Subgroups — C₁₇×#61176 #16918920

Order 4352.

2026 conjugacy classes of subgroups.

The subgroup lattice has 1226 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×#3493	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₇×#3486	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₇×#3329	C₂	1	2	yes	maximal, complemented
4	C₁₇×#3328	C₂	1	2	yes	maximal, complemented
5	C₁₇×#3327	C₂	1	2	yes	maximal, complemented
6	C₁₇×#3326	C₂	1	2	yes	maximal, complemented
7	C₁₇×#3321	C₂	1	2	yes	maximal, complemented
8	C₁₇×#3320	C₂	1	2	yes	maximal, complemented
9	C₁₇×#3313	C₂	1	2	yes	maximal, complemented
10	C₁₇×#3312	C₂	1	2	yes	maximal, complemented
11	C₁₇×#3137	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₇×#3097	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₇×#3093	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₇×#3082	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₇×#3063	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₇×#3054	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₇×#3046	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₇×#3013	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₇×#3004	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₇×#2947	C₂	1	1	yes	maximal, characteristic, complemented
21	C₁₇×#2930	C₂	1	1	yes	maximal, characteristic, complemented
22	C₁₇×#2898	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₁₇×#419	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₁₇×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
25	C₂³×Q₈×C₁₇	C₂²	1	1	yes	characteristic
26	C₂×C₁₇×#137	C₂²	1	1	yes	characteristic
27	C₂×C₁₇×#137	C₂²	1	1	yes	characteristic
28	C₂×C₁₇×#135	C₂²	1	1	yes	characteristic
29	C₂×C₁₇×#131	C₂²	1	1	yes	characteristic
30	C₂²×M₁₆×C₁₇	C₂²	1	1	yes	characteristic
31	C₁₇×#556	—	2	1	no	—
32	C₁₇×#556	C₂²	1	2	yes	—
33	C₁₇×#555	—	2	1	no	—
34	C₁₇×#555	C₂²	1	2	yes	—
35	C₁₇×#553	—	2	1	no	—
36	C₁₇×#553	C₂²	1	2	yes	—
37	C₁₇×#552	—	2	1	no	—
38	C₁₇×#552	C₂²	1	2	yes	—
39	D₄×Q₈×C₁₇	—	2	1	no	—
40	D₄×Q₈×C₁₇	—	2	1	no	—
41	D₄×Q₈×C₁₇	C₂²	1	2	yes	—
42	D₄×Q₈×C₁₇	C₂²	1	2	yes	—
43	C₁₇×#548	—	2	1	no	—
44	C₁₇×#548	—	2	1	no	—
45	C₁₇×#548	C₂²	1	2	yes	—
46	C₁₇×#548	C₂²	1	2	yes	—
47	C₁₇×#544	C₂²	1	1	yes	characteristic
48	C₁₇×#538	—	2	2	no	—
49	C₁₇×#537	C₂²	1	1	yes	characteristic
50	C₁₇×#536	—	2	2	no	—
51	C₁₇×#536	C₂²	1	1	yes	characteristic
52	C₁₇×#536	C₂²	1	1	yes	characteristic
53	C₁₇×#529	—	2	2	no	—
54	C₁₇×#525	—	2	2	no	—
55	C₁₇×#525	C₂²	1	1	yes	characteristic
56	C₁₇×#525	C₂²	1	1	yes	characteristic
57	C₁₇×#525	C₂²	1	1	yes	characteristic
58	C₁₇×#520	C₂²	1	1	yes	characteristic
59	C₁₇×#520	C₂²	1	1	yes	characteristic
60	C₁₇×#519	C₂²	1	1	yes	characteristic
61	C₂×C₁₇×#117	C₂²	1	1	yes	characteristic
62	C₁₇×#491	C₂²	1	2	yes	complemented
63	C₁₇×#489	C₂²	1	2	yes	complemented
64	C₁₇×#488	C₂²	1	2	yes	complemented
65	C₁₇×#487	C₂²	1	2	yes	complemented
66	C₁₇×#485	C₂²	1	2	yes	—
67	C₁₇×#485	C₂²	1	2	yes	—
68	C₁₇×#485	C₂²	1	2	yes	complemented
69	C₁₇×#485	C₂²	1	2	yes	complemented
70	C₁₇×#484	C₂²	1	2	yes	complemented
71	C₁₇×#483	C₂²	1	2	yes	complemented
72	C₁₇×#482	C₂²	1	2	yes	—
73	C₁₇×#482	C₂²	1	2	yes	—
74	C₁₇×#479	C₂²	1	2	yes	complemented
75	C₁₇×#479	C₂²	1	2	yes	complemented
76	C₁₇×#477	C₂²	1	2	yes	complemented
77	C₁₇×#475	C₂²	1	2	yes	complemented
78	C₁₇×#470	C₂²	1	1	yes	characteristic
79	C₁₇×#470	C₂²	1	1	yes	characteristic
80	C₁₇×#470	C₂²	1	2	yes	complemented
81	C₁₇×#469	C₂²	1	1	yes	characteristic
82	C₁₇×#469	C₂²	1	1	yes	characteristic
83	C₁₇×#468	C₂²	1	1	yes	characteristic
84	C₁₇×#468	C₂²	1	1	yes	characteristic
85	C₁₇×#468	C₂²	1	1	yes	characteristic
86	C₁₇×#468	C₂²	1	1	yes	characteristic
87	C₁₇×#468	C₂²	1	2	yes	complemented
88	C₁₇×#467	C₂²	1	2	yes	complemented
89	C₁₇×#465	C₂²	1	2	yes	complemented
90	C₁₇×#464	C₂²	1	2	yes	complemented
91	C₁₇×#463	C₂²	1	2	yes	complemented
92	C₁₇×#462	C₂²	1	2	yes	complemented
93	C₁₇×#461	C₂²	1	2	yes	complemented
94	C₁₇×#452	C₂²	1	2	yes	complemented
95	C₁₇×#451	C₂²	1	2	yes	—
96	C₁₇×#451	C₂²	1	2	yes	—
97	C₁₇×#451	C₂²	1	2	yes	complemented
98	C₁₇×#449	C₂²	1	2	yes	complemented
99	C₁₇×#448	C₂²	1	2	yes	—
100	C₁₇×#448	C₂²	1	2	yes	—
101	C₁₇×#448	C₂²	1	2	yes	complemented
102	C₁₇×#441	C₂²	1	2	yes	complemented
103	C₁₇×#440	C₂²	1	2	yes	complemented
104	C₄×Q₁₆×C₁₇	C₂²	1	2	yes	complemented
105	C₄×SD₁₆×C₁₇	C₂²	1	2	yes	complemented
106	C₁₇×#436	C₂²	1	2	yes	—
107	C₁₇×#436	C₂²	1	2	yes	—
108	C₁₇×#435	C₂²	1	2	yes	—
109	C₁₇×#435	C₂²	1	2	yes	—
110	C₁₇×#428	C₂²	1	1	yes	characteristic
111	C₁₇×#428	C₂²	1	1	yes	characteristic
112	C₁₇×#427	C₂²	1	1	yes	characteristic
113	C₁₇×#424	C₂²	1	1	yes	characteristic
114	C₁₇×#419	C₂²	1	1	yes	characteristic
115	C₁₇×#419	C₂²	1	1	yes	characteristic
116	C₁₇×#419	C₂²	1	2	yes	—
117	C₁₇×#419	C₂²	1	2	yes	—
118	C₁₇×#419	C₂²	1	2	yes	—
119	C₁₇×#419	C₂²	1	2	yes	—
120	C₁₇×#419	C₂²	1	2	yes	complemented
121	C₁₇×#417	C₂²	1	1	yes	characteristic
122	C₁₇×#417	C₂²	1	1	yes	characteristic
123	C₁₇×#417	C₂²	1	2	yes	complemented
124	C₁₇×#416	C₂²	1	1	yes	characteristic
125	C₁₇×#416	C₂²	1	1	yes	characteristic
126	C₁₇×#416	C₂²	1	2	yes	complemented
127	C₂×C₁₇×#103	C₂²	1	1	yes	characteristic
128	C₂×C₁₇×#103	C₂²	1	1	yes	characteristic
129	C₂×C₁₇×#103	C₂²	1	1	yes	characteristic
