Subgroups — C₁₀₃×#25325 #39930600

Order 26368.

930 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#486×C₁₀₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#460×C₁₀₃	C₂	1	1	yes	maximal, characteristic
3	C₁₀₃×#2568	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₀₃×#2366	C₂	1	1	yes	maximal, characteristic
5	C₁₀₃×#2073	C₂	1	2	yes	maximal, complemented
6	C₁₀₃×#2055	C₂	1	2	yes	maximal, complemented
7	C₁₀₃×#1988	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₀₃×#1939	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₀₃×#1877	C₂	1	2	yes	maximal, complemented
10	C₁₀₃×#1804	C₂	1	2	yes	maximal, complemented
11	C₄×#103×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×SD₁₆×C₁₀₃	C₂²	1	2	yes	—
13	C₂×C₄⋊Q₈×C₁₀₃	C₂²	1	1	yes	characteristic
14	C₂×#127×C₁₀₃	C₂²	1	1	yes	characteristic
15	C₂×C₄×Q₈×C₁₀₃	C₂²	1	1	yes	characteristic
16	C₂×C₄×D₄×C₁₀₃	—	2	1	no	—
17	C₂×C₄×D₄×C₁₀₃	C₂²	1	2	yes	—
18	#486×C₁₀₃	—	2	4	no	—
19	#460×C₁₀₃	—	2	4	no	—
20	C₂×C₄⋊C₈×C₁₀₃	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊C₈×C₁₀₃	C₂²	1	2	yes	—
22	C₂×#103×C₁₀₃	C₂²	1	1	yes	characteristic
23	C₂×#103×C₁₀₃	C₂²	1	1	yes	characteristic
24	C₂×#102×C₁₀₃	C₂²	1	2	yes	—
25	C₂×#102×C₁₀₃	C₂²	1	2	yes	—
26	C₂×#102×C₁₀₃	C₂²	1	2	yes	—
27	C₂×C₄×C₈×C₁₀₃	C₂²	1	1	yes	characteristic
28	#400×C₁₀₃	—	2	2	no	—
29	#391×C₁₀₃	—	2	1	no	—
30	#391×C₁₀₃	—	2	1	no	—
31	#391×C₁₀₃	C₂²	1	2	yes	—
32	#390×C₁₀₃	—	2	1	no	—
33	#390×C₁₀₃	C₂²	1	2	yes	—
34	#386×C₁₀₃	—	2	2	no	—
35	#382×C₁₀₃	C₂²	1	2	yes	—
36	C₄×C₄⋊C₄×C₁₀₃	C₂²	1	1	yes	characteristic
37	C₄×C₄⋊C₄×C₁₀₃	C₂²	1	1	yes	characteristic
38	#340×C₁₀₃	C₂²	1	2	yes	—
39	#340×C₁₀₃	C₂²	1	2	yes	—
40	#340×C₁₀₃	C₂²	1	1	yes	characteristic
41	#340×C₁₀₃	C₂²	1	1	yes	characteristic
42	#336×C₁₀₃	C₂²	1	2	yes	—
43	C₂²×Q₈×C₁₀₃	—	2	1	no	—
44	C₂²×Q₈×C₁₀₃	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₁₀₃	—	2	1	no	—
46	C₂²×D₄×C₁₀₃	—	2	1	no	—
47	C₂²×D₄×C₁₀₃	C₂³	1	2	yes	—
48	C₂³×C₄×C₁₀₃	—	2	2	no	—
