Subgroups — C₁₀₃×#33250 #39938525

Order 26368.

912 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	C₂×#501×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#497×C₁₀₃	C₂	1	1	yes	maximal, characteristic
3	C₂×#491×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#489×C₁₀₃	C₂	1	1	yes	maximal, characteristic
5	C₁₀₃×#2862	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₀₃×#2861	C₂	1	1	yes	maximal, characteristic
7	C₁₀₃×#1973	C₂	1	2	yes	maximal
8	C₁₀₃×#1971	C₂	1	2	yes	maximal, complemented
9	C₁₀₃×#1969	C₂	1	2	yes	maximal, complemented
10	C₁₀₃×#1968	C₂	1	2	yes	maximal
11	C₄×#97×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×Q₁₆×C₁₀₃	C₂²	1	2	yes	—
13	C₂²×SD₁₆×C₁₀₃	C₂²	1	2	yes	—
14	C₂×C₄⋊Q₈×C₁₀₃	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊Q₈×C₁₀₃	C₂²	1	1	yes	characteristic
16	C₂×#125×C₁₀₃	C₂²	1	1	yes	characteristic
17	C₂×#124×C₁₀₃	C₂²	1	1	yes	characteristic
18	#501×C₁₀₃	—	2	4	no	—
19	#497×C₁₀₃	—	2	4	no	—
20	#491×C₁₀₃	—	2	4	no	—
21	#489×C₁₀₃	—	2	4	no	—
22	C₂×#107×C₁₀₃	C₂²	1	2	yes	—
23	C₂×#106×C₁₀₃	C₂²	1	2	yes	—
24	C₂×#103×C₁₀₃	C₂²	1	2	yes	—
25	C₂×#103×C₁₀₃	C₂²	1	2	yes	—
26	C₂×#103×C₁₀₃	C₂²	1	2	yes	—
27	C₂×#102×C₁₀₃	C₂²	1	2	yes	—
28	C₂×#97×C₁₀₃	C₂²	1	2	yes	—
29	C₂×#97×C₁₀₃	C₂²	1	1	yes	characteristic
30	C₂×#97×C₁₀₃	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₈×C₁₀₃	C₂²	1	2	yes	—
32	#391×C₁₀₃	—	2	2	no	—
33	#391×C₁₀₃	C₂²	1	2	yes	—
34	#391×C₁₀₃	C₂²	1	1	yes	characteristic
35	#391×C₁₀₃	C₂²	1	1	yes	characteristic
36	#391×C₁₀₃	C₂²	1	2	yes	—
37	#390×C₁₀₃	C₂²	1	1	yes	characteristic
38	#390×C₁₀₃	C₂²	1	1	yes	characteristic
39	#388×C₁₀₃	—	2	2	no	—
40	#388×C₁₀₃	—	2	2	no	—
41	#382×C₁₀₃	—	2	2	no	—
42	C₄³×C₁₀₃	C₂²	1	1	yes	characteristic
43	C₂²×Q₈×C₁₀₃	—	2	1	no	—
44	C₂²×Q₈×C₁₀₃	C₂³	1	1	yes	characteristic
45	C₂²×Q₈×C₁₀₃	C₂³	1	2	yes	—
46	C₂²×D₄×C₁₀₃	C₂³	1	1	yes	characteristic
47	C₂×Q₁₆×C₁₀₃	—	2	4	no	—
