Subgroups — C₁₀₃×#25394 #39930669

Order 26368.

986 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#470×C₁₀₃	C₂	1	2	yes	maximal, complemented
2	C₂×#462×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#436×C₁₀₃	C₂	1	1	yes	maximal, characteristic
4	C₁₀₃×#2542	C₂	1	1	yes	maximal, characteristic
5	C₁₀₃×#2538	C₂	1	1	yes	maximal, characteristic
6	C₁₀₃×#2035	C₂	1	2	yes	maximal, complemented
7	C₁₀₃×#2001	C₂	1	2	yes	maximal, complemented
8	C₁₀₃×#1956	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₀₃×#1948	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₀₃×#1894	C₂	1	2	yes	maximal, complemented
11	C₄×#103×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×Q₁₆×C₁₀₃	C₂²	1	2	yes	—
13	C₂²×M₁₆×C₁₀₃	C₂²	1	2	yes	—
14	C₂×C₄⋊Q₈×C₁₀₃	C₂²	1	1	yes	characteristic
15	C₂×C₂²⋊Q₈×C₁₀₃	C₂²	1	2	yes	—
16	C₂×C₂²⋊Q₈×C₁₀₃	C₂²	1	2	yes	—
17	C₂×C₂²⋊Q₈×C₁₀₃	C₂²	1	2	yes	—
18	C₂×C₄×Q₈×C₁₀₃	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₄×C₁₀₃	C₂²	1	1	yes	characteristic
20	#470×C₁₀₃	—	2	8	no	—
21	#462×C₁₀₃	—	2	4	no	—
22	#436×C₁₀₃	—	2	4	no	—
23	C₂×#106×C₁₀₃	C₂²	1	2	yes	—
24	C₂×C₄⋊C₈×C₁₀₃	C₂²	1	1	yes	characteristic
25	C₂×#103×C₁₀₃	C₂²	1	2	yes	—
26	C₂×#103×C₁₀₃	C₂²	1	1	yes	characteristic
27	C₂×#103×C₁₀₃	C₂²	1	2	yes	—
28	C₂×#103×C₁₀₃	C₂²	1	2	yes	—
29	C₂×#103×C₁₀₃	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊C₈×C₁₀₃	C₂²	1	2	yes	—
31	C₂×C₄×C₈×C₁₀₃	C₂²	1	1	yes	characteristic
32	#399×C₁₀₃	—	2	2	no	—
33	#396×C₁₀₃	—	2	2	no	—
34	#390×C₁₀₃	—	2	1	no	—
35	#390×C₁₀₃	—	2	1	no	—
36	#389×C₁₀₃	—	2	1	no	—
37	#384×C₁₀₃	—	2	1	no	—
38	#384×C₁₀₃	C₂²	1	1	yes	characteristic
39	#380×C₁₀₃	C₂²	1	2	yes	—
40	C₄×C₄⋊C₄×C₁₀₃	C₂²	1	1	yes	characteristic
41	#340×C₁₀₃	C₂²	1	2	yes	—
42	#340×C₁₀₃	C₂²	1	1	yes	characteristic
43	#340×C₁₀₃	C₂²	1	1	yes	characteristic
44	C₂²×Q₈×C₁₀₃	C₂³	1	2	yes	—
45	C₂²×Q₈×C₁₀₃	C₂³	1	1	yes	characteristic
46	C₂²×D₄×C₁₀₃	D₄	1	1	yes	characteristic
47	C₂³×C₄×C₁₀₃	C₂³	1	2	yes	—
48	C₂×Q₁₆×C₁₀₃	—	2	4	no	—
49	C₂×Q₁₆×C₁₀₃	—	2	4	no	—
50	C₂×Q₁₆×C₁₀₃	—	4	2	no	—
51	C₂×M₁₆×C₁₀₃	—	2	4	no	—