49	C₂×SD₁₆×C₁₀₃	—	2	4	no	—
50	C₂×SD₁₆×C₁₀₃	—	2	4	no	—
51	C₂×SD₁₆×C₁₀₃	—	4	2	no	—
52	C₂²×C₈×C₁₀₃	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₁₀₃	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₁₀₃	C₂³	1	2	yes	—
55	C₄⋊Q₈×C₁₀₃	—	2	2	no	—
56	C₄⋊Q₈×C₁₀₃	—	2	2	no	—
57	#127×C₁₀₃	—	2	2	no	—
58	#127×C₁₀₃	D₄	1	4	yes	—
59	C₄×Q₈×C₁₀₃	—	2	2	no	—
60	C₄×Q₈×C₁₀₃	—	2	2	no	—
61	C₄×D₄×C₁₀₃	—	2	4	no	—
62	C₄×D₄×C₁₀₃	—	4	2	no	—
63	C₄×D₄×C₁₀₃	—	4	4	no	—
64	C₂×C₄⋊C₄×C₁₀₃	—	2	1	no	—
65	C₂×C₄⋊C₄×C₁₀₃	—	2	1	no	—
66	C₂×C₄⋊C₄×C₁₀₃	D₄	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₁₀₃	D₄	1	1	yes	characteristic
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×C₄⋊C₄×C₁₀₃	C₂³	1	1	yes	characteristic
72	C₂×C₂²⋊C₄×C₁₀₃	—	2	2	no	—
73	C₂×C₂²⋊C₄×C₁₀₃	—	2	2	no	—
74	C₂×C₂²⋊C₄×C₁₀₃	—	2	2	no	—
75	C₂×C₄²×C₁₀₃	—	2	1	no	—
76	C₂×C₄²×C₁₀₃	—	2	1	no	—
77	C₂×C₄²×C₁₀₃	C₂³	1	2	yes	—
78	C₂×C₄²×C₁₀₃	C₂³	1	1	yes	characteristic
79	C₄⋊C₈×C₁₀₃	—	2	2	no	—
80	C₄⋊C₈×C₁₀₃	—	4	2	no	—
81	#103×C₁₀₃	—	2	2	no	—
82	#103×C₁₀₃	—	2	2	no	—
83	#102×C₁₀₃	—	2	4	no	—
84	#102×C₁₀₃	—	2	4	no	—
85	#102×C₁₀₃	—	2	4	no	—
86	C₄×C₈×C₁₀₃	—	2	2	no	—
87	#95×C₁₀₃	—	2	1	no	—
88	#95×C₁₀₃	—	2	2	no	—
89	#95×C₁₀₃	—	2	2	no	—
90	#95×C₁₀₃	—	2	2	no	—
91	#95×C₁₀₃	—	2	2	no	—
92	#95×C₁₀₃	D₄	1	2	yes	—
93	C₂⁴×C₁₀₃	—	2	2	no	—
94	C₂×Q₈×C₁₀₃	—	2	1	no	—
95	C₂×Q₈×C₁₀₃	—	2	1	no	—
96	C₂×Q₈×C₁₀₃	—	2	1	no	—
97	C₂×Q₈×C₁₀₃	—	2	1	no	—
98	C₂×Q₈×C₁₀₃	—	2	1	no	—
99	C₂×Q₈×C₁₀₃	—	4	2	no	—
100	C₂×Q₈×C₁₀₃	—	4	2	no	—
101	C₂×Q₈×C₁₀₃	—	4	2	no	—
102	C₂×Q₈×C₁₀₃	#41	1	2	yes	—
103	C₂×D₄×C₁₀₃	—	2	4	no	—
104	C₂×D₄×C₁₀₃	—	2	4	no	—
105	C₂×D₄×C₁₀₃	—	2	2	no	—
106	C₂×D₄×C₁₀₃	—	2	2	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	—	4	2	no	—
112	C₂×D₄×C₁₀₃	—	8	1	no	—
113	C₂×D₄×C₁₀₃	—	8	1	no	—
114	C₂×D₄×C₁₀₃	C₂×D₄	1	4	yes	—
115	C₂²×C₄×C₁₀₃	—	2	1	no	—
116	C₂²×C₄×C₁₀₃	—	2	1	no	—
117	C₂²×C₄×C₁₀₃	—	2	1	no	—
118	C₂²×C₄×C₁₀₃	—	2	2	no	—
119	C₂²×C₄×C₁₀₃	—	2	1	no	—
120	C₂²×C₄×C₁₀₃	—	4	4	no	—