48	C₂×Q₁₆×C₁₀₃	—	2	4	no	—
49	C₂×Q₁₆×C₁₀₃	—	2	4	no	—
50	C₂×SD₁₆×C₁₀₃	—	2	4	no	—
51	C₂×SD₁₆×C₁₀₃	—	2	4	no	—
52	C₂×SD₁₆×C₁₀₃	—	2	4	no	—
53	C₂²×C₈×C₁₀₃	C₂³	1	2	yes	—
54	C₂²×C₈×C₁₀₃	C₂³	1	2	yes	—
55	C₄⋊Q₈×C₁₀₃	—	2	2	no	—
56	C₄⋊Q₈×C₁₀₃	—	2	2	no	—
57	C₄⋊Q₈×C₁₀₃	—	2	2	no	—
58	C₄⋊Q₈×C₁₀₃	—	2	2	no	—
59	#125×C₁₀₃	—	2	2	no	—
60	#125×C₁₀₃	—	2	2	no	—
61	#124×C₁₀₃	—	2	2	no	—
62	#124×C₁₀₃	—	2	2	no	—
63	C₂×C₄⋊C₄×C₁₀₃	—	2	1	no	—
64	C₂×C₄⋊C₄×C₁₀₃	—	2	1	no	—
65	C₂×C₄⋊C₄×C₁₀₃	—	2	1	no	—
66	C₂×C₄⋊C₄×C₁₀₃	—	2	1	no	—
67	C₂×C₄⋊C₄×C₁₀₃	—	2	1	no	—
68	C₂×C₄⋊C₄×C₁₀₃	C₂³	1	1	yes	characteristic
69	C₂×C₄⋊C₄×C₁₀₃	C₂³	1	1	yes	characteristic
70	C₂×C₄⋊C₄×C₁₀₃	C₂³	1	2	yes	—
71	C₂×C₂²⋊C₄×C₁₀₃	—	2	2	no	—
72	C₂×C₂²⋊C₄×C₁₀₃	—	2	2	no	—
73	C₂×C₂²⋊C₄×C₁₀₃	—	2	1	no	—
74	C₂×C₂²⋊C₄×C₁₀₃	—	2	1	no	—
75	C₂×C₄²×C₁₀₃	D₄	1	2	yes	—
76	C₂×C₄²×C₁₀₃	D₄	1	2	yes	—
77	C₂×C₄²×C₁₀₃	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₁₀₃	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₁₀₃	C₂³	1	1	yes	characteristic
80	#107×C₁₀₃	—	2	4	no	—
81	#106×C₁₀₃	—	2	4	no	—
82	#103×C₁₀₃	—	2	4	no	—
83	#103×C₁₀₃	—	2	4	no	—
84	#103×C₁₀₃	—	2	4	no	—
85	#102×C₁₀₃	—	2	4	no	—
86	#97×C₁₀₃	—	2	4	no	—
87	#97×C₁₀₃	D₄	1	4	yes	—
88	#97×C₁₀₃	D₄	1	4	yes	—
89	C₄×C₈×C₁₀₃	—	2	4	no	—
90	#95×C₁₀₃	—	2	4	no	—
91	#95×C₁₀₃	—	2	4	no	—
92	#95×C₁₀₃	—	2	2	no	—
93	#95×C₁₀₃	—	2	2	no	—
94	C₂⁴×C₁₀₃	—	2	1	no	—
95	C₂×Q₈×C₁₀₃	—	2	1	no	—
96	C₂×Q₈×C₁₀₃	—	2	2	no	—
97	C₂×Q₈×C₁₀₃	—	2	1	no	—
98	C₂×Q₈×C₁₀₃	—	2	2	no	—
99	C₂×Q₈×C₁₀₃	—	2	2	no	—
100	C₂×Q₈×C₁₀₃	—	2	2	no	—
101	C₂×Q₈×C₁₀₃	—	2	2	no	—
102	C₂×Q₈×C₁₀₃	—	2	2	no	—
103	C₂×Q₈×C₁₀₃	—	2	2	no	—
104	C₂×Q₈×C₁₀₃	—	2	2	no	—
105	C₂×Q₈×C₁₀₃	—	4	4	no	—
106	C₂×Q₈×C₁₀₃	—	4	2	no	—
107	C₂×D₄×C₁₀₃	—	2	1	no	—
108	C₂×D₄×C₁₀₃	—	2	1	no	—
109	C₂×D₄×C₁₀₃	—	2	2	no	—
110	C₂×D₄×C₁₀₃	—	2	2	no	—
111	C₂²×C₄×C₁₀₃	—	2	1	no	—
112	C₂²×C₄×C₁₀₃	—	2	2	no	—
113	C₂²×C₄×C₁₀₃	—	2	2	no	—
114	C₂²×C₄×C₁₀₃	—	2	1	no	—
115	C₂²×C₄×C₁₀₃	—	2	1	no	—
