Subgroups — #15768864

Order 3328.

730 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	C₂²×#88059	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718767	C₂	1	1	yes	maximal, characteristic
3	C₂×#11718151	C₂	1	2	yes	maximal
4	#13114545	C₂	1	2	yes	maximal
5	C₂×C₁₃×#405	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
7	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
8	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
9	C₂×#88180	C₂²	1	2	yes	—
10	C₂²×#6099	C₂²	1	2	yes	—
11	C₁₃×#405	—	2	1	no	—
12	C₁₃×#405	—	2	1	no	—
13	C₁₃×#405	C₄	1	2	yes	complemented
14	C₁₃×#405	C₄	1	2	yes	complemented
15	C₂×C₁₃×#97	—	2	1	no	—
16	C₂×C₄×C₈×C₁₃	—	2	1	no	—
17	C₂×#88059	—	2	2	no	—
18	C₂×#88059	—	2	1	no	—
19	C₂×#88059	—	2	1	no	—
20	C₂×#88059	C₄	1	4	yes	complemented
21	#11718767	—	2	2	no	—
22	#11718767	C₄	1	4	yes	complemented
23	C₂×#88058	—	2	1	no	—
24	C₂×#88057	—	2	1	no	—
25	#11718151	—	2	4	no	—
26	#11718124	—	2	4	no	—
27	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
28	C₂×C₁₃×M₁₆	—	2	1	no	—
29	C₂×C₁₃×M₁₆	—	2	1	no	—
30	C₂×C₁₃×M₁₆	—	2	1	no	—
31	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
32	C₂×C₁₃×M₁₆	D₄	1	2	yes	—
33	C₂×C₁₃×M₁₆	Q₈	1	2	yes	—
34	C₂²×C₈×C₁₃	—	2	1	no	—
35	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
36	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
37	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
38	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₈×C₁₃	D₄	1	2	yes	—
40	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
41	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
42	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
43	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
44	C₂²×C₈×C₁₃	Q₈	1	2	yes	—
45	C₁₃×#117	—	2	1	no	—
46	C₁₃×#117	—	2	1	no	—
47	C₁₃×#117	C₂×C₄	1	2	yes	—
48	C₁₃×#117	D₄	1	2	yes	—
49	C₂×C₁₃×C₄⋊C₄	Q₈	1	2	yes	—
50	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
51	C₂×C₄²×C₁₃	—	2	1	no	—
52	C₂×C₂²⋊Dic₁₃	—	2	2	no	—
53	#88180	—	2	2	no	—
54	#88180	—	2	2	no	—
55	#88180	—	2	2	no	—
56	#88180	C₂×C₄	1	4	yes	—
57	C₂×C₄⋊Dic₁₃	—	2	2	no	—
58	C₂×C₄×Dic₁₃	—	2	2	no	—
59	C₂×#6099	—	2	2	no	—
60	C₂×#6099	—	2	2	no	—
61	C₂×#6099	—	2	2	no	—
62	C₂×#6099	—	2	2	no	—
63	C₂×#6099	—	2	2	no	—
64	C₂×#6099	C₂×C₄	1	4	yes	—
65	C₂²×#1055	—	2	2	no	—
66	C₁₃×#97	—	2	2	no	—
67	C₁₃×#97	—	2	2	no	—
68	C₄×C₈×C₁₃	—	2	2	no	—
69	C₄×C₈×C₁₃	—	2	2	no	—
70	#88059	—	2	4	no	—
71	#88059	—	2	4	no	—
72	#88058	—	2	4	no	—
73	#88057	—	2	4	no	—
74	#10872	—	13	1	no	maximal, Sylow
75	C₂⁴×C₁₃	#41	1	1	yes	characteristic
76	C₂²×C₄×C₁₃	—	2	2	no	—
77	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
86	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
87	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
88	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
89	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
90	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
91	C₂²×Dic₁₃	—	4	2	no	—
92	C₁₃×M₁₆	—	2	2	no	—
93	C₁₃×M₁₆	—	2	2	no	—
94	C₁₃×M₁₆	—	2	2	no	—
