Subgroups — C₂×C₁₃×#3027 #15746735

Order 3328.

5110 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#585	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#535	C₂	1	3	yes	maximal, complemented
3	C₁₃×#3027	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×B(4,𝔽₂)	C₂	1	8	yes	maximal, complemented
5	C₂×C₁₃×#410	C₂	1	3	yes	maximal, complemented
6	C₁₃×#585	—	2	12	no	—
7	C₁₃×#585	C₂²	1	8	yes	complemented
8	C₂×C₁₃×2₋¹⁺⁴	—	2	3	no	—
9	C₂×C₁₃×H(5,𝔽₂)	—	2	3	no	—
10	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	4	yes	—
11	C₂²×C₁₃×#41	—	2	6	no	—
12	C₂²×C₁₃×#41	C₂²	1	3	yes	—
13	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
14	C₁₃×#535	—	2	12	no	—
15	C₁₃×#535	C₂²	1	24	yes	complemented
16	C₂×C₁₃×#127	—	2	3	no	—
17	C₂×C₁₃×#124	—	2	3	no	—
18	C₂×C₁₃×#121	—	2	6	no	—
19	C₂×C₁₃×#120	C₂²	1	12	yes	complemented
20	C₂×C₁₃×#117	C₂²	1	3	yes	complemented
21	C₁₃×B(4,𝔽₂)	C₂²	1	64	yes	complemented
22	C₁₃×#410	C₂²	1	24	yes	complemented
23	C₂×C₁₃×#99	C₂²	1	12	yes	complemented
24	C₂⁵×C₁₃	C₂³	1	2	yes	—
25	C₁₃×2₋¹⁺⁴	—	2	24	no	—
26	C₁₃×2₋¹⁺⁴	—	2	24	no	—
27	C₁₃×H(5,𝔽₂)	—	2	24	no	—
28	C₁₃×H(5,𝔽₂)	—	2	24	no	—
29	C₁₃×H(5,𝔽₂)	—	2	24	no	—
30	C₁₃×H(5,𝔽₂)	C₂³	1	16	yes	—
31	C₂×C₁₃×#41	—	2	4	no	—
32	C₂×C₁₃×#41	—	2	12	no	—
33	C₂×C₁₃×#41	—	2	48	no	—
34	C₂×C₁₃×#41	—	2	6	no	—
35	C₂×C₁₃×#41	—	2	12	no	—
36	C₂×C₁₃×#41	—	2	6	no	—
37	C₂×C₁₃×#41	—	2	12	no	—
38	C₂×C₁₃×#41	—	2	48	no	—
39	C₂×C₁₃×#41	D₄	1	12	yes	complemented
40	C₂×C₁₃×#41	C₂³	1	12	yes	—
41	C₂²×Q₈×C₁₃	—	2	6	no	—
42	C₂²×Q₈×C₁₃	D₄	1	3	yes	complemented
43	C₂²×D₄×C₁₃	—	2	6	no	—
44	C₂²×D₄×C₁₃	—	2	12	no	—
45	C₂²×D₄×C₁₃	—	2	12	no	—
46	C₂²×D₄×C₁₃	—	2	3	no	—
47	C₂²×D₄×C₁₃	—	2	3	no	—
48	C₂²×D₄×C₁₃	—	2	6	no	—
49	C₂²×D₄×C₁₃	D₄	1	3	yes	complemented
50	C₂²×D₄×C₁₃	C₂³	1	6	yes	—
51	C₂²×D₄×C₁₃	C₂³	1	4	yes	complemented
52	C₂³×C₄×C₁₃	—	2	4	no	—
53	C₂³×C₄×C₁₃	D₄	1	6	yes	complemented
54	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
55	C₁₃×#127	—	2	24	no	—
56	C₁₃×#124	—	2	24	no	—
57	C₁₃×#121	—	2	48	no	—
58	C₁₃×#120	—	2	24	no	—
59	C₁₃×#120	C₂³	1	48	yes	complemented
60	C₁₃×#117	—	2	6	no	—
61	C₁₃×#117	C₂³	1	12	yes	complemented
62	C₂×C₁₃×C₄⋊C₄	—	2	3	no	—
63	C₂×C₁₃×C₂²⋊C₄	—	2	12	no	—