116	C₂²×C₄×C₁₀₃	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₀₃	C₂×D₄	1	2	yes	—
120	C₂²×C₄×C₁₀₃	C₂⁴	1	1	yes	characteristic
121	Q₁₆×C₁₀₃	—	4	8	no	—
122	SD₁₆×C₁₀₃	—	4	8	no	—
123	C₂×C₈×C₁₀₃	—	2	2	no	—
124	C₂×C₈×C₁₀₃	—	2	2	no	—
125	C₂×C₈×C₁₀₃	C₂×D₄	1	4	yes	—
126	C₂×C₈×C₁₀₃	C₂×D₄	1	4	yes	—
127	C₂×C₈×C₁₀₃	#41	1	4	yes	—
128	C₂×C₈×C₁₀₃	#41	1	4	yes	—
129	C₄⋊C₄×C₁₀₃	—	2	2	no	—
130	C₄⋊C₄×C₁₀₃	—	2	1	no	—
131	C₄⋊C₄×C₁₀₃	—	2	1	no	—
132	C₄⋊C₄×C₁₀₃	—	2	1	no	—
133	C₄⋊C₄×C₁₀₃	—	2	2	no	—
134	C₄⋊C₄×C₁₀₃	—	2	1	no	—
135	C₄⋊C₄×C₁₀₃	—	4	2	no	—
136	C₄⋊C₄×C₁₀₃	—	4	2	no	—
137	C₄⋊C₄×C₁₀₃	—	4	2	no	—
138	C₄⋊C₄×C₁₀₃	—	4	2	no	—
139	C₄⋊C₄×C₁₀₃	—	4	2	no	—
140	C₂²⋊C₄×C₁₀₃	—	4	4	no	—
141	C₂²⋊C₄×C₁₀₃	—	4	2	no	—
142	C₂²⋊C₄×C₁₀₃	—	4	2	no	—
143	C₂²⋊C₄×C₁₀₃	—	4	4	no	—
144	C₄²×C₁₀₃	—	2	4	no	—
145	C₄²×C₁₀₃	—	2	2	no	—
146	C₄²×C₁₀₃	—	2	2	no	—
147	C₄²×C₁₀₃	—	4	2	no	—
148	C₄²×C₁₀₃	C₂×D₄	1	2	yes	—
149	C₄²×C₁₀₃	C₂×D₄	1	2	yes	—
150	C₂³×C₁₀₃	—	4	1	no	—
151	C₂³×C₁₀₃	—	4	1	no	—
152	C₂³×C₁₀₃	—	4	1	no	—
153	C₂³×C₁₀₃	—	4	2	no	—
154	C₂³×C₁₀₃	—	4	2	no	—
155	C₂³×C₁₀₃	C₂²×D₄	1	1	yes	characteristic
156	Q₈×C₁₀₃	—	4	2	no	—
157	Q₈×C₁₀₃	—	4	2	no	—
158	Q₈×C₁₀₃	—	4	2	no	—
159	Q₈×C₁₀₃	—	4	2	no	—
160	Q₈×C₁₀₃	—	4	2	no	—
161	Q₈×C₁₀₃	—	4	2	no	—
162	Q₈×C₁₀₃	—	8	4	no	—
163	D₄×C₁₀₃	—	4	2	no	—
164	D₄×C₁₀₃	—	4	2	no	—
165	C₂×C₄×C₁₀₃	—	2	2	no	—
166	C₂×C₄×C₁₀₃	—	2	2	no	—
167	C₂×C₄×C₁₀₃	—	2	2	no	—
168	C₂×C₄×C₁₀₃	—	2	2	no	—
169	C₂×C₄×C₁₀₃	—	2	2	no	—
170	C₂×C₄×C₁₀₃	—	2	2	no	—
171	C₂×C₄×C₁₀₃	—	2	2	no	—
172	C₂×C₄×C₁₀₃	—	4	1	no	—
173	C₂×C₄×C₁₀₃	—	4	1	no	—
174	C₂×C₄×C₁₀₃	—	4	1	no	—
175	C₂×C₄×C₁₀₃	—	4	2	no	—
176	C₂×C₄×C₁₀₃	—	4	2	no	—
177	C₂×C₄×C₁₀₃	—	4	1	no	—
178	C₂×C₄×C₁₀₃	—	4	2	no	—
179	C₂×C₄×C₁₀₃	—	4	1	no	—
180	C₂×C₄×C₁₀₃	—	4	2	no	—
181	C₂×C₄×C₁₀₃	—	4	2	no	—
182	C₂×C₄×C₁₀₃	—	4	2	no	—
183	C₂×C₄×C₁₀₃	—	4	4	no	—
184	C₂×C₄×C₁₀₃	#127	1	2	yes	—
185	C₂×C₄×C₁₀₃	#127	1	2	yes	—
