Subgroups — #15768813

Order 3328.

982 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	C₂²×#88057	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₈×Dic₁₃	C₂	1	1	yes	maximal, characteristic
3	C₂×#11718121	C₂	1	2	yes	maximal
4	#13113065	C₂	1	2	yes	maximal
5	C₂²×C₁₃×#106	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
7	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
8	C₂²×C₄⋊Dic₁₃	C₂²	1	2	yes	—
9	C₂²×C₄×Dic₁₃	C₂²	1	1	yes	characteristic
10	C₂³×#1055	C₂²	1	1	yes	characteristic
11	C₂×C₁₃×#106	—	2	2	no	—
12	C₂×C₁₃×#106	—	2	2	no	—
13	C₂×C₁₃×#106	C₄	1	4	yes	complemented
14	C₂×#88071	—	2	4	no	—
15	C₂×#88057	—	2	2	no	—
16	C₂×#88057	—	2	2	no	—
17	C₂×#88057	C₄	1	4	yes	complemented
18	C₂×C₈×Dic₁₃	—	2	2	no	—
19	C₂×C₈×Dic₁₃	—	2	2	no	—
20	C₂×C₈×Dic₁₃	C₄	1	4	yes	complemented
21	#11718121	—	2	4	no	—
22	C₂³×C₄×C₁₃	—	2	2	no	—
23	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
24	C₂³×Dic₁₃	—	2	2	no	—
25	C₂³×Dic₁₃	D₄	1	2	yes	—
26	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
27	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
28	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
29	C₂²×C₈×C₁₃	D₄	1	2	yes	—
30	C₂²×C₈×C₁₃	D₄	1	2	yes	—
31	C₂²×C₈×C₁₃	D₄	1	2	yes	—
32	C₂²×C₈×C₁₃	Q₈	1	2	yes	—
33	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
34	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
35	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
36	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
37	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
38	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	4	yes	—
39	C₂×C₄⋊Dic₁₃	—	2	2	no	—
40	C₂×C₄⋊Dic₁₃	—	2	2	no	—
41	C₂×C₄⋊Dic₁₃	—	2	2	no	—
42	C₂×C₄⋊Dic₁₃	—	2	2	no	—
43	C₂×C₄⋊Dic₁₃	—	2	2	no	—
44	C₂×C₄⋊Dic₁₃	C₂×C₄	1	4	yes	—
45	C₂×C₄×Dic₁₃	—	2	1	no	—
46	C₂×C₄×Dic₁₃	—	2	1	no	—
47	C₂×C₄×Dic₁₃	—	2	1	no	—
48	C₂×C₄×Dic₁₃	—	2	1	no	—
49	C₂×C₄×Dic₁₃	C₂×C₄	1	2	yes	—
50	C₂×C₄×Dic₁₃	Q₈	1	2	yes	—
51	C₂²×#1055	—	2	1	no	—
52	C₂²×#1055	—	2	1	no	—
53	C₂²×#1055	—	2	1	no	—
54	C₂²×#1055	—	2	1	no	—
55	C₂²×#1055	C₂×C₄	1	2	yes	—
56	C₂²×#1055	D₄	1	2	yes	—
57	C₂²×#1055	Q₈	1	2	yes	—
58	C₁₃×#106	—	2	8	no	—
59	#88071	—	4	8	no	—
60	#88057	—	2	8	no	—
61	C₈×Dic₁₃	—	2	8	no	—
62	#10861	—	13	1	no	maximal, Sylow
63	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
64	C₂²×C₄×C₁₃	—	2	4	no	—
65	C₂²×C₄×C₁₃	—	4	2	no	—
66	C₂²×C₄×C₁₃	—	4	2	no	—
67	C₂²×C₄×C₁₃	—	4	4	no	—
68	C₂²×C₄×C₁₃	—	4	4	no	—
69	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
