Subgroups — C₂×C₁₃×#3291 #15747441

Order 3328.

2682 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#577	C₂	1	4	yes	maximal, complemented
2	C₁₃×#3291	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₁₃×#492	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₃×#471	C₂	1	4	yes	maximal, complemented
5	C₂×C₁₃×#456	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#453	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#443	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	2	yes	—
9	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	2	yes	complemented
10	C₁₃×#577	—	2	16	no	—
11	C₁₃×#577	C₂²	1	32	yes	complemented
12	C₂×C₁₃×#137	—	2	4	no	—
13	C₂×C₁₃×#137	C₂²	1	4	yes	complemented
14	C₂×C₁₃×AGL(1,ℤ/8)	—	2	4	no	—
15	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	4	yes	—
16	C₂×C₁₃×#135	—	2	4	no	—
17	C₂×C₁₃×#135	C₂²	1	2	yes	—
18	C₂²×C₁₃×SD₁₆	—	2	4	no	—
19	C₂²×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
20	C₂×C₁₃×#131	C₂²	1	4	yes	complemented
21	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
23	C₁₃×#492	C₂²	1	8	yes	complemented
24	C₁₃×#471	C₂²	1	32	yes	complemented
25	C₁₃×#456	C₂²	1	16	yes	complemented
26	C₁₃×#453	C₂²	1	16	yes	complemented
27	C₁₃×#443	C₂²	1	16	yes	complemented
28	C₂×C₁₃×#108	C₂²	1	2	yes	complemented
29	C₂×C₁₃×#104	C₂²	1	4	yes	complemented
30	C₂×C₁₃×#101	C₂²	1	2	yes	complemented
31	C₂×C₁₃×#100	C₂²	1	2	yes	complemented
32	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
33	C₁₃×2₋¹⁺⁴	—	2	8	no	—
34	C₁₃×2₋¹⁺⁴	—	4	2	no	—
35	C₁₃×2₋¹⁺⁴	C₂³	1	8	yes	—
36	C₁₃×H(5,𝔽₂)	—	2	8	no	—
37	C₁₃×H(5,𝔽₂)	—	4	2	no	—
38	C₁₃×H(5,𝔽₂)	C₂³	1	8	yes	complemented
39	C₂×C₁₃×#41	—	2	4	no	—
40	C₂×C₁₃×#41	—	2	4	no	—
41	C₂×C₁₃×#41	—	4	2	no	—
42	C₂×C₁₃×#41	C₂³	1	4	yes	—
43	C₂²×Q₈×C₁₃	—	2	4	no	—
44	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
45	C₂²×D₄×C₁₃	—	2	4	no	—
46	C₂²×D₄×C₁₃	—	4	1	no	—
47	C₂²×D₄×C₁₃	—	4	2	no	—
48	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
49	C₁₃×#137	—	2	8	no	—
50	C₁₃×#137	—	2	32	no	—
51	C₁₃×#137	C₂³	1	16	yes	complemented
52	C₁₃×AGL(1,ℤ/8)	—	2	8	no	—
53	C₁₃×AGL(1,ℤ/8)	—	2	32	no	—
54	C₁₃×AGL(1,ℤ/8)	C₂³	1	16	yes	—
55	C₁₃×#135	—	2	32	no	—
56	C₁₃×#135	D₄	1	8	yes	complemented
57	C₁₃×#135	C₂³	1	8	yes	—
58	C₂×C₁₃×Q₁₆	—	2	4	no	—
59	C₂×C₁₃×Q₁₆	D₄	1	2	yes	complemented
60	C₂×C₁₃×SD₁₆	—	2	4	no	—
