Subgroups — C₁₀₃×#17905 #39923180

Order 26368.

698 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₀₃×#3101	C₂	1	1	yes	maximal, characteristic
2	C₁₀₃×#2960	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₈×D₄×C₁₀₃	C₂	1	1	yes	maximal, characteristic
4	C₁₀₃×#1585	C₂	1	4	yes	maximal, complemented
5	C₁₀₃×SD₁₆⋊C₈	C₂	1	4	yes	maximal, complemented
6	C₁₀₃×#1571	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₀₃×#1486	C₂	1	1	yes	maximal, characteristic
8	C₁₀₃×#1481	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₀₃×#1452	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×C₈×C₁₀₃	—	2	1	no	—
11	#533×C₁₀₃	C₂²	1	1	yes	characteristic
12	C₂×C₄×D₄×C₁₀₃	C₂²	1	1	yes	characteristic
13	#483×C₁₀₃	C₄	1	2	yes	—
14	#476×C₁₀₃	C₄	1	2	yes	—
15	#461×C₁₀₃	C₄	1	2	yes	—
16	#450×C₁₀₃	C₄	1	2	yes	—
17	#446×C₁₀₃	—	2	1	no	—
18	#446×C₁₀₃	C₂²	1	2	yes	complemented
19	C₈×Q₈×C₁₀₃	—	2	1	no	—
20	C₈×Q₈×C₁₀₃	C₂²	1	2	yes	complemented
21	C₄×SD₁₆×C₁₀₃	C₂²	1	4	yes	—
22	C₈×D₄×C₁₀₃	—	2	1	no	—
23	C₈×D₄×C₁₀₃	—	2	1	no	—
24	C₈×D₄×C₁₀₃	C₂²	1	2	yes	—
25	C₈×D₄×C₁₀₃	C₂²	1	2	yes	—
26	#431×C₁₀₃	C₂²	1	1	yes	characteristic
27	#431×C₁₀₃	C₂²	1	1	yes	characteristic
28	#424×C₁₀₃	—	2	1	no	—
29	#423×C₁₀₃	C₂²	1	1	yes	characteristic
30	C₂×C₄⋊C₈×C₁₀₃	C₂²	1	1	yes	characteristic
31	C₂×C₂²⋊C₈×C₁₀₃	—	2	1	no	—
32	#405×C₁₀₃	—	2	1	no	—
33	C₂×C₄×C₈×C₁₀₃	C₂²	1	1	yes	characteristic
34	#335×C₁₀₃	C₂²	1	4	yes	complemented
35	Q₈⋊C₈×C₁₀₃	C₂²	1	4	yes	complemented
36	D₄⋊C₈×C₁₀₃	C₂²	1	4	yes	—
37	#322×C₁₀₃	C₂²	1	2	yes	complemented
38	#322×C₁₀₃	C₂²	1	2	yes	complemented
39	C₂²×D₄×C₁₀₃	C₂×C₄	1	1	yes	characteristic
40	C₂³×C₄×C₁₀₃	—	2	1	no	—
41	C₂×SD₁₆×C₁₀₃	C₂×C₄	1	4	yes	—
42	C₂×M₁₆×C₁₀₃	—	2	1	no	—
43	C₂²×C₈×C₁₀₃	—	2	1	no	—
44	C₂²×C₈×C₁₀₃	—	2	2	no	—
45	C₂²×C₈×C₁₀₃	—	2	2	no	—
46	C₂²×C₈×C₁₀₃	—	4	4	no	—
47	C₂²×C₈×C₁₀₃	D₄	1	1	yes	characteristic
48	C₂²×C₈×C₁₀₃	D₄	1	1	yes	characteristic