70	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
71	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
72	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
73	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
77	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
78	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
79	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
80	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
81	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
82	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
83	C₂²×Dic₁₃	—	2	2	no	—
84	C₂²×Dic₁₃	—	2	2	no	—
85	C₂²×Dic₁₃	—	2	4	no	—
86	C₂²×Dic₁₃	—	2	4	no	—
87	C₂²×Dic₁₃	—	4	2	no	—
88	C₂²×Dic₁₃	—	4	2	no	—
89	C₂²×Dic₁₃	—	4	4	no	—
90	C₂²×Dic₁₃	—	4	4	no	—
91	C₂²×Dic₁₃	C₄⋊C₄	1	4	yes	—
92	C₂²×Dic₁₃	SD₁₆	1	8	yes	—
93	C₂×C₈×C₁₃	C₄²	1	4	yes	—
94	C₂×C₈×C₁₃	C₂²⋊C₄	1	4	yes	—
95	C₂×C₈×C₁₃	C₂²⋊C₄	1	4	yes	—
96	C₂×C₈×C₁₃	C₂²⋊C₄	1	4	yes	—
97	C₂×C₈×C₁₃	C₄⋊C₄	1	4	yes	—
98	C₂×C₈×C₁₃	C₄⋊C₄	1	4	yes	—
99	C₂×C₈×C₁₃	C₄⋊C₄	1	4	yes	—
100	C₁₃×C₄⋊C₄	—	2	4	no	—
101	C₁₃×C₄⋊C₄	—	2	4	no	—
102	C₁₃×C₄⋊C₄	—	4	2	no	—
103	C₁₃×C₄⋊C₄	—	4	2	no	—
104	C₄⋊Dic₁₃	—	2	4	no	—
105	C₄⋊Dic₁₃	—	2	4	no	—
106	C₄⋊Dic₁₃	—	4	2	no	—
107	C₄⋊Dic₁₃	—	4	2	no	—
108	C₄×Dic₁₃	—	2	2	no	—
109	C₄×Dic₁₃	—	2	2	no	—
110	C₄×Dic₁₃	—	2	2	no	—
111	C₄×Dic₁₃	—	2	2	no	—
112	C₂×#1055	—	2	2	no	—
113	C₂×#1055	—	2	2	no	—
114	C₂×#1055	—	2	2	no	—
115	C₂×#1055	—	2	2	no	—
116	C₂×#1055	—	2	2	no	—
117	C₂×#1055	—	2	2	no	—
118	C₂×#1055	C₄⋊C₄	1	4	yes	—
119	C₂²×#106	—	13	1	no	—
120	C₂²×#106	D₁₃	1	1	yes	characteristic
121	C₂²×C₄×C₈	—	13	1	no	—
122	C₂×#340	—	13	2	no	—
123	C₄⋊#95	—	13	2	no	—
124	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
125	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
126	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
127	C₂³×C₁₃	#121	1	1	yes	characteristic
128	C₂³×C₁₃	#121	1	1	yes	characteristic
129	C₂³×C₁₃	#127	1	1	yes	characteristic
130	C₂³×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
131	C₂³×C₁₃	C₂×SD₁₆	1	4	yes	—
132	C₂³×C₁₃	#135	1	4	yes	—
133	C₂×C₄×C₁₃	—	4	4	no	—
134	C₂×C₄×C₁₃	—	4	8	no	—
135	C₂×C₄×C₁₃	—	8	4	no	—
136	C₂×C₄×C₁₃	—	8	2	no	—
137	C₂×C₄×C₁₃	—	8	2	no	—
138	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
139	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
140	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
141	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
142	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
143	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
