Subgroups — C₁₀₃×#24200 #39929475

Order 26368.

1380 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#550×C₁₀₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#460×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#440×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₀₃×#2581	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₀₃×#2041	C₂	1	2	yes	maximal, complemented
6	C₁₀₃×#2014	C₂	1	2	yes	maximal, complemented
7	C₁₀₃×#1985	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₀₃×#1961	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₀₃×#1877	C₂	1	2	yes	maximal, complemented
10	C₁₀₃×#1862	C₂	1	2	yes	maximal, complemented
11	C₁₀₃×#1804	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₁₀₃	—	2	1	no	—
13	C₂²×SD₁₆×C₁₀₃	C₂²	1	1	yes	characteristic
14	C₂²×SD₁₆×C₁₀₃	C₂²	1	2	yes	—
15	#550×C₁₀₃	—	2	4	no	—
16	#550×C₁₀₃	—	2	4	no	—
17	C₂×#127×C₁₀₃	C₂²	1	2	yes	—
18	C₂×#127×C₁₀₃	C₂²	1	1	yes	characteristic
19	C₂×#121×C₁₀₃	—	2	2	no	—
20	C₂×#121×C₁₀₃	—	2	1	no	—
21	C₂×C₄×Q₈×C₁₀₃	C₂²	1	1	yes	characteristic
22	C₂×C₄×Q₈×C₁₀₃	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₁₀₃	C₂²	1	2	yes	—
24	C₂×C₄×D₄×C₁₀₃	C₂²	1	1	yes	characteristic
25	#460×C₁₀₃	—	2	4	no	—
26	#440×C₁₀₃	—	2	4	no	—
27	C₂×#107×C₁₀₃	C₂²	1	1	yes	characteristic
28	C₂×C₄⋊C₈×C₁₀₃	C₂²	1	1	yes	characteristic
29	C₂×#103×C₁₀₃	C₂²	1	1	yes	characteristic
30	C₂×#102×C₁₀₃	C₂²	1	2	yes	—
31	C₂×#102×C₁₀₃	C₂²	1	2	yes	—
32	C₂×#102×C₁₀₃	C₂²	1	1	yes	characteristic
33	C₂×#102×C₁₀₃	C₂²	1	2	yes	—
34	C₂×#102×C₁₀₃	C₂²	1	2	yes	—
35	C₂×#97×C₁₀₃	C₂²	1	1	yes	characteristic
36	#400×C₁₀₃	—	2	1	no	—
37	#395×C₁₀₃	—	2	1	no	—
38	#391×C₁₀₃	C₂²	1	2	yes	—
39	#389×C₁₀₃	C₂²	1	2	yes	—
40	#387×C₁₀₃	—	2	2	no	—
41	#382×C₁₀₃	C₂²	1	1	yes	characteristic
42	#340×C₁₀₃	C₂²	1	2	yes	—
43	#336×C₁₀₃	C₂²	1	2	yes	—
44	#336×C₁₀₃	C₂²	1	2	yes	—
45	C₂×#41×C₁₀₃	—	2	8	no	—
46	C₂×#41×C₁₀₃	—	4	8	no	—
47	C₂²×Q₈×C₁₀₃	D₄	1	1	yes	characteristic
48	C₂²×Q₈×C₁₀₃	C₂³	1	1	yes	characteristic
49	C₂²×D₄×C₁₀₃	—	2	1	no	—
50	C₂²×D₄×C₁₀₃	—	2	2	no	—
51	C₂²×D₄×C₁₀₃	—	2	2	no	—
52	C₂²×D₄×C₁₀₃	—	2	1	no	—
53	C₂²×D₄×C₁₀₃	C₂³	1	2	yes	—
54	C₂²×D₄×C₁₀₃	C₂³	1	1	yes	characteristic
