Subgroups — C₁₇×#25529 #16883273

Order 4352.

1014 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×#3495	C₂	1	1	yes	maximal, characteristic
2	C₁₇×#3095	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₇×#3056	C₂	1	1	yes	maximal, characteristic
4	C₁₇×#2621	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₇×#2061	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₇×#2038	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₇×#2028	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₇×#2005	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₇×#1901	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₇×#1897	C₂	1	1	yes	maximal, characteristic
11	C₁₇×#1886	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₇×#1882	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₇×#1860	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₇×#1857	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₇×#1733	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₇×#137	C₂²	1	1	yes	characteristic
17	C₂²×M₁₆×C₁₇	C₂²	1	1	yes	characteristic
18	C₁₇×#556	—	2	1	no	—
19	C₁₇×#554	—	2	1	no	—
20	C₁₇×#552	—	2	1	no	—
21	C₁₇×#552	—	2	2	no	—
22	C₁₇×#552	—	2	1	no	—
23	C₁₇×#551	—	2	2	no	—
24	C₁₇×#544	C₂²	1	1	yes	characteristic
25	C₁₇×#542	—	2	1	no	—
26	C₁₇×#541	—	2	1	no	—
27	C₁₇×#536	C₂²	1	1	yes	characteristic
28	C₁₇×#533	—	2	1	no	—
29	C₂×C₁₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
30	C₁₇×#529	—	2	1	no	—
31	C₁₇×#525	C₂²	1	1	yes	characteristic
32	C₂×C₁₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
33	C₂×C₁₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
34	C₁₇×#520	C₂²	1	1	yes	characteristic
35	C₁₇×#519	C₂²	1	1	yes	characteristic
36	C₂×C₁₇×#117	C₂²	1	1	yes	characteristic
37	C₂×C₁₇×#117	C₂²	1	1	yes	characteristic
38	C₁₇×#485	—	2	1	no	—
39	C₁₇×#485	—	2	1	no	—
40	C₁₇×#484	—	2	1	no	—
41	C₁₇×#483	—	2	1	no	—
42	C₁₇×#470	—	2	1	no	—
43	C₁₇×#468	—	2	1	no	—
44	C₁₇×#467	—	2	1	no	—
45	C₁₇×#465	—	2	1	no	—
46	C₁₇×#428	C₂²	1	1	yes	characteristic
47	C₁₇×#428	C₂²	1	1	yes	characteristic
48	C₁₇×#428	C₂²	1	1	yes	characteristic
49	C₂×C₁₇×#104	C₂²	1	1	yes	characteristic
50	C₂×C₁₇×#104	C₂²	1	1	yes	characteristic
51	C₁₇×#419	C₂²	1	1	yes	characteristic
52	C₁₇×#419	C₂²	1	1	yes	characteristic
53	C₁₇×#419	C₂²	1	1	yes	characteristic
54	C₁₇×#417	C₂²	1	1	yes	characteristic
55	C₂×C₁₇×#101	C₂²	1	1	yes	characteristic
56	C₂×C₁₇×#101	C₂²	1	1	yes	characteristic
57	C₁₇×#407	C₂²	1	1	yes	characteristic
58	C₁₇×#398	—	2	2	no	—
59	C₁₇×#397	—	2	2	no	—
60	C₁₇×#391	C₂²	1	1	yes	characteristic
61	C₁₇×#391	C₂²	1	1	yes	characteristic
62	C₁₇×#382	C₂²	1	1	yes	characteristic
63	C₁₇×#343	C₂²	1	1	yes	characteristic
64	C₁₇×#343	C₂²	1	1	yes	characteristic
65	C₁₇×#339	C₂²	1	1	yes	characteristic
66	C₁₇×#339	C₂²	1	1	yes	characteristic
67	C₁₇×#339	C₂²	1	1	yes	characteristic
68	C₁₇×#339	C₂²	1	1	yes	characteristic
69	C₁₇×#339	C₂²	1	1	yes	characteristic
70	C₁₇×#339	C₂²	1	1	yes	characteristic
71	C₂×#41×C₁₇	C₂³	1	1	yes	characteristic
72	C₂²×Q₈×C₁₇	C₂³	1	1	yes	characteristic
73	C₂²×Q₈×C₁₇	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₁₇	C₂³	1	1	yes	characteristic
75	C₁₇×#137	—	2	2	no	—
76	C₁₇×#137	—	4	1	no	—
77	C₂×Q₁₆×C₁₇	—	2	1	no	—
78	C₂×SD₁₆×C₁₇	—	2	1	no	—
79	C₂×M₁₆×C₁₇	—	2	1	no	—
80	C₂×M₁₆×C₁₇	—	2	2	no	—