64	C₂×C₁₃×C₂²⋊C₄	C₂³	1	6	yes	—
65	C₂×C₄²×C₁₃	—	2	3	no	—
66	C₁₃×#99	C₂³	1	48	yes	complemented
67	C₂×#3027	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
68	C₂⁴×C₁₃	—	2	4	no	—
69	C₂⁴×C₁₃	—	2	6	no	—
70	C₂⁴×C₁₃	—	2	6	no	—
71	C₂⁴×C₁₃	—	8	4	no	—
72	C₂⁴×C₁₃	C₂×D₄	1	6	yes	—
73	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
74	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
75	C₁₃×#41	—	2	32	no	—
76	C₁₃×#41	—	2	48	no	—
77	C₁₃×#41	—	2	96	no	—
78	C₁₃×#41	—	2	24	no	—
79	C₁₃×#41	—	2	24	no	—
80	C₁₃×#41	—	2	24	no	—
81	C₁₃×#41	—	2	48	no	—
82	C₁₃×#41	—	2	24	no	—
83	C₂×Q₈×C₁₃	—	2	4	no	—
84	C₂×Q₈×C₁₃	—	2	48	no	—
85	C₂×Q₈×C₁₃	—	2	6	no	—
86	C₂×Q₈×C₁₃	—	2	6	no	—
87	C₂×Q₈×C₁₃	C₂×D₄	1	12	yes	complemented
88	C₂×D₄×C₁₃	—	2	12	no	—
89	C₂×D₄×C₁₃	—	2	48	no	—
90	C₂×D₄×C₁₃	—	2	48	no	—
91	C₂×D₄×C₁₃	—	2	12	no	—
92	C₂×D₄×C₁₃	—	2	48	no	—
93	C₂×D₄×C₁₃	—	2	12	no	—
94	C₂×D₄×C₁₃	—	2	48	no	—
95	C₂×D₄×C₁₃	—	2	6	no	—
96	C₂×D₄×C₁₃	—	2	6	no	—
97	C₂×D₄×C₁₃	—	2	12	no	—
98	C₂×D₄×C₁₃	—	2	12	no	—
99	C₂×D₄×C₁₃	—	4	6	no	—
100	C₂×D₄×C₁₃	—	4	6	no	—
101	C₂×D₄×C₁₃	—	4	1	no	—
102	C₂×D₄×C₁₃	—	4	3	no	—
103	C₂×D₄×C₁₃	—	8	24	no	—
104	C₂×D₄×C₁₃	C₂×D₄	1	12	yes	—
105	C₂×D₄×C₁₃	C₂×D₄	1	12	yes	complemented
106	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
107	C₂²×C₄×C₁₃	—	2	12	no	—
108	C₂²×C₄×C₁₃	—	2	32	no	—
109	C₂²×C₄×C₁₃	—	2	6	no	—
110	C₂²×C₄×C₁₃	—	2	6	no	—
111	C₂²×C₄×C₁₃	—	2	12	no	—
112	C₂²×C₄×C₁₃	—	2	6	no	—
113	C₂²×C₄×C₁₃	C₂×D₄	1	6	yes	—
114	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
115	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
116	C₂²×C₄×C₁₃	C₂×D₄	1	6	yes	—
117	C₂²×C₄×C₁₃	C₂×D₄	1	24	yes	complemented
118	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
119	C₁₃×C₄⋊C₄	—	2	12	no	—
120	C₁₃×C₂²⋊C₄	—	2	6	no	—
121	C₁₃×C₂²⋊C₄	—	2	48	no	—
122	C₁₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
123	C₄²×C₁₃	—	2	12	no	—
124	C₂×#585	C₂×C₁₃	1	1	yes	characteristic, complemented
125	C₂×#535	C₂×C₁₃	1	3	yes	complemented
126	#3027	C₂×C₁₃	1	16	yes	direct product factor
127	C₂×B(4,𝔽₂)	C₂×C₁₃	1	8	yes	complemented
128	C₂×#410	C₂×C₁₃	1	3	yes	complemented
129	C₂³×C₁₃	—	2	16	no	—
130	C₂³×C₁₃	—	2	6	no	—
