Subgroups — C₁₀₃×#19679 #39924954

Order 26368.

806 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₀₃×#3230	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₀₃×#3208	C₂	1	1	yes	maximal, characteristic
3	C₁₀₃×#3170	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₀₃×#3165	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#492×C₁₀₃	C₂	1	1	yes	maximal, characteristic
6	C₁₀₃×#3138	C₂	1	1	yes	maximal, characteristic
7	C₁₀₃×#1722	C₂	1	2	yes	maximal, complemented
8	C₁₀₃×#1719	C₂	1	2	yes	maximal, complemented
9	C₁₀₃×#1714	C₂	1	2	yes	maximal, complemented
10	C₁₀₃×#1714	C₂	1	2	yes	maximal, complemented
11	C₁₀₃×#1451	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×SD₁₆×C₁₀₃	—	2	2	no	—
13	#533×C₁₀₃	C₂²	1	1	yes	characteristic
14	#533×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	#501×C₁₀₃	—	2	2	no	—
18	#500×C₁₀₃	C₂²	1	2	yes	complemented
19	#500×C₁₀₃	C₂²	1	1	yes	characteristic, complemented
20	#500×C₁₀₃	C₂²	1	2	yes	complemented
21	#498×C₁₀₃	C₂²	1	2	yes	complemented
22	#494×C₁₀₃	C₂²	1	1	yes	characteristic, complemented
23	#492×C₁₀₃	—	2	2	no	—
24	#492×C₁₀₃	C₂²	1	2	yes	—
25	#492×C₁₀₃	C₂²	1	2	yes	—
26	#492×C₁₀₃	C₂²	1	2	yes	—
27	#490×C₁₀₃	—	2	2	no	—
28	#487×C₁₀₃	C₂²	1	2	yes	complemented
29	#487×C₁₀₃	C₂²	1	1	yes	characteristic, complemented
30	#487×C₁₀₃	C₂²	1	1	yes	characteristic, complemented
31	#486×C₁₀₃	C₂²	1	2	yes	—
32	#486×C₁₀₃	C₂²	1	2	yes	—
33	#486×C₁₀₃	C₂²	1	2	yes	—
34	#484×C₁₀₃	—	2	2	no	—
35	#477×C₁₀₃	—	2	2	no	—
36	#467×C₁₀₃	—	2	2	no	—
37	#460×C₁₀₃	—	2	2	no	—
38	#450×C₁₀₃	—	2	2	no	—
39	C₄×Q₁₆×C₁₀₃	—	2	2	no	—
40	#431×C₁₀₃	C₂²	1	1	yes	characteristic
41	#428×C₁₀₃	—	2	2	no	—
42	#418×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	C₂²×Q₈×C₁₀₃	—	2	1	no	—
48	C₂²×D₄×C₁₀₃	—	2	1	no	—
49	C₂²×D₄×C₁₀₃	—	2	1	no	—
50	C₂²×D₄×C₁₀₃	—	2	1	no	—
51	C₂×Q₁₆×C₁₀₃	—	2	2	no	—
52	C₂×SD₁₆×C₁₀₃	—	2	4	no	—
53	C₂×SD₁₆×C₁₀₃	—	2	4	no	—
54	C₂×SD₁₆×C₁₀₃	—	2	4	no	—
55	C₂×SD₁₆×C₁₀₃	—	4	8	no	—
56	C₂×M₁₆×C₁₀₃	D₄	1	2	yes	—