95	C₁₃×M₁₆	C₄⋊C₄	1	4	yes	—
96	C₂×C₈×C₁₃	—	2	2	no	—
97	C₂×C₈×C₁₃	—	2	2	no	—
98	C₂×C₈×C₁₃	—	2	2	no	—
99	C₂×C₈×C₁₃	C₄²	1	2	yes	—
100	C₂×C₈×C₁₃	C₄²	1	2	yes	—
101	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
102	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
103	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
104	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
105	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
106	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
107	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
108	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
109	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
110	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
111	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
112	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
113	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
114	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
115	C₁₃×C₄⋊C₄	—	2	2	no	—
116	C₁₃×C₄⋊C₄	C₄⋊C₄	1	4	yes	—
117	C₁₃×C₂²⋊C₄	—	2	2	no	—
118	C₁₃×C₂²⋊C₄	—	2	2	no	—
119	C₄²×C₁₃	—	2	2	no	—
120	C₄²×C₁₃	—	2	2	no	—
121	C₂²⋊Dic₁₃	—	2	4	no	—
122	C₂²⋊Dic₁₃	—	4	2	no	—
123	C₄⋊Dic₁₃	—	2	4	no	—
124	C₄⋊Dic₁₃	—	4	2	no	—
125	C₄×Dic₁₃	—	2	4	no	—
126	C₄×Dic₁₃	—	4	2	no	—
127	#6099	—	2	4	no	—
128	#6099	—	2	4	no	—
129	#6099	—	4	2	no	—
130	#6099	—	4	2	no	—
131	C₂×#1055	—	2	4	no	—
132	C₂×#1055	—	4	2	no	—
133	C₂×#1055	—	4	2	no	—
134	C₂²×#108	—	13	1	no	—
135	C₂×#427	—	13	1	no	—
136	C₂×#405	D₁₃	1	1	yes	characteristic
137	C₂×#344	—	13	2	no	—
138	#1733	—	13	2	no	—
139	C₂³×C₁₃	—	4	2	no	—
140	C₂³×C₁₃	#117	1	1	yes	characteristic
141	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
142	C₂³×C₁₃	C₄×Q₈	1	1	yes	characteristic
143	C₂³×C₁₃	#121	1	1	yes	characteristic
144	C₂³×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
145	C₂³×C₁₃	#124	1	1	yes	characteristic
146	C₂³×C₁₃	#125	1	1	yes	characteristic
147	C₂×C₄×C₁₃	—	2	4	no	—
148	C₂×C₄×C₁₃	—	4	4	no	—
149	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
150	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
152	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
154	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
155	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
156	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
157	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
158	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
159	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
160	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
161	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
162	C₂×C₄×C₁₃	C₄×Q₈	1	1	yes	characteristic
163	C₂×C₄×C₁₃	C₄×Q₈	1	1	yes	characteristic
164	C₂×C₄×C₁₃	C₄×Q₈	1	1	yes	characteristic
165	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
166	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
167	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
168	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
169	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