144	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
145	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
146	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
147	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
148	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
149	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
150	C₂×C₄×C₁₃	C₄×Q₈	1	1	yes	characteristic
151	C₂×C₄×C₁₃	C₄×Q₈	1	1	yes	characteristic
152	C₂×C₄×C₁₃	C₄×Q₈	1	1	yes	characteristic
153	C₂×C₄×C₁₃	C₄×Q₈	1	1	yes	characteristic
154	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
155	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
156	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
157	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
158	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
159	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
160	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
161	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
162	C₂×C₄×C₁₃	#125	1	1	yes	characteristic
163	C₂×C₄×C₁₃	#125	1	1	yes	characteristic
164	C₂×C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
165	C₂×C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
166	C₂×Dic₁₃	—	2	4	no	—
167	C₂×Dic₁₃	—	2	4	no	—
168	C₂×Dic₁₃	—	2	8	no	—
169	C₂×Dic₁₃	—	2	8	no	—
170	C₂×Dic₁₃	—	4	4	no	—
171	C₂×Dic₁₃	—	4	8	no	—
172	C₂×Dic₁₃	—	8	4	no	—
173	C₂×Dic₁₃	—	8	2	no	—
174	C₂×Dic₁₃	—	8	2	no	—
175	C₂×Dic₁₃	#106	1	8	yes	complemented
176	C₈×C₁₃	#95	1	8	yes	complemented
177	#1055	—	2	4	no	—
178	C₂³×C₈	—	13	1	no	—
179	C₂³×C₈	C₂×D₁₃	1	1	yes	characteristic
180	C₂²×C₄⋊C₄	—	13	2	no	—
181	C₂²×C₄⋊C₄	C₂×D₁₃	1	2	yes	—
182	C₂²×C₄²	—	13	1	no	—
183	C₂×#106	—	2	2	no	—
184	C₂×#106	—	2	2	no	—
185	C₂×#106	—	13	4	no	—
186	C₂×#106	—	26	2	no	—
187	C₂×#106	—	26	2	no	—
188	C₂×#106	Dic₁₃	1	4	yes	complemented
189	C₂×C₄×C₈	—	13	4	no	—
190	C₂×C₄×C₈	—	26	2	no	—
191	C₂×C₄×C₈	—	26	2	no	—
192	C₂×#95	—	26	4	no	—
193	#340	—	26	4	no	—
194	C₂²×C₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
195	C₂²×C₁₃	#380	1	1	yes	characteristic
196	C₂²×C₁₃	#384	1	1	yes	characteristic
197	C₂²×C₁₃	#389	1	1	yes	characteristic
198	C₂²×C₁₃	#389	1	1	yes	characteristic
199	C₂²×C₁₃	#390	1	1	yes	characteristic
200	C₂²×C₁₃	#390	1	1	yes	characteristic
201	C₂²×C₁₃	C₂×#106	1	2	yes	—
202	C₂²×C₁₃	#427	1	2	yes	—
203	C₂²×C₁₃	C₄×SD₁₆	1	4	yes	—
204	C₂²×C₁₃	C₄×SD₁₆	1	4	yes	—
205	C₂²×C₁₃	#465	1	4	yes	—
206	C₂²×C₁₃	#465	1	4	yes	—
207	C₂²×C₁₃	#492	1	2	yes	—