52	C₂×M₁₆×C₁₀₃	—	2	4	no	—
53	C₂×M₁₆×C₁₀₃	—	4	2	no	—
54	C₂²×C₈×C₁₀₃	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₁₀₃	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₁₀₃	C₂³	1	2	yes	—
57	C₄⋊Q₈×C₁₀₃	—	2	2	no	—
58	C₄⋊Q₈×C₁₀₃	—	2	2	no	—
59	C₂²⋊Q₈×C₁₀₃	—	2	4	no	—
60	C₂²⋊Q₈×C₁₀₃	—	2	4	no	—
61	C₂²⋊Q₈×C₁₀₃	—	2	4	no	—
62	C₂²⋊Q₈×C₁₀₃	—	4	2	no	—
63	C₂²⋊Q₈×C₁₀₃	—	4	2	no	—
64	C₂²⋊Q₈×C₁₀₃	—	4	2	no	—
65	C₄×Q₈×C₁₀₃	—	2	2	no	—
66	C₄×Q₈×C₁₀₃	—	2	2	no	—
67	C₄×D₄×C₁₀₃	—	2	2	no	—
68	C₄×D₄×C₁₀₃	—	2	2	no	—
69	C₂×C₄⋊C₄×C₁₀₃	—	2	1	no	—
70	C₂×C₄⋊C₄×C₁₀₃	—	2	2	no	—
71	C₂×C₄⋊C₄×C₁₀₃	—	2	2	no	—
72	C₂×C₄⋊C₄×C₁₀₃	—	2	1	no	—
73	C₂×C₄⋊C₄×C₁₀₃	—	2	2	no	—
74	C₂×C₄⋊C₄×C₁₀₃	—	2	1	no	—
75	C₂×C₄⋊C₄×C₁₀₃	—	2	1	no	—
76	C₂×C₄⋊C₄×C₁₀₃	—	2	1	no	—
77	C₂×C₄⋊C₄×C₁₀₃	D₄	1	1	yes	characteristic
78	C₂×C₄⋊C₄×C₁₀₃	C₂³	1	1	yes	characteristic
79	C₂×C₄⋊C₄×C₁₀₃	C₂³	1	2	yes	—
80	C₂×C₄⋊C₄×C₁₀₃	C₂³	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₁₀₃	C₂³	1	1	yes	characteristic
82	C₂×C₂²⋊C₄×C₁₀₃	—	2	2	no	—
83	C₂×C₂²⋊C₄×C₁₀₃	—	2	2	no	—
84	C₂×C₂²⋊C₄×C₁₀₃	—	2	2	no	—
85	C₂×C₂²⋊C₄×C₁₀₃	—	2	2	no	—
86	C₂×C₂²⋊C₄×C₁₀₃	D₄	1	2	yes	—
87	C₂×C₄²×C₁₀₃	—	2	1	no	—
88	C₂×C₄²×C₁₀₃	—	2	1	no	—
89	C₂×C₄²×C₁₀₃	C₂³	1	1	yes	characteristic
90	#106×C₁₀₃	—	2	4	no	—
91	C₄⋊C₈×C₁₀₃	D₄	1	4	yes	—
92	#103×C₁₀₃	—	2	4	no	—
93	#103×C₁₀₃	—	2	4	no	—
94	#103×C₁₀₃	—	2	2	no	—
95	#103×C₁₀₃	—	4	2	no	—
96	#103×C₁₀₃	D₄	1	4	yes	complemented
97	C₂²⋊C₈×C₁₀₃	—	2	4	no	—
98	C₄×C₈×C₁₀₃	—	2	2	no	—
99	#95×C₁₀₃	—	2	1	no	—
100	#95×C₁₀₃	—	2	2	no	—
101	C₂⁴×C₁₀₃	C₂×D₄	1	2	yes	—
102	C₂×Q₈×C₁₀₃	—	2	1	no	—
103	C₂×Q₈×C₁₀₃	—	2	1	no	—
104	C₂×Q₈×C₁₀₃	—	2	2	no	—
105	C₂×Q₈×C₁₀₃	—	2	2	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	—	2	2	no	—
110	C₂×Q₈×C₁₀₃	—	2	1	no	—
111	C₂×Q₈×C₁₀₃	—	2	2	no	—
112	C₂×Q₈×C₁₀₃	—	2	2	no	—
113	C₂×Q₈×C₁₀₃	C₂×D₄	1	2	yes	—
114	C₂×D₄×C₁₀₃	—	2	2	no	—
115	C₂×D₄×C₁₀₃	—	2	2	no	—
116	C₂×D₄×C₁₀₃	—	2	2	no	—
117	C₂²×C₄×C₁₀₃	—	2	1	no	—
118	C₂²×C₄×C₁₀₃	—	2	1	no	—
119	C₂²×C₄×C₁₀₃	—	2	1	no	—
120	C₂²×C₄×C₁₀₃	—	2	2	no	—
121	C₂²×C₄×C₁₀₃	—	2	2	no	—
122	C₂²×C₄×C₁₀₃	—	2	2	no	—
