₃	—	2	2	no	—
315	C₂×C₁₃	—	8	6	no	—
316	C₂×C₁₃	C₂×#550	1	1	yes	characteristic
317	C₂×C₁₃	C₂²×#135	1	1	yes	characteristic
318	C₂×C₁₃	#3584	1	1	yes	characteristic
319	#41	—	2	12	no	—
320	#41	—	2	12	no	—
321	#41	—	4	8	no	—
322	C₂×Q₈	—	2	4	no	—
323	C₂×Q₈	C₂×D₄×C₁₃	1	3	yes	—
324	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
325	C₂×Q₈	C₂⁴×C₁₃	1	6	yes	—
326	C₂×D₄	—	2	6	no	—
327	C₂×D₄	—	2	6	no	—
328	C₂×D₄	—	2	6	no	—
329	C₂×D₄	C₂⁴×C₁₃	1	6	yes	—
330	C₂²×C₄	—	2	6	no	—
331	C₂²×C₄	—	2	6	no	—
332	C₂²×C₄	—	2	6	no	—
333	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
334	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
335	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
336	Q₁₆	—	2	6	no	—
337	Q₁₆	—	4	6	no	—
338	SD₁₆	—	2	12	no	—
339	SD₁₆	—	4	12	no	—
340	D₈	—	2	6	no	—
341	D₈	—	4	6	no	—
342	C₂×C₈	—	2	6	no	—
343	C₂×C₈	C₁₃×#41	1	4	yes	complemented
344	C₂×C₈	C₂⁴×C₁₃	1	3	yes	—
345	C₂×C₈	C₂⁴×C₁₃	1	3	yes	—
346	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
347	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
348	C₄⋊C₄	—	2	6	no	—
349	C₄⋊C₄	—	2	6	no	—
350	C₄⋊C₄	—	2	6	no	—
351	C₄⋊C₄	—	2	6	no	—
352	C₄⋊C₄	C₂×D₄×C₁₃	1	3	yes	—
353	C₄⋊C₄	C₂×D₄×C₁₃	1	3	yes	—
354	C₄⋊C₄	C₂×D₄×C₁₃	1	6	yes	—
355	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
356	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
357	C₂²⋊C₄	—	2	2	no	—
358	C₂²⋊C₄	—	2	12	no	—
359	C₂²⋊C₄	—	2	6	no	—
360	C₂²⋊C₄	—	2	6	no	—
361	C₂²⋊C₄	—	2	12	no	—
362	C₄²	—	2	2	no	—
363	C₄²	—	2	6	no	—
364	C₄²	—	2	6	no	—
365	C₄²	C₂×D₄×C₁₃	1	3	yes	—
366	C₄²	C₂×D₄×C₁₃	1	3	yes	—
367	C₄²	C₂⁴×C₁₃	1	3	yes	—
368	C₄²	C₂⁴×C₁₃	1	3	yes	—
369	C₁₃	#61393	1	1	yes	characteristic, direct product factor, Sylow
370	C₂³	—	2	6	no	—
371	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
372	Q₈	—	2	6	no	—
373	Q₈	—	2	6	no	—
374	Q₈	—	2	6	no	—
375	Q₈	C₁₃×#135	1	4	yes	complemented
376	D₄	—	2	6	no	—
377	D₄	—	2	6	no	—
378	D₄	—	4	12	no	—
379	D₄	—	4	12	no	—
380	D₄	—	8	6	no	—
381	C₂×C₄	—	2	6	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	6	no	—
385	C₂×C₄	—	4	3	no	—
386	C₂×C₄	—	4	12	no	—
387	C₂×C₄	—	4	12	no	—
388	C₂×C₄	—	8	6	no	—
389	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
390	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
391	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
392	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
393	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
394	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
395	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
396	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
397	C₈	—	2	3	no	—
398	C₈	—	2	3	no	—
399	C₈	C₂×C₁₃×#41	1	2	yes	—
400	C₈	C₂×C₁₃×#41	1	2	yes	—
401	C₂²	—	2	1	no	—
402	C₂²	—	2	1	no	—
403	C₂²	—	4	6	no	—
404	C₂²	—	4	6	no	—
405	C₂²	—	4	6	no	—
406	C₂²	C₁₃×#550	1	2	yes	—
407	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
408	C₄	—	2	3	no	—
409	C₄	—	2	3	no	—
410	C₄	—	2	3	no	—
411	C₄	—	4	2	no	—
412	C₄	—	4	2	no	—
413	C₄	—	4	6	no	—
414	C₄	C₁₃×#550	1	2	yes	—
415	C₄	C₂×C₁₃×#135	1	6	yes	—
416	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
417	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
418	C₂	—	2	2	no	—
419	C₂	—	8	6	no	—
420	C₂	C₂×C₁₃×#550	1	1	yes	characteristic
421	C₂	C₂²×C₁₃×#135	1	1	yes	characteristic
422	C₂	C₁₃×#3584	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
socle	C₂²×C₁₃	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂×C₄×Q₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3480	C₂	semidirect
2. C₁₃×#3396	C₂	semidirect
3. C₁₃×#3395	C₂	semidirect
4. C₁₃×#3394	C₂	semidirect
5. C₁₃×#3393	C₂	semidirect
6. C₁₃×#3392	C₂	semidirect
7. C₁₃×#3391	C₂	semidirect
8. C₁₃×#3147	C₂	semidirect
9. C₁₃×#3035	C₂	semidirect
10. C₂×C₈×Q₈×C₁₃	C₂	semidirect
11. C₄×C₁₃×#135	C₂	semidirect
108. #61393	C₁₃	direct (N × H)
133. C₂×C₈×C₁₃	#41	semidirect
159. #3480	C₂×C₁₃	semidirect
160. #3396	C₂×C₁₃	semidirect
161. #3395	C₂×C₁₃	semidirect
162. #3394	C₂×C₁₃	semidirect
163. #3393	C₂×C₁₃	semidirect
164. #3392	C₂×C₁₃	semidirect
165. #3391	C₂×C₁₃	semidirect
166. #3147	C₂×C₁₃	semidirect
167. #3035	C₂×C₁₃	semidirect
168. C₂×C₈×Q₈	C₂×C₁₃	semidirect
169. C₄×#135	C₂×C₁₃	semidirect
175. Q₈×C₁₃	#135	semidirect
343. C₂×C₈	C₁₃×#41	semidirect
369. C₁₃	#61393	direct (N × H)
375. Q₈	C₁₃×#135	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#3480	2
C₁₃×#3396	2
C₁₃×#3395	2
C₁₃×#3394	2
C₁₃×#3393	2
C₁₃×#3392	2
C₁₃×#3391	2
C₁₃×#3147	2
C₁₃×#3035	2
C₂×C₈×Q₈×C₁₃	2
C₄×C₁₃×#135	2
#61393	13

Subgroups — C13×#61393 #15747732

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61393 #15747732