55	C₂³×C₄×C₁₀₃	—	2	2	no	—
56	C₂³×C₄×C₁₀₃	—	2	1	no	—
57	C₂×SD₁₆×C₁₀₃	—	2	2	no	—
58	C₂×SD₁₆×C₁₀₃	—	2	2	no	—
59	C₂×SD₁₆×C₁₀₃	—	2	4	no	—
60	C₂×SD₁₆×C₁₀₃	—	2	4	no	—
61	C₂×SD₁₆×C₁₀₃	—	2	2	no	—
62	C₂×SD₁₆×C₁₀₃	—	4	2	no	—
63	C₂²×C₈×C₁₀₃	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₁₀₃	C₂³	1	2	yes	—
65	C₂²×C₈×C₁₀₃	C₂³	1	1	yes	characteristic
66	#127×C₁₀₃	—	2	4	no	—
67	#127×C₁₀₃	—	2	4	no	—
68	#127×C₁₀₃	—	2	2	no	—
69	#127×C₁₀₃	D₄	1	4	yes	—
70	#121×C₁₀₃	—	2	8	no	—
71	#121×C₁₀₃	—	2	16	no	—
72	C₄×Q₈×C₁₀₃	—	2	2	no	—
73	C₄×Q₈×C₁₀₃	—	2	2	no	—
74	C₄×Q₈×C₁₀₃	—	2	2	no	—
75	C₄×Q₈×C₁₀₃	—	2	2	no	—
76	C₄×D₄×C₁₀₃	—	2	4	no	—
77	C₄×D₄×C₁₀₃	—	2	4	no	—
78	C₄×D₄×C₁₀₃	—	2	2	no	—
79	C₄×D₄×C₁₀₃	D₄	1	4	yes	—
80	C₂×C₄⋊C₄×C₁₀₃	—	2	2	no	—
81	C₂×C₄⋊C₄×C₁₀₃	—	2	1	no	—
82	C₂×C₄⋊C₄×C₁₀₃	D₄	1	2	yes	—
83	C₂×C₄⋊C₄×C₁₀₃	D₄	1	1	yes	characteristic
84	C₂×C₄⋊C₄×C₁₀₃	C₂³	1	2	yes	—
85	C₂×C₄⋊C₄×C₁₀₃	C₂³	1	1	yes	characteristic
86	C₂×C₄⋊C₄×C₁₀₃	C₂³	1	1	yes	characteristic
87	C₂×C₂²⋊C₄×C₁₀₃	—	2	2	no	—
88	C₂×C₂²⋊C₄×C₁₀₃	—	2	1	no	—
89	C₂×C₄²×C₁₀₃	—	2	1	no	—
90	C₂×C₄²×C₁₀₃	C₂³	1	2	yes	—
91	C₂×C₄²×C₁₀₃	C₂³	1	1	yes	characteristic
92	#107×C₁₀₃	—	2	2	no	—
93	C₄⋊C₈×C₁₀₃	—	2	2	no	—
94	#103×C₁₀₃	—	2	2	no	—
95	#102×C₁₀₃	—	2	2	no	—
96	#102×C₁₀₃	—	2	4	no	—
97	#102×C₁₀₃	—	2	4	no	—
98	#102×C₁₀₃	—	4	2	no	—
99	#102×C₁₀₃	—	4	2	no	—
100	#97×C₁₀₃	—	2	2	no	—
101	#95×C₁₀₃	—	2	1	no	—
102	#95×C₁₀₃	—	2	1	no	—
103	#95×C₁₀₃	—	2	2	no	—
104	#95×C₁₀₃	—	2	2	no	—
105	#95×C₁₀₃	—	2	2	no	—
106	C₂⁴×C₁₀₃	—	2	2	no	—
107	C₂⁴×C₁₀₃	—	2	1	no	—
108	#41×C₁₀₃	—	4	32	no	—
109	C₂×Q₈×C₁₀₃	—	2	2	no	—
110	C₂×Q₈×C₁₀₃	—	2	4	no	—
111	C₂×Q₈×C₁₀₃	—	2	1	no	—
112	C₂×Q₈×C₁₀₃	—	2	1	no	—
113	C₂×Q₈×C₁₀₃	—	2	1	no	—
114	C₂×Q₈×C₁₀₃	—	2	1	no	—
115	C₂×Q₈×C₁₀₃	—	2	1	no	—
116	C₂×Q₈×C₁₀₃	#41	1	2	yes	complemented
117	C₂×D₄×C₁₀₃	—	2	8	no	—
118	C₂×D₄×C₁₀₃	—	2	8	no	—
119	C₂×D₄×C₁₀₃	—	2	4	no	—
120	C₂×D₄×C₁₀₃	—	2	4	no	—
121	C₂×D₄×C₁₀₃	—	2	2	no	—
122	C₂×D₄×C₁₀₃	—	2	1	no	—
123	C₂×D₄×C₁₀₃	—	2	2	no	—
124	C₂×D₄×C₁₀₃	—	2	1	no	—
125	C₂×D₄×C₁₀₃	—	2	2	no	—
126	C₂×D₄×C₁₀₃	—	2	1	no	—
127	C₂×D₄×C₁₀₃	—	2	1	no	—
128	C₂×D₄×C₁₀₃	—	2	2	no	—
129	C₂×D₄×C₁₀₃	—	2	1	no	—
130	C₂×D₄×C₁₀₃	—	2	2	no	—
131	C₂×D₄×C₁₀₃	—	4	4	no	—