123	C₂²×C₄×C₁₀₃	—	2	2	no	—
124	C₂²×C₄×C₁₀₃	—	2	2	no	—
125	C₂²×C₄×C₁₀₃	—	2	2	no	—
126	C₂²×C₄×C₁₀₃	—	2	1	no	—
127	C₂²×C₄×C₁₀₃	—	2	2	no	—
128	C₂²×C₄×C₁₀₃	—	2	2	no	—
129	C₂²×C₄×C₁₀₃	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₀₃	C₂⁴	1	1	yes	characteristic
133	Q₁₆×C₁₀₃	—	4	8	no	—
134	M₁₆×C₁₀₃	—	4	8	no	—
135	C₂×C₈×C₁₀₃	—	2	1	no	—
136	C₂×C₈×C₁₀₃	—	2	2	no	—
137	C₂×C₈×C₁₀₃	—	2	1	no	—
138	C₂×C₈×C₁₀₃	—	2	2	no	—
139	C₂×C₈×C₁₀₃	—	2	1	no	—
140	C₂×C₈×C₁₀₃	—	2	1	no	—
141	C₂×C₈×C₁₀₃	—	2	1	no	—
142	C₂×C₈×C₁₀₃	C₂×D₄	1	4	yes	—
143	C₂×C₈×C₁₀₃	C₂×D₄	1	2	yes	—
144	C₄⋊C₄×C₁₀₃	—	2	2	no	—
145	C₄⋊C₄×C₁₀₃	—	2	1	no	—
146	C₄⋊C₄×C₁₀₃	—	2	1	no	—
147	C₄⋊C₄×C₁₀₃	—	2	1	no	—
148	C₄⋊C₄×C₁₀₃	—	2	2	no	—
149	C₄⋊C₄×C₁₀₃	—	2	1	no	—
150	C₄⋊C₄×C₁₀₃	—	2	2	no	—
151	C₄⋊C₄×C₁₀₃	—	4	4	no	—
152	C₄⋊C₄×C₁₀₃	—	4	4	no	—
153	C₄⋊C₄×C₁₀₃	—	4	4	no	—
154	C₄⋊C₄×C₁₀₃	—	4	2	no	—
155	C₄⋊C₄×C₁₀₃	—	4	2	no	—
156	C₄⋊C₄×C₁₀₃	—	4	2	no	—
157	C₄⋊C₄×C₁₀₃	—	4	2	no	—
158	C₄⋊C₄×C₁₀₃	—	8	1	no	—
159	C₄⋊C₄×C₁₀₃	C₂×D₄	1	2	yes	—
160	C₄⋊C₄×C₁₀₃	#41	1	2	yes	—
161	C₂²⋊C₄×C₁₀₃	—	2	4	no	—
162	C₂²⋊C₄×C₁₀₃	—	4	4	no	—
163	C₂²⋊C₄×C₁₀₃	—	4	4	no	—
164	C₂²⋊C₄×C₁₀₃	—	4	4	no	—
165	C₂²⋊C₄×C₁₀₃	—	8	2	no	—
166	C₄²×C₁₀₃	—	4	2	no	—
167	C₄²×C₁₀₃	—	4	2	no	—
168	C₄²×C₁₀₃	C₂×D₄	1	2	yes	—
169	C₄²×C₁₀₃	#41	1	2	yes	—
170	C₂³×C₁₀₃	—	2	2	no	—
171	C₂³×C₁₀₃	—	2	2	no	—
172	C₂³×C₁₀₃	—	2	2	no	—
173	C₂³×C₁₀₃	—	2	2	no	—
174	C₂³×C₁₀₃	—	2	2	no	—
175	C₂³×C₁₀₃	—	2	2	no	—
176	C₂³×C₁₀₃	—	2	2	no	—
177	C₂³×C₁₀₃	C₂²×D₄	1	1	yes	characteristic
178	Q₈×C₁₀₃	—	2	2	no	—
179	Q₈×C₁₀₃	—	2	2	no	—
180	Q₈×C₁₀₃	—	4	1	no	—
181	Q₈×C₁₀₃	—	4	1	no	—
182	Q₈×C₁₀₃	—	4	2	no	—
183	Q₈×C₁₀₃	—	4	2	no	—
184	Q₈×C₁₀₃	—	4	2	no	—
185	Q₈×C₁₀₃	—	4	2	no	—
186	D₄×C₁₀₃	—	4	4	no	—
187	C₂×C₄×C₁₀₃	—	2	1	no	—
188	C₂×C₄×C₁₀₃	—	2	1	no	—
189	C₂×C₄×C₁₀₃	—	2	2	no	—
190	C₂×C₄×C₁₀₃	—	2	2	no	—
191	C₂×C₄×C₁₀₃	—	2	2	no	—
192	C₂×C₄×C₁₀₃	—	2	2	no	—
193	C₂×C₄×C₁₀₃	—	2	2	no	—
194	C₂×C₄×C₁₀₃	—	2	2	no	—
195	C₂×C₄×C₁₀₃	—	4	1	no	—
196	C₂×C₄×C₁₀₃	—	4	1	no	—
197	C₂×C₄×C₁₀₃	—	4	1	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	—	4	2	no	—
202	C₂×C₄×C₁₀₃	—	4	2	no	—