130	C₂×C₁₇×#103	C₂²	1	1	yes	characteristic
131	C₂×C₁₇×#103	C₂²	1	2	yes	complemented
132	C₁₇×#408	C₂²	1	1	yes	characteristic
133	C₁₇×#407	C₂²	1	1	yes	characteristic
134	C₁₇×#405	C₂²	1	1	yes	characteristic
135	C₁₇×2₋¹⁺⁴	—	2	4	no	—
136	C₁₇×2₋¹⁺⁴	—	4	2	no	—
137	C₂×#41×C₁₇	—	2	2	no	—
138	C₂×#41×C₁₇	—	2	1	no	—
139	C₂×#41×C₁₇	C₂³	1	1	yes	characteristic
140	C₂×#41×C₁₇	C₂³	1	1	yes	characteristic
141	C₂×#41×C₁₇	C₂³	1	2	yes	—
142	C₂×#41×C₁₇	C₂³	1	1	yes	characteristic
143	C₂²×Q₈×C₁₇	—	2	1	no	—
144	C₂²×Q₈×C₁₇	—	2	1	no	—
145	C₂²×Q₈×C₁₇	—	2	1	no	—
146	C₂²×Q₈×C₁₇	—	2	1	no	—
147	C₂²×Q₈×C₁₇	—	2	4	no	—
148	C₂²×Q₈×C₁₇	—	4	2	no	—
149	C₂²×Q₈×C₁₇	C₂³	1	1	yes	characteristic
150	C₂²×Q₈×C₁₇	C₂³	1	2	yes	—
151	C₂²×Q₈×C₁₇	C₂³	1	2	yes	—
152	C₂²×Q₈×C₁₇	C₂³	1	2	yes	—
153	C₂²×Q₈×C₁₇	C₂³	1	1	yes	characteristic
154	C₂³×C₄×C₁₇	—	2	1	no	—
155	C₂³×C₄×C₁₇	C₂³	1	1	yes	characteristic
156	C₁₇×#137	—	2	4	no	—
157	C₁₇×#137	—	4	2	no	—
158	C₁₇×#135	—	4	2	no	—
159	C₂×Q₁₆×C₁₇	C₂³	1	2	yes	—
160	C₂×Q₁₆×C₁₇	C₂³	1	1	yes	characteristic
161	C₂×Q₁₆×C₁₇	C₂³	1	2	yes	—
162	C₂×SD₁₆×C₁₇	C₂³	1	2	yes	—
163	C₂×SD₁₆×C₁₇	C₂³	1	1	yes	characteristic
164	C₂×SD₁₆×C₁₇	C₂³	1	1	yes	characteristic
165	C₂×SD₁₆×C₁₇	C₂³	1	2	yes	—
166	C₂×D₈×C₁₇	C₂³	1	1	yes	characteristic
167	C₁₇×#131	—	4	2	no	—
168	C₂×M₁₆×C₁₇	—	4	2	no	—
169	C₂×M₁₆×C₁₇	C₂³	1	1	yes	characteristic
170	C₂×M₁₆×C₁₇	C₂³	1	1	yes	characteristic
171	C₂×M₁₆×C₁₇	C₂³	1	1	yes	characteristic
172	C₂×M₁₆×C₁₇	C₂³	1	1	yes	characteristic
173	C₂×M₁₆×C₁₇	C₂³	1	1	yes	characteristic
174	C₂×M₁₆×C₁₇	C₂³	1	1	yes	characteristic
175	C₂×M₁₆×C₁₇	C₂³	1	2	yes	—
176	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
177	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
178	C₂²×C₈×C₁₇	C₂³	1	2	yes	—
179	C₁₇×C₄⋊Q₈	—	2	1	no	—
180	C₁₇×C₄⋊Q₈	—	2	2	no	—
181	C₁₇×C₄⋊Q₈	—	2	2	no	—
182	C₁₇×C₄⋊Q₈	—	2	1	no	—
183	C₁₇×C₄⋊Q₈	C₂³	1	2	yes	—
184	C₁₇×C₄⋊Q₈	C₂³	1	2	yes	—
185	C₁₇×#126	—	2	2	no	—
186	C₁₇×#126	—	2	2	no	—
187	C₁₇×#126	—	2	2	no	—
188	C₁₇×#126	—	2	2	no	—
189	C₁₇×#125	—	2	2	no	—
190	C₁₇×#125	—	2	1	no	—
191	C₁₇×#125	C₂³	1	2	yes	—
192	C₁₇×#124	—	2	1	no	—
193	C₁₇×#124	—	2	2	no	—
194	C₁₇×#124	—	2	2	no	—
195	C₁₇×#124	—	2	2	no	—
196	C₁₇×#124	—	2	2	no	—
197	C₁₇×#124	—	2	2	no	—
198	C₁₇×#124	C₂³	1	2	yes	—
199	C₁₇×#123	—	2	2	no	—
200	C₁₇×#123	—	2	2	no	—
201	C₁₇×#123	—	2	1	no	—
202	C₁₇×#123	—	2	1	no	—
203	C₁₇×#123	—	2	2	no	—
204	C₁₇×#123	—	2	2	no	—
205	C₁₇×#123	D₄	1	2	yes	—
206	C₁₇×C₂²⋊Q₈	—	2	1	no	—
207	C₁₇×C₂²⋊Q₈	—	2	2	no	—
208	C₁₇×C₂²⋊Q₈	—	2	2	no	—
209	C₁₇×C₂²⋊Q₈	—	2	1	no	—
210	C₁₇×C₂²⋊Q₈	—	2	1	no	—
211	C₁₇×C₂²⋊Q₈	—	2	2	no	—
212	C₁₇×C₂²⋊Q₈	—	2	2	no	—
213	C₁₇×C₂²⋊Q₈	—	2	2	no	—
214	C₁₇×C₂²⋊Q₈	—	2	2	no	—
215	C₁₇×C₂²⋊Q₈	—	2	2	no	—
216	C₁₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
217	C₁₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
218	C₁₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
219	C₁₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
220	C₁₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
221	C₁₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
222	C₁₇×C₂²⋊Q₈	C₂³	1	2	yes	—
223	C₁₇×C₂²⋊Q₈	C₂³	1	2	yes	—
224	C₁₇×C₂²⋊Q₈	C₂³	1	2	yes	—
225	C₁₇×#121	—	2	2	no	—
226	C₁₇×#121	—	2	2	no	—
227	C₁₇×#121	—	2	2	no	—
228	C₁₇×#121	—	2	1	no	—
229	C₁₇×#121	—	2	2	no	—
230	C₁₇×#121	—	2	2	no	—
231	C₁₇×#121	D₄	1	1	yes	characteristic
232	C₁₇×#121	D₄	1	1	yes	characteristic
233	C₁₇×#121	C₂³	1	1	yes	characteristic
234	C₁₇×#121	C₂³	1	1	yes	characteristic
235	C₁₇×#121	C₂³	1	1	yes	characteristic
236	C₁₇×#121	C₂³	1	1	yes	characteristic
237	C₁₇×#121	C₂³	1	2	yes	—
238	C₁₇×#120	—	2	1	no	—
239	C₁₇×#120	—	2	1	no	—
240	C₁₇×#120	D₄	1	2	yes	—
241	C₄×Q₈×C₁₇	—	2	1	no	—
242	C₄×Q₈×C₁₇	—	2	1	no	—
243	C₄×Q₈×C₁₇	—	2	1	no	—
244	C₄×Q₈×C₁₇	—	2	2	no	—
245	C₄×Q₈×C₁₇	C₂³	1	2	yes	—
246	C₄×Q₈×C₁₇	C₂³	1	2	yes	—
247	C₄×Q₈×C₁₇	C₂³	1	2	yes	—
248	C₄×D₄×C₁₇	—	2	2	no	—
249	C₄×D₄×C₁₇	—	2	1	no	—
250	C₄×D₄×C₁₇	—	2	2	no	—
251	C₄×D₄×C₁₇	—	2	2	no	—
252	C₄×D₄×C₁₇	—	2	1	no	—
253	C₄×D₄×C₁₇	—	2	1	no	—
254	C₄×D₄×C₁₇	—	2	1	no	—
255	C₄×D₄×C₁₇	—	2	1	no	—
256	C₄×D₄×C₁₇	—	2	2	no	—
257	C₄×D₄×C₁₇	—	2	2	no	—
258	C₄×D₄×C₁₇	—	2	2	no	—
259	C₄×D₄×C₁₇	—	2	2	no	—
260	C₄×D₄×C₁₇	C₂³	1	2	yes	—
261	C₄×D₄×C₁₇	C₂³	1	2	yes	—
262	C₄×D₄×C₁₇	C₂³	1	2	yes	—
263	C₁₇×#117	—	2	1	no	—
264	C₁₇×#117	—	2	1	no	—
265	C₁₇×#117	—	2	1	no	—
266	C₁₇×#117	—	2	2	no	—
267	C₁₇×#117	—	2	2	no	—
268	C₁₇×#117	—	2	2	no	—
269	C₁₇×#117	C₂³	1	2	yes	—
270	C₁₇×#117	C₂³	1	2	yes	—
271	C₁₇×#117	C₂³	1	1	yes	characteristic
272	C₁₇×#117	C₂³	1	1	yes	characteristic
273	C₁₇×#117	C₂³	1	2	yes	—
274	C₁₇×#117	C₂³	1	1	yes	characteristic
275	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
276	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
277	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
278	C₂×C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
279	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
280	C₂×C₄²×C₁₇	—	2	1	no	—
281	C₁₇×#107	C₂³	1	1	yes	characteristic
282	C₁₇×#107	C₂³	1	1	yes	characteristic
283	C₁₇×#107	C₂³	1	2	yes	—
284	C₁₇×#107	C₂³	1	2	yes	—
285	C₁₇×#106	C₂³	1	1	yes	characteristic
286	C₁₇×#106	C₂³	1	1	yes	characteristic
287	C₁₇×#106	C₂³	1	2	yes	—
288	C₁₇×#106	C₂³	1	2	yes	—
289	C₁₇×C₄⋊C₈	C₂³	1	2	yes	—
290	C₁₇×C₄⋊C₈	C₂³	1	2	yes	—