208	C₂²×C₁₃	#495	1	2	yes	—
209	C₂²×C₁₃	#498	1	2	yes	—
210	C₂²×C₁₃	#499	1	2	yes	—
211	C₄×C₁₃	—	8	4	no	—
212	C₄×C₁₃	C₂×#95	1	1	yes	characteristic
213	C₄×C₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
214	C₄×C₁₃	#380	1	1	yes	characteristic
215	C₄×C₁₃	#382	1	1	yes	characteristic
216	C₄×C₁₃	#389	1	1	yes	characteristic
217	C₄×C₁₃	#389	1	1	yes	characteristic
218	C₄×C₁₃	#391	1	1	yes	characteristic
219	C₄×C₁₃	#391	1	1	yes	characteristic
220	Dic₁₃	—	2	8	no	—
221	Dic₁₃	—	8	4	no	—
222	C₂³×C₄	—	2	2	no	—
223	C₂³×C₄	—	13	2	no	—
224	C₂³×C₄	—	26	2	no	—
225	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
226	C₂²×C₈	—	13	2	no	—
227	C₂²×C₈	—	13	2	no	—
228	C₂²×C₈	—	13	2	no	—
229	C₂²×C₈	—	26	1	no	—
230	C₂²×C₈	—	26	1	no	—
231	C₂²×C₈	—	26	1	no	—
232	C₂²×C₈	—	26	1	no	—
233	C₂²×C₈	Dic₂₆	1	2	yes	—
234	C₂²×C₈	C₄×D₁₃	1	2	yes	—
235	C₂²×C₈	C₄×D₁₃	1	2	yes	—
236	C₂²×C₈	D₅₂	1	2	yes	—
237	C₂²×C₈	C₂×Dic₁₃	1	2	yes	—
238	C₂²×C₈	C₂²⋊D₁₃	1	2	yes	—
239	C₂²×C₈	C₂²⋊D₁₃	1	2	yes	—
240	C₂×C₄⋊C₄	—	2	2	no	—
241	C₂×C₄⋊C₄	—	2	2	no	—
242	C₂×C₄⋊C₄	—	2	2	no	—
243	C₂×C₄⋊C₄	—	2	2	no	—
244	C₂×C₄⋊C₄	—	2	2	no	—
245	C₂×C₄⋊C₄	—	13	4	no	—
246	C₂×C₄⋊C₄	—	26	2	no	—
247	C₂×C₄⋊C₄	—	26	2	no	—
248	C₂×C₄⋊C₄	—	26	2	no	—
249	C₂×C₄⋊C₄	—	26	2	no	—
250	C₂×C₄⋊C₄	—	26	2	no	—
251	C₂×C₄⋊C₄	C₂×Dic₁₃	1	4	yes	—
252	C₂×C₄²	—	13	2	no	—
253	C₂×C₄²	—	13	2	no	—
254	C₂×C₄²	—	26	1	no	—
255	C₂×C₄²	—	26	1	no	—
256	C₂×C₄²	—	26	1	no	—
257	C₂×C₄²	—	26	1	no	—
258	#106	—	2	8	no	—
259	#106	—	26	8	no	—
260	C₄×C₈	—	26	8	no	—
261	#95	—	52	8	no	—
262	C₂×C₁₃	C₄⋊#95	1	1	yes	characteristic
263	C₂×C₁₃	C₄×#106	1	2	yes	—
264	C₂×C₁₃	#1807	1	2	yes	—
265	C₂×C₁₃	#1844	1	1	yes	characteristic
266	C₂×C₁₃	#1846	1	1	yes	characteristic
267	C₂×C₁₃	#1941	1	2	yes	—
268	C₂×C₁₃	#1941	1	2	yes	—
269	C₂×C₁₃	#1968	1	2	yes	—
270	C₂×C₁₃	#1968	1	2	yes	—
271	C₂⁴	D₄×D₁₃	1	1	yes	characteristic
272	C₂²×C₄	—	2	4	no	—
273	C₂²×C₄	—	4	4	no	—
274	C₂²×C₄	—	4	4	no	—
275	C₂²×C₄	—	4	2	no	—
276	C₂²×C₄	—	4	2	no	—
277	C₂²×C₄	—	13	4	no	—
278	C₂²×C₄	—	13	8	no	—
279	C₂²×C₄	—	26	2	no	—
280	C₂²×C₄	—	26	4	no	—
281	C₂²×C₄	—	26	2	no	—
282	C₂²×C₄	—	26	4	no	—
283	C₂²×C₄	—	52	2	no	—
284	C₂²×C₄	—	52	4	no	—
285	C₂²×C₄	—	52	4	no	—
286	C₂²×C₄	—	52	2	no	—
287	C₂²×C₄	C₂×Dic₂₆	1	1	yes	characteristic
288	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
289	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
290	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
291	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
292	C₂²×C₄	#6129	1	1	yes	characteristic