170	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
171	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
172	C₂×C₄×C₁₃	#125	1	1	yes	characteristic
173	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
174	C₂×C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
175	C₂×C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
176	C₂×C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
177	C₂×Dic₁₃	—	4	4	no	—
178	C₂×Dic₁₃	—	8	4	no	—
179	C₈×C₁₃	—	2	4	no	—
180	C₈×C₁₃	#95	1	2	yes	—
181	C₈×C₁₃	#95	1	2	yes	—
182	C₈×C₁₃	#95	1	2	yes	—
183	C₈×C₁₃	#95	1	2	yes	—
184	#1055	—	4	4	no	—
185	C₂²×M₁₆	—	13	2	no	—
186	C₂²×M₁₆	C₂×D₁₃	1	1	yes	characteristic
187	C₂³×C₈	C₂×D₁₃	1	1	yes	characteristic
188	C₂×#117	—	13	2	no	—
189	C₂×#117	C₂×D₁₃	1	1	yes	characteristic
190	C₂×#108	—	13	4	no	—
191	C₂×#108	—	26	2	no	—
192	C₂×#108	—	26	1	no	—
193	C₂×#108	—	26	1	no	—
194	#427	—	13	4	no	—
195	#427	—	26	2	no	—
196	C₂×#107	—	26	1	no	—
197	C₂×#106	—	26	1	no	—
198	#405	—	2	1	no	—
199	#405	—	2	1	no	—
200	#405	Dic₁₃	1	2	yes	complemented
201	#405	Dic₁₃	1	2	yes	complemented
202	C₂×#97	—	2	1	no	—
203	C₂×C₄×C₈	—	2	1	no	—
204	#344	—	26	4	no	—
205	#339	—	26	4	no	—
206	C₂²×C₁₃	—	2	2	no	—
207	C₂²×C₁₃	—	2	2	no	—
208	C₂²×C₁₃	—	2	2	no	—
209	C₂²×C₁₃	—	4	1	no	—
210	C₂²×C₁₃	—	4	1	no	—
211	C₂²×C₁₃	—	4	1	no	—
212	C₂²×C₁₃	—	4	1	no	—
213	C₂²×C₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
214	C₂²×C₁₃	#380	1	1	yes	characteristic
215	C₂²×C₁₃	#382	1	1	yes	characteristic
216	C₂²×C₁₃	#389	1	1	yes	characteristic
217	C₂²×C₁₃	#389	1	1	yes	characteristic
218	C₂²×C₁₃	#390	1	1	yes	characteristic
219	C₂²×C₁₃	#391	1	1	yes	characteristic
220	C₄×C₁₃	—	4	4	no	—
221	C₄×C₁₃	C₂×#95	1	1	yes	characteristic
222	C₄×C₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
223	C₄×C₁₃	#380	1	1	yes	characteristic
224	C₄×C₁₃	#384	1	1	yes	characteristic
225	C₄×C₁₃	#389	1	1	yes	characteristic
226	C₄×C₁₃	#389	1	1	yes	characteristic
227	C₄×C₁₃	#390	1	1	yes	characteristic
228	C₄×C₁₃	#391	1	1	yes	characteristic
229	Dic₁₃	—	8	4	no	—
230	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
231	C₂×M₁₆	—	2	1	no	—
232	C₂×M₁₆	—	2	1	no	—
233	C₂×M₁₆	—	2	1	no	—
234	C₂×M₁₆	—	13	4	no	—
235	C₂×M₁₆	—	26	2	no	—
236	C₂×M₁₆	—	26	2	no	—
237	C₂×M₁₆	—	26	2	no	—
238	C₂×M₁₆	—	26	2	no	—
239	C₂×M₁₆	—	26	2	no	—
240	C₂×M₁₆	Dic₂₆	1	2	yes	—
241	C₂×M₁₆	D₅₂	1	2	yes	—
242	C₂×M₁₆	C₂×Dic₁₃	1	2	yes	—
243	C₂²×C₈	—	2	1	no	—
244	C₂²×C₈	—	26	2	no	—
245	C₂²×C₈	Dic₂₆	1	2	yes	—
246	C₂²×C₈	C₄×D₁₃	1	2	yes	—
247	C₂²×C₈	C₄×D₁₃	1	2	yes	—
248	C₂²×C₈	D₅₂	1	2	yes	—
249	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
250	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
251	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
252	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
253	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
254	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
255	#117	—	2	1	no	—
256	#117	—	2	1	no	—
257	#117	—	13	4	no	—
258	#117	—	26	2	no	—
259	#117	—	26	2	no	—