291	C₁₇×#103	C₂³	1	1	yes	characteristic
292	C₁₇×#103	C₂³	1	2	yes	—
293	C₁₇×#103	C₂³	1	2	yes	—
294	C₁₇×#103	C₂³	1	2	yes	—
295	C₁₇×#103	C₂³	1	2	yes	—
296	C₁₇×#103	C₂³	1	2	yes	—
297	C₁₇×#103	C₂³	1	2	yes	—
298	C₁₇×#103	C₂³	1	2	yes	—
299	C₁₇×#103	C₂³	1	2	yes	—
300	C₁₇×#103	C₂³	1	2	yes	—
301	C₁₇×#103	C₂³	1	2	yes	—
302	C₁₇×#103	C₂³	1	2	yes	—
303	C₁₇×#103	C₂³	1	2	yes	—
304	C₁₇×#103	C₂³	1	1	yes	characteristic
305	C₁₇×#103	C₂³	1	1	yes	characteristic
306	C₁₇×#103	C₂³	1	1	yes	characteristic
307	C₁₇×#103	C₂³	1	2	yes	—
308	C₁₇×#103	C₂³	1	2	yes	—
309	C₁₇×#102	C₂³	1	1	yes	characteristic
310	C₁₇×#102	C₂³	1	1	yes	characteristic
311	C₁₇×#102	C₂³	1	1	yes	characteristic
312	C₁₇×#102	C₂³	1	1	yes	characteristic
313	C₁₇×#102	C₂³	1	2	yes	—
314	C₁₇×#102	C₂³	1	2	yes	—
315	C₁₇×C₂²⋊C₈	C₂³	1	2	yes	—
316	C₁₇×C₂²⋊C₈	C₂³	1	2	yes	—
317	C₁₇×C₂²⋊C₈	C₂³	1	2	yes	—
318	C₁₇×C₂²⋊C₈	C₂³	1	2	yes	—
319	C₁₇×#97	C₂³	1	2	yes	—
320	C₄×C₈×C₁₇	C₂³	1	2	yes	—
321	C₂⁴×C₁₇	C₂×D₄	1	1	yes	characteristic
322	#41×C₁₇	—	2	2	no	—
323	#41×C₁₇	—	2	2	no	—
324	#41×C₁₇	—	2	4	no	—
325	#41×C₁₇	—	2	2	no	—
326	#41×C₁₇	—	2	2	no	—
327	#41×C₁₇	—	2	2	no	—
328	#41×C₁₇	—	2	2	no	—
329	#41×C₁₇	—	4	2	no	—
330	#41×C₁₇	—	4	8	no	—
331	#41×C₁₇	—	4	4	no	—
332	C₂×Q₈×C₁₇	—	2	1	no	—
333	C₂×Q₈×C₁₇	—	2	2	no	—
334	C₂×Q₈×C₁₇	—	2	2	no	—
335	C₂×Q₈×C₁₇	—	2	1	no	—
336	C₂×Q₈×C₁₇	—	2	2	no	—
337	C₂×Q₈×C₁₇	—	2	2	no	—
338	C₂×Q₈×C₁₇	—	2	2	no	—
339	C₂×Q₈×C₁₇	—	2	4	no	—
340	C₂×Q₈×C₁₇	—	2	4	no	—
341	C₂×Q₈×C₁₇	—	2	4	no	—
342	C₂×Q₈×C₁₇	—	2	2	no	—
343	C₂×Q₈×C₁₇	—	2	2	no	—
344	C₂×Q₈×C₁₇	—	4	4	no	—
345	C₂×Q₈×C₁₇	—	4	2	no	—
346	C₂×Q₈×C₁₇	—	4	2	no	—
347	C₂×Q₈×C₁₇	—	4	2	no	—
348	C₂×Q₈×C₁₇	—	4	4	no	—
349	C₂×Q₈×C₁₇	—	4	4	no	—
350	C₂×Q₈×C₁₇	—	4	4	no	—
351	C₂×Q₈×C₁₇	C₂×D₄	1	1	yes	characteristic
352	C₂×Q₈×C₁₇	#41	1	4	yes	—
353	C₂×Q₈×C₁₇	C₂⁴	1	1	yes	characteristic
354	C₂×Q₈×C₁₇	C₂⁴	1	2	yes	—
355	C₂×Q₈×C₁₇	C₂⁴	1	1	yes	characteristic
356	C₂×Q₈×C₁₇	C₂⁴	1	2	yes	—
357	C₂×D₄×C₁₇	—	2	1	no	—
358	C₂×D₄×C₁₇	—	2	1	no	—
359	C₂×D₄×C₁₇	—	2	2	no	—
360	C₂×D₄×C₁₇	—	2	1	no	—
361	C₂×D₄×C₁₇	—	2	1	no	—
362	C₂×D₄×C₁₇	—	2	1	no	—
363	C₂×D₄×C₁₇	—	2	1	no	—
364	C₂×D₄×C₁₇	—	2	2	no	—
365	C₂×D₄×C₁₇	C₂×D₄	1	2	yes	—
366	C₂×D₄×C₁₇	C₂×D₄	1	1	yes	characteristic
367	C₂×D₄×C₁₇	C₂×D₄	1	2	yes	—
368	C₂×D₄×C₁₇	C₂×D₄	1	2	yes	—
369	C₂×D₄×C₁₇	C₂⁴	1	1	yes	characteristic
370	C₂×D₄×C₁₇	C₂⁴	1	1	yes	characteristic
371	C₂²×C₄×C₁₇	—	2	1	no	—
372	C₂²×C₄×C₁₇	—	2	2	no	—
373	C₂²×C₄×C₁₇	—	2	2	no	—
374	C₂²×C₄×C₁₇	—	2	2	no	—
375	C₂²×C₄×C₁₇	—	2	2	no	—
376	C₂²×C₄×C₁₇	—	2	2	no	—
377	C₂²×C₄×C₁₇	—	2	1	no	—
378	C₂²×C₄×C₁₇	—	2	1	no	—
379	C₂²×C₄×C₁₇	—	2	2	no	—
380	C₂²×C₄×C₁₇	—	2	1	no	—
381	C₂²×C₄×C₁₇	—	2	2	no	—
382	C₂²×C₄×C₁₇	—	2	1	no	—
383	C₂²×C₄×C₁₇	—	2	1	no	—
384	C₂²×C₄×C₁₇	—	2	2	no	—
385	C₂²×C₄×C₁₇	—	4	4	no	—
386	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
387	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
388	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
389	C₂²×C₄×C₁₇	C₂⁴	1	2	yes	—
390	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
391	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
392	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
393	Q₁₆×C₁₇	—	2	4	no	—
394	Q₁₆×C₁₇	—	4	1	no	—
395	Q₁₆×C₁₇	—	4	2	no	—
396	SD₁₆×C₁₇	—	2	4	no	—
397	SD₁₆×C₁₇	—	4	1	no	—
398	SD₁₆×C₁₇	—	4	1	no	—
399	SD₁₆×C₁₇	—	4	2	no	—
400	D₈×C₁₇	—	4	1	no	—
401	M₁₆×C₁₇	—	2	2	no	—
402	M₁₆×C₁₇	—	2	2	no	—
403	M₁₆×C₁₇	—	4	1	no	—
404	M₁₆×C₁₇	—	4	1	no	—
405	M₁₆×C₁₇	—	4	1	no	—
406	M₁₆×C₁₇	—	4	1	no	—
407	M₁₆×C₁₇	—	4	2	no	—
408	C₂×C₈×C₁₇	—	2	2	no	—
409	C₂×C₈×C₁₇	—	2	2	no	—
410	C₂×C₈×C₁₇	—	4	2	no	—
411	C₂×C₈×C₁₇	C₂⁴	1	1	yes	characteristic
412	C₂×C₈×C₁₇	C₂⁴	1	1	yes	characteristic
413	C₂×C₈×C₁₇	C₂⁴	1	1	yes	characteristic
414	C₂×C₈×C₁₇	C₂⁴	1	1	yes	characteristic
415	C₂×C₈×C₁₇	C₂⁴	1	2	yes	—
416	C₂×C₈×C₁₇	C₂⁴	1	2	yes	—
417	C₄⋊C₄×C₁₇	—	2	2	no	—
418	C₄⋊C₄×C₁₇	—	2	2	no	—
419	C₄⋊C₄×C₁₇	—	2	2	no	—
420	C₄⋊C₄×C₁₇	—	2	2	no	—
421	C₄⋊C₄×C₁₇	—	2	2	no	—
422	C₄⋊C₄×C₁₇	—	2	2	no	—
423	C₄⋊C₄×C₁₇	—	2	1	no	—
424	C₄⋊C₄×C₁₇	—	2	1	no	—
425	C₄⋊C₄×C₁₇	—	2	2	no	—
426	C₄⋊C₄×C₁₇	—	2	2	no	—
427	C₄⋊C₄×C₁₇	—	2	2	no	—
428	C₄⋊C₄×C₁₇	—	2	1	no	—
429	C₄⋊C₄×C₁₇	—	2	2	no	—
430	C₄⋊C₄×C₁₇	—	2	1	no	—
431	C₄⋊C₄×C₁₇	—	2	1	no	—
432	C₄⋊C₄×C₁₇	—	2	2	no	—
433	C₄⋊C₄×C₁₇	—	2	2	no	—
434	C₄⋊C₄×C₁₇	—	2	1	no	—
435	C₄⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
436	C₄⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
437	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
438	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
439	C₄⋊C₄×C₁₇	C₂⁴	1	1	yes	characteristic
440	C₄⋊C₄×C₁₇	C₂⁴	1	1	yes	characteristic
441	C₄⋊C₄×C₁₇	C₂⁴	1	1	yes	characteristic
442	C₄⋊C₄×C₁₇	C₂⁴	1	2	yes	—
443	C₄⋊C₄×C₁₇	C₂⁴	1	1	yes	characteristic
444	C₄⋊C₄×C₁₇	C₂⁴	1	2	yes	—
445	C₂²⋊C₄×C₁₇	—	2	1	no	—
446	C₂²⋊C₄×C₁₇	—	2	1	no	—
447	C₂²⋊C₄×C₁₇	—	2	1	no	—
448	C₂²⋊C₄×C₁₇	—	2	2	no	—
449	C₂²⋊C₄×C₁₇	—	2	2	no	—
450	C₂²⋊C₄×C₁₇	—	2	1	no	—
451	C₂²⋊C₄×C₁₇	—	2	2	no	—
452	C₂²⋊C₄×C₁₇	—	2	1	no	—
453	C₂²⋊C₄×C₁₇	—	2	1	no	—
454	C₂²⋊C₄×C₁₇	—	2	2	no	—
455	C₂²⋊C₄×C₁₇	—	2	2	no	—
456	C₂²⋊C₄×C₁₇	—	2	2	no	—
457	C₂²⋊C₄×C₁₇	—	2	1	no	—
458	C₂²⋊C₄×C₁₇	—	2	1	no	—
459	C₂²⋊C₄×C₁₇	—	2	2	no	—
460	C₂²⋊C₄×C₁₇	—	2	2	no	—
461	C₂²⋊C₄×C₁₇	—	2	2	no	—
462	C₂²⋊C₄×C₁₇	—	2	1	no	—
463	C₂²⋊C₄×C₁₇	—	2	1	no	—
464	C₂²⋊C₄×C₁₇	—	2	2	no	—