81	C₂×M₁₆×C₁₇	—	4	1	no	—
82	C₂×M₁₆×C₁₇	C₂³	1	1	yes	characteristic
83	C₂×M₁₆×C₁₇	C₂³	1	1	yes	characteristic
84	C₂×M₁₆×C₁₇	C₂³	1	1	yes	characteristic
85	C₂×M₁₆×C₁₇	C₂³	1	1	yes	characteristic
86	C₂²×C₈×C₁₇	—	2	1	no	—
87	C₁₇×C₄⋊Q₈	—	2	1	no	—
88	C₁₇×C₄⋊Q₈	—	2	1	no	—
89	C₁₇×C₄⋊Q₈	—	2	1	no	—
90	C₁₇×C₄⋊Q₈	—	2	2	no	—
91	C₁₇×C₄⋊Q₈	—	4	1	no	—
92	C₁₇×#126	—	2	2	no	—
93	C₁₇×#126	—	2	2	no	—
94	C₁₇×#126	—	2	2	no	—
95	C₁₇×#126	—	2	2	no	—
96	C₁₇×#125	—	2	2	no	—
97	C₁₇×#125	—	2	2	no	—
98	C₁₇×#125	—	2	2	no	—
99	C₁₇×#125	—	2	1	no	—
100	C₁₇×#125	—	2	1	no	—
101	C₁₇×#124	—	2	2	no	—
102	C₁₇×#124	—	2	1	no	—
103	C₁₇×#123	—	2	2	no	—
104	C₁₇×#123	—	2	2	no	—
105	C₁₇×#123	—	2	1	no	—
106	C₁₇×#123	—	2	2	no	—
107	C₁₇×C₂²⋊Q₈	—	2	2	no	—
108	C₁₇×C₂²⋊Q₈	—	2	2	no	—
109	C₁₇×C₂²⋊Q₈	—	2	1	no	—
110	C₁₇×C₂²⋊Q₈	—	2	1	no	—
111	C₁₇×C₂²⋊Q₈	—	2	1	no	—
112	C₁₇×C₂²⋊Q₈	—	2	1	no	—
113	C₁₇×C₂²⋊Q₈	—	2	2	no	—
114	C₁₇×C₂²⋊Q₈	—	2	1	no	—
115	C₁₇×C₂²⋊Q₈	—	2	1	no	—
116	C₁₇×C₂²⋊Q₈	—	2	1	no	—
117	C₁₇×C₂²⋊Q₈	—	2	1	no	—
118	C₁₇×C₂²⋊Q₈	—	2	1	no	—
119	C₁₇×C₂²⋊Q₈	—	2	1	no	—
120	C₁₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
121	C₁₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
122	C₁₇×#121	D₄	1	1	yes	characteristic
123	C₁₇×#121	D₄	1	1	yes	characteristic
124	C₁₇×#120	—	2	1	no	—
125	C₄×Q₈×C₁₇	—	2	2	no	—
126	C₄×Q₈×C₁₇	—	2	1	no	—
127	C₄×Q₈×C₁₇	—	2	1	no	—
128	C₄×Q₈×C₁₇	—	2	1	no	—
129	C₄×Q₈×C₁₇	—	2	1	no	—
130	C₄×Q₈×C₁₇	—	2	1	no	—
131	C₄×D₄×C₁₇	—	2	2	no	—
132	C₄×D₄×C₁₇	—	2	1	no	—
133	C₄×D₄×C₁₇	—	2	2	no	—
134	C₄×D₄×C₁₇	—	2	1	no	—
135	C₄×D₄×C₁₇	—	2	1	no	—
136	C₁₇×#117	—	2	2	no	—
137	C₁₇×#117	—	2	2	no	—
138	C₁₇×#117	—	2	1	no	—
139	C₁₇×#117	—	2	1	no	—
140	C₁₇×#117	—	2	2	no	—
141	C₁₇×#117	—	2	1	no	—
142	C₁₇×#117	—	2	2	no	—
143	C₁₇×#117	—	4	1	no	—
144	C₁₇×#117	D₄	1	1	yes	characteristic
145	C₁₇×#117	D₄	1	1	yes	characteristic
146	C₁₇×#117	C₂³	1	1	yes	characteristic
147	C₁₇×#117	C₂³	1	1	yes	characteristic
148	C₁₇×#117	C₂³	1	1	yes	characteristic
149	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
150	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
151	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
152	C₂×C₄⋊C₄×C₁₇	—	2	2	no	—
153	C₂×C₄⋊C₄×C₁₇	D₄	1	2	yes	—
154	C₂×C₄⋊C₄×C₁₇	D₄	1	1	yes	characteristic
155	C₂×C₄⋊C₄×C₁₇	D₄	1	1	yes	characteristic
156	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
157	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
158	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
159	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
160	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
161	C₂×C₂²⋊C₄×C₁₇	D₄	1	2	yes	—
162	C₂×C₄²×C₁₇	—	2	1	no	—
163	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
164	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
165	C₁₇×#107	—	2	1	no	—
166	C₁₇×#107	—	2	1	no	—
167	C₁₇×#107	—	2	1	no	—
168	C₁₇×#106	—	2	1	no	—
169	C₁₇×#106	—	2	1	no	—
170	C₁₇×#106	—	2	1	no	—
171	C₁₇×#104	—	2	2	no	—
172	C₁₇×#104	—	4	1	no	—
173	C₁₇×#103	—	2	1	no	—
174	C₁₇×#103	—	2	1	no	—
175	C₁₇×#103	—	2	1	no	—
176	C₁₇×#103	—	2	1	no	—
177	C₁₇×#103	—	2	1	no	—
178	C₁₇×#103	—	2	1	no	—
179	C₁₇×#103	—	2	1	no	—
180	C₁₇×#102	—	2	1	no	—
181	C₁₇×#101	—	2	2	no	—
182	C₁₇×#101	—	4	1	no	—
183	C₁₇×C₂²⋊C₈	—	2	1	no	—
184	C₁₇×C₂²⋊C₈	—	2	1	no	—
185	C₁₇×#95	—	2	2	no	—
