Subgroups — C₁₀₃×#19160 #39924435

Order 26368.

642 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₀₃×#3169	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₀₃×#3106	C₂	1	2	yes	maximal, complemented
3	C₁₀₃×#2965	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₀₃×#1698	C₂	1	2	yes	maximal, complemented
5	C₁₀₃×#1697	C₂	1	2	yes	maximal, complemented
6	C₁₀₃×#1696	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₀₃×#1695	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₀₃×#1688	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₀₃×#1687	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₀₃×#1564	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₀₃×#1543	C₂	1	2	yes	maximal, complemented
12	#532×C₁₀₃	C₂²	1	2	yes	—
13	C₄×#41×C₁₀₃	C₂²	1	1	yes	characteristic
14	#500×C₁₀₃	C₂²	1	1	yes	characteristic
15	#493×C₁₀₃	C₂²	1	1	yes	characteristic
16	#486×C₁₀₃	C₂²	1	2	yes	—
17	#482×C₁₀₃	—	2	2	no	—
18	#477×C₁₀₃	C₂²	1	2	yes	—
19	#476×C₁₀₃	C₂²	1	2	yes	—
20	#466×C₁₀₃	—	2	1	no	—
21	#466×C₁₀₃	—	2	1	no	—
22	#460×C₁₀₃	C₂²	1	2	yes	—
23	#459×C₁₀₃	C₂²	1	2	yes	—
24	#449×C₁₀₃	—	2	2	no	—
25	#446×C₁₀₃	C₂²	1	1	yes	characteristic
26	#446×C₁₀₃	C₂²	1	1	yes	characteristic
27	C₄×SD₁₆×C₁₀₃	—	2	2	no	—
28	C₄×D₈×C₁₀₃	—	2	2	no	—
29	C₄×D₈×C₁₀₃	—	2	1	no	—
30	C₄×D₈×C₁₀₃	—	2	1	no	—
31	#436×C₁₀₃	C₂²	1	1	yes	characteristic
32	#436×C₁₀₃	C₂²	1	1	yes	characteristic
33	#435×C₁₀₃	—	2	1	no	—
34	#435×C₁₀₃	—	2	1	no	—
35	#431×C₁₀₃	—	2	1	no	—
36	#431×C₁₀₃	C₂²	1	1	yes	characteristic
37	#431×C₁₀₃	C₂²	1	2	yes	—
38	C₄×M₁₆×C₁₀₃	—	2	1	no	—
39	C₂×C₄×C₈×C₁₀₃	C₂²	1	1	yes	characteristic
40	#335×C₁₀₃	C₂²	1	2	yes	—
41	#334×C₁₀₃	C₂²	1	1	yes	characteristic
42	#334×C₁₀₃	C₂²	1	1	yes	characteristic
43	#333×C₁₀₃	C₂²	1	2	yes	—
44	#333×C₁₀₃	C₂²	1	2	yes	—
45	#331×C₁₀₃	C₂²	1	2	yes	—
46	#331×C₁₀₃	C₂²	1	2	yes	—
47	C₂×#41×C₁₀₃	—	2	2	no	—
48	C₂×#41×C₁₀₃	D₄	1	1	yes	characteristic
49	C₂×SD₁₆×C₁₀₃	—	2	2	no	—
50	C₂×D₈×C₁₀₃	—	2	2	no	—
51	C₂×D₈×C₁₀₃	—	2	1	no	—
52	C₂×D₈×C₁₀₃	—	2	1	no	—
53	C₂×M₁₆×C₁₀₃	—	2	1	no	—