132	C₂×D₄×C₁₀₃	—	4	4	no	—
133	C₂×D₄×C₁₀₃	—	4	4	no	—
134	C₂×D₄×C₁₀₃	—	8	2	no	—
135	C₂×D₄×C₁₀₃	—	8	2	no	—
136	C₂×D₄×C₁₀₃	—	8	2	no	—
137	C₂×D₄×C₁₀₃	C₂×D₄	1	4	yes	—
138	C₂×D₄×C₁₀₃	C₂×D₄	1	2	yes	—
139	C₂²×C₄×C₁₀₃	—	2	8	no	—
140	C₂²×C₄×C₁₀₃	—	2	1	no	—
141	C₂²×C₄×C₁₀₃	—	2	1	no	—
142	C₂²×C₄×C₁₀₃	—	2	4	no	—
143	C₂²×C₄×C₁₀₃	—	2	2	no	—
144	C₂²×C₄×C₁₀₃	—	2	1	no	—
145	C₂²×C₄×C₁₀₃	—	4	4	no	—
146	C₂²×C₄×C₁₀₃	—	4	4	no	—
147	C₂²×C₄×C₁₀₃	—	4	4	no	—
148	C₂²×C₄×C₁₀₃	C₂×D₄	1	2	yes	—
149	C₂²×C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₁₀₃	C₂×D₄	1	2	yes	—
152	C₂²×C₄×C₁₀₃	C₂⁴	1	1	yes	characteristic
153	SD₁₆×C₁₀₃	—	2	8	no	—
154	SD₁₆×C₁₀₃	—	4	8	no	—
155	C₂×C₈×C₁₀₃	—	2	1	no	—
156	C₂×C₈×C₁₀₃	—	2	1	no	—
157	C₂×C₈×C₁₀₃	—	2	1	no	—
158	C₂×C₈×C₁₀₃	—	2	2	no	—
159	C₂×C₈×C₁₀₃	—	2	2	no	—
160	C₂×C₈×C₁₀₃	—	2	1	no	—
161	C₂×C₈×C₁₀₃	—	2	2	no	—
162	C₂×C₈×C₁₀₃	—	2	1	no	—
163	C₂×C₈×C₁₀₃	#41	1	2	yes	complemented
164	C₄⋊C₄×C₁₀₃	—	2	4	no	—
165	C₄⋊C₄×C₁₀₃	—	2	2	no	—
166	C₄⋊C₄×C₁₀₃	—	2	1	no	—
167	C₄⋊C₄×C₁₀₃	—	2	1	no	—
168	C₄⋊C₄×C₁₀₃	—	2	1	no	—
169	C₄⋊C₄×C₁₀₃	—	2	2	no	—
170	C₄⋊C₄×C₁₀₃	—	2	2	no	—
171	C₄⋊C₄×C₁₀₃	—	4	2	no	—
172	C₄⋊C₄×C₁₀₃	—	4	4	no	—
173	C₄⋊C₄×C₁₀₃	C₂×D₄	1	2	yes	—
174	C₂²⋊C₄×C₁₀₃	—	2	8	no	—
175	C₂²⋊C₄×C₁₀₃	—	2	4	no	—
176	C₄²×C₁₀₃	—	2	2	no	—
177	C₄²×C₁₀₃	—	2	2	no	—
178	C₄²×C₁₀₃	—	4	2	no	—
179	C₄²×C₁₀₃	C₂×D₄	1	2	yes	—
180	C₄²×C₁₀₃	C₂×D₄	1	2	yes	—
181	C₂³×C₁₀₃	—	2	4	no	—
182	C₂³×C₁₀₃	—	2	2	no	—
183	C₂³×C₁₀₃	—	4	1	no	—
184	C₂³×C₁₀₃	—	4	2	no	—
185	C₂³×C₁₀₃	—	4	2	no	—
186	C₂³×C₁₀₃	—	4	1	no	—
187	C₂³×C₁₀₃	—	4	2	no	—
188	C₂³×C₁₀₃	—	4	2	no	—
189	C₂³×C₁₀₃	—	4	2	no	—
190	C₂³×C₁₀₃	—	4	2	no	—
191	C₂³×C₁₀₃	—	4	2	no	—
192	C₂³×C₁₀₃	—	4	2	no	—
193	C₂³×C₁₀₃	C₂²×D₄	1	1	yes	characteristic
194	Q₈×C₁₀₃	—	2	8	no	—
195	Q₈×C₁₀₃	—	2	2	no	—
196	Q₈×C₁₀₃	—	2	2	no	—
197	Q₈×C₁₀₃	—	4	1	no	—
198	Q₈×C₁₀₃	—	4	1	no	—
199	D₄×C₁₀₃	—	2	2	no	—
200	D₄×C₁₀₃	—	2	2	no	—
201	D₄×C₁₀₃	—	2	4	no	—
202	D₄×C₁₀₃	—	2	4	no	—
203	D₄×C₁₀₃	—	4	8	no	—
204	D₄×C₁₀₃	—	4	16	no	—
205	D₄×C₁₀₃	—	4	2	no	—
206	D₄×C₁₀₃	—	4	2	no	—
207	D₄×C₁₀₃	—	4	1	no	—
208	D₄×C₁₀₃	—	4	1	no	—
209	D₄×C₁₀₃	—	8	4	no	—
210	D₄×C₁₀₃	—	8	8	no	—
211	C₂×C₄×C₁₀₃	—	2	2	no	—
