Subgroups — #36367192

Order 22144.

1900 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19149724	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₂²⋊D₁₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#26012131	C₂	1	4	yes	maximal, complemented
4	#26012128	C₂	1	4	yes	maximal, complemented
5	D₄×C₂²⋊D₁₇₃	C₂	1	4	yes	maximal, complemented
6	#26012123	C₂	1	4	yes	maximal, complemented
7	#26012056	C₂	1	2	yes	maximal, complemented
8	#26012053	C₂	1	1	yes	maximal, characteristic, complemented
9	#26012051	C₂	1	2	yes	maximal, complemented
10	#26012050	C₂	1	1	yes	maximal, characteristic, complemented
11	#26011997	C₂	1	2	yes	maximal, complemented
12	C₂×#19149648	C₂	1	1	yes	maximal, characteristic, complemented
13	#120×D₁₇₃	C₂	1	2	yes	maximal, complemented
14	#26011964	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#120×C₁₇₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂⁴×D₁₇₃	C₂²	1	1	yes	characteristic, complemented
17	#19149724	—	2	8	no	—
18	C₂×#14583826	C₂²	1	2	yes	complemented
19	C₂×#14583825	C₂²	1	2	yes	complemented
20	C₂×#14583825	C₂²	1	2	yes	complemented
21	C₂²×C₂²⋊D₁₇₃	—	2	8	no	—
22	C₂²×C₂²⋊D₁₇₃	C₂²	1	1	yes	characteristic
23	C₂²×C₂²⋊D₁₇₃	C₂²	1	1	yes	characteristic, complemented
24	C₂²×C₂²⋊D₁₇₃	C₂²	1	1	yes	characteristic, complemented
25	C₂²×C₂²⋊D₁₇₃	C₂²	1	1	yes	characteristic, complemented
26	C₂²×C₂²⋊D₁₇₃	C₂²	1	4	yes	complemented
27	C₂²×C₂²⋊D₁₇₃	C₂²	1	4	yes	complemented
28	C₂²×C₂²⋊D₁₇₃	C₂²	1	1	yes	characteristic, complemented
29	C₂²×C₂²⋊D₁₇₃	C₂²	1	2	yes	complemented
30	C₂²×C₂²⋊D₁₇₃	C₂²	1	2	yes	complemented
31	C₂×D₄×D₁₇₃	C₂²	1	2	yes	complemented
32	C₂×D₄×D₁₇₃	C₂²	1	2	yes	complemented
33	C₂×D₄×D₁₇₃	C₂²	1	4	yes	complemented
34	C₂³×Dic₁₇₃	C₂²	1	1	yes	characteristic, complemented
35	#19149675	C₂²	1	4	yes	complemented
36	#19149665	C₂²	1	4	yes	complemented
37	#19149663	C₂²	1	2	yes	complemented
38	#19149663	C₂²	1	2	yes	complemented
39	#19149662	C₂²	1	2	yes	complemented
40	#19149661	C₂²	1	4	yes	complemented
41	#19149660	C₂²	1	2	yes	complemented
42	#19149656	C₂²	1	4	yes	complemented
43	#19149653	C₂²	1	4	yes	complemented
44	#19149652	C₂²	1	4	yes	complemented
45	#19149652	C₂²	1	4	yes	complemented
46	#19149651	C₂²	1	4	yes	complemented
47	#19149651	C₂²	1	4	yes	complemented
48	#19149651	C₂²	1	4	yes	complemented
49	#19149650	C₂²	1	4	yes	complemented
50	#19149649	C₂²	1	2	yes	complemented
51	#19149649	C₂²	1	4	yes	complemented
52	#19149649	C₂²	1	2	yes	complemented
53	#19149648	C₂²	1	2	yes	complemented
54	#19149648	C₂²	1	2	yes	complemented
55	#19149648	C₂²	1	4	yes	complemented
56	#19149648	C₂²	1	2	yes	complemented
57	#19149647	C₂²	1	4	yes	complemented