121	C₂²×C₄×C₁₀₃	—	4	4	no	—
122	C₂²×C₄×C₁₀₃	—	8	2	no	—
123	C₂²×C₄×C₁₀₃	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₁₀₃	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₀₃	C₂⁴	1	1	yes	characteristic
128	SD₁₆×C₁₀₃	—	4	8	no	—
129	C₂×C₈×C₁₀₃	—	2	1	no	—
130	C₂×C₈×C₁₀₃	—	2	1	no	—
131	C₂×C₈×C₁₀₃	—	2	2	no	—
132	C₂×C₈×C₁₀₃	—	2	1	no	—
133	C₂×C₈×C₁₀₃	—	2	1	no	—
134	C₂×C₈×C₁₀₃	—	2	2	no	—
135	C₂×C₈×C₁₀₃	—	2	1	no	—
136	C₂×C₈×C₁₀₃	—	2	2	no	—
137	C₂×C₈×C₁₀₃	—	2	1	no	—
138	C₄⋊C₄×C₁₀₃	—	2	2	no	—
139	C₄⋊C₄×C₁₀₃	—	2	2	no	—
140	C₄⋊C₄×C₁₀₃	—	2	1	no	—
141	C₄⋊C₄×C₁₀₃	—	2	1	no	—
142	C₄⋊C₄×C₁₀₃	—	2	2	no	—
143	C₄⋊C₄×C₁₀₃	—	2	1	no	—
144	C₄⋊C₄×C₁₀₃	—	2	1	no	—
145	C₄⋊C₄×C₁₀₃	—	2	2	no	—
146	C₄⋊C₄×C₁₀₃	—	2	1	no	—
147	C₄⋊C₄×C₁₀₃	—	4	2	no	—
148	C₄⋊C₄×C₁₀₃	—	4	2	no	—
149	C₄⋊C₄×C₁₀₃	#41	1	2	yes	—
150	C₂²⋊C₄×C₁₀₃	—	4	4	no	—
151	C₂²⋊C₄×C₁₀₃	—	4	4	no	—
152	C₂²⋊C₄×C₁₀₃	—	8	2	no	—
153	C₄²×C₁₀₃	—	2	2	no	—
154	C₄²×C₁₀₃	—	2	2	no	—
155	C₄²×C₁₀₃	—	4	2	no	—
156	C₄²×C₁₀₃	—	4	2	no	—
157	C₄²×C₁₀₃	C₂×D₄	1	2	yes	—
158	C₄²×C₁₀₃	#41	1	2	yes	—
159	C₂³×C₁₀₃	—	2	4	no	—
160	C₂³×C₁₀₃	—	4	2	no	—
161	C₂³×C₁₀₃	—	4	2	no	—
162	C₂³×C₁₀₃	—	4	2	no	—
163	C₂³×C₁₀₃	—	4	2	no	—
164	C₂³×C₁₀₃	—	4	2	no	—
165	C₂³×C₁₀₃	—	4	2	no	—
166	C₂³×C₁₀₃	C₂²×D₄	1	1	yes	characteristic
167	Q₈×C₁₀₃	—	2	2	no	—
168	Q₈×C₁₀₃	—	2	2	no	—
169	Q₈×C₁₀₃	—	4	1	no	—
170	Q₈×C₁₀₃	—	4	1	no	—
171	Q₈×C₁₀₃	—	8	4	no	—
172	D₄×C₁₀₃	—	2	4	no	—
173	D₄×C₁₀₃	—	2	4	no	—
174	D₄×C₁₀₃	—	4	2	no	—
175	D₄×C₁₀₃	—	4	2	no	—
176	D₄×C₁₀₃	—	4	8	no	—
177	D₄×C₁₀₃	—	8	4	no	—
178	C₂×C₄×C₁₀₃	—	2	1	no	—
179	C₂×C₄×C₁₀₃	—	2	1	no	—
180	C₂×C₄×C₁₀₃	—	2	2	no	—
181	C₂×C₄×C₁₀₃	—	2	2	no	—
182	C₂×C₄×C₁₀₃	—	2	2	no	—
183	C₂×C₄×C₁₀₃	—	2	2	no	—
184	C₂×C₄×C₁₀₃	—	2	2	no	—
185	C₂×C₄×C₁₀₃	—	2	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	1	no	—
191	C₂×C₄×C₁₀₃	—	4	1	no	—
192	C₂×C₄×C₁₀₃	—	4	1	no	—
193	C₂×C₄×C₁₀₃	—	4	2	no	—
194	C₂×C₄×C₁₀₃	—	4	1	no	—
195	C₂×C₄×C₁₀₃	—	4	2	no	—
196	C₂×C₄×C₁₀₃	—	4	1	no	—