49	C₄⋊Q₈×C₁₀₃	C₂×C₄	1	1	yes	characteristic
50	C₄⋊Q₈×C₁₀₃	C₂×C₄	1	1	yes	characteristic
51	#125×C₁₀₃	—	2	1	no	—
52	C₂²⋊Q₈×C₁₀₃	—	2	1	no	—
53	C₂²⋊Q₈×C₁₀₃	C₂×C₄	1	2	yes	—
54	C₄×Q₈×C₁₀₃	—	2	1	no	—
55	C₄×Q₈×C₁₀₃	C₂³	1	2	yes	—
56	C₄×D₄×C₁₀₃	—	2	1	no	—
57	C₄×D₄×C₁₀₃	—	2	1	no	—
58	C₄×D₄×C₁₀₃	C₂×C₄	1	2	yes	—
59	C₄×D₄×C₁₀₃	C₂³	1	2	yes	—
60	#117×C₁₀₃	—	2	1	no	—
61	C₂×C₄⋊C₄×C₁₀₃	C₂×C₄	1	1	yes	characteristic
62	C₂×C₂²⋊C₄×C₁₀₃	—	2	1	no	—
63	C₂×C₄²×C₁₀₃	C₂³	1	1	yes	characteristic
64	#106×C₁₀₃	C₂×C₄	1	4	yes	—
65	C₄⋊C₈×C₁₀₃	—	2	2	no	—
66	C₄⋊C₈×C₁₀₃	—	2	2	no	—
67	C₄⋊C₈×C₁₀₃	—	2	1	no	—
68	C₄⋊C₈×C₁₀₃	—	2	1	no	—
69	C₄⋊C₈×C₁₀₃	—	2	1	no	—
70	C₄⋊C₈×C₁₀₃	C₂×C₄	1	2	yes	—
71	C₄⋊C₈×C₁₀₃	C₂³	1	2	yes	—
72	C₄⋊C₈×C₁₀₃	C₂³	1	2	yes	—
73	#103×C₁₀₃	C₂×C₄	1	4	yes	—
74	#102×C₁₀₃	C₂×C₄	1	4	yes	—
75	C₂²⋊C₈×C₁₀₃	—	2	1	no	—
76	C₂²⋊C₈×C₁₀₃	—	2	2	no	—
77	C₂²⋊C₈×C₁₀₃	—	2	2	no	—
78	C₂²⋊C₈×C₁₀₃	C₂×C₄	1	2	yes	—
79	#97×C₁₀₃	—	2	2	no	—
80	C₄×C₈×C₁₀₃	—	2	2	no	—
81	C₄×C₈×C₁₀₃	D₄	1	1	yes	characteristic
82	C₄×C₈×C₁₀₃	D₄	1	1	yes	characteristic
83	C₄×C₈×C₁₀₃	C₂³	1	2	yes	—
84	C₄×C₈×C₁₀₃	C₂³	1	2	yes	—
85	C₄×C₈×C₁₀₃	C₂³	1	1	yes	characteristic
86	C₄×C₈×C₁₀₃	C₂³	1	1	yes	characteristic
87	C₂⁴×C₁₀₃	—	2	1	no	—
88	C₂×Q₈×C₁₀₃	—	2	1	no	—
89	C₂×Q₈×C₁₀₃	C₂²×C₄	1	2	yes	—
90	C₂×D₄×C₁₀₃	—	2	4	no	—
91	C₂×D₄×C₁₀₃	—	2	1	no	—
92	C₂×D₄×C₁₀₃	C₂²×C₄	1	2	yes	—
93	C₂²×C₄×C₁₀₃	—	2	1	no	—
94	C₂²×C₄×C₁₀₃	—	2	2	no	—
95	C₂²×C₄×C₁₀₃	—	2	2	no	—
96	C₂²×C₄×C₁₀₃	—	4	2	no	—
97	C₂²×C₄×C₁₀₃	—	4	2	no	—
98	C₂²×C₄×C₁₀₃	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₀₃	#41	1	1	yes	characteristic
101	SD₁₆×C₁₀₃	—	2	8	no	—
102	M₁₆×C₁₀₃	—	4	2	no	—
103	C₂×C₈×C₁₀₃	—	2	2	no	—
104	C₂×C₈×C₁₀₃	—	2	2	no	—
105	C₂×C₈×C₁₀₃	—	2	2	no	—
106	C₂×C₈×C₁₀₃	—	2	2	no	—
107	C₂×C₈×C₁₀₃	—	2	2	no	—
108	C₂×C₈×C₁₀₃	—	4	4	no	—
109	C₂×C₈×C₁₀₃	—	4	4	no	—
110	C₂×C₈×C₁₀₃	—	4	2	no	—
111	C₂×C₈×C₁₀₃	C₂²×C₄	1	4	yes	—
112	C₂×C₈×C₁₀₃	C₂×D₄	1	1	yes	characteristic
