Subgroups — #124×#1055 #15870785

Order 3328.

974 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×#1055	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₄×#1055	C₂	1	1	yes	maximal, characteristic
3	#13115773	C₂	1	1	yes	maximal, characteristic, complemented
4	#13115631	C₂	1	1	yes	maximal, characteristic
5	#13115444	C₂	1	4	yes	maximal, complemented
6	#13114953	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²⋊C₄×#1055	C₂	1	4	yes	maximal, complemented
8	C₄²×#1055	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×C₁₃×#124	C₂	1	1	yes	maximal, characteristic
10	C₂×C₁₃×#124	C₄	1	1	yes	characteristic
11	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
12	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
13	C₂³×#1055	C₂²	1	2	yes	—
14	C₁₃×#391	C₄	1	1	yes	characteristic
15	C₁₃×#390	C₄	1	1	yes	characteristic
16	C₁₃×#388	C₄	1	4	yes	—
17	C₁₃×#382	C₄	1	1	yes	characteristic
18	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
19	C₄³×C₁₃	C₂²	1	1	yes	characteristic
20	C₂×C₂²⋊#1055	C₂²	1	2	yes	—
21	C₂×C₂²⋊#1055	C₂²	1	4	yes	—
22	Q₈×#1055	—	2	4	no	—
23	D₄×#1055	—	2	4	no	—
24	C₂×C₄⋊#1055	C₂²	1	2	yes	—
25	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
27	C₂×C₄×#1055	C₂²	1	2	yes	—
28	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
29	C₂×C₄×#1055	C₂²	1	2	yes	—
30	C₂×C₄×#1055	C₂²	1	2	yes	—
31	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
32	#11718116	C₂²	1	4	yes	—
33	#11718116	C₂²	1	4	yes	—
34	C₂²×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
35	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
36	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
37	C₁₃×#124	C₈	1	8	yes	complemented
38	C₄×Q₈×C₁₃	—	2	2	no	—
39	C₄×Q₈×C₁₃	—	2	2	no	—
40	C₄×D₄×C₁₃	—	2	2	no	—
41	C₄×D₄×C₁₃	—	2	2	no	—
42	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
43	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
44	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
45	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	4	yes	—
46	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
47	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	4	yes	—
48	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
49	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
52	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
53	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
54	C₂²×#1055	—	2	4	no	—
55	C₂²×#1055	—	2	8	no	—
56	C₂²×#1055	C₂³	1	2	yes	—
57	C₂²×#1055	C₂³	1	2	yes	—
58	C₂²×#1055	C₂³	1	1	yes	characteristic
