Subgroups — C₂×C₁₃×#2378 #15720680

Order 3328.

2566 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2378	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₁₃×#391	C₂	1	2	yes	maximal, complemented
4	C₂×C₁₃×#389	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₃×#388	C₂	1	2	yes	maximal
6	C₂×C₁₃×#388	C₂	1	2	yes	maximal
7	C₂×C₁₃×#387	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×#387	C₂	1	2	yes	maximal, complemented
9	C₂×C₁₃×#381	C₂	1	1	yes	maximal, characteristic
10	C₂×C₁₃×#380	C₂	1	1	yes	maximal, characteristic
11	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
12	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×C₂²⋊Q₈	C₄	1	16	yes	complemented
14	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	8	yes	—
15	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
16	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
17	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
18	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
19	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
20	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
21	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
22	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
23	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
24	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
25	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
26	C₁₃×#391	C₂²	1	16	yes	complemented
27	C₁₃×#389	C₂²	1	16	yes	complemented
28	C₁₃×#388	C₂²	1	16	yes	—
29	C₁₃×#388	C₂²	1	16	yes	—
30	C₁₃×#387	C₂²	1	16	yes	complemented
31	C₁₃×#387	C₂²	1	16	yes	complemented
32	C₁₃×#381	C₂²	1	8	yes	—
33	C₁₃×#380	C₂²	1	8	yes	—
34	C₂×C₁₃×#95	C₂²	1	2	yes	—
35	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×#95	C₂²	1	2	yes	—
37	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×#95	C₂²	1	2	yes	—
39	C₂×C₁₃×#95	C₂²	1	2	yes	—
40	C₂×C₁₃×#95	C₂²	1	2	yes	—
41	C₂×C₁₃×#95	C₂²	1	2	yes	—
42	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
43	C₂²×Q₈×C₁₃	—	4	4	no	—
44	C₂²×Q₈×C₁₃	C₂×C₄	1	8	yes	—
45	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
46	C₂³×C₄×C₁₃	—	4	4	no	—
47	C₂³×C₄×C₁₃	C₂×C₄	1	8	yes	—
48	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
49	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
50	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
51	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
52	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
53	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
54	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
55	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
56	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
57	C₁₃×C₂²⋊Q₈	C₂×C₄	1	64	yes	complemented
58	C₂×C₁₃×C₄⋊C₄	—	4	4	no	—
59	C₂×C₁₃×C₄⋊C₄	—	4	4	no	—
60	C₂×C₁₃×C₄⋊C₄	—	4	4	no	—
61	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	8	yes	—
62	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	16	yes	—
63	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
64	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
65	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
66	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
67	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
68	C₂×C₁₃×C₂²⋊C₄	—	4	2	no	—
69	C₂×C₁₃×C₂²⋊C₄	—	4	4	no	—
70	C₂×C₁₃×C₂²⋊C₄	—	4	2	no	—
71	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	16	yes	—
72	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
73	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