465	C₂²⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
466	C₂²⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
467	C₂²⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
468	C₂²⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
469	C₂²⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
470	C₄²×C₁₇	—	2	2	no	—
471	C₄²×C₁₇	—	2	2	no	—
472	C₄²×C₁₇	—	2	2	no	—
473	C₄²×C₁₇	—	2	2	no	—
474	C₄²×C₁₇	—	2	2	no	—
475	C₄²×C₁₇	—	2	1	no	—
476	C₄²×C₁₇	—	2	1	no	—
477	C₄²×C₁₇	—	2	2	no	—
478	C₄²×C₁₇	C₂⁴	1	2	yes	—
479	#61176	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
480	C₂³×C₁₇	—	2	2	no	—
481	C₂³×C₁₇	—	2	1	no	—
482	C₂³×C₁₇	—	2	1	no	—
483	C₂³×C₁₇	—	4	1	no	—
484	C₂³×C₁₇	—	4	1	no	—
485	C₂³×C₁₇	C₂²×D₄	1	1	yes	characteristic
486	C₂³×C₁₇	C₂²×D₄	1	1	yes	characteristic
487	C₂³×C₁₇	C₂²×D₄	1	2	yes	—
488	C₂³×C₁₇	C₂²×D₄	1	1	yes	characteristic
489	Q₈×C₁₇	—	2	4	no	—
490	Q₈×C₁₇	—	2	2	no	—
491	Q₈×C₁₇	—	2	2	no	—
492	Q₈×C₁₇	—	2	1	no	—
493	Q₈×C₁₇	—	2	2	no	—
494	Q₈×C₁₇	—	2	1	no	—
495	Q₈×C₁₇	—	2	1	no	—
496	Q₈×C₁₇	—	2	2	no	—
497	Q₈×C₁₇	—	2	1	no	—
498	Q₈×C₁₇	—	4	4	no	—
499	Q₈×C₁₇	—	4	4	no	—
500	Q₈×C₁₇	—	4	4	no	—
501	Q₈×C₁₇	—	4	2	no	—
502	Q₈×C₁₇	—	8	2	no	—
503	Q₈×C₁₇	C₂×#41	1	4	yes	—
504	D₄×C₁₇	—	2	4	no	—
505	D₄×C₁₇	—	2	2	no	—
506	D₄×C₁₇	—	2	1	no	—
507	D₄×C₁₇	—	2	1	no	—
508	D₄×C₁₇	—	2	1	no	—
509	D₄×C₁₇	—	2	1	no	—
510	D₄×C₁₇	—	4	2	no	—
511	D₄×C₁₇	—	4	2	no	—
512	D₄×C₁₇	—	4	4	no	—
513	D₄×C₁₇	—	4	2	no	—
514	D₄×C₁₇	—	4	2	no	—
515	D₄×C₁₇	—	4	2	no	—
516	D₄×C₁₇	—	4	2	no	—
517	D₄×C₁₇	—	8	1	no	—
518	D₄×C₁₇	—	8	2	no	—
519	D₄×C₁₇	—	8	1	no	—
520	C₂×C₄×C₁₇	—	2	2	no	—
521	C₂×C₄×C₁₇	—	2	4	no	—
522	C₂×C₄×C₁₇	—	2	2	no	—
523	C₂×C₄×C₁₇	—	2	2	no	—
524	C₂×C₄×C₁₇	—	2	2	no	—
525	C₂×C₄×C₁₇	—	2	1	no	—
526	C₂×C₄×C₁₇	—	2	1	no	—
527	C₂×C₄×C₁₇	—	2	2	no	—
528	C₂×C₄×C₁₇	—	2	2	no	—
529	C₂×C₄×C₁₇	—	2	1	no	—
530	C₂×C₄×C₁₇	—	2	1	no	—
531	C₂×C₄×C₁₇	—	2	2	no	—
532	C₂×C₄×C₁₇	—	2	1	no	—
533	C₂×C₄×C₁₇	—	2	1	no	—
534	C₂×C₄×C₁₇	—	2	1	no	—
535	C₂×C₄×C₁₇	—	2	1	no	—
536	C₂×C₄×C₁₇	—	2	2	no	—
537	C₂×C₄×C₁₇	—	2	1	no	—
538	C₂×C₄×C₁₇	—	2	2	no	—
539	C₂×C₄×C₁₇	—	2	1	no	—
540	C₂×C₄×C₁₇	—	4	4	no	—
541	C₂×C₄×C₁₇	—	4	4	no	—
542	C₂×C₄×C₁₇	—	4	4	no	—
543	C₂×C₄×C₁₇	—	4	4	no	—
544	C₂×C₄×C₁₇	—	4	2	no	—
545	C₂×C₄×C₁₇	—	4	2	no	—
546	C₂×C₄×C₁₇	—	4	2	no	—
547	C₂×C₄×C₁₇	—	8	2	no	—
548	C₂×C₄×C₁₇	—	8	1	no	—
549	C₂×C₄×C₁₇	—	8	2	no	—
550	C₂×C₄×C₁₇	—	8	1	no	—
551	C₂×C₄×C₁₇	C₂²×D₄	1	2	yes	—
552	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
553	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
554	C₂×C₄×C₁₇	C₂²×D₄	1	2	yes	—
555	C₂×C₄×C₁₇	C₂²×D₄	1	2	yes	—
556	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
557	C₂×C₄×C₁₇	C₂×#41	1	2	yes	—
558	C₂×C₄×C₁₇	H(5,𝔽₂)	1	2	yes	—
559	C₂×C₄×C₁₇	C₂⁵	1	1	yes	characteristic
560	C₈×C₁₇	—	2	2	no	—
561	C₈×C₁₇	—	2	1	no	—
562	C₈×C₁₇	—	2	1	no	—
563	C₈×C₁₇	—	2	1	no	—
564	C₈×C₁₇	—	2	1	no	—
565	C₈×C₁₇	—	2	2	no	—
566	#3493	C₂×C₁₇	1	1	yes	characteristic, complemented
567	#3486	C₂×C₁₇	1	1	yes	characteristic, complemented
568	#3329	C₂×C₁₇	1	2	yes	complemented
569	#3328	C₂×C₁₇	1	2	yes	complemented
570	#3327	C₂×C₁₇	1	2	yes	complemented
571	#3326	C₂×C₁₇	1	2	yes	complemented
572	#3321	C₂×C₁₇	1	2	yes	complemented
573	#3320	C₂×C₁₇	1	2	yes	complemented
574	#3313	C₂×C₁₇	1	2	yes	complemented
575	#3312	C₂×C₁₇	1	2	yes	complemented
576	#3137	C₂×C₁₇	1	1	yes	characteristic, complemented
577	#3097	C₂×C₁₇	1	1	yes	characteristic, complemented
578	#3093	C₂×C₁₇	1	1	yes	characteristic, complemented
579	#3082	C₂×C₁₇	1	1	yes	characteristic, complemented
580	#3063	C₂×C₁₇	1	1	yes	characteristic, complemented
581	#3054	C₂×C₁₇	1	1	yes	characteristic, complemented
582	#3046	C₂×C₁₇	1	1	yes	characteristic, complemented
583	#3013	C₂×C₁₇	1	1	yes	characteristic, complemented
584	#3004	C₂×C₁₇	1	1	yes	characteristic, complemented
585	#2947	C₂×C₁₇	1	1	yes	characteristic, complemented
586	#2930	C₂×C₁₇	1	1	yes	characteristic, complemented
587	#2898	C₂×C₁₇	1	1	yes	characteristic, complemented
588	C₂×#419	C₂×C₁₇	1	1	yes	characteristic, complemented
589	C₂²×C₁₇	—	2	1	no	—
590	C₂²×C₁₇	—	2	1	no	—
591	C₂²×C₁₇	—	2	2	no	—
592	C₂²×C₁₇	—	2	1	no	—
593	C₂²×C₁₇	—	2	1	no	—
594	C₂²×C₁₇	—	2	2	no	—
595	C₂²×C₁₇	—	2	1	no	—
596	C₂²×C₁₇	—	2	1	no	—
597	C₂²×C₁₇	—	2	1	no	—
598	C₂²×C₁₇	—	2	1	no	—
599	C₂²×C₁₇	—	2	2	no	—
600	C₂²×C₁₇	—	4	4	no	—
601	C₂²×C₁₇	—	4	1	no	—
602	C₂²×C₁₇	—	4	1	no	—
603	C₂²×C₁₇	—	4	1	no	—
604	C₂²×C₁₇	—	4	1	no	—
605	C₂²×C₁₇	—	4	1	no	—
606	C₂²×C₁₇	—	4	1	no	—
607	C₂²×C₁₇	#546	1	2	yes	—
608	C₂²×C₁₇	C₂³×D₄	1	1	yes	characteristic
609	C₄×C₁₇	—	2	2	no	—
610	C₄×C₁₇	—	2	2	no	—
611	C₄×C₁₇	—	2	1	no	—
612	C₄×C₁₇	—	2	1	no	—
613	C₄×C₁₇	—	2	4	no	—
614	C₄×C₁₇	—	2	2	no	—
615	C₄×C₁₇	—	4	2	no	—
616	C₄×C₁₇	—	4	1	no	—
617	C₄×C₁₇	—	4	2	no	—
618	C₄×C₁₇	—	4	1	no	—
619	C₄×C₁₇	—	4	1	no	—
620	C₄×C₁₇	—	4	1	no	—
621	C₄×C₁₇	—	4	1	no	—
622	C₄×C₁₇	—	4	2	no	—
623	C₄×C₁₇	—	4	1	no	—
624	C₄×C₁₇	#546	1	2	yes	—
625	C₄×C₁₇	C₂²×#41	1	1	yes	characteristic
626	C₄×C₁₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
627	C₂×2₋¹⁺⁴	C₂²×C₁₇	1	1	yes	characteristic
628	C₂³×Q₈	C₂²×C₁₇	1	1	yes	characteristic
629	C₂×#137	C₂²×C₁₇	1	1	yes	characteristic
630	C₂×#137	C₂²×C₁₇	1	1	yes	characteristic
631	C₂×#135	C₂²×C₁₇	1	1	yes	characteristic
