Subgroups — C₁₀₃×#19673 #39924948

Order 26368.

862 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₀₃×#3206	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₀₃×#3205	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₀₃×#3169	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₀₃×#3151	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₀₃×#3141	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#486×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₀₃×#1721	C₂	1	2	yes	maximal, complemented
8	C₁₀₃×#1719	C₂	1	2	yes	maximal, complemented
9	C₁₀₃×#1717	C₂	1	2	yes	maximal, complemented
10	C₁₀₃×#1717	C₂	1	2	yes	maximal, complemented
11	C₁₀₃×#1451	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×AGL(1,ℤ/8)×C₁₀₃	—	2	2	no	—
13	#532×C₁₀₃	C₂²	1	1	yes	characteristic
14	#532×C₁₀₃	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊Q₈×C₁₀₃	C₂²	1	1	yes	characteristic
16	C₂×#127×C₁₀₃	C₂²	1	1	yes	characteristic
17	#500×C₁₀₃	C₂²	1	1	yes	characteristic, complemented
18	#496×C₁₀₃	—	2	2	no	—
19	#493×C₁₀₃	C₂²	1	2	yes	—
20	#493×C₁₀₃	C₂²	1	2	yes	—
21	#493×C₁₀₃	C₂²	1	1	yes	characteristic, complemented
22	#492×C₁₀₃	C₂²	1	2	yes	—
23	#492×C₁₀₃	C₂²	1	2	yes	complemented
24	#489×C₁₀₃	—	2	2	no	—
25	#487×C₁₀₃	C₂²	1	2	yes	complemented
26	#487×C₁₀₃	C₂²	1	2	yes	complemented
27	#486×C₁₀₃	—	2	2	no	—
28	#486×C₁₀₃	C₂²	1	2	yes	—
29	#486×C₁₀₃	C₂²	1	2	yes	—
30	#486×C₁₀₃	C₂²	1	2	yes	—
31	#486×C₁₀₃	C₂²	1	1	yes	characteristic, complemented
32	#486×C₁₀₃	C₂²	1	1	yes	characteristic, complemented
33	#486×C₁₀₃	C₂²	1	2	yes	complemented
34	#466×C₁₀₃	—	2	2	no	—
35	#461×C₁₀₃	—	2	2	no	—
36	#459×C₁₀₃	—	2	2	no	—
37	#448×C₁₀₃	—	2	2	no	—
38	#447×C₁₀₃	—	2	2	no	—
39	C₄×D₈×C₁₀₃	—	2	2	no	—
40	#431×C₁₀₃	C₂²	1	1	yes	characteristic
41	#417×C₁₀₃	—	2	2	no	—
42	C₂×#102×C₁₀₃	—	2	2	no	—
43	C₄×M₁₆×C₁₀₃	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₈×C₁₀₃	C₂²	1	1	yes	characteristic
45	#322×C₁₀₃	C₂²	1	2	yes	complemented