197	C₂×C₄×C₁₀₃	—	4	2	no	—
198	C₂×C₄×C₁₀₃	—	4	1	no	—
199	C₂×C₄×C₁₀₃	—	4	1	no	—
200	C₂×C₄×C₁₀₃	—	4	1	no	—
201	C₂×C₄×C₁₀₃	—	8	8	no	—
202	C₂×C₄×C₁₀₃	#121	1	2	yes	—
203	C₂×C₄×C₁₀₃	#121	1	2	yes	—
204	C₂×C₄×C₁₀₃	#135	1	2	yes	—
205	C₂×C₄×C₁₀₃	AGL(1,ℤ/8)	1	2	yes	—
206	C₂×C₄×C₁₀₃	C₂²×D₄	1	1	yes	characteristic
207	C₂×C₄×C₁₀₃	C₂×#41	1	1	yes	characteristic
208	C₂×C₄×C₁₀₃	C₂×#41	1	1	yes	characteristic
209	C₂×C₄×C₁₀₃	C₂×#41	1	1	yes	characteristic
210	C₂×C₄×C₁₀₃	H(5,𝔽₂)	1	1	yes	characteristic
211	C₂×C₄×C₁₀₃	2₋¹⁺⁴	1	1	yes	characteristic
212	C₈×C₁₀₃	—	4	1	no	—
213	C₈×C₁₀₃	—	4	2	no	—
214	C₈×C₁₀₃	—	4	1	no	—
215	C₂²×C₁₀₃	—	4	4	no	—
216	C₂²×C₁₀₃	—	4	4	no	—
217	C₂²×C₁₀₃	—	4	4	no	—
218	C₂²×C₁₀₃	—	8	2	no	—
219	C₂²×C₁₀₃	—	8	2	no	—
220	C₂²×C₁₀₃	—	8	2	no	—
221	C₂²×C₁₀₃	—	8	2	no	—
222	C₂²×C₁₀₃	C₂×#121	1	1	yes	characteristic
223	C₂²×C₁₀₃	#546	1	1	yes	characteristic
224	C₂²×C₁₀₃	#548	1	1	yes	characteristic
225	C₂²×C₁₀₃	C₂×#135	1	1	yes	characteristic
226	C₂²×C₁₀₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
227	C₂²×C₁₀₃	#577	1	1	yes	characteristic
228	C₂²×C₁₀₃	#577	1	1	yes	characteristic
229	C₄×C₁₀₃	—	2	2	no	—
230	C₄×C₁₀₃	—	4	2	no	—
231	C₄×C₁₀₃	—	4	2	no	—
232	C₄×C₁₀₃	—	4	2	no	—
233	C₄×C₁₀₃	—	4	2	no	—
234	C₄×C₁₀₃	—	8	1	no	—
235	C₄×C₁₀₃	—	8	2	no	—
236	C₄×C₁₀₃	—	8	1	no	—
237	C₄×C₁₀₃	#463	1	4	yes	—
238	C₄×C₁₀₃	#529	1	1	yes	characteristic
239	C₄×C₁₀₃	#542	1	1	yes	characteristic
240	C₄×C₁₀₃	#546	1	1	yes	characteristic
241	C₄×C₁₀₃	#547	1	1	yes	characteristic
242	#25325	C₁₀₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
243	C₂×C₁₀₃	—	8	4	no	—
244	C₂×C₁₀₃	#2427	1	1	yes	characteristic
245	C₂×C₁₀₃	C₂×#463	1	1	yes	characteristic
246	C₂×C₁₀₃	#3042	1	1	yes	characteristic
247	C₂×C₁₀₃	#3304	1	1	yes	characteristic
248	C₂×C₁₀₃	#3324	1	1	yes	characteristic
249	C₂×C₁₀₃	#3365	1	1	yes	characteristic
250	C₂×C₁₀₃	#3368	1	1	yes	characteristic
251	C₂×#486	C₂×C₁₀₃	1	1	yes	characteristic
252	C₂×#460	C₂×C₁₀₃	1	1	yes	characteristic