632	C₂×#131	C₂²×C₁₇	1	1	yes	characteristic
633	C₂²×M₁₆	C₂²×C₁₇	1	1	yes	characteristic
634	#556	—	2	1	no	—
635	#556	C₂²×C₁₇	1	2	yes	—
636	#555	—	2	1	no	—
637	#555	C₂²×C₁₇	1	2	yes	—
638	#553	—	2	1	no	—
639	#553	C₂²×C₁₇	1	2	yes	—
640	#552	—	2	1	no	—
641	#552	C₂²×C₁₇	1	2	yes	—
642	D₄×Q₈	—	2	1	no	—
643	D₄×Q₈	—	2	1	no	—
644	D₄×Q₈	C₂²×C₁₇	1	2	yes	—
645	D₄×Q₈	C₂²×C₁₇	1	2	yes	—
646	#548	—	2	1	no	—
647	#548	—	2	1	no	—
648	#548	C₂²×C₁₇	1	2	yes	—
649	#548	C₂²×C₁₇	1	2	yes	—
650	#544	C₂²×C₁₇	1	1	yes	characteristic
651	#538	—	2	2	no	—
652	#537	C₂²×C₁₇	1	1	yes	characteristic
653	#536	—	2	2	no	—
654	#536	C₂²×C₁₇	1	1	yes	characteristic
655	#536	C₂²×C₁₇	1	1	yes	characteristic
656	#529	—	2	2	no	—
657	#525	—	2	2	no	—
658	#525	C₂²×C₁₇	1	1	yes	characteristic
659	#525	C₂²×C₁₇	1	1	yes	characteristic
660	#525	C₂²×C₁₇	1	1	yes	characteristic
661	#520	C₂²×C₁₇	1	1	yes	characteristic
662	#520	C₂²×C₁₇	1	1	yes	characteristic
663	#519	C₂²×C₁₇	1	1	yes	characteristic
664	C₂×#117	C₂²×C₁₇	1	1	yes	characteristic
665	#491	C₂²×C₁₇	1	2	yes	complemented
666	#489	C₂²×C₁₇	1	2	yes	complemented
667	#488	C₂²×C₁₇	1	2	yes	complemented
668	#487	C₂²×C₁₇	1	2	yes	complemented
669	#485	C₂²×C₁₇	1	2	yes	—
670	#485	C₂²×C₁₇	1	2	yes	—
671	#485	C₂²×C₁₇	1	2	yes	complemented
672	#485	C₂²×C₁₇	1	2	yes	complemented
673	#484	C₂²×C₁₇	1	2	yes	complemented
674	#483	C₂²×C₁₇	1	2	yes	complemented
675	#482	C₂²×C₁₇	1	2	yes	—
676	#482	C₂²×C₁₇	1	2	yes	—
677	#479	C₂²×C₁₇	1	2	yes	complemented
678	#479	C₂²×C₁₇	1	2	yes	complemented
679	#477	C₂²×C₁₇	1	2	yes	complemented
680	#475	C₂²×C₁₇	1	2	yes	complemented
681	#470	C₂²×C₁₇	1	1	yes	characteristic
682	#470	C₂²×C₁₇	1	1	yes	characteristic
683	#470	C₂²×C₁₇	1	2	yes	complemented
684	#469	C₂²×C₁₇	1	1	yes	characteristic
685	#469	C₂²×C₁₇	1	1	yes	characteristic
686	#468	C₂²×C₁₇	1	1	yes	characteristic
687	#468	C₂²×C₁₇	1	1	yes	characteristic
688	#468	C₂²×C₁₇	1	1	yes	characteristic
689	#468	C₂²×C₁₇	1	1	yes	characteristic
690	#468	C₂²×C₁₇	1	2	yes	complemented
691	#467	C₂²×C₁₇	1	2	yes	complemented
692	#465	C₂²×C₁₇	1	2	yes	complemented
693	#464	C₂²×C₁₇	1	2	yes	complemented
694	#463	C₂²×C₁₇	1	2	yes	complemented
695	#462	C₂²×C₁₇	1	2	yes	complemented
696	#461	C₂²×C₁₇	1	2	yes	complemented
697	#452	C₂²×C₁₇	1	2	yes	complemented
698	#451	C₂²×C₁₇	1	2	yes	—
699	#451	C₂²×C₁₇	1	2	yes	—
700	#451	C₂²×C₁₇	1	2	yes	complemented
701	#449	C₂²×C₁₇	1	2	yes	complemented
702	#448	C₂²×C₁₇	1	2	yes	—
703	#448	C₂²×C₁₇	1	2	yes	—
704	#448	C₂²×C₁₇	1	2	yes	complemented
705	#441	C₂²×C₁₇	1	2	yes	complemented
706	#440	C₂²×C₁₇	1	2	yes	complemented
707	C₄×Q₁₆	C₂²×C₁₇	1	2	yes	complemented
708	C₄×SD₁₆	C₂²×C₁₇	1	2	yes	complemented
709	#436	C₂²×C₁₇	1	2	yes	—
710	#436	C₂²×C₁₇	1	2	yes	—
711	#435	C₂²×C₁₇	1	2	yes	—
712	#435	C₂²×C₁₇	1	2	yes	—
713	#428	C₂²×C₁₇	1	1	yes	characteristic
714	#428	C₂²×C₁₇	1	1	yes	characteristic
715	#427	C₂²×C₁₇	1	1	yes	characteristic
716	#424	C₂²×C₁₇	1	1	yes	characteristic
717	#419	C₂²×C₁₇	1	2	yes	—
718	#419	C₂²×C₁₇	1	2	yes	—
719	#419	C₂²×C₁₇	1	1	yes	characteristic
720	#419	C₂²×C₁₇	1	1	yes	characteristic
721	#419	C₂²×C₁₇	1	2	yes	—
722	#419	C₂²×C₁₇	1	2	yes	—
723	#419	C₂²×C₁₇	1	2	yes	complemented
724	#417	C₂²×C₁₇	1	1	yes	characteristic
725	#417	C₂²×C₁₇	1	1	yes	characteristic
726	#417	C₂²×C₁₇	1	2	yes	complemented
727	#416	C₂²×C₁₇	1	1	yes	characteristic
728	#416	C₂²×C₁₇	1	1	yes	characteristic
729	#416	C₂²×C₁₇	1	2	yes	complemented
730	C₂×#103	C₂²×C₁₇	1	1	yes	characteristic
731	C₂×#103	C₂²×C₁₇	1	1	yes	characteristic
732	C₂×#103	C₂²×C₁₇	1	1	yes	characteristic
733	C₂×#103	C₂²×C₁₇	1	1	yes	characteristic
734	C₂×#103	C₂²×C₁₇	1	2	yes	complemented
735	#408	C₂²×C₁₇	1	1	yes	characteristic
736	#407	C₂²×C₁₇	1	1	yes	characteristic
737	#405	C₂²×C₁₇	1	1	yes	characteristic
738	C₂×C₁₇	—	2	2	no	—
739	C₂×C₁₇	—	4	2	no	—
740	C₂×C₁₇	—	4	1	no	—
741	C₂×C₁₇	—	4	1	no	—
742	C₂×C₁₇	—	8	1	no	—
743	C₂×C₁₇	—	8	1	no	—
744	C₂×C₁₇	C₂×#546	1	1	yes	characteristic
745	C₂×C₁₇	#3586	1	1	yes	characteristic
746	C₂×C₁₇	#3586	1	1	yes	characteristic
747	2₋¹⁺⁴	—	2	4	no	—
748	2₋¹⁺⁴	—	4	2	no	—
749	C₂×#41	—	2	2	no	—
750	C₂×#41	—	2	1	no	—
751	C₂×#41	C₂³×C₁₇	1	1	yes	characteristic
752	C₂×#41	C₂³×C₁₇	1	1	yes	characteristic
753	C₂×#41	C₂³×C₁₇	1	2	yes	—
754	C₂×#41	C₂³×C₁₇	1	1	yes	characteristic
755	C₂²×Q₈	—	2	1	no	—
756	C₂²×Q₈	—	2	1	no	—
757	C₂²×Q₈	—	2	1	no	—
758	C₂²×Q₈	—	2	1	no	—
759	C₂²×Q₈	—	2	4	no	—
760	C₂²×Q₈	—	4	2	no	—
761	C₂²×Q₈	C₂³×C₁₇	1	1	yes	characteristic
762	C₂²×Q₈	C₂³×C₁₇	1	2	yes	—
763	C₂²×Q₈	C₂³×C₁₇	1	2	yes	—
764	C₂²×Q₈	C₂³×C₁₇	1	2	yes	—
765	C₂²×Q₈	C₂³×C₁₇	1	1	yes	characteristic
766	C₂³×C₄	—	2	1	no	—
767	C₂³×C₄	C₂³×C₁₇	1	1	yes	characteristic
768	#137	—	2	4	no	—
769	#137	—	4	2	no	—
770	#135	—	4	2	no	—
771	C₂×Q₁₆	C₂³×C₁₇	1	2	yes	—
772	C₂×Q₁₆	C₂³×C₁₇	1	1	yes	characteristic
773	C₂×Q₁₆	C₂³×C₁₇	1	2	yes	—
774	C₂×SD₁₆	C₂³×C₁₇	1	2	yes	—
775	C₂×SD₁₆	C₂³×C₁₇	1	1	yes	characteristic
776	C₂×SD₁₆	C₂³×C₁₇	1	1	yes	characteristic
777	C₂×SD₁₆	C₂³×C₁₇	1	2	yes	—
778	C₂×D₈	C₂³×C₁₇	1	1	yes	characteristic
779	#131	—	4	2	no	—
780	C₂×M₁₆	—	4	2	no	—
781	C₂×M₁₆	C₂³×C₁₇	1	1	yes	characteristic
782	C₂×M₁₆	C₂³×C₁₇	1	1	yes	characteristic
783	C₂×M₁₆	C₂³×C₁₇	1	1	yes	characteristic
784	C₂×M₁₆	C₂³×C₁₇	1	1	yes	characteristic
785	C₂×M₁₆	C₂³×C₁₇	1	1	yes	characteristic