113	C₂×C₈×C₁₀₃	C₂×D₄	1	1	yes	characteristic
114	C₂×C₈×C₁₀₃	C₂×D₄	1	1	yes	characteristic
115	C₂×C₈×C₁₀₃	C₂×D₄	1	1	yes	characteristic
116	C₄⋊C₄×C₁₀₃	—	2	1	no	—
117	C₄⋊C₄×C₁₀₃	—	2	1	no	—
118	C₄⋊C₄×C₁₀₃	—	2	1	no	—
119	C₄⋊C₄×C₁₀₃	—	2	1	no	—
120	C₄⋊C₄×C₁₀₃	—	2	2	no	—
121	C₄⋊C₄×C₁₀₃	—	2	2	no	—
122	C₄⋊C₄×C₁₀₃	C₂²×C₄	1	2	yes	—
123	C₄⋊C₄×C₁₀₃	C₂²×C₄	1	2	yes	—
124	C₂²⋊C₄×C₁₀₃	—	2	2	no	—
125	C₂²⋊C₄×C₁₀₃	—	2	2	no	—
126	C₂²⋊C₄×C₁₀₃	—	2	2	no	—
127	C₄²×C₁₀₃	—	2	2	no	—
128	C₄²×C₁₀₃	C₂²×C₄	1	1	yes	characteristic
129	C₄²×C₁₀₃	C₂×D₄	1	1	yes	characteristic
130	C₄²×C₁₀₃	#41	1	1	yes	characteristic
131	C₄²×C₁₀₃	C₂⁴	1	1	yes	characteristic
132	C₂³×C₁₀₃	—	2	4	no	—
133	C₂³×C₁₀₃	—	2	2	no	—
134	C₂³×C₁₀₃	—	4	2	no	—
135	C₂³×C₁₀₃	—	4	2	no	—
136	C₂³×C₁₀₃	C₄×D₄	1	1	yes	characteristic
137	Q₈×C₁₀₃	—	2	4	no	—
138	Q₈×C₁₀₃	—	4	2	no	—
139	D₄×C₁₀₃	—	2	4	no	—
140	D₄×C₁₀₃	—	2	2	no	—
141	D₄×C₁₀₃	#131	1	4	yes	—
142	C₂×C₄×C₁₀₃	—	2	2	no	—
143	C₂×C₄×C₁₀₃	—	2	2	no	—
144	C₂×C₄×C₁₀₃	—	2	2	no	—
145	C₂×C₄×C₁₀₃	—	2	2	no	—
146	C₂×C₄×C₁₀₃	—	4	1	no	—
147	C₂×C₄×C₁₀₃	—	4	2	no	—
148	C₂×C₄×C₁₀₃	—	4	2	no	—
149	C₂×C₄×C₁₀₃	—	4	2	no	—
150	C₂×C₄×C₁₀₃	—	4	4	no	—
151	C₂×C₄×C₁₀₃	C₄×D₄	1	1	yes	characteristic
152	C₂×C₄×C₁₀₃	C₄×D₄	1	1	yes	characteristic
153	C₂×C₄×C₁₀₃	C₄×D₄	1	1	yes	characteristic
154	C₂×C₄×C₁₀₃	AGL(1,ℤ/8)	1	2	yes	—
155	C₂×C₄×C₁₀₃	#137	1	2	yes	—
156	C₂×C₄×C₁₀₃	C₂³×C₄	1	1	yes	characteristic
157	C₂×C₄×C₁₀₃	C₂²×D₄	1	1	yes	characteristic
158	C₂×C₄×C₁₀₃	C₂×#41	1	1	yes	characteristic
159	C₈×C₁₀₃	—	2	4	no	—
160	C₈×C₁₀₃	—	2	1	no	—
161	C₈×C₁₀₃	—	2	1	no	—
162	C₈×C₁₀₃	—	2	1	no	—
163	C₈×C₁₀₃	—	2	1	no	—
164	C₈×C₁₀₃	—	4	2	no	—
165	C₈×C₁₀₃	—	4	2	no	—
166	C₈×C₁₀₃	—	4	2	no	—
167	C₂²×C₁₀₃	—	2	1	no	—
168	C₂²×C₁₀₃	—	2	1	no	—
169	C₂²×C₁₀₃	—	2	4	no	—
170	C₂²×C₁₀₃	—	4	8	no	—
171	C₂²×C₁₀₃	—	4	2	no	—
172	C₂²×C₁₀₃	—	4	2	no	—
173	C₂²×C₁₀₃	#440	1	2	yes	—
174	C₂²×C₁₀₃	C₂×C₄×D₄	1	1	yes	characteristic