131	C₂³×C₁₃	—	2	6	no	—
132	C₂³×C₁₃	—	2	12	no	—
133	C₂³×C₁₃	—	4	2	no	—
134	C₂³×C₁₃	—	4	12	no	—
135	C₂³×C₁₃	—	4	24	no	—
136	C₂³×C₁₃	—	4	6	no	—
137	C₂³×C₁₃	—	4	2	no	—
138	C₂³×C₁₃	—	8	4	no	—
139	C₂³×C₁₃	—	8	8	no	—
140	C₂³×C₁₃	—	8	12	no	—
141	C₂³×C₁₃	C₂²×D₄	1	3	yes	—
142	C₂³×C₁₃	C₂²×D₄	1	12	yes	—
143	C₂³×C₁₃	C₂²×D₄	1	3	yes	—
144	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
145	Q₈×C₁₃	—	2	16	no	—
146	Q₈×C₁₃	—	2	24	no	—
147	D₄×C₁₃	—	2	48	no	—
148	D₄×C₁₃	—	2	24	no	—
149	D₄×C₁₃	—	2	24	no	—
150	D₄×C₁₃	—	2	24	no	—
151	D₄×C₁₃	—	4	4	no	—
152	D₄×C₁₃	—	4	12	no	—
153	D₄×C₁₃	—	8	48	no	—
154	C₂×C₄×C₁₃	—	2	48	no	—
155	C₂×C₄×C₁₃	—	2	6	no	—
156	C₂×C₄×C₁₃	—	2	6	no	—
157	C₂×C₄×C₁₃	—	2	24	no	—
158	C₂×C₄×C₁₃	—	2	24	no	—
159	C₂×C₄×C₁₃	—	2	12	no	—
160	C₂×C₄×C₁₃	—	4	12	no	—
161	C₂×C₄×C₁₃	#120	1	6	yes	—
162	C₂×C₄×C₁₃	#120	1	6	yes	—
163	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
164	C₂×C₄×C₁₃	#120	1	3	yes	—
165	C₂×C₄×C₁₃	C₂²×D₄	1	12	yes	—
166	C₂×C₄×C₁₃	C₂²×D₄	1	6	yes	—
167	C₂×C₄×C₁₃	C₂²×D₄	1	6	yes	—
168	#585	—	2	12	no	—
169	#585	C₂²×C₁₃	1	8	yes	complemented
170	C₂×2₋¹⁺⁴	—	2	3	no	—
171	C₂×H(5,𝔽₂)	—	2	3	no	—
172	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	4	yes	—
173	C₂²×#41	—	2	6	no	—
174	C₂²×#41	C₂²×C₁₃	1	3	yes	—
175	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
176	#535	—	2	12	no	—
177	#535	C₂²×C₁₃	1	24	yes	complemented
178	C₂×#127	—	2	3	no	—
179	C₂×#124	—	2	3	no	—
180	C₂×#121	—	2	6	no	—
181	C₂×#120	C₂²×C₁₃	1	12	yes	complemented
182	C₂×#117	C₂²×C₁₃	1	3	yes	complemented
183	B(4,𝔽₂)	C₂²×C₁₃	1	64	yes	complemented
184	#410	C₂²×C₁₃	1	24	yes	complemented
185	C₂×#99	C₂²×C₁₃	1	12	yes	complemented
186	C₂²×C₁₃	—	2	6	no	—
187	C₂²×C₁₃	—	2	12	no	—
188	C₂²×C₁₃	—	4	3	no	—
189	C₂²×C₁₃	—	4	1	no	—
190	C₂²×C₁₃	—	4	12	no	—
191	C₂²×C₁₃	—	4	24	no	—
192	C₂²×C₁₃	—	4	12	no	—
193	C₂²×C₁₃	—	4	4	no	—
194	C₂²×C₁₃	—	8	6	no	—
195	C₂²×C₁₃	—	8	12	no	—
196	C₂²×C₁₃	—	8	16	no	—
197	C₂²×C₁₃	—	8	4	no	—
198	C₂²×C₁₃	C₂×#120	1	3	yes	—
199	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
200	C₂²×C₁₃	C₂³×D₄	1	3	yes	—
201	C₄×C₁₃	—	2	12	no	—
202	C₄×C₁₃	—	4	12	no	—
203	C₄×C₁₃	C₂×#120	1	2	yes	—
204	C₄×C₁₃	C₂×#120	1	6	yes	—