253	#2568	C₂×C₁₀₃	1	1	yes	characteristic, complemented
254	#2366	C₂×C₁₀₃	1	1	yes	characteristic
255	#2073	C₂×C₁₀₃	1	2	yes	complemented
256	#2055	C₂×C₁₀₃	1	2	yes	complemented
257	#1988	C₂×C₁₀₃	1	1	yes	characteristic, complemented
258	#1939	C₂×C₁₀₃	1	1	yes	characteristic, complemented
259	#1877	C₂×C₁₀₃	1	2	yes	complemented
260	#1804	C₂×C₁₀₃	1	2	yes	complemented
261	C₄×#103	C₂×C₁₀₃	1	1	yes	characteristic, complemented
262	C₁₀₃	#25325	1	1	yes	characteristic, direct product factor, Sylow
263	C₂²×SD₁₆	C₂²×C₁₀₃	1	2	yes	—
264	C₂×C₄⋊Q₈	C₂²×C₁₀₃	1	1	yes	characteristic
265	C₂×#127	C₂²×C₁₀₃	1	1	yes	characteristic
266	C₂×C₄×Q₈	C₂²×C₁₀₃	1	1	yes	characteristic
267	C₂×C₄×D₄	—	2	1	no	—
268	C₂×C₄×D₄	C₂²×C₁₀₃	1	2	yes	—
269	#486	—	2	4	no	—
270	#460	—	2	4	no	—
271	C₂×C₄⋊C₈	C₂²×C₁₀₃	1	1	yes	characteristic
272	C₂×C₄⋊C₈	C₂²×C₁₀₃	1	2	yes	—
273	C₂×#103	C₂²×C₁₀₃	1	1	yes	characteristic
274	C₂×#103	C₂²×C₁₀₃	1	1	yes	characteristic
275	C₂×#102	C₂²×C₁₀₃	1	2	yes	—
276	C₂×#102	C₂²×C₁₀₃	1	2	yes	—
277	C₂×#102	C₂²×C₁₀₃	1	2	yes	—
278	C₂×C₄×C₈	C₂²×C₁₀₃	1	1	yes	characteristic
279	#400	—	2	2	no	—
280	#391	—	2	1	no	—
281	#391	—	2	1	no	—
282	#391	C₂²×C₁₀₃	1	2	yes	—
283	#390	—	2	1	no	—
284	#390	C₂²×C₁₀₃	1	2	yes	—
285	#386	—	2	2	no	—
286	#382	C₂²×C₁₀₃	1	2	yes	—
287	C₄×C₄⋊C₄	C₂²×C₁₀₃	1	1	yes	characteristic
288	C₄×C₄⋊C₄	C₂²×C₁₀₃	1	1	yes	characteristic
289	#340	C₂²×C₁₀₃	1	2	yes	—
290	#340	C₂²×C₁₀₃	1	1	yes	characteristic
291	#340	C₂²×C₁₀₃	1	2	yes	—
292	#340	C₂²×C₁₀₃	1	1	yes	characteristic
293	#336	C₂²×C₁₀₃	1	2	yes	—
294	C₂²×Q₈	—	2	1	no	—
295	C₂²×Q₈	C₂³×C₁₀₃	1	1	yes	characteristic
296	C₂²×D₄	—	2	1	no	—
297	C₂²×D₄	—	2	1	no	—
298	C₂²×D₄	C₂³×C₁₀₃	1	2	yes	—
299	C₂³×C₄	—	2	2	no	—
300	C₂×SD₁₆	—	2	4	no	—
301	C₂×SD₁₆	—	2	4	no	—
302	C₂×SD₁₆	—	4	2	no	—
303	C₂²×C₈	C₂³×C₁₀₃	1	2	yes	—
304	C₂²×C₈	C₂³×C₁₀₃	1	1	yes	characteristic
305	C₂²×C₈	C₂³×C₁₀₃	1	1	yes	characteristic
306	C₄⋊Q₈	—	2	2	no	—
307	C₄⋊Q₈	—	2	2	no	—