54	C₂×M₁₆×C₁₀₃	—	2	1	no	—
55	C₂²×C₈×C₁₀₃	D₄	1	1	yes	characteristic
56	C₂²×C₈×C₁₀₃	D₄	1	1	yes	characteristic
57	C₄⋊Q₈×C₁₀₃	C₂³	1	2	yes	—
58	#127×C₁₀₃	C₂³	1	2	yes	—
59	#124×C₁₀₃	—	2	2	no	—
60	#121×C₁₀₃	—	2	2	no	—
61	#121×C₁₀₃	—	2	2	no	—
62	C₄×Q₈×C₁₀₃	D₄	1	1	yes	characteristic
63	C₄×Q₈×C₁₀₃	C₂³	1	1	yes	characteristic
64	C₄×D₄×C₁₀₃	—	2	1	no	—
65	C₄×D₄×C₁₀₃	—	2	1	no	—
66	C₄×D₄×C₁₀₃	—	2	2	no	—
67	C₄×D₄×C₁₀₃	—	2	2	no	—
68	C₄×D₄×C₁₀₃	D₄	1	1	yes	characteristic
69	C₄×D₄×C₁₀₃	C₂³	1	1	yes	characteristic
70	#117×C₁₀₃	—	2	1	no	—
71	#117×C₁₀₃	D₄	1	1	yes	characteristic
72	C₂×C₄²×C₁₀₃	—	2	1	no	—
73	C₂×C₄²×C₁₀₃	C₂³	1	1	yes	characteristic
74	#107×C₁₀₃	—	2	1	no	—
75	#107×C₁₀₃	—	2	1	no	—
76	#107×C₁₀₃	—	2	2	no	—
77	#106×C₁₀₃	—	2	2	no	—
78	C₄⋊C₈×C₁₀₃	—	2	1	no	—
79	C₄⋊C₈×C₁₀₃	—	2	1	no	—
80	C₄⋊C₈×C₁₀₃	C₂³	1	1	yes	characteristic
81	C₄⋊C₈×C₁₀₃	C₂³	1	1	yes	characteristic
82	C₄⋊C₈×C₁₀₃	C₂³	1	2	yes	—
83	C₄⋊C₈×C₁₀₃	C₂³	1	2	yes	—
84	#103×C₁₀₃	—	2	2	no	—
85	#102×C₁₀₃	—	2	2	no	—
86	#102×C₁₀₃	—	2	2	no	—
87	#102×C₁₀₃	—	2	2	no	—
88	#102×C₁₀₃	—	2	2	no	—
89	#102×C₁₀₃	—	2	2	no	—
90	C₂²⋊C₈×C₁₀₃	—	2	1	no	—
91	C₂²⋊C₈×C₁₀₃	—	2	2	no	—
92	C₂²⋊C₈×C₁₀₃	—	2	1	no	—
93	C₂²⋊C₈×C₁₀₃	—	2	1	no	—
94	#97×C₁₀₃	—	2	1	no	—
95	#97×C₁₀₃	—	2	1	no	—
96	C₄×C₈×C₁₀₃	—	2	1	no	—
97	C₄×C₈×C₁₀₃	—	2	2	no	—
98	C₄×C₈×C₁₀₃	D₄	1	1	yes	characteristic
99	C₄×C₈×C₁₀₃	D₄	1	1	yes	characteristic
100	C₄×C₈×C₁₀₃	C₂³	1	1	yes	characteristic
101	C₄×C₈×C₁₀₃	C₂³	1	1	yes	characteristic
102	#41×C₁₀₃	—	4	2	no	—
103	#41×C₁₀₃	—	8	4	no	—
104	C₂×Q₈×C₁₀₃	—	2	2	no	—
105	C₂×Q₈×C₁₀₃	C₂×D₄	1	1	yes	characteristic
106	C₂×D₄×C₁₀₃	—	2	1	no	—
107	C₂×D₄×C₁₀₃	—	2	2	no	—
108	C₂×D₄×C₁₀₃	—	2	2	no	—
109	C₂×D₄×C₁₀₃	—	2	2	no	—
110	C₂×D₄×C₁₀₃	—	4	2	no	—
111	C₂×D₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₀₃	—	2	1	no	—
113	C₂²×C₄×C₁₀₃	—	2	1	no	—
114	C₂²×C₄×C₁₀₃	—	2	1	no	—
115	C₂²×C₄×C₁₀₃	—	4	2	no	—
116	C₂²×C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₀₃	#41	1	1	yes	characteristic
119	SD₁₆×C₁₀₃	—	4	4	no	—
120	D₈×C₁₀₃	—	4	2	no	—
