Subgroups — C₁₁₃×#23399 #43291419

Order 28928.

2062 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#575×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁₃×#3449	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#532×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×#104×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁₃×#2896	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#413×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₁₃×#2005	C₂	1	2	yes	maximal, complemented
8	C₁₁₃×#2004	C₂	1	2	yes	maximal, complemented
9	C₁₁₃×#2003	C₂	1	2	yes	maximal, complemented
10	C₁₁₃×#2002	C₂	1	2	yes	maximal, complemented
11	C₂×#339×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₁₁₃	C₂²	1	1	yes	characteristic
13	C₂²×#41×C₁₁₃	C₂²	1	1	yes	characteristic
14	C₂²×#41×C₁₁₃	C₂²	1	1	yes	characteristic
15	#575×C₁₁₃	—	2	4	no	—
16	#575×C₁₁₃	—	2	4	no	—
17	C₂×#137×C₁₁₃	—	2	1	no	—
18	C₂×#137×C₁₁₃	C₂²	1	2	yes	—
19	C₂×AGL(1,ℤ/8)×C₁₁₃	—	2	1	no	—
20	C₂×AGL(1,ℤ/8)×C₁₁₃	C₂²	1	2	yes	—
21	C₂×#135×C₁₁₃	—	2	2	no	—
22	C₂²×M₁₆×C₁₁₃	C₂²	1	1	yes	characteristic
23	C₂²×M₁₆×C₁₁₃	C₂²	1	1	yes	characteristic
24	#537×C₁₁₃	—	2	2	no	—
25	#536×C₁₁₃	—	2	1	no	—
26	#536×C₁₁₃	C₂²	1	2	yes	—
27	#535×C₁₁₃	—	2	1	no	—
28	#535×C₁₁₃	C₂²	1	2	yes	—
29	#534×C₁₁₃	—	2	2	no	—
30	#532×C₁₁₃	—	2	4	no	—
31	#532×C₁₁₃	—	2	2	no	—
32	#532×C₁₁₃	—	2	4	no	—
33	C₂×C₄⋊Q₈×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
34	C₂×#127×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
35	C₂×#124×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
36	C₂×#124×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
37	#525×C₁₁₃	—	2	2	no	—
38	#525×C₁₁₃	—	2	2	no	—
39	C₂×#121×C₁₁₃	—	2	2	no	—
40	C₂×C₄×D₄×C₁₁₃	—	2	2	no	—
41	C₂×#117×C₁₁₃	C₂²	1	1	yes	characteristic
42	C₂²×C₄²×C₁₁₃	C₂²	1	1	yes	characteristic
43	C₂×#104×C₁₁₃	—	2	4	no	—
44	C₂×#104×C₁₁₃	C₂²	1	2	yes	—
45	C₂×#104×C₁₁₃	C₂²	1	2	yes	—
46	#419×C₁₁₃	C₂²	1	2	yes	complemented
47	#418×C₁₁₃	C₂²	1	2	yes	complemented
48	#417×C₁₁₃	—	2	2	no	—
49	#416×C₁₁₃	—	2	2	no	—
50	#413×C₁₁₃	—	2	4	no	—
51	C₂×#101×C₁₁₃	C₂²	1	2	yes	complemented
52	C₂×#100×C₁₁₃	C₂²	1	2	yes	complemented
53	#339×C₁₁₃	C₂²	1	2	yes	complemented
54	#339×C₁₁₃	C₂²	1	2	yes	complemented
55	C₂×#41×C₁₁₃	—	2	1	no	—
56	C₂×#41×C₁₁₃	—	2	1	no	—
57	C₂×#41×C₁₁₃	—	2	2	no	—
58	C₂×#41×C₁₁₃	—	2	2	no	—
59	C₂×#41×C₁₁₃	—	2	2	no	—
60	C₂×#41×C₁₁₃	—	2	1	no	—
61	C₂×#41×C₁₁₃	—	2	1	no	—
62	C₂×#41×C₁₁₃	—	2	1	no	—
63	C₂×#41×C₁₁₃	—	2	1	no	—
64	C₂×#41×C₁₁₃	—	2	2	no	—
65	C₂×#41×C₁₁₃	—	2	2	no	—
66	C₂×#41×C₁₁₃	—	2	1	no	—
67	C₂×#41×C₁₁₃	—	2	1	no	—
68	C₂×#41×C₁₁₃	—	2	2	no	—
69	C₂×#41×C₁₁₃	—	2	2	no	—
70	C₂×#41×C₁₁₃	—	2	2	no	—
71	C₂×#41×C₁₁₃	—	2	1	no	—
72	C₂×#41×C₁₁₃	—	2	1	no	—
73	C₂×#41×C₁₁₃	—	2	2	no	—
74	C₂×#41×C₁₁₃	—	2	2	no	—
75	C₂×#41×C₁₁₃	—	2	2	no	—
76	C₂×#41×C₁₁₃	D₄	1	2	yes	complemented
77	C₂×#41×C₁₁₃	D₄	1	4	yes	complemented
78	C₂×#41×C₁₁₃	C₂³	1	2	yes	—
79	C₂²×Q₈×C₁₁₃	D₄	1	1	yes	characteristic, complemented
80	C₂²×Q₈×C₁₁₃	C₂³	1	1	yes	characteristic
81	C₂²×Q₈×C₁₁₃	C₂³	1	1	yes	characteristic
82	C₂²×D₄×C₁₁₃	—	2	2	no	—
83	C₂²×D₄×C₁₁₃	—	2	1	no	—
84	C₂²×D₄×C₁₁₃	—	2	1	no	—
85	C₂²×D₄×C₁₁₃	D₄	1	2	yes	—
86	C₂²×D₄×C₁₁₃	D₄	1	1	yes	characteristic, complemented
87	C₂²×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
88	C₂²×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₁₁₃	—	2	1	no	—
90	C₂³×C₄×C₁₁₃	—	2	1	no	—
91	C₂³×C₄×C₁₁₃	—	2	1	no	—