175	C₄×C₁₀₃	—	2	1	no	—
176	C₄×C₁₀₃	—	2	1	no	—
177	C₄×C₁₀₃	—	2	1	no	—
178	C₄×C₁₀₃	—	4	2	no	—
179	C₄×C₁₀₃	—	4	2	no	—
180	C₄×C₁₀₃	—	4	2	no	—
181	C₄×C₁₀₃	#440	1	2	yes	—
182	C₄×C₁₀₃	C₂×#131	1	2	yes	—
183	C₄×C₁₀₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
184	C₄×C₁₀₃	C₂×#137	1	1	yes	characteristic
185	#17905	C₁₀₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
186	C₂×C₁₀₃	—	2	2	no	—
187	C₂×C₁₀₃	—	4	4	no	—
188	C₂×C₁₀₃	#2929	1	1	yes	characteristic
189	C₂×C₁₀₃	C₂×#440	1	1	yes	characteristic
190	C₂×C₁₀₃	#2955	1	1	yes	characteristic
191	#3101	C₂×C₁₀₃	1	1	yes	characteristic
192	#2960	C₂×C₁₀₃	1	1	yes	characteristic, complemented
193	C₂×C₈×D₄	C₂×C₁₀₃	1	1	yes	characteristic
194	#1585	C₂×C₁₀₃	1	4	yes	complemented
195	SD₁₆⋊C₈	C₂×C₁₀₃	1	4	yes	complemented
196	#1571	C₂×C₁₀₃	1	1	yes	characteristic, complemented
197	#1486	C₂×C₁₀₃	1	1	yes	characteristic
198	#1481	C₂×C₁₀₃	1	1	yes	characteristic, complemented
199	#1452	C₂×C₁₀₃	1	1	yes	characteristic, complemented
200	C₁₀₃	#17905	1	1	yes	characteristic, direct product factor, Sylow
201	C₂³×C₈	—	2	1	no	—
202	#533	C₂²×C₁₀₃	1	1	yes	characteristic
203	C₂×C₄×D₄	C₂²×C₁₀₃	1	1	yes	characteristic
204	#483	C₄×C₁₀₃	1	2	yes	—
205	#476	C₄×C₁₀₃	1	2	yes	—
206	#461	C₄×C₁₀₃	1	2	yes	—
207	#450	C₄×C₁₀₃	1	2	yes	—
208	#446	—	2	1	no	—
209	#446	C₂²×C₁₀₃	1	2	yes	complemented
210	C₈×Q₈	—	2	1	no	—
211	C₈×Q₈	C₂²×C₁₀₃	1	2	yes	complemented
212	C₄×SD₁₆	C₂²×C₁₀₃	1	4	yes	—
213	C₈×D₄	—	2	1	no	—
214	C₈×D₄	—	2	1	no	—
215	C₈×D₄	C₂²×C₁₀₃	1	2	yes	—
216	C₈×D₄	C₂²×C₁₀₃	1	2	yes	—
217	#431	C₂²×C₁₀₃	1	1	yes	characteristic
218	#431	C₂²×C₁₀₃	1	1	yes	characteristic
219	#424	—	2	1	no	—
220	#423	C₂²×C₁₀₃	1	1	yes	characteristic
221	C₂×C₄⋊C₈	C₂²×C₁₀₃	1	1	yes	characteristic
222	C₂×C₂²⋊C₈	—	2	1	no	—
223	#405	—	2	1	no	—
224	C₂×C₄×C₈	C₂²×C₁₀₃	1	1	yes	characteristic
225	#335	C₂²×C₁₀₃	1	4	yes	complemented