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	C₂×#41	1	2	yes	—
190	C₂×C₄×C₁₀₃	C₂×#41	1	2	yes	—
191	C₈×C₁₀₃	—	2	4	no	—
192	C₈×C₁₀₃	#124	1	8	yes	—
193	C₂²×C₁₀₃	—	8	1	no	—
194	C₂²×C₁₀₃	—	8	1	no	—
195	C₂²×C₁₀₃	—	8	1	no	—
196	C₂²×C₁₀₃	—	8	2	no	—
197	C₂²×C₁₀₃	—	8	2	no	—
198	C₂²×C₁₀₃	C₂×#127	1	1	yes	characteristic
199	C₂²×C₁₀₃	#532	1	1	yes	characteristic
200	C₂²×C₁₀₃	#532	1	1	yes	characteristic
201	C₂²×C₁₀₃	C₂×#137	1	2	yes	—
202	C₂²×C₁₀₃	#575	1	2	yes	—
203	C₄×C₁₀₃	—	2	2	no	—
204	C₄×C₁₀₃	—	2	2	no	—
205	C₄×C₁₀₃	—	2	4	no	—
206	C₄×C₁₀₃	—	4	2	no	—
207	C₄×C₁₀₃	—	8	1	no	—
208	C₄×C₁₀₃	—	8	2	no	—
209	C₄×C₁₀₃	—	8	1	no	—
210	C₄×C₁₀₃	—	8	1	no	—
211	C₄×C₁₀₃	—	8	2	no	—
212	C₄×C₁₀₃	C₂×#124	1	2	yes	—
213	C₄×C₁₀₃	#532	1	2	yes	—
214	#33250	C₁₀₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
215	C₂×C₁₀₃	—	16	1	no	—
216	C₂×C₁₀₃	#2858	1	1	yes	characteristic
217	C₂×C₁₀₃	#3152	1	1	yes	characteristic
218	C₂×C₁₀₃	#3153	1	1	yes	characteristic
219	C₂×C₁₀₃	#3172	1	2	yes	—
220	C₂×C₁₀₃	#3181	1	2	yes	—
221	C₂×#501	C₂×C₁₀₃	1	1	yes	characteristic, complemented
222	C₂×#497	C₂×C₁₀₃	1	1	yes	characteristic
223	C₂×#491	C₂×C₁₀₃	1	1	yes	characteristic, complemented
224	C₂×#489	C₂×C₁₀₃	1	1	yes	characteristic
225	#2862	C₂×C₁₀₃	1	1	yes	characteristic, complemented
226	#2861	C₂×C₁₀₃	1	1	yes	characteristic
227	#1973	C₂×C₁₀₃	1	2	yes	—
228	#1971	C₂×C₁₀₃	1	2	yes	complemented
229	#1969	C₂×C₁₀₃	1	2	yes	complemented
230	#1968	C₂×C₁₀₃	1	2	yes	—
231	C₄×#97	C₂×C₁₀₃	1	1	yes	characteristic, complemented
232	C₁₀₃	#33250	1	1	yes	characteristic, direct product factor, Sylow
233	C₂²×Q₁₆	C₂²×C₁₀₃	1	2	yes	—
234	C₂²×SD₁₆	C₂²×C₁₀₃	1	2	yes	—
235	C₂×C₄⋊Q₈	C₂²×C₁₀₃	1	1	yes	characteristic
236	C₂×C₄⋊Q₈	C₂²×C₁₀₃	1	1	yes	characteristic
237	C₂×#125	C₂²×C₁₀₃	1	1	yes	characteristic
238	C₂×#124	C₂²×C₁₀₃	1	1	yes	characteristic
239	#501	—	2	4	no	—
240	#497	—	2	4	no	—
241	#491	—	2	4	no	—
242	#489	—	2	4	no	—
243	C₂×#107	C₂²×C₁₀₃	1	2	yes	—