205	C₂⁵	C₂³×C₁₃	1	2	yes	—
206	2₋¹⁺⁴	—	2	24	no	—
207	2₋¹⁺⁴	—	2	24	no	—
208	H(5,𝔽₂)	—	2	24	no	—
209	H(5,𝔽₂)	—	2	24	no	—
210	H(5,𝔽₂)	—	2	24	no	—
211	H(5,𝔽₂)	C₂³×C₁₃	1	16	yes	—
212	C₂×#41	—	2	4	no	—
213	C₂×#41	—	2	12	no	—
214	C₂×#41	—	2	48	no	—
215	C₂×#41	—	2	6	no	—
216	C₂×#41	—	2	12	no	—
217	C₂×#41	—	2	6	no	—
218	C₂×#41	—	2	12	no	—
219	C₂×#41	—	2	48	no	—
220	C₂×#41	D₄×C₁₃	1	12	yes	complemented
221	C₂×#41	C₂³×C₁₃	1	12	yes	—
222	C₂²×Q₈	—	2	6	no	—
223	C₂²×Q₈	D₄×C₁₃	1	3	yes	complemented
224	C₂²×D₄	—	2	6	no	—
225	C₂²×D₄	—	2	12	no	—
226	C₂²×D₄	—	2	12	no	—
227	C₂²×D₄	—	2	3	no	—
228	C₂²×D₄	—	2	3	no	—
229	C₂²×D₄	—	2	6	no	—
230	C₂²×D₄	D₄×C₁₃	1	3	yes	complemented
231	C₂²×D₄	C₂³×C₁₃	1	6	yes	—
232	C₂²×D₄	C₂³×C₁₃	1	4	yes	complemented
233	C₂³×C₄	—	2	4	no	—
234	C₂³×C₄	D₄×C₁₃	1	6	yes	complemented
235	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
236	#127	—	2	24	no	—
237	#124	—	2	24	no	—
238	#121	—	2	48	no	—
239	#120	—	2	24	no	—
240	#120	C₂³×C₁₃	1	48	yes	complemented
241	#117	—	2	6	no	—
242	#117	C₂³×C₁₃	1	12	yes	complemented
243	C₂×C₄⋊C₄	—	2	3	no	—
244	C₂×C₂²⋊C₄	—	2	12	no	—
245	C₂×C₂²⋊C₄	C₂³×C₁₃	1	6	yes	—
246	C₂×C₄²	—	2	3	no	—
247	#99	C₂³×C₁₃	1	48	yes	complemented
248	C₂×C₁₃	—	2	3	no	—
249	C₂×C₁₃	—	2	3	no	—
250	C₂×C₁₃	—	4	12	no	—
251	C₂×C₁₃	—	8	4	no	—
252	C₂×C₁₃	#3027	1	2	yes	direct product factor
253	C₂×C₁₃	C₂²×#120	1	1	yes	characteristic
254	C₂⁴	—	2	4	no	—
255	C₂⁴	—	2	6	no	—
256	C₂⁴	—	2	6	no	—
257	C₂⁴	—	8	4	no	—
258	C₂⁴	C₂×D₄×C₁₃	1	6	yes	—
259	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
260	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
261	#41	—	2	32	no	—
262	#41	—	2	48	no	—
263	#41	—	2	96	no	—
264	#41	—	2	24	no	—
265	#41	—	2	24	no	—
266	#41	—	2	24	no	—
267	#41	—	2	48	no	—
268	#41	—	2	24	no	—
269	C₂×Q₈	—	2	4	no	—
270	C₂×Q₈	—	2	48	no	—
271	C₂×Q₈	—	2	6	no	—
272	C₂×Q₈	—	2	6	no	—
273	C₂×Q₈	C₂×D₄×C₁₃	1	12	yes	complemented
274	C₂×D₄	—	2	12	no	—
275	C₂×D₄	—	2	48	no	—
276	C₂×D₄	—	2	48	no	—
277	C₂×D₄	—	2	12	no	—
278	C₂×D₄	—	2	48	no	—
279	C₂×D₄	—	2	12	no	—
280	C₂×D₄	—	2	48	no	—
281	C₂×D₄	—	2	6	no	—
282	C₂×D₄	—	2	6	no	—
283	C₂×D₄	—	2	12	no	—
284	C₂×D₄	—	2	12	no	—
285	C₂×D₄	—	4	1	no	—
286	C₂×D₄	—	4	3	no	—