293	C₂²×C₄	#6129	1	1	yes	characteristic
294	C₂²×C₄	Q₈×D₁₃	1	1	yes	characteristic
295	C₂²×C₄	Q₈×D₁₃	1	1	yes	characteristic
296	C₂²×C₄	#6131	1	1	yes	characteristic
297	C₂²×C₄	#6131	1	1	yes	characteristic
298	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
299	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
300	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
301	C₂×C₈	—	13	4	no	—
302	C₂×C₈	—	26	2	no	—
303	C₂×C₈	—	26	2	no	—
304	C₂×C₈	—	26	2	no	—
305	C₂×C₈	—	26	2	no	—
306	C₂×C₈	—	26	2	no	—
307	C₂×C₈	—	26	2	no	—
308	C₂×C₈	C₄×Dic₁₃	1	4	yes	—
309	C₂×C₈	#6101	1	4	yes	—
310	C₂×C₈	#6101	1	4	yes	—
311	C₂×C₈	C₄⋊Dic₁₃	1	4	yes	—
312	C₂×C₈	#6103	1	4	yes	—
313	C₂×C₈	#6103	1	4	yes	—
314	C₂×C₈	C₂²⋊Dic₁₃	1	4	yes	—
315	C₄⋊C₄	—	2	4	no	—
316	C₄⋊C₄	—	2	4	no	—
317	C₄⋊C₄	—	4	2	no	—
318	C₄⋊C₄	—	4	2	no	—
319	C₄⋊C₄	—	26	4	no	—
320	C₄⋊C₄	—	26	4	no	—
321	C₄⋊C₄	—	52	2	no	—
322	C₄⋊C₄	—	52	2	no	—
323	C₄²	—	26	2	no	—
324	C₄²	—	26	2	no	—
325	C₄²	—	26	2	no	—
326	C₄²	—	26	2	no	—
327	C₁₃	#10861	1	1	yes	characteristic, complemented, Sylow
328	C₂³	#88142	1	1	yes	characteristic
329	C₂³	C₄⋊C₄×D₁₃	1	1	yes	characteristic
330	C₂³	#88147	1	1	yes	characteristic
331	C₂³	#88149	1	1	yes	characteristic
332	C₂³	SD₁₆×D₁₃	1	4	yes	—
333	C₂³	#88170	1	4	yes	—
334	C₂³	D₄×Dic₁₃	1	1	yes	characteristic
335	C₂³	#88192	1	1	yes	characteristic
336	C₂³	#88194	1	1	yes	characteristic
337	C₂×C₄	—	4	8	no	—
338	C₂×C₄	—	4	4	no	—
339	C₂×C₄	—	8	2	no	—
340	C₂×C₄	—	8	4	no	—
341	C₂×C₄	—	8	2	no	—
342	C₂×C₄	—	13	8	no	—
343	C₂×C₄	—	26	4	no	—
344	C₂×C₄	—	26	8	no	—
345	C₂×C₄	—	26	8	no	—
346	C₂×C₄	—	26	4	no	—
347	C₂×C₄	—	52	8	no	—
348	C₂×C₄	—	52	4	no	—
349	C₂×C₄	—	104	4	no	—
350	C₂×C₄	—	104	2	no	—
351	C₂×C₄	—	104	2	no	—
352	C₂×C₄	#88141	1	1	yes	characteristic
353	C₂×C₄	#88141	1	1	yes	characteristic
354	C₂×C₄	#88142	1	1	yes	characteristic
355	C₂×C₄	#88144	1	1	yes	characteristic
356	C₂×C₄	#88144	1	1	yes	characteristic
357	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
358	C₂×C₄	#88146	1	1	yes	characteristic
359	C₂×C₄	#88146	1	1	yes	characteristic
360	C₂×C₄	#88147	1	1	yes	characteristic
361	C₂×C₄	#88149	1	1	yes	characteristic
362	C₂×C₄	#88151	1	1	yes	characteristic
363	C₂×C₄	#88151	1	1	yes	characteristic
364	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
365	C₂×C₄	C₂×#6101	1	1	yes	characteristic
366	C₂×C₄	C₂×#6101	1	1	yes	characteristic
367	C₂×C₄	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
368	C₂×C₄	C₂×#6103	1	1	yes	characteristic
369	C₂×C₄	C₂×#6103	1	1	yes	characteristic