92	C₂³×C₄×C₁₁₃	D₄	1	2	yes	—
93	C₂³×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
94	#137×C₁₁₃	—	2	8	no	—
95	#137×C₁₁₃	—	2	4	no	—
96	#137×C₁₁₃	—	2	4	no	—
97	AGL(1,ℤ/8)×C₁₁₃	—	2	8	no	—
98	AGL(1,ℤ/8)×C₁₁₃	—	2	4	no	—
99	AGL(1,ℤ/8)×C₁₁₃	—	2	4	no	—
100	#135×C₁₁₃	—	2	16	no	—
101	C₂×Q₁₆×C₁₁₃	—	2	2	no	—
102	C₂×SD₁₆×C₁₁₃	—	2	2	no	—
103	C₂×SD₁₆×C₁₁₃	—	2	2	no	—
104	C₂×D₈×C₁₁₃	—	2	2	no	—
105	C₂×M₁₆×C₁₁₃	—	2	1	no	—
106	C₂×M₁₆×C₁₁₃	—	2	2	no	—
107	C₂×M₁₆×C₁₁₃	—	2	1	no	—
108	C₂×M₁₆×C₁₁₃	—	2	2	no	—
109	C₂×M₁₆×C₁₁₃	—	2	2	no	—
110	C₂×M₁₆×C₁₁₃	D₄	1	4	yes	complemented
111	C₂×M₁₆×C₁₁₃	C₂³	1	2	yes	—
112	C₂×M₁₆×C₁₁₃	C₂³	1	2	yes	—
113	C₂²×C₈×C₁₁₃	—	2	1	no	—
114	C₂²×C₈×C₁₁₃	—	2	1	no	—
115	C₄⋊Q₈×C₁₁₃	—	2	2	no	—
116	C₄⋊Q₈×C₁₁₃	—	2	2	no	—
117	C₄⋊Q₈×C₁₁₃	—	2	2	no	—
118	#127×C₁₁₃	—	2	2	no	—
119	#127×C₁₁₃	—	2	2	no	—
120	#127×C₁₁₃	—	2	2	no	—
121	#124×C₁₁₃	—	2	2	no	—
122	#124×C₁₁₃	—	2	2	no	—
123	#124×C₁₁₃	—	2	2	no	—
124	#124×C₁₁₃	—	2	2	no	—
125	#124×C₁₁₃	—	2	2	no	—
126	#124×C₁₁₃	—	2	2	no	—
127	#123×C₁₁₃	—	2	4	no	—
128	#123×C₁₁₃	—	2	4	no	—
129	C₂²⋊Q₈×C₁₁₃	—	2	4	no	—
130	C₂²⋊Q₈×C₁₁₃	—	2	4	no	—
131	#121×C₁₁₃	—	2	16	no	—
132	#121×C₁₁₃	—	2	4	no	—
133	#121×C₁₁₃	—	2	8	no	—
134	#121×C₁₁₃	—	2	4	no	—
135	#120×C₁₁₃	—	2	4	no	—
136	#120×C₁₁₃	—	2	4	no	—
137	C₄×D₄×C₁₁₃	—	2	16	no	—
138	C₄×D₄×C₁₁₃	—	2	8	no	—
139	#117×C₁₁₃	—	2	1	no	—
140	#117×C₁₁₃	—	2	1	no	—
141	#117×C₁₁₃	D₄	1	2	yes	complemented
142	#117×C₁₁₃	C₂³	1	2	yes	—
143	C₂×C₄⋊C₄×C₁₁₃	—	2	2	no	—
144	C₂×C₄⋊C₄×C₁₁₃	D₄	1	2	yes	complemented
145	C₂×C₂²⋊C₄×C₁₁₃	—	2	1	no	—
146	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
147	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
148	C₂×C₄²×C₁₁₃	—	2	1	no	—
149	C₂×C₄²×C₁₁₃	—	2	2	no	—
150	C₂×C₄²×C₁₁₃	—	2	1	no	—
151	C₂×C₄²×C₁₁₃	D₄	1	4	yes	complemented
152	C₂×C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
153	C₂×C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
154	#104×C₁₁₃	—	2	4	no	—
155	#104×C₁₁₃	—	2	4	no	—
156	#103×C₁₁₃	—	2	4	no	—
157	#102×C₁₁₃	—	2	4	no	—
158	#101×C₁₁₃	—	2	4	no	—
159	#100×C₁₁₃	—	2	4	no	—
160	C₂⁴×C₁₁₃	—	2	1	no	—
161	C₂⁴×C₁₁₃	—	2	1	no	—
162	C₂⁴×C₁₁₃	C₂×D₄	1	2	yes	—
163	C₂⁴×C₁₁₃	C₂×D₄	1	1	yes	characteristic
164	#41×C₁₁₃	—	2	4	no	—
165	#41×C₁₁₃	—	2	4	no	—
166	#41×C₁₁₃	—	2	4	no	—
167	#41×C₁₁₃	—	2	4	no	—
168	#41×C₁₁₃	—	2	4	no	—
169	#41×C₁₁₃	—	2	4	no	—
170	#41×C₁₁₃	—	2	2	no	—
171	#41×C₁₁₃	—	2	2	no	—
172	#41×C₁₁₃	—	2	2	no	—
173	#41×C₁₁₃	—	2	2	no	—
174	#41×C₁₁₃	—	4	2	no	—
175	#41×C₁₁₃	—	4	2	no	—
176	#41×C₁₁₃	—	4	2	no	—
177	#41×C₁₁₃	—	4	2	no	—
178	#41×C₁₁₃	—	4	2	no	—
179	#41×C₁₁₃	—	4	2	no	—
180	#41×C₁₁₃	—	4	2	no	—
181	#41×C₁₁₃	—	4	2	no	—
182	#41×C₁₁₃	—	4	2	no	—
183	#41×C₁₁₃	—	4	2	no	—
184	#41×C₁₁₃	—	4	2	no	—
185	#41×C₁₁₃	—	4	2	no	—
186	#41×C₁₁₃	—	4	2	no	—
187	#41×C₁₁₃	—	4	2	no	—
188	#41×C₁₁₃	—	4	2	no	—
189	#41×C₁₁₃	—	4	2	no	—
190	C₂×Q₈×C₁₁₃	—	2	1	no	—
191	C₂×Q₈×C₁₁₃	—	2	1	no	—
192	C₂×Q₈×C₁₁₃	—	2	1	no	—
193	C₂×Q₈×C₁₁₃	—	2	1	no	—
194	C₂×Q₈×C₁₁₃	—	2	1	no	—
195	C₂×Q₈×C₁₁₃	—	2	1	no	—
196	C₂×Q₈×C₁₁₃	—	2	1	no	—
197	C₂×Q₈×C₁₁₃	—	2	1	no	—
198	C₂×Q₈×C₁₁₃	—	2	2	no	—
199	C₂×Q₈×C₁₁₃	—	2	2	no	—
200	C₂×Q₈×C₁₁₃	—	2	1	no	—
201	C₂×Q₈×C₁₁₃	—	2	1	no	—
202	C₂×Q₈×C₁₁₃	—	2	1	no	—
203	C₂×Q₈×C₁₁₃	—	2	1	no	—
204	C₂×Q₈×C₁₁₃	C₂×D₄	1	2	yes	—
205	C₂×Q₈×C₁₁₃	C₂×D₄	1	2	yes	—
206	C₂×D₄×C₁₁₃	—	2	8	no	—
207	C₂×D₄×C₁₁₃	—	2	2	no	—
208	C₂×D₄×C₁₁₃	—	2	2	no	—
209	C₂×D₄×C₁₁₃	—	2	4	no	—
210	C₂×D₄×C₁₁₃	—	2	2	no	—
211	C₂×D₄×C₁₁₃	—	2	4	no	—