74	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
75	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
76	C₂×C₄²×C₁₃	—	4	4	no	—
77	C₂×C₄²×C₁₃	—	4	4	no	—
78	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
79	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
80	C₁₃×#95	C₂³	1	8	yes	—
81	C₁₃×#95	C₂³	1	4	yes	—
82	C₁₃×#95	C₂³	1	8	yes	—
83	C₁₃×#95	C₂³	1	4	yes	—
84	C₁₃×#95	C₂³	1	8	yes	—
85	C₁₃×#95	C₂³	1	8	yes	—
86	C₁₃×#95	C₂³	1	8	yes	—
87	C₁₃×#95	C₂³	1	8	yes	—
88	C₂×#2378	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
89	C₂⁴×C₁₃	—	2	2	no	—
90	C₂⁴×C₁₃	—	2	4	no	—
91	C₂⁴×C₁₃	—	2	4	no	—
92	C₂⁴×C₁₃	—	2	2	no	—
93	C₂⁴×C₁₃	C₂²×C₄	1	4	yes	—
94	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
95	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
96	C₂×Q₈×C₁₃	—	4	16	no	—
97	C₂×Q₈×C₁₃	—	4	8	no	—
98	C₂×Q₈×C₁₃	C₂²×C₄	1	16	yes	—
99	C₂²×C₄×C₁₃	—	2	4	no	—
100	C₂²×C₄×C₁₃	—	2	4	no	—
101	C₂²×C₄×C₁₃	—	2	4	no	—
102	C₂²×C₄×C₁₃	—	2	4	no	—
103	C₂²×C₄×C₁₃	—	2	4	no	—
104	C₂²×C₄×C₁₃	—	2	4	no	—
105	C₂²×C₄×C₁₃	—	2	4	no	—
106	C₂²×C₄×C₁₃	—	2	4	no	—
107	C₂²×C₄×C₁₃	—	2	4	no	—
108	C₂²×C₄×C₁₃	—	2	4	no	—
109	C₂²×C₄×C₁₃	—	2	4	no	—
110	C₂²×C₄×C₁₃	—	2	4	no	—
111	C₂²×C₄×C₁₃	—	2	4	no	—
112	C₂²×C₄×C₁₃	—	2	4	no	—
113	C₂²×C₄×C₁₃	—	2	4	no	—
114	C₂²×C₄×C₁₃	—	2	4	no	—
115	C₂²×C₄×C₁₃	—	2	4	no	—
116	C₂²×C₄×C₁₃	—	2	4	no	—
117	C₂²×C₄×C₁₃	—	4	16	no	—
118	C₂²×C₄×C₁₃	—	4	8	no	—
119	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
120	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
121	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
122	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
123	C₂²×C₄×C₁₃	C₂²×C₄	1	16	yes	—
124	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
125	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
126	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
127	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
128	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
129	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
130	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
131	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
132	C₁₃×C₄⋊C₄	—	4	8	no	—
133	C₁₃×C₄⋊C₄	—	4	8	no	—
134	C₁₃×C₄⋊C₄	—	4	8	no	—
135	C₁₃×C₄⋊C₄	C₂²×C₄	1	16	yes	—
136	C₁₃×C₄⋊C₄	C₂²×C₄	1	32	yes	—
137	C₁₃×C₂²⋊C₄	—	4	4	no	—
138	C₁₃×C₂²⋊C₄	—	4	8	no	—
139	C₁₃×C₂²⋊C₄	—	4	4	no	—
140	C₁₃×C₂²⋊C₄	C₂²×C₄	1	32	yes	—
141	C₄²×C₁₃	—	4	8	no	—
142	C₄²×C₁₃	—	4	8	no	—
143	C₂²×C₂²⋊Q₈	C₂×C₁₃	1	1	yes	characteristic
144	#2378	C₂×C₁₃	1	16	yes	direct product factor
145	C₂×#391	C₂×C₁₃	1	2	yes	complemented
146	C₂×#389	C₂×C₁₃	1	2	yes	complemented
147	C₂×#388	C₂×C₁₃	1	2	yes	—
148	C₂×#388	C₂×C₁₃	1	2	yes	—
149	C₂×#387	C₂×C₁₃	1	2	yes	complemented
150	C₂×#387	C₂×C₁₃	1	2	yes	complemented
151	C₂×#381	C₂×C₁₃	1	1	yes	characteristic
152	C₂×#380	C₂×C₁₃	1	1	yes	characteristic
153	C₂³×C₁₃	—	2	8	no	—
154	C₂³×C₁₃	—	2	8	no	—
155	C₂³×C₁₃	—	2	8	no	—
156	C₂³×C₁₃	—	2	2	no	—
157	C₂³×C₁₃	—	2	4	no	—
158	C₂³×C₁₃	—	2	4	no	—
159	C₂³×C₁₃	—	2	2	no	—
160	C₂³×C₁₃	—	4	8	no	—
161	C₂³×C₁₃	—	4	8	no	—
162	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
163	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
164	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
165	C₂³×C₁₃	H(5,𝔽₂)	1	2	yes	—
166	C₂³×C₁₃	2₋¹⁺⁴	1	4	yes	—
167	C₂³×C₁₃	2₋¹⁺⁴	1	2	yes	—
168	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
169	Q₈×C₁₃	—	4	16	no	—
170	C₂×C₄×C₁₃	—	2	8	no	—
171	C₂×C₄×C₁₃	—	2	8	no	—
172	C₂×C₄×C₁₃	—	2	16	no	—
173	C₂×C₄×C₁₃	—	2	16	no	—