57	C₂²×C₈×C₁₀₃	D₄	1	2	yes	—
58	C₄⋊Q₈×C₁₀₃	—	2	1	no	—
59	C₄⋊Q₈×C₁₀₃	—	2	1	no	—
60	C₄⋊Q₈×C₁₀₃	—	2	1	no	—
61	C₄⋊Q₈×C₁₀₃	C₂³	1	1	yes	characteristic
62	C₄⋊Q₈×C₁₀₃	C₂³	1	1	yes	characteristic
63	C₄⋊Q₈×C₁₀₃	C₂³	1	1	yes	characteristic
64	C₄⋊Q₈×C₁₀₃	C₂³	1	1	yes	characteristic
65	C₄⋊Q₈×C₁₀₃	C₂³	1	2	yes	—
66	#127×C₁₀₃	—	2	1	no	—
67	#127×C₁₀₃	—	2	1	no	—
68	#127×C₁₀₃	—	2	1	no	—
69	#127×C₁₀₃	C₂³	1	2	yes	—
70	#125×C₁₀₃	—	2	1	no	—
71	#125×C₁₀₃	—	2	1	no	—
72	C₂²⋊Q₈×C₁₀₃	—	2	1	no	—
73	C₂²⋊Q₈×C₁₀₃	—	2	1	no	—
74	C₂²⋊Q₈×C₁₀₃	—	2	1	no	—
75	C₂²⋊Q₈×C₁₀₃	—	2	1	no	—
76	C₄×Q₈×C₁₀₃	—	2	1	no	—
77	C₄×Q₈×C₁₀₃	—	2	1	no	—
78	C₄×Q₈×C₁₀₃	—	2	1	no	—
79	C₄×Q₈×C₁₀₃	—	2	1	no	—
80	#117×C₁₀₃	—	2	1	no	—
81	#117×C₁₀₃	—	2	1	no	—
82	C₂×C₄⋊C₄×C₁₀₃	—	2	1	no	—
83	C₂×C₄⋊C₄×C₁₀₃	—	2	1	no	—
84	C₂×C₄²×C₁₀₃	C₂³	1	1	yes	characteristic
85	#107×C₁₀₃	—	2	4	no	—
86	#107×C₁₀₃	—	2	2	no	—
87	#107×C₁₀₃	—	2	4	no	—
88	#106×C₁₀₃	—	2	4	no	—
89	C₄⋊C₈×C₁₀₃	D₄	1	2	yes	—
90	#103×C₁₀₃	—	2	2	no	—
91	#103×C₁₀₃	—	2	2	no	—
92	#103×C₁₀₃	—	2	4	no	—
93	#102×C₁₀₃	—	2	4	no	—
94	#102×C₁₀₃	—	2	4	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	C₂×Q₈×C₁₀₃	—	2	1	no	—
105	C₂×Q₈×C₁₀₃	—	2	1	no	—
106	C₂×Q₈×C₁₀₃	—	2	1	no	—
107	C₂×Q₈×C₁₀₃	—	2	1	no	—
108	C₂×Q₈×C₁₀₃	—	2	2	no	—
109	C₂×Q₈×C₁₀₃	—	4	4	no	—
110	C₂×Q₈×C₁₀₃	—	4	1	no	—
111	C₂×D₄×C₁₀₃	—	2	2	no	—
112	C₂×D₄×C₁₀₃	—	2	2	no	—
113	C₂×D₄×C₁₀₃	—	2	2	no	—
114	C₂×D₄×C₁₀₃	—	4	4	no	—
115	C₂×D₄×C₁₀₃	—	4	1	no	—
116	C₂×D₄×C₁₀₃	—	4	1	no	—
117	C₂×D₄×C₁₀₃	—	4	1	no	—
118	C₂×D₄×C₁₀₃	—	4	4	no	—
119	C₂×D₄×C₁₀₃	—	8	2	no	—
120	C₂²×C₄×C₁₀₃	—	4	1	no	—
121	C₂²×C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
124	Q₁₆×C₁₀₃	—	4	4	no	—
125	SD₁₆×C₁₀₃	—	4	8	no	—
126	SD₁₆×C₁₀₃	—	4	8	no	—
127	SD₁₆×C₁₀₃	—	8	4	no	—
128	M₁₆×C₁₀₃	—	2	4	no	—
129	C₂×C₈×C₁₀₃	—	2	4	no	—
130	C₂×C₈×C₁₀₃	C₂×D₄	1	2	yes	—
131	C₂×C₈×C₁₀₃	C₂×D₄	1	4	yes	—
132	C₂×C₈×C₁₀₃	C₂×D₄	1	4	yes	—
133	C₂×C₈×C₁₀₃	C₂×D₄	1	2	yes	—
134	C₄⋊C₄×C₁₀₃	—	2	1	no	—
135	C₄⋊C₄×C₁₀₃	—	2	1	no	—
136	C₄⋊C₄×C₁₀₃	—	2	1	no	—