212	C₂×D₄×C₁₁₃	—	2	4	no	—
213	C₂×D₄×C₁₁₃	—	2	2	no	—
214	C₂×D₄×C₁₁₃	—	2	8	no	—
215	C₂×D₄×C₁₁₃	—	2	2	no	—
216	C₂×D₄×C₁₁₃	—	2	1	no	—
217	C₂×D₄×C₁₁₃	—	2	2	no	—
218	C₂×D₄×C₁₁₃	—	2	1	no	—
219	C₂×D₄×C₁₁₃	—	2	1	no	—
220	C₂×D₄×C₁₁₃	—	2	1	no	—
221	C₂×D₄×C₁₁₃	—	2	1	no	—
222	C₂×D₄×C₁₁₃	—	2	1	no	—
223	C₂×D₄×C₁₁₃	—	2	1	no	—
224	C₂×D₄×C₁₁₃	—	2	1	no	—
225	C₂×D₄×C₁₁₃	—	2	1	no	—
226	C₂×D₄×C₁₁₃	—	2	1	no	—
227	C₂×D₄×C₁₁₃	—	2	1	no	—
228	C₂×D₄×C₁₁₃	—	2	1	no	—
229	C₂×D₄×C₁₁₃	—	4	8	no	—
230	C₂×D₄×C₁₁₃	—	4	1	no	—
231	C₂×D₄×C₁₁₃	—	4	1	no	—
232	C₂×D₄×C₁₁₃	—	4	2	no	—
233	C₂×D₄×C₁₁₃	—	4	2	no	—
234	C₂×D₄×C₁₁₃	—	4	2	no	—
235	C₂×D₄×C₁₁₃	C₂×D₄	1	2	yes	—
236	C₂×D₄×C₁₁₃	C₂×D₄	1	2	yes	—
237	C₂²×C₄×C₁₁₃	—	2	1	no	—
238	C₂²×C₄×C₁₁₃	—	2	4	no	—
239	C₂²×C₄×C₁₁₃	—	2	1	no	—
240	C₂²×C₄×C₁₁₃	—	2	1	no	—
241	C₂²×C₄×C₁₁₃	—	2	1	no	—
242	C₂²×C₄×C₁₁₃	—	2	2	no	—
243	C₂²×C₄×C₁₁₃	—	2	4	no	—
244	C₂²×C₄×C₁₁₃	—	2	4	no	—
245	C₂²×C₄×C₁₁₃	—	2	2	no	—
246	C₂²×C₄×C₁₁₃	—	2	2	no	—
247	C₂²×C₄×C₁₁₃	—	2	2	no	—
248	C₂²×C₄×C₁₁₃	—	2	4	no	—
249	C₂²×C₄×C₁₁₃	—	2	2	no	—
250	C₂²×C₄×C₁₁₃	—	4	4	no	—
251	C₂²×C₄×C₁₁₃	—	4	1	no	—
252	C₂²×C₄×C₁₁₃	—	4	1	no	—
253	C₂²×C₄×C₁₁₃	—	4	2	no	—
254	C₂²×C₄×C₁₁₃	—	4	2	no	—
255	C₂²×C₄×C₁₁₃	—	4	2	no	—
256	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
257	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
258	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
259	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
260	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
261	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
262	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
263	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
264	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
265	C₂²×C₄×C₁₁₃	#41	1	2	yes	—
266	C₂²×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
267	Q₁₆×C₁₁₃	—	2	8	no	—
268	SD₁₆×C₁₁₃	—	2	8	no	—
269	SD₁₆×C₁₁₃	—	2	8	no	—
270	D₈×C₁₁₃	—	2	8	no	—
271	M₁₆×C₁₁₃	—	2	4	no	—
272	M₁₆×C₁₁₃	—	2	2	no	—
273	M₁₆×C₁₁₃	—	2	2	no	—
274	M₁₆×C₁₁₃	—	2	2	no	—
275	M₁₆×C₁₁₃	—	4	2	no	—
276	M₁₆×C₁₁₃	C₂×D₄	1	4	yes	—
277	C₂×C₈×C₁₁₃	—	2	4	no	—
278	C₂×C₈×C₁₁₃	—	2	2	no	—
279	C₂×C₈×C₁₁₃	—	2	2	no	—
280	C₂×C₈×C₁₁₃	—	4	2	no	—
281	C₄⋊C₄×C₁₁₃	—	2	8	no	—
282	C₄⋊C₄×C₁₁₃	—	2	8	no	—
283	C₄⋊C₄×C₁₁₃	—	2	2	no	—
284	C₄⋊C₄×C₁₁₃	C₂×D₄	1	4	yes	—
285	C₂²⋊C₄×C₁₁₃	—	2	8	no	—
286	C₂²⋊C₄×C₁₁₃	—	2	8	no	—
287	C₂²⋊C₄×C₁₁₃	—	2	8	no	—
288	C₂²⋊C₄×C₁₁₃	—	2	8	no	—
289	C₂²⋊C₄×C₁₁₃	—	2	2	no	—
290	C₂²⋊C₄×C₁₁₃	—	2	2	no	—
291	C₄²×C₁₁₃	—	2	4	no	—
292	C₄²×C₁₁₃	—	2	2	no	—
293	C₄²×C₁₁₃	—	2	1	no	—
294	C₄²×C₁₁₃	—	2	1	no	—
295	C₄²×C₁₁₃	—	2	2	no	—
296	C₄²×C₁₁₃	C₂×D₄	1	2	yes	—
297	C₄²×C₁₁₃	C₂×D₄	1	2	yes	—
298	C₂³×C₁₁₃	—	2	2	no	—
299	C₂³×C₁₁₃	—	2	2	no	—
300	C₂³×C₁₁₃	—	2	2	no	—
301	C₂³×C₁₁₃	—	2	2	no	—
302	C₂³×C₁₁₃	—	2	2	no	—
303	C₂³×C₁₁₃	—	4	2	no	—
304	C₂³×C₁₁₃	—	4	4	no	—
305	C₂³×C₁₁₃	—	4	4	no	—
306	C₂³×C₁₁₃	—	4	1	no	—
307	C₂³×C₁₁₃	—	4	1	no	—
308	C₂³×C₁₁₃	—	4	2	no	—
309	C₂³×C₁₁₃	—	8	2	no	—
310	C₂³×C₁₁₃	#120	1	1	yes	characteristic
311	C₂³×C₁₁₃	#120	1	1	yes	characteristic
312	C₂³×C₁₁₃	#120	1	2	yes	—
313	C₂³×C₁₁₃	#121	1	2	yes	—
314	C₂³×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
315	Q₈×C₁₁₃	—	2	2	no	—
316	Q₈×C₁₁₃	—	2	2	no	—
317	Q₈×C₁₁₃	—	2	2	no	—
318	Q₈×C₁₁₃	—	2	2	no	—
319	Q₈×C₁₁₃	—	4	1	no	—
320	Q₈×C₁₁₃	—	4	1	no	—
321	Q₈×C₁₁₃	—	4	1	no	—
322	Q₈×C₁₁₃	—	4	1	no	—
323	Q₈×C₁₁₃	—	4	1	no	—
324	Q₈×C₁₁₃	—	4	1	no	—
325	Q₈×C₁₁₃	—	4	2	no	—