61	C₂×C₁₃×SD₁₆	—	2	4	no	—
62	C₂×C₁₃×SD₁₆	—	2	32	no	—
63	C₂×C₁₃×SD₁₆	—	2	4	no	—
64	C₂×C₁₃×SD₁₆	—	2	4	no	—
65	C₂×C₁₃×SD₁₆	—	2	8	no	—
66	C₂×C₁₃×SD₁₆	D₄	1	4	yes	complemented
67	C₂×C₁₃×SD₁₆	C₂³	1	16	yes	complemented
68	C₂×C₁₃×D₈	—	2	4	no	—
69	C₂×C₁₃×D₈	D₄	1	2	yes	complemented
70	C₁₃×#131	—	2	8	no	—
71	C₁₃×#131	C₂³	1	16	yes	complemented
72	C₂×C₁₃×M₁₆	—	2	4	no	—
73	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
74	C₂²×C₈×C₁₃	—	2	4	no	—
75	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
76	C₁₃×C₄⋊Q₈	—	4	1	no	—
77	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	complemented
78	C₁₃×#127	—	4	1	no	—
79	C₁₃×#127	C₂³	1	4	yes	—
80	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
81	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
82	C₁₃×#108	C₂³	1	8	yes	complemented
83	C₁₃×#104	C₂³	1	16	yes	complemented
84	C₁₃×#101	C₂³	1	8	yes	complemented
85	C₁₃×#100	C₂³	1	8	yes	complemented
86	C₄×C₈×C₁₃	C₂³	1	4	yes	complemented
87	C₂×#3291	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
88	C₂⁴×C₁₃	—	2	2	no	—
89	C₂⁴×C₁₃	—	4	2	no	—
90	C₁₃×#41	—	2	4	no	—
91	C₁₃×#41	—	2	4	no	—
92	C₁₃×#41	—	2	16	no	—
93	C₁₃×#41	—	2	16	no	—
94	C₁₃×#41	—	4	8	no	—
95	C₁₃×#41	—	4	8	no	—
96	C₁₃×#41	—	4	8	no	—
97	C₁₃×#41	—	4	8	no	—
98	C₁₃×#41	C₂×D₄	1	8	yes	—
99	C₁₃×#41	C₂⁴	1	8	yes	—
100	C₂×Q₈×C₁₃	—	2	2	no	—
101	C₂×Q₈×C₁₃	—	2	16	no	—
102	C₂×Q₈×C₁₃	—	2	4	no	—
103	C₂×Q₈×C₁₃	—	2	4	no	—
104	C₂×Q₈×C₁₃	—	4	2	no	—
105	C₂×Q₈×C₁₃	—	4	8	no	—
106	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
107	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
108	C₂×D₄×C₁₃	—	2	4	no	—
109	C₂×D₄×C₁₃	—	2	16	no	—
110	C₂×D₄×C₁₃	—	2	4	no	—
111	C₂×D₄×C₁₃	—	2	4	no	—
112	C₂×D₄×C₁₃	—	2	2	no	—
113	C₂×D₄×C₁₃	—	4	8	no	—
114	C₂×D₄×C₁₃	—	4	4	no	—
115	C₂×D₄×C₁₃	—	4	4	no	—
116	C₂×D₄×C₁₃	—	4	8	no	—
117	C₂×D₄×C₁₃	—	4	8	no	—
118	C₂×D₄×C₁₃	—	4	2	no	—
119	C₂×D₄×C₁₃	—	8	4	no	—
120	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
121	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
122	C₂²×C₄×C₁₃	—	2	1	no	—
123	C₂²×C₄×C₁₃	—	2	4	no	—
124	C₂²×C₄×C₁₃	—	2	2	no	—
125	C₂²×C₄×C₁₃	—	4	2	no	—
126	C₂²×C₄×C₁₃	—	4	4	no	—
127	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
128	C₁₃×Q₁₆	—	2	16	no	—
129	C₁₃×Q₁₆	C₂×D₄	1	8	yes	complemented
130	C₁₃×SD₁₆	—	2	16	no	—
131	C₁₃×SD₁₆	—	2	16	no	—
132	C₁₃×SD₁₆	—	2	16	no	—