58	#19149647	C₂²	1	2	yes	complemented
59	#19149647	C₂²	1	4	yes	complemented
60	D₄×Dic₁₇₃	C₂²	1	4	yes	complemented
61	C₄×C₂²⋊D₁₇₃	C₂²	1	4	yes	complemented
62	#19149639	C₂²	1	4	yes	complemented
63	#19149639	C₂²	1	4	yes	complemented
64	#19149635	C₂²	1	2	yes	complemented
65	C₂×C₂²⋊Dic₁₇₃	C₂²	1	1	yes	characteristic, complemented
66	C₂×C₂²⋊Dic₁₇₃	C₂²	1	2	yes	complemented
67	C₂²⋊C₄×D₁₇₃	C₂²	1	2	yes	complemented
68	C₂²⋊C₄×D₁₇₃	C₂²	1	4	yes	complemented
69	C₂⁵×C₁₇₃	C₂²	1	1	yes	characteristic, complemented
70	C₂²×D₄×C₁₇₃	C₂²	1	1	yes	characteristic, complemented
71	C₂²×D₄×C₁₇₃	C₂²	1	2	yes	complemented
72	#120×C₁₇₃	C₂²	1	2	yes	complemented
73	#120×C₁₇₃	C₂²	1	2	yes	complemented
74	#120×C₁₇₃	C₂²	1	4	yes	complemented
75	C₂×C₂²⋊C₄×C₁₇₃	C₂²	1	1	yes	characteristic, complemented
76	C₂×C₂²⋊C₄×C₁₇₃	C₂²	1	2	yes	complemented
77	C₂³×D₁₇₃	—	2	4	no	—
78	C₂³×D₁₇₃	—	4	4	no	—
79	C₂³×D₁₇₃	C₂³	1	4	yes	—
80	C₂³×D₁₇₃	C₂³	1	1	yes	characteristic
81	C₂³×D₁₇₃	C₂³	1	1	yes	characteristic
82	C₂³×D₁₇₃	C₂³	1	2	yes	complemented
83	C₂³×D₁₇₃	C₂³	1	1	yes	characteristic, complemented
84	#14583826	—	2	8	no	—
85	#14583825	—	2	8	no	—
86	#14583825	—	2	8	no	—
87	C₂×Dic₃₄₆	C₂³	1	2	yes	complemented
88	C₂×D₆₉₂	C₂³	1	2	yes	complemented
89	C₂×D₆₉₂	C₂³	1	4	yes	complemented
90	C₂×C₂²⋊D₁₇₃	—	2	4	no	—
91	C₂×C₂²⋊D₁₇₃	—	2	16	no	—
92	C₂×C₂²⋊D₁₇₃	—	2	16	no	—
93	C₂×C₂²⋊D₁₇₃	—	2	8	no	—
94	C₂×C₂²⋊D₁₇₃	—	2	4	no	—
95	C₂×C₂²⋊D₁₇₃	—	2	4	no	—
96	C₂×C₂²⋊D₁₇₃	—	2	4	no	—
97	C₂×C₂²⋊D₁₇₃	—	4	4	no	—
98	C₂×C₂²⋊D₁₇₃	D₄	1	8	yes	complemented
99	C₂×C₂²⋊D₁₇₃	C₂³	1	4	yes	—
100	C₂×C₂²⋊D₁₇₃	C₂³	1	4	yes	—
101	C₂×C₂²⋊D₁₇₃	C₂³	1	2	yes	—
102	C₂×C₂²⋊D₁₇₃	C₂³	1	2	yes	—
103	C₂×C₂²⋊D₁₇₃	C₂³	1	2	yes	—
104	C₂×C₂²⋊D₁₇₃	C₂³	1	4	yes	—
105	C₂×C₂²⋊D₁₇₃	C₂³	1	2	yes	—
106	C₂×C₂²⋊D₁₇₃	C₂³	1	2	yes	—
107	C₂×C₂²⋊D₁₇₃	C₂³	1	2	yes	complemented
108	C₂×C₂²⋊D₁₇₃	C₂³	1	2	yes	complemented
109	C₂×C₂²⋊D₁₇₃	C₂³	1	2	yes	complemented
110	C₂×C₂²⋊D₁₇₃	C₂³	1	4	yes	complemented
111	C₂×C₂²⋊D₁₇₃	C₂³	1	4	yes	complemented
112	D₄×D₁₇₃	—	2	8	no	—
113	D₄×D₁₇₃	—	2	8	no	—
114	D₄×D₁₇₃	—	4	8	no	—
115	C₂²×Dic₁₇₃	—	2	4	no	—
116	C₂²×Dic₁₇₃	C₂³	1	4	yes	—
117	C₂²×Dic₁₇₃	C₂³	1	1	yes	characteristic
118	C₂²×Dic₁₇₃	C₂³	1	1	yes	characteristic
119	C₂²×Dic₁₇₃	C₂³	1	1	yes	characteristic, complemented
120	C₂²×Dic₁₇₃	C₂³	1	2	yes	complemented
121	C₂²×Dic₁₇₃	C₂³	1	2	yes	complemented
122	C₂×C₄×D₁₇₃	C₂³	1	2	yes	complemented
123	C₂×C₄×D₁₇₃	C₂³	1	2	yes	complemented
124	C₂×C₄×D₁₇₃	C₂³	1	4	yes	complemented
125	C₄⋊Dic₁₇₃	C₂³	1	4	yes	complemented
126	#14583805	C₂³	1	4	yes	complemented
127	#14583805	C₂³	1	4	yes	complemented
128	C₂²⋊Dic₁₇₃	C₂³	1	2	yes	—
129	C₂²⋊Dic₁₇₃	C₂³	1	4	yes	—