326	D₄×C₁₁₃	—	2	2	no	—
327	D₄×C₁₁₃	—	2	2	no	—
328	D₄×C₁₁₃	—	2	2	no	—
329	D₄×C₁₁₃	—	2	2	no	—
330	D₄×C₁₁₃	—	4	16	no	—
331	D₄×C₁₁₃	—	4	2	no	—
332	D₄×C₁₁₃	—	4	2	no	—
333	D₄×C₁₁₃	—	4	4	no	—
334	D₄×C₁₁₃	—	4	4	no	—
335	D₄×C₁₁₃	—	4	4	no	—
336	D₄×C₁₁₃	—	4	4	no	—
337	D₄×C₁₁₃	—	4	4	no	—
338	D₄×C₁₁₃	—	4	1	no	—
339	D₄×C₁₁₃	—	4	1	no	—
340	D₄×C₁₁₃	—	4	1	no	—
341	D₄×C₁₁₃	—	4	1	no	—
342	D₄×C₁₁₃	—	4	1	no	—
343	D₄×C₁₁₃	—	4	1	no	—
344	D₄×C₁₁₃	—	4	2	no	—
345	D₄×C₁₁₃	—	8	8	no	—
346	C₂×C₄×C₁₁₃	—	2	4	no	—
347	C₂×C₄×C₁₁₃	—	2	2	no	—
348	C₂×C₄×C₁₁₃	—	2	2	no	—
349	C₂×C₄×C₁₁₃	—	2	4	no	—
350	C₂×C₄×C₁₁₃	—	2	2	no	—
351	C₂×C₄×C₁₁₃	—	2	2	no	—
352	C₂×C₄×C₁₁₃	—	2	2	no	—
353	C₂×C₄×C₁₁₃	—	2	2	no	—
354	C₂×C₄×C₁₁₃	—	2	2	no	—
355	C₂×C₄×C₁₁₃	—	4	8	no	—
356	C₂×C₄×C₁₁₃	—	4	2	no	—
357	C₂×C₄×C₁₁₃	—	4	1	no	—
358	C₂×C₄×C₁₁₃	—	4	1	no	—
359	C₂×C₄×C₁₁₃	—	4	2	no	—
360	C₂×C₄×C₁₁₃	—	4	2	no	—
361	C₂×C₄×C₁₁₃	—	4	2	no	—
362	C₂×C₄×C₁₁₃	—	4	4	no	—
363	C₂×C₄×C₁₁₃	—	4	4	no	—
364	C₂×C₄×C₁₁₃	—	4	4	no	—
365	C₂×C₄×C₁₁₃	—	4	4	no	—
366	C₂×C₄×C₁₁₃	—	4	4	no	—
367	C₂×C₄×C₁₁₃	—	8	2	no	—
368	C₂×C₄×C₁₁₃	#120	1	2	yes	—
369	C₂×C₄×C₁₁₃	#120	1	2	yes	—
370	C₂×C₄×C₁₁₃	#120	1	2	yes	—
371	C₂×C₄×C₁₁₃	#120	1	1	yes	characteristic
372	C₂×C₄×C₁₁₃	#120	1	1	yes	characteristic
373	C₂×C₄×C₁₁₃	#121	1	2	yes	—
374	C₂×C₄×C₁₁₃	#121	1	2	yes	—
375	C₂×C₄×C₁₁₃	#121	1	2	yes	—
376	C₂×C₄×C₁₁₃	#121	1	2	yes	—
377	C₂×C₄×C₁₁₃	#121	1	2	yes	—
378	C₂×C₄×C₁₁₃	#127	1	2	yes	—
379	C₂×C₄×C₁₁₃	#127	1	2	yes	—
380	C₂×C₄×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
381	C₂×C₄×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
382	C₂×C₄×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
383	C₂×C₄×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
384	C₂×C₄×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
385	C₂×C₄×C₁₁₃	C₂×#41	1	1	yes	characteristic
386	C₈×C₁₁₃	—	2	4	no	—
387	C₈×C₁₁₃	—	4	2	no	—
388	C₂²×C₁₁₃	—	2	2	no	—
389	C₂²×C₁₁₃	—	2	2	no	—
390	C₂²×C₁₁₃	—	2	2	no	—
391	C₂²×C₁₁₃	—	4	2	no	—
392	C₂²×C₁₁₃	—	4	2	no	—
393	C₂²×C₁₁₃	—	4	4	no	—
394	C₂²×C₁₁₃	—	4	4	no	—
395	C₂²×C₁₁₃	—	4	2	no	—
396	C₂²×C₁₁₃	—	4	2	no	—
397	C₂²×C₁₁₃	—	4	2	no	—
398	C₂²×C₁₁₃	—	4	4	no	—
399	C₂²×C₁₁₃	—	4	4	no	—
400	C₂²×C₁₁₃	—	8	2	no	—
401	C₂²×C₁₁₃	—	8	2	no	—
402	C₂²×C₁₁₃	—	8	4	no	—
403	C₂²×C₁₁₃	—	8	2	no	—
404	C₂²×C₁₁₃	#392	1	2	yes	—
405	C₂²×C₁₁₃	#392	1	2	yes	—
406	C₂²×C₁₁₃	C₂×#120	1	1	yes	characteristic
407	C₂²×C₁₁₃	C₂×#120	1	1	yes	characteristic
408	C₂²×C₁₁₃	C₂×#121	1	1	yes	characteristic
409	C₄×C₁₁₃	—	2	4	no	—
410	C₄×C₁₁₃	—	4	2	no	—
411	C₄×C₁₁₃	—	4	2	no	—
412	C₄×C₁₁₃	—	4	2	no	—
413	C₄×C₁₁₃	—	4	2	no	—
414	C₄×C₁₁₃	—	4	4	no	—
415	C₄×C₁₁₃	#392	1	2	yes	—
416	C₄×C₁₁₃	#392	1	2	yes	—
417	C₄×C₁₁₃	C₂×#120	1	1	yes	characteristic
418	C₄×C₁₁₃	C₂×#121	1	1	yes	characteristic
419	C₄×C₁₁₃	C₂×#121	1	1	yes	characteristic
420	C₄×C₁₁₃	C₂×#127	1	1	yes	characteristic
421	#23399	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
422	C₂×C₁₁₃	—	2	1	no	—
423	C₂×C₁₁₃	—	2	1	no	—
424	C₂×C₁₁₃	—	2	2	no	—
425	C₂×C₁₁₃	—	2	2	no	—
426	C₂×C₁₁₃	—	8	2	no	—
427	C₂×C₁₁₃	—	8	2	no	—
428	C₂×C₁₁₃	—	8	2	no	—
429	C₂×C₁₁₃	C₂×#392	1	1	yes	characteristic
430	C₂×C₁₁₃	#3018	1	2	yes	—
431	C₂×#575	C₂×C₁₁₃	1	1	yes	characteristic, complemented
432	#3449	C₂×C₁₁₃	1	1	yes	characteristic, complemented
433	C₂×#532	C₂×C₁₁₃	1	1	yes	characteristic, complemented
434	C₂²×#104	C₂×C₁₁₃	1	1	yes	characteristic, complemented
435	#2896	C₂×C₁₁₃	1	1	yes	characteristic, complemented