226	Q₈⋊C₈	C₂²×C₁₀₃	1	4	yes	complemented
227	D₄⋊C₈	C₂²×C₁₀₃	1	4	yes	—
228	#322	C₂²×C₁₀₃	1	2	yes	complemented
229	#322	C₂²×C₁₀₃	1	2	yes	complemented
230	C₂²×D₄	C₂×C₄×C₁₀₃	1	1	yes	characteristic
231	C₂³×C₄	—	2	1	no	—
232	C₂×SD₁₆	C₂×C₄×C₁₀₃	1	4	yes	—
233	C₂×M₁₆	—	2	1	no	—
234	C₂²×C₈	—	2	1	no	—
235	C₂²×C₈	—	2	2	no	—
236	C₂²×C₈	—	2	2	no	—
237	C₂²×C₈	—	4	4	no	—
238	C₂²×C₈	D₄×C₁₀₃	1	1	yes	characteristic
239	C₂²×C₈	D₄×C₁₀₃	1	1	yes	characteristic
240	C₄⋊Q₈	C₂×C₄×C₁₀₃	1	1	yes	characteristic
241	C₄⋊Q₈	C₂×C₄×C₁₀₃	1	1	yes	characteristic
242	#125	—	2	1	no	—
243	C₂²⋊Q₈	—	2	1	no	—
244	C₂²⋊Q₈	C₂×C₄×C₁₀₃	1	2	yes	—
245	C₄×Q₈	—	2	1	no	—
246	C₄×Q₈	C₂³×C₁₀₃	1	2	yes	—
247	C₄×D₄	—	2	1	no	—
248	C₄×D₄	—	2	1	no	—
249	C₄×D₄	C₂×C₄×C₁₀₃	1	2	yes	—
250	C₄×D₄	C₂³×C₁₀₃	1	2	yes	—
251	#117	—	2	1	no	—
252	C₂×C₄⋊C₄	C₂×C₄×C₁₀₃	1	1	yes	characteristic
253	C₂×C₂²⋊C₄	—	2	1	no	—
254	C₂×C₄²	C₂³×C₁₀₃	1	1	yes	characteristic
255	#106	C₂×C₄×C₁₀₃	1	4	yes	—
256	C₄⋊C₈	—	2	2	no	—
257	C₄⋊C₈	—	2	2	no	—
258	C₄⋊C₈	—	2	1	no	—
259	C₄⋊C₈	—	2	1	no	—
260	C₄⋊C₈	—	2	1	no	—
261	C₄⋊C₈	C₂×C₄×C₁₀₃	1	2	yes	—
262	C₄⋊C₈	C₂³×C₁₀₃	1	2	yes	—
263	C₄⋊C₈	C₂³×C₁₀₃	1	2	yes	—
264	#103	C₂×C₄×C₁₀₃	1	4	yes	—
265	#102	C₂×C₄×C₁₀₃	1	4	yes	—
266	C₂²⋊C₈	—	2	1	no	—
267	C₂²⋊C₈	—	2	2	no	—
268	C₂²⋊C₈	—	2	2	no	—
269	C₂²⋊C₈	C₂×C₄×C₁₀₃	1	2	yes	—
270	#97	—	2	2	no	—
271	C₄×C₈	—	2	2	no	—
272	C₄×C₈	D₄×C₁₀₃	1	1	yes	characteristic
273	C₄×C₈	D₄×C₁₀₃	1	1	yes	characteristic
274	C₄×C₈	C₂³×C₁₀₃	1	2	yes	—
275	C₄×C₈	C₂³×C₁₀₃	1	2	yes	—
276	C₄×C₈	C₂³×C₁₀₃	1	1	yes	characteristic
277	C₄×C₈	C₂³×C₁₀₃	1	1	yes	characteristic
278	C₂⁴	—	2	1	no	—
279	C₂×Q₈	—	2	1	no	—
280	C₂×Q₈	C₂²×C₄×C₁₀₃	1	2	yes	—
281	C₂×D₄	—	2	4	no	—
282	C₂×D₄	—	2	1	no	—
283	C₂×D₄	C₂²×C₄×C₁₀₃	1	2	yes	—
284	C₂²×C₄	—	2	1	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	4	2	no	—
288	C₂²×C₄	—	4	2	no	—
289	C₂²×C₄	C₂²×C₄×C₁₀₃	1	1	yes	characteristic
290	C₂²×C₄	C₂×D₄×C₁₀₃	1	1	yes	characteristic