59	C₂²×#1055	C₂³	1	2	yes	—
60	C₂²×#1055	C₂³	1	1	yes	characteristic
61	C₁₃×#95	C₂×C₄	1	4	yes	—
62	C₁₃×#95	C₂×C₄	1	4	yes	—
63	C₂²⋊#1055	—	2	4	no	—
64	C₂²⋊#1055	—	2	8	no	—
65	C₄⋊#1055	—	2	2	no	—
66	C₄⋊#1055	—	2	2	no	—
67	C₄⋊#1055	—	2	4	no	—
68	C₄×#1055	—	2	2	no	—
69	C₄×#1055	—	2	4	no	—
70	C₄×#1055	—	2	4	no	—
71	C₄×#1055	—	2	4	no	—
72	C₄×#1055	D₄	1	4	yes	—
73	C₈×#124	—	13	1	no	maximal, Sylow
74	C₂⁴×C₁₃	C₂²×C₄	1	2	yes	—
75	C₂×Q₈×C₁₃	—	2	2	no	—
76	C₂×Q₈×C₁₃	—	2	2	no	—
77	C₂×Q₈×C₁₃	C₂×C₈	1	4	yes	complemented
78	C₂×D₄×C₁₃	—	2	2	no	—
79	C₂×D₄×C₁₃	—	2	2	no	—
80	C₂×D₄×C₁₃	C₂×C₈	1	4	yes	—
81	C₂²×C₄×C₁₃	—	2	2	no	—
82	C₂²×C₄×C₁₃	—	2	4	no	—
83	C₂²×C₄×C₁₃	—	2	4	no	—
84	C₂²×C₄×C₁₃	—	2	2	no	—
85	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
86	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
87	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
89	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
90	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
91	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
93	C₁₃×C₄⋊C₄	—	2	2	no	—
94	C₁₃×C₄⋊C₄	—	2	4	no	—
95	C₁₃×C₄⋊C₄	—	2	2	no	—
96	C₁₃×C₂²⋊C₄	—	2	4	no	—
97	C₁₃×C₂²⋊C₄	—	2	8	no	—
98	C₁₃×C₂²⋊C₄	C₂×C₈	1	16	yes	complemented
99	C₄²×C₁₃	—	2	4	no	—
100	C₄²×C₁₃	—	2	2	no	—
101	C₄²×C₁₃	—	2	2	no	—
102	C₄²×C₁₃	—	2	2	no	—
103	C₄²×C₁₃	—	2	2	no	—
104	C₄²×C₁₃	—	2	2	no	—
105	C₄²×C₁₃	C₂×C₈	1	4	yes	complemented
106	C₄²×C₁₃	C₂×D₄	1	2	yes	—
107	C₄²×C₁₃	#41	1	2	yes	—
108	C₂×#1055	—	2	2	no	—
109	C₂×#1055	—	2	2	no	—
110	C₂×#1055	—	2	2	no	—
111	C₂×#1055	—	2	2	no	—
112	C₂×#1055	—	2	2	no	—
113	C₂×#1055	—	2	4	no	—
114	C₂×#1055	—	2	4	no	—
115	C₂×#1055	—	4	8	no	—
116	C₂×#1055	C₂×D₄	1	2	yes	—
117	C₂×#1055	C₂×D₄	1	2	yes	—
118	C₂×#1055	#41	1	4	yes	—
119	C₂×#1055	#41	1	4	yes	—
120	C₂×C₈×Q₈	—	13	1	no	—
121	C₂×C₈×D₄	—	13	1	no	—
122	C₄×#124	D₁₃	1	1	yes	characteristic
123	#1984	—	13	1	no	—
124	#1954	—	13	1	no	—
125	#1923	—	13	4	no	—
126	#1831	—	13	1	no	—
127	C₈×C₂²⋊C₄	—	13	4	no	—
128	C₄²×C₈	—	13	1	no	—
129	C₂³×C₁₃	—	2	2	no	—
130	C₂³×C₁₃	—	2	4	no	—
131	C₂³×C₁₃	—	2	4	no	—
132	C₂³×C₁₃	—	2	2	no	—
133	C₂³×C₁₃	C₂²×C₈	1	4	yes	—
134	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
135	Q₈×C₁₃	—	2	8	no	—
136	D₄×C₁₃	—	2	8	no	—
137	C₂×C₄×C₁₃	—	2	2	no	—
138	C₂×C₄×C₁₃	—	2	2	no	—
139	C₂×C₄×C₁₃	—	2	2	no	—
140	C₂×C₄×C₁₃	—	2	2	no	—
141	C₂×C₄×C₁₃	—	2	2	no	—
142	C₂×C₄×C₁₃	—	2	2	no	—
143	C₂×C₄×C₁₃	—	2	2	no	—
144	C₂×C₄×C₁₃	—	2	2	no	—
145	C₂×C₄×C₁₃	—	2	2	no	—
146	C₂×C₄×C₁₃	—	2	4	no	—
147	C₂×C₄×C₁₃	—	2	4	no	—
148	C₂×C₄×C₁₃	—	4	2	no	—