137	C₄⋊C₄×C₁₀₃	—	2	2	no	—
138	C₄⋊C₄×C₁₀₃	—	2	1	no	—
139	C₄⋊C₄×C₁₀₃	—	2	1	no	—
140	C₄⋊C₄×C₁₀₃	—	2	1	no	—
141	C₄⋊C₄×C₁₀₃	—	2	2	no	—
142	C₄⋊C₄×C₁₀₃	—	2	1	no	—
143	C₄⋊C₄×C₁₀₃	—	2	1	no	—
144	C₄⋊C₄×C₁₀₃	—	4	1	no	—
145	C₄⋊C₄×C₁₀₃	—	4	1	no	—
146	C₄⋊C₄×C₁₀₃	—	4	1	no	—
147	C₄⋊C₄×C₁₀₃	—	4	1	no	—
148	C₄⋊C₄×C₁₀₃	—	4	1	no	—
149	C₄⋊C₄×C₁₀₃	—	4	1	no	—
150	C₂²⋊C₄×C₁₀₃	—	4	1	no	—
151	C₂²⋊C₄×C₁₀₃	—	4	1	no	—
152	C₄²×C₁₀₃	—	4	1	no	—
153	C₄²×C₁₀₃	—	4	1	no	—
154	C₄²×C₁₀₃	C₂×D₄	1	1	yes	characteristic
155	C₄²×C₁₀₃	C₂×D₄	1	1	yes	characteristic
156	C₄²×C₁₀₃	C₂×D₄	1	1	yes	characteristic
157	C₄²×C₁₀₃	C₂⁴	1	1	yes	characteristic
158	C₂³×C₁₀₃	—	4	2	no	—
159	C₂³×C₁₀₃	—	8	2	no	—
160	C₂³×C₁₀₃	—	8	2	no	—
161	C₂³×C₁₀₃	—	8	2	no	—
162	C₂³×C₁₀₃	#127	1	1	yes	characteristic
163	Q₈×C₁₀₃	—	4	4	no	—
164	Q₈×C₁₀₃	—	4	2	no	—
165	Q₈×C₁₀₃	—	4	2	no	—
166	Q₈×C₁₀₃	—	4	2	no	—
167	Q₈×C₁₀₃	—	4	2	no	—
168	Q₈×C₁₀₃	—	8	2	no	—
169	D₄×C₁₀₃	—	4	4	no	—
170	D₄×C₁₀₃	—	4	4	no	—
171	D₄×C₁₀₃	—	4	4	no	—
172	D₄×C₁₀₃	—	8	2	no	—
173	D₄×C₁₀₃	—	8	2	no	—
174	D₄×C₁₀₃	—	8	2	no	—
175	C₂×C₄×C₁₀₃	—	2	2	no	—
176	C₂×C₄×C₁₀₃	—	2	2	no	—
177	C₂×C₄×C₁₀₃	—	4	1	no	—
178	C₂×C₄×C₁₀₃	—	4	1	no	—
179	C₂×C₄×C₁₀₃	—	4	1	no	—
180	C₂×C₄×C₁₀₃	—	4	1	no	—
181	C₂×C₄×C₁₀₃	—	4	2	no	—
182	C₂×C₄×C₁₀₃	—	8	2	no	—
183	C₂×C₄×C₁₀₃	#127	1	1	yes	characteristic
184	C₂×C₄×C₁₀₃	#127	1	1	yes	characteristic
185	C₂×C₄×C₁₀₃	#127	1	1	yes	characteristic
186	C₂×C₄×C₁₀₃	#137	1	4	yes	—
187	C₂×C₄×C₁₀₃	C₂²×D₄	1	1	yes	characteristic
188	C₂×C₄×C₁₀₃	C₂²×D₄	1	1	yes	characteristic
189	C₂×C₄×C₁₀₃	C₂²×D₄	1	1	yes	characteristic
190	C₈×C₁₀₃	—	2	2	no	—
191	C₈×C₁₀₃	—	2	4	no	—
192	C₈×C₁₀₃	—	2	4	no	—
193	C₈×C₁₀₃	AGL(1,ℤ/8)	1	4	yes	—
194	C₂²×C₁₀₃	—	2	1	no	—
195	C₂²×C₁₀₃	—	2	1	no	—
196	C₂²×C₁₀₃	—	8	2	no	—
197	C₂²×C₁₀₃	—	8	2	no	—
198	C₂²×C₁₀₃	—	8	2	no	—
199	C₂²×C₁₀₃	—	16	4	no	—
200	C₂²×C₁₀₃	#497	1	2	yes	—
201	C₂²×C₁₀₃	C₂×#127	1	1	yes	characteristic
202	C₄×C₁₀₃	—	2	1	no	—
203	C₄×C₁₀₃	—	2	1	no	—
204	C₄×C₁₀₃	—	8	2	no	—
205	C₄×C₁₀₃	—	8	1	no	—