308	#127	—	2	2	no	—
309	#127	D₄×C₁₀₃	1	4	yes	—
310	C₄×Q₈	—	2	2	no	—
311	C₄×Q₈	—	2	2	no	—
312	C₄×D₄	—	2	4	no	—
313	C₄×D₄	—	4	2	no	—
314	C₄×D₄	—	4	4	no	—
315	C₂×C₄⋊C₄	—	2	1	no	—
316	C₂×C₄⋊C₄	—	2	1	no	—
317	C₂×C₄⋊C₄	D₄×C₁₀₃	1	1	yes	characteristic
318	C₂×C₄⋊C₄	D₄×C₁₀₃	1	1	yes	characteristic
319	C₂×C₄⋊C₄	C₂³×C₁₀₃	1	1	yes	characteristic
320	C₂×C₄⋊C₄	C₂³×C₁₀₃	1	2	yes	—
321	C₂×C₄⋊C₄	C₂³×C₁₀₃	1	1	yes	characteristic
322	C₂×C₄⋊C₄	C₂³×C₁₀₃	1	1	yes	characteristic
323	C₂×C₂²⋊C₄	—	2	2	no	—
324	C₂×C₂²⋊C₄	—	2	2	no	—
325	C₂×C₂²⋊C₄	—	2	2	no	—
326	C₂×C₄²	—	2	1	no	—
327	C₂×C₄²	—	2	1	no	—
328	C₂×C₄²	C₂³×C₁₀₃	1	2	yes	—
329	C₂×C₄²	C₂³×C₁₀₃	1	1	yes	characteristic
330	C₄⋊C₈	—	2	2	no	—
331	C₄⋊C₈	—	4	2	no	—
332	#103	—	2	2	no	—
333	#103	—	2	2	no	—
334	#102	—	2	4	no	—
335	#102	—	2	4	no	—
336	#102	—	2	4	no	—
337	C₄×C₈	—	2	2	no	—
338	#95	—	2	1	no	—
339	#95	—	2	2	no	—
340	#95	—	2	2	no	—
341	#95	—	2	2	no	—
342	#95	—	2	2	no	—
343	#95	D₄×C₁₀₃	1	2	yes	—
344	C₂⁴	—	2	2	no	—
345	C₂×Q₈	—	2	1	no	—
346	C₂×Q₈	—	2	1	no	—
347	C₂×Q₈	—	2	1	no	—
348	C₂×Q₈	—	2	1	no	—
349	C₂×Q₈	—	2	1	no	—
350	C₂×Q₈	—	4	2	no	—
351	C₂×Q₈	—	4	2	no	—
352	C₂×Q₈	—	4	2	no	—
353	C₂×Q₈	#41×C₁₀₃	1	2	yes	—
354	C₂×D₄	—	2	4	no	—
355	C₂×D₄	—	2	4	no	—
356	C₂×D₄	—	2	2	no	—
357	C₂×D₄	—	2	2	no	—
358	C₂×D₄	—	2	2	no	—
359	C₂×D₄	—	2	2	no	—
360	C₂×D₄	—	2	2	no	—
361	C₂×D₄	—	4	2	no	—
362	C₂×D₄	—	4	2	no	—
363	C₂×D₄	—	8	1	no	—
364	C₂×D₄	—	8	1	no	—
365	C₂×D₄	C₂×D₄×C₁₀₃	1	4	yes	—
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	1	no	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	2	1	no	—
371	C₂²×C₄	—	4	4	no	—
372	C₂²×C₄	—	4	4	no	—
373	C₂²×C₄	—	8	2	no	—
374	C₂²×C₄	C₂×D₄×C₁₀₃	1	2	yes	—
375	C₂²×C₄	C₂×D₄×C₁₀₃	1	2	yes	—
376	C₂²×C₄	C₂×D₄×C₁₀₃	1	1	yes	characteristic
377	C₂²×C₄	C₂×D₄×C₁₀₃	1	1	yes	characteristic
378	C₂²×C₄	C₂⁴×C₁₀₃	1	1	yes	characteristic
379	SD₁₆	—	4	8	no	—
380	C₂×C₈	—	2	1	no	—
381	C₂×C₈	—	2	1	no	—
382	C₂×C₈	—	2	2	no	—
383	C₂×C₈	—	2	1	no	—