212	C₂×C₄×C₁₀₃	—	2	2	no	—
213	C₂×C₄×C₁₀₃	—	2	2	no	—
214	C₂×C₄×C₁₀₃	—	2	2	no	—
215	C₂×C₄×C₁₀₃	—	2	2	no	—
216	C₂×C₄×C₁₀₃	—	2	2	no	—
217	C₂×C₄×C₁₀₃	—	2	2	no	—
218	C₂×C₄×C₁₀₃	—	2	2	no	—
219	C₂×C₄×C₁₀₃	—	2	2	no	—
220	C₂×C₄×C₁₀₃	—	4	8	no	—
221	C₂×C₄×C₁₀₃	—	4	16	no	—
222	C₂×C₄×C₁₀₃	—	4	1	no	—
223	C₂×C₄×C₁₀₃	—	4	1	no	—
224	C₂×C₄×C₁₀₃	—	4	2	no	—
225	C₂×C₄×C₁₀₃	—	4	1	no	—
226	C₂×C₄×C₁₀₃	—	4	2	no	—
227	C₂×C₄×C₁₀₃	—	4	2	no	—
228	C₂×C₄×C₁₀₃	—	4	2	no	—
229	C₂×C₄×C₁₀₃	—	4	2	no	—
230	C₂×C₄×C₁₀₃	#120	1	2	yes	—
231	C₂×C₄×C₁₀₃	#120	1	2	yes	—
232	C₂×C₄×C₁₀₃	AGL(1,ℤ/8)	1	4	yes	—
233	C₂×C₄×C₁₀₃	C₂²×D₄	1	1	yes	characteristic
234	C₂×C₄×C₁₀₃	C₂²×D₄	1	1	yes	characteristic
235	C₂×C₄×C₁₀₃	C₂×#41	1	1	yes	characteristic
236	C₂×C₄×C₁₀₃	C₂×#41	1	1	yes	characteristic
237	C₂×C₄×C₁₀₃	H(5,𝔽₂)	1	1	yes	characteristic
238	C₂×C₄×C₁₀₃	2₋¹⁺⁴	1	1	yes	characteristic
239	C₈×C₁₀₃	—	2	2	no	—
240	C₈×C₁₀₃	—	4	1	no	—
241	C₈×C₁₀₃	—	4	2	no	—
242	C₂²×C₁₀₃	—	4	2	no	—
243	C₂²×C₁₀₃	—	4	4	no	—
244	C₂²×C₁₀₃	—	4	2	no	—
245	C₂²×C₁₀₃	—	4	4	no	—
246	C₂²×C₁₀₃	—	4	4	no	—
247	C₂²×C₁₀₃	—	4	2	no	—
248	C₂²×C₁₀₃	—	8	2	no	—
249	C₂²×C₁₀₃	—	8	2	no	—
250	C₂²×C₁₀₃	—	8	2	no	—
251	C₂²×C₁₀₃	—	8	2	no	—
252	C₂²×C₁₀₃	—	8	2	no	—
253	C₂²×C₁₀₃	—	8	2	no	—
254	C₂²×C₁₀₃	C₂×#120	1	1	yes	characteristic
255	C₂²×C₁₀₃	#548	1	1	yes	characteristic
256	C₂²×C₁₀₃	#550	1	1	yes	characteristic
257	C₂²×C₁₀₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
258	C₂²×C₁₀₃	#577	1	2	yes	—
259	C₄×C₁₀₃	—	2	2	no	—
260	C₄×C₁₀₃	—	2	4	no	—
261	C₄×C₁₀₃	—	2	2	no	—
262	C₄×C₁₀₃	—	4	2	no	—
263	C₄×C₁₀₃	—	4	2	no	—
264	C₄×C₁₀₃	—	4	2	no	—
265	C₄×C₁₀₃	—	8	2	no	—
266	C₄×C₁₀₃	—	8	1	no	—
267	C₄×C₁₀₃	#525	1	1	yes	characteristic
268	C₄×C₁₀₃	#537	1	1	yes	characteristic
269	C₄×C₁₀₃	#546	1	1	yes	characteristic
270	C₄×C₁₀₃	#547	1	1	yes	characteristic
271	#24200	C₁₀₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
272	C₂×C₁₀₃	—	8	2	no	—
273	C₂×C₁₀₃	—	8	4	no	—
274	C₂×C₁₀₃	#2407	1	1	yes	characteristic
275	C₂×C₁₀₃	#3003	1	1	yes	characteristic
276	C₂×C₁₀₃	#3009	1	1	yes	characteristic
277	C₂×C₁₀₃	#3368	1	2	yes	—
278	C₂×C₁₀₃	#3397	1	2	yes	—
279	C₂×#550	C₂×C₁₀₃	1	1	yes	characteristic