206	C₄×C₁₀₃	—	8	1	no	—
207	C₄×C₁₀₃	—	8	1	no	—
208	C₄×C₁₀₃	—	8	1	no	—
209	C₄×C₁₀₃	#497	1	2	yes	—
210	C₄×C₁₀₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
211	C₄×C₁₀₃	C₂×#137	1	2	yes	—
212	C₄×C₁₀₃	#577	1	2	yes	—
213	#19679	C₁₀₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
214	C₂×C₁₀₃	—	2	2	no	—
215	C₂×C₁₀₃	—	16	2	no	—
216	C₂×C₁₀₃	C₂×#497	1	1	yes	characteristic
217	C₂×C₁₀₃	#3151	1	1	yes	characteristic
218	C₂×C₁₀₃	#3154	1	1	yes	characteristic
219	#3230	C₂×C₁₀₃	1	1	yes	characteristic, complemented
220	#3208	C₂×C₁₀₃	1	1	yes	characteristic
221	#3170	C₂×C₁₀₃	1	1	yes	characteristic, complemented
222	#3165	C₂×C₁₀₃	1	1	yes	characteristic, complemented
223	C₂×#492	C₂×C₁₀₃	1	1	yes	characteristic
224	#3138	C₂×C₁₀₃	1	1	yes	characteristic
225	#1722	C₂×C₁₀₃	1	2	yes	complemented
226	#1719	C₂×C₁₀₃	1	2	yes	complemented
227	#1714	C₂×C₁₀₃	1	2	yes	complemented
228	#1714	C₂×C₁₀₃	1	2	yes	complemented
229	#1451	C₂×C₁₀₃	1	1	yes	characteristic, complemented
230	C₁₀₃	#19679	1	1	yes	characteristic, direct product factor, Sylow
231	C₂²×SD₁₆	—	2	2	no	—
232	#533	C₂²×C₁₀₃	1	1	yes	characteristic
233	#533	C₂²×C₁₀₃	1	1	yes	characteristic
234	C₂×C₄⋊Q₈	C₂²×C₁₀₃	1	1	yes	characteristic
235	C₂×#127	C₂²×C₁₀₃	1	1	yes	characteristic
236	#501	—	2	2	no	—
237	#500	C₂²×C₁₀₃	1	2	yes	complemented
238	#500	C₂²×C₁₀₃	1	1	yes	characteristic, complemented
239	#500	C₂²×C₁₀₃	1	2	yes	complemented
240	#498	C₂²×C₁₀₃	1	2	yes	complemented
241	#494	C₂²×C₁₀₃	1	1	yes	characteristic, complemented
242	#492	—	2	2	no	—
243	#492	C₂²×C₁₀₃	1	2	yes	—
244	#492	C₂²×C₁₀₃	1	2	yes	—
245	#492	C₂²×C₁₀₃	1	2	yes	—
246	#490	—	2	2	no	—
247	#487	C₂²×C₁₀₃	1	1	yes	characteristic, complemented
248	#487	C₂²×C₁₀₃	1	1	yes	characteristic, complemented
249	#487	C₂²×C₁₀₃	1	2	yes	complemented
250	#486	C₂²×C₁₀₃	1	2	yes	—
251	#486	C₂²×C₁₀₃	1	2	yes	—
252	#486	C₂²×C₁₀₃	1	2	yes	—
253	#484	—	2	2	no	—
254	#477	—	2	2	no	—
255	#467	—	2	2	no	—
256	#460	—	2	2	no	—
257	#450	—	2	2	no	—
258	C₄×Q₁₆	—	2	2	no	—