133	C₁₃×SD₁₆	—	2	16	no	—
134	C₁₃×SD₁₆	C₂×D₄	1	16	yes	complemented
135	C₁₃×D₈	—	2	16	no	—
136	C₁₃×D₈	C₂×D₄	1	8	yes	complemented
137	C₁₃×M₁₆	—	2	4	no	—
138	C₁₃×M₁₆	—	2	16	no	—
139	C₁₃×M₁₆	C₂⁴	1	8	yes	—
140	C₂×C₈×C₁₃	—	2	4	no	—
141	C₂×C₈×C₁₃	—	2	16	no	—
142	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
143	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
144	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
145	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
146	C₁₃×C₄⋊C₄	—	4	4	no	—
147	C₄²×C₁₃	—	2	1	no	—
148	C₄²×C₁₃	C₂⁴	1	2	yes	—
149	C₂×#577	C₂×C₁₃	1	4	yes	complemented
150	#3291	C₂×C₁₃	1	16	yes	direct product factor
151	C₂×#492	C₂×C₁₃	1	1	yes	characteristic, complemented
152	C₂×#471	C₂×C₁₃	1	4	yes	complemented
153	C₂×#456	C₂×C₁₃	1	2	yes	complemented
154	C₂×#453	C₂×C₁₃	1	2	yes	complemented
155	C₂×#443	C₂×C₁₃	1	2	yes	complemented
156	C₂³×C₁₃	—	2	4	no	—
157	C₂³×C₁₃	—	2	4	no	—
158	C₂³×C₁₃	—	4	8	no	—
159	C₂³×C₁₃	—	4	2	no	—
160	C₂³×C₁₃	—	4	2	no	—
161	C₂³×C₁₃	—	8	4	no	—
162	C₂³×C₁₃	—	16	4	no	—
163	C₂³×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
164	Q₈×C₁₃	—	2	4	no	—
165	Q₈×C₁₃	—	2	8	no	—
166	Q₈×C₁₃	—	4	8	no	—
167	Q₈×C₁₃	—	4	4	no	—
168	Q₈×C₁₃	C₂²×D₄	1	8	yes	—
169	D₄×C₁₃	—	2	8	no	—
170	D₄×C₁₃	—	2	8	no	—
171	D₄×C₁₃	—	2	4	no	—
172	D₄×C₁₃	—	2	8	no	—
173	D₄×C₁₃	—	4	16	no	—
174	D₄×C₁₃	—	4	8	no	—
175	D₄×C₁₃	—	4	4	no	—
176	D₄×C₁₃	—	8	8	no	—
177	D₄×C₁₃	C₂²×D₄	1	8	yes	—
178	C₂×C₄×C₁₃	—	2	4	no	—
179	C₂×C₄×C₁₃	—	2	4	no	—
180	C₂×C₄×C₁₃	—	2	2	no	—
181	C₂×C₄×C₁₃	—	2	8	no	—
182	C₂×C₄×C₁₃	—	2	8	no	—
183	C₂×C₄×C₁₃	—	2	4	no	—
184	C₂×C₄×C₁₃	—	4	8	no	—
185	C₂×C₄×C₁₃	—	4	16	no	—
186	C₂×C₄×C₁₃	—	4	2	no	—
187	C₂×C₄×C₁₃	—	4	2	no	—
188	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
189	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
190	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
191	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
192	C₈×C₁₃	—	2	8	no	—
193	C₈×C₁₃	C₂²×D₄	1	4	yes	—
194	C₈×C₁₃	C₂²×D₄	1	4	yes	—
195	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	2	yes	—
196	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	2	yes	complemented
197	#577	—	2	16	no	—
198	#577	C₂²×C₁₃	1	32	yes	complemented
199	C₂×#137	—	2	4	no	—
200	C₂×#137	C₂²×C₁₃	1	4	yes	complemented
201	C₂×AGL(1,ℤ/8)	—	2	4	no	—
202	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	4	yes	—