384	C₂×C₈	—	2	1	no	—
385	C₂×C₈	—	2	2	no	—
386	C₂×C₈	—	2	1	no	—
387	C₂×C₈	—	2	2	no	—
388	C₂×C₈	—	2	1	no	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	2	1	no	—
392	C₄⋊C₄	—	2	1	no	—
393	C₄⋊C₄	—	2	2	no	—
394	C₄⋊C₄	—	2	1	no	—
395	C₄⋊C₄	—	2	1	no	—
396	C₄⋊C₄	—	2	2	no	—
397	C₄⋊C₄	—	2	1	no	—
398	C₄⋊C₄	—	4	2	no	—
399	C₄⋊C₄	—	4	2	no	—
400	C₄⋊C₄	#41×C₁₀₃	1	2	yes	—
401	C₂²⋊C₄	—	4	4	no	—
402	C₂²⋊C₄	—	4	4	no	—
403	C₂²⋊C₄	—	8	2	no	—
404	C₄²	—	2	2	no	—
405	C₄²	—	2	2	no	—
406	C₄²	—	4	2	no	—
407	C₄²	—	4	2	no	—
408	C₄²	C₂×D₄×C₁₀₃	1	2	yes	—
409	C₄²	#41×C₁₀₃	1	2	yes	—
410	C₂³	—	2	4	no	—
411	C₂³	—	4	2	no	—
412	C₂³	—	4	2	no	—
413	C₂³	—	4	2	no	—
414	C₂³	—	4	2	no	—
415	C₂³	—	4	2	no	—
416	C₂³	—	4	2	no	—
417	C₂³	C₂²×D₄×C₁₀₃	1	1	yes	characteristic
418	Q₈	—	2	2	no	—
419	Q₈	—	2	2	no	—
420	Q₈	—	4	1	no	—
421	Q₈	—	4	1	no	—
422	Q₈	—	8	4	no	—
423	D₄	—	2	4	no	—
424	D₄	—	2	4	no	—
425	D₄	—	4	8	no	—
426	D₄	—	4	2	no	—
427	D₄	—	4	2	no	—
428	D₄	—	8	4	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	4	1	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	1	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	1	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	1	no	—
450	C₂×C₄	—	4	1	no	—
451	C₂×C₄	—	4	1	no	—
452	C₂×C₄	—	8	8	no	—
453	C₂×C₄	#121×C₁₀₃	1	2	yes	—
454	C₂×C₄	#121×C₁₀₃	1	2	yes	—
455	C₂×C₄	#135×C₁₀₃	1	2	yes	—
456	C₂×C₄	AGL(1,ℤ/8)×C₁₀₃	1	2	yes	—
457	C₂×C₄	C₂²×D₄×C₁₀₃	1	1	yes	characteristic
458	C₂×C₄	C₂×#41×C₁₀₃	1	1	yes	characteristic
459	C₂×C₄	C₂×#41×C₁₀₃	1	1	yes	characteristic
460	C₂×C₄	C₂×#41×C₁₀₃	1	1	yes	characteristic
461	C₂×C₄	H(5,𝔽₂)×C₁₀₃	1	1	yes	characteristic
462	C₂×C₄	2₋¹⁺⁴×C₁₀₃	1	1	yes	characteristic
463	C₈	—	4	2	no	—
464	C₈	—	4	1	no	—
465	C₈	—	4	1	no	—
466	C₂²	—	4	4	no	—
467	C₂²	—	4	4	no	—
468	C₂²	—	4	4	no	—
469	C₂²	—	8	2	no	—
470	C₂²	—	8	2	no	—
471	C₂²	—	8	2	no	—
472	C₂²	—	8	2	no	—
473	C₂²	C₂×#121×C₁₀₃	1	1	yes	characteristic
474	C₂²	#546×C₁₀₃	1	1	yes	characteristic
475	C₂²	#548×C₁₀₃	1	1	yes	characteristic