259	#431	C₂²×C₁₀₃	1	1	yes	characteristic
260	#428	—	2	2	no	—
261	#418	—	2	2	no	—
262	C₄×M₁₆	C₂²×C₁₀₃	1	1	yes	characteristic
263	C₂×C₄×C₈	C₂²×C₁₀₃	1	1	yes	characteristic
264	#322	C₂²×C₁₀₃	1	2	yes	complemented
265	#322	C₂²×C₁₀₃	1	2	yes	complemented
266	C₂²×Q₈	—	2	1	no	—
267	C₂²×D₄	—	2	1	no	—
268	C₂²×D₄	—	2	1	no	—
269	C₂²×D₄	—	2	1	no	—
270	C₂×Q₁₆	—	2	2	no	—
271	C₂×SD₁₆	—	2	4	no	—
272	C₂×SD₁₆	—	2	4	no	—
273	C₂×SD₁₆	—	2	4	no	—
274	C₂×SD₁₆	—	4	8	no	—
275	C₂×M₁₆	D₄×C₁₀₃	1	2	yes	—
276	C₂²×C₈	D₄×C₁₀₃	1	2	yes	—
277	C₄⋊Q₈	—	2	1	no	—
278	C₄⋊Q₈	—	2	1	no	—
279	C₄⋊Q₈	—	2	1	no	—
280	C₄⋊Q₈	C₂³×C₁₀₃	1	2	yes	—
281	C₄⋊Q₈	C₂³×C₁₀₃	1	1	yes	characteristic
282	C₄⋊Q₈	C₂³×C₁₀₃	1	1	yes	characteristic
283	C₄⋊Q₈	C₂³×C₁₀₃	1	1	yes	characteristic
284	C₄⋊Q₈	C₂³×C₁₀₃	1	1	yes	characteristic
285	#127	—	2	1	no	—
286	#127	—	2	1	no	—
287	#127	—	2	1	no	—
288	#127	C₂³×C₁₀₃	1	2	yes	—
289	#125	—	2	1	no	—
290	#125	—	2	1	no	—
291	C₂²⋊Q₈	—	2	1	no	—
292	C₂²⋊Q₈	—	2	1	no	—
293	C₂²⋊Q₈	—	2	1	no	—
294	C₂²⋊Q₈	—	2	1	no	—
295	C₄×Q₈	—	2	1	no	—
296	C₄×Q₈	—	2	1	no	—
297	C₄×Q₈	—	2	1	no	—
298	C₄×Q₈	—	2	1	no	—
299	#117	—	2	1	no	—
300	#117	—	2	1	no	—
301	C₂×C₄⋊C₄	—	2	1	no	—
302	C₂×C₄⋊C₄	—	2	1	no	—
303	C₂×C₄²	C₂³×C₁₀₃	1	1	yes	characteristic
304	#107	—	2	4	no	—
305	#107	—	2	2	no	—
306	#107	—	2	4	no	—
307	#106	—	2	4	no	—
308	C₄⋊C₈	D₄×C₁₀₃	1	2	yes	—
309	#103	—	2	2	no	—
310	#103	—	2	2	no	—
311	#103	—	2	4	no	—
312	#102	—	2	4	no	—
313	#102	—	2	4	no	—
314	#102	—	2	4	no	—
315	C₂²⋊C₈	D₄×C₁₀₃	1	2	yes	—
316	#97	D₄×C₁₀₃	1	2	yes	—
317	C₄×C₈	D₄×C₁₀₃	1	2	yes	—
318	C₄×C₈	C₂³×C₁₀₃	1	1	yes	characteristic
319	C₄×C₈	C₂³×C₁₀₃	1	1	yes	characteristic
320	C₄×C₈	C₂³×C₁₀₃	1	2	yes	—
321	C₄×C₈	C₂³×C₁₀₃	1	2	yes	—
322	C₂⁴	—	4	1	no	—
323	C₂×Q₈	—	2	1	no	—
324	C₂×Q₈	—	2	1	no	—
325	C₂×Q₈	—	2	1	no	—
326	C₂×Q₈	—	2	1	no	—
327	C₂×Q₈	—	2	2	no	—
328	C₂×Q₈	—	4	4	no	—
329	C₂×Q₈	—	4	1	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	2	2	no	—
333	C₂×D₄	—	4	4	no	—
334	C₂×D₄	—	4	1	no	—
335	C₂×D₄	—	4	1	no	—