130	C₂²⋊Dic₁₇₃	C₂³	1	2	yes	complemented
131	C₂²⋊Dic₁₇₃	C₂³	1	4	yes	complemented
132	C₂²⋊Dic₁₇₃	C₂³	1	4	yes	complemented
133	#14583803	C₂³	1	4	yes	complemented
134	#14583803	C₂³	1	4	yes	complemented
135	#14583803	C₂³	1	4	yes	complemented
136	#14583803	C₂³	1	4	yes	complemented
137	C₄×Dic₁₇₃	C₂³	1	4	yes	complemented
138	C₂⁴×C₁₇₃	—	2	4	no	—
139	C₂⁴×C₁₇₃	—	4	4	no	—
140	C₂⁴×C₁₇₃	C₂³	1	1	yes	characteristic
141	C₂⁴×C₁₇₃	C₂³	1	2	yes	—
142	C₂⁴×C₁₇₃	C₂³	1	2	yes	—
143	C₂⁴×C₁₇₃	C₂³	1	1	yes	characteristic
144	C₂⁴×C₁₇₃	C₂³	1	1	yes	characteristic
145	C₂⁴×C₁₇₃	C₂³	1	1	yes	characteristic, complemented
146	C₂×D₄×C₁₇₃	—	2	4	no	—
147	C₂×D₄×C₁₇₃	—	4	4	no	—
148	C₂×D₄×C₁₇₃	C₂³	1	4	yes	—
149	C₂×D₄×C₁₇₃	C₂³	1	2	yes	—
150	C₂×D₄×C₁₇₃	C₂³	1	2	yes	complemented
151	C₂×D₄×C₁₇₃	C₂³	1	4	yes	complemented
152	C₂²×C₄×C₁₇₃	C₂³	1	1	yes	characteristic, complemented
153	C₂²×C₄×C₁₇₃	C₂³	1	2	yes	complemented
154	C₂²⋊C₄×C₁₇₃	C₂³	1	2	yes	—
155	C₂²⋊C₄×C₁₇₃	C₂³	1	4	yes	—
156	C₂²⋊C₄×C₁₇₃	C₂³	1	2	yes	complemented
157	C₂²⋊C₄×C₁₇₃	C₂³	1	4	yes	complemented
158	C₂²×D₁₇₃	—	2	2	no	—
159	C₂²×D₁₇₃	—	2	8	no	—
160	C₂²×D₁₇₃	—	2	2	no	—
161	C₂²×D₁₇₃	—	2	8	no	—
162	C₂²×D₁₇₃	—	2	4	no	—
163	C₂²×D₁₇₃	—	4	2	no	—
164	C₂²×D₁₇₃	—	4	4	no	—
165	C₂²×D₁₇₃	—	4	2	no	—
166	C₂²×D₁₇₃	—	4	4	no	—
167	C₂²×D₁₇₃	—	4	2	no	—
168	C₂²×D₁₇₃	—	4	16	no	—
169	C₂²×D₁₇₃	C₂×D₄	1	4	yes	complemented
170	C₂²×D₁₇₃	C₂⁴	1	2	yes	—
171	C₂²×D₁₇₃	C₂⁴	1	2	yes	—
172	C₂²×D₁₇₃	C₂⁴	1	2	yes	—
173	Dic₃₄₆	—	2	4	no	—
174	D₆₉₂	—	2	4	no	—
175	D₆₉₂	—	4	4	no	—
176	C₂²⋊D₁₇₃	—	2	4	no	—
177	C₂²⋊D₁₇₃	—	2	4	no	—
178	C₂²⋊D₁₇₃	—	2	4	no	—
179	C₂²⋊D₁₇₃	—	2	4	no	—
180	C₂²⋊D₁₇₃	—	2	8	no	—
181	C₂²⋊D₁₇₃	—	2	4	no	—
182	C₂²⋊D₁₇₃	—	2	8	no	—
183	C₂²⋊D₁₇₃	—	2	4	no	—
184	C₂²⋊D₁₇₃	—	2	8	no	—
185	C₂²⋊D₁₇₃	—	4	4	no	—
186	C₂²⋊D₁₇₃	—	4	4	no	—
187	C₂²⋊D₁₇₃	C₂×D₄	1	8	yes	complemented
188	C₂²⋊D₁₇₃	C₂×D₄	1	8	yes	complemented
189	C₂×Dic₁₇₃	—	2	2	no	—
190	C₂×Dic₁₇₃	—	2	2	no	—
191	C₂×Dic₁₇₃	—	2	8	no	—
192	C₂×Dic₁₇₃	—	2	4	no	—
193	C₂×Dic₁₇₃	—	4	2	no	—
194	C₂×Dic₁₇₃	C₂×D₄	1	4	yes	complemented
195	C₂×Dic₁₇₃	C₂⁴	1	2	yes	—
196	C₂×Dic₁₇₃	C₂⁴	1	4	yes	—
197	C₂×Dic₁₇₃	C₂⁴	1	2	yes	—
198	C₂×Dic₁₇₃	C₂⁴	1	2	yes	—
199	C₄×D₁₇₃	—	2	4	no	—
200	C₄×D₁₇₃	—	2	4	no	—
201	C₄×D₁₇₃	—	4	4	no	—
202	C₂³×C₁₇₃	—	2	2	no	—
203	C₂³×C₁₇₃	—	2	4	no	—
204	C₂³×C₁₇₃	—	2	4	no	—
205	C₂³×C₁₇₃	—	2	4	no	—
206	C₂³×C₁₇₃	—	2	2	no	—
207	C₂³×C₁₇₃	—	2	4	no	—
208	C₂³×C₁₇₃	—	2	4	no	—
209	C₂³×C₁₇₃	—	2	2	no	—
210	C₂³×C₁₇₃	—	4	2	no	—
211	C₂³×C₁₇₃	—	4	2	no	—
212	C₂³×C₁₇₃	—	4	2	no	—
213	C₂³×C₁₇₃	—	4	2	no	—
214	C₂³×C₁₇₃	—	4	2	no	—
215	C₂³×C₁₇₃	—	4	16	no	—
216	C₂³×C₁₇₃	C₂×D₄	1	4	yes	complemented
217	C₂³×C₁₇₃	C₂⁴	1	2	yes	—
218	C₂³×C₁₇₃	C₂⁴	1	2	yes	—