786	C₂×M₁₆	C₂³×C₁₇	1	1	yes	characteristic
787	C₂×M₁₆	C₂³×C₁₇	1	2	yes	—
788	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
789	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
790	C₂²×C₈	C₂³×C₁₇	1	2	yes	—
791	C₄⋊Q₈	—	2	1	no	—
792	C₄⋊Q₈	—	2	2	no	—
793	C₄⋊Q₈	—	2	2	no	—
794	C₄⋊Q₈	—	2	1	no	—
795	C₄⋊Q₈	C₂³×C₁₇	1	2	yes	—
796	C₄⋊Q₈	C₂³×C₁₇	1	2	yes	—
797	#126	—	2	2	no	—
798	#126	—	2	2	no	—
799	#126	—	2	2	no	—
800	#126	—	2	2	no	—
801	#125	—	2	2	no	—
802	#125	—	2	1	no	—
803	#125	C₂³×C₁₇	1	2	yes	—
804	#124	—	2	1	no	—
805	#124	—	2	2	no	—
806	#124	—	2	2	no	—
807	#124	—	2	2	no	—
808	#124	—	2	2	no	—
809	#124	—	2	2	no	—
810	#124	C₂³×C₁₇	1	2	yes	—
811	#123	—	2	2	no	—
812	#123	—	2	2	no	—
813	#123	—	2	1	no	—
814	#123	—	2	1	no	—
815	#123	—	2	2	no	—
816	#123	—	2	2	no	—
817	#123	D₄×C₁₇	1	2	yes	—
818	C₂²⋊Q₈	—	2	1	no	—
819	C₂²⋊Q₈	—	2	2	no	—
820	C₂²⋊Q₈	—	2	2	no	—
821	C₂²⋊Q₈	—	2	1	no	—
822	C₂²⋊Q₈	—	2	1	no	—
823	C₂²⋊Q₈	—	2	2	no	—
824	C₂²⋊Q₈	—	2	2	no	—
825	C₂²⋊Q₈	—	2	2	no	—
826	C₂²⋊Q₈	—	2	2	no	—
827	C₂²⋊Q₈	—	2	2	no	—
828	C₂²⋊Q₈	D₄×C₁₇	1	1	yes	characteristic
829	C₂²⋊Q₈	D₄×C₁₇	1	1	yes	characteristic
830	C₂²⋊Q₈	C₂³×C₁₇	1	1	yes	characteristic
831	C₂²⋊Q₈	C₂³×C₁₇	1	1	yes	characteristic
832	C₂²⋊Q₈	C₂³×C₁₇	1	1	yes	characteristic
833	C₂²⋊Q₈	C₂³×C₁₇	1	1	yes	characteristic
834	C₂²⋊Q₈	C₂³×C₁₇	1	2	yes	—
835	C₂²⋊Q₈	C₂³×C₁₇	1	2	yes	—
836	C₂²⋊Q₈	C₂³×C₁₇	1	2	yes	—
837	#121	—	2	2	no	—
838	#121	—	2	2	no	—
839	#121	—	2	2	no	—
840	#121	—	2	1	no	—
841	#121	—	2	2	no	—
842	#121	—	2	2	no	—
843	#121	D₄×C₁₇	1	1	yes	characteristic
844	#121	D₄×C₁₇	1	1	yes	characteristic
845	#121	C₂³×C₁₇	1	1	yes	characteristic
846	#121	C₂³×C₁₇	1	1	yes	characteristic
847	#121	C₂³×C₁₇	1	1	yes	characteristic
848	#121	C₂³×C₁₇	1	1	yes	characteristic
849	#121	C₂³×C₁₇	1	2	yes	—
850	#120	—	2	1	no	—
851	#120	—	2	1	no	—
852	#120	D₄×C₁₇	1	2	yes	—
853	C₄×Q₈	—	2	1	no	—
854	C₄×Q₈	—	2	1	no	—
855	C₄×Q₈	—	2	1	no	—
856	C₄×Q₈	—	2	2	no	—
857	C₄×Q₈	C₂³×C₁₇	1	2	yes	—
858	C₄×Q₈	C₂³×C₁₇	1	2	yes	—
859	C₄×Q₈	C₂³×C₁₇	1	2	yes	—
860	C₄×D₄	—	2	2	no	—
861	C₄×D₄	—	2	1	no	—
862	C₄×D₄	—	2	2	no	—
863	C₄×D₄	—	2	2	no	—
864	C₄×D₄	—	2	1	no	—
865	C₄×D₄	—	2	1	no	—
866	C₄×D₄	—	2	1	no	—
867	C₄×D₄	—	2	1	no	—
868	C₄×D₄	—	2	2	no	—
869	C₄×D₄	—	2	2	no	—
870	C₄×D₄	—	2	2	no	—
871	C₄×D₄	—	2	2	no	—
872	C₄×D₄	C₂³×C₁₇	1	2	yes	—
873	C₄×D₄	C₂³×C₁₇	1	2	yes	—
874	C₄×D₄	C₂³×C₁₇	1	2	yes	—
875	#117	—	2	1	no	—
876	#117	—	2	1	no	—
877	#117	—	2	1	no	—
878	#117	—	2	2	no	—
879	#117	—	2	2	no	—
880	#117	—	2	2	no	—
881	#117	C₂³×C₁₇	1	2	yes	—
882	#117	C₂³×C₁₇	1	2	yes	—
883	#117	C₂³×C₁₇	1	1	yes	characteristic
884	#117	C₂³×C₁₇	1	1	yes	characteristic
885	#117	C₂³×C₁₇	1	2	yes	—
886	#117	C₂³×C₁₇	1	1	yes	characteristic
887	C₂×C₄⋊C₄	—	2	1	no	—
888	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
889	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
890	C₂×C₄⋊C₄	C₂³×C₁₇	1	2	yes	—
891	C₂×C₂²⋊C₄	—	2	1	no	—
892	C₂×C₄²	—	2	1	no	—
893	#107	C₂³×C₁₇	1	1	yes	characteristic
894	#107	C₂³×C₁₇	1	1	yes	characteristic
895	#107	C₂³×C₁₇	1	2	yes	—
896	#107	C₂³×C₁₇	1	2	yes	—
897	#106	C₂³×C₁₇	1	1	yes	characteristic
898	#106	C₂³×C₁₇	1	1	yes	characteristic
899	#106	C₂³×C₁₇	1	2	yes	—
900	#106	C₂³×C₁₇	1	2	yes	—
901	C₄⋊C₈	C₂³×C₁₇	1	2	yes	—
902	C₄⋊C₈	C₂³×C₁₇	1	2	yes	—
903	#103	C₂³×C₁₇	1	2	yes	—
904	#103	C₂³×C₁₇	1	2	yes	—
905	#103	C₂³×C₁₇	1	2	yes	—
906	#103	C₂³×C₁₇	1	2	yes	—
907	#103	C₂³×C₁₇	1	2	yes	—
908	#103	C₂³×C₁₇	1	2	yes	—
909	#103	C₂³×C₁₇	1	2	yes	—
910	#103	C₂³×C₁₇	1	2	yes	—
911	#103	C₂³×C₁₇	1	1	yes	characteristic
912	#103	C₂³×C₁₇	1	2	yes	—
913	#103	C₂³×C₁₇	1	2	yes	—
914	#103	C₂³×C₁₇	1	1	yes	characteristic
915	#103	C₂³×C₁₇	1	1	yes	characteristic
916	#103	C₂³×C₁₇	1	1	yes	characteristic
917	#103	C₂³×C₁₇	1	2	yes	—
918	#103	C₂³×C₁₇	1	2	yes	—
919	#103	C₂³×C₁₇	1	2	yes	—
920	#103	C₂³×C₁₇	1	2	yes	—
921	#102	C₂³×C₁₇	1	1	yes	characteristic
922	#102	C₂³×C₁₇	1	1	yes	characteristic
923	#102	C₂³×C₁₇	1	1	yes	characteristic
924	#102	C₂³×C₁₇	1	1	yes	characteristic
925	#102	C₂³×C₁₇	1	2	yes	—
926	#102	C₂³×C₁₇	1	2	yes	—
927	C₂²⋊C₈	C₂³×C₁₇	1	2	yes	—
928	C₂²⋊C₈	C₂³×C₁₇	1	2	yes	—
929	C₂²⋊C₈	C₂³×C₁₇	1	2	yes	—
930	C₂²⋊C₈	C₂³×C₁₇	1	2	yes	—
931	#97	C₂³×C₁₇	1	2	yes	—
932	C₄×C₈	C₂³×C₁₇	1	2	yes	—
933	C₁₇	#61176	1	1	yes	characteristic, direct product factor, Sylow
934	C₂⁴	C₂×D₄×C₁₇	1	1	yes	characteristic
935	#41	—	2	2	no	—
936	#41	—	2	2	no	—
937	#41	—	2	4	no	—
938	#41	—	2	2	no	—
939	#41	—	2	2	no	—
940	#41	—	2	2	no	—
941	#41	—	2	2	no	—
942	#41	—	4	2	no	—
943	#41	—	4	8	no	—
944	#41	—	4	4	no	—
945	C₂×Q₈	—	2	1	no	—
946	C₂×Q₈	—	2	2	no	—
947	C₂×Q₈	—	2	2	no	—
948	C₂×Q₈	—	2	1	no	—
949	C₂×Q₈	—	2	2	no	—
950	C₂×Q₈	—	2	2	no	—
951	C₂×Q₈	—	2	2	no	—
952	C₂×Q₈	—	2	4	no	—
953	C₂×Q₈	—	2	4	no	—
954	C₂×Q₈	—	2	4	no	—
955	C₂×Q₈	—	2	2	no	—
956	C₂×Q₈	—	2	2	no	—
957	C₂×Q₈	—	4	4	no	—
958	C₂×Q₈	—	4	2	no	—
959	C₂×Q₈	—	4	2	no	—
960	C₂×Q₈	—	4	2	no	—
961	C₂×Q₈	—	4	4	no	—
962	C₂×Q₈	—	4	4	no	—
963	C₂×Q₈	—	4	4	no	—
964	C₂×Q₈	C₂×D₄×C₁₇	1	1	yes	characteristic
965	C₂×Q₈	#41×C₁₇	1	4	yes	—
966	C₂×Q₈	C₂⁴×C₁₇	1	2	yes	—
967	C₂×Q₈	C₂⁴×C₁₇	1	1	yes	characteristic
968	C₂×Q₈	C₂⁴×C₁₇	1	1	yes	characteristic
969	C₂×Q₈	C₂⁴×C₁₇	1	2	yes	—
970	C₂×D₄	—	2	1	no	—
971	C₂×D₄	—	2	1	no	—
972	C₂×D₄	—	2	1	no	—
973	C₂×D₄	—	2	1	no	—
974	C₂×D₄	—	2	2	no	—
975	C₂×D₄	—	2	1	no	—