186	C₁₇×#95	—	2	2	no	—
187	C₁₇×#95	—	2	2	no	—
188	C₂⁴×C₁₇	C₂×D₄	1	1	yes	characteristic
189	#41×C₁₇	—	2	1	no	—
190	#41×C₁₇	—	2	1	no	—
191	#41×C₁₇	—	2	1	no	—
192	#41×C₁₇	—	2	1	no	—
193	C₂×Q₈×C₁₇	—	2	2	no	—
194	C₂×Q₈×C₁₇	—	2	1	no	—
195	C₂×Q₈×C₁₇	—	2	1	no	—
196	C₂×Q₈×C₁₇	—	2	1	no	—
197	C₂×Q₈×C₁₇	—	2	1	no	—
198	C₂×Q₈×C₁₇	—	2	1	no	—
199	C₂×Q₈×C₁₇	—	2	1	no	—
200	C₂×Q₈×C₁₇	—	2	1	no	—
201	C₂×Q₈×C₁₇	—	2	1	no	—
202	C₂×Q₈×C₁₇	—	2	1	no	—
203	C₂×Q₈×C₁₇	—	2	1	no	—
204	C₂×Q₈×C₁₇	—	2	1	no	—
205	C₂×Q₈×C₁₇	—	2	1	no	—
206	C₂×Q₈×C₁₇	C₂×D₄	1	1	yes	characteristic
207	C₂×D₄×C₁₇	—	2	1	no	—
208	C₂×D₄×C₁₇	—	2	1	no	—
209	C₂×D₄×C₁₇	—	2	1	no	—
210	C₂×D₄×C₁₇	C₂×D₄	1	1	yes	characteristic
211	C₂²×C₄×C₁₇	—	2	1	no	—
212	C₂²×C₄×C₁₇	—	2	1	no	—
213	C₂²×C₄×C₁₇	—	2	1	no	—
214	C₂²×C₄×C₁₇	—	2	1	no	—
215	C₂²×C₄×C₁₇	—	2	1	no	—
216	C₂²×C₄×C₁₇	—	2	1	no	—
217	C₂²×C₄×C₁₇	—	2	2	no	—
218	C₂²×C₄×C₁₇	—	2	1	no	—
219	C₂²×C₄×C₁₇	—	2	1	no	—
220	C₂²×C₄×C₁₇	—	2	1	no	—
221	C₂²×C₄×C₁₇	—	2	1	no	—
222	C₂²×C₄×C₁₇	—	2	1	no	—
223	C₂²×C₄×C₁₇	C₂×D₄	1	2	yes	—
224	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
225	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
226	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
227	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
228	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
229	C₂²×C₄×C₁₇	C₂×D₄	1	2	yes	—
230	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
231	Q₁₆×C₁₇	—	4	2	no	—
232	SD₁₆×C₁₇	—	4	2	no	—
233	M₁₆×C₁₇	—	2	1	no	—
234	M₁₆×C₁₇	—	2	1	no	—
235	M₁₆×C₁₇	—	2	1	no	—
236	M₁₆×C₁₇	—	2	1	no	—
237	M₁₆×C₁₇	—	2	1	no	—
238	M₁₆×C₁₇	—	2	1	no	—
239	M₁₆×C₁₇	—	2	1	no	—
240	M₁₆×C₁₇	—	4	2	no	—
241	M₁₆×C₁₇	#41	1	2	yes	—
242	C₂×C₈×C₁₇	—	2	1	no	—
243	C₂×C₈×C₁₇	—	2	1	no	—
244	C₂×C₈×C₁₇	—	2	1	no	—
245	C₂×C₈×C₁₇	—	2	1	no	—
246	C₂×C₈×C₁₇	—	4	2	no	—
247	C₄⋊C₄×C₁₇	—	2	2	no	—
248	C₄⋊C₄×C₁₇	—	2	2	no	—
249	C₄⋊C₄×C₁₇	—	2	2	no	—
250	C₄⋊C₄×C₁₇	—	2	2	no	—
251	C₄⋊C₄×C₁₇	—	2	2	no	—
252	C₄⋊C₄×C₁₇	—	2	2	no	—
253	C₄⋊C₄×C₁₇	—	2	2	no	—
254	C₄⋊C₄×C₁₇	—	2	2	no	—
255	C₄⋊C₄×C₁₇	—	2	2	no	—
256	C₄⋊C₄×C₁₇	—	2	1	no	—
257	C₄⋊C₄×C₁₇	—	2	2	no	—
258	C₄⋊C₄×C₁₇	—	2	1	no	—
259	C₄⋊C₄×C₁₇	—	2	1	no	—
260	C₄⋊C₄×C₁₇	—	2	1	no	—
261	C₄⋊C₄×C₁₇	—	2	1	no	—
262	C₄⋊C₄×C₁₇	—	2	1	no	—
263	C₄⋊C₄×C₁₇	—	2	1	no	—
264	C₄⋊C₄×C₁₇	—	2	1	no	—
265	C₄⋊C₄×C₁₇	—	4	4	no	—
266	C₄⋊C₄×C₁₇	—	4	2	no	—
267	C₄⋊C₄×C₁₇	—	4	1	no	—
268	C₄⋊C₄×C₁₇	—	4	1	no	—
269	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
270	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
271	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
272	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
273	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
274	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
275	C₂²⋊C₄×C₁₇	—	2	2	no	—
276	C₂²⋊C₄×C₁₇	—	2	2	no	—
277	C₂²⋊C₄×C₁₇	—	2	2	no	—
278	C₂²⋊C₄×C₁₇	—	2	2	no	—
279	C₂²⋊C₄×C₁₇	—	2	1	no	—
280	C₂²⋊C₄×C₁₇	—	2	2	no	—
281	C₂²⋊C₄×C₁₇	—	2	1	no	—
282	C₂²⋊C₄×C₁₇	—	2	1	no	—
283	C₂²⋊C₄×C₁₇	—	2	1	no	—
284	C₂²⋊C₄×C₁₇	—	2	1	no	—
285	C₂²⋊C₄×C₁₇	—	2	1	no	—
286	C₂²⋊C₄×C₁₇	—	2	1	no	—
287	C₂²⋊C₄×C₁₇	—	2	1	no	—
288	C₂²⋊C₄×C₁₇	—	2	1	no	—
289	C₂²⋊C₄×C₁₇	—	4	2	no	—
290	C₂²⋊C₄×C₁₇	—	4	1	no	—
291	C₂²⋊C₄×C₁₇	—	4	1	no	—
292	C₄²×C₁₇	—	2	2	no	—
293	C₄²×C₁₇	—	2	2	no	—
294	C₄²×C₁₇	—	2	2	no	—
295	C₄²×C₁₇	—	2	1	no	—
