Subgroups — C₂×#13115627 #15866488

Order 3328.

858 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718786	C₂	1	2	yes	maximal
2	C₂²×#88059	C₂	1	1	yes	maximal, characteristic
3	C₂×#11718762	C₂	1	1	yes	maximal, characteristic
4	#13115627	C₂	1	8	yes	maximal, direct product factor
5	C₂×#11718151	C₂	1	2	yes	maximal
6	C₂²×C₁₃×#108	C₂	1	1	yes	maximal, characteristic
7	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	—
8	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
9	C₂×#88180	C₂²	1	1	yes	characteristic
10	C₂²×#6099	C₂²	1	2	yes	—
11	C₂²×#6099	C₂²	1	1	yes	characteristic
12	C₂×C₁₃×#108	C₄	1	4	yes	complemented
13	C₂×C₁₃×#108	C₄	1	4	yes	complemented
14	C₂×C₁₃×#108	C₂²	1	4	yes	—
15	#11718786	—	2	4	no	—
16	#11718786	C₂²	1	8	yes	—
17	C₂×#88059	—	2	1	no	—
18	C₂×#88059	—	2	1	no	—
19	C₂×#88059	—	2	2	no	—
20	C₂×#88059	—	2	4	no	—
21	C₂×#88059	C₂²	1	4	yes	—
22	#11718762	—	2	2	no	—
23	#11718762	C₂²	1	4	yes	—
24	C₂×#88055	—	2	1	no	—
25	C₂×C₈×Dic₁₃	—	2	1	no	—
26	#11718151	C₂²	1	8	yes	—
27	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
28	C₂×C₁₃×M₁₆	—	2	2	no	—
29	C₂×C₁₃×M₁₆	—	2	2	no	—
30	C₂×C₁₃×M₁₆	—	2	2	no	—
31	C₂×C₁₃×M₁₆	C₂×C₄	1	4	yes	—
32	C₂×C₁₃×M₁₆	C₂×C₄	1	4	yes	—
33	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
34	C₂²×C₈×C₁₃	—	2	2	no	—
35	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
36	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
37	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
38	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
39	C₂²×C₈×C₁₃	D₄	1	2	yes	—
40	C₂²×C₈×C₁₃	Q₈	1	2	yes	—
41	C₂²×C₈×C₁₃	Q₈	1	2	yes	—
42	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
43	C₂×C₂²⋊Dic₁₃	Q₈	1	2	yes	—
44	#88180	—	2	1	no	—
45	#88180	—	2	1	no	—
46	#88180	Q₈	1	2	yes	—
47	#88180	C₂³	1	2	yes	—
48	C₂×C₄⋊Dic₁₃	—	2	1	no	—
49	C₂×C₄×Dic₁₃	—	2	1	no	—
50	C₂×#6099	—	2	1	no	—
51	C₂×#6099	—	2	1	no	—
52	C₂×#6099	—	2	1	no	—
53	C₂×#6099	—	2	2	no	—
54	C₂×#6099	—	2	2	no	—
55	C₂×#6099	—	2	2	no	—
56	C₂×#6099	—	2	2	no	—
57	C₂×#6099	—	2	2	no	—
58	C₂×#6099	D₄	1	2	yes	—
59	C₂×#6099	D₄	1	2	yes	—
60	C₂×#6099	C₂³	1	4	yes	—
61	C₂×#6099	C₂³	1	2	yes	—
62	C₂²×#1055	—	2	1	no	—
63	C₂²×#1055	—	2	2	no	—
64	C₁₃×#108	C₂×C₄	1	16	yes	complemented
65	#88059	—	2	4	no	—
66	#88059	—	2	4	no	—
67	#88059	—	2	16	no	—
68	#88055	—	2	4	no	—
69	C₈×Dic₁₃	—	2	4	no	—
70	C₂×#1953	—	13	1	no	maximal, Sylow
71	C₂⁴×C₁₃	C₂×Q₈	1	1	yes	characteristic
72	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
73	C₂²×C₄×C₁₃	C₂²×C₄	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×D₄	1	1	yes	characteristic
77	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
79	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
80	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
81	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
82	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
83	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
84	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