203	C₂×#135	—	2	4	no	—
204	C₂×#135	C₂²×C₁₃	1	2	yes	—
205	C₂²×SD₁₆	—	2	4	no	—
206	C₂²×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
207	C₂×#131	C₂²×C₁₃	1	4	yes	complemented
208	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
209	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
210	#492	C₂²×C₁₃	1	8	yes	complemented
211	#471	C₂²×C₁₃	1	32	yes	complemented
212	#456	C₂²×C₁₃	1	16	yes	complemented
213	#453	C₂²×C₁₃	1	16	yes	complemented
214	#443	C₂²×C₁₃	1	16	yes	complemented
215	C₂×#108	C₂²×C₁₃	1	2	yes	complemented
216	C₂×#104	C₂²×C₁₃	1	4	yes	complemented
217	C₂×#101	C₂²×C₁₃	1	2	yes	complemented
218	C₂×#100	C₂²×C₁₃	1	2	yes	complemented
219	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
220	C₂²×C₁₃	—	2	2	no	—
221	C₂²×C₁₃	—	2	8	no	—
222	C₂²×C₁₃	—	4	8	no	—
223	C₂²×C₁₃	—	4	4	no	—
224	C₂²×C₁₃	—	8	4	no	—
225	C₂²×C₁₃	—	8	4	no	—
226	C₂²×C₁₃	—	16	2	no	—
227	C₂²×C₁₃	—	16	8	no	—
228	C₂²×C₁₃	D₄²	1	1	yes	characteristic
229	C₂²×C₁₃	D₄²	1	1	yes	characteristic
230	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
231	C₄×C₁₃	—	2	4	no	—
232	C₄×C₁₃	—	2	8	no	—
233	C₄×C₁₃	—	4	4	no	—
234	C₄×C₁₃	D₄²	1	2	yes	—
235	C₄×C₁₃	C₂³×D₄	1	2	yes	—
236	2₋¹⁺⁴	—	2	8	no	—
237	2₋¹⁺⁴	—	4	2	no	—
238	2₋¹⁺⁴	C₂³×C₁₃	1	8	yes	—
239	H(5,𝔽₂)	—	2	8	no	—
240	H(5,𝔽₂)	—	4	2	no	—
241	H(5,𝔽₂)	C₂³×C₁₃	1	8	yes	complemented
242	C₂×#41	—	2	4	no	—
243	C₂×#41	—	2	4	no	—
244	C₂×#41	—	4	2	no	—
245	C₂×#41	C₂³×C₁₃	1	4	yes	—
246	C₂²×Q₈	—	2	4	no	—
247	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
248	C₂²×D₄	—	2	4	no	—
249	C₂²×D₄	—	4	1	no	—
250	C₂²×D₄	—	4	2	no	—
251	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
252	#137	—	2	8	no	—
253	#137	—	2	32	no	—
254	#137	C₂³×C₁₃	1	16	yes	complemented
255	AGL(1,ℤ/8)	—	2	8	no	—
256	AGL(1,ℤ/8)	—	2	32	no	—
257	AGL(1,ℤ/8)	C₂³×C₁₃	1	16	yes	—
258	#135	—	2	32	no	—
259	#135	D₄×C₁₃	1	8	yes	complemented
260	#135	C₂³×C₁₃	1	8	yes	—
261	C₂×Q₁₆	—	2	4	no	—
262	C₂×Q₁₆	D₄×C₁₃	1	2	yes	complemented
263	C₂×SD₁₆	—	2	4	no	—
264	C₂×SD₁₆	—	2	4	no	—
265	C₂×SD₁₆	—	2	32	no	—
266	C₂×SD₁₆	—	2	4	no	—
267	C₂×SD₁₆	—	2	4	no	—
268	C₂×SD₁₆	—	2	8	no	—
269	C₂×SD₁₆	D₄×C₁₃	1	4	yes	complemented
270	C₂×SD₁₆	C₂³×C₁₃	1	16	yes	complemented
271	C₂×D₈	—	2	4	no	—
272	C₂×D₈	D₄×C₁₃	1	2	yes	complemented
273	#131	—	2	8	no	—
274	#131	C₂³×C₁₃	1	16	yes	complemented