121	D₈×C₁₀₃	—	4	4	no	—
122	D₈×C₁₀₃	—	4	2	no	—
123	M₁₆×C₁₀₃	—	4	2	no	—
124	M₁₆×C₁₀₃	—	4	2	no	—
125	C₂×C₈×C₁₀₃	—	2	2	no	—
126	C₂×C₈×C₁₀₃	—	2	1	no	—
127	C₂×C₈×C₁₀₃	—	2	1	no	—
128	C₂×C₈×C₁₀₃	—	2	2	no	—
129	C₂×C₈×C₁₀₃	—	2	2	no	—
130	C₂×C₈×C₁₀₃	—	4	1	no	—
131	C₂×C₈×C₁₀₃	C₂×D₄	1	1	yes	characteristic
132	C₂×C₈×C₁₀₃	C₂×D₄	1	1	yes	characteristic
133	C₂×C₈×C₁₀₃	C₂×D₄	1	1	yes	characteristic
134	C₂×C₈×C₁₀₃	C₂×D₄	1	1	yes	characteristic
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	2	no	—
139	C₄⋊C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
140	C₄⋊C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
141	C₂²⋊C₄×C₁₀₃	—	2	1	no	—
142	C₂²⋊C₄×C₁₀₃	—	2	1	no	—
143	C₂²⋊C₄×C₁₀₃	—	2	1	no	—
144	C₂²⋊C₄×C₁₀₃	—	4	2	no	—
145	C₂²⋊C₄×C₁₀₃	—	4	2	no	—
146	C₄²×C₁₀₃	—	2	1	no	—
147	C₄²×C₁₀₃	—	2	1	no	—
148	C₄²×C₁₀₃	—	2	1	no	—
149	C₄²×C₁₀₃	C₂×D₄	1	1	yes	characteristic
150	C₄²×C₁₀₃	C₂×D₄	1	1	yes	characteristic
151	C₄²×C₁₀₃	#41	1	1	yes	characteristic
152	C₄²×C₁₀₃	C₂⁴	1	1	yes	characteristic
153	C₂³×C₁₀₃	—	2	1	no	—
154	C₂³×C₁₀₃	—	4	2	no	—
155	C₂³×C₁₀₃	#121	1	1	yes	characteristic
156	Q₈×C₁₀₃	—	2	2	no	—
157	Q₈×C₁₀₃	—	8	2	no	—
158	D₄×C₁₀₃	—	2	2	no	—
159	D₄×C₁₀₃	—	4	2	no	—
160	D₄×C₁₀₃	—	4	2	no	—
161	D₄×C₁₀₃	—	4	2	no	—
162	D₄×C₁₀₃	—	4	2	no	—
163	D₄×C₁₀₃	—	4	2	no	—
164	D₄×C₁₀₃	—	8	2	no	—
165	D₄×C₁₀₃	—	8	4	no	—
166	C₂×C₄×C₁₀₃	—	2	1	no	—
167	C₂×C₄×C₁₀₃	—	2	1	no	—
168	C₂×C₄×C₁₀₃	—	2	2	no	—
169	C₂×C₄×C₁₀₃	—	2	2	no	—
170	C₂×C₄×C₁₀₃	—	2	1	no	—
171	C₂×C₄×C₁₀₃	—	2	1	no	—
172	C₂×C₄×C₁₀₃	—	2	1	no	—
173	C₂×C₄×C₁₀₃	—	4	2	no	—
174	C₂×C₄×C₁₀₃	—	4	1	no	—
175	C₂×C₄×C₁₀₃	—	4	1	no	—
176	C₂×C₄×C₁₀₃	—	4	2	no	—
177	C₂×C₄×C₁₀₃	—	4	2	no	—
178	C₂×C₄×C₁₀₃	—	8	4	no	—
179	C₂×C₄×C₁₀₃	#121	1	1	yes	characteristic
180	C₂×C₄×C₁₀₃	#121	1	1	yes	characteristic
181	C₂×C₄×C₁₀₃	#121	1	1	yes	characteristic
182	C₂×C₄×C₁₀₃	C₂²×D₄	1	1	yes	characteristic
183	C₂×C₄×C₁₀₃	C₂²×D₄	1	1	yes	characteristic
184	C₂×C₄×C₁₀₃	C₂×#41	1	1	yes	characteristic
185	C₈×C₁₀₃	—	2	1	no	—
186	C₈×C₁₀₃	—	2	1	no	—
187	C₈×C₁₀₃	—	2	1	no	—
188	C₈×C₁₀₃	—	4	1	no	—