296	C₄²×C₁₇	—	2	1	no	—
297	C₄²×C₁₇	—	2	1	no	—
298	C₄²×C₁₇	—	2	1	no	—
299	C₄²×C₁₇	—	2	1	no	—
300	C₄²×C₁₇	—	2	1	no	—
301	C₄²×C₁₇	—	2	1	no	—
302	C₄²×C₁₇	—	2	1	no	—
303	C₄²×C₁₇	#41	1	2	yes	—
304	#25529	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
305	C₂³×C₁₇	—	2	1	no	—
306	C₂³×C₁₇	—	2	1	no	—
307	C₂³×C₁₇	—	2	1	no	—
308	C₂³×C₁₇	—	4	1	no	—
309	C₂³×C₁₇	—	4	1	no	—
310	C₂³×C₁₇	#120	1	1	yes	characteristic
311	C₂³×C₁₇	#120	1	1	yes	characteristic
312	C₂³×C₁₇	C₂²×D₄	1	1	yes	characteristic
313	Q₈×C₁₇	—	2	1	no	—
314	Q₈×C₁₇	—	2	1	no	—
315	Q₈×C₁₇	—	4	1	no	—
316	Q₈×C₁₇	—	4	1	no	—
317	Q₈×C₁₇	—	4	1	no	—
318	Q₈×C₁₇	—	4	1	no	—
319	Q₈×C₁₇	—	4	1	no	—
320	Q₈×C₁₇	—	4	1	no	—
321	Q₈×C₁₇	—	4	1	no	—
322	Q₈×C₁₇	—	4	1	no	—
323	Q₈×C₁₇	—	8	2	no	—
324	D₄×C₁₇	—	2	1	no	—
325	D₄×C₁₇	—	2	1	no	—
326	D₄×C₁₇	—	4	2	no	—
327	D₄×C₁₇	—	4	1	no	—
328	D₄×C₁₇	—	4	1	no	—
329	D₄×C₁₇	—	8	1	no	—
330	C₂×C₄×C₁₇	—	2	1	no	—
331	C₂×C₄×C₁₇	—	2	1	no	—
332	C₂×C₄×C₁₇	—	2	1	no	—
333	C₂×C₄×C₁₇	—	2	1	no	—
334	C₂×C₄×C₁₇	—	2	1	no	—
335	C₂×C₄×C₁₇	—	2	1	no	—
336	C₂×C₄×C₁₇	—	2	1	no	—
337	C₂×C₄×C₁₇	—	2	1	no	—
338	C₂×C₄×C₁₇	—	2	1	no	—
339	C₂×C₄×C₁₇	—	2	1	no	—
340	C₂×C₄×C₁₇	—	2	1	no	—
341	C₂×C₄×C₁₇	—	2	1	no	—
342	C₂×C₄×C₁₇	—	2	1	no	—
343	C₂×C₄×C₁₇	—	2	1	no	—
344	C₂×C₄×C₁₇	—	2	1	no	—
345	C₂×C₄×C₁₇	—	2	2	no	—
346	C₂×C₄×C₁₇	—	2	1	no	—
347	C₂×C₄×C₁₇	—	2	1	no	—
348	C₂×C₄×C₁₇	—	2	2	no	—
349	C₂×C₄×C₁₇	—	2	2	no	—
350	C₂×C₄×C₁₇	—	2	2	no	—
351	C₂×C₄×C₁₇	—	2	2	no	—
352	C₂×C₄×C₁₇	—	4	1	no	—
353	C₂×C₄×C₁₇	—	4	1	no	—
354	C₂×C₄×C₁₇	—	4	2	no	—
355	C₂×C₄×C₁₇	—	4	1	no	—
356	C₂×C₄×C₁₇	—	4	1	no	—
357	C₂×C₄×C₁₇	—	4	2	no	—
358	C₂×C₄×C₁₇	—	4	1	no	—
359	C₂×C₄×C₁₇	—	4	1	no	—
360	C₂×C₄×C₁₇	—	4	2	no	—
361	C₂×C₄×C₁₇	—	4	1	no	—
362	C₂×C₄×C₁₇	—	4	1	no	—
363	C₂×C₄×C₁₇	—	4	1	no	—
364	C₂×C₄×C₁₇	—	4	1	no	—
365	C₂×C₄×C₁₇	—	4	1	no	—
366	C₂×C₄×C₁₇	—	8	1	no	—
367	C₂×C₄×C₁₇	—	8	2	no	—
368	C₂×C₄×C₁₇	#120	1	1	yes	characteristic
369	C₂×C₄×C₁₇	#120	1	1	yes	characteristic
370	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
371	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
372	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
373	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
374	C₂×C₄×C₁₇	H(5,𝔽₂)	1	1	yes	characteristic
375	C₂×C₄×C₁₇	2₋¹⁺⁴	1	1	yes	characteristic
376	C₈×C₁₇	—	2	2	no	—
377	C₈×C₁₇	—	4	1	no	—
378	C₈×C₁₇	—	4	1	no	—
379	C₈×C₁₇	—	4	1	no	—
380	#3495	C₂×C₁₇	1	1	yes	characteristic
381	#3095	C₂×C₁₇	1	1	yes	characteristic, complemented
382	#3056	C₂×C₁₇	1	1	yes	characteristic
383	#2621	C₂×C₁₇	1	1	yes	characteristic, complemented
384	#2061	C₂×C₁₇	1	1	yes	characteristic, complemented
385	#2038	C₂×C₁₇	1	1	yes	characteristic, complemented
386	#2028	C₂×C₁₇	1	1	yes	characteristic, complemented
387	#2005	C₂×C₁₇	1	1	yes	characteristic, complemented
388	#1901	C₂×C₁₇	1	1	yes	characteristic, complemented
389	#1897	C₂×C₁₇	1	1	yes	characteristic
390	#1886	C₂×C₁₇	1	1	yes	characteristic, complemented
391	#1882	C₂×C₁₇	1	1	yes	characteristic, complemented
392	#1860	C₂×C₁₇	1	1	yes	characteristic, complemented
393	#1857	C₂×C₁₇	1	1	yes	characteristic, complemented
394	#1733	C₂×C₁₇	1	1	yes	characteristic, complemented
395	C₂²×C₁₇	—	2	1	no	—
396	C₂²×C₁₇	—	2	1	no	—
397	C₂²×C₁₇	—	2	1	no	—
398	C₂²×C₁₇	—	2	1	no	—
399	C₂²×C₁₇	—	2	1	no	—
400	C₂²×C₁₇	—	2	1	no	—