275	C₂×M₁₆	—	2	4	no	—
276	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
277	C₂²×C₈	—	2	4	no	—
278	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
279	C₄⋊Q₈	—	4	1	no	—
280	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	complemented
281	#127	—	4	1	no	—
282	#127	C₂³×C₁₃	1	4	yes	—
283	C₂×C₄⋊C₄	—	4	1	no	—
284	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
285	#108	C₂³×C₁₃	1	8	yes	complemented
286	#104	C₂³×C₁₃	1	16	yes	complemented
287	#101	C₂³×C₁₃	1	8	yes	complemented
288	#100	C₂³×C₁₃	1	8	yes	complemented
289	C₄×C₈	C₂³×C₁₃	1	4	yes	complemented
290	C₂×C₁₃	—	2	1	no	—
291	C₂×C₁₃	—	2	1	no	—
292	C₂×C₁₃	—	4	8	no	—
293	C₂×C₁₃	—	8	4	no	—
294	C₂×C₁₃	#3291	1	2	yes	direct product factor
295	C₂×C₁₃	C₂×D₄²	1	1	yes	characteristic
296	C₂⁴	—	2	2	no	—
297	C₂⁴	—	4	2	no	—
298	#41	—	2	4	no	—
299	#41	—	2	4	no	—
300	#41	—	2	16	no	—
301	#41	—	2	16	no	—
302	#41	—	4	8	no	—
303	#41	—	4	8	no	—
304	#41	—	4	8	no	—
305	#41	—	4	8	no	—
306	#41	C₂×D₄×C₁₃	1	8	yes	—
307	#41	C₂⁴×C₁₃	1	8	yes	—
308	C₂×Q₈	—	2	2	no	—
309	C₂×Q₈	—	2	16	no	—
310	C₂×Q₈	—	2	4	no	—
311	C₂×Q₈	—	2	4	no	—
312	C₂×Q₈	—	4	2	no	—
313	C₂×Q₈	—	4	8	no	—
314	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
315	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
316	C₂×D₄	—	2	4	no	—
317	C₂×D₄	—	2	16	no	—
318	C₂×D₄	—	2	4	no	—
319	C₂×D₄	—	2	4	no	—
320	C₂×D₄	—	2	2	no	—
321	C₂×D₄	—	4	8	no	—
322	C₂×D₄	—	4	4	no	—
323	C₂×D₄	—	4	4	no	—
324	C₂×D₄	—	4	8	no	—
325	C₂×D₄	—	4	8	no	—
326	C₂×D₄	—	4	2	no	—
327	C₂×D₄	—	8	4	no	—
328	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
329	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	4	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	4	2	no	—
334	C₂²×C₄	—	4	4	no	—
335	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
336	Q₁₆	—	2	16	no	—
337	Q₁₆	C₂×D₄×C₁₃	1	8	yes	complemented
338	SD₁₆	—	2	16	no	—
339	SD₁₆	—	2	16	no	—
340	SD₁₆	—	2	16	no	—
341	SD₁₆	—	2	16	no	—
342	SD₁₆	C₂×D₄×C₁₃	1	16	yes	complemented
343	D₈	—	2	16	no	—
344	D₈	C₂×D₄×C₁₃	1	8	yes	complemented
345	M₁₆	—	2	4	no	—
346	M₁₆	—	2	16	no	—
347	M₁₆	C₂⁴×C₁₃	1	8	yes	—
348	C₂×C₈	—	2	4	no	—
349	C₂×C₈	—	2	16	no	—
350	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
351	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
352	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