287	C₂×D₄	—	4	6	no	—
288	C₂×D₄	—	4	6	no	—
289	C₂×D₄	—	8	24	no	—
290	C₂×D₄	C₂×D₄×C₁₃	1	12	yes	—
291	C₂×D₄	C₂×D₄×C₁₃	1	12	yes	complemented
292	C₂×D₄	C₂⁴×C₁₃	1	12	yes	—
293	C₂²×C₄	—	2	12	no	—
294	C₂²×C₄	—	2	32	no	—
295	C₂²×C₄	—	2	6	no	—
296	C₂²×C₄	—	2	6	no	—
297	C₂²×C₄	—	2	12	no	—
298	C₂²×C₄	—	2	6	no	—
299	C₂²×C₄	C₂×D₄×C₁₃	1	6	yes	—
300	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
301	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
302	C₂²×C₄	C₂×D₄×C₁₃	1	6	yes	—
303	C₂²×C₄	C₂×D₄×C₁₃	1	24	yes	complemented
304	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
305	C₄⋊C₄	—	2	12	no	—
306	C₂²⋊C₄	—	2	6	no	—
307	C₂²⋊C₄	—	2	48	no	—
308	C₂²⋊C₄	C₂⁴×C₁₃	1	12	yes	—
309	C₄²	—	2	12	no	—
310	C₁₃	C₂×#3027	1	1	yes	characteristic, direct product factor, Sylow
311	C₂³	—	2	16	no	—
312	C₂³	—	2	6	no	—
313	C₂³	—	2	6	no	—
314	C₂³	—	2	12	no	—
315	C₂³	—	4	2	no	—
316	C₂³	—	4	12	no	—
317	C₂³	—	4	24	no	—
318	C₂³	—	4	6	no	—
319	C₂³	—	4	2	no	—
320	C₂³	—	8	4	no	—
321	C₂³	—	8	12	no	—
322	C₂³	—	8	8	no	—
323	C₂³	C₂²×D₄×C₁₃	1	3	yes	—
324	C₂³	C₂²×D₄×C₁₃	1	12	yes	—
325	C₂³	C₂²×D₄×C₁₃	1	3	yes	—
326	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
327	Q₈	—	2	16	no	—
328	Q₈	—	2	24	no	—
329	D₄	—	2	48	no	—
330	D₄	—	2	24	no	—
331	D₄	—	2	24	no	—
332	D₄	—	2	24	no	—
333	D₄	—	4	4	no	—
334	D₄	—	4	12	no	—
335	D₄	—	8	48	no	—
336	C₂×C₄	—	2	48	no	—
337	C₂×C₄	—	2	6	no	—
338	C₂×C₄	—	2	6	no	—
339	C₂×C₄	—	2	24	no	—
340	C₂×C₄	—	2	24	no	—
341	C₂×C₄	—	2	12	no	—
342	C₂×C₄	—	4	12	no	—
343	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
344	C₂×C₄	C₁₃×#120	1	3	yes	—
345	C₂×C₄	C₁₃×#120	1	6	yes	—
346	C₂×C₄	C₁₃×#120	1	6	yes	—
347	C₂×C₄	C₂²×D₄×C₁₃	1	12	yes	—
348	C₂×C₄	C₂²×D₄×C₁₃	1	6	yes	—
349	C₂×C₄	C₂²×D₄×C₁₃	1	6	yes	—
350	C₂²	—	2	6	no	—
351	C₂²	—	2	12	no	—
352	C₂²	—	4	3	no	—
353	C₂²	—	4	1	no	—
354	C₂²	—	4	12	no	—
355	C₂²	—	4	24	no	—
356	C₂²	—	4	12	no	—
357	C₂²	—	4	4	no	—
358	C₂²	—	8	6	no	—
359	C₂²	—	8	12	no	—
360	C₂²	—	8	16	no	—
361	C₂²	—	8	4	no	—
362	C₂²	C₂×C₁₃×#120	1	3	yes	—
363	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
364	C₂²	C₂³×D₄×C₁₃	1	3	yes	—
365	C₄	—	2	12	no	—
366	C₄	—	4	12	no	—
367	C₄	C₂×C₁₃×#120	1	2	yes	—