219	C₂³×C₁₇₃	C₂⁴	1	1	yes	characteristic
220	C₂³×C₁₇₃	C₂⁴	1	1	yes	characteristic
221	C₂³×C₁₇₃	C₂⁴	1	1	yes	characteristic
222	C₂³×C₁₇₃	C₂⁴	1	2	yes	—
223	D₄×C₁₇₃	—	2	4	no	—
224	D₄×C₁₇₃	—	2	4	no	—
225	D₄×C₁₇₃	—	2	8	no	—
226	D₄×C₁₇₃	—	4	4	no	—
227	C₂×C₄×C₁₇₃	—	2	2	no	—
228	C₂×C₄×C₁₇₃	—	4	2	no	—
229	C₂×C₄×C₁₇₃	C₂⁴	1	2	yes	—
230	C₂×C₄×C₁₇₃	C₂⁴	1	4	yes	—
231	C₂²×C₁₇₃	—	2	8	no	—
232	C₂²×C₁₇₃	—	2	2	no	—
233	C₂²×C₁₇₃	—	2	2	no	—
234	C₂²×C₁₇₃	—	2	2	no	—
235	C₂²×C₁₇₃	—	2	2	no	—
236	C₂²×C₁₇₃	—	2	2	no	—
237	C₂²×C₁₇₃	—	2	2	no	—
238	C₂²×C₁₇₃	—	2	2	no	—
239	C₂²×C₁₇₃	—	2	4	no	—
240	C₂²×C₁₇₃	—	2	2	no	—
241	C₂²×C₁₇₃	—	2	2	no	—
242	C₂²×C₁₇₃	—	4	4	no	—
243	C₂²×C₁₇₃	—	4	8	no	—
244	C₂²×C₁₇₃	—	4	8	no	—
245	C₂²×C₁₇₃	—	4	4	no	—
246	C₂²×C₁₇₃	—	8	2	no	—
247	C₂²×C₁₇₃	C₂²×D₄	1	2	yes	—
248	C₂²×C₁₇₃	C₂²×D₄	1	2	yes	—
249	C₂²×C₁₇₃	C₂²×D₄	1	2	yes	—
250	C₂²×C₁₇₃	H(5,𝔽₂)	1	4	yes	complemented
251	C₂²×C₁₇₃	C₂⁵	1	1	yes	characteristic
252	C₂×D₁₇₃	—	2	4	no	—
253	C₂×D₁₇₃	—	2	2	no	—
254	C₂×D₁₇₃	—	2	2	no	—
255	C₂×D₁₇₃	—	2	4	no	—
256	C₂×D₁₇₃	—	2	4	no	—
257	C₂×D₁₇₃	—	4	4	no	—
258	C₂×D₁₇₃	—	4	16	no	—
259	C₂×D₁₇₃	—	4	4	no	—
260	C₂×D₁₇₃	—	8	4	no	—
261	C₂×D₁₇₃	—	8	2	no	—
262	C₂×D₁₇₃	C₂²×D₄	1	4	yes	—
263	C₄×C₁₇₃	—	2	2	no	—
264	C₄×C₁₇₃	—	2	4	no	—
265	Dic₁₇₃	—	2	2	no	—
266	Dic₁₇₃	—	2	2	no	—
267	Dic₁₇₃	—	2	4	no	—
268	Dic₁₇₃	C₂²×D₄	1	4	yes	—
269	C₂×C₁₇₃	—	2	2	no	—
270	C₂×C₁₇₃	—	2	4	no	—
271	C₂×C₁₇₃	—	2	2	no	—
272	C₂×C₁₇₃	—	2	2	no	—
273	C₂×C₁₇₃	—	4	2	no	—
274	C₂×C₁₇₃	—	4	2	no	—
275	C₂×C₁₇₃	C₂³×D₄	1	1	yes	characteristic
276	C₂×C₁₇₃	C₂×H(5,𝔽₂)	1	2	yes	—
277	D₁₇₃	—	2	4	no	—
278	D₁₇₃	—	4	2	no	—
279	D₁₇₃	—	4	2	no	—
280	C₁₇₃	#3484	1	1	yes	characteristic, complemented, Sylow
281	#3484	—	173	1	no	maximal, Sylow
282	C₂×H(5,𝔽₂)	—	173	1	no	—
283	C₂³×D₄	—	173	1	no	—
284	#546	—	173	4	no	—
285	#546	—	173	4	no	—
286	D₄²	—	173	4	no	—
287	D₄²	—	173	4	no	—
288	#535	—	173	2	no	—
289	#534	—	173	1	no	—
290	#534	—	173	2	no	—
291	#534	—	173	1	no	—
292	#525	—	173	2	no	—
293	C₂×#120	—	173	1	no	—
294	C₂×#120	—	173	2	no	—
295	C₂×#120	D₁₇₃	1	1	yes	characteristic, complemented
296	#518	—	173	1	no	—
297	C₂⁵	—	173	1	no	—
298	C₂⁵	C₂×D₁₇₃	1	1	yes	characteristic, complemented
299	H(5,𝔽₂)	—	346	8	no	—
300	C₂×#41	—	173	2	no	—
301	C₂×#41	—	173	2	no	—
302	C₂×#41	—	173	2	no	—
303	C₂²×D₄	—	346	8	no	—
304	C₂²×D₄	—	173	1	no	—
305	C₂²×D₄	—	173	1	no	—
306	C₂²×D₄	—	173	1	no	—
307	C₂²×D₄	—	173	1	no	—
308	C₂²×D₄	—	173	4	no	—
309	C₂²×D₄	—	173	4	no	—
310	C₂²×D₄	—	173	2	no	—
311	C₂²×D₄	—	173	2	no	—
312	C₂²×D₄	—	173	2	no	—
313	C₂²×D₄	—	173	1	no	—
314	C₂²×D₄	—	173	2	no	—
315	C₂²×D₄	—	173	4	no	—
316	C₂²×D₄	C₂×D₁₇₃	1	1	yes	characteristic, complemented