189	C₈×C₁₀₃	—	4	1	no	—
190	C₈×C₁₀₃	—	4	2	no	—
191	C₈×C₁₀₃	—	4	2	no	—
192	C₈×C₁₀₃	#135	1	2	yes	—
193	C₂²×C₁₀₃	—	2	1	no	—
194	C₂²×C₁₀₃	—	2	1	no	—
195	C₂²×C₁₀₃	—	2	1	no	—
196	C₂²×C₁₀₃	—	4	1	no	—
197	C₂²×C₁₀₃	—	4	1	no	—
198	C₂²×C₁₀₃	—	4	1	no	—
199	C₂²×C₁₀₃	—	8	2	no	—
200	C₂²×C₁₀₃	—	8	2	no	—
201	C₂²×C₁₀₃	—	8	2	no	—
202	C₂²×C₁₀₃	C₂×#121	1	1	yes	characteristic
203	C₄×C₁₀₃	—	2	1	no	—
204	C₄×C₁₀₃	—	2	1	no	—
205	C₄×C₁₀₃	—	2	1	no	—
206	C₄×C₁₀₃	—	4	1	no	—
207	C₄×C₁₀₃	—	4	1	no	—
208	C₄×C₁₀₃	—	4	1	no	—
209	C₄×C₁₀₃	—	8	2	no	—
210	C₄×C₁₀₃	#472	1	2	yes	—
211	C₄×C₁₀₃	C₂×#135	1	1	yes	characteristic
212	C₄×C₁₀₃	#575	1	1	yes	characteristic
213	C₄×C₁₀₃	#575	1	2	yes	—
214	#19160	C₁₀₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
215	C₂×C₁₀₃	—	4	1	no	—
216	C₂×C₁₀₃	—	8	1	no	—
217	C₂×C₁₀₃	—	16	2	no	—
218	C₂×C₁₀₃	#3035	1	1	yes	characteristic
219	C₂×C₁₀₃	#3054	1	1	yes	characteristic
220	C₂×C₁₀₃	C₂×#472	1	1	yes	characteristic
221	#3169	C₂×C₁₀₃	1	1	yes	characteristic, complemented
222	#3106	C₂×C₁₀₃	1	2	yes	complemented
223	#2965	C₂×C₁₀₃	1	1	yes	characteristic, complemented
224	#1698	C₂×C₁₀₃	1	2	yes	complemented
225	#1697	C₂×C₁₀₃	1	2	yes	complemented
226	#1696	C₂×C₁₀₃	1	1	yes	characteristic, complemented
227	#1695	C₂×C₁₀₃	1	1	yes	characteristic, complemented
228	#1688	C₂×C₁₀₃	1	1	yes	characteristic, complemented
229	#1687	C₂×C₁₀₃	1	1	yes	characteristic, complemented
230	#1564	C₂×C₁₀₃	1	1	yes	characteristic, complemented
231	#1543	C₂×C₁₀₃	1	2	yes	complemented
232	C₁₀₃	#19160	1	1	yes	characteristic, direct product factor, Sylow
233	#532	C₂²×C₁₀₃	1	2	yes	—
234	C₄×#41	C₂²×C₁₀₃	1	1	yes	characteristic
235	#500	C₂²×C₁₀₃	1	1	yes	characteristic
236	#493	C₂²×C₁₀₃	1	1	yes	characteristic
237	#486	C₂²×C₁₀₃	1	2	yes	—
238	#482	—	2	2	no	—
239	#477	C₂²×C₁₀₃	1	2	yes	—
240	#476	C₂²×C₁₀₃	1	2	yes	—
241	#466	—	2	1	no	—
242	#466	—	2	1	no	—
243	#460	C₂²×C₁₀₃	1	2	yes	—
244	#459	C₂²×C₁₀₃	1	2	yes	—
245	#449	—	2	2	no	—
246	#446	C₂²×C₁₀₃	1	1	yes	characteristic
247	#446	C₂²×C₁₀₃	1	1	yes	characteristic