149	C₂×C₄×C₁₃	—	4	4	no	—
150	C₂×C₄×C₁₃	—	4	2	no	—
151	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
152	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
153	C₂×C₄×C₁₃	C₂²×C₈	1	4	yes	—
154	C₂×C₄×C₁₃	C₂²×C₈	1	4	yes	—
155	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
156	C₂×C₄×C₁₃	#131	1	4	yes	—
157	C₂×C₄×C₁₃	#131	1	2	yes	—
158	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
159	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
160	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
161	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
162	#1055	—	2	4	no	—
163	#1055	—	2	2	no	—
164	#1055	—	4	2	no	—
165	#1055	—	4	2	no	—
166	#1055	#124	1	4	yes	direct product factor
167	C₂³×C₈	—	13	2	no	—
168	C₂×#124	Dic₁₃	1	1	yes	characteristic
169	C₂×C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic
170	C₂×C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
171	C₈×Q₈	—	26	4	no	—
172	C₈×D₄	—	26	4	no	—
173	C₂×C₄⋊C₈	—	13	1	no	—
174	C₂×C₄⋊C₈	—	13	1	no	—
175	C₂×C₄⋊C₈	—	13	2	no	—
176	C₂×C₂²⋊C₈	—	13	2	no	—
177	C₂×C₂²⋊C₈	—	13	4	no	—
178	C₂×C₄×C₈	—	13	1	no	—
179	C₂×C₄×C₈	—	13	2	no	—
180	C₂×C₄×C₈	—	13	2	no	—
181	C₂×C₄×C₈	—	13	1	no	—
182	C₂×C₄×C₈	—	13	2	no	—
183	#391	Dic₁₃	1	1	yes	characteristic
184	#390	Dic₁₃	1	1	yes	characteristic
185	#388	Dic₁₃	1	4	yes	—
186	#382	Dic₁₃	1	1	yes	characteristic
187	C₄×C₂²⋊C₄	C₂×D₁₃	1	4	yes	—
188	C₄³	C₂×D₁₃	1	1	yes	characteristic
189	#336	—	13	4	no	—
190	#336	—	13	4	no	—
191	C₂²×C₁₃	—	2	4	no	—
192	C₂²×C₁₃	—	2	8	no	—
193	C₂²×C₁₃	—	4	2	no	—
194	C₂²×C₁₃	—	4	4	no	—
195	C₂²×C₁₃	—	4	2	no	—
196	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
197	C₂²×C₁₃	C₄×#41	1	2	yes	—
198	C₂²×C₁₃	C₂³×C₈	1	1	yes	characteristic
199	C₂²×C₁₃	C₂×#131	1	1	yes	characteristic
200	C₂²×C₁₃	C₂×#131	1	2	yes	—
201	C₄×C₁₃	—	2	4	no	—
202	C₄×C₁₃	—	2	2	no	—
203	C₄×C₁₃	—	2	4	no	—
204	C₄×C₁₃	—	2	4	no	—
205	C₄×C₁₃	—	4	2	no	—
206	C₄×C₁₃	—	4	2	no	—
207	C₄×C₁₃	C₈×D₄	1	4	yes	—
208	C₄×C₁₃	C₂×#124	1	1	yes	characteristic
209	C₄×C₁₃	#529	1	2	yes	—
210	C₄×C₁₃	#532	1	1	yes	characteristic
211	C₂²×Q₈	C₂×Dic₁₃	1	1	yes	characteristic
212	C₂²×D₄	C₂×Dic₁₃	1	1	yes	characteristic
213	C₂³×C₄	C₂²×D₁₃	1	2	yes	—
214	C₂²×C₈	—	13	1	no	—
215	C₂²×C₈	—	13	2	no	—
216	C₂²×C₈	—	13	1	no	—
217	C₂²×C₈	—	13	2	no	—
218	C₂²×C₈	—	13	2	no	—
219	C₂²×C₈	—	26	8	no	—
220	C₂²×C₈	—	26	4	no	—
221	#124	#1055	1	8	yes	direct product factor
222	C₄×Q₈	—	2	2	no	—
223	C₄×Q₈	—	2	2	no	—
224	C₄×D₄	—	2	2	no	—
225	C₄×D₄	—	2	2	no	—