244	C₂×#106	C₂²×C₁₀₃	1	2	yes	—
245	C₂×#103	C₂²×C₁₀₃	1	2	yes	—
246	C₂×#103	C₂²×C₁₀₃	1	2	yes	—
247	C₂×#103	C₂²×C₁₀₃	1	2	yes	—
248	C₂×#102	C₂²×C₁₀₃	1	2	yes	—
249	C₂×#97	C₂²×C₁₀₃	1	2	yes	—
250	C₂×#97	C₂²×C₁₀₃	1	1	yes	characteristic
251	C₂×#97	C₂²×C₁₀₃	1	1	yes	characteristic
252	C₂×C₄×C₈	C₂²×C₁₀₃	1	2	yes	—
253	#391	—	2	2	no	—
254	#391	C₂²×C₁₀₃	1	1	yes	characteristic
255	#391	C₂²×C₁₀₃	1	1	yes	characteristic
256	#391	C₂²×C₁₀₃	1	2	yes	—
257	#391	C₂²×C₁₀₃	1	2	yes	—
258	#390	C₂²×C₁₀₃	1	1	yes	characteristic
259	#390	C₂²×C₁₀₃	1	1	yes	characteristic
260	#388	—	2	2	no	—
261	#388	—	2	2	no	—
262	#382	—	2	2	no	—
263	C₄³	C₂²×C₁₀₃	1	1	yes	characteristic
264	C₂²×Q₈	—	2	1	no	—
265	C₂²×Q₈	C₂³×C₁₀₃	1	1	yes	characteristic
266	C₂²×Q₈	C₂³×C₁₀₃	1	2	yes	—
267	C₂²×D₄	C₂³×C₁₀₃	1	1	yes	characteristic
268	C₂×Q₁₆	—	2	4	no	—
269	C₂×Q₁₆	—	2	4	no	—
270	C₂×Q₁₆	—	2	4	no	—
271	C₂×SD₁₆	—	2	4	no	—
272	C₂×SD₁₆	—	2	4	no	—
273	C₂×SD₁₆	—	2	4	no	—
274	C₂²×C₈	C₂³×C₁₀₃	1	2	yes	—
275	C₂²×C₈	C₂³×C₁₀₃	1	2	yes	—
276	C₄⋊Q₈	—	2	2	no	—
277	C₄⋊Q₈	—	2	2	no	—
278	C₄⋊Q₈	—	2	2	no	—
279	C₄⋊Q₈	—	2	2	no	—
280	#125	—	2	2	no	—
281	#125	—	2	2	no	—
282	#124	—	2	2	no	—
283	#124	—	2	2	no	—
284	C₂×C₄⋊C₄	—	2	1	no	—
285	C₂×C₄⋊C₄	—	2	1	no	—
286	C₂×C₄⋊C₄	—	2	1	no	—
287	C₂×C₄⋊C₄	—	2	1	no	—
288	C₂×C₄⋊C₄	—	2	1	no	—
289	C₂×C₄⋊C₄	C₂³×C₁₀₃	1	1	yes	characteristic
290	C₂×C₄⋊C₄	C₂³×C₁₀₃	1	1	yes	characteristic
291	C₂×C₄⋊C₄	C₂³×C₁₀₃	1	2	yes	—
292	C₂×C₂²⋊C₄	—	2	1	no	—
293	C₂×C₂²⋊C₄	—	2	1	no	—
294	C₂×C₂²⋊C₄	—	2	2	no	—
295	C₂×C₂²⋊C₄	—	2	2	no	—
296	C₂×C₄²	D₄×C₁₀₃	1	2	yes	—
297	C₂×C₄²	D₄×C₁₀₃	1	2	yes	—
298	C₂×C₄²	C₂³×C₁₀₃	1	1	yes	characteristic
299	C₂×C₄²	C₂³×C₁₀₃	1	1	yes	characteristic
300	C₂×C₄²	C₂³×C₁₀₃	1	1	yes	characteristic
301	#107	—	2	4	no	—
302	#106	—	2	4	no	—
303	#103	—	2	4	no	—
304	#103	—	2	4	no	—
305	#103	—	2	4	no	—
306	#102	—	2	4	no	—
307	#97	—	2	4	no	—
308	#97	D₄×C₁₀₃	1	4	yes	—
309	#97	D₄×C₁₀₃	1	4	yes	—