46	#322×C₁₀₃	C₂²	1	2	yes	complemented
47	C₂×#41×C₁₀₃	—	2	1	no	—
48	C₂×#41×C₁₀₃	—	2	1	no	—
49	C₂²×Q₈×C₁₀₃	—	2	1	no	—
50	C₂²×D₄×C₁₀₃	—	2	1	no	—
51	C₂²×D₄×C₁₀₃	—	2	1	no	—
52	C₂²×D₄×C₁₀₃	—	2	1	no	—
53	AGL(1,ℤ/8)×C₁₀₃	—	4	8	no	—
54	C₂×SD₁₆×C₁₀₃	—	2	4	no	—
55	C₂×SD₁₆×C₁₀₃	—	2	4	no	—
56	C₂×D₈×C₁₀₃	—	2	2	no	—
57	C₂×D₈×C₁₀₃	—	2	4	no	—
58	C₂×D₈×C₁₀₃	—	2	4	no	—
59	C₂×M₁₆×C₁₀₃	D₄	1	2	yes	—
60	C₂²×C₈×C₁₀₃	D₄	1	2	yes	—
61	C₄⋊Q₈×C₁₀₃	—	2	1	no	—
62	C₄⋊Q₈×C₁₀₃	—	2	1	no	—
63	C₄⋊Q₈×C₁₀₃	—	2	1	no	—
64	C₄⋊Q₈×C₁₀₃	C₂³	1	2	yes	—
65	C₄⋊Q₈×C₁₀₃	C₂³	1	1	yes	characteristic
66	C₄⋊Q₈×C₁₀₃	C₂³	1	1	yes	characteristic
67	#127×C₁₀₃	—	2	1	no	—
68	#127×C₁₀₃	—	2	1	no	—
69	#127×C₁₀₃	—	2	1	no	—
70	#127×C₁₀₃	C₂³	1	2	yes	—
71	#127×C₁₀₃	C₂³	1	1	yes	characteristic
72	#127×C₁₀₃	C₂³	1	1	yes	characteristic
73	#124×C₁₀₃	—	2	1	no	—
74	#124×C₁₀₃	—	2	1	no	—
75	#121×C₁₀₃	—	2	1	no	—
76	#121×C₁₀₃	—	2	1	no	—
77	#121×C₁₀₃	—	2	1	no	—
78	#121×C₁₀₃	—	2	1	no	—
79	C₄×D₄×C₁₀₃	—	2	1	no	—
80	C₄×D₄×C₁₀₃	—	2	1	no	—
81	C₄×D₄×C₁₀₃	—	2	1	no	—
82	C₄×D₄×C₁₀₃	—	2	1	no	—
83	C₂×C₄⋊C₄×C₁₀₃	—	2	1	no	—
84	C₂×C₄⋊C₄×C₁₀₃	—	2	1	no	—
85	C₂×C₄²×C₁₀₃	C₂³	1	1	yes	characteristic
86	#107×C₁₀₃	—	2	2	no	—
87	C₄⋊C₈×C₁₀₃	D₄	1	2	yes	—
88	#103×C₁₀₃	—	2	4	no	—
89	#103×C₁₀₃	—	2	4	no	—
90	#102×C₁₀₃	—	2	4	no	—
91	#102×C₁₀₃	—	2	4	no	—
92	#102×C₁₀₃	—	2	4	no	—
93	#102×C₁₀₃	—	2	2	no	—
94	#102×C₁₀₃	—	2	2	no	—
95	#102×C₁₀₃	—	2	4	no	—
96	C₂²⋊C₈×C₁₀₃	D₄	1	2	yes	—
97	#97×C₁₀₃	D₄	1	2	yes	—
98	C₄×C₈×C₁₀₃	D₄	1	2	yes	—
99	C₄×C₈×C₁₀₃	C₂³	1	1	yes	characteristic
100	C₄×C₈×C₁₀₃	C₂³	1	1	yes	characteristic
101	C₄×C₈×C₁₀₃	C₂³	1	2	yes	—
102	C₄×C₈×C₁₀₃	C₂³	1	2	yes	—
103	C₂⁴×C₁₀₃	—	4	1	no	—
104	#41×C₁₀₃	—	4	4	no	—
105	#41×C₁₀₃	—	4	4	no	—
106	C₂×Q₈×C₁₀₃	—	2	1	no	—
107	C₂×Q₈×C₁₀₃	—	2	2	no	—
108	C₂×Q₈×C₁₀₃	—	2	1	no	—
109	C₂×Q₈×C₁₀₃	—	4	1	no	—
110	C₂×Q₈×C₁₀₃	—	8	2	no	—
111	C₂×D₄×C₁₀₃	—	2	1	no	—
112	C₂×D₄×C₁₀₃	—	2	2	no	—
113	C₂×D₄×C₁₀₃	—	2	1	no	—
114	C₂×D₄×C₁₀₃	—	2	1	no	—
115	C₂×D₄×C₁₀₃	—	2	2	no	—