248	C₄×SD₁₆	—	2	2	no	—
249	C₄×D₈	—	2	2	no	—
250	C₄×D₈	—	2	1	no	—
251	C₄×D₈	—	2	1	no	—
252	#436	C₂²×C₁₀₃	1	1	yes	characteristic
253	#436	C₂²×C₁₀₃	1	1	yes	characteristic
254	#435	—	2	1	no	—
255	#435	—	2	1	no	—
256	#431	—	2	1	no	—
257	#431	C₂²×C₁₀₃	1	1	yes	characteristic
258	#431	C₂²×C₁₀₃	1	2	yes	—
259	C₄×M₁₆	—	2	1	no	—
260	C₂×C₄×C₈	C₂²×C₁₀₃	1	1	yes	characteristic
261	#335	C₂²×C₁₀₃	1	2	yes	—
262	#334	C₂²×C₁₀₃	1	1	yes	characteristic
263	#334	C₂²×C₁₀₃	1	1	yes	characteristic
264	#333	C₂²×C₁₀₃	1	2	yes	—
265	#333	C₂²×C₁₀₃	1	2	yes	—
266	#331	C₂²×C₁₀₃	1	2	yes	—
267	#331	C₂²×C₁₀₃	1	2	yes	—
268	C₂×#41	—	2	2	no	—
269	C₂×#41	D₄×C₁₀₃	1	1	yes	characteristic
270	C₂×SD₁₆	—	2	2	no	—
271	C₂×D₈	—	2	2	no	—
272	C₂×D₈	—	2	1	no	—
273	C₂×D₈	—	2	1	no	—
274	C₂×M₁₆	—	2	1	no	—
275	C₂×M₁₆	—	2	1	no	—
276	C₂²×C₈	D₄×C₁₀₃	1	1	yes	characteristic
277	C₂²×C₈	D₄×C₁₀₃	1	1	yes	characteristic
278	C₄⋊Q₈	C₂³×C₁₀₃	1	2	yes	—
279	#127	C₂³×C₁₀₃	1	2	yes	—
280	#124	—	2	2	no	—
281	#121	—	2	2	no	—
282	#121	—	2	2	no	—
283	C₄×Q₈	D₄×C₁₀₃	1	1	yes	characteristic
284	C₄×Q₈	C₂³×C₁₀₃	1	1	yes	characteristic
285	C₄×D₄	—	2	1	no	—
286	C₄×D₄	—	2	1	no	—
287	C₄×D₄	—	2	2	no	—
288	C₄×D₄	—	2	2	no	—
289	C₄×D₄	D₄×C₁₀₃	1	1	yes	characteristic
290	C₄×D₄	C₂³×C₁₀₃	1	1	yes	characteristic
291	#117	—	2	1	no	—
292	#117	D₄×C₁₀₃	1	1	yes	characteristic
293	C₂×C₄²	—	2	1	no	—
294	C₂×C₄²	C₂³×C₁₀₃	1	1	yes	characteristic
295	#107	—	2	1	no	—
296	#107	—	2	1	no	—
297	#107	—	2	2	no	—
298	#106	—	2	2	no	—
299	C₄⋊C₈	—	2	1	no	—
300	C₄⋊C₈	—	2	1	no	—
301	C₄⋊C₈	C₂³×C₁₀₃	1	1	yes	characteristic
302	C₄⋊C₈	C₂³×C₁₀₃	1	1	yes	characteristic
303	C₄⋊C₈	C₂³×C₁₀₃	1	2	yes	—
304	C₄⋊C₈	C₂³×C₁₀₃	1	2	yes	—
305	#103	—	2	2	no	—
306	#102	—	2	2	no	—
307	#102	—	2	2	no	—
308	#102	—	2	2	no	—
309	#102	—	2	2	no	—
310	#102	—	2	2	no	—
311	C₂²⋊C₈	—	2	1	no	—
312	C₂²⋊C₈	—	2	2	no	—
313	C₂²⋊C₈	—	2	1	no	—
314	C₂²⋊C₈	—	2	1	no	—
315	#97	—	2	1	no	—
316	#97	—	2	1	no	—
317	C₄×C₈	—	2	1	no	—
318	C₄×C₈	—	2	2	no	—
319	C₄×C₈	D₄×C₁₀₃	1	1	yes	characteristic
320	C₄×C₈	D₄×C₁₀₃	1	1	yes	characteristic