85	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
86	C₂²×Dic₁₃	—	2	2	no	—
87	C₁₃×M₁₆	—	2	4	no	—
88	C₁₃×M₁₆	—	2	4	no	—
89	C₁₃×M₁₆	—	2	4	no	—
90	C₁₃×M₁₆	C₂²×C₄	1	8	yes	—
91	C₂×C₈×C₁₃	—	2	4	no	—
92	C₂×C₈×C₁₃	—	2	4	no	—
93	C₂×C₈×C₁₃	—	2	4	no	—
94	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
95	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
96	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
97	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
98	C₂×C₈×C₁₃	C₄⋊C₄	1	4	yes	—
99	C₂×C₈×C₁₃	C₄⋊C₄	1	4	yes	—
100	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
101	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
102	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
103	C₂×C₈×C₁₃	C₂×Q₈	1	4	yes	—
104	C₂²⋊Dic₁₃	—	2	2	no	—
105	C₂²⋊Dic₁₃	C₂×Q₈	1	4	yes	—
106	C₄⋊Dic₁₃	—	2	2	no	—
107	C₄⋊Dic₁₃	—	2	2	no	—
108	C₄×Dic₁₃	—	2	2	no	—
109	C₄×Dic₁₃	—	2	2	no	—
110	#6099	—	2	2	no	—
111	#6099	—	2	2	no	—
112	#6099	—	2	2	no	—
113	#6099	—	2	4	no	—
114	#6099	—	2	4	no	—
115	#6099	—	4	2	no	—
116	#6099	—	4	2	no	—
117	#6099	C₂×D₄	1	4	yes	—
118	C₂×#1055	—	2	2	no	—
119	C₂×#1055	—	2	2	no	—
120	C₂×#1055	—	2	2	no	—
121	C₂×#1055	—	2	4	no	—
122	C₂×#1055	—	4	2	no	—
123	C₂×#1055	—	4	2	no	—
124	C₂×#430	—	13	2	no	—
125	C₂²×#108	—	13	1	no	—
126	C₂²×#108	D₁₃	1	1	yes	characteristic
127	C₂×#405	—	13	1	no	—
128	#1953	—	13	8	no	—
129	C₂×#344	—	13	2	no	—
130	C₂³×C₁₃	—	4	2	no	—
131	C₂³×C₁₃	C₄×Q₈	1	1	yes	characteristic
132	C₂³×C₁₃	C₄×Q₈	1	1	yes	characteristic
133	C₂³×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
134	C₂³×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
135	C₂³×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
136	C₂³×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
137	C₂³×C₁₃	C₂²×Q₈	1	1	yes	characteristic
138	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
139	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
140	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
141	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
142	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
143	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
144	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
145	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
146	C₂×C₄×C₁₃	C₄×Q₈	1	1	yes	characteristic
147	C₂×C₄×C₁₃	C₄×Q₈	1	1	yes	characteristic
148	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
149	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
150	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
151	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
152	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
153	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
154	C₂×C₄×C₁₃	#125	1	1	yes	characteristic
155	C₂×C₄×C₁₃	#125	1	1	yes	characteristic
156	C₂×C₄×C₁₃	#125	1	1	yes	characteristic
157	C₂×C₄×C₁₃	#125	1	1	yes	characteristic
158	C₂×C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