116	C₂×D₄×C₁₀₃	—	2	1	no	—
117	C₂×D₄×C₁₀₃	—	2	1	no	—
118	C₂×D₄×C₁₀₃	—	2	1	no	—
119	C₂×D₄×C₁₀₃	—	2	2	no	—
120	C₂×D₄×C₁₀₃	—	4	4	no	—
121	C₂×D₄×C₁₀₃	—	4	1	no	—
122	C₂×D₄×C₁₀₃	—	4	1	no	—
123	C₂×D₄×C₁₀₃	—	4	1	no	—
124	C₂×D₄×C₁₀₃	—	4	1	no	—
125	C₂×D₄×C₁₀₃	—	4	1	no	—
126	C₂×D₄×C₁₀₃	—	4	4	no	—
127	C₂×D₄×C₁₀₃	—	8	2	no	—
128	C₂²×C₄×C₁₀₃	—	4	1	no	—
129	C₂²×C₄×C₁₀₃	—	4	1	no	—
130	C₂²×C₄×C₁₀₃	—	4	1	no	—
131	C₂²×C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
134	SD₁₆×C₁₀₃	—	4	8	no	—
135	SD₁₆×C₁₀₃	—	8	4	no	—
136	D₈×C₁₀₃	—	4	4	no	—
137	D₈×C₁₀₃	—	4	8	no	—
138	D₈×C₁₀₃	—	8	4	no	—
139	M₁₆×C₁₀₃	—	2	4	no	—
140	C₂×C₈×C₁₀₃	—	4	2	no	—
141	C₂×C₈×C₁₀₃	C₂×D₄	1	2	yes	—
142	C₂×C₈×C₁₀₃	C₂×D₄	1	2	yes	—
143	C₂×C₈×C₁₀₃	C₂×D₄	1	4	yes	—
144	C₂×C₈×C₁₀₃	C₂×D₄	1	4	yes	—
145	C₄⋊C₄×C₁₀₃	—	2	2	no	—
146	C₄⋊C₄×C₁₀₃	—	2	1	no	—
147	C₄⋊C₄×C₁₀₃	—	2	2	no	—
148	C₄⋊C₄×C₁₀₃	—	2	1	no	—
149	C₄⋊C₄×C₁₀₃	—	2	1	no	—
150	C₄⋊C₄×C₁₀₃	—	2	1	no	—
151	C₄⋊C₄×C₁₀₃	—	4	1	no	—
152	C₄⋊C₄×C₁₀₃	—	4	1	no	—
153	C₂²⋊C₄×C₁₀₃	—	4	1	no	—
154	C₂²⋊C₄×C₁₀₃	—	4	1	no	—
155	C₂²⋊C₄×C₁₀₃	—	4	1	no	—
156	C₂²⋊C₄×C₁₀₃	—	4	1	no	—
157	C₄²×C₁₀₃	C₂×D₄	1	1	yes	characteristic
158	C₄²×C₁₀₃	C₂×D₄	1	1	yes	characteristic
159	C₄²×C₁₀₃	C₂×D₄	1	1	yes	characteristic
160	C₄²×C₁₀₃	C₂⁴	1	1	yes	characteristic
161	C₂³×C₁₀₃	—	4	1	no	—
162	C₂³×C₁₀₃	—	4	1	no	—
163	C₂³×C₁₀₃	—	4	2	no	—
164	C₂³×C₁₀₃	—	8	2	no	—
165	C₂³×C₁₀₃	—	8	2	no	—
166	C₂³×C₁₀₃	—	8	2	no	—
167	C₂³×C₁₀₃	#127	1	1	yes	characteristic
168	Q₈×C₁₀₃	—	4	2	no	—
169	Q₈×C₁₀₃	—	4	2	no	—
170	Q₈×C₁₀₃	—	4	4	no	—
171	Q₈×C₁₀₃	—	8	2	no	—
172	D₄×C₁₀₃	—	4	2	no	—
173	D₄×C₁₀₃	—	4	4	no	—
174	D₄×C₁₀₃	—	4	2	no	—
175	D₄×C₁₀₃	—	4	2	no	—
176	D₄×C₁₀₃	—	4	2	no	—
177	D₄×C₁₀₃	—	4	4	no	—
178	D₄×C₁₀₃	—	4	2	no	—
179	D₄×C₁₀₃	—	4	4	no	—
180	D₄×C₁₀₃	—	4	2	no	—
181	D₄×C₁₀₃	—	8	2	no	—
182	D₄×C₁₀₃	—	8	2	no	—
183	D₄×C₁₀₃	—	8	2	no	—
184	D₄×C₁₀₃	—	8	2	no	—
185	D₄×C₁₀₃	—	8	2	no	—
186	C₂×C₄×C₁₀₃	—	2	2	no	—
187	C₂×C₄×C₁₀₃	—	2	2	no	—
188	C₂×C₄×C₁₀₃	—	4	1	no	—