368	C₄	C₂×C₁₃×#120	1	6	yes	—
369	C₂	—	2	3	no	—
370	C₂	—	2	3	no	—
371	C₂	—	4	12	no	—
372	C₂	—	8	4	no	—
373	C₂	C₁₃×#3027	1	2	yes	direct product factor
374	C₂	C₂²×C₁₃×#120	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#120
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
LCS	G ▷ C₂³ ▷ 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×#585	C₂	semidirect
2. C₂×C₁₃×#535	C₂	semidirect
3. C₁₃×#3027	C₂	direct (N × H)
4. C₂×C₁₃×B(4,𝔽₂)	C₂	semidirect
5. C₂×C₁₃×#410	C₂	semidirect
7. C₁₃×#585	C₂²	semidirect
13. C₂³×D₄×C₁₃	C₂²	semidirect
15. C₁₃×#535	C₂²	semidirect
19. C₂×C₁₃×#120	C₂²	semidirect
20. C₂×C₁₃×#117	C₂²	semidirect
21. C₁₃×B(4,𝔽₂)	C₂²	semidirect
22. C₁₃×#410	C₂²	semidirect
23. C₂×C₁₃×#99	C₂²	semidirect
39. C₂×C₁₃×#41	D₄	semidirect
42. C₂²×Q₈×C₁₃	D₄	semidirect
49. C₂²×D₄×C₁₃	D₄	semidirect
51. C₂²×D₄×C₁₃	C₂³	semidirect
53. C₂³×C₄×C₁₃	D₄	semidirect
59. C₁₃×#120	C₂³	semidirect
61. C₁₃×#117	C₂³	semidirect
66. C₁₃×#99	C₂³	semidirect
67. C₂×#3027	C₁₃	direct (N × H)
87. C₂×Q₈×C₁₃	C₂×D₄	semidirect
105. C₂×D₄×C₁₃	C₂×D₄	semidirect
117. C₂²×C₄×C₁₃	C₂×D₄	semidirect
124. C₂×#585	C₂×C₁₃	semidirect
125. C₂×#535	C₂×C₁₃	semidirect
126. #3027	C₂×C₁₃	direct (N × H)
127. C₂×B(4,𝔽₂)	C₂×C₁₃	semidirect
128. C₂×#410	C₂×C₁₃	semidirect
169. #585	C₂²×C₁₃	semidirect
175. C₂³×D₄	C₂²×C₁₃	semidirect
177. #535	C₂²×C₁₃	semidirect
181. C₂×#120	C₂²×C₁₃	semidirect
182. C₂×#117	C₂²×C₁₃	semidirect
183. B(4,𝔽₂)	C₂²×C₁₃	semidirect
184. #410	C₂²×C₁₃	semidirect
185. C₂×#99	C₂²×C₁₃	semidirect
220. C₂×#41	D₄×C₁₃	semidirect
223. C₂²×Q₈	D₄×C₁₃	semidirect
230. C₂²×D₄	D₄×C₁₃	semidirect
232. C₂²×D₄	C₂³×C₁₃	semidirect
234. C₂³×C₄	D₄×C₁₃	semidirect
240. #120	C₂³×C₁₃	semidirect
242. #117	C₂³×C₁₃	semidirect
247. #99	C₂³×C₁₃	semidirect
252. C₂×C₁₃	#3027	direct (N × H)
273. C₂×Q₈	C₂×D₄×C₁₃	semidirect
291. C₂×D₄	C₂×D₄×C₁₃	semidirect
303. C₂²×C₄	C₂×D₄×C₁₃	semidirect
310. C₁₃	C₂×#3027	direct (N × H)
373. C₂	C₁₃×#3027	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×#585	2
C₂×C₁₃×#535	2
C₁₃×#3027	2
C₂×C₁₃×B(4,𝔽₂)	2
C₂×C₁₃×#410	2
C₂×#3027	13

Subgroups — C2×C13×#3027 #15746735

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3027 #15746735