159	C₂×C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
160	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
161	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
163	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
164	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
165	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
166	C₂×Dic₁₃	—	2	4	no	—
167	C₂×Dic₁₃	—	4	4	no	—
168	C₈×C₁₃	—	2	8	no	—
169	C₈×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
170	C₈×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
171	#1055	—	2	4	no	—
172	#1055	—	4	4	no	—
173	C₂²×M₁₆	—	13	1	no	—
174	C₂²×M₁₆	—	13	2	no	—
175	C₂²×M₁₆	C₂×D₁₃	1	2	yes	—
176	C₂³×C₈	C₂×D₁₃	1	1	yes	characteristic
177	C₂×#117	—	13	1	no	—
178	#430	—	13	8	no	—
179	#430	—	26	4	no	—
180	C₂×#108	—	13	4	no	—
181	C₂×#108	—	26	4	no	—
182	C₂×#108	—	26	1	no	—
183	C₂×#108	—	26	1	no	—
184	C₂×#108	—	26	2	no	—
185	C₂×#108	Dic₁₃	1	4	yes	complemented
186	C₂×#108	Dic₁₃	1	4	yes	complemented
187	C₂×#108	C₂×D₁₃	1	4	yes	—
188	#405	—	13	4	no	—
189	#405	—	26	2	no	—
190	C₂×#97	—	26	1	no	—
191	C₂×C₄×C₈	—	26	1	no	—
192	#344	—	13	8	no	—
193	C₂²×C₁₃	—	2	2	no	—
194	C₂²×C₁₃	—	2	2	no	—
195	C₂²×C₁₃	—	2	2	no	—
196	C₂²×C₁₃	—	4	1	no	—
197	C₂²×C₁₃	—	4	1	no	—
198	C₂²×C₁₃	—	4	1	no	—
199	C₂²×C₁₃	—	4	1	no	—
200	C₂²×C₁₃	#389	1	1	yes	characteristic
201	C₂²×C₁₃	#389	1	1	yes	characteristic
202	C₂²×C₁₃	#389	1	1	yes	characteristic
203	C₂²×C₁₃	#389	1	1	yes	characteristic
204	C₂²×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
205	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
206	C₂²×C₁₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
207	C₄×C₁₃	#389	1	1	yes	characteristic
208	C₄×C₁₃	#389	1	1	yes	characteristic
209	C₄×C₁₃	#389	1	1	yes	characteristic
210	C₄×C₁₃	#389	1	1	yes	characteristic
211	C₄×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
212	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
213	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
214	C₄×C₁₃	C₂×#125	1	1	yes	characteristic
215	Dic₁₃	—	4	4	no	—
216	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
217	C₂×M₁₆	—	2	2	no	—
218	C₂×M₁₆	—	2	2	no	—
219	C₂×M₁₆	—	2	2	no	—
220	C₂×M₁₆	—	13	2	no	—
221	C₂×M₁₆	—	13	2	no	—
222	C₂×M₁₆	—	13	2	no	—
223	C₂×M₁₆	—	13	4	no	—
224	C₂×M₁₆	—	26	1	no	—
225	C₂×M₁₆	—	26	1	no	—
226	C₂×M₁₆	—	26	1	no	—
227	C₂×M₁₆	—	26	2	no	—
228	C₂×M₁₆	—	26	2	no	—
229	C₂×M₁₆	—	26	2	no	—
230	C₂×M₁₆	—	26	2	no	—
231	C₂×M₁₆	—	26	2	no	—
232	C₂×M₁₆	C₂×Dic₁₃	1	4	yes	—
233	C₂×M₁₆	C₂×Dic₁₃	1	4	yes	—
234	C₂×M₁₆	C₂²×D₁₃	1	4	yes	—
235	C₂²×C₈	—	2	2	no	—
236	C₂²×C₈	—	26	1	no	—
237	C₂²×C₈	—	26	2	no	—
238	C₂²×C₈	Dic₂₆	1	2	yes	—
239	C₂²×C₈	Dic₂₆	1	2	yes	—
240	C₂²×C₈	D₅₂	1	1	yes	characteristic
241	C₂²×C₈	D₅₂	1	1	yes	characteristic
242	C₂²×C₈	D₅₂	1	2	yes	—
243	C₂²×C₈	C₂×Dic₁₃	1	2	yes	—
244	C₂²×C₈	C₂×Dic₁₃	1	2	yes	—
245	C₂²×C₈	C₂²×D₁₃	1	2	yes	—
246	#117	—	13	2	no	—
247	#117	—	13	2	no	—
248	#117	—	26	1	no	—
249	#117	—	26	1	no	—