260	#117	—	26	2	no	—
261	#117	D₅₂	1	2	yes	—
262	#117	C₂×Dic₁₃	1	2	yes	—
263	C₂×C₄⋊C₄	—	26	2	no	—
264	C₂×C₄⋊C₄	Dic₂₆	1	2	yes	—
265	C₂×C₂²⋊C₄	—	2	1	no	—
266	C₂×C₂²⋊C₄	—	26	2	no	—
267	C₂×C₄²	—	2	1	no	—
268	C₂×C₄²	—	26	2	no	—
269	#108	—	26	4	no	—
270	#108	—	26	4	no	—
271	#107	—	26	4	no	—
272	#106	—	26	4	no	—
273	#97	—	2	2	no	—
274	#97	—	2	2	no	—
275	C₄×C₈	—	2	2	no	—
276	C₄×C₈	—	2	2	no	—
277	C₂×C₁₃	—	2	1	no	—
278	C₂×C₁₃	—	2	1	no	—
279	C₂×C₁₃	—	2	1	no	—
280	C₂×C₁₃	—	2	1	no	—
281	C₂×C₁₃	—	2	1	no	—
282	C₂×C₁₃	—	2	1	no	—
283	C₂×C₁₃	C₄⋊#95	1	1	yes	characteristic
284	C₂×C₁₃	#1814	1	2	yes	—
285	C₂⁴	#6127	1	1	yes	characteristic
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	52	2	no	—
288	C₂²×C₄	C₂×Dic₂₆	1	1	yes	characteristic
289	C₂²×C₄	C₂×Dic₂₆	1	1	yes	characteristic
290	C₂²×C₄	C₂×Dic₂₆	1	1	yes	characteristic
291	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
292	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
293	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
294	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
295	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
296	C₂²×C₄	#6127	1	1	yes	characteristic
297	C₂²×C₄	#6127	1	1	yes	characteristic
298	C₂²×C₄	#6127	1	1	yes	characteristic
299	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
300	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
301	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
302	M₁₆	—	2	2	no	—
303	M₁₆	—	2	2	no	—
304	M₁₆	—	2	2	no	—
305	M₁₆	—	26	4	no	—
306	M₁₆	—	26	4	no	—
307	M₁₆	—	52	2	no	—
308	M₁₆	—	52	2	no	—
309	M₁₆	C₄⋊Dic₁₃	1	4	yes	—
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	26	4	no	—
314	C₂×C₈	—	52	2	no	—
315	C₂×C₈	—	52	2	no	—
316	C₂×C₈	C₄×Dic₁₃	1	2	yes	—
317	C₂×C₈	C₄×Dic₁₃	1	2	yes	—
318	C₂×C₈	#6101	1	2	yes	—
319	C₂×C₈	#6101	1	2	yes	—
320	C₂×C₈	#6101	1	2	yes	—
321	C₂×C₈	#6101	1	2	yes	—
322	C₂×C₈	C₄⋊Dic₁₃	1	2	yes	—
323	C₂×C₈	C₄⋊Dic₁₃	1	2	yes	—
324	C₂×C₈	#6103	1	2	yes	—
325	C₂×C₈	#6103	1	2	yes	—
326	C₂×C₈	#6103	1	2	yes	—
327	C₂×C₈	#6103	1	2	yes	—
328	C₂×C₈	C₂²⋊Dic₁₃	1	1	yes	characteristic
329	C₂×C₈	C₂²⋊Dic₁₃	1	1	yes	characteristic
330	C₂×C₈	C₂²⋊Dic₁₃	1	1	yes	characteristic
331	C₂×C₈	C₂²⋊Dic₁₃	1	1	yes	characteristic
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	26	4	no	—
334	C₄⋊C₄	—	52	2	no	—
335	C₄⋊C₄	C₄⋊Dic₁₃	1	4	yes	—
336	C₂²⋊C₄	—	2	2	no	—
337	C₂²⋊C₄	—	2	2	no	—
338	C₂²⋊C₄	—	26	4	no	—
339	C₂²⋊C₄	—	52	2	no	—
340	C₄²	—	2	2	no	—
341	C₄²	—	2	2	no	—
342	C₄²	—	26	4	no	—
343	C₄²	—	52	2	no	—
344	C₁₃	#10872	1	1	yes	characteristic, complemented, Sylow
345	C₂³	—	4	2	no	—
346	C₂³	C₄×Dic₂₆	1	1	yes	characteristic
347	C₂³	#88124	1	1	yes	characteristic
348	C₂³	C₄×D₅₂	1	1	yes	characteristic
349	C₂³	#88129	1	1	yes	characteristic
350	C₂³	#88178	1	1	yes	characteristic
351	C₂³	#88180	1	1	yes	characteristic
352	C₂³	#88184	1	1	yes	characteristic
353	C₂×C₄	—	2	4	no	—
354	C₂×C₄	—	4	4	no	—
355	C₂×C₄	—	52	4	no	—
356	C₂×C₄	—	104	4	no	—
357	C₂×C₄	C₄×Dic₂₆	1	1	yes	characteristic
358	C₂×C₄	C₄×Dic₂₆	1	1	yes	characteristic