401	C₂²×C₁₇	—	2	1	no	—
402	C₂²×C₁₇	—	2	1	no	—
403	C₂²×C₁₇	—	4	1	no	—
404	C₂²×C₁₇	—	4	1	no	—
405	C₂²×C₁₇	—	4	1	no	—
406	C₂²×C₁₇	—	8	1	no	—
407	C₂²×C₁₇	—	8	1	no	—
408	C₂²×C₁₇	C₂×#120	1	1	yes	characteristic
409	C₂²×C₁₇	#546	1	1	yes	characteristic
410	C₂²×C₁₇	#547	1	1	yes	characteristic
411	C₄×C₁₇	—	2	1	no	—
412	C₄×C₁₇	—	2	1	no	—
413	C₄×C₁₇	—	4	2	no	—
414	C₄×C₁₇	—	4	2	no	—
415	C₄×C₁₇	—	4	1	no	—
416	C₄×C₁₇	—	4	1	no	—
417	C₄×C₁₇	—	4	1	no	—
418	C₄×C₁₇	—	4	1	no	—
419	C₄×C₁₇	—	4	2	no	—
420	C₄×C₁₇	—	4	1	no	—
421	C₄×C₁₇	—	4	1	no	—
422	C₄×C₁₇	—	4	1	no	—
423	C₄×C₁₇	—	8	1	no	—
424	C₄×C₁₇	—	8	1	no	—
425	C₄×C₁₇	—	8	1	no	—
426	C₄×C₁₇	#532	1	1	yes	characteristic
427	C₄×C₁₇	#537	1	1	yes	characteristic
428	C₄×C₁₇	#546	1	1	yes	characteristic
429	C₄×C₁₇	#547	1	1	yes	characteristic
430	C₂×#137	C₂²×C₁₇	1	1	yes	characteristic
431	C₂²×M₁₆	C₂²×C₁₇	1	1	yes	characteristic
432	#556	—	2	1	no	—
433	#554	—	2	1	no	—
434	#552	—	2	1	no	—
435	#552	—	2	2	no	—
436	#552	—	2	1	no	—
437	#551	—	2	2	no	—
438	#544	C₂²×C₁₇	1	1	yes	characteristic
439	#542	—	2	1	no	—
440	#541	—	2	1	no	—
441	#536	C₂²×C₁₇	1	1	yes	characteristic
442	#533	—	2	1	no	—
443	C₂×C₄⋊Q₈	C₂²×C₁₇	1	1	yes	characteristic
444	#529	—	2	1	no	—
445	#525	C₂²×C₁₇	1	1	yes	characteristic
446	C₂×C₂²⋊Q₈	C₂²×C₁₇	1	1	yes	characteristic
447	C₂×C₂²⋊Q₈	C₂²×C₁₇	1	1	yes	characteristic
448	#520	C₂²×C₁₇	1	1	yes	characteristic
449	#519	C₂²×C₁₇	1	1	yes	characteristic
450	C₂×#117	C₂²×C₁₇	1	1	yes	characteristic
451	C₂×#117	C₂²×C₁₇	1	1	yes	characteristic
452	#485	—	2	1	no	—
453	#485	—	2	1	no	—
454	#484	—	2	1	no	—
455	#483	—	2	1	no	—
456	#470	—	2	1	no	—
457	#468	—	2	1	no	—
458	#467	—	2	1	no	—
459	#465	—	2	1	no	—
460	#428	C₂²×C₁₇	1	1	yes	characteristic
461	#428	C₂²×C₁₇	1	1	yes	characteristic
462	#428	C₂²×C₁₇	1	1	yes	characteristic
463	C₂×#104	C₂²×C₁₇	1	1	yes	characteristic
464	C₂×#104	C₂²×C₁₇	1	1	yes	characteristic
465	#419	C₂²×C₁₇	1	1	yes	characteristic
466	#419	C₂²×C₁₇	1	1	yes	characteristic
467	#419	C₂²×C₁₇	1	1	yes	characteristic
468	#417	C₂²×C₁₇	1	1	yes	characteristic
469	C₂×#101	C₂²×C₁₇	1	1	yes	characteristic
470	C₂×#101	C₂²×C₁₇	1	1	yes	characteristic
471	#407	C₂²×C₁₇	1	1	yes	characteristic
472	#398	—	2	2	no	—
473	#397	—	2	2	no	—
474	#391	C₂²×C₁₇	1	1	yes	characteristic
475	#391	C₂²×C₁₇	1	1	yes	characteristic
476	#382	C₂²×C₁₇	1	1	yes	characteristic
477	#343	C₂²×C₁₇	1	1	yes	characteristic
478	#343	C₂²×C₁₇	1	1	yes	characteristic
479	#339	C₂²×C₁₇	1	1	yes	characteristic
480	#339	C₂²×C₁₇	1	1	yes	characteristic
481	#339	C₂²×C₁₇	1	1	yes	characteristic
482	#339	C₂²×C₁₇	1	1	yes	characteristic
483	#339	C₂²×C₁₇	1	1	yes	characteristic
484	#339	C₂²×C₁₇	1	1	yes	characteristic
485	C₂×C₁₇	—	2	1	no	—
486	C₂×C₁₇	—	2	1	no	—
487	C₂×C₁₇	—	4	1	no	—
488	C₂×C₁₇	—	4	1	no	—
489	C₂×C₁₇	—	8	1	no	—
490	C₂×C₁₇	#2430	1	1	yes	characteristic
491	C₂×C₁₇	#3020	1	1	yes	characteristic
492	C₂×C₁₇	#3022	1	1	yes	characteristic
493	C₂×#41	C₂³×C₁₇	1	1	yes	characteristic
494	C₂²×Q₈	C₂³×C₁₇	1	1	yes	characteristic
495	C₂²×Q₈	C₂³×C₁₇	1	1	yes	characteristic
496	C₂³×C₄	C₂³×C₁₇	1	1	yes	characteristic
497	#137	—	2	2	no	—
498	#137	—	4	1	no	—
499	C₂×Q₁₆	—	2	1	no	—
500	C₂×SD₁₆	—	2	1	no	—
501	C₂×M₁₆	—	2	1	no	—
502	C₂×M₁₆	—	2	2	no	—
503	C₂×M₁₆	—	4	1	no	—
504	C₂×M₁₆	C₂³×C₁₇	1	1	yes	characteristic