203	C₂×C₄×C₁₀₃	—	4	2	no	—
204	C₂×C₄×C₁₀₃	—	4	2	no	—
205	C₂×C₄×C₁₀₃	—	4	1	no	—
206	C₂×C₄×C₁₀₃	—	4	2	no	—
207	C₂×C₄×C₁₀₃	—	4	2	no	—
208	C₂×C₄×C₁₀₃	—	4	2	no	—
209	C₂×C₄×C₁₀₃	—	4	2	no	—
210	C₂×C₄×C₁₀₃	—	4	2	no	—
211	C₂×C₄×C₁₀₃	—	4	1	no	—
212	C₂×C₄×C₁₀₃	—	4	2	no	—
213	C₂×C₄×C₁₀₃	—	4	1	no	—
214	C₂×C₄×C₁₀₃	#121	1	2	yes	—
215	C₂×C₄×C₁₀₃	#121	1	2	yes	—
216	C₂×C₄×C₁₀₃	#137	1	2	yes	—
217	C₂×C₄×C₁₀₃	#137	1	2	yes	—
218	C₂×C₄×C₁₀₃	C₂²×D₄	1	1	yes	characteristic
219	C₂×C₄×C₁₀₃	C₂²×D₄	1	1	yes	characteristic
220	C₂×C₄×C₁₀₃	C₂×#41	1	1	yes	characteristic
221	C₂×C₄×C₁₀₃	C₂×#41	1	1	yes	characteristic
222	C₂×C₄×C₁₀₃	H(5,𝔽₂)	1	1	yes	characteristic
223	C₂×C₄×C₁₀₃	H(5,𝔽₂)	1	1	yes	characteristic
224	C₈×C₁₀₃	—	2	2	no	—
225	C₈×C₁₀₃	—	2	4	no	—
226	C₈×C₁₀₃	—	4	1	no	—
227	C₂²×C₁₀₃	—	4	2	no	—
228	C₂²×C₁₀₃	—	4	2	no	—
229	C₂²×C₁₀₃	—	4	2	no	—
230	C₂²×C₁₀₃	—	4	2	no	—
231	C₂²×C₁₀₃	—	4	2	no	—
232	C₂²×C₁₀₃	—	4	2	no	—
233	C₂²×C₁₀₃	—	4	2	no	—
234	C₂²×C₁₀₃	C₂×#121	1	1	yes	characteristic
235	C₂²×C₁₀₃	D₄²	1	1	yes	characteristic
236	C₂²×C₁₀₃	#546	1	1	yes	characteristic
237	C₂²×C₁₀₃	C₂×#137	1	1	yes	characteristic
238	C₂²×C₁₀₃	C₂×#137	1	1	yes	characteristic
239	C₂²×C₁₀₃	#577	1	1	yes	characteristic
240	C₂²×C₁₀₃	#578	1	1	yes	characteristic
241	C₄×C₁₀₃	—	2	2	no	—
242	C₄×C₁₀₃	—	4	2	no	—
243	C₄×C₁₀₃	—	4	2	no	—
244	C₄×C₁₀₃	—	4	2	no	—
245	C₄×C₁₀₃	—	4	2	no	—
246	C₄×C₁₀₃	—	8	2	no	—
247	C₄×C₁₀₃	—	8	2	no	—
248	C₄×C₁₀₃	—	8	1	no	—
249	C₄×C₁₀₃	#470	1	4	yes	complemented
250	C₄×C₁₀₃	#532	1	1	yes	characteristic
251	C₄×C₁₀₃	#540	1	1	yes	characteristic
252	C₄×C₁₀₃	D₄²	1	1	yes	characteristic
253	C₄×C₁₀₃	#550	1	1	yes	characteristic
254	#25394	C₁₀₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
255	C₂×C₁₀₃	—	8	2	no	—
256	C₂×C₁₀₃	#2428	1	1	yes	characteristic
257	C₂×C₁₀₃	C₂×#470	1	1	yes	characteristic
258	C₂×C₁₀₃	#3063	1	1	yes	characteristic
259	C₂×C₁₀₃	#3276	1	1	yes	characteristic
260	C₂×C₁₀₃	#3278	1	1	yes	characteristic
261	C₂×C₁₀₃	#3328	1	1	yes	characteristic
262	C₂×C₁₀₃	#3331	1	1	yes	characteristic
263	C₂×#470	C₂×C₁₀₃	1	2	yes	complemented