359	C₂×C₄	C₄×Dic₂₆	1	1	yes	characteristic
360	C₂×C₄	#88123	1	1	yes	characteristic
361	C₂×C₄	#88123	1	1	yes	characteristic
362	C₂×C₄	#88123	1	1	yes	characteristic
363	C₂×C₄	#88124	1	1	yes	characteristic
364	C₂×C₄	C₄×D₅₂	1	1	yes	characteristic
365	C₂×C₄	C₄×D₅₂	1	1	yes	characteristic
366	C₂×C₄	C₄×D₅₂	1	1	yes	characteristic
367	C₂×C₄	#88128	1	1	yes	characteristic
368	C₂×C₄	#88129	1	1	yes	characteristic
369	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
370	C₂×C₄	C₂×#6101	1	1	yes	characteristic
371	C₂×C₄	C₂×#6101	1	1	yes	characteristic
372	C₂×C₄	#88178	1	1	yes	characteristic
373	C₂×C₄	#88178	1	1	yes	characteristic
374	C₂×C₄	#88178	1	1	yes	characteristic
375	C₂×C₄	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
376	C₂×C₄	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
377	C₂×C₄	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
378	C₂×C₄	#88180	1	1	yes	characteristic
379	C₂×C₄	C₂×#6103	1	1	yes	characteristic
380	C₂×C₄	C₂×#6103	1	1	yes	characteristic
381	C₂×C₄	#88184	1	1	yes	characteristic
382	C₂×C₄	#88184	1	1	yes	characteristic
383	C₂×C₄	#88184	1	1	yes	characteristic
384	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
385	C₈	—	2	4	no	—
386	C₈	—	52	4	no	—
387	C₈	#88071	1	2	yes	—
388	C₈	#88071	1	2	yes	—
389	C₈	#88071	1	2	yes	—
390	C₈	#88071	1	2	yes	—
391	C₂²	—	2	2	no	—
392	C₂²	—	2	2	no	—
393	C₂²	—	2	2	no	—
394	C₂²	—	4	1	no	—
395	C₂²	—	4	1	no	—
396	C₂²	—	4	1	no	—
397	C₂²	—	4	1	no	—
398	C₂²	#11718589	1	1	yes	characteristic
399	C₂²	#11718589	1	1	yes	characteristic
400	C₂²	#11718590	1	1	yes	characteristic
401	C₂²	C₄×C₄⋊Dic₁₃	1	1	yes	characteristic
402	C₂²	#11718597	1	1	yes	characteristic
403	C₂²	#11718600	1	1	yes	characteristic
404	C₂²	#11718873	1	1	yes	characteristic
405	C₄	—	4	4	no	—
406	C₄	—	104	4	no	—
407	C₄	#11718589	1	1	yes	characteristic
408	C₄	#11718589	1	1	yes	characteristic
409	C₄	#11718590	1	1	yes	characteristic
410	C₄	C₄×C₄⋊Dic₁₃	1	1	yes	characteristic
411	C₄	#11718596	1	1	yes	characteristic
412	C₄	#11718600	1	1	yes	characteristic
413	C₄	C₂×#88071	1	1	yes	characteristic
414	C₄	#11718873	1	1	yes	characteristic
415	C₂	—	2	1	no	—
416	C₂	—	2	1	no	—
417	C₂	—	2	1	no	—
418	C₂	—	2	1	no	—
419	C₂	—	2	1	no	—
420	C₂	—	2	1	no	—
421	C₂	#13113066	1	1	yes	characteristic
422	C₂	#13114890	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	#88184
commutator	C₂×C₄×C₁₃	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₃
Fitting	C₂×C₁₃×#405	C₂
socle	C₂²×C₁₃	#380
prime radical	C₂⁴×C₁₃	#41
cosocle	C₂³×C₄×C₁₃	C₂³
hypercenter	C₂×#405	D₁₃
hypocenter	C₁₃	#10872
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂×#405

Complements

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

N	H ≅ G/N	type
13. C₁₃×#405	C₄	semidirect
14. C₁₃×#405	C₄	semidirect
20. C₂×#88059	C₄	semidirect
22. #11718767	C₄	semidirect
200. #405	Dic₁₃	semidirect
201. #405	Dic₁₃	semidirect
344. C₁₃	#10872	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#88059	2
C₂×#11718767	2
C₂×#11718151	2
#13114545	2
C₂×C₁₃×#405	2
#10872	13