505	C₂×M₁₆	C₂³×C₁₇	1	1	yes	characteristic
506	C₂×M₁₆	C₂³×C₁₇	1	1	yes	characteristic
507	C₂×M₁₆	C₂³×C₁₇	1	1	yes	characteristic
508	C₂²×C₈	—	2	1	no	—
509	C₄⋊Q₈	—	2	1	no	—
510	C₄⋊Q₈	—	2	1	no	—
511	C₄⋊Q₈	—	2	1	no	—
512	C₄⋊Q₈	—	2	2	no	—
513	C₄⋊Q₈	—	4	1	no	—
514	#126	—	2	2	no	—
515	#126	—	2	2	no	—
516	#126	—	2	2	no	—
517	#126	—	2	2	no	—
518	#125	—	2	2	no	—
519	#125	—	2	2	no	—
520	#125	—	2	2	no	—
521	#125	—	2	1	no	—
522	#125	—	2	1	no	—
523	#124	—	2	2	no	—
524	#124	—	2	1	no	—
525	#123	—	2	2	no	—
526	#123	—	2	2	no	—
527	#123	—	2	1	no	—
528	#123	—	2	2	no	—
529	C₂²⋊Q₈	—	2	2	no	—
530	C₂²⋊Q₈	—	2	2	no	—
531	C₂²⋊Q₈	—	2	1	no	—
532	C₂²⋊Q₈	—	2	1	no	—
533	C₂²⋊Q₈	—	2	1	no	—
534	C₂²⋊Q₈	—	2	1	no	—
535	C₂²⋊Q₈	—	2	2	no	—
536	C₂²⋊Q₈	—	2	1	no	—
537	C₂²⋊Q₈	—	2	1	no	—
538	C₂²⋊Q₈	—	2	1	no	—
539	C₂²⋊Q₈	—	2	1	no	—
540	C₂²⋊Q₈	—	2	1	no	—
541	C₂²⋊Q₈	—	2	1	no	—
542	C₂²⋊Q₈	D₄×C₁₇	1	1	yes	characteristic
543	C₂²⋊Q₈	D₄×C₁₇	1	1	yes	characteristic
544	#121	D₄×C₁₇	1	1	yes	characteristic
545	#121	D₄×C₁₇	1	1	yes	characteristic
546	#120	—	2	1	no	—
547	C₄×Q₈	—	2	2	no	—
548	C₄×Q₈	—	2	1	no	—
549	C₄×Q₈	—	2	1	no	—
550	C₄×Q₈	—	2	1	no	—
551	C₄×Q₈	—	2	1	no	—
552	C₄×Q₈	—	2	1	no	—
553	C₄×D₄	—	2	2	no	—
554	C₄×D₄	—	2	1	no	—
555	C₄×D₄	—	2	2	no	—
556	C₄×D₄	—	2	1	no	—
557	C₄×D₄	—	2	1	no	—
558	#117	—	2	2	no	—
559	#117	—	2	2	no	—
560	#117	—	2	1	no	—
561	#117	—	2	1	no	—
562	#117	—	2	2	no	—
563	#117	—	2	1	no	—
564	#117	—	2	2	no	—
565	#117	—	4	1	no	—
566	#117	D₄×C₁₇	1	1	yes	characteristic
567	#117	D₄×C₁₇	1	1	yes	characteristic
568	#117	C₂³×C₁₇	1	1	yes	characteristic
569	#117	C₂³×C₁₇	1	1	yes	characteristic
570	#117	C₂³×C₁₇	1	1	yes	characteristic
571	C₂×C₄⋊C₄	—	2	1	no	—
572	C₂×C₄⋊C₄	—	2	1	no	—
573	C₂×C₄⋊C₄	—	2	1	no	—
574	C₂×C₄⋊C₄	—	2	2	no	—
575	C₂×C₄⋊C₄	D₄×C₁₇	1	2	yes	—
576	C₂×C₄⋊C₄	D₄×C₁₇	1	1	yes	characteristic
577	C₂×C₄⋊C₄	D₄×C₁₇	1	1	yes	characteristic
578	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
579	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
580	C₂×C₂²⋊C₄	—	2	1	no	—
581	C₂×C₂²⋊C₄	—	2	1	no	—
582	C₂×C₂²⋊C₄	—	2	1	no	—
583	C₂×C₂²⋊C₄	D₄×C₁₇	1	2	yes	—
584	C₂×C₄²	—	2	1	no	—
585	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
586	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
587	#107	—	2	1	no	—
588	#107	—	2	1	no	—
589	#107	—	2	1	no	—
590	#106	—	2	1	no	—
591	#106	—	2	1	no	—
592	#106	—	2	1	no	—
593	#104	—	2	2	no	—
594	#104	—	4	1	no	—
595	#103	—	2	1	no	—
596	#103	—	2	1	no	—
597	#103	—	2	1	no	—
598	#103	—	2	1	no	—
599	#103	—	2	1	no	—
600	#103	—	2	1	no	—
601	#103	—	2	1	no	—
602	#102	—	2	1	no	—
603	#101	—	2	2	no	—
604	#101	—	4	1	no	—
605	C₂²⋊C₈	—	2	1	no	—
606	C₂²⋊C₈	—	2	1	no	—
607	#95	—	2	2	no	—
608	#95	—	2	2	no	—
609	#95	—	2	2	no	—
610	C₁₇	#25529	1	1	yes	characteristic, direct product factor, Sylow
611	C₂⁴	C₂×D₄×C₁₇	1	1	yes	characteristic
612	#41	—	2	1	no	—
613	#41	—	2	1	no	—
614	#41	—	2	1	no	—
615	#41	—	2	1	no	—
616	C₂×Q₈	—	2	2	no	—
617	C₂×Q₈	—	2	1	no	—
618	C₂×Q₈	—	2	1	no	—
619	C₂×Q₈	—	2	1	no	—
620	C₂×Q₈	—	2	1	no	—
621	C₂×Q₈	—	2	1	no	—
622	C₂×Q₈	—	2	1	no	—
623	C₂×Q₈	—	2	1	no	—
624	C₂×Q₈	—	2	1	no	—
625	C₂×Q₈	—	2	1	no	—
626	C₂×Q₈	—	2	1	no	—
627	C₂×Q₈	—	2	1	no	—
628	C₂×Q₈	—	2	1	no	—
629	C₂×Q₈	C₂×D₄×C₁₇	1	1	yes	characteristic
630	C₂×D₄	—	2	1	no	—
631	C₂×D₄	—	2	1	no	—
632	C₂×D₄	—	2	1	no	—