264	C₂×#462	C₂×C₁₀₃	1	1	yes	characteristic, complemented
265	C₂×#436	C₂×C₁₀₃	1	1	yes	characteristic
266	#2542	C₂×C₁₀₃	1	1	yes	characteristic
267	#2538	C₂×C₁₀₃	1	1	yes	characteristic
268	#2035	C₂×C₁₀₃	1	2	yes	complemented
269	#2001	C₂×C₁₀₃	1	2	yes	complemented
270	#1956	C₂×C₁₀₃	1	1	yes	characteristic, complemented
271	#1948	C₂×C₁₀₃	1	1	yes	characteristic, complemented
272	#1894	C₂×C₁₀₃	1	2	yes	complemented
273	C₄×#103	C₂×C₁₀₃	1	1	yes	characteristic, complemented
274	C₁₀₃	#25394	1	1	yes	characteristic, direct product factor, Sylow
275	C₂²×Q₁₆	C₂²×C₁₀₃	1	2	yes	—
276	C₂²×M₁₆	C₂²×C₁₀₃	1	2	yes	—
277	C₂×C₄⋊Q₈	C₂²×C₁₀₃	1	1	yes	characteristic
278	C₂×C₂²⋊Q₈	C₂²×C₁₀₃	1	2	yes	—
279	C₂×C₂²⋊Q₈	C₂²×C₁₀₃	1	2	yes	—
280	C₂×C₂²⋊Q₈	C₂²×C₁₀₃	1	2	yes	—
281	C₂×C₄×Q₈	C₂²×C₁₀₃	1	1	yes	characteristic
282	C₂×C₄×D₄	C₂²×C₁₀₃	1	1	yes	characteristic
283	#470	—	2	8	no	—
284	#462	—	2	4	no	—
285	#436	—	2	4	no	—
286	C₂×#106	C₂²×C₁₀₃	1	2	yes	—
287	C₂×C₄⋊C₈	C₂²×C₁₀₃	1	1	yes	characteristic
288	C₂×#103	C₂²×C₁₀₃	1	2	yes	—
289	C₂×#103	C₂²×C₁₀₃	1	2	yes	—
290	C₂×#103	C₂²×C₁₀₃	1	1	yes	characteristic
291	C₂×#103	C₂²×C₁₀₃	1	2	yes	—
292	C₂×#103	C₂²×C₁₀₃	1	1	yes	characteristic
293	C₂×C₂²⋊C₈	C₂²×C₁₀₃	1	2	yes	—
294	C₂×C₄×C₈	C₂²×C₁₀₃	1	1	yes	characteristic
295	#399	—	2	2	no	—
296	#396	—	2	2	no	—
297	#390	—	2	1	no	—
298	#390	—	2	1	no	—
299	#389	—	2	1	no	—
300	#384	—	2	1	no	—
301	#384	C₂²×C₁₀₃	1	1	yes	characteristic
302	#380	C₂²×C₁₀₃	1	2	yes	—
303	C₄×C₄⋊C₄	C₂²×C₁₀₃	1	1	yes	characteristic
304	#340	C₂²×C₁₀₃	1	1	yes	characteristic
305	#340	C₂²×C₁₀₃	1	2	yes	—
306	#340	C₂²×C₁₀₃	1	1	yes	characteristic
307	C₂²×Q₈	C₂³×C₁₀₃	1	2	yes	—
308	C₂²×Q₈	C₂³×C₁₀₃	1	1	yes	characteristic
309	C₂²×D₄	D₄×C₁₀₃	1	1	yes	characteristic
310	C₂³×C₄	C₂³×C₁₀₃	1	2	yes	—
311	C₂×Q₁₆	—	2	4	no	—
312	C₂×Q₁₆	—	2	4	no	—
313	C₂×Q₁₆	—	4	2	no	—
314	C₂×M₁₆	—	2	4	no	—
315	C₂×M₁₆	—	2	4	no	—
316	C₂×M₁₆	—	4	2	no	—
317	C₂²×C₈	C₂³×C₁₀₃	1	1	yes	characteristic
318	C₂²×C₈	C₂³×C₁₀₃	1	1	yes	characteristic
319	C₂²×C₈	C₂³×C₁₀₃	1	2	yes	—
320	C₄⋊Q₈	—	2	2	no	—
321	C₄⋊Q₈	—	2	2	no	—