189	C₂×C₄×C₁₀₃	—	4	1	no	—
190	C₂×C₄×C₁₀₃	—	4	2	no	—
191	C₂×C₄×C₁₀₃	—	8	2	no	—
192	C₂×C₄×C₁₀₃	—	8	2	no	—
193	C₂×C₄×C₁₀₃	—	8	2	no	—
194	C₂×C₄×C₁₀₃	#127	1	1	yes	characteristic
195	C₂×C₄×C₁₀₃	#127	1	1	yes	characteristic
196	C₂×C₄×C₁₀₃	#127	1	1	yes	characteristic
197	C₂×C₄×C₁₀₃	AGL(1,ℤ/8)	1	4	yes	—
198	C₂×C₄×C₁₀₃	C₂²×D₄	1	1	yes	characteristic
199	C₂×C₄×C₁₀₃	C₂²×D₄	1	1	yes	characteristic
200	C₂×C₄×C₁₀₃	C₂²×D₄	1	1	yes	characteristic
201	C₈×C₁₀₃	—	2	4	no	—
202	C₈×C₁₀₃	—	2	2	no	—
203	C₈×C₁₀₃	—	2	2	no	—
204	C₈×C₁₀₃	—	2	4	no	—
205	C₂²×C₁₀₃	—	2	1	no	—
206	C₂²×C₁₀₃	—	2	1	no	—
207	C₂²×C₁₀₃	—	8	1	no	—
208	C₂²×C₁₀₃	—	8	1	no	—
209	C₂²×C₁₀₃	—	8	2	no	—
210	C₂²×C₁₀₃	—	8	2	no	—
211	C₂²×C₁₀₃	—	8	1	no	—
212	C₂²×C₁₀₃	—	8	1	no	—
213	C₂²×C₁₀₃	—	8	2	no	—
214	C₂²×C₁₀₃	—	8	1	no	—
215	C₂²×C₁₀₃	—	8	1	no	—
216	C₂²×C₁₀₃	—	16	4	no	—
217	C₂²×C₁₀₃	#496	1	2	yes	—
218	C₂²×C₁₀₃	C₂×#127	1	1	yes	characteristic
219	C₄×C₁₀₃	—	2	1	no	—
220	C₄×C₁₀₃	—	2	1	no	—
221	C₄×C₁₀₃	—	8	1	no	—
222	C₄×C₁₀₃	—	8	1	no	—
223	C₄×C₁₀₃	—	8	2	no	—
224	C₄×C₁₀₃	#496	1	2	yes	—
225	C₄×C₁₀₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
226	C₄×C₁₀₃	#575	1	2	yes	—
227	C₄×C₁₀₃	#576	1	2	yes	—
228	#19673	C₁₀₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
229	C₂×C₁₀₃	—	2	2	no	—
230	C₂×C₁₀₃	—	16	1	no	—
231	C₂×C₁₀₃	—	16	1	no	—
232	C₂×C₁₀₃	—	16	2	no	—
233	C₂×C₁₀₃	C₂×#496	1	1	yes	characteristic
234	C₂×C₁₀₃	#3153	1	1	yes	characteristic
235	C₂×C₁₀₃	#3155	1	1	yes	characteristic
236	#3206	C₂×C₁₀₃	1	1	yes	characteristic, complemented
237	#3205	C₂×C₁₀₃	1	1	yes	characteristic, complemented
238	#3169	C₂×C₁₀₃	1	1	yes	characteristic, complemented
239	#3151	C₂×C₁₀₃	1	1	yes	characteristic, complemented
240	#3141	C₂×C₁₀₃	1	1	yes	characteristic, complemented
241	C₂×#486	C₂×C₁₀₃	1	1	yes	characteristic, complemented
242	#1721	C₂×C₁₀₃	1	2	yes	complemented
243	#1719	C₂×C₁₀₃	1	2	yes	complemented
244	#1717	C₂×C₁₀₃	1	2	yes	complemented
245	#1717	C₂×C₁₀₃	1	2	yes	complemented