280	C₂×#460	C₂×C₁₀₃	1	1	yes	characteristic, complemented
281	C₂×#440	C₂×C₁₀₃	1	1	yes	characteristic, complemented
282	#2581	C₂×C₁₀₃	1	1	yes	characteristic, complemented
283	#2041	C₂×C₁₀₃	1	2	yes	complemented
284	#2014	C₂×C₁₀₃	1	2	yes	complemented
285	#1985	C₂×C₁₀₃	1	1	yes	characteristic, complemented
286	#1961	C₂×C₁₀₃	1	1	yes	characteristic, complemented
287	#1877	C₂×C₁₀₃	1	2	yes	complemented
288	#1862	C₂×C₁₀₃	1	2	yes	complemented
289	#1804	C₂×C₁₀₃	1	1	yes	characteristic, complemented
290	C₁₀₃	#24200	1	1	yes	characteristic, direct product factor, Sylow
291	C₂²×#41	—	2	1	no	—
292	C₂²×SD₁₆	C₂²×C₁₀₃	1	1	yes	characteristic
293	C₂²×SD₁₆	C₂²×C₁₀₃	1	2	yes	—
294	#550	—	2	4	no	—
295	#550	—	2	4	no	—
296	C₂×#127	C₂²×C₁₀₃	1	2	yes	—
297	C₂×#127	C₂²×C₁₀₃	1	1	yes	characteristic
298	C₂×#121	—	2	2	no	—
299	C₂×#121	—	2	1	no	—
300	C₂×C₄×Q₈	C₂²×C₁₀₃	1	1	yes	characteristic
301	C₂×C₄×Q₈	C₂²×C₁₀₃	1	1	yes	characteristic
302	C₂×C₄×D₄	C₂²×C₁₀₃	1	2	yes	—
303	C₂×C₄×D₄	C₂²×C₁₀₃	1	1	yes	characteristic
304	#460	—	2	4	no	—
305	#440	—	2	4	no	—
306	C₂×#107	C₂²×C₁₀₃	1	1	yes	characteristic
307	C₂×C₄⋊C₈	C₂²×C₁₀₃	1	1	yes	characteristic
308	C₂×#103	C₂²×C₁₀₃	1	1	yes	characteristic
309	C₂×#102	C₂²×C₁₀₃	1	2	yes	—
310	C₂×#102	C₂²×C₁₀₃	1	2	yes	—
311	C₂×#102	C₂²×C₁₀₃	1	1	yes	characteristic
312	C₂×#102	C₂²×C₁₀₃	1	2	yes	—
313	C₂×#102	C₂²×C₁₀₃	1	2	yes	—
314	C₂×#97	C₂²×C₁₀₃	1	1	yes	characteristic
315	#400	—	2	1	no	—
316	#395	—	2	1	no	—
317	#391	C₂²×C₁₀₃	1	2	yes	—
318	#389	C₂²×C₁₀₃	1	2	yes	—
319	#387	—	2	2	no	—
320	#382	C₂²×C₁₀₃	1	1	yes	characteristic
321	#340	C₂²×C₁₀₃	1	2	yes	—
322	#336	C₂²×C₁₀₃	1	2	yes	—
323	#336	C₂²×C₁₀₃	1	2	yes	—
324	C₂×#41	—	2	8	no	—
325	C₂×#41	—	4	8	no	—
326	C₂²×Q₈	D₄×C₁₀₃	1	1	yes	characteristic
327	C₂²×Q₈	C₂³×C₁₀₃	1	1	yes	characteristic
328	C₂²×D₄	—	2	1	no	—
329	C₂²×D₄	—	2	2	no	—
330	C₂²×D₄	—	2	2	no	—
331	C₂²×D₄	—	2	1	no	—
332	C₂²×D₄	C₂³×C₁₀₃	1	2	yes	—
333	C₂²×D₄	C₂³×C₁₀₃	1	1	yes	characteristic
334	C₂³×C₄	—	2	2	no	—
335	C₂³×C₄	—	2	1	no	—
336	C₂×SD₁₆	—	2	2	no	—
337	C₂×SD₁₆	—	2	2	no	—
338	C₂×SD₁₆	—	2	4	no	—
339	C₂×SD₁₆	—	2	4	no	—
340	C₂×SD₁₆	—	2	2	no	—
341	C₂×SD₁₆	—	4	2	no	—
342	C₂²×C₈	C₂³×C₁₀₃	1	2	yes	—