291	C₂²×C₄	#41×C₁₀₃	1	1	yes	characteristic
292	SD₁₆	—	2	8	no	—
293	M₁₆	—	4	2	no	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	—	2	2	no	—
299	C₂×C₈	—	4	4	no	—
300	C₂×C₈	—	4	4	no	—
301	C₂×C₈	—	4	2	no	—
302	C₂×C₈	C₂²×C₄×C₁₀₃	1	4	yes	—
303	C₂×C₈	C₂×D₄×C₁₀₃	1	1	yes	characteristic
304	C₂×C₈	C₂×D₄×C₁₀₃	1	1	yes	characteristic
305	C₂×C₈	C₂×D₄×C₁₀₃	1	1	yes	characteristic
306	C₂×C₈	C₂×D₄×C₁₀₃	1	1	yes	characteristic
307	C₄⋊C₄	—	2	1	no	—
308	C₄⋊C₄	—	2	1	no	—
309	C₄⋊C₄	—	2	1	no	—
310	C₄⋊C₄	—	2	1	no	—
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	—	2	2	no	—
313	C₄⋊C₄	C₂²×C₄×C₁₀₃	1	2	yes	—
314	C₄⋊C₄	C₂²×C₄×C₁₀₃	1	2	yes	—
315	C₂²⋊C₄	—	2	2	no	—
316	C₂²⋊C₄	—	2	2	no	—
317	C₂²⋊C₄	—	2	2	no	—
318	C₄²	—	2	2	no	—
319	C₄²	C₂²×C₄×C₁₀₃	1	1	yes	characteristic
320	C₄²	C₂×D₄×C₁₀₃	1	1	yes	characteristic
321	C₄²	#41×C₁₀₃	1	1	yes	characteristic
322	C₄²	C₂⁴×C₁₀₃	1	1	yes	characteristic
323	C₂³	—	2	4	no	—
324	C₂³	—	2	2	no	—
325	C₂³	—	4	2	no	—
326	C₂³	—	4	2	no	—
327	C₂³	C₄×D₄×C₁₀₃	1	1	yes	characteristic
328	Q₈	—	2	4	no	—
329	Q₈	—	4	2	no	—
330	D₄	—	2	4	no	—
331	D₄	—	2	2	no	—
332	D₄	#131×C₁₀₃	1	4	yes	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	4	1	no	—
338	C₂×C₄	—	4	2	no	—
339	C₂×C₄	—	4	4	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	4	2	no	—
342	C₂×C₄	C₄×D₄×C₁₀₃	1	1	yes	characteristic
343	C₂×C₄	C₄×D₄×C₁₀₃	1	1	yes	characteristic
344	C₂×C₄	C₄×D₄×C₁₀₃	1	1	yes	characteristic
345	C₂×C₄	AGL(1,ℤ/8)×C₁₀₃	1	2	yes	—
346	C₂×C₄	#137×C₁₀₃	1	2	yes	—
347	C₂×C₄	C₂³×C₄×C₁₀₃	1	1	yes	characteristic
348	C₂×C₄	C₂²×D₄×C₁₀₃	1	1	yes	characteristic
349	C₂×C₄	C₂×#41×C₁₀₃	1	1	yes	characteristic
350	C₈	—	2	4	no	—
351	C₈	—	2	1	no	—
352	C₈	—	2	1	no	—
353	C₈	—	2	1	no	—
354	C₈	—	2	1	no	—
355	C₈	—	4	2	no	—
356	C₈	—	4	2	no	—
357	C₈	—	4	2	no	—
358	C₂²	—	2	1	no	—
359	C₂²	—	2	1	no	—
360	C₂²	—	2	4	no	—
361	C₂²	—	4	8	no	—
362	C₂²	—	4	2	no	—