246	#1451	C₂×C₁₀₃	1	1	yes	characteristic, complemented
247	C₁₀₃	#19673	1	1	yes	characteristic, direct product factor, Sylow
248	C₂×AGL(1,ℤ/8)	—	2	2	no	—
249	#532	C₂²×C₁₀₃	1	1	yes	characteristic
250	#532	C₂²×C₁₀₃	1	1	yes	characteristic
251	C₂×C₄⋊Q₈	C₂²×C₁₀₃	1	1	yes	characteristic
252	C₂×#127	C₂²×C₁₀₃	1	1	yes	characteristic
253	#500	C₂²×C₁₀₃	1	1	yes	characteristic, complemented
254	#496	—	2	2	no	—
255	#493	C₂²×C₁₀₃	1	2	yes	—
256	#493	C₂²×C₁₀₃	1	2	yes	—
257	#493	C₂²×C₁₀₃	1	1	yes	characteristic, complemented
258	#492	C₂²×C₁₀₃	1	2	yes	—
259	#492	C₂²×C₁₀₃	1	2	yes	complemented
260	#489	—	2	2	no	—
261	#487	C₂²×C₁₀₃	1	2	yes	complemented
262	#487	C₂²×C₁₀₃	1	2	yes	complemented
263	#486	—	2	2	no	—
264	#486	C₂²×C₁₀₃	1	2	yes	—
265	#486	C₂²×C₁₀₃	1	2	yes	—
266	#486	C₂²×C₁₀₃	1	2	yes	—
267	#486	C₂²×C₁₀₃	1	2	yes	complemented
268	#486	C₂²×C₁₀₃	1	1	yes	characteristic, complemented
269	#486	C₂²×C₁₀₃	1	1	yes	characteristic, complemented
270	#466	—	2	2	no	—
271	#461	—	2	2	no	—
272	#459	—	2	2	no	—
273	#448	—	2	2	no	—
274	#447	—	2	2	no	—
275	C₄×D₈	—	2	2	no	—
276	#431	C₂²×C₁₀₃	1	1	yes	characteristic
277	#417	—	2	2	no	—
278	C₂×#102	—	2	2	no	—
279	C₄×M₁₆	C₂²×C₁₀₃	1	1	yes	characteristic
280	C₂×C₄×C₈	C₂²×C₁₀₃	1	1	yes	characteristic
281	#322	C₂²×C₁₀₃	1	2	yes	complemented
282	#322	C₂²×C₁₀₃	1	2	yes	complemented
283	C₂×#41	—	2	1	no	—
284	C₂×#41	—	2	1	no	—
285	C₂²×Q₈	—	2	1	no	—
286	C₂²×D₄	—	2	1	no	—
287	C₂²×D₄	—	2	1	no	—
288	C₂²×D₄	—	2	1	no	—
289	AGL(1,ℤ/8)	—	4	8	no	—
290	C₂×SD₁₆	—	2	4	no	—
291	C₂×SD₁₆	—	2	4	no	—
292	C₂×D₈	—	2	4	no	—
293	C₂×D₈	—	2	2	no	—
294	C₂×D₈	—	2	4	no	—
295	C₂×M₁₆	D₄×C₁₀₃	1	2	yes	—
296	C₂²×C₈	D₄×C₁₀₃	1	2	yes	—
297	C₄⋊Q₈	—	2	1	no	—
298	C₄⋊Q₈	—	2	1	no	—
299	C₄⋊Q₈	—	2	1	no	—
300	C₄⋊Q₈	C₂³×C₁₀₃	1	2	yes	—
301	C₄⋊Q₈	C₂³×C₁₀₃	1	1	yes	characteristic
302	C₄⋊Q₈	C₂³×C₁₀₃	1	1	yes	characteristic
303	#127	—	2	1	no	—
304	#127	—	2	1	no	—
305	#127	—	2	1	no	—
306	#127	C₂³×C₁₀₃	1	2	yes	—