317	C₂²×D₄	C₂×D₁₇₃	1	2	yes	complemented
318	C₂³×C₄	—	173	1	no	—
319	#127	—	173	4	no	—
320	#124	—	173	4	no	—
321	#123	—	173	2	no	—
322	#123	—	173	2	no	—
323	#123	—	173	2	no	—
324	#123	—	173	4	no	—
325	#123	—	173	2	no	—
326	C₂²⋊Q₈	—	173	4	no	—
327	#121	—	173	4	no	—
328	#121	—	173	4	no	—
329	#121	—	173	4	no	—
330	#121	—	173	4	no	—
331	#121	—	173	4	no	—
332	#121	—	173	4	no	—
333	#121	—	173	4	no	—
334	#120	—	173	2	no	—
335	#120	—	173	2	no	—
336	#120	—	173	4	no	—
337	#120	—	173	2	no	—
338	#120	—	173	2	no	—
339	#120	—	173	4	no	—
340	#120	—	173	4	no	—
341	#120	—	173	2	no	—
342	#120	—	173	4	no	—
343	#120	—	173	2	no	—
344	#120	C₂×D₁₇₃	1	2	yes	complemented
345	#120	C₂×D₁₇₃	1	2	yes	complemented
346	#120	C₂×D₁₇₃	1	4	yes	complemented
347	C₄×D₄	—	173	4	no	—
348	C₄×D₄	—	173	4	no	—
349	C₄×D₄	—	173	4	no	—
350	C₄×D₄	—	173	4	no	—
351	#117	—	173	2	no	—
352	C₂×C₂²⋊C₄	—	173	1	no	—
353	C₂×C₂²⋊C₄	—	173	2	no	—
354	C₂×C₂²⋊C₄	—	173	2	no	—
355	C₂×C₂²⋊C₄	—	173	4	no	—
356	C₂×C₂²⋊C₄	C₂×D₁₇₃	1	1	yes	characteristic, complemented
357	C₂×C₂²⋊C₄	C₂×D₁₇₃	1	2	yes	complemented
358	C₂⁴	—	2	4	no	—
359	C₂⁴	—	4	4	no	—
360	C₂⁴	—	346	4	no	—
361	C₂⁴	—	173	4	no	—
362	C₂⁴	—	173	1	no	—
363	C₂⁴	—	173	2	no	—
364	C₂⁴	—	173	1	no	—
365	C₂⁴	—	173	1	no	—
366	C₂⁴	—	692	4	no	—
367	C₂⁴	C₂²×D₁₇₃	1	1	yes	characteristic
368	C₂⁴	C₂²×D₁₇₃	1	2	yes	—
369	C₂⁴	C₂²×D₁₇₃	1	2	yes	—
370	C₂⁴	C₂²×D₁₇₃	1	1	yes	characteristic
371	C₂⁴	C₂²×D₁₇₃	1	1	yes	characteristic
372	C₂⁴	C₂²×D₁₇₃	1	1	yes	characteristic, complemented
373	#41	—	346	8	no	—
374	#41	—	346	8	no	—
375	#41	—	346	8	no	—
376	C₂×Q₈	—	173	2	no	—
377	C₂×D₄	—	2	4	no	—
378	C₂×D₄	—	4	4	no	—
379	C₂×D₄	—	346	8	no	—
380	C₂×D₄	—	346	8	no	—
381	C₂×D₄	—	346	4	no	—
382	C₂×D₄	—	346	4	no	—
383	C₂×D₄	—	346	4	no	—
384	C₂×D₄	—	346	16	no	—
385	C₂×D₄	—	346	16	no	—
386	C₂×D₄	—	346	8	no	—
387	C₂×D₄	—	346	4	no	—
388	C₂×D₄	—	173	4	no	—
389	C₂×D₄	—	173	2	no	—
390	C₂×D₄	—	173	4	no	—
391	C₂×D₄	—	173	2	no	—
392	C₂×D₄	—	173	2	no	—
393	C₂×D₄	—	173	4	no	—
394	C₂×D₄	—	173	2	no	—
395	C₂×D₄	—	173	2	no	—
396	C₂×D₄	—	173	2	no	—
397	C₂×D₄	—	173	8	no	—
398	C₂×D₄	—	173	2	no	—
399	C₂×D₄	—	173	2	no	—
400	C₂×D₄	—	173	4	no	—
401	C₂×D₄	—	173	4	no	—
402	C₂×D₄	—	173	2	no	—
403	C₂×D₄	—	173	4	no	—
404	C₂×D₄	—	692	8	no	—
405	C₂×D₄	—	692	4	no	—
406	C₂×D₄	C₂²×D₁₇₃	1	4	yes	—
407	C₂×D₄	C₂²×D₁₇₃	1	2	yes	—
408	C₂×D₄	C₂²×D₁₇₃	1	2	yes	complemented
409	C₂×D₄	C₂²×D₁₇₃	1	4	yes	complemented
410	C₂²×C₄	—	346	4	no	—
411	C₂²×C₄	—	173	4	no	—
412	C₂²×C₄	—	173	1	no	—
413	C₂²×C₄	—	173	1	no	—
414	C₂²×C₄	—	173	2	no	—
415	C₂²×C₄	—	173	2	no	—
416	C₂²×C₄	—	173	2	no	—
417	C₂²×C₄	—	173	1	no	—
418	C₂²×C₄	—	173	2	no	—
419	C₂²×C₄	—	173	4	no	—