310	C₄×C₈	—	2	4	no	—
311	#95	—	2	4	no	—
312	#95	—	2	4	no	—
313	#95	—	2	2	no	—
314	#95	—	2	2	no	—
315	C₂⁴	—	2	1	no	—
316	C₂×Q₈	—	2	1	no	—
317	C₂×Q₈	—	2	2	no	—
318	C₂×Q₈	—	2	1	no	—
319	C₂×Q₈	—	2	2	no	—
320	C₂×Q₈	—	2	2	no	—
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	—	2	2	no	—
324	C₂×Q₈	—	2	2	no	—
325	C₂×Q₈	—	2	2	no	—
326	C₂×Q₈	—	4	4	no	—
327	C₂×Q₈	—	4	2	no	—
328	C₂×D₄	—	2	1	no	—
329	C₂×D₄	—	2	1	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂²×C₄	—	2	1	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	C₂×D₄×C₁₀₃	1	2	yes	—
338	C₂²×C₄	C₂×D₄×C₁₀₃	1	1	yes	characteristic
339	C₂²×C₄	C₂×D₄×C₁₀₃	1	1	yes	characteristic
340	C₂²×C₄	C₂×D₄×C₁₀₃	1	2	yes	—
341	C₂²×C₄	C₂⁴×C₁₀₃	1	1	yes	characteristic
342	Q₁₆	—	4	8	no	—
343	SD₁₆	—	4	8	no	—
344	C₂×C₈	—	2	2	no	—
345	C₂×C₈	—	2	2	no	—
346	C₂×C₈	C₂×D₄×C₁₀₃	1	4	yes	—
347	C₂×C₈	C₂×D₄×C₁₀₃	1	4	yes	—
348	C₂×C₈	#41×C₁₀₃	1	4	yes	—
349	C₂×C₈	#41×C₁₀₃	1	4	yes	—
350	C₄⋊C₄	—	2	2	no	—
351	C₄⋊C₄	—	2	1	no	—
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	—	2	1	no	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	2	1	no	—
356	C₄⋊C₄	—	4	2	no	—
357	C₄⋊C₄	—	4	2	no	—
358	C₄⋊C₄	—	4	2	no	—
359	C₄⋊C₄	—	4	2	no	—
360	C₄⋊C₄	—	4	2	no	—
361	C₂²⋊C₄	—	4	4	no	—
362	C₂²⋊C₄	—	4	2	no	—
363	C₂²⋊C₄	—	4	2	no	—
364	C₂²⋊C₄	—	4	4	no	—
365	C₄²	—	2	4	no	—
366	C₄²	—	2	2	no	—
367	C₄²	—	2	2	no	—
368	C₄²	—	4	2	no	—
369	C₄²	C₂×D₄×C₁₀₃	1	2	yes	—
370	C₄²	C₂×D₄×C₁₀₃	1	2	yes	—
371	C₂³	—	4	1	no	—
372	C₂³	—	4	1	no	—
373	C₂³	—	4	1	no	—
374	C₂³	—	4	2	no	—
375	C₂³	—	4	2	no	—
376	C₂³	C₂²×D₄×C₁₀₃	1	1	yes	characteristic
377	Q₈	—	4	2	no	—
378	Q₈	—	4	2	no	—
379	Q₈	—	4	2	no	—
380	Q₈	—	4	2	no	—
381	Q₈	—	4	2	no	—
382	Q₈	—	4	2	no	—
383	Q₈	—	8	4	no	—
384	D₄	—	4	2	no	—
385	D₄	—	4	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	4	no	—
405	C₂×C₄	#127×C₁₀₃	1	2	yes	—
406	C₂×C₄	#127×C₁₀₃	1	2	yes	—
407	C₂×C₄	#137×C₁₀₃	1	4	yes	—