436	C₂×#413	C₂×C₁₁₃	1	1	yes	characteristic, complemented
437	#2005	C₂×C₁₁₃	1	2	yes	complemented
438	#2004	C₂×C₁₁₃	1	2	yes	complemented
439	#2003	C₂×C₁₁₃	1	2	yes	complemented
440	#2002	C₂×C₁₁₃	1	2	yes	complemented
441	C₂×#339	C₂×C₁₁₃	1	1	yes	characteristic, complemented
442	C₁₁₃	#23399	1	1	yes	characteristic, direct product factor, Sylow
443	C₂²×#41	C₂²×C₁₁₃	1	1	yes	characteristic
444	C₂²×#41	C₂²×C₁₁₃	1	1	yes	characteristic
445	C₂²×#41	C₂²×C₁₁₃	1	1	yes	characteristic
446	#575	—	2	4	no	—
447	#575	—	2	4	no	—
448	C₂×#137	—	2	1	no	—
449	C₂×#137	C₂²×C₁₁₃	1	2	yes	—
450	C₂×AGL(1,ℤ/8)	—	2	1	no	—
451	C₂×AGL(1,ℤ/8)	C₂²×C₁₁₃	1	2	yes	—
452	C₂×#135	—	2	2	no	—
453	C₂²×M₁₆	C₂²×C₁₁₃	1	1	yes	characteristic
454	C₂²×M₁₆	C₂²×C₁₁₃	1	1	yes	characteristic
455	#537	—	2	2	no	—
456	#536	—	2	1	no	—
457	#536	C₂²×C₁₁₃	1	2	yes	—
458	#535	—	2	1	no	—
459	#535	C₂²×C₁₁₃	1	2	yes	—
460	#534	—	2	2	no	—
461	#532	—	2	4	no	—
462	#532	—	2	2	no	—
463	#532	—	2	4	no	—
464	C₂×C₄⋊Q₈	C₂²×C₁₁₃	1	1	yes	characteristic, complemented
465	C₂×#127	C₂²×C₁₁₃	1	1	yes	characteristic, complemented
466	C₂×#124	C₂²×C₁₁₃	1	1	yes	characteristic, complemented
467	C₂×#124	C₂²×C₁₁₃	1	1	yes	characteristic, complemented
468	#525	—	2	2	no	—
469	#525	—	2	2	no	—
470	C₂×#121	—	2	2	no	—
471	C₂×C₄×D₄	—	2	2	no	—
472	C₂×#117	C₂²×C₁₁₃	1	1	yes	characteristic
473	C₂²×C₄²	C₂²×C₁₁₃	1	1	yes	characteristic
474	C₂×#104	—	2	4	no	—
475	C₂×#104	C₂²×C₁₁₃	1	2	yes	—
476	C₂×#104	C₂²×C₁₁₃	1	2	yes	—
477	#419	C₂²×C₁₁₃	1	2	yes	complemented
478	#418	C₂²×C₁₁₃	1	2	yes	complemented
479	#417	—	2	2	no	—
480	#416	—	2	2	no	—
481	#413	—	2	4	no	—
482	C₂×#101	C₂²×C₁₁₃	1	2	yes	complemented
483	C₂×#100	C₂²×C₁₁₃	1	2	yes	complemented
484	#339	C₂²×C₁₁₃	1	2	yes	complemented
485	#339	C₂²×C₁₁₃	1	2	yes	complemented
486	C₂×#41	—	2	1	no	—
487	C₂×#41	—	2	1	no	—
488	C₂×#41	—	2	2	no	—
489	C₂×#41	—	2	1	no	—
490	C₂×#41	—	2	2	no	—
491	C₂×#41	—	2	2	no	—
492	C₂×#41	—	2	1	no	—
493	C₂×#41	—	2	1	no	—
494	C₂×#41	—	2	1	no	—
495	C₂×#41	—	2	2	no	—
496	C₂×#41	—	2	2	no	—
497	C₂×#41	—	2	1	no	—
498	C₂×#41	—	2	1	no	—
499	C₂×#41	—	2	2	no	—
500	C₂×#41	—	2	2	no	—
501	C₂×#41	—	2	2	no	—
502	C₂×#41	—	2	1	no	—
503	C₂×#41	—	2	1	no	—
504	C₂×#41	—	2	2	no	—
505	C₂×#41	—	2	2	no	—
506	C₂×#41	—	2	2	no	—
507	C₂×#41	D₄×C₁₁₃	1	2	yes	complemented
508	C₂×#41	D₄×C₁₁₃	1	4	yes	complemented
509	C₂×#41	C₂³×C₁₁₃	1	2	yes	—
510	C₂²×Q₈	D₄×C₁₁₃	1	1	yes	characteristic, complemented
511	C₂²×Q₈	C₂³×C₁₁₃	1	1	yes	characteristic
512	C₂²×Q₈	C₂³×C₁₁₃	1	1	yes	characteristic
513	C₂²×D₄	—	2	2	no	—
514	C₂²×D₄	—	2	1	no	—
515	C₂²×D₄	—	2	1	no	—
516	C₂²×D₄	D₄×C₁₁₃	1	2	yes	—
517	C₂²×D₄	D₄×C₁₁₃	1	1	yes	characteristic, complemented
518	C₂²×D₄	C₂³×C₁₁₃	1	1	yes	characteristic
519	C₂²×D₄	C₂³×C₁₁₃	1	1	yes	characteristic
520	C₂³×C₄	—	2	1	no	—
521	C₂³×C₄	—	2	1	no	—
522	C₂³×C₄	—	2	1	no	—
523	C₂³×C₄	D₄×C₁₁₃	1	2	yes	—
524	C₂³×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
525	#137	—	2	8	no	—
526	#137	—	2	4	no	—
527	#137	—	2	4	no	—
528	AGL(1,ℤ/8)	—	2	8	no	—
529	AGL(1,ℤ/8)	—	2	4	no	—
530	AGL(1,ℤ/8)	—	2	4	no	—
531	#135	—	2	16	no	—
532	C₂×Q₁₆	—	2	2	no	—
533	C₂×SD₁₆	—	2	2	no	—
534	C₂×SD₁₆	—	2	2	no	—
535	C₂×D₈	—	2	2	no	—
536	C₂×M₁₆	—	2	1	no	—
537	C₂×M₁₆	—	2	2	no	—
538	C₂×M₁₆	—	2	1	no	—
539	C₂×M₁₆	—	2	2	no	—
540	C₂×M₁₆	—	2	2	no	—
541	C₂×M₁₆	D₄×C₁₁₃	1	4	yes	complemented
542	C₂×M₁₆	C₂³×C₁₁₃	1	2	yes	—
543	C₂×M₁₆	C₂³×C₁₁₃	1	2	yes	—