420	C₂²×C₄	C₂²×D₁₇₃	1	1	yes	characteristic, complemented
421	C₂²×C₄	C₂²×D₁₇₃	1	2	yes	complemented
422	C₄⋊C₄	—	173	4	no	—
423	C₄⋊C₄	—	173	4	no	—
424	C₄⋊C₄	—	173	4	no	—
425	C₂²⋊C₄	—	173	2	no	—
426	C₂²⋊C₄	—	173	4	no	—
427	C₂²⋊C₄	—	173	2	no	—
428	C₂²⋊C₄	—	173	4	no	—
429	C₂²⋊C₄	—	173	4	no	—
430	C₂²⋊C₄	—	173	4	no	—
431	C₂²⋊C₄	—	173	4	no	—
432	C₂²⋊C₄	—	173	4	no	—
433	C₂²⋊C₄	—	173	4	no	—
434	C₂²⋊C₄	C₂²×D₁₇₃	1	2	yes	—
435	C₂²⋊C₄	C₂²×D₁₇₃	1	4	yes	—
436	C₂²⋊C₄	C₂²×D₁₇₃	1	2	yes	complemented
437	C₂²⋊C₄	C₂²×D₁₇₃	1	4	yes	complemented
438	C₄²	—	173	4	no	—
439	C₂³	—	2	2	no	—
440	C₂³	—	2	4	no	—
441	C₂³	—	2	4	no	—
442	C₂³	—	2	4	no	—
443	C₂³	—	2	2	no	—
444	C₂³	—	2	4	no	—
445	C₂³	—	2	4	no	—
446	C₂³	—	2	2	no	—
447	C₂³	—	4	2	no	—
448	C₂³	—	4	2	no	—
449	C₂³	—	4	2	no	—
450	C₂³	—	4	2	no	—
451	C₂³	—	4	2	no	—
452	C₂³	—	4	16	no	—
453	C₂³	—	346	4	no	—
454	C₂³	—	346	8	no	—
455	C₂³	—	346	2	no	—
456	C₂³	—	346	2	no	—
457	C₂³	—	346	8	no	—
458	C₂³	—	173	2	no	—
459	C₂³	—	173	2	no	—
460	C₂³	—	173	2	no	—
461	C₂³	—	173	4	no	—
462	C₂³	—	692	2	no	—
463	C₂³	—	692	4	no	—
464	C₂³	—	692	2	no	—
465	C₂³	—	692	4	no	—
466	C₂³	—	692	2	no	—
467	C₂³	—	692	16	no	—
468	C₂³	D₄×D₁₇₃	1	4	yes	complemented
469	C₂³	C₂³×D₁₇₃	1	2	yes	—
470	C₂³	C₂³×D₁₇₃	1	2	yes	—
471	C₂³	C₂³×D₁₇₃	1	1	yes	characteristic
472	C₂³	C₂³×D₁₇₃	1	1	yes	characteristic
473	C₂³	C₂³×D₁₇₃	1	1	yes	characteristic
474	C₂³	C₂³×D₁₇₃	1	2	yes	—
475	Q₈	—	346	4	no	—
476	D₄	—	2	4	no	—
477	D₄	—	2	4	no	—
478	D₄	—	2	8	no	—
479	D₄	—	4	4	no	—
480	D₄	—	346	4	no	—
481	D₄	—	346	8	no	—
482	D₄	—	346	4	no	—
483	D₄	—	346	4	no	—
484	D₄	—	346	4	no	—
485	D₄	—	346	4	no	—
486	D₄	—	346	4	no	—
487	D₄	—	346	8	no	—
488	D₄	—	346	8	no	—
489	D₄	—	346	4	no	—
490	D₄	—	173	8	no	—
491	D₄	—	173	8	no	—
492	D₄	—	692	4	no	—
493	D₄	—	692	4	no	—
494	D₄	—	692	4	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	4	2	no	—
497	C₂×C₄	—	346	4	no	—
498	C₂×C₄	—	346	4	no	—
499	C₂×C₄	—	346	2	no	—
500	C₂×C₄	—	346	2	no	—
501	C₂×C₄	—	346	8	no	—
502	C₂×C₄	—	346	4	no	—
503	C₂×C₄	—	173	4	no	—
504	C₂×C₄	—	173	2	no	—
505	C₂×C₄	—	173	2	no	—
506	C₂×C₄	—	173	4	no	—
507	C₂×C₄	—	173	2	no	—
508	C₂×C₄	—	692	4	no	—
509	C₂×C₄	—	692	2	no	—
510	C₂×C₄	C₂³×D₁₇₃	1	4	yes	—
511	C₂×C₄	C₂³×D₁₇₃	1	2	yes	—
512	C₂²	—	2	8	no	—
513	C₂²	—	2	2	no	—
514	C₂²	—	2	2	no	—
515	C₂²	—	2	2	no	—
516	C₂²	—	2	2	no	—
517	C₂²	—	2	2	no	—
518	C₂²	—	2	2	no	—
519	C₂²	—	2	2	no	—
520	C₂²	—	2	4	no	—
521	C₂²	—	2	2	no	—
522	C₂²	—	2	2	no	—
523	C₂²	—	4	4	no	—
524	C₂²	—	4	8	no	—
525	C₂²	—	4	8	no	—
526	C₂²	—	4	4	no	—
527	C₂²	—	8	2	no	—
528	C₂²	—	346	4	no	—
529	C₂²	—	346	2	no	—
530	C₂²	—	346	2	no	—
531	C₂²	—	346	4	no	—
532	C₂²	—	346	4	no	—