250	C₂×C₄⋊C₄	—	26	1	no	—
251	C₂×C₂²⋊C₄	—	13	2	no	—
252	C₂×C₄²	—	26	1	no	—
253	#108	—	26	16	no	—
254	#108	—	26	4	no	—
255	#108	—	26	4	no	—
256	#108	C₂×Dic₁₃	1	16	yes	complemented
257	#97	—	26	4	no	—
258	C₄×C₈	—	26	4	no	—
259	C₂×C₁₃	—	2	1	no	—
260	C₂×C₁₃	—	2	1	no	—
261	C₂×C₁₃	—	2	1	no	—
262	C₂×C₁₃	—	2	1	no	—
263	C₂×C₁₃	—	2	1	no	—
264	C₂×C₁₃	—	2	1	no	—
265	C₂×C₁₃	#1953	1	2	yes	complemented
266	C₂×C₁₃	C₂×#389	1	1	yes	characteristic
267	C₂⁴	Q₈×D₁₃	1	1	yes	characteristic
268	C₂²×C₄	—	26	2	no	—
269	C₂²×C₄	C₂×Dic₂₆	1	1	yes	characteristic
270	C₂²×C₄	C₂×Dic₂₆	1	1	yes	characteristic
271	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
272	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
273	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
274	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
275	C₂²×C₄	#6129	1	1	yes	characteristic
276	C₂²×C₄	#6129	1	1	yes	characteristic
277	C₂²×C₄	Q₈×D₁₃	1	1	yes	characteristic
278	C₂²×C₄	#6131	1	1	yes	characteristic
279	C₂²×C₄	#6131	1	1	yes	characteristic
280	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
281	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
282	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
283	M₁₆	—	2	4	no	—
284	M₁₆	—	2	4	no	—
285	M₁₆	—	2	4	no	—
286	M₁₆	—	13	4	no	—
287	M₁₆	—	26	2	no	—
288	M₁₆	—	26	2	no	—
289	M₁₆	—	26	2	no	—
290	M₁₆	—	26	4	no	—
291	M₁₆	—	26	4	no	—
292	M₁₆	—	52	2	no	—
293	M₁₆	—	52	2	no	—
294	M₁₆	C₂²×Dic₁₃	1	8	yes	—
295	C₂×C₈	—	2	4	no	—
296	C₂×C₈	—	2	4	no	—
297	C₂×C₈	—	2	4	no	—
298	C₂×C₈	—	26	2	no	—
299	C₂×C₈	—	26	2	no	—
300	C₂×C₈	—	26	2	no	—
301	C₂×C₈	—	26	4	no	—
302	C₂×C₈	—	52	2	no	—
303	C₂×C₈	—	52	2	no	—
304	C₂×C₈	C₄⋊Dic₁₃	1	2	yes	—
305	C₂×C₈	C₄⋊Dic₁₃	1	2	yes	—
306	C₂×C₈	C₄⋊Dic₁₃	1	2	yes	—
307	C₂×C₈	C₄⋊Dic₁₃	1	2	yes	—
308	C₂×C₈	C₄⋊Dic₁₃	1	4	yes	—
309	C₂×C₈	C₄⋊Dic₁₃	1	4	yes	—
310	C₂×C₈	C₂×Dic₂₆	1	4	yes	—
311	C₂×C₈	C₂×D₅₂	1	2	yes	—
312	C₂×C₈	C₂×D₅₂	1	2	yes	—
313	C₂×C₈	C₂²×Dic₁₃	1	4	yes	—
314	C₄⋊C₄	—	26	2	no	—
315	C₄⋊C₄	—	26	2	no	—
316	C₂²⋊C₄	—	13	4	no	—
317	C₂²⋊C₄	—	26	2	no	—
318	C₄²	—	26	2	no	—
319	C₄²	—	26	2	no	—
320	C₁₃	C₂×#1953	1	1	yes	characteristic, complemented, Sylow
321	C₂³	—	4	2	no	—
322	C₂³	#88142	1	1	yes	characteristic
323	C₂³	#88142	1	1	yes	characteristic
324	C₂³	#88151	1	1	yes	characteristic
325	C₂³	#88151	1	1	yes	characteristic
326	C₂³	Q₈×Dic₁₃	1	1	yes	characteristic
327	C₂³	Q₈×Dic₁₃	1	1	yes	characteristic
328	C₂³	C₂×Q₈×D₁₃	1	1	yes	characteristic
329	C₂×C₄	—	26	4	no	—
330	C₂×C₄	—	52	4	no	—
331	C₂×C₄	#88142	1	1	yes	characteristic
332	C₂×C₄	#88142	1	1	yes	characteristic
333	C₂×C₄	#88144	1	1	yes	characteristic
334	C₂×C₄	#88144	1	1	yes	characteristic
335	C₂×C₄	#88144	1	1	yes	characteristic
336	C₂×C₄	#88144	1	1	yes	characteristic
337	C₂×C₄	#88149	1	1	yes	characteristic
338	C₂×C₄	#88149	1	1	yes	characteristic
339	C₂×C₄	#88149	1	1	yes	characteristic
340	C₂×C₄	#88149	1	1	yes	characteristic
341	C₂×C₄	#88151	1	1	yes	characteristic
342	C₂×C₄	#88151	1	1	yes	characteristic