544	C₂²×C₈	—	2	1	no	—
545	C₂²×C₈	—	2	1	no	—
546	C₄⋊Q₈	—	2	2	no	—
547	C₄⋊Q₈	—	2	2	no	—
548	C₄⋊Q₈	—	2	2	no	—
549	#127	—	2	2	no	—
550	#127	—	2	2	no	—
551	#127	—	2	2	no	—
552	#124	—	2	2	no	—
553	#124	—	2	2	no	—
554	#124	—	2	2	no	—
555	#124	—	2	2	no	—
556	#124	—	2	2	no	—
557	#124	—	2	2	no	—
558	#123	—	2	4	no	—
559	#123	—	2	4	no	—
560	C₂²⋊Q₈	—	2	4	no	—
561	C₂²⋊Q₈	—	2	4	no	—
562	#121	—	2	16	no	—
563	#121	—	2	4	no	—
564	#121	—	2	8	no	—
565	#121	—	2	4	no	—
566	#120	—	2	4	no	—
567	#120	—	2	4	no	—
568	C₄×D₄	—	2	16	no	—
569	C₄×D₄	—	2	8	no	—
570	#117	—	2	1	no	—
571	#117	—	2	1	no	—
572	#117	D₄×C₁₁₃	1	2	yes	complemented
573	#117	C₂³×C₁₁₃	1	2	yes	—
574	C₂×C₄⋊C₄	—	2	2	no	—
575	C₂×C₄⋊C₄	D₄×C₁₁₃	1	2	yes	complemented
576	C₂×C₂²⋊C₄	—	2	1	no	—
577	C₂×C₂²⋊C₄	—	2	2	no	—
578	C₂×C₂²⋊C₄	—	2	2	no	—
579	C₂×C₄²	—	2	1	no	—
580	C₂×C₄²	—	2	1	no	—
581	C₂×C₄²	—	2	2	no	—
582	C₂×C₄²	D₄×C₁₁₃	1	4	yes	complemented
583	C₂×C₄²	C₂³×C₁₁₃	1	1	yes	characteristic
584	C₂×C₄²	C₂³×C₁₁₃	1	1	yes	characteristic
585	#104	—	2	4	no	—
586	#104	—	2	4	no	—
587	#103	—	2	4	no	—
588	#102	—	2	4	no	—
589	#101	—	2	4	no	—
590	#100	—	2	4	no	—
591	C₂⁴	—	2	1	no	—
592	C₂⁴	—	2	1	no	—
593	C₂⁴	C₂×D₄×C₁₁₃	1	2	yes	—
594	C₂⁴	C₂×D₄×C₁₁₃	1	1	yes	characteristic
595	#41	—	2	4	no	—
596	#41	—	2	4	no	—
597	#41	—	2	4	no	—
598	#41	—	2	4	no	—
599	#41	—	2	4	no	—
600	#41	—	2	4	no	—
601	#41	—	2	2	no	—
602	#41	—	2	2	no	—
603	#41	—	2	2	no	—
604	#41	—	2	2	no	—
605	#41	—	4	2	no	—
606	#41	—	4	2	no	—
607	#41	—	4	2	no	—
608	#41	—	4	2	no	—
609	#41	—	4	2	no	—
610	#41	—	4	2	no	—
611	#41	—	4	2	no	—
612	#41	—	4	2	no	—
613	#41	—	4	2	no	—
614	#41	—	4	2	no	—
615	#41	—	4	2	no	—
616	#41	—	4	2	no	—
617	#41	—	4	2	no	—
618	#41	—	4	2	no	—
619	#41	—	4	2	no	—
620	#41	—	4	2	no	—
621	C₂×Q₈	—	2	1	no	—
622	C₂×Q₈	—	2	1	no	—
623	C₂×Q₈	—	2	1	no	—
624	C₂×Q₈	—	2	1	no	—
625	C₂×Q₈	—	2	1	no	—
626	C₂×Q₈	—	2	1	no	—
627	C₂×Q₈	—	2	1	no	—
628	C₂×Q₈	—	2	1	no	—
629	C₂×Q₈	—	2	2	no	—
630	C₂×Q₈	—	2	2	no	—
631	C₂×Q₈	—	2	1	no	—
632	C₂×Q₈	—	2	1	no	—
633	C₂×Q₈	—	2	1	no	—
634	C₂×Q₈	—	2	1	no	—
635	C₂×Q₈	C₂×D₄×C₁₁₃	1	2	yes	—
636	C₂×Q₈	C₂×D₄×C₁₁₃	1	2	yes	—
637	C₂×D₄	—	2	8	no	—
638	C₂×D₄	—	2	2	no	—
639	C₂×D₄	—	2	2	no	—
640	C₂×D₄	—	2	4	no	—
641	C₂×D₄	—	2	2	no	—
642	C₂×D₄	—	2	4	no	—
643	C₂×D₄	—	2	4	no	—
644	C₂×D₄	—	2	2	no	—
645	C₂×D₄	—	2	8	no	—
646	C₂×D₄	—	2	2	no	—
647	C₂×D₄	—	2	1	no	—
648	C₂×D₄	—	2	2	no	—
649	C₂×D₄	—	2	1	no	—
650	C₂×D₄	—	2	1	no	—
651	C₂×D₄	—	2	1	no	—
652	C₂×D₄	—	2	1	no	—
653	C₂×D₄	—	2	1	no	—
654	C₂×D₄	—	2	1	no	—
655	C₂×D₄	—	2	1	no	—
656	C₂×D₄	—	2	1	no	—
657	C₂×D₄	—	2	1	no	—
658	C₂×D₄	—	2	1	no	—
659	C₂×D₄	—	2	1	no	—
660	C₂×D₄	—	4	8	no	—
661	C₂×D₄	—	4	1	no	—
662	C₂×D₄	—	4	1	no	—
663	C₂×D₄	—	4	2	no	—
664	C₂×D₄	—	4	2	no	—
665	C₂×D₄	—	4	2	no	—
666	C₂×D₄	C₂×D₄×C₁₁₃	1	2	yes	—
667	C₂×D₄	C₂×D₄×C₁₁₃	1	2	yes	—
668	C₂²×C₄	—	2	1	no	—
669	C₂²×C₄	—	2	4	no	—
670	C₂²×C₄	—	2	1	no	—
671	C₂²×C₄	—	2	1	no	—
672	C₂²×C₄	—	2	1	no	—
673	C₂²×C₄	—	2	2	no	—
674	C₂²×C₄	—	2	2	no	—
675	C₂²×C₄	—	2	4	no	—
676	C₂²×C₄	—	2	2	no	—
677	C₂²×C₄	—	2	4	no	—
678	C₂²×C₄	—	2	2	no	—
679	C₂²×C₄	—	2	4	no	—
680	C₂²×C₄	—	2	2	no	—
681	C₂²×C₄	—	4	4	no	—
682	C₂²×C₄	—	4	1	no	—
683	C₂²×C₄	—	4	1	no	—
684	C₂²×C₄	—	4	2	no	—
685	C₂²×C₄	—	4	2	no	—
686	C₂²×C₄	—	4	2	no	—
687	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
688	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
689	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