408	C₂×C₄	C₂²×D₄×C₁₀₃	1	1	yes	characteristic
409	C₂×C₄	C₂²×D₄×C₁₀₃	1	1	yes	characteristic
410	C₂×C₄	C₂×#41×C₁₀₃	1	2	yes	—
411	C₂×C₄	C₂×#41×C₁₀₃	1	2	yes	—
412	C₈	—	2	4	no	—
413	C₈	#124×C₁₀₃	1	8	yes	—
414	C₂²	—	8	1	no	—
415	C₂²	—	8	1	no	—
416	C₂²	—	8	1	no	—
417	C₂²	—	8	2	no	—
418	C₂²	—	8	2	no	—
419	C₂²	C₂×#127×C₁₀₃	1	1	yes	characteristic
420	C₂²	#532×C₁₀₃	1	1	yes	characteristic
421	C₂²	#532×C₁₀₃	1	1	yes	characteristic
422	C₂²	C₂×#137×C₁₀₃	1	2	yes	—
423	C₂²	#575×C₁₀₃	1	2	yes	—
424	C₄	—	2	2	no	—
425	C₄	—	2	2	no	—
426	C₄	—	2	4	no	—
427	C₄	—	4	2	no	—
428	C₄	—	8	1	no	—
429	C₄	—	8	2	no	—
430	C₄	—	8	1	no	—
431	C₄	—	8	2	no	—
432	C₄	—	8	1	no	—
433	C₄	C₂×#124×C₁₀₃	1	2	yes	—
434	C₄	#532×C₁₀₃	1	2	yes	—
435	C₂	—	16	1	no	—
436	C₂	C₁₀₃×#2858	1	1	yes	characteristic
437	C₂	C₁₀₃×#3152	1	1	yes	characteristic
438	C₂	C₁₀₃×#3153	1	1	yes	characteristic
439	C₂	C₁₀₃×#3172	1	2	yes	—
440	C₂	C₁₀₃×#3181	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₀₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₀₃
prime radical	C₂²×D₄×C₁₀₃	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₀₃ ◁ C₄³×C₁₀₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#501×C₁₀₃	C₂	semidirect
3. C₂×#491×C₁₀₃	C₂	semidirect
5. C₁₀₃×#2862	C₂	semidirect
8. C₁₀₃×#1971	C₂	semidirect
9. C₁₀₃×#1969	C₂	semidirect
11. C₄×#97×C₁₀₃	C₂	semidirect
214. #33250	C₁₀₃	direct (N × H)
221. C₂×#501	C₂×C₁₀₃	semidirect
223. C₂×#491	C₂×C₁₀₃	semidirect
225. #2862	C₂×C₁₀₃	semidirect
228. #1971	C₂×C₁₀₃	semidirect
229. #1969	C₂×C₁₀₃	semidirect
231. C₄×#97	C₂×C₁₀₃	semidirect
232. C₁₀₃	#33250	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#501×C₁₀₃	2
C₂×#497×C₁₀₃	2
C₂×#491×C₁₀₃	2
C₂×#489×C₁₀₃	2
C₁₀₃×#2862	2
C₁₀₃×#2861	2
C₁₀₃×#1973	2
C₁₀₃×#1971	2
C₁₀₃×#1969	2
C₁₀₃×#1968	2
C₄×#97×C₁₀₃	2
#33250	103

Subgroups — C103×#33250 #39938525

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₃×#33250 #39938525