174	C₂×C₄×C₁₃	—	2	4	no	—
175	C₂×C₄×C₁₃	—	2	4	no	—
176	C₂×C₄×C₁₃	—	2	4	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	—	2	4	no	—
182	C₂×C₄×C₁₃	—	2	4	no	—
183	C₂×C₄×C₁₃	—	2	4	no	—
184	C₂×C₄×C₁₃	—	2	4	no	—
185	C₂×C₄×C₁₃	—	2	4	no	—
186	C₂×C₄×C₁₃	—	2	4	no	—
187	C₂×C₄×C₁₃	—	2	4	no	—
188	C₂×C₄×C₁₃	—	2	4	no	—
189	C₂×C₄×C₁₃	—	2	4	no	—
190	C₂×C₄×C₁₃	—	2	4	no	—
191	C₂×C₄×C₁₃	—	2	4	no	—
192	C₂×C₄×C₁₃	—	4	16	no	—
193	C₂×C₄×C₁₃	—	4	8	no	—
194	C₂×C₄×C₁₃	—	4	8	no	—
195	C₂×C₄×C₁₃	—	4	8	no	—
196	C₂×C₄×C₁₃	—	4	8	no	—
197	C₂×C₄×C₁₃	C₂³×C₄	1	8	yes	—
198	C₂×C₄×C₁₃	C₂³×C₄	1	8	yes	—
199	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
200	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
201	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
202	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
203	C₂×C₂²⋊Q₈	C₄×C₁₃	1	16	yes	complemented
204	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	8	yes	—
205	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
206	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
207	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
208	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
209	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
210	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
211	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
212	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
213	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
214	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
215	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
216	#391	C₂²×C₁₃	1	16	yes	complemented
217	#389	C₂²×C₁₃	1	16	yes	complemented
218	#388	C₂²×C₁₃	1	16	yes	—
219	#388	C₂²×C₁₃	1	16	yes	—
220	#387	C₂²×C₁₃	1	16	yes	complemented
221	#387	C₂²×C₁₃	1	16	yes	complemented
222	#381	C₂²×C₁₃	1	8	yes	—
223	#380	C₂²×C₁₃	1	8	yes	—
224	C₂×#95	C₂²×C₁₃	1	2	yes	—
225	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
226	C₂×#95	C₂²×C₁₃	1	2	yes	—
227	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
228	C₂×#95	C₂²×C₁₃	1	2	yes	—
229	C₂×#95	C₂²×C₁₃	1	2	yes	—
230	C₂×#95	C₂²×C₁₃	1	2	yes	—
231	C₂×#95	C₂²×C₁₃	1	2	yes	—
232	C₂²×C₁₃	—	2	4	no	—
233	C₂²×C₁₃	—	2	4	no	—
234	C₂²×C₁₃	—	2	4	no	—
235	C₂²×C₁₃	—	4	16	no	—
236	C₂²×C₁₃	—	4	4	no	—
237	C₂²×C₁₃	—	4	4	no	—
238	C₂²×C₁₃	#518	1	4	yes	—
239	C₂²×C₁₃	#519	1	4	yes	—
240	C₂²×C₁₃	#520	1	4	yes	—
241	C₂²×C₁₃	#562	1	8	yes	—
242	C₂²×C₁₃	#563	1	8	yes	—
243	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
244	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
245	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
246	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
247	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
248	C₄×C₁₃	—	2	4	no	—
249	C₄×C₁₃	—	2	4	no	—
250	C₄×C₁₃	—	2	8	no	—
251	C₄×C₁₃	—	2	8	no	—
252	C₄×C₁₃	—	4	4	no	—
253	C₄×C₁₃	—	4	4	no	—
254	C₄×C₁₃	—	4	4	no	—
255	C₄×C₁₃	—	4	4	no	—
256	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
257	C₂²×Q₈	—	4	4	no	—
258	C₂²×Q₈	C₂×C₄×C₁₃	1	8	yes	—
259	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
260	C₂³×C₄	—	4	4	no	—
261	C₂³×C₄	C₂×C₄×C₁₃	1	8	yes	—
262	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
263	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
264	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
265	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
266	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
267	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