633	C₂×D₄	C₂×D₄×C₁₇	1	1	yes	characteristic
634	C₂²×C₄	—	2	1	no	—
635	C₂²×C₄	—	2	1	no	—
636	C₂²×C₄	—	2	1	no	—
637	C₂²×C₄	—	2	1	no	—
638	C₂²×C₄	—	2	1	no	—
639	C₂²×C₄	—	2	1	no	—
640	C₂²×C₄	—	2	2	no	—
641	C₂²×C₄	—	2	1	no	—
642	C₂²×C₄	—	2	1	no	—
643	C₂²×C₄	—	2	1	no	—
644	C₂²×C₄	—	2	1	no	—
645	C₂²×C₄	—	2	1	no	—
646	C₂²×C₄	C₂×D₄×C₁₇	1	2	yes	—
647	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
648	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
649	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
650	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
651	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
652	C₂²×C₄	C₂×D₄×C₁₇	1	2	yes	—
653	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
654	Q₁₆	—	4	2	no	—
655	SD₁₆	—	4	2	no	—
656	M₁₆	—	2	1	no	—
657	M₁₆	—	2	1	no	—
658	M₁₆	—	2	1	no	—
659	M₁₆	—	2	1	no	—
660	M₁₆	—	2	1	no	—
661	M₁₆	—	2	1	no	—
662	M₁₆	—	2	1	no	—
663	M₁₆	—	4	2	no	—
664	M₁₆	#41×C₁₇	1	2	yes	—
665	C₂×C₈	—	2	1	no	—
666	C₂×C₈	—	2	1	no	—
667	C₂×C₈	—	2	1	no	—
668	C₂×C₈	—	2	1	no	—
669	C₂×C₈	—	4	2	no	—
670	C₄⋊C₄	—	2	2	no	—
671	C₄⋊C₄	—	2	2	no	—
672	C₄⋊C₄	—	2	2	no	—
673	C₄⋊C₄	—	2	2	no	—
674	C₄⋊C₄	—	2	2	no	—
675	C₄⋊C₄	—	2	2	no	—
676	C₄⋊C₄	—	2	2	no	—
677	C₄⋊C₄	—	2	2	no	—
678	C₄⋊C₄	—	2	1	no	—
679	C₄⋊C₄	—	2	1	no	—
680	C₄⋊C₄	—	2	1	no	—
681	C₄⋊C₄	—	2	1	no	—
682	C₄⋊C₄	—	2	2	no	—
683	C₄⋊C₄	—	2	2	no	—
684	C₄⋊C₄	—	2	1	no	—
685	C₄⋊C₄	—	2	1	no	—
686	C₄⋊C₄	—	2	1	no	—
687	C₄⋊C₄	—	2	1	no	—
688	C₄⋊C₄	—	4	2	no	—
689	C₄⋊C₄	—	4	4	no	—
690	C₄⋊C₄	—	4	1	no	—
691	C₄⋊C₄	—	4	1	no	—
692	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
693	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
694	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
695	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
696	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
697	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
698	C₂²⋊C₄	—	2	2	no	—
699	C₂²⋊C₄	—	2	2	no	—
700	C₂²⋊C₄	—	2	2	no	—
701	C₂²⋊C₄	—	2	1	no	—
702	C₂²⋊C₄	—	2	1	no	—
703	C₂²⋊C₄	—	2	1	no	—
704	C₂²⋊C₄	—	2	1	no	—
705	C₂²⋊C₄	—	2	1	no	—
706	C₂²⋊C₄	—	2	2	no	—
707	C₂²⋊C₄	—	2	2	no	—
708	C₂²⋊C₄	—	2	1	no	—
709	C₂²⋊C₄	—	2	1	no	—
710	C₂²⋊C₄	—	2	1	no	—
711	C₂²⋊C₄	—	2	1	no	—
712	C₂²⋊C₄	—	4	2	no	—
713	C₂²⋊C₄	—	4	1	no	—
714	C₂²⋊C₄	—	4	1	no	—
715	C₄²	—	2	2	no	—
716	C₄²	—	2	2	no	—
717	C₄²	—	2	2	no	—
718	C₄²	—	2	1	no	—
719	C₄²	—	2	1	no	—
720	C₄²	—	2	1	no	—
721	C₄²	—	2	1	no	—
722	C₄²	—	2	1	no	—
723	C₄²	—	2	1	no	—
724	C₄²	—	2	1	no	—
725	C₄²	—	2	1	no	—
726	C₄²	#41×C₁₇	1	2	yes	—
727	C₂³	—	2	1	no	—
728	C₂³	—	2	1	no	—
729	C₂³	—	2	1	no	—
730	C₂³	—	4	1	no	—
731	C₂³	—	4	1	no	—
732	C₂³	C₁₇×#120	1	1	yes	characteristic
733	C₂³	C₁₇×#120	1	1	yes	characteristic
734	C₂³	C₂²×D₄×C₁₇	1	1	yes	characteristic
735	Q₈	—	2	1	no	—
736	Q₈	—	2	1	no	—
737	Q₈	—	4	1	no	—
738	Q₈	—	4	1	no	—
739	Q₈	—	4	1	no	—
740	Q₈	—	4	1	no	—
741	Q₈	—	4	1	no	—
742	Q₈	—	4	1	no	—
743	Q₈	—	4	1	no	—
744	Q₈	—	4	1	no	—
745	Q₈	—	8	2	no	—
746	D₄	—	2	1	no	—
747	D₄	—	2	1	no	—
748	D₄	—	4	2	no	—
749	D₄	—	4	1	no	—
750	D₄	—	4	1	no	—
751	D₄	—	8	1	no	—
752	C₂×C₄	—	2	1	no	—
753	C₂×C₄	—	2	1	no	—
754	C₂×C₄	—	2	1	no	—
755	C₂×C₄	—	2	1	no	—
756	C₂×C₄	—	2	1	no	—
757	C₂×C₄	—	2	1	no	—
758	C₂×C₄	—	2	1	no	—
759	C₂×C₄	—	2	1	no	—
760	C₂×C₄	—	2	1	no	—
761	C₂×C₄	—	2	1	no	—
762	C₂×C₄	—	2	1	no	—
763	C₂×C₄	—	2	1	no	—