307	#127	C₂³×C₁₀₃	1	1	yes	characteristic
308	#127	C₂³×C₁₀₃	1	1	yes	characteristic
309	#124	—	2	1	no	—
310	#124	—	2	1	no	—
311	#121	—	2	1	no	—
312	#121	—	2	1	no	—
313	#121	—	2	1	no	—
314	#121	—	2	1	no	—
315	C₄×D₄	—	2	1	no	—
316	C₄×D₄	—	2	1	no	—
317	C₄×D₄	—	2	1	no	—
318	C₄×D₄	—	2	1	no	—
319	C₂×C₄⋊C₄	—	2	1	no	—
320	C₂×C₄⋊C₄	—	2	1	no	—
321	C₂×C₄²	C₂³×C₁₀₃	1	1	yes	characteristic
322	#107	—	2	2	no	—
323	C₄⋊C₈	D₄×C₁₀₃	1	2	yes	—
324	#103	—	2	4	no	—
325	#103	—	2	4	no	—
326	#102	—	2	4	no	—
327	#102	—	2	4	no	—
328	#102	—	2	4	no	—
329	#102	—	2	2	no	—
330	#102	—	2	2	no	—
331	#102	—	2	4	no	—
332	C₂²⋊C₈	D₄×C₁₀₃	1	2	yes	—
333	#97	D₄×C₁₀₃	1	2	yes	—
334	C₄×C₈	D₄×C₁₀₃	1	2	yes	—
335	C₄×C₈	C₂³×C₁₀₃	1	1	yes	characteristic
336	C₄×C₈	C₂³×C₁₀₃	1	1	yes	characteristic
337	C₄×C₈	C₂³×C₁₀₃	1	2	yes	—
338	C₄×C₈	C₂³×C₁₀₃	1	2	yes	—
339	C₂⁴	—	4	1	no	—
340	#41	—	4	4	no	—
341	#41	—	4	4	no	—
342	C₂×Q₈	—	2	1	no	—
343	C₂×Q₈	—	2	2	no	—
344	C₂×Q₈	—	2	1	no	—
345	C₂×Q₈	—	4	1	no	—
346	C₂×Q₈	—	8	2	no	—
347	C₂×D₄	—	2	1	no	—
348	C₂×D₄	—	2	2	no	—
349	C₂×D₄	—	2	1	no	—
350	C₂×D₄	—	2	1	no	—
351	C₂×D₄	—	2	2	no	—
352	C₂×D₄	—	2	1	no	—
353	C₂×D₄	—	2	1	no	—
354	C₂×D₄	—	2	1	no	—
355	C₂×D₄	—	2	2	no	—
356	C₂×D₄	—	4	4	no	—
357	C₂×D₄	—	4	1	no	—
358	C₂×D₄	—	4	1	no	—
359	C₂×D₄	—	4	1	no	—
360	C₂×D₄	—	4	1	no	—
361	C₂×D₄	—	4	1	no	—
362	C₂×D₄	—	4	4	no	—
363	C₂×D₄	—	8	2	no	—
364	C₂²×C₄	—	4	1	no	—
365	C₂²×C₄	—	4	1	no	—
366	C₂²×C₄	—	4	1	no	—
367	C₂²×C₄	C₂×D₄×C₁₀₃	1	1	yes	characteristic
368	C₂²×C₄	C₂×D₄×C₁₀₃	1	1	yes	characteristic
369	C₂²×C₄	C₂×D₄×C₁₀₃	1	1	yes	characteristic
370	SD₁₆	—	4	8	no	—
371	SD₁₆	—	8	4	no	—
372	D₈	—	4	4	no	—
373	D₈	—	4	8	no	—
374	D₈	—	8	4	no	—
375	M₁₆	—	2	4	no	—
376	C₂×C₈	—	4	2	no	—
377	C₂×C₈	C₂×D₄×C₁₀₃	1	2	yes	—
378	C₂×C₈	C₂×D₄×C₁₀₃	1	2	yes	—
379	C₂×C₈	C₂×D₄×C₁₀₃	1	4	yes	—
380	C₂×C₈	C₂×D₄×C₁₀₃	1	4	yes	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	—	2	1	no	—
385	C₄⋊C₄	—	2	1	no	—
386	C₄⋊C₄	—	2	1	no	—
387	C₄⋊C₄	—	4	1	no	—
388	C₄⋊C₄	—	4	1	no	—