690	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
691	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
692	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
693	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
694	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
695	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
696	C₂²×C₄	#41×C₁₁₃	1	2	yes	—
697	C₂²×C₄	C₂⁴×C₁₁₃	1	1	yes	characteristic
698	Q₁₆	—	2	8	no	—
699	SD₁₆	—	2	8	no	—
700	SD₁₆	—	2	8	no	—
701	D₈	—	2	8	no	—
702	M₁₆	—	2	4	no	—
703	M₁₆	—	2	2	no	—
704	M₁₆	—	2	2	no	—
705	M₁₆	—	2	2	no	—
706	M₁₆	—	4	2	no	—
707	M₁₆	C₂×D₄×C₁₁₃	1	4	yes	—
708	C₂×C₈	—	2	4	no	—
709	C₂×C₈	—	2	2	no	—
710	C₂×C₈	—	2	2	no	—
711	C₂×C₈	—	4	2	no	—
712	C₄⋊C₄	—	2	8	no	—
713	C₄⋊C₄	—	2	8	no	—
714	C₄⋊C₄	—	2	2	no	—
715	C₄⋊C₄	C₂×D₄×C₁₁₃	1	4	yes	—
716	C₂²⋊C₄	—	2	8	no	—
717	C₂²⋊C₄	—	2	8	no	—
718	C₂²⋊C₄	—	2	8	no	—
719	C₂²⋊C₄	—	2	8	no	—
720	C₂²⋊C₄	—	2	2	no	—
721	C₂²⋊C₄	—	2	2	no	—
722	C₄²	—	2	4	no	—
723	C₄²	—	2	2	no	—
724	C₄²	—	2	1	no	—
725	C₄²	—	2	1	no	—
726	C₄²	—	2	2	no	—
727	C₄²	C₂×D₄×C₁₁₃	1	2	yes	—
728	C₄²	C₂×D₄×C₁₁₃	1	2	yes	—
729	C₂³	—	2	2	no	—
730	C₂³	—	2	2	no	—
731	C₂³	—	2	2	no	—
732	C₂³	—	2	2	no	—
733	C₂³	—	2	2	no	—
734	C₂³	—	4	2	no	—
735	C₂³	—	4	4	no	—
736	C₂³	—	4	4	no	—
737	C₂³	—	4	1	no	—
738	C₂³	—	4	1	no	—
739	C₂³	—	4	2	no	—
740	C₂³	—	8	2	no	—
741	C₂³	#120×C₁₁₃	1	1	yes	characteristic
742	C₂³	#120×C₁₁₃	1	1	yes	characteristic
743	C₂³	#120×C₁₁₃	1	2	yes	—
744	C₂³	#121×C₁₁₃	1	2	yes	—
745	C₂³	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
746	Q₈	—	2	2	no	—
747	Q₈	—	2	2	no	—
748	Q₈	—	2	2	no	—
749	Q₈	—	2	2	no	—
750	Q₈	—	4	1	no	—
751	Q₈	—	4	1	no	—
752	Q₈	—	4	1	no	—
753	Q₈	—	4	1	no	—
754	Q₈	—	4	1	no	—
755	Q₈	—	4	1	no	—
756	Q₈	—	4	2	no	—
757	D₄	—	2	2	no	—
758	D₄	—	2	2	no	—
759	D₄	—	2	2	no	—
760	D₄	—	2	2	no	—
761	D₄	—	4	16	no	—
762	D₄	—	4	2	no	—
763	D₄	—	4	2	no	—
764	D₄	—	4	4	no	—
765	D₄	—	4	4	no	—
766	D₄	—	4	4	no	—
767	D₄	—	4	4	no	—
768	D₄	—	4	4	no	—
769	D₄	—	4	1	no	—
770	D₄	—	4	1	no	—
771	D₄	—	4	1	no	—
772	D₄	—	4	1	no	—
773	D₄	—	4	1	no	—
774	D₄	—	4	1	no	—
775	D₄	—	4	2	no	—
776	D₄	—	8	8	no	—
777	C₂×C₄	—	2	4	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	4	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	4	8	no	—
787	C₂×C₄	—	4	2	no	—
788	C₂×C₄	—	4	1	no	—
789	C₂×C₄	—	4	1	no	—
790	C₂×C₄	—	4	2	no	—
791	C₂×C₄	—	4	2	no	—
792	C₂×C₄	—	4	2	no	—
793	C₂×C₄	—	4	4	no	—
794	C₂×C₄	—	4	4	no	—
795	C₂×C₄	—	4	4	no	—
796	C₂×C₄	—	4	4	no	—
797	C₂×C₄	—	4	4	no	—
798	C₂×C₄	—	8	2	no	—
799	C₂×C₄	#120×C₁₁₃	1	2	yes	—
800	C₂×C₄	#120×C₁₁₃	1	2	yes	—
801	C₂×C₄	#120×C₁₁₃	1	1	yes	characteristic
802	C₂×C₄	#120×C₁₁₃	1	2	yes	—
803	C₂×C₄	#120×C₁₁₃	1	1	yes	characteristic
804	C₂×C₄	#121×C₁₁₃	1	2	yes	—
805	C₂×C₄	#121×C₁₁₃	1	2	yes	—
806	C₂×C₄	#121×C₁₁₃	1	2	yes	—
807	C₂×C₄	#121×C₁₁₃	1	2	yes	—
808	C₂×C₄	#121×C₁₁₃	1	2	yes	—
809	C₂×C₄	#127×C₁₁₃	1	2	yes	—
810	C₂×C₄	#127×C₁₁₃	1	2	yes	—
811	C₂×C₄	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
812	C₂×C₄	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
813	C₂×C₄	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
814	C₂×C₄	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
815	C₂×C₄	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
816	C₂×C₄	C₂×#41×C₁₁₃	1	1	yes	characteristic
817	C₈	—	2	4	no	—
818	C₈	—	4	2	no	—
819	C₂²	—	2	2	no	—
820	C₂²	—	2	2	no	—
821	C₂²	—	2	2	no	—
822	C₂²	—	4	2	no	—
823	C₂²	—	4	2	no	—