343	C₂²×C₈	C₂³×C₁₀₃	1	1	yes	characteristic
344	C₂²×C₈	C₂³×C₁₀₃	1	1	yes	characteristic
345	#127	—	2	4	no	—
346	#127	—	2	4	no	—
347	#127	—	2	2	no	—
348	#127	D₄×C₁₀₃	1	4	yes	—
349	#121	—	2	8	no	—
350	#121	—	2	16	no	—
351	C₄×Q₈	—	2	2	no	—
352	C₄×Q₈	—	2	2	no	—
353	C₄×Q₈	—	2	2	no	—
354	C₄×Q₈	—	2	2	no	—
355	C₄×D₄	—	2	4	no	—
356	C₄×D₄	—	2	4	no	—
357	C₄×D₄	—	2	2	no	—
358	C₄×D₄	D₄×C₁₀₃	1	4	yes	—
359	C₂×C₄⋊C₄	—	2	1	no	—
360	C₂×C₄⋊C₄	—	2	2	no	—
361	C₂×C₄⋊C₄	D₄×C₁₀₃	1	2	yes	—
362	C₂×C₄⋊C₄	D₄×C₁₀₃	1	1	yes	characteristic
363	C₂×C₄⋊C₄	C₂³×C₁₀₃	1	1	yes	characteristic
364	C₂×C₄⋊C₄	C₂³×C₁₀₃	1	2	yes	—
365	C₂×C₄⋊C₄	C₂³×C₁₀₃	1	1	yes	characteristic
366	C₂×C₂²⋊C₄	—	2	2	no	—
367	C₂×C₂²⋊C₄	—	2	1	no	—
368	C₂×C₄²	—	2	1	no	—
369	C₂×C₄²	C₂³×C₁₀₃	1	2	yes	—
370	C₂×C₄²	C₂³×C₁₀₃	1	1	yes	characteristic
371	#107	—	2	2	no	—
372	C₄⋊C₈	—	2	2	no	—
373	#103	—	2	2	no	—
374	#102	—	2	2	no	—
375	#102	—	2	4	no	—
376	#102	—	2	4	no	—
377	#102	—	4	2	no	—
378	#102	—	4	2	no	—
379	#97	—	2	2	no	—
380	#95	—	2	1	no	—
381	#95	—	2	1	no	—
382	#95	—	2	2	no	—
383	#95	—	2	2	no	—
384	#95	—	2	2	no	—
385	C₂⁴	—	2	2	no	—
386	C₂⁴	—	2	1	no	—
387	#41	—	4	32	no	—
388	C₂×Q₈	—	2	2	no	—
389	C₂×Q₈	—	2	4	no	—
390	C₂×Q₈	—	2	1	no	—
391	C₂×Q₈	—	2	1	no	—
392	C₂×Q₈	—	2	1	no	—
393	C₂×Q₈	—	2	1	no	—
394	C₂×Q₈	—	2	1	no	—
395	C₂×Q₈	#41×C₁₀₃	1	2	yes	complemented
396	C₂×D₄	—	2	8	no	—
397	C₂×D₄	—	2	8	no	—
398	C₂×D₄	—	2	4	no	—
399	C₂×D₄	—	2	4	no	—
400	C₂×D₄	—	2	2	no	—
401	C₂×D₄	—	2	1	no	—
402	C₂×D₄	—	2	2	no	—
403	C₂×D₄	—	2	1	no	—
404	C₂×D₄	—	2	2	no	—
405	C₂×D₄	—	2	1	no	—
406	C₂×D₄	—	2	1	no	—
407	C₂×D₄	—	2	2	no	—
408	C₂×D₄	—	2	1	no	—
409	C₂×D₄	—	2	2	no	—
410	C₂×D₄	—	4	4	no	—
411	C₂×D₄	—	4	4	no	—
412	C₂×D₄	—	4	4	no	—
413	C₂×D₄	—	8	2	no	—
414	C₂×D₄	—	8	2	no	—
415	C₂×D₄	—	8	2	no	—
416	C₂×D₄	C₂×D₄×C₁₀₃	1	4	yes	—
417	C₂×D₄	C₂×D₄×C₁₀₃	1	2	yes	—
418	C₂²×C₄	—	2	8	no	—
419	C₂²×C₄	—	2	1	no	—
420	C₂²×C₄	—	2	1	no	—
421	C₂²×C₄	—	2	4	no	—
422	C₂²×C₄	—	2	2	no	—
423	C₂²×C₄	—	2	1	no	—
424	C₂²×C₄	—	4	4	no	—
425	C₂²×C₄	—	4	4	no	—
426	C₂²×C₄	—	4	4	no	—
427	C₂²×C₄	C₂×D₄×C₁₀₃	1	2	yes	—
428	C₂²×C₄	C₂×D₄×C₁₀₃	1	1	yes	characteristic
429	C₂²×C₄	C₂×D₄×C₁₀₃	1	1	yes	characteristic