322	C₂²⋊Q₈	—	2	4	no	—
323	C₂²⋊Q₈	—	2	4	no	—
324	C₂²⋊Q₈	—	2	4	no	—
325	C₂²⋊Q₈	—	4	2	no	—
326	C₂²⋊Q₈	—	4	2	no	—
327	C₂²⋊Q₈	—	4	2	no	—
328	C₄×Q₈	—	2	2	no	—
329	C₄×Q₈	—	2	2	no	—
330	C₄×D₄	—	2	2	no	—
331	C₄×D₄	—	2	2	no	—
332	C₂×C₄⋊C₄	—	2	1	no	—
333	C₂×C₄⋊C₄	—	2	2	no	—
334	C₂×C₄⋊C₄	—	2	2	no	—
335	C₂×C₄⋊C₄	—	2	2	no	—
336	C₂×C₄⋊C₄	—	2	1	no	—
337	C₂×C₄⋊C₄	—	2	1	no	—
338	C₂×C₄⋊C₄	—	2	1	no	—
339	C₂×C₄⋊C₄	—	2	1	no	—
340	C₂×C₄⋊C₄	D₄×C₁₀₃	1	1	yes	characteristic
341	C₂×C₄⋊C₄	C₂³×C₁₀₃	1	1	yes	characteristic
342	C₂×C₄⋊C₄	C₂³×C₁₀₃	1	2	yes	—
343	C₂×C₄⋊C₄	C₂³×C₁₀₃	1	1	yes	characteristic
344	C₂×C₄⋊C₄	C₂³×C₁₀₃	1	1	yes	characteristic
345	C₂×C₂²⋊C₄	—	2	2	no	—
346	C₂×C₂²⋊C₄	—	2	2	no	—
347	C₂×C₂²⋊C₄	—	2	2	no	—
348	C₂×C₂²⋊C₄	—	2	2	no	—
349	C₂×C₂²⋊C₄	D₄×C₁₀₃	1	2	yes	—
350	C₂×C₄²	—	2	1	no	—
351	C₂×C₄²	—	2	1	no	—
352	C₂×C₄²	C₂³×C₁₀₃	1	1	yes	characteristic
353	#106	—	2	4	no	—
354	C₄⋊C₈	D₄×C₁₀₃	1	4	yes	—
355	#103	—	2	4	no	—
356	#103	—	2	4	no	—
357	#103	—	2	2	no	—
358	#103	—	4	2	no	—
359	#103	D₄×C₁₀₃	1	4	yes	complemented
360	C₂²⋊C₈	—	2	4	no	—
361	C₄×C₈	—	2	2	no	—
362	#95	—	2	1	no	—
363	#95	—	2	2	no	—
364	C₂⁴	C₂×D₄×C₁₀₃	1	2	yes	—
365	C₂×Q₈	—	2	1	no	—
366	C₂×Q₈	—	2	1	no	—
367	C₂×Q₈	—	2	2	no	—
368	C₂×Q₈	—	2	2	no	—
369	C₂×Q₈	—	2	1	no	—
370	C₂×Q₈	—	2	1	no	—
371	C₂×Q₈	—	2	2	no	—
372	C₂×Q₈	—	2	2	no	—
373	C₂×Q₈	—	2	1	no	—
374	C₂×Q₈	—	2	2	no	—
375	C₂×Q₈	—	2	2	no	—
376	C₂×Q₈	C₂×D₄×C₁₀₃	1	2	yes	—
377	C₂×D₄	—	2	2	no	—
378	C₂×D₄	—	2	2	no	—
379	C₂×D₄	—	2	2	no	—
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	2	1	no	—
382	C₂²×C₄	—	2	1	no	—
383	C₂²×C₄	—	2	2	no	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	2	2	no	—
387	C₂²×C₄	—	2	2	no	—
388	C₂²×C₄	—	2	2	no	—
389	C₂²×C₄	—	2	1	no	—
390	C₂²×C₄	—	2	2	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	C₂×D₄×C₁₀₃	1	2	yes	—
393	C₂²×C₄	C₂×D₄×C₁₀₃	1	1	yes	characteristic
394	C₂²×C₄	C₂×D₄×C₁₀₃	1	1	yes	characteristic
395	C₂²×C₄	C₂⁴×C₁₀₃	1	1	yes	characteristic
396	Q₁₆	—	4	8	no	—
397	M₁₆	—	4	8	no	—
398	C₂×C₈	—	2	1	no	—
399	C₂×C₈	—	2	2	no	—
400	C₂×C₈	—	2	1	no	—