389	C₂²⋊C₄	—	4	1	no	—
390	C₂²⋊C₄	—	4	1	no	—
391	C₂²⋊C₄	—	4	1	no	—
392	C₂²⋊C₄	—	4	1	no	—
393	C₄²	C₂×D₄×C₁₀₃	1	1	yes	characteristic
394	C₄²	C₂×D₄×C₁₀₃	1	1	yes	characteristic
395	C₄²	C₂×D₄×C₁₀₃	1	1	yes	characteristic
396	C₄²	C₂⁴×C₁₀₃	1	1	yes	characteristic
397	C₂³	—	4	1	no	—
398	C₂³	—	4	1	no	—
399	C₂³	—	4	2	no	—
400	C₂³	—	8	2	no	—
401	C₂³	—	8	2	no	—
402	C₂³	—	8	2	no	—
403	C₂³	#127×C₁₀₃	1	1	yes	characteristic
404	Q₈	—	4	2	no	—
405	Q₈	—	4	2	no	—
406	Q₈	—	4	4	no	—
407	Q₈	—	8	2	no	—
408	D₄	—	4	2	no	—
409	D₄	—	4	4	no	—
410	D₄	—	4	2	no	—
411	D₄	—	4	2	no	—
412	D₄	—	4	2	no	—
413	D₄	—	4	4	no	—
414	D₄	—	4	2	no	—
415	D₄	—	4	4	no	—
416	D₄	—	4	2	no	—
417	D₄	—	8	2	no	—
418	D₄	—	8	2	no	—
419	D₄	—	8	2	no	—
420	D₄	—	8	2	no	—
421	D₄	—	8	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	4	1	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	8	2	no	—
428	C₂×C₄	—	8	2	no	—
429	C₂×C₄	—	8	2	no	—
430	C₂×C₄	#127×C₁₀₃	1	1	yes	characteristic
431	C₂×C₄	#127×C₁₀₃	1	1	yes	characteristic
432	C₂×C₄	#127×C₁₀₃	1	1	yes	characteristic
433	C₂×C₄	AGL(1,ℤ/8)×C₁₀₃	1	4	yes	—
434	C₂×C₄	C₂²×D₄×C₁₀₃	1	1	yes	characteristic
435	C₂×C₄	C₂²×D₄×C₁₀₃	1	1	yes	characteristic
436	C₂×C₄	C₂²×D₄×C₁₀₃	1	1	yes	characteristic
437	C₈	—	2	4	no	—
438	C₈	—	2	2	no	—
439	C₈	—	2	2	no	—
440	C₈	—	2	4	no	—
441	C₂²	—	2	1	no	—
442	C₂²	—	2	1	no	—
443	C₂²	—	8	1	no	—
444	C₂²	—	8	1	no	—
445	C₂²	—	8	2	no	—
446	C₂²	—	8	2	no	—
447	C₂²	—	8	1	no	—
448	C₂²	—	8	1	no	—
449	C₂²	—	8	2	no	—
450	C₂²	—	8	1	no	—
451	C₂²	—	8	1	no	—
452	C₂²	—	16	4	no	—
453	C₂²	#496×C₁₀₃	1	2	yes	—
454	C₂²	C₂×#127×C₁₀₃	1	1	yes	characteristic
455	C₄	—	2	1	no	—
456	C₄	—	2	1	no	—
457	C₄	—	8	1	no	—
458	C₄	—	8	1	no	—
459	C₄	—	8	2	no	—
460	C₄	#496×C₁₀₃	1	2	yes	—
461	C₄	C₂×AGL(1,ℤ/8)×C₁₀₃	1	2	yes	—
462	C₄	#575×C₁₀₃	1	2	yes	—
463	C₄	#576×C₁₀₃	1	2	yes	—
464	C₂	—	2	2	no	—
465	C₂	—	16	2	no	—
466	C₂	—	16	1	no	—
467	C₂	—	16	1	no	—
468	C₂	C₂×#496×C₁₀₃	1	1	yes	characteristic
469	C₂	C₁₀₃×#3153	1	1	yes	characteristic