321	C₄×C₈	C₂³×C₁₀₃	1	1	yes	characteristic
322	C₄×C₈	C₂³×C₁₀₃	1	1	yes	characteristic
323	#41	—	4	2	no	—
324	#41	—	8	4	no	—
325	C₂×Q₈	—	2	2	no	—
326	C₂×Q₈	C₂×D₄×C₁₀₃	1	1	yes	characteristic
327	C₂×D₄	—	2	1	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	4	2	no	—
332	C₂×D₄	C₂×D₄×C₁₀₃	1	1	yes	characteristic
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	4	2	no	—
337	C₂²×C₄	C₂×D₄×C₁₀₃	1	1	yes	characteristic
338	C₂²×C₄	C₂×D₄×C₁₀₃	1	1	yes	characteristic
339	C₂²×C₄	#41×C₁₀₃	1	1	yes	characteristic
340	SD₁₆	—	4	4	no	—
341	D₈	—	4	2	no	—
342	D₈	—	4	4	no	—
343	D₈	—	4	2	no	—
344	M₁₆	—	4	2	no	—
345	M₁₆	—	4	2	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	4	1	no	—
352	C₂×C₈	C₂×D₄×C₁₀₃	1	1	yes	characteristic
353	C₂×C₈	C₂×D₄×C₁₀₃	1	1	yes	characteristic
354	C₂×C₈	C₂×D₄×C₁₀₃	1	1	yes	characteristic
355	C₂×C₈	C₂×D₄×C₁₀₃	1	1	yes	characteristic
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	C₂×D₄×C₁₀₃	1	1	yes	characteristic
361	C₄⋊C₄	C₂×D₄×C₁₀₃	1	1	yes	characteristic
362	C₂²⋊C₄	—	2	1	no	—
363	C₂²⋊C₄	—	2	1	no	—
364	C₂²⋊C₄	—	2	1	no	—
365	C₂²⋊C₄	—	4	2	no	—
366	C₂²⋊C₄	—	4	2	no	—
367	C₄²	—	2	1	no	—
368	C₄²	—	2	1	no	—
369	C₄²	—	2	1	no	—
370	C₄²	C₂×D₄×C₁₀₃	1	1	yes	characteristic
371	C₄²	C₂×D₄×C₁₀₃	1	1	yes	characteristic
372	C₄²	#41×C₁₀₃	1	1	yes	characteristic
373	C₄²	C₂⁴×C₁₀₃	1	1	yes	characteristic
374	C₂³	—	2	1	no	—
375	C₂³	—	4	2	no	—
376	C₂³	#121×C₁₀₃	1	1	yes	characteristic
377	Q₈	—	2	2	no	—
378	Q₈	—	8	2	no	—
379	D₄	—	2	2	no	—
380	D₄	—	4	2	no	—
381	D₄	—	4	2	no	—
382	D₄	—	4	2	no	—
383	D₄	—	4	2	no	—
384	D₄	—	4	2	no	—
385	D₄	—	8	2	no	—
386	D₄	—	8	4	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	8	4	no	—
400	C₂×C₄	#121×C₁₀₃	1	1	yes	characteristic
401	C₂×C₄	#121×C₁₀₃	1	1	yes	characteristic
402	C₂×C₄	#121×C₁₀₃	1	1	yes	characteristic
403	C₂×C₄	C₂²×D₄×C₁₀₃	1	1	yes	characteristic
404	C₂×C₄	C₂²×D₄×C₁₀₃	1	1	yes	characteristic
405	C₂×C₄	C₂×#41×C₁₀₃	1	1	yes	characteristic
406	C₈	—	2	1	no	—
407	C₈	—	2	1	no	—
408	C₈	—	2	1	no	—