336	C₂×D₄	—	4	1	no	—
337	C₂×D₄	—	4	4	no	—
338	C₂×D₄	—	8	2	no	—
339	C₂²×C₄	—	4	1	no	—
340	C₂²×C₄	C₂×D₄×C₁₀₃	1	1	yes	characteristic
341	C₂²×C₄	C₂×D₄×C₁₀₃	1	1	yes	characteristic
342	C₂²×C₄	C₂×D₄×C₁₀₃	1	1	yes	characteristic
343	Q₁₆	—	4	4	no	—
344	SD₁₆	—	4	8	no	—
345	SD₁₆	—	4	8	no	—
346	SD₁₆	—	8	4	no	—
347	M₁₆	—	2	4	no	—
348	C₂×C₈	—	2	4	no	—
349	C₂×C₈	C₂×D₄×C₁₀₃	1	2	yes	—
350	C₂×C₈	C₂×D₄×C₁₀₃	1	4	yes	—
351	C₂×C₈	C₂×D₄×C₁₀₃	1	4	yes	—
352	C₂×C₈	C₂×D₄×C₁₀₃	1	2	yes	—
353	C₄⋊C₄	—	2	1	no	—
354	C₄⋊C₄	—	2	1	no	—
355	C₄⋊C₄	—	2	1	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	4	1	no	—
364	C₄⋊C₄	—	4	1	no	—
365	C₄⋊C₄	—	4	1	no	—
366	C₄⋊C₄	—	4	1	no	—
367	C₄⋊C₄	—	4	1	no	—
368	C₄⋊C₄	—	4	1	no	—
369	C₂²⋊C₄	—	4	1	no	—
370	C₂²⋊C₄	—	4	1	no	—
371	C₄²	—	4	1	no	—
372	C₄²	—	4	1	no	—
373	C₄²	C₂×D₄×C₁₀₃	1	1	yes	characteristic
374	C₄²	C₂×D₄×C₁₀₃	1	1	yes	characteristic
375	C₄²	C₂×D₄×C₁₀₃	1	1	yes	characteristic
376	C₄²	C₂⁴×C₁₀₃	1	1	yes	characteristic
377	C₂³	—	4	2	no	—
378	C₂³	—	8	2	no	—
379	C₂³	—	8	2	no	—
380	C₂³	—	8	2	no	—
381	C₂³	#127×C₁₀₃	1	1	yes	characteristic
382	Q₈	—	4	4	no	—
383	Q₈	—	4	2	no	—
384	Q₈	—	4	2	no	—
385	Q₈	—	4	2	no	—
386	Q₈	—	4	2	no	—
387	Q₈	—	8	2	no	—
388	D₄	—	4	4	no	—
389	D₄	—	4	4	no	—
390	D₄	—	4	4	no	—
391	D₄	—	8	2	no	—
392	D₄	—	8	2	no	—
393	D₄	—	8	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	8	2	no	—
402	C₂×C₄	#127×C₁₀₃	1	1	yes	characteristic
403	C₂×C₄	#127×C₁₀₃	1	1	yes	characteristic
404	C₂×C₄	#127×C₁₀₃	1	1	yes	characteristic
405	C₂×C₄	#137×C₁₀₃	1	4	yes	—
406	C₂×C₄	C₂²×D₄×C₁₀₃	1	1	yes	characteristic
407	C₂×C₄	C₂²×D₄×C₁₀₃	1	1	yes	characteristic
408	C₂×C₄	C₂²×D₄×C₁₀₃	1	1	yes	characteristic
409	C₈	—	2	2	no	—
410	C₈	—	2	4	no	—
411	C₈	—	2	4	no	—
412	C₈	AGL(1,ℤ/8)×C₁₀₃	1	4	yes	—
413	C₂²	—	2	1	no	—
414	C₂²	—	2	1	no	—
415	C₂²	—	8	2	no	—
416	C₂²	—	8	2	no	—
417	C₂²	—	8	2	no	—
418	C₂²	—	16	4	no	—
419	C₂²	#497×C₁₀₃	1	2	yes	—
420	C₂²	C₂×#127×C₁₀₃	1	1	yes	characteristic
421	C₄	—	2	1	no	—
422	C₄	—	2	1	no	—