370	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
371	C₂×C₄	#88190	1	1	yes	characteristic
372	C₂×C₄	#88192	1	1	yes	characteristic
373	C₂×C₄	#88198	1	1	yes	characteristic
374	C₂×C₄	Q₈×Dic₁₃	1	1	yes	characteristic
375	C₂×C₄	Q₈×Dic₁₃	1	1	yes	characteristic
376	C₂×C₄	#88200	1	1	yes	characteristic
377	C₂×C₄	#88200	1	1	yes	characteristic
378	C₂×C₄	#88201	1	1	yes	characteristic
379	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
380	C₈	—	26	4	no	—
381	C₈	#88071	1	8	yes	complemented
382	C₂²	#11718513	1	4	yes	—
383	C₂²	#11718516	1	2	yes	—
384	C₂²	#11718519	1	2	yes	—
385	C₂²	D₁₃×#106	1	2	yes	—
386	C₂²	#11718521	1	2	yes	—
387	C₂²	#11718525	1	4	yes	—
388	C₂²	#11718634	1	1	yes	characteristic
389	C₂²	C₄⋊C₄×Dic₁₃	1	1	yes	characteristic
390	C₂²	#11718637	1	1	yes	characteristic
391	C₂²	#11718646	1	1	yes	characteristic
392	C₂²	#11718648	1	1	yes	characteristic
393	C₂²	#11718649	1	1	yes	characteristic
394	C₂²	SD₁₆×Dic₁₃	1	4	yes	—
395	C₂²	#11718829	1	2	yes	—
396	C₂²	#11718832	1	4	yes	—
397	C₂²	#11718836	1	2	yes	—
398	C₂²	#11718882	1	1	yes	characteristic
399	C₄	—	8	4	no	—
400	C₄	—	26	8	no	—
401	C₄	—	104	4	no	—
402	C₄	#11718634	1	1	yes	characteristic
403	C₄	#11718635	1	1	yes	characteristic
404	C₄	C₄⋊C₄×Dic₁₃	1	1	yes	characteristic
405	C₄	#11718638	1	1	yes	characteristic
406	C₄	#11718646	1	1	yes	characteristic
407	C₄	#11718648	1	1	yes	characteristic
408	C₄	C₂×#88071	1	1	yes	characteristic
409	C₄	#11718891	1	1	yes	characteristic
410	C₂	#13113065	1	1	yes	characteristic
411	C₂	#106×Dic₁₃	1	2	yes	—
412	C₂	#13114858	1	2	yes	—
413	C₂	#13114991	1	1	yes	characteristic
414	C₂	#13114997	1	1	yes	characteristic
415	C₂	#13115562	1	2	yes	—
416	C₂	#13115565	1	2	yes	—
417	C₂	#13115688	1	2	yes	—
418	C₂	#13115692	1	2	yes	—

	subgroup	G/H
center	C₂⁴	D₄×D₁₃
commutator	C₂×C₄×C₁₃	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₃
Fitting	C₂²×C₁₃×#106	C₂
socle, prime radical	C₂⁴×C₁₃	C₂×D₄
cosocle	C₂³×C₄×C₁₃	C₂³
hypercenter	C₂²×#106	D₁₃
hypocenter	C₁₃	#10861
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄ ◁ C₂²×#106

Complements

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

N	H ≅ G/N	type
13. C₂×C₁₃×#106	C₄	semidirect
17. C₂×#88057	C₄	semidirect
20. C₂×C₈×Dic₁₃	C₄	semidirect
175. C₂×Dic₁₃	#106	semidirect
176. C₈×C₁₃	#95	semidirect
188. C₂×#106	Dic₁₃	semidirect
327. C₁₃	#10861	semidirect
381. C₈	#88071	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#88057	2
C₂²×C₈×Dic₁₃	2
C₂×#11718121	2
#13113065	2
C₂²×C₁₃×#106	2
#10861	13