976	C₂×D₄	—	2	1	no	—
977	C₂×D₄	—	2	2	no	—
978	C₂×D₄	C₂×D₄×C₁₇	1	2	yes	—
979	C₂×D₄	C₂×D₄×C₁₇	1	1	yes	characteristic
980	C₂×D₄	C₂×D₄×C₁₇	1	2	yes	—
981	C₂×D₄	C₂×D₄×C₁₇	1	2	yes	—
982	C₂×D₄	C₂⁴×C₁₇	1	1	yes	characteristic
983	C₂×D₄	C₂⁴×C₁₇	1	1	yes	characteristic
984	C₂²×C₄	—	2	1	no	—
985	C₂²×C₄	—	2	2	no	—
986	C₂²×C₄	—	2	2	no	—
987	C₂²×C₄	—	2	2	no	—
988	C₂²×C₄	—	2	2	no	—
989	C₂²×C₄	—	2	2	no	—
990	C₂²×C₄	—	2	1	no	—
991	C₂²×C₄	—	2	1	no	—
992	C₂²×C₄	—	2	1	no	—
993	C₂²×C₄	—	2	2	no	—
994	C₂²×C₄	—	2	1	no	—
995	C₂²×C₄	—	2	2	no	—
996	C₂²×C₄	—	2	1	no	—
997	C₂²×C₄	—	2	2	no	—
998	C₂²×C₄	—	4	4	no	—
999	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
1000	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
1001	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
1002	C₂²×C₄	C₂⁴×C₁₇	1	2	yes	—
1003	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
1004	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
1005	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
1006	Q₁₆	—	2	4	no	—
1007	Q₁₆	—	4	1	no	—
1008	Q₁₆	—	4	2	no	—
1009	SD₁₆	—	2	4	no	—
1010	SD₁₆	—	4	1	no	—
1011	SD₁₆	—	4	1	no	—
1012	SD₁₆	—	4	2	no	—
1013	D₈	—	4	1	no	—
1014	M₁₆	—	2	2	no	—
1015	M₁₆	—	2	2	no	—
1016	M₁₆	—	4	1	no	—
1017	M₁₆	—	4	1	no	—
1018	M₁₆	—	4	1	no	—
1019	M₁₆	—	4	1	no	—
1020	M₁₆	—	4	2	no	—
1021	C₂×C₈	—	2	2	no	—
1022	C₂×C₈	—	2	2	no	—
1023	C₂×C₈	—	4	2	no	—
1024	C₂×C₈	C₂⁴×C₁₇	1	1	yes	characteristic
1025	C₂×C₈	C₂⁴×C₁₇	1	2	yes	—
1026	C₂×C₈	C₂⁴×C₁₇	1	1	yes	characteristic
1027	C₂×C₈	C₂⁴×C₁₇	1	2	yes	—
1028	C₂×C₈	C₂⁴×C₁₇	1	1	yes	characteristic
1029	C₂×C₈	C₂⁴×C₁₇	1	1	yes	characteristic
1030	C₄⋊C₄	—	2	1	no	—
1031	C₄⋊C₄	—	2	2	no	—
1032	C₄⋊C₄	—	2	1	no	—
1033	C₄⋊C₄	—	2	2	no	—
1034	C₄⋊C₄	—	2	1	no	—
1035	C₄⋊C₄	—	2	2	no	—
1036	C₄⋊C₄	—	2	2	no	—
1037	C₄⋊C₄	—	2	2	no	—
1038	C₄⋊C₄	—	2	2	no	—
1039	C₄⋊C₄	—	2	1	no	—
1040	C₄⋊C₄	—	2	2	no	—
1041	C₄⋊C₄	—	2	2	no	—
1042	C₄⋊C₄	—	2	2	no	—
1043	C₄⋊C₄	—	2	2	no	—
1044	C₄⋊C₄	—	2	1	no	—
1045	C₄⋊C₄	—	2	1	no	—
1046	C₄⋊C₄	—	2	2	no	—
1047	C₄⋊C₄	—	2	2	no	—
1048	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
1049	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
1050	C₄⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
1051	C₄⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
1052	C₄⋊C₄	C₂⁴×C₁₇	1	2	yes	—
1053	C₄⋊C₄	C₂⁴×C₁₇	1	1	yes	characteristic
1054	C₄⋊C₄	C₂⁴×C₁₇	1	2	yes	—
1055	C₄⋊C₄	C₂⁴×C₁₇	1	1	yes	characteristic
1056	C₄⋊C₄	C₂⁴×C₁₇	1	1	yes	characteristic
1057	C₄⋊C₄	C₂⁴×C₁₇	1	1	yes	characteristic
1058	C₂²⋊C₄	—	2	2	no	—
1059	C₂²⋊C₄	—	2	2	no	—
1060	C₂²⋊C₄	—	2	1	no	—
1061	C₂²⋊C₄	—	2	2	no	—
1062	C₂²⋊C₄	—	2	1	no	—
1063	C₂²⋊C₄	—	2	2	no	—
1064	C₂²⋊C₄	—	2	1	no	—
1065	C₂²⋊C₄	—	2	1	no	—
1066	C₂²⋊C₄	—	2	1	no	—
1067	C₂²⋊C₄	—	2	1	no	—
1068	C₂²⋊C₄	—	2	2	no	—
1069	C₂²⋊C₄	—	2	2	no	—
1070	C₂²⋊C₄	—	2	1	no	—
1071	C₂²⋊C₄	—	2	2	no	—
1072	C₂²⋊C₄	—	2	2	no	—
1073	C₂²⋊C₄	—	2	1	no	—
1074	C₂²⋊C₄	—	2	2	no	—
1075	C₂²⋊C₄	—	2	2	no	—
1076	C₂²⋊C₄	—	2	1	no	—
1077	C₂²⋊C₄	—	2	1	no	—
1078	C₂²⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
1079	C₂²⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
1080	C₂²⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
1081	C₂²⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
1082	C₂²⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
1083	C₄²	—	2	2	no	—
1084	C₄²	—	2	2	no	—
1085	C₄²	—	2	2	no	—
1086	C₄²	—	2	2	no	—
1087	C₄²	—	2	2	no	—
1088	C₄²	—	2	2	no	—
1089	C₄²	—	2	1	no	—
1090	C₄²	—	2	1	no	—
1091	C₄²	C₂⁴×C₁₇	1	2	yes	—
1092	C₂³	—	2	2	no	—
1093	C₂³	—	2	1	no	—
1094	C₂³	—	2	1	no	—
1095	C₂³	—	4	1	no	—
1096	C₂³	—	4	1	no	—
1097	C₂³	C₂²×D₄×C₁₇	1	1	yes	characteristic
1098	C₂³	C₂²×D₄×C₁₇	1	1	yes	characteristic
1099	C₂³	C₂²×D₄×C₁₇	1	2	yes	—
1100	C₂³	C₂²×D₄×C₁₇	1	1	yes	characteristic
1101	Q₈	—	2	4	no	—
1102	Q₈	—	2	2	no	—
1103	Q₈	—	2	2	no	—
1104	Q₈	—	2	1	no	—
1105	Q₈	—	2	2	no	—
1106	Q₈	—	2	1	no	—
1107	Q₈	—	2	1	no	—
1108	Q₈	—	2	2	no	—
1109	Q₈	—	2	1	no	—
1110	Q₈	—	4	4	no	—
1111	Q₈	—	4	4	no	—
1112	Q₈	—	4	4	no	—
1113	Q₈	—	4	2	no	—
1114	Q₈	—	8	2	no	—
1115	Q₈	C₂×#41×C₁₇	1	4	yes	—
1116	D₄	—	2	4	no	—
1117	D₄	—	2	2	no	—
1118	D₄	—	2	1	no	—
1119	D₄	—	2	1	no	—
1120	D₄	—	2	1	no	—
1121	D₄	—	2	1	no	—
1122	D₄	—	4	2	no	—
1123	D₄	—	4	2	no	—
1124	D₄	—	4	4	no	—
1125	D₄	—	4	2	no	—
1126	D₄	—	4	2	no	—
1127	D₄	—	4	2	no	—
1128	D₄	—	4	2	no	—
1129	D₄	—	8	1	no	—
1130	D₄	—	8	2	no	—
1131	D₄	—	8	1	no	—
1132	C₂×C₄	—	2	2	no	—
1133	C₂×C₄	—	2	4	no	—
1134	C₂×C₄	—	2	2	no	—
1135	C₂×C₄	—	2	2	no	—
1136	C₂×C₄	—	2	2	no	—
1137	C₂×C₄	—	2	1	no	—
1138	C₂×C₄	—	2	1	no	—
1139	C₂×C₄	—	2	2	no	—
1140	C₂×C₄	—	2	2	no	—
1141	C₂×C₄	—	2	1	no	—
1142	C₂×C₄	—	2	1	no	—
1143	C₂×C₄	—	2	2	no	—
1144	C₂×C₄	—	2	1	no	—
1145	C₂×C₄	—	2	1	no	—
1146	C₂×C₄	—	2	1	no	—
1147	C₂×C₄	—	2	1	no	—
1148	C₂×C₄	—	2	2	no	—
1149	C₂×C₄	—	2	1	no	—
1150	C₂×C₄	—	2	2	no	—
1151	C₂×C₄	—	2	1	no	—
1152	C₂×C₄	—	4	4	no	—
1153	C₂×C₄	—	4	4	no	—
1154	C₂×C₄	—	4	4	no	—
1155	C₂×C₄	—	4	4	no	—
1156	C₂×C₄	—	4	2	no	—
1157	C₂×C₄	—	4	2	no	—
1158	C₂×C₄	—	4	2	no	—
1159	C₂×C₄	—	8	2	no	—
1160	C₂×C₄	—	8	1	no	—
1161	C₂×C₄	—	8	2	no	—
1162	C₂×C₄	—	8	1	no	—
1163	C₂×C₄	C₂²×D₄×C₁₇	1	2	yes	—
1164	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
1165	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
1166	C₂×C₄	C₂²×D₄×C₁₇	1	2	yes	—