423	C₄	—	8	2	no	—
424	C₄	—	8	1	no	—
425	C₄	—	8	1	no	—
426	C₄	—	8	1	no	—
427	C₄	—	8	1	no	—
428	C₄	#497×C₁₀₃	1	2	yes	—
429	C₄	C₂×AGL(1,ℤ/8)×C₁₀₃	1	2	yes	—
430	C₄	C₂×#137×C₁₀₃	1	2	yes	—
431	C₄	#577×C₁₀₃	1	2	yes	—
432	C₂	—	2	2	no	—
433	C₂	—	16	2	no	—
434	C₂	C₂×#497×C₁₀₃	1	1	yes	characteristic
435	C₂	C₁₀₃×#3151	1	1	yes	characteristic
436	C₂	C₁₀₃×#3154	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₀₃	C₂×#127
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₀₃
prime radical	C₂×#127×C₁₀₃	C₂²
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×#3230	C₂	semidirect
3. C₁₀₃×#3170	C₂	semidirect
4. C₁₀₃×#3165	C₂	semidirect
7. C₁₀₃×#1722	C₂	semidirect
8. C₁₀₃×#1719	C₂	semidirect
9. C₁₀₃×#1714	C₂	semidirect
10. C₁₀₃×#1714	C₂	semidirect
11. C₁₀₃×#1451	C₂	semidirect
18. #500×C₁₀₃	C₂²	semidirect
19. #500×C₁₀₃	C₂²	semidirect
20. #500×C₁₀₃	C₂²	semidirect
21. #498×C₁₀₃	C₂²	semidirect
22. #494×C₁₀₃	C₂²	semidirect
28. #487×C₁₀₃	C₂²	semidirect
29. #487×C₁₀₃	C₂²	semidirect
30. #487×C₁₀₃	C₂²	semidirect
45. #322×C₁₀₃	C₂²	semidirect
46. #322×C₁₀₃	C₂²	semidirect
213. #19679	C₁₀₃	direct (N × H)
219. #3230	C₂×C₁₀₃	semidirect
221. #3170	C₂×C₁₀₃	semidirect
222. #3165	C₂×C₁₀₃	semidirect
225. #1722	C₂×C₁₀₃	semidirect
226. #1719	C₂×C₁₀₃	semidirect
227. #1714	C₂×C₁₀₃	semidirect
228. #1714	C₂×C₁₀₃	semidirect
229. #1451	C₂×C₁₀₃	semidirect
230. C₁₀₃	#19679	direct (N × H)
237. #500	C₂²×C₁₀₃	semidirect
238. #500	C₂²×C₁₀₃	semidirect
239. #500	C₂²×C₁₀₃	semidirect
240. #498	C₂²×C₁₀₃	semidirect
241. #494	C₂²×C₁₀₃	semidirect
247. #487	C₂²×C₁₀₃	semidirect
248. #487	C₂²×C₁₀₃	semidirect
249. #487	C₂²×C₁₀₃	semidirect
264. #322	C₂²×C₁₀₃	semidirect
265. #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×#3230	2
C₁₀₃×#3208	2
C₁₀₃×#3170	2
C₁₀₃×#3165	2
C₂×#492×C₁₀₃	2
C₁₀₃×#3138	2
C₁₀₃×#1722	2
C₁₀₃×#1719	2
C₁₀₃×#1714	2
C₁₀₃×#1451	2
#19679	103

Subgroups — C103×#19679 #39924954

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₃×#19679 #39924954