824	C₂²	—	4	4	no	—
825	C₂²	—	4	4	no	—
826	C₂²	—	4	2	no	—
827	C₂²	—	4	2	no	—
828	C₂²	—	4	2	no	—
829	C₂²	—	4	4	no	—
830	C₂²	—	4	4	no	—
831	C₂²	—	8	2	no	—
832	C₂²	—	8	2	no	—
833	C₂²	—	8	4	no	—
834	C₂²	—	8	2	no	—
835	C₂²	#392×C₁₁₃	1	2	yes	—
836	C₂²	#392×C₁₁₃	1	2	yes	—
837	C₂²	C₂×#120×C₁₁₃	1	1	yes	characteristic
838	C₂²	C₂×#120×C₁₁₃	1	1	yes	characteristic
839	C₂²	C₂×#121×C₁₁₃	1	1	yes	characteristic
840	C₄	—	2	4	no	—
841	C₄	—	4	2	no	—
842	C₄	—	4	2	no	—
843	C₄	—	4	2	no	—
844	C₄	—	4	2	no	—
845	C₄	—	4	4	no	—
846	C₄	#392×C₁₁₃	1	2	yes	—
847	C₄	#392×C₁₁₃	1	2	yes	—
848	C₄	C₂×#120×C₁₁₃	1	1	yes	characteristic
849	C₄	C₂×#121×C₁₁₃	1	1	yes	characteristic
850	C₄	C₂×#121×C₁₁₃	1	1	yes	characteristic
851	C₄	C₂×#127×C₁₁₃	1	1	yes	characteristic
852	C₂	—	2	1	no	—
853	C₂	—	2	1	no	—
854	C₂	—	2	2	no	—
855	C₂	—	2	2	no	—
856	C₂	—	8	2	no	—
857	C₂	—	8	2	no	—
858	C₂	—	8	2	no	—
859	C₂	C₂×#392×C₁₁₃	1	1	yes	characteristic
860	C₂	C₁₁₃×#3018	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₁₃	#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁₃
socle	C₂²×C₁₁₃	C₂×#120
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁₃ ◁ C₂³×C₄×C₁₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#575×C₁₁₃	C₂	semidirect
2. C₁₁₃×#3449	C₂	semidirect
3. C₂×#532×C₁₁₃	C₂	semidirect
4. C₂²×#104×C₁₁₃	C₂	semidirect
5. C₁₁₃×#2896	C₂	semidirect
6. C₂×#413×C₁₁₃	C₂	semidirect
7. C₁₁₃×#2005	C₂	semidirect
8. C₁₁₃×#2004	C₂	semidirect
9. C₁₁₃×#2003	C₂	semidirect
10. C₁₁₃×#2002	C₂	semidirect
11. C₂×#339×C₁₁₃	C₂	semidirect
33. C₂×C₄⋊Q₈×C₁₁₃	C₂²	semidirect
34. C₂×#127×C₁₁₃	C₂²	semidirect
35. C₂×#124×C₁₁₃	C₂²	semidirect
36. C₂×#124×C₁₁₃	C₂²	semidirect
46. #419×C₁₁₃	C₂²	semidirect
47. #418×C₁₁₃	C₂²	semidirect
51. C₂×#101×C₁₁₃	C₂²	semidirect
52. C₂×#100×C₁₁₃	C₂²	semidirect
53. #339×C₁₁₃	C₂²	semidirect
54. #339×C₁₁₃	C₂²	semidirect
76. C₂×#41×C₁₁₃	D₄	semidirect
77. C₂×#41×C₁₁₃	D₄	semidirect
79. C₂²×Q₈×C₁₁₃	D₄	semidirect
86. C₂²×D₄×C₁₁₃	D₄	semidirect
110. C₂×M₁₆×C₁₁₃	D₄	semidirect
141. #117×C₁₁₃	D₄	semidirect
144. C₂×C₄⋊C₄×C₁₁₃	D₄	semidirect
151. C₂×C₄²×C₁₁₃	D₄	semidirect
421. #23399	C₁₁₃	direct (N × H)
431. C₂×#575	C₂×C₁₁₃	semidirect
432. #3449	C₂×C₁₁₃	semidirect
433. C₂×#532	C₂×C₁₁₃	semidirect
434. C₂²×#104	C₂×C₁₁₃	semidirect
435. #2896	C₂×C₁₁₃	semidirect
436. C₂×#413	C₂×C₁₁₃	semidirect
437. #2005	C₂×C₁₁₃	semidirect
438. #2004	C₂×C₁₁₃	semidirect
439. #2003	C₂×C₁₁₃	semidirect
440. #2002	C₂×C₁₁₃	semidirect
441. C₂×#339	C₂×C₁₁₃	semidirect
442. C₁₁₃	#23399	direct (N × H)
464. C₂×C₄⋊Q₈	C₂²×C₁₁₃	semidirect
465. C₂×#127	C₂²×C₁₁₃	semidirect
466. C₂×#124	C₂²×C₁₁₃	semidirect
467. C₂×#124	C₂²×C₁₁₃	semidirect
477. #419	C₂²×C₁₁₃	semidirect
478. #418	C₂²×C₁₁₃	semidirect
482. C₂×#101	C₂²×C₁₁₃	semidirect
483. C₂×#100	C₂²×C₁₁₃	semidirect
484. #339	C₂²×C₁₁₃	semidirect
485. #339	C₂²×C₁₁₃	semidirect
507. C₂×#41	D₄×C₁₁₃	semidirect
508. C₂×#41	D₄×C₁₁₃	semidirect
510. C₂²×Q₈	D₄×C₁₁₃	semidirect
517. C₂²×D₄	D₄×C₁₁₃	semidirect
541. C₂×M₁₆	D₄×C₁₁₃	semidirect
572. #117	D₄×C₁₁₃	semidirect
575. C₂×C₄⋊C₄	D₄×C₁₁₃	semidirect
582. C₂×C₄²	D₄×C₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#575×C₁₁₃	2
C₁₁₃×#3449	2
C₂×#532×C₁₁₃	2
C₂²×#104×C₁₁₃	2
C₁₁₃×#2896	2
C₂×#413×C₁₁₃	2
C₁₁₃×#2005	2
C₁₁₃×#2004	2
C₁₁₃×#2003	2
C₁₁₃×#2002	2
C₂×#339×C₁₁₃	2
#23399	113

Subgroups — C113×#23399 #43291419

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁₃×#23399 #43291419