470	C₂	C₁₀₃×#3155	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₀₃	C₂×#127
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₀₃
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₃ ◁ C₂×C₄²×C₁₀₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₀₃×#3206	C₂	semidirect
2. C₁₀₃×#3205	C₂	semidirect
3. C₁₀₃×#3169	C₂	semidirect
4. C₁₀₃×#3151	C₂	semidirect
5. C₁₀₃×#3141	C₂	semidirect
6. C₂×#486×C₁₀₃	C₂	semidirect
7. C₁₀₃×#1721	C₂	semidirect
8. C₁₀₃×#1719	C₂	semidirect
9. C₁₀₃×#1717	C₂	semidirect
10. C₁₀₃×#1717	C₂	semidirect
11. C₁₀₃×#1451	C₂	semidirect
17. #500×C₁₀₃	C₂²	semidirect
21. #493×C₁₀₃	C₂²	semidirect
23. #492×C₁₀₃	C₂²	semidirect
25. #487×C₁₀₃	C₂²	semidirect
26. #487×C₁₀₃	C₂²	semidirect
31. #486×C₁₀₃	C₂²	semidirect
32. #486×C₁₀₃	C₂²	semidirect
33. #486×C₁₀₃	C₂²	semidirect
45. #322×C₁₀₃	C₂²	semidirect
46. #322×C₁₀₃	C₂²	semidirect
228. #19673	C₁₀₃	direct (N × H)
236. #3206	C₂×C₁₀₃	semidirect
237. #3205	C₂×C₁₀₃	semidirect
238. #3169	C₂×C₁₀₃	semidirect
239. #3151	C₂×C₁₀₃	semidirect
240. #3141	C₂×C₁₀₃	semidirect
241. C₂×#486	C₂×C₁₀₃	semidirect
242. #1721	C₂×C₁₀₃	semidirect
243. #1719	C₂×C₁₀₃	semidirect
244. #1717	C₂×C₁₀₃	semidirect
245. #1717	C₂×C₁₀₃	semidirect
246. #1451	C₂×C₁₀₃	semidirect
247. C₁₀₃	#19673	direct (N × H)
253. #500	C₂²×C₁₀₃	semidirect
257. #493	C₂²×C₁₀₃	semidirect
259. #492	C₂²×C₁₀₃	semidirect
261. #487	C₂²×C₁₀₃	semidirect
262. #487	C₂²×C₁₀₃	semidirect
267. #486	C₂²×C₁₀₃	semidirect
268. #486	C₂²×C₁₀₃	semidirect
269. #486	C₂²×C₁₀₃	semidirect
281. #322	C₂²×C₁₀₃	semidirect
282. #322	C₂²×C₁₀₃	semidirect

Maximal subgroups

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

subgroup	index
C₁₀₃×#3206	2
C₁₀₃×#3205	2
C₁₀₃×#3169	2
C₁₀₃×#3151	2
C₁₀₃×#3141	2
C₂×#486×C₁₀₃	2
C₁₀₃×#1721	2
C₁₀₃×#1719	2
C₁₀₃×#1717	2
C₁₀₃×#1451	2
#19673	103

Subgroups — C103×#19673 #39924948

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₃×#19673 #39924948