401	C₂×C₈	—	2	2	no	—
402	C₂×C₈	—	2	1	no	—
403	C₂×C₈	—	2	1	no	—
404	C₂×C₈	—	2	1	no	—
405	C₂×C₈	C₂×D₄×C₁₀₃	1	4	yes	—
406	C₂×C₈	C₂×D₄×C₁₀₃	1	2	yes	—
407	C₄⋊C₄	—	2	2	no	—
408	C₄⋊C₄	—	2	1	no	—
409	C₄⋊C₄	—	2	1	no	—
410	C₄⋊C₄	—	2	1	no	—
411	C₄⋊C₄	—	2	2	no	—
412	C₄⋊C₄	—	2	1	no	—
413	C₄⋊C₄	—	2	2	no	—
414	C₄⋊C₄	—	4	4	no	—
415	C₄⋊C₄	—	4	4	no	—
416	C₄⋊C₄	—	4	4	no	—
417	C₄⋊C₄	—	4	2	no	—
418	C₄⋊C₄	—	4	2	no	—
419	C₄⋊C₄	—	4	2	no	—
420	C₄⋊C₄	—	4	2	no	—
421	C₄⋊C₄	—	8	1	no	—
422	C₄⋊C₄	C₂×D₄×C₁₀₃	1	2	yes	—
423	C₄⋊C₄	#41×C₁₀₃	1	2	yes	—
424	C₂²⋊C₄	—	2	4	no	—
425	C₂²⋊C₄	—	4	4	no	—
426	C₂²⋊C₄	—	4	4	no	—
427	C₂²⋊C₄	—	4	4	no	—
428	C₂²⋊C₄	—	8	2	no	—
429	C₄²	—	4	2	no	—
430	C₄²	—	4	2	no	—
431	C₄²	C₂×D₄×C₁₀₃	1	2	yes	—
432	C₄²	#41×C₁₀₃	1	2	yes	—
433	C₂³	—	2	2	no	—
434	C₂³	—	2	2	no	—
435	C₂³	—	2	2	no	—
436	C₂³	—	2	2	no	—
437	C₂³	—	2	2	no	—
438	C₂³	—	2	2	no	—
439	C₂³	—	2	2	no	—
440	C₂³	C₂²×D₄×C₁₀₃	1	1	yes	characteristic
441	Q₈	—	2	2	no	—
442	Q₈	—	2	2	no	—
443	Q₈	—	4	1	no	—
444	Q₈	—	4	1	no	—
445	Q₈	—	4	2	no	—
446	Q₈	—	4	2	no	—
447	Q₈	—	4	2	no	—
448	Q₈	—	4	2	no	—
449	D₄	—	4	4	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	4	1	no	—
459	C₂×C₄	—	4	1	no	—
460	C₂×C₄	—	4	1	no	—
461	C₂×C₄	—	4	1	no	—
462	C₂×C₄	—	4	1	no	—
463	C₂×C₄	—	4	1	no	—
464	C₂×C₄	—	4	2	no	—
465	C₂×C₄	—	4	2	no	—
466	C₂×C₄	—	4	2	no	—
467	C₂×C₄	—	4	2	no	—
468	C₂×C₄	—	4	1	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	—	4	2	no	—
471	C₂×C₄	—	4	2	no	—
472	C₂×C₄	—	4	2	no	—
473	C₂×C₄	—	4	2	no	—
474	C₂×C₄	—	4	1	no	—
475	C₂×C₄	—	4	2	no	—
476	C₂×C₄	—	4	1	no	—
477	C₂×C₄	#121×C₁₀₃	1	2	yes	—
478	C₂×C₄	#121×C₁₀₃	1	2	yes	—
479	C₂×C₄	#137×C₁₀₃	1	2	yes	—
480	C₂×C₄	#137×C₁₀₃	1	2	yes	—
481	C₂×C₄	C₂²×D₄×C₁₀₃	1	1	yes	characteristic
482	C₂×C₄	C₂²×D₄×C₁₀₃	1	1	yes	characteristic
483	C₂×C₄	C₂×#41×C₁₀₃	1	1	yes	characteristic
484	C₂×C₄	C₂×#41×C₁₀₃	1	1	yes	characteristic
485	C₂×C₄	H(5,𝔽₂)×C₁₀₃	1	1	yes	characteristic
486	C₂×C₄	H(5,𝔽₂)×C₁₀₃	1	1	yes	characteristic
487	C₈	—	2	2	no	—
488	C₈	—	2	4	no	—
489	C₈	—	4	1	no	—
490	C₂²	—	4	2	no	—
491	C₂²	—	4	2	no	—
492	C₂²	—	4	2	no	—