226	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
227	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
228	C₂×C₄⋊C₄	C₂×Dic₁₃	1	2	yes	—
229	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	2	yes	—
230	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	4	yes	—
231	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	4	yes	—
232	C₂×C₄²	C₂×Dic₁₃	1	2	yes	—
233	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
234	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
235	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
236	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
237	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
238	C₄⋊C₈	—	26	4	no	—
239	C₄⋊C₈	—	26	2	no	—
240	C₄⋊C₈	—	26	2	no	—
241	C₂²⋊C₈	—	26	8	no	—
242	C₂²⋊C₈	—	26	4	no	—
243	C₄×C₈	—	13	4	no	—
244	C₄×C₈	—	26	4	no	—
245	C₄×C₈	—	26	4	no	—
246	C₄×C₈	—	26	4	no	—
247	C₄×C₈	—	26	2	no	—
248	#95	C₂×Dic₁₃	1	4	yes	—
249	#95	C₂×Dic₁₃	1	4	yes	—
250	C₂×C₁₃	—	4	4	no	—
251	C₂×C₁₃	C₄×#124	1	1	yes	characteristic
252	C₂×C₁₃	C₂×C₈×D₄	1	1	yes	characteristic
253	C₂×C₁₃	#2931	1	1	yes	characteristic
254	C₂×C₁₃	C₈×#41	1	2	yes	—
255	C₂×C₁₃	#2966	1	2	yes	—
256	C₂⁴	C₂²×Dic₁₃	1	2	yes	—
257	C₂×Q₈	—	2	2	no	—
258	C₂×Q₈	—	2	2	no	—
259	C₂×Q₈	C₂×#1055	1	4	yes	complemented
260	C₂×D₄	—	2	2	no	—
261	C₂×D₄	—	2	2	no	—
262	C₂×D₄	C₂×#1055	1	4	yes	—
263	C₂²×C₄	—	2	2	no	—
264	C₂²×C₄	—	2	2	no	—
265	C₂²×C₄	—	2	4	no	—
266	C₂²×C₄	—	2	4	no	—
267	C₂²×C₄	C₂²×Dic₁₃	1	2	yes	—
268	C₂²×C₄	C₂²×Dic₁₃	1	2	yes	—
269	C₂²×C₄	C₂²×Dic₁₃	1	2	yes	—
270	C₂²×C₄	C₂²×Dic₁₃	1	2	yes	—
271	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
272	C₂²×C₄	C₂²×Dic₁₃	1	2	yes	—
273	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
274	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
275	C₂×C₈	—	13	2	no	—
276	C₂×C₈	—	13	4	no	—
277	C₂×C₈	—	13	2	no	—
278	C₂×C₈	—	13	4	no	—
279	C₂×C₈	—	26	2	no	—
280	C₂×C₈	—	26	2	no	—
281	C₂×C₈	—	26	2	no	—
282	C₂×C₈	—	26	2	no	—
283	C₂×C₈	—	26	2	no	—
284	C₂×C₈	—	26	4	no	—
285	C₂×C₈	—	26	4	no	—
286	C₂×C₈	—	52	8	no	—
287	C₄⋊C₄	—	2	2	no	—
288	C₄⋊C₄	—	2	4	no	—
289	C₄⋊C₄	—	2	2	no	—
290	C₂²⋊C₄	—	2	4	no	—
291	C₂²⋊C₄	—	2	8	no	—
292	C₂²⋊C₄	C₂×#1055	1	16	yes	complemented
293	C₄²	—	2	4	no	—
294	C₄²	—	2	2	no	—
295	C₄²	—	2	2	no	—
296	C₄²	—	2	2	no	—
297	C₄²	—	2	2	no	—
298	C₄²	—	2	2	no	—
299	C₄²	C₂×#1055	1	4	yes	complemented
300	C₄²	D₄×D₁₃	1	2	yes	—
301	C₄²	#6129	1	2	yes	—
302	C₁₃	C₈×#124	1	1	yes	characteristic, complemented, Sylow
303	C₂³	—	2	2	no	—
304	C₂³	—	2	4	no	—
305	C₂³	—	2	2	no	—
306	C₂³	—	2	4	no	—