268	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
269	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
270	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
271	C₂²⋊Q₈	C₂×C₄×C₁₃	1	64	yes	complemented
272	C₂×C₄⋊C₄	—	4	4	no	—
273	C₂×C₄⋊C₄	—	4	4	no	—
274	C₂×C₄⋊C₄	—	4	4	no	—
275	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	8	yes	—
276	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	16	yes	—
277	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
278	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
279	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
280	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
281	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
282	C₂×C₂²⋊C₄	—	4	2	no	—
283	C₂×C₂²⋊C₄	—	4	4	no	—
284	C₂×C₂²⋊C₄	—	4	2	no	—
285	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	16	yes	—
286	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
287	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
288	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
289	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
290	C₂×C₄²	—	4	4	no	—
291	C₂×C₄²	—	4	4	no	—
292	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
293	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
294	#95	C₂³×C₁₃	1	8	yes	—
295	#95	C₂³×C₁₃	1	4	yes	—
296	#95	C₂³×C₁₃	1	8	yes	—
297	#95	C₂³×C₁₃	1	4	yes	—
298	#95	C₂³×C₁₃	1	8	yes	—
299	#95	C₂³×C₁₃	1	8	yes	—
300	#95	C₂³×C₁₃	1	8	yes	—
301	#95	C₂³×C₁₃	1	8	yes	—
302	C₂×C₁₃	—	4	4	no	—
303	C₂×C₁₃	#2378	1	8	yes	direct product factor
304	C₂×C₁₃	C₂×#518	1	1	yes	characteristic
305	C₂×C₁₃	C₂×#519	1	1	yes	characteristic
306	C₂×C₁₃	C₂×#520	1	1	yes	characteristic
307	C₂×C₁₃	C₂×#562	1	2	yes	—
308	C₂×C₁₃	C₂×#563	1	2	yes	—
309	C₂⁴	—	2	2	no	—
310	C₂⁴	—	2	4	no	—
311	C₂⁴	—	2	4	no	—
312	C₂⁴	—	2	2	no	—
313	C₂⁴	C₂²×C₄×C₁₃	1	4	yes	—
314	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
315	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
316	C₂×Q₈	—	4	16	no	—
317	C₂×Q₈	—	4	8	no	—
318	C₂×Q₈	C₂²×C₄×C₁₃	1	16	yes	—
319	C₂²×C₄	—	2	4	no	—
320	C₂²×C₄	—	2	4	no	—
321	C₂²×C₄	—	2	4	no	—
322	C₂²×C₄	—	2	4	no	—
323	C₂²×C₄	—	2	4	no	—
324	C₂²×C₄	—	2	4	no	—
325	C₂²×C₄	—	2	4	no	—
326	C₂²×C₄	—	2	4	no	—
327	C₂²×C₄	—	2	4	no	—
328	C₂²×C₄	—	2	4	no	—
329	C₂²×C₄	—	2	4	no	—
330	C₂²×C₄	—	2	4	no	—
331	C₂²×C₄	—	2	4	no	—
332	C₂²×C₄	—	2	4	no	—
333	C₂²×C₄	—	2	4	no	—
334	C₂²×C₄	—	2	4	no	—
335	C₂²×C₄	—	2	4	no	—
336	C₂²×C₄	—	2	4	no	—
337	C₂²×C₄	—	4	16	no	—
338	C₂²×C₄	—	4	8	no	—
339	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
340	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
341	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
342	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
343	C₂²×C₄	C₂²×C₄×C₁₃	1	16	yes	—
344	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
345	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
346	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
347	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
348	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
349	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
350	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
351	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
352	C₄⋊C₄	—	4	8	no	—
353	C₄⋊C₄	—	4	8	no	—
354	C₄⋊C₄	—	4	8	no	—
355	C₄⋊C₄	C₂²×C₄×C₁₃	1	16	yes	—
356	C₄⋊C₄	C₂²×C₄×C₁₃	1	32	yes	—
357	C₂²⋊C₄	—	4	4	no	—
358	C₂²⋊C₄	—	4	8	no	—
359	C₂²⋊C₄	—	4	4	no	—
360	C₂²⋊C₄	C₂²×C₄×C₁₃	1	32	yes	—
361	C₄²	—	4	8	no	—
362	C₄²	—	4	8	no	—