764	C₂×C₄	—	2	1	no	—
765	C₂×C₄	—	2	1	no	—
766	C₂×C₄	—	2	1	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	1	no	—
769	C₂×C₄	—	2	1	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	4	1	no	—
775	C₂×C₄	—	4	1	no	—
776	C₂×C₄	—	4	2	no	—
777	C₂×C₄	—	4	1	no	—
778	C₂×C₄	—	4	1	no	—
779	C₂×C₄	—	4	2	no	—
780	C₂×C₄	—	4	1	no	—
781	C₂×C₄	—	4	1	no	—
782	C₂×C₄	—	4	2	no	—
783	C₂×C₄	—	4	1	no	—
784	C₂×C₄	—	4	1	no	—
785	C₂×C₄	—	4	1	no	—
786	C₂×C₄	—	4	1	no	—
787	C₂×C₄	—	4	1	no	—
788	C₂×C₄	—	8	1	no	—
789	C₂×C₄	—	8	2	no	—
790	C₂×C₄	C₁₇×#120	1	1	yes	characteristic
791	C₂×C₄	C₁₇×#120	1	1	yes	characteristic
792	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
793	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
794	C₂×C₄	C₂×#41×C₁₇	1	1	yes	characteristic
795	C₂×C₄	C₂×#41×C₁₇	1	1	yes	characteristic
796	C₂×C₄	C₁₇×H(5,𝔽₂)	1	1	yes	characteristic
797	C₂×C₄	C₁₇×2₋¹⁺⁴	1	1	yes	characteristic
798	C₈	—	2	2	no	—
799	C₈	—	4	1	no	—
800	C₈	—	4	1	no	—
801	C₈	—	4	1	no	—
802	C₂²	—	2	1	no	—
803	C₂²	—	2	1	no	—
804	C₂²	—	2	1	no	—
805	C₂²	—	2	1	no	—
806	C₂²	—	2	1	no	—
807	C₂²	—	2	1	no	—
808	C₂²	—	2	1	no	—
809	C₂²	—	2	1	no	—
810	C₂²	—	4	1	no	—
811	C₂²	—	4	1	no	—
812	C₂²	—	4	1	no	—
813	C₂²	—	8	1	no	—
814	C₂²	—	8	1	no	—
815	C₂²	C₂×C₁₇×#120	1	1	yes	characteristic
816	C₂²	C₁₇×#546	1	1	yes	characteristic
817	C₂²	C₁₇×#547	1	1	yes	characteristic
818	C₄	—	2	1	no	—
819	C₄	—	2	1	no	—
820	C₄	—	4	2	no	—
821	C₄	—	4	1	no	—
822	C₄	—	4	1	no	—
823	C₄	—	4	1	no	—
824	C₄	—	4	2	no	—
825	C₄	—	4	1	no	—
826	C₄	—	4	1	no	—
827	C₄	—	4	1	no	—
828	C₄	—	4	2	no	—
829	C₄	—	4	1	no	—
830	C₄	—	8	1	no	—
831	C₄	—	8	1	no	—
832	C₄	—	8	1	no	—
833	C₄	C₁₇×#532	1	1	yes	characteristic
834	C₄	C₁₇×#537	1	1	yes	characteristic
835	C₄	C₁₇×#546	1	1	yes	characteristic
836	C₄	C₁₇×#547	1	1	yes	characteristic
837	C₂	—	2	1	no	—
838	C₂	—	2	1	no	—
839	C₂	—	4	1	no	—
840	C₂	—	4	1	no	—
841	C₂	—	8	1	no	—
842	C₂	C₁₇×#2430	1	1	yes	characteristic
843	C₂	C₁₇×#3020	1	1	yes	characteristic
844	C₂	C₁₇×#3022	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₇
prime radical	C₁₇×#525	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂³×C₄×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₇×#3095	C₂	semidirect
4. C₁₇×#2621	C₂	semidirect
5. C₁₇×#2061	C₂	semidirect
6. C₁₇×#2038	C₂	semidirect
7. C₁₇×#2028	C₂	semidirect
8. C₁₇×#2005	C₂	semidirect
9. C₁₇×#1901	C₂	semidirect
11. C₁₇×#1886	C₂	semidirect
12. C₁₇×#1882	C₂	semidirect
13. C₁₇×#1860	C₂	semidirect
14. C₁₇×#1857	C₂	semidirect
15. C₁₇×#1733	C₂	semidirect
304. #25529	C₁₇	direct (N × H)
381. #3095	C₂×C₁₇	semidirect
383. #2621	C₂×C₁₇	semidirect
384. #2061	C₂×C₁₇	semidirect
385. #2038	C₂×C₁₇	semidirect
386. #2028	C₂×C₁₇	semidirect
387. #2005	C₂×C₁₇	semidirect
388. #1901	C₂×C₁₇	semidirect
390. #1886	C₂×C₁₇	semidirect
391. #1882	C₂×C₁₇	semidirect
392. #1860	C₂×C₁₇	semidirect
393. #1857	C₂×C₁₇	semidirect
394. #1733	C₂×C₁₇	semidirect
610. C₁₇	#25529	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₇×#3495	2
C₁₇×#3095	2
C₁₇×#3056	2
C₁₇×#2621	2
C₁₇×#2061	2
C₁₇×#2038	2
C₁₇×#2028	2
C₁₇×#2005	2
C₁₇×#1901	2
C₁₇×#1897	2
C₁₇×#1886	2
C₁₇×#1882	2
C₁₇×#1860	2
C₁₇×#1857	2
C₁₇×#1733	2
#25529	17

Subgroups — C17×#25529 #16883273

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#25529 #16883273