493	C₂²	—	4	2	no	—
494	C₂²	—	4	2	no	—
495	C₂²	—	4	2	no	—
496	C₂²	—	4	2	no	—
497	C₂²	C₂×#121×C₁₀₃	1	1	yes	characteristic
498	C₂²	D₄²×C₁₀₃	1	1	yes	characteristic
499	C₂²	#546×C₁₀₃	1	1	yes	characteristic
500	C₂²	C₂×#137×C₁₀₃	1	1	yes	characteristic
501	C₂²	C₂×#137×C₁₀₃	1	1	yes	characteristic
502	C₂²	#577×C₁₀₃	1	1	yes	characteristic
503	C₂²	#578×C₁₀₃	1	1	yes	characteristic
504	C₄	—	2	2	no	—
505	C₄	—	4	2	no	—
506	C₄	—	4	2	no	—
507	C₄	—	4	2	no	—
508	C₄	—	4	2	no	—
509	C₄	—	8	2	no	—
510	C₄	—	8	1	no	—
511	C₄	—	8	2	no	—
512	C₄	#470×C₁₀₃	1	4	yes	complemented
513	C₄	#532×C₁₀₃	1	1	yes	characteristic
514	C₄	#540×C₁₀₃	1	1	yes	characteristic
515	C₄	D₄²×C₁₀₃	1	1	yes	characteristic
516	C₄	#550×C₁₀₃	1	1	yes	characteristic
517	C₂	—	8	2	no	—
518	C₂	C₁₀₃×#2428	1	1	yes	characteristic
519	C₂	C₂×#470×C₁₀₃	1	1	yes	characteristic
520	C₂	C₁₀₃×#3063	1	1	yes	characteristic
521	C₂	C₁₀₃×#3276	1	1	yes	characteristic
522	C₂	C₁₀₃×#3278	1	1	yes	characteristic
523	C₂	C₁₀₃×#3328	1	1	yes	characteristic
524	C₂	C₁₀₃×#3331	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×#470×C₁₀₃	C₂	semidirect
2. C₂×#462×C₁₀₃	C₂	semidirect
6. C₁₀₃×#2035	C₂	semidirect
7. C₁₀₃×#2001	C₂	semidirect
8. C₁₀₃×#1956	C₂	semidirect
9. C₁₀₃×#1948	C₂	semidirect
10. C₁₀₃×#1894	C₂	semidirect
11. C₄×#103×C₁₀₃	C₂	semidirect
96. #103×C₁₀₃	D₄	semidirect
249. C₄×C₁₀₃	#470	semidirect
254. #25394	C₁₀₃	direct (N × H)
263. C₂×#470	C₂×C₁₀₃	semidirect
264. C₂×#462	C₂×C₁₀₃	semidirect
268. #2035	C₂×C₁₀₃	semidirect
269. #2001	C₂×C₁₀₃	semidirect
270. #1956	C₂×C₁₀₃	semidirect
271. #1948	C₂×C₁₀₃	semidirect
272. #1894	C₂×C₁₀₃	semidirect
273. C₄×#103	C₂×C₁₀₃	semidirect
274. C₁₀₃	#25394	direct (N × H)
359. #103	D₄×C₁₀₃	semidirect
512. C₄	#470×C₁₀₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#470×C₁₀₃	2
C₂×#462×C₁₀₃	2
C₂×#436×C₁₀₃	2
C₁₀₃×#2542	2
C₁₀₃×#2538	2
C₁₀₃×#2035	2
C₁₀₃×#2001	2
C₁₀₃×#1956	2
C₁₀₃×#1948	2
C₁₀₃×#1894	2
C₄×#103×C₁₀₃	2
#25394	103

Subgroups — C103×#25394 #39930669

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₃×#25394 #39930669