430	C₂²×C₄	C₂×D₄×C₁₀₃	1	2	yes	—
431	C₂²×C₄	C₂⁴×C₁₀₃	1	1	yes	characteristic
432	SD₁₆	—	2	8	no	—
433	SD₁₆	—	4	8	no	—
434	C₂×C₈	—	2	1	no	—
435	C₂×C₈	—	2	1	no	—
436	C₂×C₈	—	2	1	no	—
437	C₂×C₈	—	2	2	no	—
438	C₂×C₈	—	2	2	no	—
439	C₂×C₈	—	2	1	no	—
440	C₂×C₈	—	2	2	no	—
441	C₂×C₈	—	2	1	no	—
442	C₂×C₈	#41×C₁₀₃	1	2	yes	complemented
443	C₄⋊C₄	—	2	4	no	—
444	C₄⋊C₄	—	2	2	no	—
445	C₄⋊C₄	—	2	1	no	—
446	C₄⋊C₄	—	2	1	no	—
447	C₄⋊C₄	—	2	1	no	—
448	C₄⋊C₄	—	2	2	no	—
449	C₄⋊C₄	—	2	2	no	—
450	C₄⋊C₄	—	4	2	no	—
451	C₄⋊C₄	—	4	4	no	—
452	C₄⋊C₄	C₂×D₄×C₁₀₃	1	2	yes	—
453	C₂²⋊C₄	—	2	8	no	—
454	C₂²⋊C₄	—	2	4	no	—
455	C₄²	—	2	2	no	—
456	C₄²	—	2	2	no	—
457	C₄²	—	4	2	no	—
458	C₄²	C₂×D₄×C₁₀₃	1	2	yes	—
459	C₄²	C₂×D₄×C₁₀₃	1	2	yes	—
460	C₂³	—	2	4	no	—
461	C₂³	—	2	2	no	—
462	C₂³	—	4	1	no	—
463	C₂³	—	4	2	no	—
464	C₂³	—	4	2	no	—
465	C₂³	—	4	1	no	—
466	C₂³	—	4	2	no	—
467	C₂³	—	4	2	no	—
468	C₂³	—	4	2	no	—
469	C₂³	—	4	2	no	—
470	C₂³	—	4	2	no	—
471	C₂³	—	4	2	no	—
472	C₂³	C₂²×D₄×C₁₀₃	1	1	yes	characteristic
473	Q₈	—	2	8	no	—
474	Q₈	—	2	2	no	—
475	Q₈	—	2	2	no	—
476	Q₈	—	4	1	no	—
477	Q₈	—	4	1	no	—
478	D₄	—	2	2	no	—
479	D₄	—	2	2	no	—
480	D₄	—	2	4	no	—
481	D₄	—	2	4	no	—
482	D₄	—	4	8	no	—
483	D₄	—	4	16	no	—
484	D₄	—	4	2	no	—
485	D₄	—	4	2	no	—
486	D₄	—	4	1	no	—
487	D₄	—	4	1	no	—
488	D₄	—	8	4	no	—
489	D₄	—	8	8	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	4	8	no	—
500	C₂×C₄	—	4	16	no	—
501	C₂×C₄	—	4	1	no	—
502	C₂×C₄	—	4	1	no	—
503	C₂×C₄	—	4	2	no	—
504	C₂×C₄	—	4	1	no	—
505	C₂×C₄	—	4	2	no	—
506	C₂×C₄	—	4	2	no	—
507	C₂×C₄	—	4	2	no	—
508	C₂×C₄	—	4	2	no	—
509	C₂×C₄	#120×C₁₀₃	1	2	yes	—
510	C₂×C₄	#120×C₁₀₃	1	2	yes	—
511	C₂×C₄	AGL(1,ℤ/8)×C₁₀₃	1	4	yes	—
512	C₂×C₄	C₂²×D₄×C₁₀₃	1	1	yes	characteristic
513	C₂×C₄	C₂²×D₄×C₁₀₃	1	1	yes	characteristic
514	C₂×C₄	C₂×#41×C₁₀₃	1	1	yes	characteristic
515	C₂×C₄	C₂×#41×C₁₀₃	1	1	yes	characteristic
516	C₂×C₄	H(5,𝔽₂)×C₁₀₃	1	1	yes	characteristic
517	C₂×C₄	2₋¹⁺⁴×C₁₀₃	1	1	yes	characteristic
518	C₈	—	2	2	no	—
519	C₈	—	4	1	no	—
520	C₈	—	4	2	no	—
521	C₂²	—	4	2	no	—
522	C₂²	—	4	4	no	—
523	C₂²	—	4	4	no	—
524	C₂²	—	4	2	no	—
525	C₂²	—	4	2	no	—
526	C₂²	—	4	4	no	—
527	C₂²	—	8	2	no	—
528	C₂²	—	8	2	no	—
529	C₂²	—	8	2	no	—