409	C₈	—	4	1	no	—
410	C₈	—	4	1	no	—
411	C₈	—	4	2	no	—
412	C₈	—	4	2	no	—
413	C₈	#135×C₁₀₃	1	2	yes	—
414	C₂²	—	2	1	no	—
415	C₂²	—	2	1	no	—
416	C₂²	—	2	1	no	—
417	C₂²	—	4	1	no	—
418	C₂²	—	4	1	no	—
419	C₂²	—	4	1	no	—
420	C₂²	—	8	2	no	—
421	C₂²	—	8	2	no	—
422	C₂²	—	8	2	no	—
423	C₂²	C₂×#121×C₁₀₃	1	1	yes	characteristic
424	C₄	—	2	1	no	—
425	C₄	—	2	1	no	—
426	C₄	—	2	1	no	—
427	C₄	—	4	1	no	—
428	C₄	—	4	1	no	—
429	C₄	—	4	1	no	—
430	C₄	—	8	2	no	—
431	C₄	#472×C₁₀₃	1	2	yes	—
432	C₄	C₂×#135×C₁₀₃	1	1	yes	characteristic
433	C₄	#575×C₁₀₃	1	1	yes	characteristic
434	C₄	#575×C₁₀₃	1	2	yes	—
435	C₂	—	4	1	no	—
436	C₂	—	8	1	no	—
437	C₂	—	16	2	no	—
438	C₂	C₁₀₃×#3035	1	1	yes	characteristic
439	C₂	C₁₀₃×#3054	1	1	yes	characteristic
440	C₂	C₂×#472×C₁₀₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₀₃	#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₀₃
socle	C₂²×C₁₀₃	C₂×#121
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₀₃ ◁ C₂×C₄²×C₁₀₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₀₃×#3169	C₂	semidirect
2. C₁₀₃×#3106	C₂	semidirect
3. C₁₀₃×#2965	C₂	semidirect
4. C₁₀₃×#1698	C₂	semidirect
5. C₁₀₃×#1697	C₂	semidirect
6. C₁₀₃×#1696	C₂	semidirect
7. C₁₀₃×#1695	C₂	semidirect
8. C₁₀₃×#1688	C₂	semidirect
9. C₁₀₃×#1687	C₂	semidirect
10. C₁₀₃×#1564	C₂	semidirect
11. C₁₀₃×#1543	C₂	semidirect
214. #19160	C₁₀₃	direct (N × H)
221. #3169	C₂×C₁₀₃	semidirect
222. #3106	C₂×C₁₀₃	semidirect
223. #2965	C₂×C₁₀₃	semidirect
224. #1698	C₂×C₁₀₃	semidirect
225. #1697	C₂×C₁₀₃	semidirect
226. #1696	C₂×C₁₀₃	semidirect
227. #1695	C₂×C₁₀₃	semidirect
228. #1688	C₂×C₁₀₃	semidirect
229. #1687	C₂×C₁₀₃	semidirect
230. #1564	C₂×C₁₀₃	semidirect
231. #1543	C₂×C₁₀₃	semidirect
232. C₁₀₃	#19160	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₀₃×#3169	2
C₁₀₃×#3106	2
C₁₀₃×#2965	2
C₁₀₃×#1698	2
C₁₀₃×#1697	2
C₁₀₃×#1696	2
C₁₀₃×#1695	2
C₁₀₃×#1688	2
C₁₀₃×#1687	2
C₁₀₃×#1564	2
C₁₀₃×#1543	2
#19160	103

Subgroups — C103×#19160 #39924435

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₃×#19160 #39924435