307	C₂³	C₂²×#1055	1	4	yes	—
308	C₂³	C₂³×Dic₁₃	1	1	yes	characteristic
309	Q₈	—	2	8	no	—
310	D₄	—	2	8	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	4	no	—
321	C₂×C₄	—	2	4	no	—
322	C₂×C₄	—	4	2	no	—
323	C₂×C₄	—	4	2	no	—
324	C₂×C₄	—	4	4	no	—
325	C₂×C₄	C₂²×#1055	1	4	yes	—
326	C₂×C₄	C₂²×#1055	1	4	yes	—
327	C₂×C₄	C₂²×#1055	1	2	yes	—
328	C₂×C₄	D₄×Dic₁₃	1	2	yes	—
329	C₂×C₄	D₄×Dic₁₃	1	2	yes	—
330	C₂×C₄	#88202	1	4	yes	—
331	C₂×C₄	#88202	1	2	yes	—
332	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
333	C₂×C₄	C₂×#6129	1	1	yes	characteristic
334	C₂×C₄	#41×D₁₃	1	2	yes	—
335	C₂×C₄	#41×D₁₃	1	2	yes	—
336	C₈	—	13	4	no	—
337	C₈	—	26	2	no	—
338	C₈	—	26	4	no	—
339	C₈	—	52	2	no	—
340	C₈	—	52	2	no	—
341	C₂²	—	2	4	no	—
342	C₂²	—	2	8	no	—
343	C₂²	—	4	2	no	—
344	C₂²	—	4	2	no	—
345	C₂²	—	4	4	no	—
346	C₂²	C₂³×#1055	1	1	yes	characteristic
347	C₂²	C₂×D₄×Dic₁₃	1	1	yes	characteristic
348	C₂²	C₂×#88202	1	1	yes	characteristic
349	C₂²	C₂×#88202	1	2	yes	—
350	C₂²	#41×Dic₁₃	1	2	yes	—
351	C₄	—	2	4	no	—
352	C₄	—	2	4	no	—
353	C₄	—	2	2	no	—
354	C₄	—	2	4	no	—
355	C₄	—	4	2	no	—
356	C₄	—	4	2	no	—
357	C₄	D₄×#1055	1	4	yes	—
358	C₄	#11719373	1	1	yes	characteristic
359	C₄	D₁₃×#124	1	1	yes	characteristic
360	C₄	#11719385	1	2	yes	—
361	C₂	—	4	4	no	—
362	C₂	#124×Dic₁₃	1	1	yes	characteristic
363	C₂	C₂×D₄×#1055	1	1	yes	characteristic
364	C₂	#13123548	1	1	yes	characteristic
365	C₂	#41×#1055	1	2	yes	—
366	C₂	#13123812	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₁₃
commutator	C₂²×C₁₃	C₂³×C₈
Fitting	C₄×C₁₃×#124	C₂
socle	C₂³×C₁₃	C₂³×C₄
prime radical	C₂²×D₄×C₁₃	C₂×C₄
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	C₄×#124	D₁₃
hypocenter	C₁₃	C₈×#124
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₄×#124

Complements

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

N	H ≅ G/N	type
1. C₂×Q₈×#1055	C₂	semidirect
3. #13115773	C₂	semidirect
5. #13115444	C₂	semidirect
6. #13114953	C₂	semidirect
7. C₂²⋊C₄×#1055	C₂	semidirect
8. C₄²×#1055	C₂	semidirect
37. C₁₃×#124	C₈	semidirect
77. C₂×Q₈×C₁₃	C₂×C₈	semidirect
98. C₁₃×C₂²⋊C₄	C₂×C₈	semidirect
105. C₄²×C₁₃	C₂×C₈	semidirect
166. #1055	#124	direct (N × H)
221. #124	#1055	direct (N × H)
259. C₂×Q₈	C₂×#1055	semidirect
292. C₂²⋊C₄	C₂×#1055	semidirect
299. C₄²	C₂×#1055	semidirect
302. C₁₃	C₈×#124	semidirect

Maximal subgroups

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

subgroup	index
C₂×Q₈×#1055	2
C₂×D₄×#1055	2
#13115773	2
#13115631	2
#13115444	2
#13114953	2
C₂²⋊C₄×#1055	2
C₄²×#1055	2
C₄×C₁₃×#124	2
C₈×#124	13