533	C₂²	—	1384	2	no	—
534	C₂²	—	1384	4	no	—
535	C₂²	—	173	4	no	—
536	C₂²	—	692	4	no	—
537	C₂²	—	692	16	no	—
538	C₂²	—	692	4	no	—
539	C₂²	C₂×D₄×D₁₇₃	1	2	yes	—
540	C₂²	C₂×D₄×D₁₇₃	1	2	yes	—
541	C₂²	C₂×D₄×D₁₇₃	1	2	yes	—
542	C₂²	#19149724	1	4	yes	complemented
543	C₂²	C₂⁴×D₁₇₃	1	1	yes	characteristic
544	C₄	—	2	2	no	—
545	C₄	—	2	4	no	—
546	C₄	—	346	2	no	—
547	C₄	—	346	2	no	—
548	C₄	—	346	4	no	—
549	C₄	—	173	4	no	—
550	C₂	—	2	2	no	—
551	C₂	—	2	4	no	—
552	C₂	—	2	2	no	—
553	C₂	—	2	2	no	—
554	C₂	—	4	2	no	—
555	C₂	—	4	2	no	—
556	C₂	—	346	4	no	—
557	C₂	—	692	2	no	—
558	C₂	—	692	2	no	—
559	C₂	C₂²×D₄×D₁₇₃	1	1	yes	characteristic
560	C₂	C₂×#19149724	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₇₃
commutator, socle, cosocle	C₂²×C₁₇₃	C₂⁵
Fitting	C₂×#120×C₁₇₃	C₂
hypercenter	C₂×#120	D₁₇₃
hypocenter	C₁₇₃	#3484
LCS	G ▷ C₂²×C₁₇₃ ▷ C₁₇₃
UCS	C₁ ◁ C₂² ◁ C₂×#120

Complements

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

N	H ≅ G/N	type
1. C₂×#19149724	C₂	semidirect
2. C₂³×C₂²⋊D₁₇₃	C₂	semidirect
3. #26012131	C₂	semidirect
4. #26012128	C₂	semidirect
5. D₄×C₂²⋊D₁₇₃	C₂	semidirect
6. #26012123	C₂	semidirect
7. #26012056	C₂	semidirect
8. #26012053	C₂	semidirect
9. #26012051	C₂	semidirect
10. #26012050	C₂	semidirect
11. #26011997	C₂	semidirect
12. C₂×#19149648	C₂	semidirect
13. #120×D₁₇₃	C₂	semidirect
14. #26011964	C₂	semidirect
15. C₂×#120×C₁₇₃	C₂	semidirect
16. C₂⁴×D₁₇₃	C₂²	semidirect
18. C₂×#14583826	C₂²	semidirect
19. C₂×#14583825	C₂²	semidirect
20. C₂×#14583825	C₂²	semidirect
23. C₂²×C₂²⋊D₁₇₃	C₂²	semidirect
24. C₂²×C₂²⋊D₁₇₃	C₂²	semidirect
25. C₂²×C₂²⋊D₁₇₃	C₂²	semidirect
26. C₂²×C₂²⋊D₁₇₃	C₂²	semidirect
27. C₂²×C₂²⋊D₁₇₃	C₂²	semidirect
28. C₂²×C₂²⋊D₁₇₃	C₂²	semidirect
29. C₂²×C₂²⋊D₁₇₃	C₂²	semidirect
30. C₂²×C₂²⋊D₁₇₃	C₂²	semidirect
31. C₂×D₄×D₁₇₃	C₂²	semidirect
32. C₂×D₄×D₁₇₃	C₂²	semidirect
33. C₂×D₄×D₁₇₃	C₂²	semidirect
34. C₂³×Dic₁₇₃	C₂²	semidirect
35. #19149675	C₂²	semidirect
36. #19149665	C₂²	semidirect
37. #19149663	C₂²	semidirect
38. #19149663	C₂²	semidirect
39. #19149662	C₂²	semidirect
40. #19149661	C₂²	semidirect
41. #19149660	C₂²	semidirect
42. #19149656	C₂²	semidirect
43. #19149653	C₂²	semidirect
44. #19149652	C₂²	semidirect
45. #19149652	C₂²	semidirect
46. #19149651	C₂²	semidirect
47. #19149651	C₂²	semidirect
48. #19149651	C₂²	semidirect
49. #19149650	C₂²	semidirect
50. #19149649	C₂²	semidirect
51. #19149649	C₂²	semidirect
52. #19149649	C₂²	semidirect
53. #19149648	C₂²	semidirect
54. #19149648	C₂²	semidirect
55. #19149648	C₂²	semidirect
56. #19149648	C₂²	semidirect
57. #19149647	C₂²	semidirect
58. #19149647	C₂²	semidirect
59. #19149647	C₂²	semidirect