530	C₂²	—	8	2	no	—
531	C₂²	—	8	2	no	—
532	C₂²	—	8	2	no	—
533	C₂²	C₂×#120×C₁₀₃	1	1	yes	characteristic
534	C₂²	#548×C₁₀₃	1	1	yes	characteristic
535	C₂²	#550×C₁₀₃	1	1	yes	characteristic
536	C₂²	C₂×AGL(1,ℤ/8)×C₁₀₃	1	2	yes	—
537	C₂²	#577×C₁₀₃	1	2	yes	—
538	C₄	—	2	2	no	—
539	C₄	—	2	4	no	—
540	C₄	—	2	2	no	—
541	C₄	—	4	2	no	—
542	C₄	—	4	2	no	—
543	C₄	—	4	2	no	—
544	C₄	—	8	1	no	—
545	C₄	—	8	2	no	—
546	C₄	#525×C₁₀₃	1	1	yes	characteristic
547	C₄	#537×C₁₀₃	1	1	yes	characteristic
548	C₄	#546×C₁₀₃	1	1	yes	characteristic
549	C₄	#547×C₁₀₃	1	1	yes	characteristic
550	C₂	—	8	4	no	—
551	C₂	—	8	2	no	—
552	C₂	C₁₀₃×#2407	1	1	yes	characteristic
553	C₂	C₁₀₃×#3003	1	1	yes	characteristic
554	C₂	C₁₀₃×#3009	1	1	yes	characteristic
555	C₂	C₁₀₃×#3368	1	2	yes	—
556	C₂	C₁₀₃×#3397	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₀₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₀₃
prime radical	C₂×#550×C₁₀₃	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₀₃ ◁ C₂×C₄×Q₈×C₁₀₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#460×C₁₀₃	C₂	semidirect
3. C₂×#440×C₁₀₃	C₂	semidirect
4. C₁₀₃×#2581	C₂	semidirect
5. C₁₀₃×#2041	C₂	semidirect
6. C₁₀₃×#2014	C₂	semidirect
7. C₁₀₃×#1985	C₂	semidirect
8. C₁₀₃×#1961	C₂	semidirect
9. C₁₀₃×#1877	C₂	semidirect
10. C₁₀₃×#1862	C₂	semidirect
11. C₁₀₃×#1804	C₂	semidirect
116. C₂×Q₈×C₁₀₃	#41	semidirect
163. C₂×C₈×C₁₀₃	#41	semidirect
271. #24200	C₁₀₃	direct (N × H)
280. C₂×#460	C₂×C₁₀₃	semidirect
281. C₂×#440	C₂×C₁₀₃	semidirect
282. #2581	C₂×C₁₀₃	semidirect
283. #2041	C₂×C₁₀₃	semidirect
284. #2014	C₂×C₁₀₃	semidirect
285. #1985	C₂×C₁₀₃	semidirect
286. #1961	C₂×C₁₀₃	semidirect
287. #1877	C₂×C₁₀₃	semidirect
288. #1862	C₂×C₁₀₃	semidirect
289. #1804	C₂×C₁₀₃	semidirect
290. C₁₀₃	#24200	direct (N × H)
395. C₂×Q₈	#41×C₁₀₃	semidirect
442. C₂×C₈	#41×C₁₀₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#550×C₁₀₃	2
C₂×#460×C₁₀₃	2
C₂×#440×C₁₀₃	2
C₁₀₃×#2581	2
C₁₀₃×#2041	2
C₁₀₃×#2014	2
C₁₀₃×#1985	2
C₁₀₃×#1961	2
C₁₀₃×#1877	2
C₁₀₃×#1862	2
C₁₀₃×#1804	2
#24200	103

Subgroups — C103×#24200 #39929475

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₃×#24200 #39929475