353	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
354	C₄⋊C₄	—	4	4	no	—
355	C₄²	—	2	1	no	—
356	C₄²	C₂⁴×C₁₃	1	2	yes	—
357	C₁₃	C₂×#3291	1	1	yes	characteristic, direct product factor, Sylow
358	C₂³	—	2	4	no	—
359	C₂³	—	2	4	no	—
360	C₂³	—	4	8	no	—
361	C₂³	—	4	2	no	—
362	C₂³	—	4	2	no	—
363	C₂³	—	8	4	no	—
364	C₂³	—	16	4	no	—
365	C₂³	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
366	Q₈	—	2	4	no	—
367	Q₈	—	2	8	no	—
368	Q₈	—	4	8	no	—
369	Q₈	—	4	4	no	—
370	Q₈	C₂²×D₄×C₁₃	1	8	yes	—
371	D₄	—	2	8	no	—
372	D₄	—	2	8	no	—
373	D₄	—	2	4	no	—
374	D₄	—	2	8	no	—
375	D₄	—	4	16	no	—
376	D₄	—	4	8	no	—
377	D₄	—	4	4	no	—
378	D₄	—	8	8	no	—
379	D₄	C₂²×D₄×C₁₃	1	8	yes	—
380	C₂×C₄	—	2	4	no	—
381	C₂×C₄	—	2	4	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	8	no	—
384	C₂×C₄	—	2	8	no	—
385	C₂×C₄	—	2	4	no	—
386	C₂×C₄	—	4	8	no	—
387	C₂×C₄	—	4	16	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
391	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
392	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
393	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
394	C₈	—	2	8	no	—
395	C₈	C₂²×D₄×C₁₃	1	4	yes	—
396	C₈	C₂²×D₄×C₁₃	1	4	yes	—
397	C₂²	—	2	2	no	—
398	C₂²	—	2	8	no	—
399	C₂²	—	4	8	no	—
400	C₂²	—	4	4	no	—
401	C₂²	—	8	4	no	—
402	C₂²	—	8	4	no	—
403	C₂²	—	16	2	no	—
404	C₂²	—	16	8	no	—
405	C₂²	D₄²×C₁₃	1	1	yes	characteristic
406	C₂²	D₄²×C₁₃	1	1	yes	characteristic
407	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
408	C₄	—	2	4	no	—
409	C₄	—	2	8	no	—
410	C₄	—	4	4	no	—
411	C₄	D₄²×C₁₃	1	2	yes	—
412	C₄	C₂³×D₄×C₁₃	1	2	yes	—
413	C₂	—	2	1	no	—
414	C₂	—	2	1	no	—
415	C₂	—	4	8	no	—
416	C₂	—	8	4	no	—
417	C₂	C₁₃×#3291	1	2	yes	direct product factor
418	C₂	C₂×D₄²×C₁₃	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	D₄²
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#577	C₂	semidirect
2. C₁₃×#3291	C₂	direct (N × H)
3. C₂×C₁₃×#492	C₂	semidirect
4. C₂×C₁₃×#471	C₂	semidirect
5. C₂×C₁₃×#456	C₂	semidirect
6. C₂×C₁₃×#453	C₂	semidirect
7. C₂×C₁₃×#443	C₂	semidirect
9. C₂×C₁₃×H(5,𝔽₂)	C₂²	semidirect
11. C₁₃×#577	C₂²	semidirect
13. C₂×C₁₃×#137	C₂²	semidirect
19. C₂²×C₁₃×SD₁₆	C₂²	semidirect
20. C₂×C₁₃×#131	C₂²	semidirect
21. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
23. C₁₃×#492	C₂²	semidirect
24. C₁₃×#471	C₂²	semidirect
25. C₁₃×#456	C₂²	semidirect
26. C₁₃×#453	C₂²	semidirect