1167	C₂×C₄	C₂²×D₄×C₁₇	1	2	yes	—
1168	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
1169	C₂×C₄	C₂×#41×C₁₇	1	2	yes	—
1170	C₂×C₄	C₁₇×H(5,𝔽₂)	1	2	yes	—
1171	C₂×C₄	C₂⁵×C₁₇	1	1	yes	characteristic
1172	C₈	—	2	2	no	—
1173	C₈	—	2	1	no	—
1174	C₈	—	2	1	no	—
1175	C₈	—	2	1	no	—
1176	C₈	—	2	1	no	—
1177	C₈	—	2	2	no	—
1178	C₂²	—	2	1	no	—
1179	C₂²	—	2	1	no	—
1180	C₂²	—	2	1	no	—
1181	C₂²	—	2	1	no	—
1182	C₂²	—	2	2	no	—
1183	C₂²	—	2	2	no	—
1184	C₂²	—	2	1	no	—
1185	C₂²	—	2	1	no	—
1186	C₂²	—	2	2	no	—
1187	C₂²	—	2	1	no	—
1188	C₂²	—	2	1	no	—
1189	C₂²	—	4	4	no	—
1190	C₂²	—	4	1	no	—
1191	C₂²	—	4	1	no	—
1192	C₂²	—	4	1	no	—
1193	C₂²	—	4	1	no	—
1194	C₂²	—	4	1	no	—
1195	C₂²	—	4	1	no	—
1196	C₂²	C₁₇×#546	1	2	yes	—
1197	C₂²	C₂³×D₄×C₁₇	1	1	yes	characteristic
1198	C₄	—	2	1	no	—
1199	C₄	—	2	1	no	—
1200	C₄	—	2	4	no	—
1201	C₄	—	2	2	no	—
1202	C₄	—	2	2	no	—
1203	C₄	—	2	2	no	—
1204	C₄	—	4	1	no	—
1205	C₄	—	4	2	no	—
1206	C₄	—	4	1	no	—
1207	C₄	—	4	2	no	—
1208	C₄	—	4	1	no	—
1209	C₄	—	4	2	no	—
1210	C₄	—	4	1	no	—
1211	C₄	—	4	1	no	—
1212	C₄	—	4	1	no	—
1213	C₄	C₁₇×#546	1	2	yes	—
1214	C₄	C₂²×#41×C₁₇	1	1	yes	characteristic
1215	C₄	C₂×C₁₇×H(5,𝔽₂)	1	1	yes	characteristic
1216	C₂	—	2	2	no	—
1217	C₂	—	4	1	no	—
1218	C₂	—	4	1	no	—
1219	C₂	—	4	2	no	—
1220	C₂	—	8	1	no	—
1221	C₂	—	8	1	no	—
1222	C₂	C₂×C₁₇×#546	1	1	yes	characteristic
1223	C₂	C₁₇×#3586	1	1	yes	characteristic
1224	C₂	C₁₇×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₁₇×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₇×#3493	C₂	semidirect
2. C₁₇×#3486	C₂	semidirect
3. C₁₇×#3329	C₂	semidirect
4. C₁₇×#3328	C₂	semidirect
5. C₁₇×#3327	C₂	semidirect
6. C₁₇×#3326	C₂	semidirect
7. C₁₇×#3321	C₂	semidirect
8. C₁₇×#3320	C₂	semidirect
9. C₁₇×#3313	C₂	semidirect
10. C₁₇×#3312	C₂	semidirect
11. C₁₇×#3137	C₂	semidirect
12. C₁₇×#3097	C₂	semidirect
13. C₁₇×#3093	C₂	semidirect
14. C₁₇×#3082	C₂	semidirect
15. C₁₇×#3063	C₂	semidirect
16. C₁₇×#3054	C₂	semidirect
17. C₁₇×#3046	C₂	semidirect
18. C₁₇×#3013	C₂	semidirect
19. C₁₇×#3004	C₂	semidirect
20. C₁₇×#2947	C₂	semidirect
21. C₁₇×#2930	C₂	semidirect
22. C₁₇×#2898	C₂	semidirect
23. C₂×C₁₇×#419	C₂	semidirect
62. C₁₇×#491	C₂²	semidirect
63. C₁₇×#489	C₂²	semidirect
64. C₁₇×#488	C₂²	semidirect
65. C₁₇×#487	C₂²	semidirect
68. C₁₇×#485	C₂²	semidirect
69. C₁₇×#485	C₂²	semidirect
70. C₁₇×#484	C₂²	semidirect
71. C₁₇×#483	C₂²	semidirect
74. C₁₇×#479	C₂²	semidirect
75. C₁₇×#479	C₂²	semidirect
76. C₁₇×#477	C₂²	semidirect
77. C₁₇×#475	C₂²	semidirect
80. C₁₇×#470	C₂²	semidirect
87. C₁₇×#468	C₂²	semidirect
88. C₁₇×#467	C₂²	semidirect
89. C₁₇×#465	C₂²	semidirect
90. C₁₇×#464	C₂²	semidirect
91. C₁₇×#463	C₂²	semidirect
92. C₁₇×#462	C₂²	semidirect
93. C₁₇×#461	C₂²	semidirect
94. C₁₇×#452	C₂²	semidirect
97. C₁₇×#451	C₂²	semidirect
98. C₁₇×#449	C₂²	semidirect
101. C₁₇×#448	C₂²	semidirect
102. C₁₇×#441	C₂²	semidirect
103. C₁₇×#440	C₂²	semidirect
104. C₄×Q₁₆×C₁₇	C₂²	semidirect
105. C₄×SD₁₆×C₁₇	C₂²	semidirect
120. C₁₇×#419	C₂²	semidirect
123. C₁₇×#417	C₂²	semidirect
126. C₁₇×#416	C₂²	semidirect
131. C₂×C₁₇×#103	C₂²	semidirect
479. #61176	C₁₇	direct (N × H)
566. #3493	C₂×C₁₇	semidirect
567. #3486	C₂×C₁₇	semidirect
568. #3329	C₂×C₁₇	semidirect
569. #3328	C₂×C₁₇	semidirect
570. #3327	C₂×C₁₇	semidirect
571. #3326	C₂×C₁₇	semidirect
572. #3321	C₂×C₁₇	semidirect
573. #3320	C₂×C₁₇	semidirect
574. #3313	C₂×C₁₇	semidirect
575. #3312	C₂×C₁₇	semidirect
576. #3137	C₂×C₁₇	semidirect
577. #3097	C₂×C₁₇	semidirect
578. #3093	C₂×C₁₇	semidirect
579. #3082	C₂×C₁₇	semidirect
580. #3063	C₂×C₁₇	semidirect
581. #3054	C₂×C₁₇	semidirect
582. #3046	C₂×C₁₇	semidirect
583. #3013	C₂×C₁₇	semidirect
584. #3004	C₂×C₁₇	semidirect
585. #2947	C₂×C₁₇	semidirect
586. #2930	C₂×C₁₇	semidirect
587. #2898	C₂×C₁₇	semidirect
588. C₂×#419	C₂×C₁₇	semidirect
665. #491	C₂²×C₁₇	semidirect
666. #489	C₂²×C₁₇	semidirect
667. #488	C₂²×C₁₇	semidirect
668. #487	C₂²×C₁₇	semidirect
671. #485	C₂²×C₁₇	semidirect
672. #485	C₂²×C₁₇	semidirect
673. #484	C₂²×C₁₇	semidirect
674. #483	C₂²×C₁₇	semidirect
677. #479	C₂²×C₁₇	semidirect
678. #479	C₂²×C₁₇	semidirect
679. #477	C₂²×C₁₇	semidirect
680. #475	C₂²×C₁₇	semidirect
683. #470	C₂²×C₁₇	semidirect
690. #468	C₂²×C₁₇	semidirect
691. #467	C₂²×C₁₇	semidirect
692. #465	C₂²×C₁₇	semidirect
693. #464	C₂²×C₁₇	semidirect
694. #463	C₂²×C₁₇	semidirect
695. #462	C₂²×C₁₇	semidirect
696. #461	C₂²×C₁₇	semidirect
697. #452	C₂²×C₁₇	semidirect
700. #451	C₂²×C₁₇	semidirect
701. #449	C₂²×C₁₇	semidirect
704. #448	C₂²×C₁₇	semidirect
705. #441	C₂²×C₁₇	semidirect
706. #440	C₂²×C₁₇	semidirect
707. C₄×Q₁₆	C₂²×C₁₇	semidirect
708. C₄×SD₁₆	C₂²×C₁₇	semidirect
723. #419	C₂²×C₁₇	semidirect
726. #417	C₂²×C₁₇	semidirect
729. #416	C₂²×C₁₇	semidirect
734. C₂×#103	C₂²×C₁₇	semidirect
933. C₁₇	#61176	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×#3493	2
C₁₇×#3486	2
C₁₇×#3329	2
C₁₇×#3328	2
C₁₇×#3327	2
C₁₇×#3326	2
C₁₇×#3321	2
C₁₇×#3320	2
C₁₇×#3313	2
C₁₇×#3312	2
C₁₇×#3137	2
C₁₇×#3097	2
C₁₇×#3093	2
C₁₇×#3082	2
C₁₇×#3063	2
C₁₇×#3054	2
C₁₇×#3046	2
C₁₇×#3013	2
C₁₇×#3004	2
C₁₇×#2947	2
C₁₇×#2930	2
C₁₇×#2898	2
C₂×C₁₇×#419	2
#61176	17

Subgroups — C17×#61176 #16918920

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#61176 #16918920