363	C₂²	—	4	2	no	—
364	C₂²	#440×C₁₀₃	1	2	yes	—
365	C₂²	C₂×C₄×D₄×C₁₀₃	1	1	yes	characteristic
366	C₄	—	2	1	no	—
367	C₄	—	2	1	no	—
368	C₄	—	2	1	no	—
369	C₄	—	4	2	no	—
370	C₄	—	4	2	no	—
371	C₄	—	4	2	no	—
372	C₄	#440×C₁₀₃	1	2	yes	—
373	C₄	C₂×#131×C₁₀₃	1	2	yes	—
374	C₄	C₂×AGL(1,ℤ/8)×C₁₀₃	1	1	yes	characteristic
375	C₄	C₂×#137×C₁₀₃	1	1	yes	characteristic
376	C₂	—	2	2	no	—
377	C₂	—	4	4	no	—
378	C₂	C₁₀₃×#2929	1	1	yes	characteristic
379	C₂	C₂×#440×C₁₀₃	1	1	yes	characteristic
380	C₂	C₁₀₃×#2955	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₀₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₀₃
Frattini, cosocle	C₄²	C₂⁴×C₁₀₃
socle	C₂²×C₁₀₃	C₂×C₄×D₄
prime radical	C₂²×D₄×C₁₀₃	C₂×C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₀₃ ◁ C₂×C₄×C₈×C₁₀₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₀₃×#2960	C₂	semidirect
4. C₁₀₃×#1585	C₂	semidirect
5. C₁₀₃×SD₁₆⋊C₈	C₂	semidirect
6. C₁₀₃×#1571	C₂	semidirect
8. C₁₀₃×#1481	C₂	semidirect
9. C₁₀₃×#1452	C₂	semidirect
18. #446×C₁₀₃	C₂²	semidirect
20. C₈×Q₈×C₁₀₃	C₂²	semidirect
34. #335×C₁₀₃	C₂²	semidirect
35. Q₈⋊C₈×C₁₀₃	C₂²	semidirect
37. #322×C₁₀₃	C₂²	semidirect
38. #322×C₁₀₃	C₂²	semidirect
185. #17905	C₁₀₃	direct (N × H)
192. #2960	C₂×C₁₀₃	semidirect
194. #1585	C₂×C₁₀₃	semidirect
195. SD₁₆⋊C₈	C₂×C₁₀₃	semidirect
196. #1571	C₂×C₁₀₃	semidirect
198. #1481	C₂×C₁₀₃	semidirect
199. #1452	C₂×C₁₀₃	semidirect
200. C₁₀₃	#17905	direct (N × H)
209. #446	C₂²×C₁₀₃	semidirect
211. C₈×Q₈	C₂²×C₁₀₃	semidirect
225. #335	C₂²×C₁₀₃	semidirect
226. Q₈⋊C₈	C₂²×C₁₀₃	semidirect
228. #322	C₂²×C₁₀₃	semidirect
229. #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×#3101	2
C₁₀₃×#2960	2
C₂×C₈×D₄×C₁₀₃	2
C₁₀₃×#1585	2
C₁₀₃×SD₁₆⋊C₈	2
C₁₀₃×#1571	2
C₁₀₃×#1486	2
C₁₀₃×#1481	2
C₁₀₃×#1452	2
#17905	103

Subgroups — C103×#17905 #39923180

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₃×#17905 #39923180