60. D₄×Dic₁₇₃	C₂²	semidirect
61. C₄×C₂²⋊D₁₇₃	C₂²	semidirect
62. #19149639	C₂²	semidirect
63. #19149639	C₂²	semidirect
64. #19149635	C₂²	semidirect
65. C₂×C₂²⋊Dic₁₇₃	C₂²	semidirect
66. C₂×C₂²⋊Dic₁₇₃	C₂²	semidirect
67. C₂²⋊C₄×D₁₇₃	C₂²	semidirect
68. C₂²⋊C₄×D₁₇₃	C₂²	semidirect
69. C₂⁵×C₁₇₃	C₂²	semidirect
70. C₂²×D₄×C₁₇₃	C₂²	semidirect
71. C₂²×D₄×C₁₇₃	C₂²	semidirect
72. #120×C₁₇₃	C₂²	semidirect
73. #120×C₁₇₃	C₂²	semidirect
74. #120×C₁₇₃	C₂²	semidirect
75. C₂×C₂²⋊C₄×C₁₇₃	C₂²	semidirect
76. C₂×C₂²⋊C₄×C₁₇₃	C₂²	semidirect
82. C₂³×D₁₇₃	C₂³	semidirect
83. C₂³×D₁₇₃	C₂³	semidirect
87. C₂×Dic₃₄₆	C₂³	semidirect
88. C₂×D₆₉₂	C₂³	semidirect
89. C₂×D₆₉₂	C₂³	semidirect
98. C₂×C₂²⋊D₁₇₃	D₄	semidirect
107. C₂×C₂²⋊D₁₇₃	C₂³	semidirect
108. C₂×C₂²⋊D₁₇₃	C₂³	semidirect
109. C₂×C₂²⋊D₁₇₃	C₂³	semidirect
110. C₂×C₂²⋊D₁₇₃	C₂³	semidirect
111. C₂×C₂²⋊D₁₇₃	C₂³	semidirect
119. C₂²×Dic₁₇₃	C₂³	semidirect
120. C₂²×Dic₁₇₃	C₂³	semidirect
121. C₂²×Dic₁₇₃	C₂³	semidirect
122. C₂×C₄×D₁₇₃	C₂³	semidirect
123. C₂×C₄×D₁₇₃	C₂³	semidirect
124. C₂×C₄×D₁₇₃	C₂³	semidirect
125. C₄⋊Dic₁₇₃	C₂³	semidirect
126. #14583805	C₂³	semidirect
127. #14583805	C₂³	semidirect
130. C₂²⋊Dic₁₇₃	C₂³	semidirect
131. C₂²⋊Dic₁₇₃	C₂³	semidirect
132. C₂²⋊Dic₁₇₃	C₂³	semidirect
133. #14583803	C₂³	semidirect
134. #14583803	C₂³	semidirect
135. #14583803	C₂³	semidirect
136. #14583803	C₂³	semidirect
137. C₄×Dic₁₇₃	C₂³	semidirect
145. C₂⁴×C₁₇₃	C₂³	semidirect
150. C₂×D₄×C₁₇₃	C₂³	semidirect
151. C₂×D₄×C₁₇₃	C₂³	semidirect
152. C₂²×C₄×C₁₇₃	C₂³	semidirect
153. C₂²×C₄×C₁₇₃	C₂³	semidirect
156. C₂²⋊C₄×C₁₇₃	C₂³	semidirect
157. C₂²⋊C₄×C₁₇₃	C₂³	semidirect
169. C₂²×D₁₇₃	C₂×D₄	semidirect
187. C₂²⋊D₁₇₃	C₂×D₄	semidirect
188. C₂²⋊D₁₇₃	C₂×D₄	semidirect
194. C₂×Dic₁₇₃	C₂×D₄	semidirect
216. C₂³×C₁₇₃	C₂×D₄	semidirect
250. C₂²×C₁₇₃	H(5,𝔽₂)	semidirect
280. C₁₇₃	#3484	semidirect
295. C₂×#120	D₁₇₃	semidirect
298. C₂⁵	C₂×D₁₇₃	semidirect
316. C₂²×D₄	C₂×D₁₇₃	semidirect
317. C₂²×D₄	C₂×D₁₇₃	semidirect
344. #120	C₂×D₁₇₃	semidirect
345. #120	C₂×D₁₇₃	semidirect
346. #120	C₂×D₁₇₃	semidirect
356. C₂×C₂²⋊C₄	C₂×D₁₇₃	semidirect
357. C₂×C₂²⋊C₄	C₂×D₁₇₃	semidirect
372. C₂⁴	C₂²×D₁₇₃	semidirect
408. C₂×D₄	C₂²×D₁₇₃	semidirect
409. C₂×D₄	C₂²×D₁₇₃	semidirect
420. C₂²×C₄	C₂²×D₁₇₃	semidirect
421. C₂²×C₄	C₂²×D₁₇₃	semidirect
436. C₂²⋊C₄	C₂²×D₁₇₃	semidirect
437. C₂²⋊C₄	C₂²×D₁₇₃	semidirect
468. C₂³	D₄×D₁₇₃	semidirect
542. C₂²	#19149724	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19149724	2
C₂³×C₂²⋊D₁₇₃	2
#26012131	2
#26012128	2
D₄×C₂²⋊D₁₇₃	2
#26012123	2
#26012056	2
#26012053	2
#26012051	2
#26012050	2
#26011997	2
C₂×#19149648	2
#120×D₁₇₃	2
#26011964	2
C₂×#120×C₁₇₃	2
#3484	173