343	C₂×C₄	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
344	C₂×C₄	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
345	C₂×C₄	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
346	C₂×C₄	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
347	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
348	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
349	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
350	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
351	C₂×C₄	Q₈×Dic₁₃	1	1	yes	characteristic
352	C₂×C₄	Q₈×Dic₁₃	1	1	yes	characteristic
353	C₂×C₄	C₂²×Dic₂₆	1	1	yes	characteristic
354	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
355	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
356	C₂×C₄	C₂×#6129	1	1	yes	characteristic
357	C₂×C₄	C₂×#6131	1	1	yes	characteristic
358	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
359	C₈	—	2	8	no	—
360	C₈	—	26	4	no	—
361	C₈	—	52	4	no	—
362	C₈	C₂×C₄⋊Dic₁₃	1	4	yes	—
363	C₈	C₂×C₄⋊Dic₁₃	1	4	yes	—
364	C₂²	—	2	2	no	—
365	C₂²	—	2	2	no	—
366	C₂²	—	2	2	no	—
367	C₂²	—	4	1	no	—
368	C₂²	—	4	1	no	—
369	C₂²	—	4	1	no	—
370	C₂²	—	4	1	no	—
371	C₂²	#11718646	1	1	yes	characteristic
372	C₂²	#11718646	1	1	yes	characteristic
373	C₂²	#11718646	1	1	yes	characteristic
374	C₂²	#11718646	1	1	yes	characteristic
375	C₂²	C₂×#88142	1	1	yes	characteristic
376	C₂²	C₂×#88151	1	1	yes	characteristic
377	C₂²	C₂×Q₈×Dic₁₃	1	1	yes	characteristic
378	C₄	—	52	4	no	—
379	C₄	#11718646	1	1	yes	characteristic
380	C₄	#11718646	1	1	yes	characteristic
381	C₄	#11718646	1	1	yes	characteristic
382	C₄	#11718646	1	1	yes	characteristic
383	C₄	C₂×#88144	1	1	yes	characteristic
384	C₄	C₂×#88149	1	1	yes	characteristic
385	C₄	C₂²×C₄⋊Dic₁₃	1	1	yes	characteristic
386	C₄	C₂×D₄×Dic₁₃	1	1	yes	characteristic
387	C₂	—	2	1	no	—
388	C₂	—	2	1	no	—
389	C₂	—	2	1	no	—
390	C₂	—	2	1	no	—
391	C₂	—	2	1	no	—
392	C₂	—	2	1	no	—
393	C₂	#13115627	1	2	yes	direct product factor
394	C₂	C₂×#11718646	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#88149
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₂²×C₁₃×#108	C₂
socle	C₂²×C₁₃	#389
prime radical	C₂⁴×C₁₃	C₂×Q₈
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	C₂²×#108	D₁₃
hypocenter	C₁₃	C₂×#1953
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂²×#108

Complements

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

N	H ≅ G/N	type
4. #13115627	C₂	direct (N × H)
12. C₂×C₁₃×#108	C₄	semidirect
13. C₂×C₁₃×#108	C₄	semidirect
64. C₁₃×#108	C₂×C₄	semidirect
185. C₂×#108	Dic₁₃	semidirect
186. C₂×#108	Dic₁₃	semidirect
256. #108	C₂×Dic₁₃	semidirect
265. C₂×C₁₃	#1953	semidirect
320. C₁₃	C₂×#1953	semidirect
393. C₂	#13115627	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×#11718786	2
C₂²×#88059	2
C₂×#11718762	2
#13115627	2
C₂×#11718151	2
C₂²×C₁₃×#108	2
C₂×#1953	13

Subgroups — C2×#13115627 #15866488

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13115627 #15866488