27. C₁₃×#443	C₂²	semidirect
28. C₂×C₁₃×#108	C₂²	semidirect
29. C₂×C₁₃×#104	C₂²	semidirect
30. C₂×C₁₃×#101	C₂²	semidirect
31. C₂×C₁₃×#100	C₂²	semidirect
32. C₂×C₄×C₈×C₁₃	C₂²	semidirect
38. C₁₃×H(5,𝔽₂)	C₂³	semidirect
51. C₁₃×#137	C₂³	semidirect
56. C₁₃×#135	D₄	semidirect
59. C₂×C₁₃×Q₁₆	D₄	semidirect
66. C₂×C₁₃×SD₁₆	D₄	semidirect
67. C₂×C₁₃×SD₁₆	C₂³	semidirect
69. C₂×C₁₃×D₈	D₄	semidirect
71. C₁₃×#131	C₂³	semidirect
77. C₁₃×C₄⋊Q₈	C₂³	semidirect
82. C₁₃×#108	C₂³	semidirect
83. C₁₃×#104	C₂³	semidirect
84. C₁₃×#101	C₂³	semidirect
85. C₁₃×#100	C₂³	semidirect
86. C₄×C₈×C₁₃	C₂³	semidirect
87. C₂×#3291	C₁₃	direct (N × H)
129. C₁₃×Q₁₆	C₂×D₄	semidirect
134. C₁₃×SD₁₆	C₂×D₄	semidirect
136. C₁₃×D₈	C₂×D₄	semidirect
149. C₂×#577	C₂×C₁₃	semidirect
150. #3291	C₂×C₁₃	direct (N × H)
151. C₂×#492	C₂×C₁₃	semidirect
152. C₂×#471	C₂×C₁₃	semidirect
153. C₂×#456	C₂×C₁₃	semidirect
154. C₂×#453	C₂×C₁₃	semidirect
155. C₂×#443	C₂×C₁₃	semidirect
196. C₂×H(5,𝔽₂)	C₂²×C₁₃	semidirect
198. #577	C₂²×C₁₃	semidirect
200. C₂×#137	C₂²×C₁₃	semidirect
206. C₂²×SD₁₆	C₂²×C₁₃	semidirect
207. C₂×#131	C₂²×C₁₃	semidirect
208. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
210. #492	C₂²×C₁₃	semidirect
211. #471	C₂²×C₁₃	semidirect
212. #456	C₂²×C₁₃	semidirect
213. #453	C₂²×C₁₃	semidirect
214. #443	C₂²×C₁₃	semidirect
215. C₂×#108	C₂²×C₁₃	semidirect
216. C₂×#104	C₂²×C₁₃	semidirect
217. C₂×#101	C₂²×C₁₃	semidirect
218. C₂×#100	C₂²×C₁₃	semidirect
219. C₂×C₄×C₈	C₂²×C₁₃	semidirect
241. H(5,𝔽₂)	C₂³×C₁₃	semidirect
254. #137	C₂³×C₁₃	semidirect
259. #135	D₄×C₁₃	semidirect
262. C₂×Q₁₆	D₄×C₁₃	semidirect
269. C₂×SD₁₆	D₄×C₁₃	semidirect
270. C₂×SD₁₆	C₂³×C₁₃	semidirect
272. C₂×D₈	D₄×C₁₃	semidirect
274. #131	C₂³×C₁₃	semidirect
280. C₄⋊Q₈	C₂³×C₁₃	semidirect
285. #108	C₂³×C₁₃	semidirect
286. #104	C₂³×C₁₃	semidirect
287. #101	C₂³×C₁₃	semidirect
288. #100	C₂³×C₁₃	semidirect
289. C₄×C₈	C₂³×C₁₃	semidirect
294. C₂×C₁₃	#3291	direct (N × H)
337. Q₁₆	C₂×D₄×C₁₃	semidirect
342. SD₁₆	C₂×D₄×C₁₃	semidirect
344. D₈	C₂×D₄×C₁₃	semidirect
357. C₁₃	C₂×#3291	direct (N × H)
417. C₂	C₁₃×#3291	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×#577	2
C₁₃×#3291	2
C₂×C₁₃×#492	2
C₂×C₁₃×#471	2
C₂×C₁₃×#456	2
C₂×C₁₃×#453	2
C₂×C₁₃×#443	2
C₂×#3291	13

Subgroups — C2×C13×#3291 #15747441

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3291 #15747441