363	C₁₃	C₂×#2378	1	1	yes	characteristic, direct product factor, Sylow
364	C₂³	—	2	8	no	—
365	C₂³	—	2	8	no	—
366	C₂³	—	2	8	no	—
367	C₂³	—	2	2	no	—
368	C₂³	—	2	4	no	—
369	C₂³	—	2	4	no	—
370	C₂³	—	2	2	no	—
371	C₂³	—	4	8	no	—
372	C₂³	—	4	8	no	—
373	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
374	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
375	C₂³	C₁₃×H(5,𝔽₂)	1	4	yes	—
376	C₂³	C₁₃×H(5,𝔽₂)	1	2	yes	—
377	C₂³	C₁₃×2₋¹⁺⁴	1	4	yes	—
378	C₂³	C₁₃×2₋¹⁺⁴	1	2	yes	—
379	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
380	Q₈	—	4	16	no	—
381	C₂×C₄	—	2	8	no	—
382	C₂×C₄	—	2	8	no	—
383	C₂×C₄	—	2	16	no	—
384	C₂×C₄	—	2	16	no	—
385	C₂×C₄	—	2	4	no	—
386	C₂×C₄	—	2	4	no	—
387	C₂×C₄	—	2	4	no	—
388	C₂×C₄	—	2	4	no	—
389	C₂×C₄	—	2	4	no	—
390	C₂×C₄	—	2	4	no	—
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	2	4	no	—
393	C₂×C₄	—	2	4	no	—
394	C₂×C₄	—	2	4	no	—
395	C₂×C₄	—	2	4	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	—	2	4	no	—
401	C₂×C₄	—	2	4	no	—
402	C₂×C₄	—	2	4	no	—
403	C₂×C₄	—	4	16	no	—
404	C₂×C₄	—	4	8	no	—
405	C₂×C₄	—	4	8	no	—
406	C₂×C₄	—	4	8	no	—
407	C₂×C₄	—	4	8	no	—
408	C₂×C₄	C₂³×C₄×C₁₃	1	8	yes	—
409	C₂×C₄	C₂³×C₄×C₁₃	1	8	yes	—
410	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
411	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
412	C₂²	—	2	4	no	—
413	C₂²	—	2	4	no	—
414	C₂²	—	2	4	no	—
415	C₂²	—	4	4	no	—
416	C₂²	—	4	4	no	—
417	C₂²	—	4	16	no	—
418	C₂²	C₁₃×#518	1	4	yes	—
419	C₂²	C₁₃×#519	1	4	yes	—
420	C₂²	C₁₃×#520	1	4	yes	—
421	C₂²	C₁₃×#562	1	8	yes	—
422	C₂²	C₁₃×#563	1	8	yes	—
423	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
424	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
425	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
426	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
427	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
428	C₄	—	2	4	no	—
429	C₄	—	2	4	no	—
430	C₄	—	2	8	no	—
431	C₄	—	2	8	no	—
432	C₄	—	4	4	no	—
433	C₄	—	4	4	no	—
434	C₄	—	4	4	no	—
435	C₄	—	4	4	no	—
436	C₂	—	4	4	no	—
437	C₂	C₁₃×#2378	1	8	yes	direct product factor
438	C₂	C₂×C₁₃×#518	1	1	yes	characteristic
439	C₂	C₂×C₁₃×#519	1	1	yes	characteristic
440	C₂	C₂×C₁₃×#520	1	1	yes	characteristic
441	C₂	C₂×C₁₃×#562	1	2	yes	—
442	C₂	C₂×C₁₃×#563	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₁₃	C₂⁴
commutator	C₂²	C₂⁴×C₄×C₁₃
Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂⁵×C₁₃	C₂³
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2378	C₂	direct (N × H)
3. C₂×C₁₃×#391	C₂	semidirect
4. C₂×C₁₃×#389	C₂	semidirect
7. C₂×C₁₃×#387	C₂	semidirect
8. C₂×C₁₃×#387	C₂	semidirect
13. C₂×C₁₃×C₂²⋊Q₈	C₄	semidirect
26. C₁₃×#391	C₂²	semidirect
27. C₁₃×#389	C₂²	semidirect
30. C₁₃×#387	C₂²	semidirect
31. C₁₃×#387	C₂²	semidirect
57. C₁₃×C₂²⋊Q₈	C₂×C₄	semidirect
88. C₂×#2378	C₁₃	direct (N × H)
144. #2378	C₂×C₁₃	direct (N × H)
145. C₂×#391	C₂×C₁₃	semidirect
146. C₂×#389	C₂×C₁₃	semidirect
149. C₂×#387	C₂×C₁₃	semidirect
150. C₂×#387	C₂×C₁₃	semidirect
203. C₂×C₂²⋊Q₈	C₄×C₁₃	semidirect
216. #391	C₂²×C₁₃	semidirect
217. #389	C₂²×C₁₃	semidirect
220. #387	C₂²×C₁₃	semidirect
221. #387	C₂²×C₁₃	semidirect
271. C₂²⋊Q₈	C₂×C₄×C₁₃	semidirect
303. C₂×C₁₃	#2378	direct (N × H)
363. C₁₃	C₂×#2378	direct (N × H)
437. C₂	C₁₃×#2378	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₃×C₂²⋊Q₈	2
C₁₃×#2378	2
C₂×C₁₃×#391	2
C₂×C₁₃×#389	2
C₂×C₁₃×#388	2
C₂×C₁₃×#387	2
C₂×C₁₃×#381	2
C₂×C₁₃×#380	2
C₂×#2378	13

Subgroups — C2×C13×#2378 #15720680

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2378 #15720680