476	C₂²	C₂×#135×C₁₀₃	1	1	yes	characteristic
477	C₂²	C₂×AGL(1,ℤ/8)×C₁₀₃	1	1	yes	characteristic
478	C₂²	#577×C₁₀₃	1	1	yes	characteristic
479	C₂²	#577×C₁₀₃	1	1	yes	characteristic
480	C₄	—	2	2	no	—
481	C₄	—	4	2	no	—
482	C₄	—	4	2	no	—
483	C₄	—	4	2	no	—
484	C₄	—	4	2	no	—
485	C₄	—	8	2	no	—
486	C₄	—	8	1	no	—
487	C₄	—	8	1	no	—
488	C₄	#463×C₁₀₃	1	4	yes	—
489	C₄	#529×C₁₀₃	1	1	yes	characteristic
490	C₄	#542×C₁₀₃	1	1	yes	characteristic
491	C₄	#546×C₁₀₃	1	1	yes	characteristic
492	C₄	#547×C₁₀₃	1	1	yes	characteristic
493	C₂	—	8	4	no	—
494	C₂	C₁₀₃×#2427	1	1	yes	characteristic
495	C₂	C₂×#463×C₁₀₃	1	1	yes	characteristic
496	C₂	C₁₀₃×#3042	1	1	yes	characteristic
497	C₂	C₁₀₃×#3304	1	1	yes	characteristic
498	C₂	C₁₀₃×#3324	1	1	yes	characteristic
499	C₂	C₁₀₃×#3365	1	1	yes	characteristic
500	C₂	C₁₀₃×#3368	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₀₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₀₃
prime radical	C₂×#127×C₁₀₃	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₀₃ ◁ C₄×C₄⋊C₄×C₁₀₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₀₃×#2568	C₂	semidirect
5. C₁₀₃×#2073	C₂	semidirect
6. C₁₀₃×#2055	C₂	semidirect
7. C₁₀₃×#1988	C₂	semidirect
8. C₁₀₃×#1939	C₂	semidirect
9. C₁₀₃×#1877	C₂	semidirect
10. C₁₀₃×#1804	C₂	semidirect
11. C₄×#103×C₁₀₃	C₂	semidirect
242. #25325	C₁₀₃	direct (N × H)
253. #2568	C₂×C₁₀₃	semidirect
255. #2073	C₂×C₁₀₃	semidirect
256. #2055	C₂×C₁₀₃	semidirect
257. #1988	C₂×C₁₀₃	semidirect
258. #1939	C₂×C₁₀₃	semidirect
259. #1877	C₂×C₁₀₃	semidirect
260. #1804	C₂×C₁₀₃	semidirect
261. C₄×#103	C₂×C₁₀₃	semidirect
262. C₁₀₃	#25325	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×#486×C₁₀₃	2
C₂×#460×C₁₀₃	2
C₁₀₃×#2568	2
C₁₀₃×#2366	2
C₁₀₃×#2073	2
C₁₀₃×#2055	2
C₁₀₃×#1988	2
C₁₀₃×#1939	2
C₁₀₃×#1877	2
C₁₀₃×#1804	2
C₄×#103×C₁₀₃	2
#25325	103

Subgroups — C103×#25325 #39930600

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₃×#25325 #39930600